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Applied Geophysics Second Edition W. M. Telford McGill University

L. P. Geldart Former Canadian lntemational Development Agency Program Director lor Brazil

R. E. Sherijf University 01 Houston

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c·L Publisbed by thc Prcss Syndicale of Ibe Universily of Cambridge The Pitt Building, Trumpinglon Strccl, Cambridge CB2 lRP 40 Wesl 20th Slrcct, Ncw York. NY 10011. USA 10 Stamford Road, Oakleigh, Melboume 3166, Australia

e Cambridge Universily Prcss 1990 First publisbed 1990 Ubrary of Congress Catllogllll-In-Pablicatlon Data Telford. W. M. (William Murray), 1917Applicd geophysics¡W. M. TcUord, L. P. Gcldart. R. E. Sheriff. 2nd cd. p. cm. Ineludes bibliograpbies and indexo ISBN 0-521-32693-} ISBN 0-52}-33938-3 (pbk)

1. Prospecling - Gcophysical mclhods. 1. Geldart, L. P. 11. Shcriff. Roberl E. III. Tille. TN269.T44 1990 622'.15-dc19 88-38761 CIP

Brldsh Ubrary CataJotlulng In Publlcadon Data Tclford, W. M. (William Murray) Applicd gcophysics. - 2nd cd. 1. Mineral dcposilS. ProspcclÍng. Applicalions of gcopbysics 1. Tille 11. Geldarl, L. P. 111. Sheriff, R. E. (Robert Edward), 1922622'.15 ISBN 0-521-32693-1 hardback ISBN 0-521-33938-3 paperback Transferred lo digital prinling 2004

L

Contents

Preface to the Second Edition / xv Excerpts from Preface to the FirstEdition / xvii Mathematical Conventions / xix 1. Introduction / 1 Reference / 5

2.

Gravity Methods / 6

2.1.

Introduction /6

2.1.1. 2.1.2. 2.2.

Principies of Gravity /7

2.2.1. 2.2.2. 2.2.3. 2.2.4. 2.2.5. 2.3.

Newton's Law oC Gravitation / 7 Acceleration oC Gravity / 7 Gravitational Potenlial / 7 Polential-Field Equations / 9 Derivatives oC the Potential / 9

Gravity of the Earth / 10

2.3.1. 2.3.2. 2.3.3. 2.3.4. 2.4.

General / 6 History of Gravity Exploration /6

Figure of the Earth /10 Gravity Reduction / 11 Densítíes oC Rocks and Minerals / 15 Density Estimates from Field Results/18

Gravity Instruments / 19

2.4.1. 2.4.2.

General/ 19 Absolute Measurement of Gravity /20

2.4.3. 2.5.

field Operations / 23

2.5.1. 2.5.2. 2.5.3. 2.5.4. 2.6.

Land Surveys/23 Drift Correction / 24 Marine Surveys / 24 Airbome Gravity / 26

Gravity Data Processing /26

2.6.1. 2.6.2. 2.6.3. 2.6.4. 2.6.5. 2.6.6. 2.6.7. 2.7.

Relative Measurement oC Gravity /20

Noise, Regionals, and Resíduals / 26 Graphical Residualizing / 27 Surface-Fitting Residualizing Methods/27 Empírical Gridding Methods/27 Second Vertical Derivative Methods/32 Wavelength Filtering / 32 Field Continuation /32

Gravity Interpretation / 34

2.7.1. 2.7.2. 2.7.3. 2.7.4. 2.7.5. 2.7.6. 2.7.7. 2.7.8. 2.7.9.

General / 34 Gravity Effect of a Sphere/3S Gravity Effect oí a Horizontal Rod/36 Gravity Effect of a Vertical Cylinder / 37 Gravity Effect ol a Thin Dipping Sheet / 39 Gravity Effect oC Horizontal Sheet s, Slabs, Dikes, and Faults/40 Applying Simple Models to Actual Anomalies / 44 Gravity Effects ol Complex Shapes/44 The Direct and Inverse

vi

Contents

2.7.10. 2.7.11. 2.7.12.

Problcms of Interpretation /46 Excess Mass / 47 Overburden Effects /48 Maximum-Depth Rules / 48

2.8.

Field fxamples /48

2.9.

Problems / 51

3.4.5. 3.4.6. 3.4.7. 3.5.

3. Magnetic Methods / 62 3.1.

3.1.1.

3.2.

3.2.2. 3.2.3. 3.2.4. 3.2.5.

3.6.3. 3.6.4. 3.6.5. 3.6.6. 3.6.7. 3.6.8.

Classical versus Electromagnetic Concepts / 63 B-H Relations: The Hysteresis Loop/64 Magnetostatic Potential for a Dipole Field / 65 The General Magnetic Anomaly /66 Poisson's Relation / 67

Magnetism of the Earth / 67

3.3.1. 3.3.2. 3.3.3. 3.3.4. 3.3.5. 3.3.6. 3.3.7. 3.3.8. 3.4.

General/62 History of Magnetic Methods/62

Nature of the Geomagnetic Field/67 The Main Field /68 The External Magnetic Field / 72 Local Magnetic Anomalies / 72 Magnetism of Rocks and Minerals / 72 Remanent Magnetism / 73 Magnetic Susceptibilities of Rocks and Minerals / 73 Magnetic Susceptibility Measurements /73

Field Instruments for Magnetic Measurements / 75

3.4.1. 3.4.2. 3.4.3. 3.4.4.

General / 75 Flux-gate Magnetometer / 75 Proton-Precession Magnetometer / 77 Optically Pumped Magnetometer / 78

3.6.9.

3.6.10. 3.1.

3.7.3. 3.7.4. 3.7.5. 3.7.6. 3.7.7. 3.7.8. 3.7.9. 3.7.10. 3.7.11.

General / 84 The Isolated Pole (Monopole) / 85 The Dipole / 87 Two-Dimensional Features / 88 Dipping Dike (Prism) / 92 Dipping Sheet / 'Y1 Horizontal Sheet (Plate) / 100 Serniinfinite Horizontal Sheet: Fault Approximation / 100 Contact between Beds of Ditrerent Susceptibilities / 103 Demagnetization / 104 General/ 106 Crude Interpretation and Structural Aspects / 106 Data Processing Operations: The Fourier Transform / 107 Derivatives / 107 Continuation / 107 Spectral Analysis / lOS Reduction to the Pole / 109 Use of Master Curves ror Dikes of Great Depth Extent / 109 Matched Filtering / 112 Werner Deconvolution / 112 Depth Estimates / 113

Field Examples / 114

3.8.1. 3.8.2. 3.9.

General /80 Airbome Magnetic Surveys / 81 Shipborne Magnetic Surveys / 83 Ground Magnetic Surveys / 83 Gradiometer Surveys / 84

Processing and Interpretatíon / 106

3.7.1. 3.7.2.

3.8.

no

Magnetic Effects of Simple Shapes / 84

3.6.1. 3.6.2.

PrincipIes and Elementary Theory /63

3.2.1.

3.3.

3.6.

Introduction /61

3.1.2.

Field Operations /

3.5.1. 3.5.2. 3.5.3. 3.5.4. 3.5.5.

References / 60

Gradiometers / 80 Instrument Recording / 80 Calibration of Magnetometers / 80

Ground Surveys /114 Airhorne Surveys /117

Problems / 114

References /134

vii

Confenfs

4. Seismic Methods / 136 Introduction /136

4.1.

4.1.1. 4.1.2. 4.1.3. 4.2.

Importance of Seismic Work/l36 History oC Seismic Exploration / 137 Outline of the Seismic Reflection Method / 139

Seismic Theory / 140

4.2.1. 4.2.2. 4.2.3. 4.2.4. 4.2.5. 4.2.6. 4.2.7. 4.2.8.

Theory of Elasticity / 140 Wave Equation and Its Solutions / 143 Body Waves: P and S Waves/147 Surface Waves /149 Energy of Waves /149 Wave Motion /151 Partitioning of Energy at an Interface / 155 Seismic Velocity /158

Ceometry of Seismic Wavepaths / 162

4.3.

4.3.1. 4.3.2. 4.3.3.

Reflection Paths in a Constant Velocity Layer / 162 Velocity Gradient and Raypath Curvature / 167 Geometry of Refraction Paths/169

Characteristics (lf Seismic Events / 175

4.4.

4.4.1. 4.4.2. 4.4.3. 4.4.4. 4.4.5. 4.4.6. 4.4.7. 4.4.8. 4.5.

Distinguishing Features of Events/175 Reflections and Refractions / 175 Diffractions /176 Multiples /178 Surface Waves /182 Effects oC Reflector Curvature / 182 Types of Seismic Noise /184 Attenuation of Noise /185

Reflection Field Methods and Equipmenl/ 186

4.5.1. 4.5.2. 4.5.3.

Field Methods for Land Surveys / 186 Field Layouts / 187 Field Equipment Cor Land Surveys / 192

4.5.4. 4.5.5. 4.6.

Refraction Field Methods and Equipment /209 ,

4.6.1. 4.6.2. 4.6.3. 4.6.4. 4.6.5. 4.6.6. 4.7.

4.7.3. 4.7.4. 4.7.5. 4.7.6. 4.7.7. 4.7.8. 4.7.9. 4.7.10. 4.7.11. 4.7.12. 4.7.13. 4.7.14.

Data Reduction / 214 Introduction to Digital Processing: Fourier Transforms / 216 Convolution / 217 Correlation /222 Phase Considerations / 226 Frequency Filtering / 226 Ve10city Analysis / 229 Common-Midpoint Stacking / 229 Apparent-Velocity (ApparentDip) Filtering / 229 The P-T Transform / 230 Relative-Amplitude Processing / 230 Migration or Imaging / 230 Measures oC Coherence / 232 Other Types oC Processing / 233

Basic Ceological Concepts in Petroleum Exploratíon / 233

4.8.1. 4.8.2. 4.9.

Comparison of Refraction and Reflection Methods / 209 In-Line Refraction /209 Broadside Refraction and Fan Shooting / 210 Engineering Surveys on Land / 211 Marine Refraction Work / 212 Refraction Data Reduction / 212

Data Processing /214

4.7.1. 4.7.2.

4.8.

Marine Equipment and Methods / 202 Measurement of Ve10city / 207

Basic Concepts / 233 Objectives of Interpretation / 235

Refractíon Interpretation /235

4.9.1. 4.9.2. 4.9.3. 4.9.4. 4.9.5.

Interpretation of Refraction Records / 235 Refraction Interpretation Methods / 237 Delay-Time Methods / 237 Wavefront Methods / 240 Engineering Applications / 242

viii

Contenrs

4.10.

Reflectíon Interpretatíon / 243 4.10.1. Interpretation Techniques / 243 4.10.2. Modeling: Synthetic Seismograms /245 4.10.3. Evidences oí Faulting /248 4.10:4. Fold and Flow Structures / 250 4.10.5. ReeCs/257 4.10.6. Unconfonnities and Seismic Facies Pattems / 262 4.10.7. Use of Velocity Information / 262 4.10.8. Hydrocarbon Indicators / 262

4.11.

Specialized Methods /264

4.11.1. 4.11.2. 4.11.3. 4.11.4. 4.11.5. 4.11.6. 4.11.7. 4.12.

Profiling / 264 Three-Dimensional Methods / 267 Use of Channe1 Waves / 270 Vertical Seismic Profiling / 270 Shear Waves in Exploration / 271 Variation of Amplitude with Offset/271 Cross·Hole Methods / 271

5.4.

Typícal Values of flectrícal Constants of Rocks and Minerals / 289 5.4.1. Resistivities of Rocks and Minerals / 289 5.4.2. Oielectric Constants of Rocks and Minerals / 291 5.4.3. Magnetic Permeability of Minerals / 292

References / 292

6.

Methods Employing Natural Electrical Sources / 293

6.1.

Self·Potential Method /293

6.1.1. 6.1.2.

6.1.3. 6.1.4.

6.2.

Problems / 273

TeJluric and Ma8netote/luric Methods /302

6.2.1. References /280

6.2.2.

5. Electrical Properties of Rocks and Minerals / 283

6.2.3. 6.2.4.

6.2.5. 5.1.

Classification of Electrical Methods / 283

6;2.6. 6.2.7.

f/ectrícal Properties of Rocks and Minerals / 283 5.2.1. Electrical Potentials /283 5.2.2. Electrical Conductivities / 284 5.2.3. Magnetic Permeability / 287 5.2.4. Polarization Potentials / 287

5.2.

5.3.

Measurement of flectrical Properlies of Rocks and Minerals / 288

5.3.1. 5.3.2.

Laboratory Measurement of Resistivity / 288 Measurement oC Dielectric Constant / 288

6.2.8.

6.3.

Origin and Characteristics oí Magnetotelluric Fields and Telluric Currents /302 Elementary Electromagnetic Theory /306 Attenolation oC EM Fields / 307 Boundary Conditions / 309 Magnetotelluric Fie1ds /309 Field Equipment and Operations / 311 Interpretation oC Telluric Oata/314 Interpretation of Magnetotelluric Data / 317


6.3.1.

6.3.2.

6.4.

Origin oí Potentials/293 Self·Potential Field Equipment / 296 Field Procedure / 296 Interpretation oC Self·Potential Oata/2fY1

Self·Potential / 327 Tellurics and Magnetotellurics / 327

Problems / 335

References / 342

i)(

Contents

7.

Electromagnetic Methods / 343 7.1.

7.6.

EM Field Procedures/383

7.7.

Interpretation / 383

Introduction and Historical Background / 343

7.2.

7.7.1. 7.7.2.

Electromagnetic Theory / 343

7.2.1. 7.2.2. 7.2.3. 7.2.4. 7.2.5. 7.2.6.

Vector and Scalar Potentials /343 Description of EM Fields: Biot-Savart Law /344 Field in the Frequency Domain/345 Combination of FD Fields /350 Mutual Inductance /353 Fields in the Time Domain /355

7.7.3. 7.7.4. 7.7.5. 7.7.6. 7.7.7.

EM Equipment /361

73.

7.3.1. 7.3.2. 7.3.3. 7.3.4. 7.3.5. 7.3.6. 7.3.7. 7.4.

General/361 Power Sources /361 Transmitter Loops /362 Receiver Coils /362 Receiver Amplifiers /362 Indicators /363 Compensating Networks /363

EM Field Systems for Ground Surveys / 364

7.4.1. 7.4.2.

7.4.3.

7.4.4. 7.4.5. 7.4.6. 7.5.

General/364 Frequency-Domain Systems; Dip-Angle Measurements /364 FD Systems for PhaseComponent Measurements /370 Time-Domain EM Ground Systems /372 Measurement oC H /376 Assessment of EM Ground Methods /377

Airborne EM 5ystems / 377

7.5.1. 7.5.2. 7.5.3. 7.5.4. 7.5.5. 7.5.6. 7.5.7. 7.5.8.

General/377 Quadrature Method /377 Turair System / 377 Airbome VLF /378 Phase-Component Measurements / 378 Transient (Input) Method /379 Cryogenic EM System / 383 Assessment of Airbome EM /383

7.7.8. 7.7.9. 7.7.10. 7.7.11. 7.7.12.

Introduction /383 General Interpretation Procedure /385 Ground Systems: FDEM over Dipping Sheet /385 Ground Systems; TDEM over Dipping Sheet /409 The Sphere Model in FD and TD Ground Systems /436 Layered Structure: EM Depth Sounding /441 Interpretation of Airbome EM Data/45O Turair /454 Airbome VLF /454 Phase-Component AEM /456 Resistivity Mapping / 460 Input AEM / 464

7.8.

Field fxamples/477

7. 9.

Problems/ 504

References/ 519

8.

Resistivity Methods / 522

8.1.

Introduction / 522

8.2.

Elementary Theory /522

8.2.1. 8.2.2. 8.2.3. 8.2.4. 8.2.5. 8.3.

Potentials in Homogeneous Media/522 Single Current Electrode at Depth/523 Single Current Electrode at Surface /523 Two Current Electrodes at Surface /524 Current Distribution / 525

fffect al Inhomogeneous Ground/527

8.3.1. 8.3.2. 8.3.3. 8.3.4.

Introduction /527 Distortion of Current Flow at a Plane Interface /527 Distortion of Potential at aPlane Interface / 527 Surface Potential due to Horizontal Beds /529

Contents

" 8.3.5. 8.3.6. 8.3.7. 8.4.

Equipment for Resistivity Field Work/532

8.4.1. 8.4.2. 8.4.3. 8.5.

Potential Due to Buried Sphere/530 Effect oC Anisotropic Ground/531 Effect of Topography /532

Power Sources / 532 Meters / 534 Electrodes and Wire / 535

Electrode Layouts and Field Procedure / 535

8.5.1. 8.5.2. 8.5.3. 8.5.4.

General /535 Apparent Resistivity / 535 Electrode Arrays (Spreads) / 535 Resistivity Field Procedures / 538

Interpretation / 539

8.6.

8.6.1. 8.6.2. 8.6.3.

8.6.4. 8.6.5. 8.6.6. 8.6.7. 8.6.8.

Introduction / 539 Resistivity Modeling / 539 Vertical Sounding; Two Horizontal Beds / 539 Vertical Sounding; Multiple Horizontal Beds / S44 Lateral Mapping; Vertical Contact / 554 The Vertical Dike / 559 Mapping Three-Dimensional Anomalies / 561 Measuring Overburden Depth and Resistivity / 562

9.3.

Induced Polarization Measurements / 581

9.3.1. 9.3.2. 9.3.3. 9.3.4. 9.3.5. 9.3.6.

9.3.7. 9.4.

IP Field Operations / S84

9.4.1. 9.4.2. 9.4.3. 9.4.4. 9.5.

General / 581 Time-Domain Measurements / 581 Frequency-Domain Measurements / 582 Relative Phase Shift and Phase Components / 582 Magnetic Induced Polarization (MIP) Measurements / 583 Relation between Time- and Frequency-Domain IP Measurements / 583 IP Response Examples / 583 General / 584 Field Equipment / 584 Field Procedures / 588 Noise Sources / 589

Interpretatíon / 591

9.5.1. 9.5.2. 9.5.3.

Plotting Methods /591 General Interpretation / 595 Theoretical and Model Work/596

9.6.

Fíefd Examples / 602

9.7.

Problems / 604

References / 609

10. Radioactivity Method /611

8.7.


10.1.

Introduction / 611

8.8.

Problems / 570

10.2.

PrincipIes of Radioactivity /611

References / 577

10.2.1.

10.2.2. 10.2.3.

9. Induced Polarization / 578 9.1.

Introduction /578

9.2.

Sources of the Induced Polarization Effects / 578

9.2.1. 9.2.2. 9.2.3. 9.2.4.

General / 578 Membrane Polarization / 579 Electrode Polarization / 579 Equivalent Electrical Circuits / 581

10.2.4. 10.2.5. 10.2.6.

10.2.7. 10.3.

Constituents of the Nuc1eus /611 Nuclear Disintegrations / 612 Radioactive Decay Processes / 614 Radioactive Equilibrium / 617 Units/618 Radioactivity of Rocks and Minerals / 619 Age Determination Using Radioisotopes / 619

Instruments /620

10.3.1. 10.3.2.

Introduction/620 Geiger-Müller Counter / 620

Contents

XI

10.3.3. 10.3.4. 10.3.5. 10.3.6.

Seintillation Meter / 621 Garnma-Ray Speetrometer / 622 Miseellaneous Instruments / 627 Calibration of Instruments / 628

11.7.

Elastic- Wave (Acoustie) Methods / 66S

10.4.

Field Operations /628

11.7.1. 11. 7.2. 11.7.3.

10.5.

Interpretation /629

11.7.4.

10.6.


10.7.

Problems /637

11.8.

11_ Geophysical Well Logging / 645 11.1.

11.1.4. 11.2.

11.2.2. 11.2.3. 11.2.4. 11.2.5. 11.2.6. 11.2.7.

Introduetion to Resistivity Logging / 648 Normal Resistivity Logging / 649 Lateral Arrangement / 650 Mierolog / 650 Focused-Current Logs / 651 Induction Log / 652 Resistivity Logging in Mineral Seareh/654

11.9 .2. 11.9.3. 11.9.4. 11.10.

11.3.4. 11.3.5.

Sourees of SP / 654 Instrumentation / 655 Uses of SP Curves in Oil-Well Logging / 656 Uses oC SP Curves in Mineral Logging / 658 Geologieal Interpretation of SP /658

General / 683 Combining Measurements from Several Logs / 683

Field Examples /684

11.11.1. Analysis of an Oil Sand /684 11.11.2. Analysis of Carbonate Section / 684 11.11.3. Coal Identifieation /684 11.11.4. Evaporites /685 11.11.5. Sulfur / 687 11.11.6. Slate and Chert /687 11.11.7. Mineral Exploration / 687 11.11.8. Borehole Methods in the USSR/689

Self-Potential (SP) Logging /654

11.3.1. 11.3.2. 11.3.3.

Gravity and Magnetie Field Logging / 681 Suseeptibility Log / 681 Nuclear Magnetie-Resonanee Log/682 Thermal Logging / 683

Well-Log Interpretation / 683

11.1 0.1. 11.10.2. 11.11.

Nuclear Processes / 673 Gamma-Ray Logging / 675 Density Log / 676 Neutron Logging / 677

Gravily, Magnetie, and Thermal Methods / 681

11.9.1.

Uses of Well Logging / 645 History of Well Logging/645 General Aspeets of Well Logging / 646 Rock Property Measurements / 647

Resistivity Methods /648

11.2.1.

11.3.

11.9.

Int;oduetion / 645

11.1.1. 11.1.2. 11.1.3.

Nuclear Methods /673

11. 8.1. 11.8.2. 11.8.3. 11.8.4.

Referenees / 644

Elastic Waves in Boreholes / 665 Sonie Log / 667 Amplitude and Full-Waveform Logs/670 Borehole Televiewer / 672

11.7 2.

Problems / 690

References / 698

12.

Integrated Geophysical Problems /700

11.4.

The Dipmeter /659

11.5.

Eleetromagnetic Wave Propagation Method/663

72.7.

Introduction /700

Indueed Polarization Logging / 665

12.2.

Examples and Problems /701

11.6.

Contenls

XII

Appendix A. Mathematical Background j 727 A 7.

Determinants /727

A. 2.

Matrices / 728

AJ. Vector Analysis / 729 A.3.1. Basje Theory /129 A.3.2. Vector Produets / 730 A.3.3. The Vector Operator 'V /731 A.3.4. Vector Theorems / 731 A.4.

Curvilínear Coordina tes / 733

AS.

Tay/or's Series; Maclaurin's Series/735

A6.

Binomial Expansion /736

A7.

Comp/ex Numbers /736

A8.

Method o( Least Squares / 737

A9. Fourier Series and Trans(orms /738 A.9.1. Fourier Series / 738 A.9.2. Fourier Integral; Fourier Transforms / 738 A.9.3. Digital Funetions; z Transforms / 740 A 10.

Convo/ution / 740

A11.

Corre/ation / 741

A.n.l. A.n.2.

Cross-Correlation / 741 Autocorrelation /741

A. 12.

Laplace Trans(orms /741

A.l2.l. A.l2.2. A.l2.3.

A 13.

Basic Theory /741 Calculatjon oC Laplace TransCorms / 742 Transforms of the Error Function and its Derivatives / 742

Linear Systems / 743

Re(erences / 744

Appendix B. Location Determination j 745 B.1.

Direction Determination /745

8.2.

Distance Measurement /745

8.3.

E/evation Measurement / 745

B.4.

Angle Measurement / 746

B.5.

Doppler Measurement o( Velocity /746

8.6.

Radionavigation /746

B.7.

Acoustic and Inertia/ Positioning /748

8.8.

Satellite Positioning / 749

Re(erence /750

Indexj751

Dr. David A. Keys, the fourth author of the first edition, died in 1978. He was one oC the authors of Applied Geophysics in rhe Search lor Minerals by Eve and Keys, first published in 1929, wbich made it one of the earliest texts in applied geophysics. It served several generations oC geophysicists in the course of four editions. In the mid-1960s, Dr. Keys suggested to the senior author that they collaborate in preparing a fiCth edition; tbis was the starting point Cor what turned out to be an entirely new book with the shorter title Applied Geophysics. Dr. Keys is remembered with great afrection and esteem by bis coauthors, two of whom (WMT, LPG) knew bim well at McGiIl University and later as Vice-President (Scientific), National Research Council oC Canada, Chalk River. We express our gratitude to the companies, individuals, and other publishers who contributed information and iIlustrations. In particular, we wish to extend our sincere thanks to Alex Becker, Jerry Roth, and Bill Gore for their invaluable help in the preparation oC Chapters, 5 to 10, 3, and 11, respectively. We owe special gratitude to John E. Riddell who provided many examples oC mineral exploration drawn from bis 35 years oC experience in tbis area.

June 1990

W. M. Telford L. P. Geldizrt R. E. Sheriff

Mathematical Conventions

A.

General functions f(x, y, z)

/, f(I)* g(l) G(v). G(w)

cp¡,( 'T) J"(x) ¡"(x) K"(x)

B.

Special functions u(t) 6( 1). 6/ boxear(t) eomb (1) sine (1)

C.

funetion of eontinuous variables (x, y. z) funetion of the discrete variable 1 = nl::J.. i! integral eonvolution of f(t) with g(t) Fourier transform of g( 1) eorrelation of f( 1) with g( t) for a displaeement 'T Bessel funetion of the first kind of order n Modified Bessel funetion of the first kind Modified Bessel function of the second kind

unit step function; u(t) = O, '1 < O; u(t) = + 1, t> O unit impulse (Dirae delta), 6(t) = ", = + 1, t = O; = O tor t O boxear (t) = + 1, - Wo :s; W :s; + wo; = O outside this range infinite series of equally spaced unit impulses (sin t)/t

*

Mathematical conventions >, < ~,

~

«,»

A

A· B } AxB V' 2

V V'cp

V·A V'xA .JII .JIIT .JII-l

Ixl del (aij)

greater than, less than greater than or equal to, less than or equal to much greater than, much smaller than of the order oC approximately equal to correspondence between a funetion and its transform vector of magnitude A scalar (dot) and vector (eross) products of vectors A and B del, the vector operator i a/ax + j a/ay + k a/az Laplacian a2/ax2 + a2/ay2 + a2/az 2 gradient of cp(x. y. z) = grad cp (see Eq. (A.l7» divergence of A(x, y, z) = div A (see Eq. (A.19» curl oC A(x, y, z) = curtA (see Eq. (A.20» matrix with elements a ij transpose oC .JII with e)ements a ji inverse of .JII absolute va)ue of x determinant with elements al)

Mathematical Conventions

1:

80

+ 81 + 82 + ... + 811

go

+ g1 + g2 + ... + gil

k-O

E8"

"

lnx logx

sum oC 8" for appropriate values of k log~x

IOglOX

U""' U"y' ~n

partíal derivatives of U wíth respect to x (twice), x and y, z (three times)

j

,( -1)

Re {!(Z)}} 1m {!(z)}

real and imaginary parts of a complex quantity f(z)

t

Chapter 1

1ntroduction Geophysics, as its name indicates. has to do with the physics oC the earth and its surrounding atmosphere. Gílbert's discovery that the eartb behaves as a great and rather irregular magnet and Newton's theory of gravitation may be said to constitute the beginning of geophysics. Mining and the search for metals date Crom the earliest times, but the scientific record began with the publication in 1556 of the famous treatise De re metal/ica by Georgius Agricola. wbich for many years was the authoritative work on mining. The initial step in applying geophysics to the search for minerals probably was talcen in 1843, when Von Wrede pointed out that the magnetic theodolite, used by Lamont to measure variations in the earth's magnetic field, might also be employed to discover bodies ol magnetic ore. However, tbis idea was not acted on until the publication in 1879 oC ProCessor Robert Thalén's book On the Examination 01 [ron Ore Deposits by Magnetic Methods. The Thalén-Tiberg magnetometer manufacture in Sweden, and later the Thomson-Thalén instrument, furnished the means of locating the strike, dip, and depth below surface of magnetic dikes. The continued expansion in the demand for metals of all kinds and the enormous increase in the use oC petroleum products since the tum of the century have led to the development of many geophysical techniques of ever-increasing sensitivity Cor the detection and mapping of unseen deposits and structures. Advances have been especially rapid since World War II because oC major improvements in instrumentation and tbe widespread application of the digital computer in the processing and interpretalion of geophysical dala. Because the great majority oC mineral deposits are beneatb tbe surface, their detection depends on those charactmstics that dilferentiate them from the surrounding media. Metbods based on variations in the elastic properties oC roco have been developed Cor determining structures associated with oil and gas. such as faults, anticlines, and synclines several kilometers below tbe surface. The variation in electrical

conductivity and natural currents in (he earth. rates oC decay oC artificial potential dilferences introduced into the ground. local ehanges in gravity. magnetismo and radioactivity - all these provide inCormation about the nature oC the structures below the surface. tbus permitting geophysicists to determine the most Cavorable places (o search for (he mineral deposits they seek. Several of the devices used by geophysicists were derived from methods used for locating gun emplacements, submarines. and aircraft during the two world wars. Attempts were made to locate artillery batteries during World War 1 by measuring the arrival times oC the elastic waves generated in tbe earth by their recoil: tbis led directly to the refraction method of seismic prospecting. Sub marines were located by transmitting sonar pulses underwater and measuring the interval between the emission and the retum of reflected pulses; knowing the velocity of sound in seawater. one can calculate the distance to the refteeting object. Sonar is now used widely for navigation in marine geophysical surveys. Radar, developed during World War n, utilized radio pulses in a similar manner to track aircraCt and sbips. Sbips, submarines, and mines were also detected in both wars by their magnetic properties. It should be pointed out that geophysics techniques can detect only a discontinuity. that is, where one region dilfers sufficiently from another in sorne property. This, however, is a universallimitation, for we canoot pereeive that wbich is homogeoeous in nature; we can discern only that which has sorne variation in time andjor space. Geopbysics deals with a1l aspects oC the pbysics of the earth, its atmosphere, and space. Geophysical measurements were made by the men who landed on the moon, and tbe atmospheres, magnetic fields, and other properties of planets are studied using geophysical data obtained by unmanned spacecraft. The principal subdivisions 01 geophysics are as follows; sorne of tbese have been iovestigated for many years simply because of their scientific

/ntroduction

2 Table 1.1. TO/d/1987 worldwide expenditures by survey type ilnd objec/ive (in thousands al U.S. dol/.m).

Type Petroleum Exploration Oevelopmenl Minerals Environmenlal Engineering Ceothermal Groundwater Oceanography ResearclJ Tolal

Land

809.394 20,161 13.076

Transition zone

10.091

25

Airborne

541,053 9,657 62

13.405 32 1),705 92

443 2,100 1,095 1,505 3,217 850,990

8,580

10,116

interest: Seismology Thennal properties of the earth Terrestrial magnetism Telluric currents Geodesy and gravitation Radioactivity of tbe earlh, sea, and almospbere; cosmic rays Atmospheric e1ectricity Meteorology Our knowledge of the Eartb has been developed by combining information from a11 tbese fields. This holds a1so for investigations in applied geophysics as well; combining several differenl approaches may help us to determine more accurately the location of a structure or deposit. Purely sclentific investigation of such subjects as the rate of evaporation of water from lakes, the chemical compositions of different rocks and waters from stre8D1S and ponds, tbe measurement of natural earth currents, potenlial variations, and impuri ties in the atmosphere - a11 these inftuence metbods of locating deposi ts that the applied geophysicist seeks. For eX8D1ple, the concentrations of radon in the air or stre8D1S may give indications of deposits of uranium, Electromagnetic waves caused by distanl thunderstonns are used to locate conducting ores at great depths below the surface. Applied geophysics in the search for minerals, oil, and gas may be divided into tbe following methods of exploration: Gravitational Magnetic Seismic Electrical Electromagnetic

Marine

1.458 6.190 556,999

300 802 28.336

Drill hole

1.504 294 58 91 235 30 283 184 2,679

Total

1.375.447 30.169 26.901 626 10,914 1.125 1.788 1.758 10.393 1,459.120

Radioactivity Wel1logging Miscellaneous chemical, thermal, and olber methods Certain geological conditions generally are associated with metallic ores, otbers with gas and oil, Ore deposits usually are found in areas where extensive igneous activity occurred. after which the rocks may or may not have been met8D1orphosed, Ultimately lhe area was eroded sufficiently lo bring tbe deposits close enougb to the surface to be discovered and exploited. Coal is the result of the rapid burial 01 vegetation that existed near a sea or large lake, and gas and oil usually are due to the deposition and subsequent burial of marine organisms. The search for metallic ores generally is concentrated in areas of known igneous and met8D1orpbic racks, such as the Rocky Mountains. the Andes, the Alps, and the Urals. However, important exceptions occur because (1) minerals can be transported away from the place of original formation, perhaps by mechanical transport. as in the case of a1luvial gold. perhaps in solution, and (2) sorne minerals such as salt and gypsum are deposited originally from aqueous solulion and hence occur in sedimentary areas. The search for coal. oil, and gas is confined to sedimenlary basins, excepl Cor rare instances in which oil or gas has migrated into fractured igneous or met8D1orphic rocks. The choice of techniques lo locate a certain mineral depends on the nature oC the mineral and of the surrounding rocks. Sometimes a method may give a direct indication of tbe presence of lhe mineral being 50ugbt, Cor eX8D1ple, tbe magnelic method when used to find magnetic ores of iron or nickel; al other limes the method may indicate only whether or not conditions are favorable lo the occurrence of the mineral

3

Infroduction

Eastern Hemisphere

11"r-""T'".....,-""T'".....,--r~--r~--r~...:..::=..:..:.,

i.. ~

Figure 1.1. To/al expenditures on pe/roleum explora/ion and del'elopment" '1977-81' (Fmm Sen/i. '1988.)

5Oughl. For example. Ihe magnetic method is used in petroleum exploration as a reconnaissance tool lo determine Ihe depth lo the basement rocks and Ihus determine where the sediments are thick enough 10 warranl exploration. Surveys using aircraft carrying magnetic. electromagnetic. and olher devices are Ihe most rapid methods oC finding geophysical anomalies. Such areal surveys are also the most inexpensive Cor covering large areas and hence are frequently used for reconnaissance; anomalies of interesl are laler investigaled using more detailed ground techniques. Seismic exploration is another method that has been used to explore large areas. both on land and offshore. though al considerably grealer costo in bOlh time and money. Table 1.1 shows world expenditures for acquisilion of geophysical data during the year 1987. The tolal expenditure oC about $1.5 billion (U.S.)' does nOI inelude work.in Ihe Soviel Union. Easlern Europe. or China. This figure is only 30% oC the 1982 figure and is below tbose of al1 the years since 1977 (Fig. 1.1). reflecting the low prices for petroleum and minerals. There seems to be a rather widespread

feeling lhal the sharp decline seen in Figure 1.1 has leveled out. although statistical data are not yet available to support this. Many (ineluding Ihe authors) expect a gradual increase in activily over Ihe next several years. Figure 1.1 also shows major shifts in the locales of geophysical work. The proportions of Ihe different geophysical metbods and unit costs are shown in Table 1.2. Cost figures are sensitive to many Cactors such as the supply and demand of particular commodities. economic conditions. governmental regulations. technological advances. and exploration philosophy. as well as operational environment. length and nature oC surveys, and other factors. Tables 1.1 and l.2 are based on the latest annual survey carried out by tbe Society of Exploration Geophysicists (Senti, 1988); this survey depends on voluntary reporting by a multitud e oC organizations. who do not necessarily report on the same bases nor in the same units. Nevertbeless, tbe perturbations

1 AlI figures in Ihis book are U.S. dollars.

Table 1.2. Ceophysical expendi/ures and uni/ cos/s. 1987. Cost basis

Unit costs

Pe/roleum explora/ion

Land seismic (2-D, P wave) Transilion zone seismic Marine sei5mie Seismic processins Sei5mic refraction land 5 wave land 3-D Marine 3-D VSP land gravily Marine sravily Masnelolellurics Airborne magnelics Olher airborne Olher

S207 X 10) /rno 198 479

72.11 0.4 20.5

S2,206/km' 1930283· 260 Sl

91 170

0.& 0.3 2.8 2.3 0.2 0.2 <0.1 <0.1 1.0 0.1 0.1

S7,S89/km1

380 12 20

&1/5In 46/km 1,548/5In 11/km

30

Seismic sources Land

Marine

Oynamite Air gun Weight drop Vibroseis 5 wave Air gun Sparker

41.61 (Iine-kilometers) 1.4 1.5 50.4 0.3 96.91 0.1

Expenditures

Unil cosls

Airborne work

Gravity Magnetics Mag. + Time-domain EM Frequency-domain EM VlF EM Radiometrlc

S283 16,575 1,660 5,759 1,608 991

x 10'

S48/km

9 24 45 20 19

Land minin,

Seismic reflection Seismic refrution Gravity Masnelics Resistivily SP Time-domain EM Frequencv-domain EM VLF EM Mag. + time-domain EM Mag. + frequencv-domain EM Mag.+ VLF EM Time-domain IP Frequencv-domain IP Complex resi51ivily IP Magnetotelluric natural freId Magnetotellurics controlled souree Gamma ray Orill hole

S3.875 77 1,298 1,070 267

S1,606/km 2.810

S24/sl" 1

10

401 417

250 71

133 801 224 1,645 197 25

862

7

51

353 6 58

120 30

Cravity-malnetic surveys by objective

Pelroleum Mineral exploration Environmenlal Engineering Geothermal Groundwater Oceanographic Research ·Excluding processing.

149 132 310 1,169 13& 165 3&2 197 351 564

61.91 24.6 0.4 0.9 0.4 0.& 1.1

9.9

5

Reference

because the data are no! homogeneous are probably small. Comparing 1987 data wi!h tha! for previous years shows an imporlant change in seismic petroleum work: a shifl from exploration. the finding oC hydrocarbons. lo reservoir studies. delailing oil/gas finds wilh Ihe objectives oC exploiting the finds more economically and increasing the oil/gas recoverable Crom Ihe finds. Applied geophysics is a relativcly new science and Ihe design of instruments. field techniques. and interpretation of the dala are undergoing rapid develop-

(

'{

men!. The following chapters will provide the reader with a survey oC Ihe different methods currently employed lo acquire and inlerpret geophysical data as an aid in the exploration Cor minerals and pelroleum and in the planning of large conslruclion projects.

REFERENCE Senti. R. J. 1988. Geophysical activity in 1987. Geoph,l'sics. Thl' Leadil,g Edgl' o/ Explora/iolf 7. No. 8. 33-56.

Chapter 2

Gravity M ethods 2.1. INTRODUCTION 2.1.1. General Gravily prospecting involves measurements oC variations in the gravitational field of tbe earth. One hopes to locate local masses of grealer or lesser density than tbe surrounding formations and learn sometbing about tbem from the irregularities in tbe earth's field. It is nOI possible, however, to determine a unique source for an observed anomaly. Observalions normally are made at tbe eartb's surface, but underground surveys also are carried out occasionally. Gravity prospecting is used as a recoonaissance tool in oil exploration; although expensive, it is still considerably cbeaper than seismic prospecting. Gravity data are also used to provide constraints in seismic interpretation. In mineral exploration, gravity prospecting usually has been employed as a secondary method, altbough it is used for detailed follow-up oC magnetic and electromagnetic anomalies during integrated base-metal surveys. Gravity surveys are sometimes used in engineering (Arzi, 1975) and archaeological studies. Like magnetics, radioactivilY, and some electrical tecbniques, gravity is a natural-source method. Local variations in the densities oí rocks near the surCace cause minute changes in the gravity field. Gravity and magnetics tecbniques often are grouped togetber as the pOlenrial melhods, bUI tbere are basic differences between tbem. Gravity is an inherent property oC mass, whereas the magnetic state: oC matter depends on otber factors, such as the inducing fields andjor tbe orientations oC magnetic domains. Density variations are relatively small, and tbe gravity effects oC local masses are very small compared with tbe effect oC tbe background field of the Earth as a whole (oCten oC the order oC 1 part in 106 to 107 ), whereas magnetic anomalies oCten are large relative to tbe main field. lbe time variation oC the magnetic field is complex, wbereas tbe gravily field is constant (ignoring "eartb tides''). Cometions lo gravity read-

ings are more complicated and more important tban in magnetic or otber geopbysical metbods. Gravity field operations are more expensive than magnetic operations, and field work is slower and requires more bighly skilled persoonel.

2.1.2. History of Gravlty Exploration Galileo Galilei, in about 1589, so legend tells us, dropped light and beavy weights Crom Ihe Leaning Tower of Pisa in an attempt lo determine how weight affects the speed at which a given object falls. Jobann Kepler worked out the laws oC planetary molion, and Ibis enabled Sir Isaac Newton lo discover Ihe universal law oC gravitalion ( Mathemalical Principies 01 Natural Philosophy. 1685-87). Tbe expeditions oC the French Academy oC Sciences lo Lapland and Pero (Ecuador) in 1735-45

gave Pierre Bouguer the opporlunily 10 establish many oC Ihe basic gravitational relationsbips, ineluding variations oC gravity with elevation and latitude, the horizontal attraction due to mountains, and the density of Ihe Earth. Captain Henry Kater, in 1817, introduced the compound pendulum, wilh interchangeable centers of oscillation and suspension, which became the major 1001 Cor gravily investigation for over a cenIUry. Because the variations in gravilalional atlraction are so small. Baron Roland von Eolvos set out to measure derivatives ralher Ihan total magnitudes. He compleled bis lirst lorsion balance (a modification oC tbe Coulomb balance) in 1890 and made the first gravily survey on the ice of Lake Balalon in 1901. F. A. Vening Meinesz, in 1923, measured gravity with pendulums on board a Dutch submarine and demonstrated gravily variations over various areas oC the oceans, especially the large gravity eCfects near the Indonesian trench. In December 1922, a torsion-balance survey oC the Spindletop oil field initiated geophysical exploration for oil. In late 1924, a test well on the Nash salt dome in Brazoria County, Texas, verified the

Principies of graviry

7

gravity interprelalion, becoming Ihe /irst geophysical hydrocarbon discovery, a1though Ihe /irst producing oil well did not come in un ti! J anuary 1926. The last half of the 1920s saw extensive gravity surveys with the torsion balance. In 1929 Ihe porlable pendulum began to be used. followed in 1932 by the stable gravirneter (and Ihe unstable gravimeler, which was not publicly described until 1937). By 1940, gravimelers had become so slable and convenienl Ihat lorsion balances and portable pendulurns disappeared from use. LaCoste (1934) described the zerolength spring, but the first workable LaCoste gravimeler did not appear unlil 1939. In subsequent years, gravimeters have been adapted (LaFehr, 1980) lo measurements under water, on moving ships and aircraCt. and in boreholes. The major addition lo our knowledge oC gravity in recenl years has come from observalions oC salellite palhs (Kahn. 1983). These have considerably increased our knowledge oC the delailed shape of the Earth. but this has not changed gravity exploration significantly. In the 1940s. graphic and grid methods of isolating anomalies were developed. and the anomalies Ihat resull from simple shapes were calculated. The computing power made available by digital computers since the 1960s has considerably increased our interpretalion capabilities. the ultimate goal being solution of the inverse problem (§2.7.9).

2.2. PRINCIPlES OF GRAVITY 2.2.1. Newton's law of Gravitation The force of gravitation is expressed by N e"rton •s law: Tbe force between two particles of masses m and m2 is direetly proporlional to the produet of Ih~ masses and inversely proportional lo Ihe square of Ihe distance belween the centers of rnass: (2.1) where F is the force on m2. r l is a unit vector direcled from m 2 loward mI' r is Ihe distance belween mi and m 2 • and 'Y is tbe universal gravitational constant. NOle Ihat the force F is a1ways attraclive. In SI unils the value of 'Y is 6.672 X 10- 11 N ot /kg2 or in cgs units 6.672 X 10- 8 dyne cni /S2.

The aceeleration g is equal lo Ihe gravitational Coree per unit mass due to mI' Ir mi is the mass oC the Earlh. M•. g beco mes the a('ce/eratiol1 o/ grm'itr and is given bv . ( 2.2b) R. being the radius oC the Earth and r l extending

downward toward the center of the Earlh. (h is customary to use the same symbol g whelher il is due lo the Earth or a rnass m.) The acceleration oC gravity was first measured by Galileo in his Camous experirnent at Pisa. The numerical value oC g al the Earth's surCace is about 980 cm/s2. In honor of Galileo. Ihe unit oC acceleration oC gravity, 1 cm/s 2• is called the galileo or Gal. Gravirneters used in field rneasuremenls have a sensitivity of about lO-s Gal or 0.01 mGaI. although the reading accuracy is generallv onlv 0.03 to 0.06 mGal. As a result. they are capable oC" distinguishing changes in Ihe value oC g with a precision oC one part in 10 8 . Microgravimeters are available with measuring accuraey oC about 5 /lGal.

2.2.3. Gravitational Potential (a) Newron;an or rhree-d;mens;onal porenrial.

Gravitational fields are conservative: thal is. the work done in moving a mass in a gravitational field is independent of the path traversed and depends only on Ihe end points (§A.3.4). If the mass is eventually retumed to its original position. the net energy expenditure is zero. regardless oC the path followed. Another way oC expressing this is 10 say that the sum oC kinetic (molion) energy and potential (position) energy is constant within a c10sed syslem. The gravitational force is a vector whose direction is along the line joining the centers oC the two masses. Tbe force giving rise lo a conservative field may be derived from a sealar potential function U(x.y, z), ealled the Nell'tonian or three-dimensiollal pote.ltial. by /inding the gradient (Eqs. (A.17), (A.30). and (A.3l)]:

-F(x. y. =)/111 2

VU(x. y. z)

-g(.\'. y. z)

(2.3a)

In spherical coordinates (Fig. A.4b) this becomes

2.2.2. Acceleration of Gravity The acceleration of m2 due to the presence oC mI can be Cound by dividing F by m2 in Equation (2.1), that is. (2.2a)

VU(r,8,
~

-F(r.8.
=

-g(r.8 • .p)

(2.3b)

Altemalively, we ean solve this equation for the

Gravity methods

8

Sometimes it is more convenient to use cylindrieal coordina tes (Figure A.4a). Because dx dy dz 'o dro d8 dz and ,2 - rJ + z2, rJ - x2 + y2, the potenlial becomes (2.6b) and tbe aeceleration in the z direetion is

Figure 2.1. Potentidl of three-dimensiondl mdSS.

In spherieal coordinates,

dx dy dz - r 2 sin 8 d, d8 d."

gravilational poteotial in the form [Eq. (A.16») heoee,

U(r,8,1#I) - [(VU) . dr 00

- - f~g· dr

u - yp jI.

(2.4)

whieh is a statement of the work done in moving a unit mass from iolioity (thal is, a véry distant point), by any path, to a poiot distant r lrom the poinl mass producing !he gravitational field. Using Equation (2.2a) in scalar form, we get

,,

(2.6a)

.

- -yp1I.fJz/r)sin8drd9d." -

-yp

because

z/, -

111 sin8 eos 8 drd8 dl#l r , •

(2.7e)

eos 9. (The minus sign indieates that

g is direeted toward lhe mass dm at the center 01 tbe

sphere.) (b) togarithmic or two-dimensiona/ potentia/. Jf lhe mass is very long in the y dircction and has a uniform eross seetion 01 arbitrary shape in tbe xz plane, the gravity attraction derives from a logarithmíe (rather than Newtonian) potential. Then Equalion (2.6a) becomes

dU - ydm/r - yp dxdydz/r

U - y jjj(p/r) dxdydz

(2.6e)

g - -au/az

00

where p(x, y, z) is Ihe densilY, and r 2 _ x2 + y2 + Z2. Then !he poteotial of the total mass m is

9 drd8 d."

Taking the z axis along the polar axis,

U( r) - -y [ m(1/r 1 ) dr - ym/r (2.5) It is often simpler lo solve gravity problems by caleulating the scalar potential U ralher than the vector I and then to obtain I from Equalion (2.3). Considering a three-dimensional mass of arbitrary sbape as in Figure 2.1, the poteotial and aceeleralion of gravity al a poínl outside the mass ean be found by dividing the mass into small elements and integrating to get the total elrcet. From Equation (2.5), the potenlial due to an elemenl 01 mass dm al tbe point (x, Y. z) a distance , from P(O,O,O) is

1' sin

r , •

U - yp

lf. dxdz{OO"", (1/r) dy

With some maoipulation (see problem 1), tbe logarithmie potenlial beeomes

" y ,

Beeause g is tbe acceleration 01 gravity in the z direction (positive vertieally downward), and assuming p constant, g- -(au/az)

- ypjjj(z/r J ) dxdydz " y

I

(2.7a)

.

U - 2yp j1In(1/r') dxdz

"

(2.8)

where r,2 - x2 + z2. The gravity elrcet for tbe lwodimensional body is

g= -au/az - 2yj1p(z/r'2) dxdz (2.9) "

I

Principies of gravity

9

2.2.4. PotentiaHield Equations

Equation (2.3a),

The diversence theorem (Gauss's theorem; Eq. (A.27)] states that the integeal oC the divergence oI a vector field g over a region of space V is equivalent to the integral oC the outward normal component of the field g over the surface enclosins the region. We have

fvV • g dv - fsg. ds

(2.10)

If tbere is no attracting matter witbin the volume, Ihe integrals are zero and V • g - O. Bul from Equalion (2.3a) the gravitational force is the geadient oC the scalar potential U, so tbat

that is, the pOlential in free space satisfies Laplace 's equalion. In cartesian coordinates, Laplace's equation is

(see Eq. (A.37) for Laplace's equation in spherical coordinates]. Also, because g"" - au/az, and any

derivative of a solution of a diITerential equation is also a solution, we have (2.llc)

If, on the other hand, there is a particle of mass at the center oC a sphere of radius r, then

(2.13b) which is Poisson' s equation. Equations (2.11a) and (2.13b) state that the gravo ily potential salisfies Laplace's equalion in free space and Poisson's equation in a regio n containing mass. These equations imply that various distributions oC mass can produce tbe same potential field over a surface (Skeels. 1947); this is sometimes called the "inherent ambiguity" oI gravity interpretation. Sometimes it is convenienl lo substitute for masses distributed throughout a volume V a liclitious surlace density of mass over a surface S enclosing V such that the eITect outside S is the same. From Equations (2.12b) and (2.13a) we have (2.14) that is, tbe component of gravity perpendicular to the surface gives the equivalent surface density. For an equipotential surface, tbis is mere1y the total gravitational lield.

2.2.5. Derivatives of the Potential Quanlitites use fui in gravily analysis may be ob· tained by diITerentiating the pOlenlial in various ways. We have already noted in Equation (2.7a) tbat vertical gravity g - - rJu/az. This is the quantity measured by gravimeters. The Iirsl vertical derivative of g [from Eq. (2.7a)] is

ag/rJz = - rJ 2U/¡}z2 = - Uzz - -4l'1'ym

(2.12a)

Ihe minus meaning tbat g. is opposite to n, the outward·drawn normal. It can be shown (see problem 2) that tbis result holds resardless of the shape of the surface and the position and size of the mass within the surCace. If the surface encloses several masses o( total mass M, we can write

where subscripts indicate derivatives of U. Measure· ments occasionally are made of the vertical sradient (Falkiewicz, 1976; Jordan, 1978: Ager and Lilard, 1982; Butler. 1984). The second vertical derivative is

a1g/iJZ'J. '" - a3u/az J

- - u".. T

If the volume V is very small, enclosins only a point, we can remove tbe integral sisn to give V • g - -4nyp

(2.13a)

where p is tbe density at the point. Then, from

- 3ypfff(SzJ/r 7

-

3z/r 5 ) dxdydz

x y z

(2.16)

lbis derivative frequentiy is employed in gravity interpretation for isolating anomalies (§2.6.5) and for upward and downward continuation (§2.6.7).

Gravity methods

10

Derivatives tend to magniCy near-surCace Ceatures by increasing the power oC the linear dimension in the denominator. 'Ibat is, because the gravity elfect varies inversely as the distance squared, the first and secood derivatives vary as the inverse oC the third and Courth powers, respectively (for three-dimensional bodies). By taking the derivatives oC g in Equation (2.1a) a10ng the x and y axes, we obtain the components of the horizontal gradient o/ gravity:

u". - - íJ g/ íJx - 3yp

fff( xz/r3) dxdydz

(2.17)

" y •

and similarly Cor the y component Uy •• The horizontal gradient can be determined from gravity profiles or map contours as the slope or rate oC change ol g with horizontal displacement. The horizontal gradient is useCuI in defining the edges and depths oC bodies (Stanley, 1911). The differential curvature (or horizontal directive tendency, HDT) is a measure oC the warped or curved shape oC the potential surCace. From Equation (2.6a),

Other components are lJ" and curvature (HDT) is given by HDT - { (U" - 3yp

- Uu

2

)

+

U",.

(W",)

(b) The referenee spheroid. The shape 01 the Earth, determined by geodetic measurements and satellite traclting, is nearly spheroidal, bulging at the equator and ftattened at the poles. The polar fiattening is (Req - Rp)/ Req ... 1/298.25, wbere R.q and Rp are the Earth's equatorial and polar radü, respectively. The re/erence spheroid is an oblate ellipsoid that approximates the mean sea-level surface (geoid), with tbe land aboye it removed. In 1930 tbe International Uníon of Geodesy and Geophysics adopted a Cormula (Nettleton, 1916, p. 11) for tbe tbeoretical value of gravity g" but tbis has been superseded (Woolard, 1919) by tbe Geodetic Reference System 1961 (GRS67):

l}l/l

f f f {(x2 + y2) /r'} J: ,

The dilferential

anomalies due to the last factor, and these anomalies generally are much smaller than the changes due to lattitude and elevation, a1though larger than the anomalies due to tidal and (usually) topograpbic elfects. Tbe change in gravity Crom equatorial to polar regions amounts to about 5 Gal, or 0.5% of the average value of g (980 Gal), and' the elfect oC elevation can be as large as 0.1 Gal, or 0.01 % of g. A gravity anomaly considered large in oil exploration, on the otber band, would be 10 mGaI' or 0.001% of g, whereas in mineral exploration a large anomaly would be 1 mGal. Thus, variations in g that are significant in prospecting are small in comparison with the magnitude of g and also in comparison with latitude and elevation elfects. Fortunately, we can, with good accuracy, remove most of the elfects oC Cactors that are not oC interesl in prospecting.

g, - 978,031.846( 1 + 0.005.278,895 sin2.¡.

dx dy dz (2.19)

•

u.,x'

It is not possible to measure lJ,y' u.", or HDT directly. Dilferential curvature can be obtained Crom torsion-balance measurements.

2.3. GRAVITY OF THE EARTH 2.3.1. Figure of the Earth (a) General. Gravity prospecting evolved Crom the study oC the Earth's gravitational field, a subject oC interest to geodesists Cor determining the shape ol the Earth. Because the Earth is not a perCect homogeneous sphere, gravitational acceleration is not constant over the Earth's surface. Tbe magnitude oC gravity depends on five Cactors: latitude, elevation, topography of the surrounding terrain, earth tides, and density variations in the subsurCace. Gravity exploration is concerned with

+0.ooo,023,462sin4 .¡.) mGal (2.20) wbere 4> is latitude. (e) The geoid. Mean continental elevations are about 500 m, and maximum land elevations and ocean depressions are oC the order of 9,000 m referred tosea leve\. Sea level is inftuenced by these variations and other lateral density changes. We define mean sea leve! (the equipotential for the Eartb's gravity plus centrifugal elfects). called tbe geoid, as tbe average sea level over tbe oceans and over tbe surface oC sea water tbat would lie in canals if they were cut througb tbe land masses. The simplified figure 01 the Earth a1lows for increasing density with deptb, but not lor lateral varialions, which are tbe objects of gravity exploration. Because of tbe lateral variations, the geoid and reference spberoid do not coincide. Local mass anomalies warp tbe geoid as in Figure 2.2a. We migbt expect

17

Gravity of the Earth Reference spherOld

Geo,d

(al Contlnenr

Rererene. sph.ro,d

~ Verilea' !\cOIk g:1·t'OIII~ c~it,!t'r;,lIcd

Occan (bl

Figure 2.2. Comparison of reference spheroid and geoid. (a) Wifrping of (he geoid local mass. (b) large-scale warping.

!he geoid to be warped upward under the continents beeause of auracting material above, and downward over tbe ocean basins because of the low density of water (Figure 2.2b). However, deviations from the spberoid do not correlate with the continents nor witb tbe lithospberic plates, suggesting that density dilferences emt below tbe Iilhosphere. The deviations between tbe two surfaces (Kahn, 1983) are as much as 100 m.

2.3.2. Gravity Reduction (a) General. Gravity readings are generally innucnced by tbe five factors listed in Section 2.3.1a, hence we musl make corrections to reduce gravity readings lo tbe values they would have on a datum equipotential suríace sueh as tbe geoid (or a surface everywhere parallel to it). (b) Latitude correction.

Botb tbe rotalion of the

Eartb and its equatorial bulge produce an inerease 01 gravity with latitude. Tbe eentrifugal aeeeleration due to the rotating Earth is maximum al the equator and uro al tbe poJes; it opposes the gravilalional acceJeration, whiJe tbe polar ftattening in creases gravity al tbe poles by making lhe geoid elaser to the Earth's center of mass. Tbe laUer elfeet is eounteracted partly by tbe increased attracting mass at the equator. A latitude correction ÁgL is obtained by

b)'

if

dilferentialing Equation (2.20):

ÁsdÁs - (l/R.) Asr/A.p - 0.811 sin 241 mGal/km

(2.21a)

- 1.305 sin 241 mGal/mile (2.21b) where Ás - N-S horizontal distanee - R. Á and R. is the radius of the Earth ( ... 6368 km). Tbe correction is a maximum at latitude 45° where it amounts lo 0.01 mGal/(13 m) and it is zero al the equator and poJes. The correction is added to S as we move toward the equator. (e) Free-air eorrection. Since gravity varies inverseJy with the square of distanee, it is necessary to correet for changes in elevation between stalions lO reduce field readings to a datum surfaee. The free air correction does not take aecount of the material between the station and the datum plane. It is obtained by dilferentiating the sealar equation equivalent to Equation (2.2b); the result is (dropping the minus sign)

AgFl>.IAR

=

2yM.IR! - 2g1R.

- 0.3086 mGal/m

(2.22a)

... 0.09406 mGai¡rt

(2.22b)

12

Crilvity methods

The Bouguer correclion is applied in the opposite sense to free air, thal ¡s, il is sublracted when lhe station is above the dalum and vice versa. When gravity measuremenls are made at underground stations, as in Figure 2.3b, the slab belween stations at depths ti and Z2 exerts an altraction downward on station 1 and upward on 2. Thus the difrerence in gravity between them is 4"YP(Z2 - ZI) mGaI, that is, lhe Bouguer correction is doubled. The Bouguer and free-air corrections are afien combined into an elevation corree/ion. From Equations (2.22) and (2.23) the resu)t is

Ofound su,r.ce

Figure 2.3. Bouguer correction. (a) Station on plilteilu. (b) Under8round stilt;ons.

iI

broad

- (0.3086 - 0.0419p) mGal/m (2.25a) - (0.0941 - O.0128p) mGal/ft (2.25b) at 45° latitude. The free-air correction is added to \he field reading when the station is above the datum plane and sublracled when below it. To make latitude and free-air corrections, station The elevalion correclion is applied in the same way posilíOD must be known precisely. For an accuracy as the free-air correction. Two assumptions were made in deriving the oC 0.01 mOal, Ihe usual accuracy of Ihe gravimeter, N-S location (al 45° latitude) must be known to Bouguer corn:ction: (1) The slab is oC uniCorm density and (2) it is oC infinite horizontal extenl; neither witbin 13 m (40 fl) and elevation to 3 cm (1 in.). is really valido To modify the first, one needs consid(d) Bouguer correction. The Bouguer correction erable knowledge of local rock lypes and densities. accounls for \he altraction of malerial between the The second is taken care of in lhe nexl reduction. slation and dalum plane \hal was ignored in lhe free-air calculation. If the slation were centrally lo- (e) Terrain correction. The lerrain correction alcated on a plateau of large horizontal extent and lows for surface irregularities in the vicinity of the uniform thlckness and densily (Fig. 2.3a), the gravity stalion. HiUs above the elevatíon oC the gravity stareading would be increased by the attractíon oC thls tion exert an upward pull on the gravimeler. whereas slab between the slation and the datum. The Bouguer valleys (Iack oC material) below il fail 10 puU downcorrection ís given by ward on il. Thus both types of topographic undula-

- 0.04192p mOal/m

(2.23a)

.;, 0.01278p mGaI/ft

(2.23b)

where p is the slab density in grams per cubic centimeter [see Eq. (2.57)]. If we assume an average density for crustal roeks of 2.67 g/cm', the numerical value is

flg./flR - 0.112 mOal/m - 0.0341 mGaI/fl

(2.24a) (2.24b)

tions afrect gravity measuremenls in the same sense and the terrain correction is added to the station reading. There are several methods for calculating terrain corrections, a11 of which require delailed knowledge 01 reliel near the slalion and a good topograpbical map (con tour interval - 10 m or 50 Ct or smaller) extendíng considerably beyond the survey area. The usual procedure is to divide thc area ioto comparto ments and compare the elevation within each compartment with the station elevation. This can be done by outlining the compartments on a transparent sheet overlying a topographic map. The most common template used concentric circles and radial Iines, making seclors whose areas increased with distance crom the station. The gravity efrect of a single seclor was calculated from Ihe collowing for-

Cravity of the Earth

13

la)

(")

Figure 2.4. Use of terrain ehart with topographie map, (a) Terrain ('hart ol'er/I'ing map, (b) Enldrged viel"" of a single zone,

mula [Eq. (2.58»):

8gr (r,O) = ypO{ (ro - r;) + (r;2 + ~z2)1/2 - (r02 + ~z2)1/2} (2.26) where O is the sector angle (radians), ~z = Iz, - zal, z, is the station elevation, za is the average elevation in the sector, and ro and r; are the outer and inner sector radü. The terrain correction ~gr is the sum oC the contributions oC al1 sectors:

,

~gT'" LL8gr (r,O) ,

(2.27)

The use of a terrain chart of this type is ilIustrated in Figure 2.4. The transparent temp1ate is placed over the topographic map with Ihe center of the cirdes at the gravity station. Tbe average elevation within a single compartment is estimated Crom the contours within it and subtracted Crom the known slalion elevation. Tbe dift"erence is ~ z in Equation (2.26), from which the contribution to ~gr is calculated for the compartment. Tables of terrain correclions such as Table 2.1 facililated this operation. [Hammer (1982) gives corrections Cor subdivisions oC the ¡nner zones required in microgravity surveys for engineering and archaeological surveys.) Note that !bere was no provision Ior relie! within 2 m of the station, that is, it has to be flat ror a 2 m distance Crom !be slation. It can be seen from Table 2.1 that the correction is small if r > 20z, r being the average distance from the compartment to the station. Other methods for segmenting the topographic map occasionally were applied¡ for instance, when contours were practical1y linear, !bere was no advantage in using circular sectors. An alternative scheme

used elementary areas so proportioned that the gravity eft"ect of each was the same regard1ess oI distance. Terrain corrections Cor outer zones are often made on a computer using elevations on a regular grid (Krohn, 1976). Regardless oC the approach. the topographic reduction is a slow and tedious task. Furthermore, in areas of steep and erratic slopes, it usually is not very accurate. particularly Cor reHe( in the vicinilY oC Ihe slalion itselC. At the edge of a steep c1ift" or gorge, Ihe terrain correction is almost inevitably in error. A better solution is to move the gravity station away Crom sharp reHef Ceatures if this is possible. Bouguer anomalies (§2.3.2h) for marine surface and airborne surveys require a different terrain correction from that discussed earHer. The Bouguer correction is calculated (for marine data) as if the water depth were everywhere constant. and hence it is discontinuous over abrupt elevation changes. The lerrain correction is made discontinuous to compensate for the Bouguer correction discontinuilies. To the left oC a two-dimensional vertical step in the sea floor (Fig, 2.5), the terrain correction is positive due lo the deeper water on Ihe right (a11alogous to a nearby valley in land work). and il is negative lo Ihe right oC the Slep. (f) Earth-tide correction. Inslruments for measuring gravity are sensitive enough lo record the changes in g caused by movement of Ihe Sun and Moon, changes that depend on latitude and time. Their range is about 0.3 mGal. Figure 2.6 shows calculated and measured tidal variations for a stationary gravimeter, Tbe correction can be calculated rrom knowledge of Ihe locations of the Sun and Moon. However, because the variation is smooth and re!atively slow.

Table 2.1. Terrain co"ections. lone 8 4 sectors

loneC 6sectors

6.56' - 54.6'

54.6' -175'

±z 0.0-1.1 1.1-1.9 1.9-2.5 2.5 - 2.9 2.9-3.4 3.4-3.7 3.7-7 7-9 9-12 12-14 14-16 16-19 19-21 21-24 24-27 27-30

dar

±z

0.00000 0.0-4.3 0.00133 4.3 -7.5 0.00267 7.5 -9.7 9.7-11.5 0.0040 0.0053 11.5-13.1 0.00&7 13.1 -14.5 0.0133 14.5 - 24 0.02&7 24-32 32-39 0.040 39-45 0.053 45-51 0.0&7 51-57 0.080 57-63 0.0935 0.107 63-68 66-74 0.120 74-80 0.133 00-86 86-91 91-97 97-104 104-110

dar

lonpD 6 sectors 175' - 558'

±z

dar

Zone E 8 sectors 558' -1280'

±z

dar

0-18 0.00000 0.00000 0.0-7.7 0.00000 7.7-13.4 0.00133 18-JO 0.00133 0.00133 0.002&7 13.4-17.3 0.002&7 JO-39 0.002&7 39-47 0.0040 0.0040 17.3-20.5 0.0040 0.0053 20.5-23.2 0.0053 47-53 0.0053 0.00&7 23.2 - 25.7 0.00&7 53-58 0.00&7 0.0133 25.7-43 0.0133 58-97 0.0133 43-5& 97 - 12& 0.02&7 0.0267 0.02&7 0.040 126-148 0.040 0.040 56-6& 0.053 6&-7& 0.053 146-170 0.053 0.0&7 170-189 0.0&7 0.0&7 76-84 189- 20& 0.000 0.080 84-92 0.080 92-100 0.0935 20&- 222 0.0935 0.0935 100-107 0.107 222-238 0.107 0.107 107-114 0.120 238- 252 0.120 0.120 0,133 114-120 0.133 252-26& 0.133 0,147 120-127 0.147 266- 280 0.147 0,160 127-133 0.160 200- 293 0.160 293-30& 0.174 0.174 133-140 0.174 30&-318 0.187 0.187 140-146 0.187 318-331 0.200 0.200 146-152 0.200

lone F 8 sectors 1280' - 2936'

loneG 12 sectors 2936' - 5018'

Zone H 12 sectors 5018' -8578'

lone 1 12 sectors 8578' -14612'

±z

dar

±z

dSr

±z

±z

0-27 27-46 46-bO 60-71 71-00 00-88 88 - 146 146 - '189 189-224 224 - 255 255 - 282 282 - 308 308- 331 331 - 353 353-374 374-394 394-413 413-431 431 - 449 449-46& 46&-483

0.00000 0.0133 0.002&7 0.0040 O.lX)53 0.00&7 0.0133 0.0267 0.040 0.053 0.0&7 0.000 0.0935 0.107 0.120 0.133 0.147 O.lbO 0.174 0.187 0.200

O-58 58-100 100-129 129-153 153-173 173 -191 191- 317 317 - 410 410-486 486-552 552-&11 611-66& 66&-716 716 - 764 764-009 009-852 852-894 894-933 933-972 972-H109 '1009- 104&

0.00000 0.00133 0.00267 0.0040 0.0053 0.00&7 0.0133 0.02&7 0.040 0.053 0.0&7 0.080 0.0935 0.107 0.120 0.133 0.147 O.1bO 0.174 0.187 0.200

0-75 75 -131 131-169 1&9- 200 200- 226 226- 250 250- 414 414- 535 535-633 633-719 719- 796 796-866 866-931 931-992 q<}2 -1050 1050-1105

dSr

0.00000 O-q<} 0.00133 q<}-171 0.00267 171 - 220 0.0040 220- 2&1 0.0053 2&1 - 296 0.00&7 296- 327 0.0133 327 - 540 0.02&7 540-&98 0.040 698-827 0.053 827-938 0.0&7 938-1038 0.080 1038-1129 0.0935 0.107 0.120 0.133

dar 0.00000 0.00133 0.002&7 0.0040 0.0053 0.00&7 0.0133 0.02&7 0.040 0.053 0.0&7 0.080

Note: dar - Byp(ro - ~ + ,(~2 + z2) - ,(ri + Z2)), ~,Ió - ¡nner, outer sector radii,.., - &.67 X 10- 8. dgr in milligals, z,~.'O in feet. and z - average sector elevalion. Source: From Hammer (1939), bul based on average densily p - 2.67 gjc~.

Gravity of the Earth

15

+0.0341

-;

~

..

O~~~~-r-+--~+--r-r~~~

"

<1

-0.034' _ _ _ _ _ _, -_ _ _....,l""'""_ _S_ea_S_u_T_fa_ce

¡

d

Pratt suggested a crust where the density varies witb topography, being lower in mountain regions and higber beneatb tbe oceans. Both hypotheses appear to be true to sorne exlent. An isostatic correction occasionally is necessary in large-scale surveys to compensate for crustal variations. (h) Bouguer and free-air anoma/ies. When all oC the preceding corrections have been applied to the observed gravity reading, we obtain the value oC the Bouguer anomaly gB for the station:

gB = gob. - g, + (tlg L + tlg FA - tlg B + tlgT ) (2.28)

D

Fisure 2.5. Mdrine terrdin correetion for vertical sea-flaar step. A., - 1.03. Aocl - 2.67. t - meters. (After Nettletan.

1971.) '1

usually it is included in tbe instrument driCt correction (§2.S.2). (g) Isos/alie eorreelion. The worldwide average oC Bouguer anomalies on land near sea level is approximately zero. In regions oC large elevalion tbey are generally negative. while in oceanic regions mainly positive. Tbese large-scale effects are due to density variations in tbe crust, indicating denser material beneatb tbe ocean and less dense material in regions oC e1evated land. In 1855, two bypotbeses were put Corward to aeeount Cor tbe density variations. Airy proposed a erust oC uniCorm density but variable thickness floating on a Iiquid substratum of higber density. whereas

where gob. is the station reading, g, is the theoretical gravity, tlg L is the latitude correction, tlg PA is the . free-air correction, tl gB is the Bouguer correction. and tlgT is the terrain correction. The correction terms in Equation (2.28) correspond to a station south of the reference latitude (in the northern herrusphere) and aboye the datum. Sometimes, rather tban the value from Equation (2.20), some particular station value in the survey area is used for g,. Note tbat tbe signs of tlgFA and tlg B change when the station is below the datum plane. Another quantity that is sometimes used (especially with marine data) is the free-air anomaly, the value of gB when tlg B (and often tlgT ) is omitted from Equation (2.28). If the Earth had no lateral variations in density, after corrections for the preceding effects, gravity readings would be identical. The Bouguer and free-air anomalies result Crom lateral variations in density (see also Ervin. 1977).

2.3.3. Densities of Rocks and Minerals The quantity 10 be determined in gravity exploration is local lateral variation in density. Generally density

Oí el

..

,§ 4

o

Oí

:g !;'

4000

sooo

6000

1000

8000

9000

Tim~ fminu~C's.

figure 2.6. farth-ride var;arions. Manrreal, Ap,ill%9. Cravitr reading~ hJ,'e been corrected for ins rrument drift.

I

Gravity methods

16 Table 2.2. Densities.

Rack type Sediments (wet) Overburden Soil Clay Gravel Sand Sandstone Shale Limestone Dolomile Sedimentary rocks (av.) Igneous rocks Rhyolite Andesite Granite Granodiorite Porphyry Quartz diorite Diorite lavas Diabase Basall Gabbro PeridOlile Acid igneous Basic igneous Melamorphic racks Quartzile Schists Graywacke Marble Serpentine Slate Gneiss Amphibolite Eclogile Melamorphic

Range (g/crñJ)

Averag'e (g/cm])

1.2- 2.4 1.&3-2.& 1.7 - 2.4 1.7-2.3 1.&1 - 2.7& 1.77-3.2 1.93-2.90 2.28- 2.90

1.92 1.92 2.21 2.0 2.0 2.35 2.40 2.55 2.70 2.50

2.35 - 2.70 2.4- 2.8 2.50- 2.81 2.&7- 2.79 2.60- 2.89 2.&2- 2.96 2.72 - 2.99 2.80-3.00 2.50- 3.20 2.70-3.30 2.70-3.50 2.78-3.37 2.30- 3.11 2.09- 3.17

2.52 2.61 2.64 2.73 2.74 2.79 2.85 2.90 2.91 2.99 3.03 3.15 2.61 2.79

2.5- 2.70 2.39- 2.9 2.6 - 2.7 2.&- 2.9 2.4- 3.10 2.7- 2.9 2.59-3.0 2.90-3.04 3.2 - 3.54 2.4 - 3.1

2.60 2.64 2.65 2.75 2.78 2.79 2.80 2.96 3.37 2.74

is not measured in situ, aJthough it. can be measured by borehole logging tool5 (see f11.8.3). Density can aJso be estimated from seismic velocity (§4.2.8a). orten density measurements are made in the laboratory on small outcrop or drill-core samples. However, Iaboratory resulta rarely give tbe true bulk

Mineral Meta"ic minerals Oxides. carbonates 8auxite limonite Siderite Rutile Manganite Chromite IImenite Pyrolusile Magnetite Franklinite Hematite Cuprite Cassiterite Wolframite Sulfides. arsenides Sphalerite Malachile Chalcopyrite Stannile Stibnile Pyrrhotite Molybdenite Marcasite Pyrile Bornite Chalcocite Coballite Arsenopyrite Bismulhlhinile Galena Cinnabar Non-metallic minerals Pelroleum Ice Sea Water lignite Soft coal Anthracile Chalk Graphite Rock sal! Gypsum Kaolinite Orthoclase Quarlz Cal cite Anhydrite Biotile Magnesite fluorite Barite

Range (gjcrfrl)

Average (g/cm])

2.3 - 2.55 3.5 -4.0 3.7-3.9 4.18-4.3 4.2 - 4.4 4.3 - 4.& 4.3 - 5.0 4.7 - 5.0 4.9- 5.2 5.0-5.22 4.9-5.3 5.7-&.15 &.8-7.1 7.1-7.5

2.45 3.78 3.83 4.25 4.32 4.3& 4.&7 4.82 5.12 5.12 5.18 5.92 6.92 7.32

3.5 -4.0 3.9 - 4.03 4.1 - 4.3 4.3 -4.52 4.5 -4.& 4.5 -4.8 4.4 - 4.8 4.7 - 4.9 4.9- 5.2 4.9- 5.4 5.5 -5.8 5.8-6.3 5.9-6.2 6.5 -6.7 7.4-7.6 8.0-8.2

3.75 4.0 4.2 4.4 4.6 4.&5 4.7 4.85 5.0 5.1 5.&5 6.1 6.1 &.57 7.5 8.1

0.6-0.9 0.88-0.92 1.01-1.05 1.1-1.25 1.2 -1.5 1.34-1.8 1.53-2.6 1.9- 2.3 2.1 - 2.6 2.2- 2.6 2.2- 2.63 2.5- 2.6 2.5 - 2.7 2.6- 2.7 2.29- 3.0 2.7 - 3.2 2.9-3.12 3.01-3.25 4.3-4.7

1.19 1.32 1.50 2.01 2.15 2.22 2.35 2.53 2.65 2.93 2.92 3.03 3.14 4.47

density because the samples may be weathered, fragmcnted, dchydratcd, or altered in the procesa of being obtained. Consequently, density is often not very well known in specific field situations. Density data are given in Table 2.2. Sedimentary roeks are usually less dense than igneous ud meta-

Gravity of the Earth

17 Density
2.0

2.2

2.4

2.6

2.8

3.0

Or-TT--'--'r--r--~~--~--r-~--,O

(a) p(aJcm) )

0r-~,2'_0-r~-.r-r-2T·S~r-r-~'-~_

0&, \

e

~

...

~\

e:

.! ~

¡!:

f21

~~ ,"lsl

o

Schleswig·Holslein

111

Norlh Germany

I

~~

~

Lower Saxony

.."o .." :3 . u ~

\1 \

[!

.., ;:1

• ...flJ

~

-+- •

11

1\

.~

I•

I 1I •

11 I,

(b)

Figure 2.7. Density versus depth. (a) Weslern Hemisphere data: Veneruelan data from Hedber8 (1936), Culf Coast datd from D;ckenson (1953). Ca/veston County data from Bib/e (1964). and remaining data (Cdnddian) from Maxdnt (1980). (b) North furope data from Hermes (1986).

morphic rocks. The wide range oC density of sedimentary roeks is primarily due to variations in porosity. The nature oC the pare fluids also affeels tbe bulk density. Sedimentary rack densily is also innuenced by age, previous history, and deptb of burial. Obviously a porous roek will be compaeled when buried. In general, density inereases with depth

(Fig. 2.7) and time. The density contras! between adjacent sedimentary formations in the field is sel· dom greater than 0.25 g/enJ! (except for the near· surfaee: §2.7.11). Although igneous rocks generally are denser than sedimentary rocks, Ihere is considerable overlap. Volcanics, particularly lavas, may have high porosi-

Cravíty methods

18

ties and, hence, low density. Generally, basic igneous rocks are heavier than acidic ones. Porosity, which affects the density of sediments so greatly, is oC minor significance in most igneous and metamorpbic rocks unless they are bigh1y fractured. Density usually increases with the degree oC melamorphism because the process tends lo fiU pore spaces and recryslallize the rock in a denser Corm. Thus metamorphosed sediments, such as marble, slate, and quartzite, generally are denser than the original limes tone, shale, and sandstone. The same is lrue Cor the metamorphic forms of igneous rocks, gneiss versus granite, amphibolite versus basalt, and so on. With few exceptions, nonmetallic mínerals have lower densities than the average Cor rocks (2.67 g/cM'). Metallic minerals, on the other hand, mainly are heavier than Ibis average, but since they rarely occur in pure form in large volumes, their effect normally is not great.

23.4. Oensity Estimares from Field Results (a) Densíty (rom underground measurements.

Sometimes it is feasible to make gravity measurements underground. lf readin~ are taken at points directly below one another (for example, at the surface and in an underground opening), then the difCerence between these values is given by [see Eqs. (2.22) and (2.23»)

4g - (0.3086 - 0.0838p) 4z

+ tr

4g - (0.0941 - 0.0256p) 4z'

mGal

+ Er mGal

wbere 4z is the elevation difference in meters, flz' in feet, p is in grams per cubic centimeter, and fr is the difference in terrain corrections (due to air-filIed mine tunnels) in milligals. (Note that the Bouguer correction has been doubled; see §2.3.2d.) Hence the average bulk density in the intervening rock is

p - 3.68 - 11.93(flg - 'r)/4z g/cnT'

(2.29a)

or p - 3.68 - 39.06( flg -

Er )/flz'

Hussain, Walach, and Weber (1981) discuss underground surveys. (b) Dens'-ty from borehole gravímeter measurements. Borehole gravimeters (§11.9.l) are able to

make gravity measurements 10 an accuracy of about S I'Gal (Schmoker, 1978; LaFehr, 1983). Terrain corrections are not necessary in borehole measurements. Differentiating Equations (2.29) keeping flz and fl z' ti xed gi ves flp - O.Oll9A(ag/az) g/coi

(2.30a)

ap - O.0391a( ag/az') g/coi

(2.30b)

where ag is in microgals. With meter accuracy of ± S I'Gal, the errorin fl(4g) can be as large as ± 10 "Gal, and measuring density 10 ± 0.01 g/cM' requires readin~ 12 m (40 ft) or more aparl. The volume contributing most to borehole gravity measurements is the portion closest to the borehole. Half oC the elfecl is produced by rocks within a radius of 0.7az, 80% from 2.4Saz (the radius 01 investigation) and 90% from within 5flz. Borehole gravity measurements (LaFehr, 1983) permit determination of the density sufficiently lar lrom the borehole so that invasion and alteration by the drilling process are unimporlant, in contrast to the lew inches oC effective penetradon achieved by other density logging tools. The main objective of borehole gravity measurements usually is to determine porosity, which is directly related to density. (e) Nettleton's method. A reasonably satislactory method ol estimating near-surface density uses a gravity profile over topography that is nOl correlatable with densily varialions (Neltleton. 1976). For example, a protile across an erosional valley that is not structure-controlled would probably be suitable. but a profile across a structure-controlled ridge might be suspect because density changes associated with the structure may correlate with elevation. Field readings are reduced to Bouguer gravity profiles assumíng different values 01 p lor tbe Bouguer and terrain correetions. The profile that reHects the topography !he least is the one with the best estimate 01 the density. The method is ilIustrated in Figure 2.8; incorreet density assumplions result in profiles either lollowing or inverting the topography. Obviously the density involved is Ihat between the elevations oC the bighest and lowest stalions.

g/cM' (2.29b)

Because tr depends upon p, Equations (2.29) are usualJy solved by successive approximatioDs.

(d) PiJrasnis' method. An analytical approach somewhat similar to Nettleton's grapbical method has been developed by Parasnis (1962, p. 40). Rearranging Equation (2.28) and using EquatioD (2.25),

Cravity instrument5

19

•

TOJlOllrap"y

U

-

Observed llra vily

),0

-; 1.'

-J E

1-0

O

2-0 Bouguer Iravily

-

1-5

-; 1.'

...

.§ 1-0

_ \.1

t:1~

-----2.L

p -

O·S

P - 2.3 ~

O O

0-$

1-0

2-0

lO

(mIles,

figure 2.8. Method for estimilting surfilce densit\,.

we oblain

of t'), the slope oC the best-fil straight lioe through the origio will be p.

( 80bl - 8, + ll8t + 0.3086z) - 8B

- (0.0419: - llsTlp)p

(2.31a) 2.4. GRAVITV INSTRUMENTS

(8ot» - S, + llSL + 0.0941z') - SB - (0.0128:' -llgrlp)p where : is in meters and z' is in fee\. determine the average bulk density for by considering the Bouguer anomaly random error of mean value zero. If we

(2.31b) We wish lo the data sel SB to be a plol

( go", - S, + llgL + 0.3086:)

versus (0.0419: - llgrlp) (or the equivalent in terms

2.4.1. General The absolute measurement oC gravily is usually carried out at a fixed ioslallation by Ihe accurale timiog of a swiogiog pendulum or_ of a falliog weight. Relative gravity measurements may be made in varlous ways. Three types of instruments have been used: the torsion balance, the peodulum and the gravimeter (or gravity meler). The latler is the sole instrument now used for prospecting, thé others having only histoncal interesl.

l~/~~I~~~¿\fV\f:~~-J

20

2.4.2. Absolute Measurement of Gravity

AI\hough Ihe liming of a freely falling body was \he lirst metbod of measuring g. \he aceuracy was poor because of \he difficulty in measuring small time intervals. The method has been revived as a result of inslrumeolation improvemeots and elaborale free-fall installatioos are now located at several national laboratorles. It is necessary lo measure time lo aboul lO-a s and distance lo < ll1m lo oblain an aceuracy of 1 mGal witb a fall of 1 or 2 m. Until recently. tbe standard method for measuring g employed a modilied form of \he reversible Kater pendulum. The value of g was obtained by liming a large number of oscillations.

-

Cravity methods ~ Strip record

,•

'K-C?Lam

,

..

p

A'

'

l' 11

Reftectins plates

Mirror-_--lo{

.1'

2.4.3. Relative Measurement of Gravity (a) Partable pendulum. The pendulum has been used for bOlh geodetic and prospecting purposes. Since g varies inversely as the square oC \he perlod T. we have

Ditrerentiating. we get

I1g - -2gAT/T - -2g(7; - 7¡)/T1

(2.32)

Thus if we can measure the perlods al two slatioos lo about 1 p.s. the gravily ditrerence is accurale lo 1 mGal. This is not difficult with precise clocks such as quartz crystal. cesium. or rubidium. The pendulum has been used extensively for geodetic work, both on land and at sea (in submarines). Porlable pendulums used in oH exploration during \he early 19305 had a sensitivity oC about 0.25 mGal. Pendulum apparatus was complex and bulky. Two pendulums, swinging in opposite phase, were used to reduce sway oC tbe mounling; Ihey were enclosed in an evacuated. thermoslatically conlrolled chamber lo eliminate pressure and temperature ef· rects. To get tbe required accuracy, readings took about! br. (b) Torsion balance. A Cairly complete aceounl of tbe salient features of tbe torsion balance can be found in Nettlelon (1976). Figure 2.9 is a schematic of tbe torsion balance. Two equal masse~ m are separated botb horizontally and vertically by rlgid bars, tbe assembly being supported by a torsion tiber witb an attached mirror lo measure rotation by the deftection of a light beam. Two complete beam as. semblies were used to reduce tbe etrects of supporl sway. Readings were taken at tbree azimuth posi·

Figure 2.9. Torsion bil/ilnce (schemiltic).

tions of Ihe beam assemblies, normaI1y 1200 apart, to gel sufficient dala to calculate tbe required results. Elaborate precaution5 were required to minimize ex· traneous etrects 5uch as temperalure and air convec. tion. Each station had to be occupied for approxi. mately one hour so Ihat daily production was only 8 to 10 stations. The deftection of the torsion balance beam is due to horizontal and vertical changes in tbe gravity field resulting from curvature of \he equipotential sur· faces. Torsion-balance measurements permitted cal· culation of U"y' U"., Uyt ' and IUn - u,."I. The plotted values are usually Ihe horizontal gradient [tbe vector (U". i + Uyt j)] and tbe differentiaJ curvature [a vector with magnitude given by Equation (2.19) and direction relative to the x axis of (1/2)tan- 1(2u,.y/lUyy - U.uD)' Measurements were usually in EOtvos unilS (EU) equal to 10- 6 mGal/cm. (e) 5table-type gravimeters. The RrSI gravimeters dating from tbe early 19305 were oC the stable type but these have now been superceded by more sensi· tive unstable meters. Nettleton (1976) descrlbes a number of different gravimeters. AII gravimeters are essentially eXlremely sensitive mechanical balances in which a mass is supported by a sprlng. Small changes in gravity move Ihe weight against tbe restorlng force of the sprlng. The basic elements of a stable gravimeter are shown in Figure 2.10. Wbereas tbe displacement oC tbe spring is small, Hooke's law applies, tbat is. tbe change in force is proportional to tbe change in lengtb; bence,

!J.F - M 8g - k 8s or 8g - k 8s/M (2.33)

21

Cravity instruments 1"" - ."

---

--~ M _.---

Fulcrum

!

Figure 2.10. Basic principie of the stable gravimeter.

where k is Ihe sprlng constant in dynes per centimeler. To me asure g lo 0.1 mOal, we must detect a fractional change in spring length of 1/107 (because Mg. ks, 8g/g'" 8s/s), bence the need for considerable magnificalion. Mechanically we can malee k/ M small by using a large mass and a weale spring, bUI this method ol enhancing sensitivity is Iimited. The period of oscillation oC this sysiem is

Figure 2.11. Basic principie of the unstable (Thyssen) gravimeter. (After Dobrin, 1960.)

T- 2.,,{M/k)1/2

Substituting Cor M in Equatioo (2.33), we gel (2.34) Thus for good sensilivilY, the perlod is very large and measuremeot of 6g requires considerable time. Slable gravimelers are extremely sensilive lO olher physical efl'ects, such as changes in pressure, temperalure, and small magnelic and seismic variations. (d) Unstable-type gravimeters. Also known as labilized or astatized grovimeters, these inslruments have an additional negative restorlng force operating agaínst Ihe restoring spring Corce, that is, in the same sense as gravity. They essentially are in a state of unstable equilibrium and this gives them grealer sensitivity than stable meters. Their linear range is less than for stable gravimeters so they are usually operated as null instruments. The Thyssen gravimeter, although now obsolete, iIlustrates very clearly the astatic principIe (Fig. 2.11). The addition oC the mass m above the pivot raíses \he center of gravity and produces the instability condítion. If g increases, the beam tilts to the right and the moment of m enhances the rotation; the converse is troe Cor a decrease in gravity. Al present the Worden and LaCosle-Romberg meters are the only types used for exploration. (e) LaCoste- Romberg gravimeter. The LaCosleRomberg gravimeter was the tirst 10 employ a zero-

length spring, now used by almost all gravimeters

Figure 2.12. Lacoste- Romberg gravimeter.

(Askania, Frost, Magnolia, and North American). A zero-Iength spring is one in which the tension is proportional lo the actual length oC the spring, that is, if all external forces were removed the spring would collapse to uro length. The advantage ol tbe zero-Iength spring is that iC it supports the beam and mass M (see Fig. 2.12) in the horizontal position, it will support them in any position (note that cos 6 in Eq. (2.35) cancels out, and g" K(1 - e/s), which always has a solulion since g is tinite). Zero-Iengthsprings are built with initial tension so tbat a threshold force is required before spring extension begins (as with a door spring). To derive the expression for the sensitivity of the LaCosle-Romberg graVÍmeler, we wrile k(s - e) for the tensíon in the spring when its length is s; thus, e is a small correction for the fact tbat lbe spring is not truly zero length. Taking moments about lhe pivot in Figure 2.12, we get Mgacos6 .. k(s - e)bsina - k{s - c)b{ycos6)/s (2.35)

Gravity methods

22

Figure 2.13. Reading a Worden grav;meler.

using the law oC sines. Thus

g - (k/M)(b/a)(l - c/s)y When g inereases by 8g, the spring lenglh inereases by 8s where 8g - (k/M)(b/a)(c/s)(y/s) 8s (2.36) For a given ehange in gravily 8g, we can make 8s as large as we wish by decreasing one or more oC lhe faetors on the right-hand side; moreover, the doser fue spring is to the zero-length spring, the smaller e is and the larger 8s becomes. In operation this is a null instrumenl, a second spring being used, which can be adjusted to restore the beam to the horizontal position. The sensiljvity of gravimeters in use in sudace exploration js generally 0.01 mGal. The instrument requires a constanttemperature environment, usually achieved by keeping it at a eonstant temperature that js higher than fue surroundings.

about 25 cm high and 12 cm in djameter) and wejghs about 2.5 kg. Its only power requirement is two penlight celts for illuminating the scale. A simplified schematie is shown in Figure 2.14. The moving system is similar to the LaCosteRomberg meter. The arm OP' and beam OM are rigidly connected and pivot about O, changing the length of the main spring p'e, which js fixed al C. We have lhe following relations: L.OCP' - L.OP'C .. ff/2 - (a + 9/2) RP.L CP

P'P.L OP

so L.RPP' - ff/2 - a

s - CP

8s - CP' - CP" b9 sin( ff/2 - a)

so

9 ... 8s/( b cosa) (f) Worden gravimeter. TIte Worden gravimeter (Fig. 2.13) is especially portable and Cast to operate. It uses small, very light weight parts of quartz (for example. the mass M weighs only 5 mg) with smal! inertia so that it js not necessary to clamp the movement between stations. Sensitivity to temperature and pressure changes is reduced by enclosing the system in a vacuum flask. The meter also employs an automatie temperature-eompensating arrangemenL The Worden meter js small (instrument dimensions are a few centimeters, the outer case is

The correction factor e that appeared in the treatment of the LaCoste-Romberg meter is negligible ror the Worden meter. Taking moments about the pivot ror the case where 9 - O. we get

Mga - ksbcosa When g increases to (g

+ 8g),

P moves along the

Field operations

;'

/' /

""

23

- --- -"\ ,

/

/ /

\ \

I f

,

\

I

o

....

-.,

----r-~tJ

\

Q

\

I

I

\

\ \

,

I \

,

I

\

"- ....

.....

---

\

-

\I -k p

P'

lI+ d ll

I /

be

Figure 2.14. Basic principIe of the Worden gravimeter.

circle to P' and

M( g + Sg) a cos 9 - kb( s + as )cos( a + 8/2) When 9 .. O, to the first approximation this becomes

M(g+6g)a - kb(s + as){cosa - (lI/2)sina} - kb( s + as){ cosa - (Bs/2b)tana) - kb{scosa - Bs(s/2b)tana + Bscosa} Subtracting the first moment equation to eliminate g. we get

Maag .. kb{ cos a - (s/2b)tana) as Using the relation sin a

so

divisions on a micrometer dial. There are several methods ror converting these seale readings to gravity units. Theoretically calibration can be carried out by ti!ting because a precise geometrical system is involved, but tbis is not the usual procedure. Generally. readings are talcen at two or more stations wbere values of g are a1ready known. If the value oC ag between the stations is large enough lO cover a reasonable fraction of the instrument range. a linear response is usually assumed between them. However. one should occupy several additional stations ir possiblc.

2.5. FIELD OPERATlONS

s/2 b, we finally get

8g- (k/M)(b/a)(cos2a/cosa)as (2.37) As in the LaCoste-Romberg meter, the sensitivity can be increased by decreasing the factors (k / M) and (b/a); in addition the factor (cos2a/cosa) approaches zero when a approaches 45°, thus Curnishing another method oC obtaining bigb sensitivity. In practice the sensitivity is about 0.01 mGal. Like the LaCoste-Romberg instrument, tbe Worden meter is read by measuring the Corce required to restore the beam to the horizontal position. (8) Calibation of gravimeters. Both the Worden and LaCoste- Romberg meters are null instruments and changes in gravity are shown as arbitrary scale

2.5.1. Land Surveys Gravity exploration is earricd out both on land and at sea. Although some attempts have been made lO develop an airbome instrument, tbis mode oC operation is not yet practica! (Paterson and Reeves, 1985). The distinction between reeonnaissance and detailed field work is based on the objective, that is. whether the purpose is to find Ceatures oC interest or to map them. Station spacings in field work with the gravimeter vary from 20 km to as Ji ttIe as 5 m. The station interval is usually selected on the basis of assumed depth and size oC the anomalies 50ugbt. For oil exp!oration, one station per 2 to 4 knr is desirable because structures associated with oil accumulation are usually !arger than tbis and hence their

Craviry merhods

24 anomalies would not be missed with such spacing. While a more-or-Iess uniform grid oí stations is desirable, stations are often ron on loops that are operationally easier. Stations 0.5 to 1.0 km apart on loop s roughly 6 X 6 km in size might be typical for a petroleum survey. In mineral exploration, gravity is normally employed as a secondary detail method for confirmalion and further anaIysis oC anomalies already outlined by magnetic and/or electrical techniques. The spacing is determined main1y by knowledge gained from the earlier surveys. Measurements are usually made at the same locations as the magnetic or electrical stations, common1y 15 to 30 m apart. Mierogravity engineering and archaeological surveys (for example, searching for cavities or bedrock) sometimes involve station spacing as c10se as 1 m (Arzi, 1975).

Field measurements with modero gravimeters are straightCorward. The gravimeter must be leveled precisely for each reading. It may be difficult to get a stable null in swampy ground and when the wind is strong, but extra care and time generally give an acceptable measurement. Similar problems arise in marine gravity work using instruments that rest on the sea ftoor. For reasonable speed of operation, a vehicle normally is used Cor getting lrom stalion to station. Precision is required in surveying gravity stations. Achieving the required precisíon (10 cm in elevation and about 30 m in latitude for 0.03 mGal accuracy) often involves the major cost of field work. Gravity measurements typícally proceed much raster than the surveying, and three or lour survey teams may be required to keep ahead oC one meter operator. InertiaJ navigation somelimes cuts tbe cost of determining location and elevation, especially where helicopter transport is used in areas oC dífficult access (LaFehr, 1980). An inertial navigalion system (§D.?) senses acceleration by means 01 three ortbogonal accelerometers mounted on a gyroscopically stabilized plallorDlj changes in horizontal and vertical position are determined by integrating twice over time. Very smal! errors teOO to accumulate rapidly lo produce large errors, but these can be reduced to acceptable amounts if the helicopler stops every 3 lo 5 min during which time the drift rate can be determined. This time interval is compatible with the travel time Crom station to station. Lynch and King (1983) claim 0.8 m elevation accuracy and 15 m horizontal accuracy in a survey in the mountainous overtbrust b¡;lt oC the Rocky Mountains, to yield Bouguer values with 0.3 mGal accuracy. In a highpreclsion survey oC a linúted area in northero Canada checked by leveling, e1evations were determined to

0.9 m and horizontal positioning to 0.43 m, so ¡nerlial navigation can achieve remarkable accuracy. With a helicopter survey, slations can be located on a more uniform grid than with land surveys (which are usually run around the perimeler on traverses), so that interpolation errors are considerably reduced.

2.5.2. Orift Correction Gravimeters change their null reading value gradually with time. This drill resullS mainly Crom creep in the springs and is usually unidirectional. Modero instruments, however, have very titde drift. Gravity readings also change with time becuase 01 tidal efCeets (§2.3.2f). The net result oC driCt and lidal effects is that repeated readings at one station give difl'erenl values. Drilt corree/ion is accomplished by reoccupying some slations. The maximum time belween repeat readings depends on the accuracy desired, but is usually 3 or 4 hr. A drift curve is shown in Figure 2.15. Its oscillalory shape is determined by tidal effects. It is not necessary to use the same station Cor checking drilt because any station can be reoccupied. lntermedi ate gravity slations occupied only once can then be corrected lor the drift that occurred. Ir lhe meter movement is nol c1amped between readings or is subjected lo sud den motion or jarring (as during transport), somewhat erratic changes (called tears or lares) may be produced. If the instrument is bumped, it is wise lo reread a known station immediately. Sínce there is no way oC allowing for erratic changes. we can only correet those points occupied while the drilt curve is smooth.

2.5.3. Marine Surveys (a) Locating marine stations. Considerable gravity work has been done on the surface 01 water-covered areas and also on the sea ftoor. Locating the station is usually done by using a radionavigation system such as Shoran, Raydist, or RPS (see §B.6). lbe accuracy ol offshore location is usually lower than on land but elevation determination is not a problem iC appropriate allowance is made for tidal variations.

Standard gravimeters have been adapted lor operation on the sea ftoor to depths 01 200 m. This method of measurement is suitable for most inland waters and coastaI areas. The meter is enc10sed in a pressure housing that is supported on a squat tripod with disk reet. About (b) Remote control systems.

Field operations 030 o~o

;;

~ .:: 'C

el

O 10

1 4

5

__ "

~~mGal) Drift

\

~

i ' :

,

0·9(}

Á'

Ol,:er "1ghl

drtft'

4~

t

25

I

: I

~~ , . ",'

Vanou\

base ... tallo,~ns;----t--~~n

Elilpsed lime (minull!s)

Figure 2.15 Cravimeter drift during a field survey.

Figure 2.16. Photogrdph of a shipboard 8ra~imeter.

hall \he total weight of tbe assembly is in the tripod in order to provide maximum stability when it is restíng on \he bottom; the overall weight of one model is 300 kg. The assembly is connected to a ship by a cable (rom which it is lowered into position on Ihe boltom. Leveling is achieved by small molors lbat raise or lower \he disk feet. Al\hough the hish sensitivity of this equipment is an advantage, operation in deep water is slow because \he assembly must be raised to the surface between stations. A problem in reoccupying statioos is \hat \he sea lloor location may be different from that previously occupied, even when the surface location is identical. This method is now tittle used. r

(e) Shípboard operations and the Eotvos eorreetion. Shipboard gravimeters (Fig. 2.16) are used for

most gravity measurements at sea. Shipboard gravimeters are mounted on an elaborate gyro-stabilized platform (Valliant and LaCoste, 1976) localed in lhe part of a ship where there is mínimum movemenl due to ron and pitch. If a gravimeter has a velocity during a measurement, the centrifugal force acting on the meter is different from that when it is al rest. An eastward component of velocity adds lo the velocity owing to tbe rotation of the Earth and hence increases the centrifugal force and decreases the gravity reading. A westward component of velocity has the opposite

Cravity methods

26 elrecL A norlhward component creates a new component of centrifugal force, which is added vectorially to the first. The correction for the velocity of the meter, AS", called the EotvOs correction, is given by

useful for regional studies and reconnaissance of large anomalies. Ormeoa (1984) achieved an aecuraey of S mGaI averaged over 20 km.

Ag" - 4.040Vcos /fI sin a + 0.OO121lV2 mOal (2.38a)

2.6. GRAVITY DATA PROCESSING 2.6.1. Noise, Regionals, and Residuals

Ag" - 7 .503V' cos /fI sin a + O.004154V'2 mOa! (2.38b) wbere V is in kilometers per bour. V' in knots, /fI is the latitude, and a is the course direction with respect to troe nortb. The accuraey of shipboard gravity depends mainly on the accuraey of the Eatvos correction. The error in the Eatvos correction due to errors in Vandais

d(Ag,,) ... (O.0705Vcos/flcosa) da +(4.040COS/flsina + 0.OO2422V) dV (2.39)

with V and dV io kilometers per hour and da in degrees. Thus the sensitivity to velocity error is greatest for an east-west course and the sensitivity to course-direction error is greatest for a north-south course. Assuming that the velocity al the moment 01 gravity reading involves an uncertainty of 0.2 kmjhr and instanlaneous beading error of 10. /fI - 40 0, and V-lO kmjhr, then d(Ag,,)-O.62 mOal lar an east-west course and 0.54 mOal lor a nortb-south

course.

2.5.4. Airbome Gravity The maio difficu1ty with airbome gravity surveys arises from very large and rapid changes in Sobo caused by changes in the aircraft altitude, linear acceleration, ron, and headiog. These elrcet, can be corrected for in shipbome gravity work because changes are slow and the vetocity is low. Hammer (1983) tells of using a heticopter ftying (in the middle 01 the nigbt to avoid air lurbulence) at a speed 01 SO lO 100 kmjhr at elevationS 01 300 to 4,000 m using an autopilot directed by a navigationsystem computer (a buman pilot is not sufficiently precise). His data, smoothed over a 2 min window (2 lO 4 km), suggest that airbome gravity would be

Because a Oouguer map sbows horizontal dilrerences in the acceleration oC gravity, only borizontal cbanges in density produce anomalies. Purely vertical cbanges in density produce the same elrect everywbere and so no anomalies result. The gravity field is a superposition af anomalies resulting from density changes (anamalaus masses) at various depths. Some anomalous masses tie at deptbs in the zone 01 interest, some result from deeper masses, and some from sballower ones. As the source of an anomaly deepens, the anomIay become more spread out and ilS amplitude decreases. The smoothness (or apparent wavelength) af anomalies is generally roughly proportional to the depth of the lateral density changes. The depth range we wish to emphasize depends on the objectives of the interpretation. Sballaw anomalies are of interest in mineral exploratioD but are usually regarded as undesirable noise in petroleum exploration. As in any geophysical tecbnique, the mast useful factor in interpretation is knowledge of the local geology. Wbereas it is possible for a distributed anomalous mass 10 givc an anomaly that appears to originate from a more concentrated deeper mass, a concentrated mass canoot appear to originate deeper. The borizontal extent and smoothness of an anomaly is therefore usually a measure of the depth of the anomalous mass, and this property can be used to partially separate the clrects al anomalous masses that tie within a deptb zone of interest from the elrects 01 both shallower and deeper masses. The elrects al sballow masses (near-surface noise) are usually 01 sbort wavelengtb. They can be removed largely by filtering out (smootbing) shartwavelengtb anomalies. Tbe elrects 01 deep masses are called the regional. The gravity field after nearsurface noise and the regional have been removed is called the residual; it presumably represents elrcets oC tbe intermediate zone of interest. The major problem in gravity interpretation is separating anomalies 01 interest from the overlapping elrects of other features; usually the main obscuring elrects result from deeper features. Residualizins attempts to remove the regional so as to emphasize the residual. However, the separation usu-

Gravity data processing a1ly is not complete; both regional and residual are distorted by the effects of each other. Residualizing can a1so be thought oC as predicting the values expected from deep features and then subtracting them from observed values, so as to leave the shallower elfects. The expected value of the regional is generally determined by averaging values in the area surrounding the station. Several methods of removing the unwanted regional are described in the next section. Gupta and Ramani (1982) discuss the application oC dilferent residualizing methods.

27 Gravity station loeations sbould be sbown on the final map to aid in distinguishing residuals that are well controlled from those possibly resulting from interpolation. The result obtained by smoothing profiles or contours is inevitably biased by the interpreter, but tbis is not necessarily bad. If the interpreter is experienced and uses additional geologie knowledge to guide him. it may be a decided advantage. It should be nOled tbat nonsmoothing methods oC residualizing also involve subjective elements. such as tbe choice of order ror surface fitting, oC grid dimensions in grid residualiz.ing. and so on.

2.6.2. Graphical Residualizing

,J.

Graphical residualizing is done by smoothing either profiles or maps. A simple example of removing the regional by smoothing is illustrated in Figure 2.17. The profile in Figure 2.17a shows disturbances oC dilferent sizes; tbe smootb, nearly linear slope is tbe regional. In Figure 2.17b, the regional contours are regular and the residual obtained by subtracting the smoothed contours Crom the map values should be reliable. Tbe emphasis in drawing a smooth regional should be on "smooth" and most of the errors or failures in residualizing are caused by the regional not being sufficiently smooth. "Smooth" implies both smooth in sbape and systematic in contour interval. Orten profiles are plotted for several parallel lines, generally in Ihe dip direction. Smooth regionals are then drawn on these parallel lines, making certain that they are consistent on a11 profiles. Often cross profiles are drawn linking tbe parallellines into a grid to ensure that tbe regional is consistent over the grid. This approach is especially suitable when tbe regional trend is mainly unidirectional. If the survey has been carried out with close, uniform spacing of stations and lines, the station values themselves can be used instead of contour values to plot the profiles, tbereby reducing errors because oC con tour interpolation. Once the regional has been contoured, the residuals are obtained by subtracting tbe regional from the Bouguer map, eitber graphically or numerically. Grapbical residualizing is sometimes done by drawing cantours of constant difference through the points wbere regional and observed contours intersect. When tbe regional is so irregular that the directional trend is nOI immediately apparent or when there are severa! superimposed regional systems, residualizing may be done iteratively, that is, one first determines and removes the most obvious regional and then finds a second-order regional from the first-order residual, and so on.

2.6.3. Surface-Fitting Residualizing Methods The regional is sometimes represented by a low-order analytic surface. The parameters of the analytic surface are usually determined by a least-squares lit (Agocs. 1951) or sorne similar operation. How close1y the surface fits the data depends on the order of the surface and the magnitude of the area being fitted. Nettleton (1976) iIIustrates orders oC lit Cor a onedimensional case (Fig. 2.18). The regional surface is often tbat given by a polynomial or the low-order components oC a 2D-Fourier surface [Eq. (A.52a)]. The selection of order is usually made by examination of trial fits of several dilferent orders. Surface fitting is sorne times done to isolate and emphasize trends. Results from Coons, Woolard, and Hershey (1967) are shown in Figure 2.l9. The trend becomes more evident as tbe order increases up to sorne point, about tenth order for the data oC Figure 2.19. The residual for low order still contains appreciable regional trend and thus low orders are not very elfective in separating the regional from the residual. Likewise, high-order surfaces are not effective because much oC the sought-after anomaly is mixed with the regional in the surface fit.

2.6.4. Empirical Gridding Methods Gridding provides a simple way of predicting the regional by regarding it as the average value of gravity in the vicinity of the station (Grimn, 1949). Usually the values averaged are those on the circumrerence oC a circle centered at the station:

g(r) = (1/2,") fffg(r, 9) d9

(2.40)

Fi8ure 2.17. Craphical residualizin8 (After Sheriff, 1978). (a) Removin8 the re8ional on a profile across a local uplift and a (ault.

T

Cravity data processing

29

(b)

Figure 2.17. (Continued)

(b) Removing rhe regional by contour smoothing.

e

Figure 2.18. /IIustraling least·squares surface·filting. Curve represents a gravify profile and curves 1,4,8, 16 represent fits of rhe respective orders. The surface (ir. and hence the residual. depends on the dimensions that are (itted (from Nettleton. 1976).

Cravity methods

30

IOUGUER ANOU"LY M'"

SURFAer InH ORDER

- RI:SIDlUAL 10TH ORDER

RESIDUAL InH ORDIER

Figure 2.19. Fits 01 surfaces of different order and the respective residuals. ("'fter Coons, Woolard, and Hershey, 1967.)

In actual practice the integral is generally replaced by a sum of discrete values (as·in Fig. 2.20a):

,(r) - {,(r,O) +g(r,9,) + ... +g(r,9,,_,)}/n (2.41) where 9", - m(2,,/n). The residual is then

'r - gB - g{r)

(2.42)

where gB is the 80uguer anomaly value. Usually the values of g(r, 9.. ) are obtained by interpolation from the gravity map contours. The result depends somewhat on the number oí points selected but even more on tbe radius oí tbe cirele. If tbe radius is so small

that part of the anomaly is ineluded on the circle, then the anomaly magnitude will be too small; if the radius is too large, the average may be biased by other anomalies. The radius is usually ol the same order ol magnitude as the depth ol the anomaly to be emphasized, but botb shallower and deeper anomalies will still contribute to tbe results. The grid spacing for points to be calculated is generally about half the radius used for averaging. Sometimes averages over several cireles of difl'erent radü Ij are used; successive cireles are assigned difl'erent weights, w/:

gr - (c/s 2){ go + w,g(r,) + ~g(r2) + ... } (2.43)

31

Gravity data processing ___ '2:\ - - - - - -.... #

(al

l.

--

" i.

V1/

/-~

"

\

"

....

L-",...

'-

'\ \ .....

~ )'

_/

/

(b)

\i

Figure 2.20. Analytical separation (b) Second-derivative me/hado

i

o(

the residual and the regional. (a) Griffin me/hod.

¡

J I I I I • I II

Analytical re¡ional

-

G,aphical ,esion.1

- - -

Observed S,.,ilY

GraphlCal ..sidual

H~AnOmaIY

,¿~HaIO AnalYllcal ,es,duol

Figure 2.21. Comparison of 8raphical and analytical methods gravity.

wbere e is a constant, s is a scale factor, and -1. Usually tbe values on the various circ1es are read at grid points as in Figure 2.2Ob. Equation (2.43) is simply tbe expression ror a 2-D convolutioD, and residualizing can be tbought of as a convolution or filtering operation. In &I'apbical metbods tbe interpreter usually draws tbe regional so that all residuals are eitber positive or

E~ -

o(

removing re8ional

negalive according to bis concepl ol the density contrasl expecled to cause tbe anomaly. However, in nongrapbical metbods, tbe average value ol the residual is usually set at zero so Ihat both positive and negative residual s result. lbis is illustrated in Figure 2.21. A consequence of Ibis is that each anomaly is surrounded by a "balo" of opposite sign, whicb does not indieale a separale anomaly.

Cravity metho ds

·32

2.6.5. Second Vertical Derivative Methods TIte second vertical derivative euhances near-surface elfects at the expense of deeper anomalies. Second derivatives are a measure of curvature, and large curvatures are associated with shallow anomalies. The second vertical derivative can be obtained from the horizontal derivatives because fue gravity field satisfies Laplace's equation

where 80 js the gravity at the statio.!!,. where the second derivatjve js being determined. 8•• g2' . .. are averages over surrou nding circ1es of various radii. "'11. W¡, ..• are weigbting coefficients such that I:~ O, e is a numerical factor, and s is the grid spacing. For example, if the survey is on a square grid and the successive radii are s, s.¡2, and s.¡5 (as in Fig. 2.20b), one form of equation (2.46a) is

(Henderson and Zietz, 1949). Gupta and Ramani (1982) show an application to mineral exploralion. For the one-dimensional case, the first derivative can be estímated by dividiDg the difl'erence between readings at two nearby locatioDS, Xl and X2' separated by fue distance b:

TIte second derivative is obtain ed from the difl'erence between nearby first derivatives:

• [{g(X3) - g(x2) }/Ax -{g(X 2) -g(xl )}/Ax ]/Ax .. {g(x 3) - 2g(X2) +g(xl )}/(A x)2 (2.45) Equation (2.45) has the same form as Equation (2.43) (a weigbted sum of the values at nearby points), and Equation (2.43) yields an estímate of the second vertical derlvative for appropriate values of A number of matberoatical treatments have been cleveloped (Henderson and Zietz, 1949; Elkins, 1951; Dean, 1958) to extraet the vertical second derivative from the average values at varlous distances from the station. Generally values over concentric circles are weigbted lo produce an expression of the form [com. pare with Eq. (2.43)]

2.6.6. Wavelength Filtering The foregoing methods of separating residuals from the regional are based on the degree of smoothness (or wave1ength - l/wave numbe r; see §4.2.2d) of anomalies. Filtering can also be done by transforming map data lo a wavenumber-wavenumber domain using a two-dimensional Fourie r transform [Eqs. (A 57)], removing certain wavenumber componenls (that js, filtering), and theo doing an inversc transfo rmatia n to reconstitute the map, but with certain wavelengths removed. What are removed are usually tbe small wavenumbers (large waveleogths) of the regional, so that fue wavenumber components involved in the inversc transform are the large ones which correspond to the short wavelengths of the residual . Wavcnumber filtering encounters the same problem as other residualizing schemes. TIte wavenumber spectra of DIOst featores are broadb and, so spectra of features at difl'erent depths overlap and consequently the fcatures canoot be separated completely by filtering.

w,.

2.6.7. Fleld Conti nuatio n

The fact that gravity fields obey Laplace's equation permits us to determine the field over an arbitrary surface if the field is knOWD completely over anothe r surface and no masses are located between the two surfaces. This pracess is calJed continuation. Following the method of Grant and West (1965, pp. 216-21 ), we let the plane z - O separate free space (z < O) from the regían containing masses (z > O) (Fig. 2.22a); P is a point in free space, Q (2.46a ) locates a point mass, and R is tbe distance PQ. If U,.

Gravity data processing

33 P(x",Yo.-

The derivatives witbin Ihe braces are the componenls of !he gradienls normal lo Ihe surface ds. Sctting the radius of the hemisphere equal to infiníty causes Ihe contribution of the curved surface 10 vanish because of Ihe factor l/Rs. and tbe integral reduces 10

h)

;r

4",U,. -

1i {l4( a/an)(l/Rs ) " y

z

-(l/Rs) aus/an} dxdy (2.41a)

(a)

The intesration is talten over that portion of Ihe xy plane where the anomalous field is significantly larger Ihan zero. We now follow the same procedure using the hemisphere in Figure 2.22b. Because v 2 U" - O wilhin the hemisphere (Eq. (2.11a)1, we gel

;r

- (l/R s ) aus/an) dxdy (2.41b) z

The ri&ht-hand sides oC Equations (2.41a) and (2.41b) appear lo be Ihe same, bUI, in faet, Ihey are dilferenl because n, !he outward uníl normal lo the surface Figure 2.22. The continua/ion theorem. (Afler Gran/ and Wesl. 1965.) (a) Hemisphere S on positive side of xy ds. is upward (- z directioD) in Equation (2.41a) plane. (b) Hemisphere on negative side of xy plane. and downward (+ z direclion) in Equation (2.41b). Thus, Us / n - - g in Equalion (2.41a) and + g in Equation (2.41b). Also, Ri - (x - xo)l + and U" are the potentials at P and Q. Equation~ (y - )b)2 + (z + h)2, so, on the xy plane, (2.6a) and (2.l3b) give (b)

a a

V,.

-.,f (p/R) dv

(a/an)(l/Rs) - Iim (a/az)(l/R s ) ' .... 0

JI'

v 2U" -

- tim { - ( z + h) / R} }

-4".yp

' .... 0

- -h/R~

E1iminalins p, we have

wruch is independent of Ihe direction oC n. Thus. subtractins Equation (2.41b) from (2.47a). we obtain We now apply Green's theorem (Eq. (A.28)1 lo tbe bemisphere in Figure 2.22a with W - l/R. U U" inside S, and U"- Us on the surface. Sinee V 2(l/R) - O, we gel

\

Ji (g/R s ) dxdy " y

fs{

- fs {Us 8/8n(1/R s ) -(l/Rs) aus/an} ds

where

Ri - (x -

+ (y

+ h2.

To get aU,./az al p. we replaee in Ri with z2, difl'er- fl'(1/R)V U"dv - 4".U,. Us v(l/R s ) entiale, and Ihen replace z wilh (- h) (nole Ihat g -(l/Rs)VUs ) . ds on the xy plane is not a function of z). The result is 2

-,-

U,. - (1/2",)

xo)2

- )b)2

h2

au,./az - g,. - (1/2".)

h1f (g/R~) dx dy " y

(2.48)

34 Since (h/R s ) - cos8 io Figure 2.22b, (g/2,,) can be regarded as a surface density of mass replaciog \he mus below the xy plane (compare with Eq. (2.14»). Equatioo (2.48) is the upward continuation equatioo that allows us to calculate the gravitatiooal acceleratioo anywhere io free space from a k.nowledge of its values over the surface. Upward continuatioo is effectively smoothing. Although upward contiouation is oot dooe much in gravity analysis, it is used in magnetic interpretation to compare measuremeots made at different flight elevations. If we can calculate the gravity field over a surface closer to the anomaly sources, the anomaly should be sharper and less confused by the effeets of deeper features. This process, ealled downward continuation, was described by Peters (1949). lt involves calculating a gravity value at depth from gravity values and derivatives 00 a shallower surfaee. The derivatives are usually evaluated by averaging over cireles of different radü as described in Seetion 2.6.5. The main theoretical limitation on the method is siogularities assoclated with masses through which the continuation process is carried. The main practical limitation is imposed by uncertainty in the measured field; because derivatives involve differences, their calculation magnifies uncertainties. The result is that minor noise is increased in the downward-continued field and this noise may outweigh the benefits 01 sharpening anomalies. We begin with Laplace's equation (2.11b) (thus implicitIy assuming that we will not continue through any masses) and the expressions for second derivatives calculated by finite differenees (Eq. (2.45)]. For the point (xo, )'0,0) and station spacing s, we write

Gravity methods equation, we get

g(xo,)b, +s) - 6g(xo, )b,O)

- ( g( Xo + s, )'o, O) +g(xo - s, )'0,0) +g(xo.)b + s,O)

+ g( xo.)'o - s,O) +g(xo'.Vo. - s)} (2.49) AlI of these terms can be found from the gravity values read from a grid except ror the last term, which can be found from Equation (2.48). Similar but more eomplicated procedures use concentrie circles passing through grid statioos. Other methods employ Fourier transform theory (see Grant and West, 1965. p. 218).

2.7. GRAVITY INTERPRETATION 2.7.1. General

After the camouftaging interference effeets of other reatures have been removed to the best ol our ability, the ioterpretation problem usually is findiog the mass distribution responsible for the residual anomaly. This orten is done by it,rativ, mod"ing (Bhattacharyya. 1978). The field of a model mass distribution is calculated and subtracted lrom the residual anomaly to determine the efrects for which the model cannot account. Then the model is changed and the calculations repeated until tbe remainiog effects become smaller tban some value considered lo be "c1ose eoough." To limit the number or possible changes, we inelude some predetermined constraints, for example. we might change only the upper surface oC the mass distribution. Before iterative modeling beeame practical. inter+ g(xo,)'o - s,O)} /s2 preters generally compared residual anomalies lO anomalies associated with simple shapes. and this procedure is still useful in many situations. Simple shapes can be modeled with a microcomputer (Reeves and MacLeod, 1983). A gravity anomaly is nOl especially sensitive to minor variations in the shape ol the anomalous mass. so that simple shapes often If we talte z to be positive downward, then yield results that are close enough to be useCu!' Study g(xo, )'o, +s) is the gravity value a distance s below 01 the gravity effcet of simple shapes also helps in the statioo g( xo. Yo. O). Substituting into Laplace's uoderslanding the types oC inCormation that can be

... Gravity interpretatían

35

10

0·8

.

0·6

E

~

00

0·4

0·2

O

.'11:

t

P

.t

9

7!

•

:

Figure 2.23. Cravit,· effect of

leamed, ror example, in determinins what aspects oC an anomaly indicate the depth. shape, density contrast, total mass, aríd so Corth. In the followins examples. the densily symbol p is the densily contrast with respect lo the laterally equivalent material (in numerical relations, p is the dilrerence in specific gravily because density is usua11y given in grams per cubic centimeters even where linear dimensions are given in English units).

iI

sphere.

where k =4'ITy/3

= 27.9 X 10- 3 when a. x,: are in meters - 8.52 X 10- 3 when a, X,: are in Ceet Note Ihat : is the deplh to the sphere center rather than lo the 10p oC the sphere and that the profile is symmetrical about the origin taken direcdy above the center. The maximum value of g is

2.7.2, Gravity Effect of a Sphere The gravity elrcet oC a sphere at a point P (Fig. 223). directed alons r, is g, ... yM/r 2 . The vertical component is

gm ... - 27.9

X 1O-lpa l /: 2

when a, z in meters

(2.5la) - 8.52 X 10- 3pa )/:2 when a. : in Ceet

(2.S1b)

g - g, cos 8 - yM:/r 3 2

2 3/2

- kpa 3:/(x + z)

mOal

(2.50)

The depth oC the center oC the sphere, z, can be found from a profile. When g ... gmu/2, : '" l.3XI/2'

. Cravity methods

36 l'

O

.,.

K

"~

I ~ ,

''1I

, " ,

I

,

.lli! ~;¡¡a~L~)~(~-;'.!;'!!i~L_¡;j'1 I---/--+j

y

(1))

(al

l'

.•

Q

(e)

V'illdiusa

Figure 2.24. Cravity effect of d horizontal rad. (a) Three-dimensional view. (b) Projeetion on the pldne eontaining the rad dnd the y axis. (e) Projeetion on the xz plane. (d) Cravity profile along the x axis (L - 00).

""here xl/2 is !he ha/f-width 01 the profile, that is, half the width at the half-maximum value. We can also express the mass of the sphere, M, in temts of xl/2 and g... : M - 25.5g... (xt/2)2 toones

(2.52a)

where Xt/2 is in meten, or, wbere xí/2 is in fcet, M - 2.61g_(xí/2)2 sbort tons (2.52b)

The spberical shape is particularly useful as a first approximation in tbe interpretation of three-dimensional anomalies that are approximately symmetrical.

2.7.3. Gravity Effect of a Horizontal Rod 1be elrcct at P(x, y,O) of a segment of lengtb di of a horizontal rod perpendicular to the x axis al a depth z (Fig. 2.24) with mass m per unít length is

d"~ - rmdl/r2 - rm(rtd+/cos2+)/r2 - rmd+/rt

""bere dI - (rl d+/OO5 2 +). The component along rl

is

dgt - dg, cos+ - ymcos+d+/rt

and !he vertical component is dg - dgl

005' - dgt(z/rl) -

ymzcos+d+/rl

Integrating from lan-l{(y - L)/rl} lo tan- l + L)/rtl, we gel

«y

37

Cravity interpretation Surrac.

I

dI d,

-

-

-

-R-

(a)

Figure 2.25. Cravi/y effec/ of a vertical cylinder. (a) Calculation of gravity over the axis. (b) Ceometry of a cylindrical slice.

Ir the rod is inftnite in length, the limits of integralion would have been ± fI/2 and the result would be

so Ihat its gravily effect is

Sg - y3m cos 4>/(,1 + (1) (2.54)

This is usually a good approximation when L > 10z. The depth z to the center oC the rod in Equation (2.54) can be found Crom lhe half-width xl/1: (2.55)

_ (2'rtpyd/)rdrCOSI/I/(r1

+

(1)

- 2f1yp di sin 1/1 dI#> on eliminating r. Inlegraling first from 1/1 - O to tan-l(R/I) Cor the disk and lhen Crom 1- z lo z + L, we gel, for the whole cylinder,

If the rod is expanded inlo a cylinder oC radius a, the only change in Equations (2.53) and (2.54) is that m '"

flQ2p.

_ 2f1YP[ L + (zl + R2)l/2

-{(z + L)Z + R2}1/2]

2.7.4. Gravity Effect of a Vertical Cylinder The gravity effect on the axis oC a vertical cylinder (which is the maximum value) can easily be calculated. First we find g on the axis Cor a disk of tbickness d( (Fig. 2.25a). We start with an elemenlary ríng oC width dr whose mass is 3m - 2'rtprdrd(,

(2.56)

where 2f1y - 41.9 X 10- 3 when z, R, L are in meters -12.77 X 10- 3 when z, R, L are in feet

38

Gravity methods

i

.

~

o

I..--L._ _...L.._ _...L.._ _" - -_ _L - . _ . . . - J ' - _ - . . I _ -,/:

_.1

-2

-1

o

.1

---.\"---l'

FiBure 2.26. Cravity effect off the axis o( a vertical cyUnder.

Tberc: ue several cases of special significance: 1. If R .....

00,

we have an infinite horizontal slab and

I - 2f1ypL

Tbe resuh is

"T - 'YP'{ (r2 - r l ) + (rf + L2)1/2

- (r; + L Z)II2} (2.58)

(2.57)

This is the Bouguer c:orrectioo giveo mSection 2.3.2d. Note that lis mdepeodent of the depth of the slab aod varies oo1y with its thickness. 2. 1be terrain c:orrectiOD can be obtained usiog a sector of the cy1ioder as sbown mFigure 2.2Sb. We bave 1m - p(rf) drdt so tbat

which is Equation (2.26) with L replacing ~:. 3. When : - O, tbe cy1ioder outcrops and we get 1- 2,,'rP { L + R - (L 2 + R2)112} (2.59) 4. If L .....

00,

we have

g - 2tr'YP{ (:2

If, in addition,

- 'rP'dtsio.d. OD elimioatiDg r. We mtegrate from . taD-1(rl/1) to tao- l (r2l't) aod from t- O to L.

1 -

+ Rz )112 -

l)

(2.60)

O, we havc

(2.61) g - 2tr 'YPR When L::. 1, we can use EquatiOD (2.60) to get tbc gravity off-axis (sec MacR.obert, 1948:151-5 or Pipes ud Hatvill, 1970:348-9). Bccause g satisfies Laplace's cquatiOD, we can cxpress it in a series of

1

39

Gravity interpretatian 10

08

'Q.

...

..

06

N

"-

04

~

__

~

____

~

__

~

____

~

__

~~

__

~

__

~L-

___ xh

O .'C

•

p

Figure 2.27. Crilvily effect o( iI Ihin sheet o( in(inile slrike lens'"

Legendre polynomials P,,(,,) where " - cos' (Pipes and Harvill, 1970:799-805). TaJcing r> z in Figure 2.26, we have Ibree cases lo consider: r > z > R, R > r> z, and r> R > z. For Ihe first case, we get

tbis holds when the slrike lengtb is aboul 20 times Ihe olher dimensions (ineluding deplb). Referring to Figure 2.27. we have th~ following relalions:

(see problem 3)

g(r .. ') - 2'11'ypR{ (R/2r) - (R/2r)J pz(")

+ 2( R/2r)5 P4 ( ,,)

-

... }

(2.62)

For Ihe second case, R > r > z. Ihe result is

g(r.')", 271ypR{1 - 2(r/2R)PI (,,) +2( r/2R)2 P2 (,,)

P - (x - hcota)sina - xsina - hcosa.

r"'psec' z .. r sine a + O - 71/2) - p(sina tan O - cos a) dz - p sin a sec1 8 d8 r _

(x2 + h2) 1/2 •

r2 -

{ (.l'

l

-2(r/2R)4 p4 (,,) + ... } (2.63)

l

,

+ tcosa) 2 + (h + tsina) 2}1/2

The result for the third case, r> R > z, is the same as Equation (2.62). showing Ibat Equation (2.62) is valid whenever r> R. From Equations (2.62) and (2.63) we gel lhe curve in Figure 2.26.

Now we apply Equation (2.9) for a Iwo-dimensional structure. The producl dx dz in Equation (2.9) represenls an element of area of Ihe eross section, Ihal is.

2.7.5. Gravity Effect of a Thin Dipping Sheet

dx dz = , dt- , csc a dz .. Ip sec 2 8 d8

Considerable simplification can be elfected when a body can be considered two-dimensional. In general.

Equation (2.9) now gives (nole tbat r' is the same as

Gravity methods

40

---/ -="-i-",.~

.• ~

- 1

•

•

Figure 2.28. Gravity effect of a semiinfinite horizontal sheet.

, here)

horizontal sheet,

B - 2YP/{ ,,/2 + tan- 1( x/h)}

- 2YPI!'-1 (sin ti tan 9 - cosa) d9

-'1

- 2yp/{sinaln(cosBl/cos9z) - (8z + 81)cosCl} - 2yp/{sinaln('Z/'I) - (Iz

+ 81)costl} (2.64)

If the sheet is vertical, Equation (2.64) simpli. fies 10

1be thin sheet is a ,ood approximation lo a prism unless the thickncss of the prism is somewhat greater than h. the depth to the topo When the dip is steep (> 6( 0 ), the depth can be rough1y estimated from the half·width, for eumple, when h. (, h. O.7xl/1 ' However, when ( is large or wben the dip is small it is nol possible to gel a reliable estimate.

1.7.6. Gravity Effect of Horizontal Sheet s,

Slabs, Oikes, and Faults (a) Horizontal thin sheet.

lion (2.64) is horizontal,

11 -

When the sheet in Equa· " and we bave

and if the sheet extends to infinity in the other direction (that is, x goes to infinity as well) we bave the Bouguer correction as in Equation (2.57) with 1 replacing L. The profile (or a semünfinite horizontal sheet is shown in Figure 2.28. The thin sheet result can be used to approximate a horizontal slab with an error Icss than 2' when 11 > 2/. A fault often can be approximated by two semünfinite horizontal sheets, one displaced above the other as in Figure 2.29. (b) Horizontal slab. Equation (2.67) can be used 10 find the gravity effect of a semiinfinite horizontal slab terminating at aplane dipping at the angle ti (Fig. 2.30). We use Equation (2.67) to get the effect of the thin sheet of thickness dz and then ¡ntegrate to find the result for the slab (Geldart, Gill, and

Sharma, 1966). We must replace x in Equation (2.67) with (x + z tan !l), so tan-1(x/h) becomes tan-1(x + z tan !l)/z} - l. Equation (2.67) now gives

g- 2ypf'a(fT/2 ~

+ 1) dz - 2YP ("'/2 +

(2.66)

If, in additioD, ( ...

00,

we bave, for a semiinfinite

f' 9dz) 1

~

We now have: tan 8 - (x + ztan!l)/z - (xlz)

B - 2yp/( 81 + 9z) - 2YP/[tan- 1{«(- x)/II} + tan-1(x/II)]

(2.67)

+ tan!l

z - x/( tan 1 - tan!l) dz - -X sec Z1 d8/(tan 1 - tan/l)l - -x cos2 !l d81siJl-(8 -!l) 2

- -x cos !l d"'/sirf '"

41

Gravity interpretatían 4 _

;;

~ ~

, -;

~-+

~,,- -~L

« _'JO

____~____~____-~10~___-~5~__~~,,~~+===-=-=-+-=-==-=-=-~_==_=_=_~_~ __ "

(a)

s

~;=====;===~t=~==~==~~--~----~----~-----!,----~---" -~

-15

-10

-5

-2

-3

(h) Figure 2,29, Cravity effect of a faulted horjzontal sheet; t - 300 m. h, - 750 m. h2 - 1350 m. and p - 1 g/cm', (a) Normal faulr dipping ti - 30 and 90·, (b) Ileverse fault. ti - - JO·,

where ." - 9 - {J. Substituting for dz. we get

Thus, g - 2yp [ ,,1/2 - x eos 2 M -.¡, cot

.¡, + ln( sin'¡')

- p eot'¡' } 1::] Using the relalion f ¿x/sirr x - - col x, we can integrate the firsl lerm by parls, that is,

2 - 2YP[ ,,'/2 + x eos P{ ( 1} + fJ)eol."

- In( sin'" ) } - 2yp [ 11'1/2

+ x eos 2 P{ (1}2 + fJ )eot 1}2 - (1}1 +

- -." col ." + In( sin ." )

1:: 1

fJ) eot 1}1

-ln( sin "'2/sin 1/11) } ]

42 /

"...

.--.----

-.- ...........

Gravity metho ds

--- --

- 90 0 elCcept where Fi8ure 2.30. (jr,wity effect of a semiinfini/e slab. t - 300 m, a otherwise noted on 'he curves, p - 18m/cm J,

so

Figure 2.30 sbows that

IJ(COl"'2 - col "'1) -IJ(A C/CP - BC/CP) -IJ(A B/CP )

-1J(t/coslJ)/(xcoslJ) - IJt/( x cos2 1J) 10

tbat we fina1ly get 2 , - 2yp{ (./2 + IJ), + xcos 1J( 12 - Fl )}

(2.68)'

A1so,

cot "', - {( ,,/cos IJ) + x sin IJ} /x cos IJ 2 - (:, + xsinlJ coslJ) /xcos 1J

Substituting in Equati on (2.68) and noting &hat t (%2 - '1)' we obtain

g - 2yp{ (,,/2 + lJ)t + (82 -IJ)

where F, - "', cot +, - ln( sin +,) 8,- tan-I« x/z,) + lanlJ}

"', - 8, -

IJI

Equation (2.68) is sometimes given in anothe r formo From Figure 2.30 we have

'1 -

r./sin( ",/2 + ¡J) - rtlOO5¡J x/sin x/sin '2 - r2/OO5 IJ

X('2 + xsinlJ toslJ) - (B¡ - IJ)( %1 + xsin IJ tos IJ)

+ X cos 2 1J ln( r2/'I)} - 2yp { (.t/2) +

(%282 -

'181)

+x(82 - 81)sin¡Jc oslJ + x cos2¡J 1n( '2/rl) }

(2.69)

43

Cravity interpretation l

r

FiBure 2.31. Cravily effecl of a di/ce. Pro files are perpendicul.Jr b - 1, Z, - 1/3, z2 - 4/3. /l- 45· (solid line), O· (dashed line).

Ir the end of the slab is vertical, Equation (2.69) gives

fJ -

O and

lO the di/ce. L -

oo.

tbis is

g-2yp[Z2(~-'4) -ZI('I-'3) +sinfJcosfJ{ X('2 - '1)

g- 2YP{(,,'/2) + (Z2~ - ZI'I)

-(x - b)('. - ',)}

+xlnh/'I)} (2.70)

'1

If the slab outcrops, - x, and

g - 2yp { (,,'/2)

'1 -

O,

'2 -

+ cos2fJ ( x ln( '2/(1)

-(x - b)ln('4/")}]

t, (JI - ,,/2,

9,) +sinfJcosfJ{ x('2 +', - '. - '1)

- 2YP[Z2('2 - '.) - zl(91

-

+ //2' + x( '2 - ,,/2) sin fJ casfJ

+b(6. - 6,)} +cos 2fJ{ x In( '2"/'.(1)

+xcos2fJln('2/x)} (2.71)

+b In( './'J)}] Figure 2.30 shOW5 curves for a senilinflnite slab. The slope is quite sensitive to the depth of tbe slab but not to the dip 01 the end. (e) Thick two-dimensional dike. The result for the dike in Fi¡ure 2.31 can be obtained by subtractin¡ two slabs, one bcin¡ displaced horizontally with respect to the other. The result is

, - 2ypcos 2fJ{x(F2 -F¡) - (x - b)(F¡ - l)} (2.72)

When the sides of the dike are vertical.

g - 2yp{ '2( 62 - '.) - tl(

(2.73)

fJ - O and

'1 -',)

+xln('2"/'.'I) + bln(,./,,)} (2.74) If the dike outcrops, zl - O, '1 - tr/2 - ',. and the result is

-

x, " - (x - b),

91

g -

2yp [ t2 ('2 - '.) + sin fJ cos p X{X('2 -'.) - b(tr/2 - '.)}

+xcoS 2 fJln{'2(X - b)/,.x} usin¡ Equation (2.68). In terms of Equation (2.69),

+b cas 2 fJ 1n{ './( x - b)}]

(2.7S)

Crdvity methods

44

..

::: J

-

~ 2 110'

----~----+_----r_--~----~~--~----+_--~r_--_+---xn

- 20.000

- 15.000

-10.000

- S.OOO

o

-1

S.OOO

10.000

U.OOO

20.000

-2

-.

-3 -5 -6

Figure 2.32. Cravity effect of a favlred horizontal bed; t - 1,200 m, z., - 150 m, 1.350 m, zJ - 600 m, z. - 1,800 m. Ir - 60°, and p - 1 g/ c~. (From Celehrl, CiII. and Sharma. 1966.) Z1 -

If the dike is also vertical, this reduces furtber to B - 2YP[Z2(92 - 91) + xln{

I'2(X -

b)/r.x}

+bln{ r./(x - b)}] (2.76) An estímate 01 zl' the depth to the top 01 the dike, is not very satislactory in terms ol xl/2' When '1 - b, we find that '1 - 0.67xl/2 wben '1 - 2b, and '1 - 0.33xl/2 wben '2 - 10b, that is, a lactor of 2 depending on the depth extent. In general, the curves become sharper as both zl and '2 get smaller. Also, it is impossible to make a good estimate 01 the width 01 the dike trom the shape of the curve. (d) Fault. lbe gravity efl'ect of the fault shOWD in Figure 2.32 can be obtained by adding the efl'ects 01: (i) A near-surfacc semiinfinite slab. (ü) A dceper infuüte slab 01 the same thickness. (m) A semünfinite slab of negalive density contrast lO wipe out the part 01 the infinite slab under the near-surface slab.

lbe result is I - 2yp [ tri

+ x cos2 11 {(12 - 1i) - (14 - 13) } ] (2.77)

A typical curve is shown in Figure 2.32 (nole that the

constant lerm 2rrypI has been omitted). Obviously one can extend Equation (2.77) to inelude a series 01 horizontal beds at increasing depths.

2.7.7. Applying Simple Models to Actual Anomalles Most of the formulas for simple shapes are far from easy to apply. Even when we can assume that a fleld result can be matched by a specific geomelry, it is sliD tedious to plot profiles from expressions that contain a number 01 geometrical unknowns in addition to the density contrast. Use 01 a collection of characteristic curves reduces the labor involved. We first establish some significant features associated with the profiles. Usually the number ol parameters is reduced by measuring in tenns ol one ol them, prelerably the one that inftuences the significant features tbe least. Orant and West (1965, pp. 273-80) discussed how lO construct curves lor the thin dipping sheet model. lbey concluded that symmctry and sharpness are the most diagnostic features, and thus they developcd curves in terms 01 ratios tha. depend principally on these properties.

2.7.8. Gravity Effects of Complex Shapes lbe gravity cfl'ects of complex shapes are usually calculated by subdividing the body inlO rectangular cells, calculating the efl'ect 01 each with a digital

45

Gravity interpretarian Sccl ion of 1100dimensional 51 rUtlure

Fig/Jre 2.33. Templ,¡te lor calculating /he gravi/y efler/ of two-dimens;on,¡/ bodies 01 irreg/Jlar cross section. (From Hubberl, 1948). ~------------x--

________

~~

,, ,, ,

, ,

1

Ox, ••. z.• ¡)

Figure 2.34. Polygon approxim,¡tion of an irregul,¡, vertical section 01 a /wo-dimension,¡1 body.

computer, and then summing. This procedure is sometimes carried out graphically using templates superimposed on a cross section to divide it into elementary areas, each of which contributes the same effect at a surface station. A template of this type is shown in Figure 2.33. The gravity effect at the cbart apex is

When the structure is not really two dimensional, lhe finite length can be talcen into account by applyíng a correctíon. For a point in the plane ol tbe cross section of a finite structure al a distance r from the section's center of gravity, the correction is

(2.78) where N is the number of segments covering lhe cross section, 41 is tbe angular separation of radial Iines. z is the separation oC borizontallines, K - 23 for z in meters and 7.1 for z in feet.

where g is the actual gravity oC the ftnite body, g", is the gravíty for a body of the same cross section and of infinite length, and Y¡. Y2 are the distances from the cross section to the ends of the body. Graphical methods have also been employed on tbree-dimensional bodies by placing templates over

Gravity methods

46 contours of the body in a horizontal planeo In effect, the body is broken up into a stack of horizontal slabs whose tbickness is determined by the contour interval. This approach is more difficult than the twodimensional procedure because the chart must have a variable scale parameter to allow lor different slab depths. One can calcula te the gravity effect ol a 2-0 body ol arbitrary cross section by using an n-sided polygon to approximate the outline ol the vertical section (Talwani, Worzel, and Landisman, 1959). A simple section is iUustrated in Figure 2.34. The gravity effect of this section is equal to a line integral around the perimeter (Hubbert, 1948). TIte relation is

From the geometry of Figure 2.34 we have the followiDg relations:

: - x tan e - (x - o,)tan., or

: - (o, tan etan.,) /( tan., - tan e) TIte line integral for the side

f.

:de -

BC

f.

Be is

c o, tan e tan.l

B

tan., - tan

e de -

Z,

Thus,

(2.80) In the most general case, Z, is given by

Z, - a, sin., cos.,

[< 9, -

91+1)

cosB,(tanB, - tan.,)

}]

+ tan., . In { COSe,+I(taneI+1 - tancfl,) (2.81) where

1/>, - tan

-1( :1+1 - z, ) x, Xl+l -

This technique has also been used for threedimensional bodies by replacing the contours in the horizontal plane with n-sided polygons. The solution, from line integrals of the polygons, is essentially a more complicated version 01 Equation (2.Sl).

2.7.9. The Dired and Inverse Problems of Interpretation The interpretation techniques outlined in previous sections employ models with simplilied sbapes. Calculating the effects of models is tbe direc:t or forward opproach to interpretation (the same procedure is used in other geophysical methods). TIte initial selection of a reasonable model is made wilh tbe aid of geological inCormation and lhe experience ol the interpreter. Interpretation in terms oC simple models, a more-or-Iess force-lit to the data, is commonly used when data and control are incomplete. Oetailed analysis is complicated by the Cact that model lits are not unique. Ambiguity is well illustrated in the classic paper of Skeels (1947), who shows a gravity prolile that could be produced by a number ol mass distributions. The ínverse problem involves determining the geometry and pbysical properties of the source from measurements oC the anomaly, rather than simply selecting a model and determining the parameters that match tbe anomaly approximately. !be inberent nonuniqueness may make such a task appear to be a waste of time; however, with additional constraints and a computer, this type oC analysis becomes increasingly useful. We outline here a typicalleast-squares procedure for the inverse method. Fírst, assume some mathematical model based on prior Imowledge of the geology and/or ol the geometry plus additíonal inCormalion gleaned rrom the general appearance 01 profiles and contours. Next, linút the number 01 parameters allowed to vary, Cor example, sorne subsel ol strike, lengtb, attitude, depth. and depth extent; this mues the inverse problem more tractable. Next, linearize the problem (because the mathematical model is oflen essentially nonlinear) to simptify computations. Matrices (§A.2) are generally used. TIte solution is obtained by using the model and a given set oC parameters to calcula te simulated data (called the model response), comparing the model response with the values given by the observed data, and then varying tbe parameters lo lit the data more closely. We ilIustrate tbis procedure as follows: 1. The model gives a relation between m parameters P)' For each set of values ol PJ' we gel a model response ¡(PI' P2. P3"'" PIft)' which has a value /;(Pl' P2' P3' ... ' P... ) at eaeh of the n data points.

Gravity interpretation Pllne

47 :-0

Thr«-dirnen.ional anomillous mass

Figure 2.35. Cillculiltion 01 excess mass.

We write e, - /¡( PI' Pl' P3"'" p",) - e,

i - 1,2, ... ,"

(2.82) where e, are the observed data that /¡ are intended to match and el are the errors between the observed data and tbe model response. We begin with an estimate 01 Pi' 2. Because /(Pl' P2' P3'00.' p",) generally involves nonlinear relations between the parameters, we simplify calculations by using a first·order Taylor-series expansion to get equations that are linear with respeet to the derivatives. Difl'erentiating Equation (2.82), we get (2.83a) where each derivative is evaluated using the current set 01 p} values. In matrix notation Equation (2.83a) becomes (2.83b) wbere !I is an (n X m) matrix wbose elements are a/¡/api' !P is an (m X 1) column matrix oC tbe sought·lor parameter changes 8P1' and 8 is an (n X 1) cotumn matrix whose elements are 8e,. 3. In the usual overdetermined case, n ::. m and !JI is not square; we use Equation (A.5b) to solve Equation (2.83b): (2.84) This solution is equivalent to " equations in tbe

m increments 8PI' Since "> m, we apply the method oC least squares (Sherifl' and Geldart, 1983, §10.1.5) to obtain the values of BPl' Tbe PI are tben replaced by P1 + BPi and the calculations are repeated. Iteration is stopped when Eel is smaller tban some acceptable (prespecified) value. Many modifications 01 Ihe preceding procedure exiSI, nOlably methods tbat stabjlize the procedure. If !I is too large to be efficiently handled by tbe computer, procedures such as sleepest deseent or conjugate gradient metbods, may be employed. Marquardt (1963) employs an adjustable damping factor, whereas Jackson (1979) and Tarantola and Valette (1982) introduce a priori informatjon lo constrain the problem (see §3.8.2, example 3, for a similar magnetic procedurc). If tbe model js bighly nonlinear, tbese methods may not work well and Monte CarIo methods may be appropriate.

2.7.10. Excess Mass Altbougb there js no unique solution to a set 01 potentjal field data, jt is possible to determine unique1y tbe total anomalous mass, regardless of jts geometrical distribution. Sometimes tbis is a useful calculation (altbougb potentially dangerous) in esti· mating ore tonnage in mineral exploration. To find the exeess mass, we start with Equation (2.12). Dropping the minus sign, we have

J.g" ds s

4fr"(M

We surround tbe mass by a hemispbere whose upper lace is the datum plane z - O. The surface integral can be separated into two parts: the integral over tbe

Gravity methods

48

circular base in the xy plane and the surface ol the half-sphere. From Figure 2.35, we have

+

q

8"R 2 sin9d9d'; - 4'1ryM

where gIl in the integral over the datum plane z - O is the residual anomaly 8(x, y) and R is the radius of the hemisphere. We take R large enough that M is in effect a point mass at the origin and g" yM/R 2 at the hemispherical surface. Integration over this surface as .; goes lrom O to 2'IT and 9 from 'IT /2 10 'Ir leads lO the value 2'ITyM, so that

ro /00 -00

As a rough estima te, we expect the overburden lO be thicker in valleys and low-lying Hat land than on steep híllsides and elevated plateaus. Abrupt changes in overburden thíckness, however, are common enough. In any gravity survey, and particularly in mineral exploralion, it is worthwhíle lo consider the extent 10 which gravity anomalies may be caused by varialions in overburden thíckness. From the Bouguer correction given in Equation (2.23) and the effect ol a semiinfinite horizontal slab, we can gel sorne idea of the magnitude of the overburden effect. The maximum gravity variation that resulls from a sudden change 6h in overburden thickness, where the density contrast is tAp, is given by 1O- 1 6pAh

(2.88a)

- 12.8 X 10- 3 ApAh'

(2.88b)

Ag....,. - 41.9 g(x, y) dxdy - 2'ITyM

X

-DQ

or

M - (1/2fTY)

¡oa ro g(x, y) dxdy -00

(2.85)

-00

In practice, the integral is evaluated by numerical integration using the relation

(2.86) where m is in metric tons or short tons according as K - 26.3 lor 6x,6y in meters, or K - 2.44 lor 6x,6y in feet The actual mass producing the anomaly can be determined ir we know its density p" and density contrast 6p. This multiplies Equation (2.86) by the factor (p,,/6p): actual mass - (p./6p) X excess mass (2.87)

lf the regional has not been properly removed, or if other residual anomalies are included, the estimate obviously wi11 be iD error.

2.7.11. Overburden Effects In many field situations, the effects of variations iD !he depth of the overburden may be larger than the efrects of difrerent rocks at depth, and so variations in overburden thickness can produce significant gravity anomalies. The average density for an assortment of overburden materials is about 1.92 g/~ when wet and 1.55 g/cm3 when dry, and the averages far wet and dry sedimentary rocks are - 2.50 and - 2.20 g/c~, respectively. Thus a contrast of 0.6 g/~ is possible.

where Ah is iD meters, Ah' is in feet, and Ag....,. is in milligals. The maximum horizontal gradient 01 gravity will, of course, be large ir overburden irregularity is tbe source. For abrupI depth changes of 10 m or more in a horizontal distance of 10 m aud Ap - 0.6 S/crrr, Ihe value of (dgmu / dx) will be about 0.03 mGal/m. In fact, this steep gradient is more diagnostic than the magnitude of gmu' Oearly the depth oloverburden should be measured in areas of shallow gravity anomalies. This is best done by small-scale refraction or surlace resistivity measurements.

2.7.12. Maximum-Oepth Rules Smith (1959) gives several lormulas for maximum depths oC gravity distribulions whose shapes are nOI knOWD, provided that the anomalous bodies have a density contrast with the host rock that is either entirely positive or entirely negative. If Ig_1 and Kag/ax)mu:1 are the maximum values of gravity and oC the horizontal derivative, respe.ctively, !he depth 10 the upper surface has a limiting value given by

z S 0.86Igmu:vl< ag/ax)_1

(2.89)

If the anomaly is two dimensional, the factor 0.86 becomes 0.65 in Equation (2.89). However, this expression is not particularly accurate.

2.8. FIELO EXAMPLES (1) Figure 2.36a shows a Bouguer gravity contour map compiled from a survey in the vicinity 01 Portland Creek Pond in nortbem Newfoundland. This was an exploralion program for oi1 and gas in

-'"

"S

~

ao ....

~ ~ ~

......

.:!

~

"2 ~

,!! "1:)

c::

;,

~

.::

-.:

:j

~

~

..gt ... c.

o;:

Q.

'O: 'O:

'"~ lO

U

;;¡

~

f

~ ~

...&~

0-': t3 'ge

~"" (sc:5 CI..

I

;.:.--

~u

;,'-

"'-

c~

"Q¡ :>-

,

:!.5 I.J .... ;, ~2

"<5 Q¡

'"

~cl.

re

Grav;ty methoos

50

no

2090

2-80 I

I

Specific gravily o~----------------~-----------

(b)

Profil. A-A

3

2

o

Dolomite p -

2.82

1---4000A---t

o

2000 n

I

Sedlmentl

ji - 2.55

(rl

Figure 2.36. (Continued) (b) Oensity lag in borehole OOH Pc/-70. (e) Comparison with ealeulated p,ofile fo, a 2-0 dipping p,ism.

an area 01 sedimentary rocks wbose thicmess, a Cew miles south, is mown to be over 5,000 rt. The topograpby is reasonably ftat and no terrain corrections were required. It is evident that the large positive anomaly is not • reftection oC deep basement structure because the

gradients are too steep. Ir we use Equation (2.68) to approximate a slab ror profile AA' iD Figure 2.361, the values oC g_ and (íJg/ax) ..... iDdicate that h is not greater than 650-800 ft. 'Ibis indicates that the source is shallow and hence must be within the sediments. One possibility is an intrusive dike 01

51

Field examples ....

-J

10

E oc

<1

ION Overburden

,

200fl

Figure 2.37. Gravity profiles ove, a copper deposit, Louvicourt. Quebec.

great linear extent, but Equation (2.74) shows that the ftanks of the anomaly in tbis case would be much less steep than the field profile; tbis suggests that the source is oC Iimited depth. A 1,600 ft drill hole was put down in the center oC Ibis gravity anomaly; its location is shown in Figure 2.36a. Density measurements on core samples at 100 ft intervals are shown in Figure 2.36b. The local presence of dolomite from near surface to 1,000 Ct and interbedded with dark sbales from 1,000 to 1,600 ft accounts for tbe positive gravity. The avera&e density of the doJomite samples was 2.82 g/cm"'. Ir the surrounding sedimentary formations are assumed to have a density of about 2.55 g/cm"', it is possible to match the field profile reasonably well witb the dipping prism sbown in Figure 2.36c. This analysis is oversimplified since tbe actual structure is neitber two dimensional (L .. 9b) nor homogeneous in Ihe bottom 500 fl. Both factors would steepen tbe ftanks on tbe profile. (2) The profiles in Figure 2.37 iIIustrate the pronounced elrect of overburden thiekness on gravity results. This is the Louvieourt Townsbip copper deposit near Val d'Or, Quebec. Discovery was made by drilling a weak Turam anomaly (§7.4.3b); the gravity survey was carried out immediately after. The original Bouguer gravity profiJe indicated a weak anomaly of 0.15 mOal directly over the conductor and a much broader and larger magnitude anomaly about 75 m to tbe north. Obviously the small peak would not bave aroused any great enthusiasm. Later, wben it had been established Ihal the overburden tbickness increased appreciabJy immedi-

alely over the sulfide zone. it was possible to correet for Ibis variable lbiekness, as discussed in Section 2.7.11. using a densily conlrasl oC about 0.08 g/cm"' belween Ihe hosl rock and the overburden. This is equivalenl lo 0.03 mGal/m of overburden tbickness. In tbe corrected field profile the larger anomaly to tbe nortb has practically disappeared and Ihe small peak has been enhanced lo 0.3 mGal. A third profile caJculated from density measurements of diamond drill cores is also shown. This example c1early indicates the importance 01 measuring the overburden thickness in conjunetion with gravity apptied to small-scale mineral exploration. This is particularly necessary in surveys ror vein-type base-metal deposits that respond to EM metbods. The overburden elrecl woutd be less pronounced in regions favorable Cor IP. that is,Jarge-area low-grade disseminated mineralization. (3) The Delson fault is a well-documenled stroctural feature in Ihe SI. Lawrence lowlands. Slriking roughJy E-W. it is located easl of Ihe SI. Lawrence River several kilometers southeast of Montreal. AJthough the area is generally covered by about 15 m of overburden. tbere are exposures 01 Utica sbales and Chazy limestones in river beds to indicate tbe Jocation and direction oC the fault. The sedimentary beds oC the lowlands are ftat-Iying shales. limestones, and dolomites of Paleozoic age underlain by Precambrian basement rocks at a deptb usually greater tban 750m. Figure 2.38 shows a Bouguer gravity profile taken across the De1son Cautt in a N-S direction, together with a geologie section. A linear regional trend of

Cravity methods

52 _

4 3

1(.

'-x Meoosured Boupcr lravily Thcorelical lravily

0-0

¡;¡

-..

~ 2

D-Faul! Inc:e as mapped T-Theorelical (Iul! Ince

~S~__~____~____~______~~__~____~____~~_N

4

Overburden 50 n

huy limeslone p - 2.71' ,

ª

Ulica Ih.le p - 2.56_'_--.¡ Trenlon limeslone p - 2.76

Beekmantown dolomile p - 2.71 1000

2000

Fisure 2.38. Cravi/y profile and se%Sic section across the De/son fau/1. Sr. Lawrence /ow/ands.

0.45 mGal/km positive to the south, has been re-

moved. The profile in Figure 2.38 resembles the gravity efl'ec:t of a horizontal slab rather thao a 'auh (compare with Figs. 2.28, 2.29, aod 2.32). The ooly appreciable gravity efl'ect from the sedimeotary beds would be provided by the juxtaposition of the Chazy aod Utica formatioos near surrace aod the displaced Potsdam layer (whose thicltness is in sorne doubt) at greater deptb. The fint pair produces a gravity profile of the proper shape with a total variation of 0.57 mGal and m8XÍmum slope of 3.7 mGal/ltm; thus the total anomaly is too small and the slope too large lo fit the field profile. The low-density Potsdam sec:tion, on the other hand, would tend to reduce the anomaly, since the bed nearer the surface Iies on the south side of the faull; the total efl'ect, however, is ooIyabout -0.1 mGal and maximum slope -0.15 mGal/ltm. By postulaling a density of 2.96 g/cm3 in the Precambrian roclts aod a step of 275 m on the faull down lo the south, we obtain a total aoomaly of 2.1 mGal with maximum slope of 1.2 mGal/ltm. The theoretical profile in Figure 2.38 is the result. The theoretical profile is shifted abaut 300 m south of the mapped fault localion. There are two explanations for this. Fint, the Delson fault is not vertical, but dips north about 80°. Second, faults very rarely show single clear-cut faces, that is, there is a faulted region of some width. The field profile also shows a small aoomaly about 2\ miles north of

the Delson fault, although there is no supporting geologica1 evidence.

2.9. PROBLEMS 1. Verify EquatioD (2.8). [Hint: Start with Equation (2.6a), integrate aloog the y axis betweeo the Iimits ±L, aod subtract the poteotial at (.x 2 + Z2) _ a2 - 1 (this avoids U -o 00 as L -o 00). By setting L - 00, we get Equation (2.8).) 2. Show that Equation (2.12a) holds for ao arbitrary closed surface S regardless of the posilion 01 m witbin S. Hinr: Wrile lhe integraod in lhe form ym(dscos9/r 2 ) - ymdO. where r is the distaoce from m lo ds, 9 is the aogle belween r and n, the outward-drawn normal to ds, aod dO is the elemen! of solid angle subtended by ds at m. Consider the case where r cuts S more than once.) 3. Verify Equations (2.62) aod (2.63). [Hint: A solution 01 Equation (2. 11 e) is (Pipes and Harvill, 1970, p. 348)

r

g(r,9)

where l' - cos 9. When r > z > R, we use the

.

53

Problems Table 2.3.

Stn

Time

gob.

Time

gob.

(hr)

(mGal)

Stn

(hr)

(mGal)

Stn

(hr)

(mGal)

182.78

42 41 40 0·39 25 26 27 28 29 30

14:29 14:31 14:35 14:37 14:50 14:52 14:55 14:59 15:01 15:05

182.95 183.06 183.15 183.13 183.82 183.97 183.99 183.% 184.25 184.48

31 32 33 34 35 36 37 38 0°39 0°53

15:07 15:10 15:12 15:14 15:16 15:19 15:22 15:25 15:27 15:45

184.48 184.81 184.53 184.33 184.17 184.03 183.73 183.38 183.35 183.01

33

10:56 11:00 11 :05 11:09 11 :15 11:20 11 :25 11 :29 11 :32 11 :35 11 :39

185.39 185.39 185.52 185.37 185.00 184.86 184.86 184.79 184.&9 18467 184.&0

44 45 46 47 48 49

11:44 11:47 11:52 11 :55 11:59 12:02 12:05 12:08 12:12 12:1& 12:28

184.53 184.56 184.64 184.67 184.67 184.7& 184.76 184.80 184.90 185.09 185.03

Aug.31 0·53 52 51 50 49 48 47 46 45 44 43

Une O 13:55 14:00 14:04 14:07 14:10 14:15 14:17 14:20 14:22 14:25 14:27

Sept. 6 0·53 25°53 25°39 24 25 26 27 28 29 30 31 32

Une 25 9:10 9:20 9:40 10:19 10:23 10:27 10:31 10:34 10:38 10:41 10:45 10:50

182.7r

182.73 182.92 183.05 183.19 182.99 182.88 182.89 182.85 182.91 185.Q2 185.11 184.93 185.86 185.66 185.65 185.66 185.59 185.47 185.51 185.46 185.39

34 35 36 37 38 25°39 40 41 42 43

right-hand series and compare it with the expansion of Equation (2.60) in terms of (R/z) [see Eq. (A.43») Cor points on the axis where 1-' = 1, Pft(l) - 1, and r - z; Ibis gives the values of b¡ and we get Equation (2.62). Doing tbe same Cor R > r > z and using tbe first series, we get Equation (2.63). Sinee r > z on physical grounds, there are, in fact, only two cases: r > R and R > r, so Equation (2.62) holds for tbe lbird case, r > R > z.) 4. Tbe data in Table 2.3 were obtained over a 2 day period of gravity Collowup on a base-metal prospect. Stations marked o were visited at least twiee for driCt correction. For example, station 53, line O, was occupied at the beginning and end oC each oC tbe 2 days, station 53, line 2S. al the beginning and end oC tbe second day's work and the stations 39 on both lines were used as base stations for checking drift at intermedia te times. Draw a drift curve for tbe 2 day period and correet all slation readings. (Note that each oC the cour stations 53 and 39 must have the same gravity readings - or very nearly so - as a result of tbe drift corrections.) S. The gravity data in Table 2.4 were obtained during a followup 00 a small sphalerite showing io eastero Ootarlo. Reduce the gravity readiogs

Time

SO 51 52 25°53 0·53

Sobo

by taking out the drift, Cree-air (ineluding height oC instrument), Bouguer (assuming an average density oC 2.67 g/cnf), and latitude corrections

(lines are N-S). Plot the two profiles. Are there any indications oC a small high-grade (10-15%) or larger low-grade (2-5%) sphalerite deposit7 Can you suggest any reason Cor the general shape of the profiles? 6. Show that the gravity anomaly produced by a vertical cone at its apex is 6g",u - 2"''rph(1 - cosa) where h is the vertical height and a half the apex angle oC the cone. Hence show that tbe terrain correction at the apex of a conical hill is 8g, - 2'IT'rph cos a If h - 1000 ft, a - 68 0 • and p - 2.67 g/cnf, with the aid of a template and Table 2.1 determine the terrain correction required at varlous points on the sloping .sides and on ftat ground surroundíng the cone (obviously the correetion is the same at any particular elevation because of symmetry). How close to tbe base can gravity measurements be made without a significant ter· rain effect7

Cravity methods

54 Table 2.4. Stn L8W

g..... (mGal)

Time

°35 3 + 25 3 + 50 3 + 75 45 4 + 25 4 + 50 4 + 75 55 5 + 25 5 + SO 5 + 75 6S °35 2 + 75 2 + 50 2 + 25 25

37.04 36,82 36,87 36.84 36,80 36,68 36.63 36.57 36.47 36.56 36.67 36,67 36.73 37.06 36,9(, 36.74 36.89 36.86

2.20 2.30 2,33 2.36 2,40 2.45

(PM)

2.48 2.52 2.55 2,57 3,00 3.04 3,06 3,13 3.17 3,23 3.28 3.30

H.1. (ft)

Elev. (ft)

5tn L8W

1.42 1.25 1,33 1.33 1.33 1.33 1.50 1.17 1.33 1,25 1.33 1.33 1.42 1.33 1,33 1,42 1.25 1.42

0,00 3.69 3,63 4,78 5.85 7.11 8,26 10.03 11.42 10,19 8,91 8.21 7,46 0.00 -0.76 1.18 1,23 1.39

1 + 75 1 + 50 1 + 25 15 0+75 0+50 0+25 B.L. L 10W B,L. 15 2S 3S 4S 55 65 L8W °3S

Time (PM)

H.I. (ft)

Elev.

(mGal) 36.86 36.88 37.49 37,77 38,00 38.03 38,07 38.03

3.33 3.37 3.42 3.45 3.49 3,53 3.59 4,02

1.42 1.58 1.33 1,08 1,10 0.83 0.83 1,17

1,60 1.84 -5.81 -9,68 -13.99 -14.93 -15.06 -15.30

37,62 37,94 37,60 37.55 37,27 37.45

4,23 4.34 4.38 4,40 4.46 4.50 4.53

1.42 1,08 1.23 1.42 1.42 1,17 1.42

-3.06 -7.41 -9.14 -8.20 -4.85 1.04 -1,04

37.10

5.00

1,17

0,00

gobo

(ft)

Note: L - line: B.L. - base line - O fl on each line; 35 - 300 fl soulh of base line, 3 + 75 - 375 tI soulh ot base line. and so on; H.I. - height of instrument (gravimeter) aboYe the surface whose elevation is given. Lal. of B.l. - 46°2S'N.

. o

~

,

Figure ],39. Topog"phic map for terrain corree/ion. 7. lbe topographic map in Figure 2.39 was prepared iD considerable detail to talee out a terraiD COrrectiOD for a gravity survey. Malee a template of appropriate scale for tbe first four or five zones of Table 2.1 (zones B-F) and calcu1ate tbe terrain correction al several stations, such as (2N. 3W), (8N, 12W), (O,9W), etc. Assuming Ihal

\he topography is reasonably ftat in tbe area surroundiDg tbe section iDustrated, how many additional zones would be Decessary to make a complete terrain correction? ID faet, there is a steep ridge to tbe northwest, striking soutbwesl-Dortheast. Al a distante of about 2 miles from the center of \he area tbe

55

Problems

elevations increase from 300 to 1.100 ft within 1/2 mile. There is also a lalee, which is roughly 1 mile across and a maximum of 100 ft in depth, situated about 2 miles to the northeast. To what extent would these large topographic reatures alreet the overall terrain correction? 8. The reduced gravity readings (Bouguer) in Table 2.5 were obtained Crom an east-west traverse with stations at 30 m intervals. An electromagnetic survey carried our earlier had outlined a conducting lone about 750 m long, striking routbly nortb-soutb, with a maximum width ol 50 m in tbe central part of the area. The gravity work was done as an attempt to assess tbe metallic content oC the conductor. Four addilional parallel gravity traverses, on lines adjacent to line 81N, produced essentially similar results. No information is available on the depth oC overburden. Plot the profile and malee a qualitative interpretation of the nature 01 the conducting lone based on the gravity survey. 9. The Bouguer gravity readings in Table 2.6 are taken from a survey in the sedimentary Pine Point area oC the Northwest Territories. Station spacing is 30 m on a N-S lineo Plot the profile and interpret tbe gravity anomaly, assuming it to be approximately two dimensional. Malee two interpretations, assuming first that (a) below is valid, tben assuming that (b) [but not (a») is valido (a) A Turam survey has not located any conductors in the area, while soil geochemistry shows minor lead and zinc. (b) The gravity anomaly coincides with a strong IP anomaly. Attempt to match the gravity profile with a simple geometrical cross section with particular regard to its depth, depth extent, and width.

Table 2.5. Une 81N.

S.

8.

SIn

(meal)

SIn

(meal)

8SE 86 87 88 89 90

1.35 1.30 1.25 1.22 120 1.15 1.07 0.87

93E 94 95 96 97 98 99

0.77 0.75 0.66 0.55 0.51 0.50 0.40

91

92

Table 2.6.

Ss

8/1

SIn

(meal)

SIn

(mGal)

85 75 65

0.02 0.06 0.08 0.09 0.08 0.06 0.01 0.04 0.19 0.41

2N 3N 4N 5N 6N 7N 8N 9N 10N l1N

0.62 0.79 0.82 0.82 0.67 0.33 0.22 0.20 0.18 0.16

SS 45 35 25 15 B.l.

lN

10. Residual gravity contours obtained from a survey over a base-metal area are shown in Figure 2.40. A regional trend 01 about 0.8 mGal/l,OOO Ct was removed lo produce this map. A profiJe along the south-north line has also beco plotted. The gravity anomaly is obviously caused by a plug-type 01 structure oC considerable positive density contrast. Make an interpretation 01 the source as precisely as possible witb tbese data.

2·0

I·S

-. .

',0 1.:)

.....e

o·s s------------------------~ N

o I

lOO I

400ft ,

Fisure 2.40. Residual sravity contours and principal profile, northwest Quebec.: 0.2 mGal. (After Seigel. 1957.)

e/.-

Crav;ty methods

56 11. Table 2.7 gives Bouguer gravity reaóings from a survey made in the Bathurst area of northem New Brunswick. Station spacing is 100 ft and the line spacing is as Doted. (L20N means 2,000 ft nortb 01 the base line.) Because 01 limited time and money, only four lines were selected for a followup 01 an earlier combined magnetic-electrical-geochemícal survey. (Although this type of spot gravity work is used lo some extent in base-metal exploration, it has obvious limitations.) lbere is a pronounced regional ¡radient, positive lo the east, bUI it is not uniform, being stronger in lhe north lines and weakest on line tON. Furthermore the large and irregular spacing betweeD the lines makes it difficult to plot well-defined CODtoUrs. On the other band, ir we attempt to remove the gradients rrom each line independently, it is not c\ear what background level should be selected; because we are looking lor massive sulfides, the teDdency is to overempbasize positive gravity areas. No measurements were made ol overburdeD depth. Try to remove the regional by graphical smoothing and by gridding (more sophisticated techniques are not warranted). Interpret any remaining residuals. 12. AdditiODal data obtained in the gravity survey of problem 4 are given iD Table 2.8. Lines are east-west, 200 m apart; stations are SO m apart with the Jarger oumbers lo tbe west. For some reason tbe base line through Sto O was cul al an angie of 20° east 01 troe oorth, so that eacb station 00 lioe O is displaced about 73 m east ol its equivalent on line 2S. Obviously there is a smalllatitude correction, 2~ being .93°. Using the data in problem 4 (corrected lor drifl), apply the appropriate reductions to obtain Bouguer gravily lor a1l statioos, using an average densily of 2.67 g/crDJ lor the local Cormations which consist ol gneiss on the westem portion extending roughly lO station 25 and ullrabasic rocn lo the east. lbere are Crequent large outcrops in the eastem region, while tbe gneiss is covered by a fairly uniform thin overburden ol 1-2 m. Plot the gravity profiles and make an interpretation of the results. 13. Figure 2.41 sbows Bouguer gravity values al 30 m intervals. The following methods of analysis are suggested: (i) Remove the regional by drawing contours and graphical smoothlng. (ü) Remove tbe regional by gridding. (ili) Calculate the second derivative. (iv) Carry out downward contiouation by any method you tnow. Compare the results achleved with tbe dilferenl

methods and consider their relative advantages and limitations. Interpret the residual anomaly or anomalies, ir any, and calculate the excess mass. Is the section large enough to give reasonable results? lable 2.7.

SIn 4W 3W 2W 1W

Bl 1E 2E 3E 4E SE bE

l20N (mGa!)

l16N (mGal)

l10N (mGal)

45.38 45.47 45.68 45.79 45.91 46.09 46.21 46.08 46.54 46.62 46.91

45.71 45.94 45.90 45.97 45.93 46.14 46.42 46.40 46.53 46.75 46.87

4b.10 4b.10

46.40 46.22 46.27 46.31 46.55 46.72 46.80 46.66 46.61

l2N (mGal)

46.43 46.48 46.60 46.68 47.00 47.09 47.00 47.12 47.50 47.61

lable 2.8. Une O

H.1.

Une 25

SIn

(m)

Elev. (m)

53 52 51 50 49 48 47 46 45 44 43 42 41 40 39

0.46 0.43 0.49 0.47 0.51 0.53 0.53 0.48 0.50 0.48 0.47 0.50 0.46 0.39 0.45

6.76 6.99 7.08 5.95 4.73 4.68 6.00 6.42 6.40 6.75 7.20 6.64 5.82 5.96 6.21

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 53

0.50 0.46 0.40 0.50 0.43 0.45 0.40 0.43 0.42 0.48 0.47 0.47 0.49 0.47 0.48 0.45

2.59 3.15 3.78 3.17 1.96 1.31 2.22 0.00 1.04 1.55 2.50 3.00 4.06 5.38 6.21 6.76

SIn 53 52 51

SO 49 48 47 46 45 44 43 42 41 40 39 24 25 26 27 28 29 30 31 32 33 34 35 36 37 36 39 53

H.I. (m)

Elev. (m)

0.46 0.44 0.43 0.43 0.46 0.46 0.47 0.46 0.40 0.41 0.43 0,42 0.45 0,44 0.48 0.44 0.46 0,41 0.42 0.42 0.45 0.46 0.42 0.42 0.45 0.45 0.44 0.45 0.46 0.46 0.45 0.43

8.03 7.85 8.20 8.50 8.75 8.91 8.61 8.36 8.64 9.03 9.06 8.41 8.02 7.65 7.62 3.84 4.74 4.88 4.69 5.69 6.15 6.03 6.51 7.01 6.89 6.34 5.39 6.56 7.80 7.67 7.62 8.03

57

Problems 6·J2 6'27 6·21 6·42 6·4] 6·39 6·32 H4 625 6·2] 628 628 1J47N I H9 6·54 648 • • • • • • • • • • • • • • • • 6'52 6-50 6·41 6049 690 "'7 679 676 6·7) 6·76 6·67 6," 6-63 6·ro 6·57 6-54 • • • • • • • • • • • • • • • • 6-80 6·7) 6·11 -' 6·68 6·90 HS H)6 7·0l 7·02 7·04 6·99 7·04 6·96 6·9f 6·95 6·18 • • • • • • • • • • • • • • • • 6·95 6'92 6·11 7-20 7-2S 7-23 7'23 7-20 7·11 7·24 1·2S 7-24 NI 7·22 7·22 • • • • • • • ." • • • • • • • •

6·7)

7-()'

139

NI

•

14J

•

146

J.l5

756

158

HO

no

ni

774

•

778

7-87

as

7-87

796

~

01

8 J6

•

• •

• •

•

•

•

• •

• • • 807 811 116 • • • •

80J

I

~O

26

• • • • l,,, 1)6 146 ISI • • • •1 o lliill

146

149

7·50

759

7-57

7-52

141

134

n5

7·16

7-D1

N4

• • • • • • • • • • 7-43 7-36 7·21 7-21 7·71 7-78 1-7S 7·71 7-62 HO • • • • • • • • • • 7-47 7·76 Hl 7-43 HO 7·96 792 7'90 7-94 76J • • • • • • • • • • ',12 8·20 1·06 8·09 7·90 775 770 7·59 H8 7-52 • • • • • • • • • • 7-87 7-12 7" 795 .34 8·35 129 8·21 816 1·06 • • • • • • • • • • 8·42 134 8·24 8·14 8·06 8·01 8·62 8·50 8·48 8·49 854 • • • 1" • • • • • • • • • In 867 879 171 8·" 8-73 8-69 1-62 l," 837 02 823 1137 N I • •, • • • • • • • • • •

• • 764 7-68 • • 712 H8 • • 8·00 1·13 • • 8·25 •. JO • •

200

O]I[J

r.

Figure 2,41. Bouguer gravity values on JO m grid; values in mil/igals. ..

-

4

fl~;F e

E

.~ j

i

iil

M

.... .!!

450 430

t

;:0:::0>

~

___

,

o

I

I

SOON

I

I

TÚ."in seclion;--I

I

IOOON

I

ISOON

I

I

I

2000N

Figure 2.42. Bouguer gravity and topographic profiles, East Africa.

14. A topographie seetion and Bouguer gravity profile over a long east-west ridge are shown in Figure 2.42. Without other inCormation, is it pos5ible to answer the Collowing questions with assurance1 (a) Was a terrain eorreetion taken out in redueing the gravity readings? (b) Js a terrain eorreetion necessary? (e) Is the gravity profiJe essentially a refleetion oC the topography1 (d) 15 a regional gravity effect present that is independent of the topography1 (e) Assuming there is a gravity anomaly eaused by a subsurface slrueture, can you loeate it and estimate its approximate section? (As an aid to making thls inlerpretation, it would be very helpCul to replot the gravity profile on an expanded vertical scale.) lS. Figure 2.43 is a Bouguer gravity eontour map ol the area whose topography is shown in Figure 2.39. The geology i5 sedimentary, with sandstone and limes tone beds Ihal are known to be over S,OOO CI thiek a few miles to the we5t. Witbin the

survey area the limestone-sandstone contact can be seen at the bottom oC the hill just west 01 the base lineo The limestone bed extends east from tbis contact at surface and appears to be less than SO ft thick; becausc it does not continue west under the hill, a fault is indieated. Under normal circumstances, the sandstone would have the lower density; but in tbis area, because the limes tone is thin and because !bere are undreground streams flowing in it, the density eontrast is probably insignificant and may even be in the opposite sensc. Problem 7, with which Figure 2.39 is connected, was an exercise in making terrain corrections in rugged ground. Preparation of the map in Figure 2.43 required more than lS man-days oC work, most oC it spent on terrain corrections Cor about 400 gravity stations. The end result is a gravity map that appears to be a fair reproduetion oC tbe topography. Do the two maps, Figures 2.39 and 2.43, resemble each other in spite of !be elaborate terrain correction or beeause of it? If the latter is

Cravity methods

58

Figure

2.43. Bouguer gravity eontours, eastern Nova Seo tia; CI. - 0.1 mGa/.

true, would this be a fundamental argument against carrying out &favity surveys in regions wbere tbe topo&fapby is bigbly irregular? On tbe otber band, if the anomalous &favity is not due to topography, how do you explain it? 16. The reduced &favity contours in Figure 2.44 show a portion of a large survey made over a base-metal property in soutbem New Brunswiek. Remove the regional. Given tbat tbere are ore&fade suJlides in tbe area, interpret tbe residual and estimate tbe excess mass. 17. Figure 2.45 shows residual Bouguer gravity across a tbree-dimensional strueture ol positive density contrast in tbe Sto Lawrence lowlands cast of Montreal. The eontours are approximately circular. Drill logs from gas and oil exploration holes in tbe vieinity have indicated ftat-lying sedimentary beds to a deptb oC over 4,000 Ct. lbe maximum density contrast among tbe dift"erent sediments is not greater tban 0.2 g/erd and general1y is eloser to 0.1. Density ol the Precambrian basement rocks is not known, but tbey are probably denser tban tbe average sediments by 0.25-0.30 g/crd. To interpret tbis anomaly, lirst consider tbe maximum &favity combined witb tbe maximum slope of tbe ftanks, witb respect 10 tbe known deptbs and density contrasts in tbe area Tbis will indicate an approximate deptb to tbe source. Then attempt to match tbe profile witb a simple

sbape, sueh as the sphere, rod, eylinder, and so lortb. (Note tbat it is possible to simulate a pillbox-type of structure by taking tbe difference between the gravity eft"eets of two long cylinders witb tbeir tops at dift"erent depths.) 18. On tbe portion of the Bouguer anomaJy map shown in Figure 2.46, the most negalive vaJues are found in the lower Jelt comer. (The numerical values shown are witb respeet 10 an arbitrary datum.) (a) A large fault strikes N200W just east of AUS. Examine tbe shape oC tbe fault anomaly by drawing the profile .04'.04. (b) For a simple eault model, tbe point where the fault's &favity expression is half its maximum value locates tbe fault. What difticulties are eneountered in tbe practical application of tbis rule'? Another rule is tbat the fault is located at tbe inftection point on the Cault profiJe. Loeate tbe Cault on tbis profile by applying these rules. What does tbe asymmetry of tbe fault profile indieate? (e) The half-width rule states tbat the deptb 10 the midpoint on a Cault is equal to the distance between the points on tbe fault's gravity profile, where the fault's gravity expression is i and 1 (or 1 and ~) ol its maximum expression. What deptb does tbis give Cor tbis lault? What difticulties are eneountered in the practieaJ applieation of this rule?

59

Problems

,.

t i

o I

200 I

400 O I

r Figure 2.44. Bouguer gravity contours. southern New Brunswick; C/. - 0.1 meal.

(mil.sl

r

Figure 1.45. Residual gravity profile over three-dimensional structure. Sto Lawrence lowlands.

Cravity methods

60

Figure 2.46. Bouguer gfilVity miJp, Western AustriJlia; C.I. - 1.0 meal. (Courtesy West Australian Petroleum.)

(d) What is the magnitude 01 this fault in milligals7 Assume that a uniform density eontrast across the fault exists from the surface to twiee the depth given in part (e), How mueb density contrast is implied? 19. On the Bouguer anomaly map of Figure 2.46, the bow in the contours about 9 km NW 01 AUS indicates a strueture. (a) Draw the profile B' B lo separate this anomaly from the lault anomaly examined in problem 18. Where is the cenler 01 the anomaly? (b) Draw a profile at right angles to B' B through tbe center 01 the anomaly. Is tbe anomalyeasier to see OD this profile? Are the residual anomalies consistent with eacb other7 What is the magnitude 01 the anomaly in milllgals7 (e) Assume that the anomaly can be approximated by a buried spberieal mass (see Fig. 2.23). How deep mUSl the center of the sphere be? If a density contrast of 0.1 g/caí' is assumed, what would be the radius of the spbere? (d) Tbe bow in the contours about S km SSW 01 AUS might be interpreted as a similar anomaly. What is unreliable about tbis anomaly?

20. A grid residual is one way 01 isolating anomalies from a regional background. Read tbe contour values on a 2 km grid over tbe Bouguer anomaly map 01 Figure 2.46. Assuming that tbe expeeted value at each grid slation is the average of (he lour values, whieh are 2 km away, the residual is the diff'erence betwen tbe observed and the ex· pected values. Determine the residuals for all the grid points and eontour the resulting map. Note how the fault sludied in problem 18 and the anomaly sludied in problem 19 are emphasized by this process.

REFERENCES Ager, C. A .• and Liard. L. O. 1982. Vertical gradienl surveys: Field results and intcrpretation in British Columbia. Geophysics 47, 919-25. Agoc:s, W. B. 1951. Leasl-squares residual anomaly determination. Geophysics 16. 686-96. Am, A. A. 1975. Microgravity ror engineering applications. Geophys. Prosp. 23. 408-25. Bhattacharyya. B. K. 1978. Computer modeling in gravity and magnctic inlerpretation. Geophysics 43, 912-29. Bible, J. L. 1964. Gravity ror tbe geologist. World Oil. Oct. and Nov. ¡ssues.

Re ferences Brozena. J. M. 1984. A preliminary analysis oC the NRL airbome gravimetry system. Geophysics 49. 1060-9. Butler. D. K. 1984. Mkrogravimetric and gravity gradient techniques for detection oC subsurCace cavities. Geophysics 49. 1084-96. Coons. R. L.. Woolard. G. P .• and Hershey. G. 1967. Structural significance ol the mid-continent gravity tugh. Bull. Am. Assoc. Pe/ro Geo/. 51. 2381-99. Dean. W. C. 1958. Frequency analysis for gravity and magnetic interpretation. Geophysics 23.97-127. Dickenson. G. 1953. Geological aspects ol abnormal reservoir pressure on Gulf Coast. Louisiana. A. A. P. G. Bulle/in 37.410-32. Dobrin. M. B. 1960. Introduction lO Geophysical prospecting. 2nd ed. New York: McGraw-HiIl. Elkins, T. A. 1951.The second derivative method of gravity interpretation. Geophysics 16. 29-50. Ervin. C. P. 1977. Theory of the Bouguer anomaly. Geophysics 42, 1468. Falklewicz. Z. J. 1976. Gravity vertical gradient ,measurements Cor the detection oC small geologie and 'anthropogenie forms. Geophysics 41, 1016-30. Geldart, L. P., GiII. D. E., and Sharma. B. 1966. Gravity anomaJies of two-dimensional laults. Geophysics 31, 372-97. Grant. F. S., and West. G. F. 1965. Interpretation Theory in Applied Geophysics. New York: McGraw-Hill. Griffin, W. R. 1949. Residual gravity in theory and practice. Geophysics 14, 39-56. Gupta, V. K., and Ramani. N. 1982. Optimum second vertical derivatives in geological mapping and mineral exploration. Geophysics 47, 1706-15. Hammer, S. 1939. Terrain cometions for gravimeter stations. Geophysics 4, 184-94. Harnmer, S. 1982. Critique ol terrain corrections lor gravity slations. Geophysics 47, 839-40. Harnmer, S. 1983. Airbome gravity is here. Geophysics 48, 213-23. Hedberg, H. 1936. The gravitational compaction ol c\ays and shales. Am. J. Sci. 31,241-87. Hendersen, R. G., and Zietz, l. 1949. The compulation of second vertical derivalives of geomagnetic fields. Geophysics 14, 508-16. Hermes, H. J. 1986. Caleulation of pre-Zechstein Bouguer anomaly in northwest Germany. Firs/ Break 4, No. 11, 13-22. Hubbert, M. K. 1948. A line integral melhod ol compuling gravimelrie efl'ects of two-dimensional masses. Geophysics 13, 215-25. Hussain, A., Walach, G., and Weber, F. 1981. Underground gravily survey in alpine regions. Geophys. Prosp. 29, 407-25. Jaekson, D. D. 1979. The use of a priori dala lo resolve non-uniqueness in linear inversion. Geophys. J. Roy. As/ron. Soco 51, 137-51. Jordan, S. K. 1918. Moving-base gravily gradiomeler surveys and interpretation. Gtophysics 43, 94-1Ol. Kahn, M. A. 1983. Salellite contributions to geopbysical exploration at sea. ID CRC Handbook of Geophysical Exploration at Sea, R. A. Geyer, ed., pp. 3-68. Boca Raton: CRC Press. Krohn, D. H. 1976. Gravity lerrain corrections using multiquadratic equatioDs. Geophysics 41, 266-75. LaCosle, L. J. B., Ir. 1934. A new type long period vertical seismograph. Physics 5, 178-SO. LaFehr, T. R. 1980. History of geophysical exploration:

61 Gravity method. Geophysics 45, 1634-9. LaFehr. T. R. 1983. Rack densily from borehole gravily surves. Geophysics 48. 341-56. Lynch, A. M .• and King. A. R. 1983. A review of paramelers afl'ecting Ihe accuracy and resolulion of gravily surveys. Bull. Aus. Soco Explor. Geophys. 14. 131-42. MacRobert. T. M. 1948. Spherical Harmonics. New York: Dover. Marquardl. D. W. 1963. An algorithm for leasl squares eSlimation of non-linear parameters. J. Soc:o Ind. and App/. Malh. 11,431-41. Maxant, J. 1980. Variation of density with rock Iype, deplh, and formation in the Westem Canada basin from density logs. Geophysics 45. 1061-76. Nettleton. L. L. 1971. E/ementary Gravi~v and Magnelics for Ge%gisls and Seism%gisIS. Tulsa: Society of Exploralion Geophysics. Nettleton, L. L. 1976. Gral'Uy and Magnetics in Oi! Prospecling. New York: McGraw-HiIl. Parasnis, D. S. 1962. Principies of Applied Geophyslcs. London: Methuen. Paterson, N. R., and Reeves, C. V. 1985. Applications of gravity and magnetic surveys: The slale of Ihe art in 1985. Geophysics SO, 2558-94. Peters, L. J. 1949. The direcl approaeh to magnelie interpretation and its practical applicalion. Geophysics 14, 290-320. Pipes, L. A., and Harvill, L. R. 1970_ Applied Mathtmatia for Engineers and Physicists. New York: McGraw-HiII. Reeves, C. V., and MacLeod, 1. N. 1983. Modeling of potential field anomalies - Sorne applieations for !he microcomputer. Firs/ Break 1, No. 8, 18-24. Schmoker, J. W. 1978. Accuracy ol borehole gravity datL Geophysics 43, 538-42. Seigel, H . O., 1957. Discovery of Mobrun Copper LId. sulfide deposil, Noranda Mining Dislrict, Quebec. In Melhods and Case Histories in Mining Geophysics. 6th Commonwealth Mining and Metal/urgical Congress. Montreal: Mereury Press. Sherifl', R. E. 1978. First COIIrse in Gtophysical Exploration and Interpreta/ion. Boston: Intemational Hum8JJ Resources Devclopmenl Co. Sherifl', R. E., and Geldart, L. P. 1983. Exploration Seismolog)', vol. 11. Cambridge: Cambridge University Press. Skeels, D. C. 1947. Ambiguity in gravily interpretation. Geophysics 12, 43-56. Smith, R. A. 1959. Sorne deplh formulae for local gravily and magnetic anomalies. Geophys. Prosp. 7, 55-63. Slanley, I. M. 1977. Simplified gravity interpretation by gradients - The geological contae!. Geophysics 42, 1230-5. Talwani, M., Worzel, J. L., and Landisman, M.1959. Rapid gravity computations for two-dimensional bodies with applications to Ihe Mendocino submarine fracture zones. J. Geophys. Res. 64,49-59. Tarantola, A., and Valelte, B. 1982. Gcneralized nonlinear inverse problems solved using Ihe least-squares criterioD. Rev. Geophys. ond Space Phys. 20-2,219-32. Vallianl, H. D., and LaCoste, L. I. B., Ir. 1976. Theory and evaluation of Ihe LaCosle and Romberg three-axis inertial platform for marine gravimetry. Gtophysla 41, 459-67. Woolard, G. P. 1979. The new gravity system- Changes in intemalional gravity base values and anomaly values. Geophysics 44, 13.52-66.

Chapter 3

Magnetic Methods

3.1. INTROOUCTION 3.1.1. General Magnetic and gravity methods have much in como mon, but magnetics is generally more complex and variations in the magnetic field are more erratic and localized. 1bis is partly due to the differenee between the dipolar magnetic field and the monopolar gravity field, partly due to the variable direction of the magnetic field, wbereas the gravity field is always in the vertical direction, and partly due to the time· dependence of the magnetic field, whereas the gravo ity lield is time-invariant (ignoring small tidal varia· tions). Whereas a gravity map usuaIly is dominated by regional eft'ects, a magnetic map generally shows a multitude of local anomalies. Magnetic measure· ments are made more easily and cheaply than most geophysical measurements and corrections are prac· tically unnecessary. Magnetic field variations are of· ten diagnostic 01 mineral structures as well as regional structures, and !he magnetic method is the most versatile of geophysical prospecting techniques. However, like all potential methods, magnetic meth· ods lack uniqueness 01 interpretation.

3.1.2. History 01 Magnetic Methods Tbe study of the eartb's magnetism is the oldest branch of geophysics. Jt has been known lor more tban three centuries that the Earth bebaves as a large and somewhat irregular magnel Sir William Gilbert (1540-1603) made tbe lirst scientilic investigation oC terrestrial magnetismo He recorded in de Magnele that knowledge oC the north·seeking property 01 a magnetite splinter (a fodes/one or leading stone) was brought to Europe from China by Marco Polo. Gilbert showed tbat tbe Eartb's magnetic fteld was rougbly equivalent to tbat of a permanent maguet lying in a general nortb-south direction near the Eartb's rotational axis.

Karl Frederick Gauss made extensive studies of· the Earth's maguetic field from about 1830 to 1842. and most oC his conc1usions are still valid. He con· c1uded from mathematical analysis that the magnetic field was entirely due lo a souree within the Earth. rather than outside of it, and he nOled a probable connection to the Earth's rotation because the axis of the dipole that accounts lor most of the field is not far from the Earth's rotational axis. Tbe terrestrial magnetic field has been studied almost continuously sinee Gilbert's time, but it was not until1843 tbat von Wrede lirst used variations in the field to locate deposits of magnetic ore. Tbe publication, in 1879, 01 The Examintllion ollron Ore Deposita by Magnelic Measurements by Tha1~n marked the lirst use oC tbe maguetic method. Until the late 19405, magnetic field measurements mosdy were made with a magnetic balance, which measured one component of the earth's field, usually the vertical component. This limited measurements mainly to the land surface. The fluxgate maguetome· ter was developed during World War 11 for detecting submarines lrom an aireraft. After the war. the flux· gate magnetometer (and radar navigation, another war development) made aeromagnetic measurements possible. Proton·precession magnetometers, devel· oped in the mid·1950s, are very reliable and tbeir operation is simple and rapid. They are the most commonly used instruments today. Optical.pump al· kali·vapor magnetometers. which began to be used in 1962, are so accurate that instrumentation no longer limits the accuracy 01 magnetic measurements. How· ever, prolon·precession and optical·pump magne· tometers measure only the magnitude, not tbe direc· tion, oC the magnetic field. Airbome gradiometer measurements began in the late 1960s, a1though ground measurements were made much earller. The gradiometer often consists 01 two magnetometers vertically spaced 1 to 30 m aparto Tbe differenee in readings not only gives the vertical gradient, but a1so, to a large extent, removes the effects 01 tempo-

PrincipIes and elementary theory

63

tal field variations, wbich are often the limiting factor on accuracy. Digital recording and processing oC magnetic data removed much of the tedium involved in reducing measurements to magnetic maps. Interpretation a1gorithms now mue it possible to produce computerdrawn profiles showing possible distributions oC magnetization. The history of magnetic surveying is discussed by Reford (1980) and the state oC the art is discussed by Paterson and Reeves (1985).

3.2. PRINCIPLES AND ELEMENT ARY THEORY 3.2.1. Classical versus Electromagnetic Concepts

t

Modern and c1assical magnetic theory dilfer in basic concepts. Classical magnetic theory is similar to electrical and gravity theory; its basic concept is that point magnetic poles are analogous to point electrical charges and point masses, with a similar inversesquare law for the forces between the poles, charges, or masses. Magnetic uníts in the centimeter-gramsecond and electromagnetic uníts (cgs and emu) system are based on tbis concept. Systeme International (SI) uníts are based on the fact that a magnetic field is electrical in origino I ts basic uní t is the dipole, which is created by a circular e1ectrical current, rather than the fictitious isolated monopole oC the cgs-emu system. Both emu and SI uníts are in currenl use. The cgs-emu system begins with the concept ol magnetic force F given by Coulomb's law:

(3.1)

I

r-

wbere F is the force on P2' in dynes, the poles ol strength PI and P2 are r centimeters apart, ¡Jo is the magnetic permeability [a property of the medium; see Eq. (3.7»), and r1 is a unít vector directed from PI loward P2' As in tbe electrical case (but unlike the gravity case, in which the force is always attractive), the magnetostatic force is attractive for poles of opposite sign and repulsive for poles oC like signo The sign convention is that a positive pole is attracted toward the Earth's north ~agnetic pole; the term north-seeking is a1so used. The magnetizing fie/d H (a1so called magnetic field strength) is defined as the force on a unít pole:

(we use a prime to indicate that H is in cgs-em

Figure 3.1. Ampere's Ii/w. A currenl I through i/length of conductor l!.1 creales a magnelizing field l!.H at i/ poi,." P:

l!.H - (1M) x r,/4",2 where l!.H is in i/mperes per meter when I i5 in amperes i/nd r and l!.I are in meters.

uníts); H' is measured in oersteds (equivalent to dynes per unit pole). A magnetic dipole is envisioned as two poles of strength + p and - p separated by a distance 2/. Tbe magnetic dipo/e moment is defined as

m - 21pr1

(3.3)

m is a vector in the direction ol tbe unit vector r) (hat extends Crom the negative pole toward tbe positive pole. A magnetic field is a consequence oC tbe flow oC an electrical current. As expressed by Ampere's law (also called the Biot-Savart law), a current 1 in a conductor oC length tll crea tes. at a point P (Fig. 3.1), a magnetizing field tlH given by tlH - (1 tl/) x r.l4"r 2

(3.4)

where H has the SI dimension amperes per meter [- 4" x 10- 3 oersted), r and tll are in meters, I is in amperes, and tlH, r1, and I t:.I have the directions indicated in Figure 3.1. A current flowing in a circular loop acts as a magnetic dipole located at the center oC the loop and oriented in the direction in which a rigbt-handed screw would advance ir turned in the direction of the current. Its dipole moment is measured in amperemeter 2 ( .. 1010 pole-cm), The orbital motions oC electrons around an atomic nucleus constitute circular currents and cause atoms to have magnetic me-

Magnetic methods

64

•

ments. Molecules also bave spin, whlcb gives tbem magnetic moments. A magnetizable body placed in an extemal magnetic field becomes magnetized by induction; tbe magnetization is due to the reorientation of atoms and molecules so tbat their spins line up. The magnetization is measured by the magnetic polarization M (also called magnetization intensity or dipole mament per Wlit volume). The lineup ol internal dipoles produces a field M, whlch, witbin the body, is added lo tbe magnetizing field H. If M is conslant and has tbe same direction throughout, a body is said to be Wliformly magnetized. The SI unit for magnetization is ampere-meter1 per meter' [- ampere per meter

s

H

o.. -

0..' - Residual maptlsm

Oc - Oc' - Coercive torce

(A/m»).

For low magnetic fields, M is proportional to H and is in the direction ol H. The degree 10 whlch a body is magnetized is determined by its magnetic $usceptibility k, whlch is defined by s'

M-kH

(3.5)

Magnetic susceptibility in emu differs from that in SI units by the factor 4'11', tbat is,

(3.6) Susceptibility is tbe fundamental rock parameter in magnetic prospecting. The magnetic response of rocks and minerals is determined by the amounts and susceptibilities ol magnetic materials in them. Tbe susceptibilities of various materials are listed in Table 3.1, Section 3.3.7. Tbe magnetic induction B is tbe total field, including the effcct of magnetization. It can be wriuen

Figure 3.2. Hysteresis loop. s, s' - saturation. r and r' remanent magnetism, e and e' - eoercive force.

called tbe gamma, 1):

11 - 10- 9 T - 1 nT There is often confusion as 10 wbetber tbe quantity involved in magnetic exploration is B or H. Altbough we measure B., we are interested in the Earth's fie1d H,. However, because B and H are linearly related (Eq. (3.7») and usually l' .. 1. we can (and do) treat a map of B. as if it were a map of H,. We also speak of mognetic.flux or mognetic Unes offorce +:

(3.8) B - I'o(H + M) - 1'0(1 + k)H - I'I'oH (3.7a)

B' - H' + 4'11'M' - (1 + 4trk')H' - I'H' (3.7b) wben H and M (H' and M') are in tbe same direction, as is usually tbe case. Tbe SI unit lor B is tbe tesla - 1 newton/ampere-meter - 1 weber/meter 2 (Wb/ur). Tbe electromagnetic unit for B' is tbe gauss [- 10- 4 tesla (1)). Tbe permeabilily ol free space 1'0 bas tbe value 4", X 10- 7 Wb/A-m. In vacuum l' - 1 and in air l' • 1. Confusion sometimes results between H' and B' because tbe em units gauss and oented are numerical1y equal and dimensiona11y tbe same, altbough conceptually different; botb H' and B' are sometimes called the "magnetic field strengtb." In magnetic prospecting, we measure B to about 10- 4 of tbe Earth's main field (whlch is about SO I'T). Tbe unit of magnetic induction generally used for geopbysical work is tbe nanotesla (also

wbere A is a vector area (§A.3.2). Thus IBI - +/IAI when A and B are parallel, that is, 8 is the density of magnetic ftux. 'Ibe SI unit for magnetic ftux is the weber (- T-m2) and the em unít is the maxwell (- 10- 8 Wb).

3.2.2. B-H Relations: The Hysteresls loop The relation between B and H can be complex in ferromagnetic materials (§3.3.S). This is iIlustrated by bysteresis (Fig. 3.2) in a cycle of magnetization. 11 a demagnetized sample is subjected to an increasing magnetizing field H, we obtain the fint portion of the curve in whlch B increases with H until it ftauens off as we approach tbe maximum value that B can bave for tbe sample (saturation). When H is decreased, the curve does not retrace tbe same path, but it does sbow a positive value of B when H - O;

:.-

65

PrincipIes and e/emenrary rheory

this is called residual (remanen') magnetismo When H is reversed, B finally becomes zero at some oegative value oC H knowo as the coercive force. The other halC oC the hysteresis loop is obtained by making H still more negative uotil revefse saturation is reached and theo returniog H to the origioal positive saturation value. The area inside the curve represents the energy 105s per cycle per unit volume as a result oC hystere5is (see Kip, 1962, pp. 235-7). Residual effects io magoetic materials will be diseussed in more detail io Section 3.3.6. lo some magnetic materials, B may be quite ¡arge as a result of previous magoetizatioo having 00 re1ation to the present value oC H.

3.2.3. Magnetostatic Potential for a Dipole Field

1'.

-p

+p

-21 __

Conceptually the magnetic scalar potential A al lhe point P is the work dooe on a unít positive pole in brioging it from iofinity by any path against a magoetic field F(r) [compare Eq. (2.4)]. (HeoceCorlh in this chapter F, F indieate magoetic field rather than force and we assume l' .., 1.) When F(r) is due to a positive pole at a distance r Crom P,

Figure 3.3. Calculating rhe field o( a magnetic dipole.

lar componeot is

r+/cos8

F, - -p { 2 3/2 (r + /2 + 2r/cosO) -

A(r)--{ F(r)·dr=p/r

& - - aA/rao; these are

(3.9)

r-teosO } (r 2 + /2 _ 2rlcosO)3/2

(3.12a)

-00

l sin 8

However, since a magnetic pole canoot exist, we consider a magoetic dipole to get a realistic entity. Referriog to Figure 3.3, we calculate A at an externa! point:

&-

p{

+

(r 2

+ 12 + 2r/cosO) t sin O

(r 2 + , 2

-

3/2

3/2

}

(3.12b)

2rtcos8)

When r» /, Equation (3.10) becomes

(3.13) 1

where m is the dipole moment of magnitude m - 2/p. Equations (3.11) and (3.13) give [§A.4 and Equation (A.33)]

- P{ (r 2 + /2 - 2/rcos O) 1/1 -

(r 2

+

,2

1

+ 2/TeosO)

1/2

} (3.10)

We can derive the vector F by taking the gradient oC

F

COI

(m/r 3 )(2cos8r1

+ sin88¡) (3.14a)

where unit vectors r¡ and 8¡ are in the direction of increasing r and (J (counterclockwise in Fig. 3.3). The resultant magnítude is

A [Eq. (A.I7)]:

F(r) .. -VA(r) Its radial component is

(3.11)

1'. - - aA/a, and its angu-

and the direction with respect to the dipole axis is tana ==

&/1'. == (1/2) tan 8

(3.14c)

Magnetic methods

66

,l'

z Figure 3. 4. General magne/ic anomaly.

Two special cases, 9 - O and fT /2 in Equation (3.12), are called Ihe Gauss·A (end-on) and Gauss-B (side·on) positions. From Equations (3.12) they are given by

9-0

F, - O

(3.1Sa)

F,-O If r ::1>

"

F, - m/(r 2 +

12)3/2

9 - ,,/2 (3.1Sb)

the body (Fig. 3.4) is A - -f.M{r) v

.v( !ro - rl 1

) drJ

(3.17)

Tbe resultan1 magnetic field can be obtained by employing Equation (3.11) with Equation (3.17). This gives

F(ro) -

vI.vM(r) • v( Iro 1- rl ) dv

(3.18)

these simplify lo 9- O } 9 - .,,/2

If M is a constant vector wilb direction ex - (i + mj + nk, then the operation

(3.1Sc)

iJ ao

(iJ

M • V - M- - M ( -

ilx

a

ay

3.2.4. The General Magnetic Anomaly A volume ol magnetic material can be considered as an assortment of magnetic dipoles that results from the magnetic moments of individual atoms and dipoles. Whetber tbey initially are aligned so that a body exhibits residual magnetism depends on its previous magnetic history. Tbey will, however, be aJigned by induction in tbe presence of a magnetizo ing field. In any case, we may regard tbe body as a continuous distribution oC dipoles resulting in a veclor dipole moment per unit volume, M, oC magnitude M. Tbe scalar potential al P [see Fig. 3.3 and Eq. (3.13») some distance away from a dipole M (r ::1> 1) is A - M(r)cos9/r 2

-

-M{r) • v{l/r) (3.16)

The p01ential for the whole body al a point outside

a)

+ m - + n-

az

(3.19) (Eq. (A.18») and

a ( drJ A- -Mila Iv !ro -

rl

)

(3.20)

The magnetic fteld in Equation (3.20) eXÍSts in the presence of the Earth's field F,. Ibat is, the total fteld F is given by

F-F,+F(ro) where Ihe directions 01 F. and F(ro) are not necessarily tbe same. If F( ro) is much smaller than F. or ir me body has no residual magnetism, F and F. will be in approximately the same direction. Where F(ro) is an appreciable lraction (say, 2S% or more) ol F. and

rYI?i~ t1 et. ( i.) OH:_ n t-i ;::ti,..!

fb

U =0'I()I. Magnetism of the farth

tvt::

has a different direction, the component of F(ro) in the direction of F" FD , becomes [Eq. (3.20»)

F -'l· VA = D ...

-

aA iJI

=

a2 dv aa al viro - rl

where ' 1 is a unit vector in the direction oC F, (§3.3.2a). Ir the magnetization is mainly induced by F., then F.

D

(~) "" o

do

a2

dv

M-f -= k F - f . - al viro - rl • a/ viro - rl l

2

(3.21b) The magnetic interpretation problem is c1ear!y more compJex than the gravity problem because oC the dipo!ar fie!d (compare §2.2.3). The magnetic potential A, like the gravitational potential U, satisfies Lap!ace's and Poisson's equalions. Following the method used to derive Equations (2.12) and (2.13), we get V .F-

-v 2A

tt":;, \,'\1

't-

leí 1

mGl~ rl¡;~b .... ¡HOn.e::. t'I.rT

nent of g in the direction

-?

í-'($'

olcv\ ~\ "':'7

II¡

ga - -dU/da'" -VU·

bi':J.t 67

is al -

-rpv(l/r) . al

M--f--

(3.21a)

a2

(".¡ . ¡;:

(3.25)

Thus,

A = (Mlrp)g"

(3.26)

If we apply tbis result to an extended body. we

must sum contributions for each e1ement of volume. Provided that M and p do nol change throughout the body, the potentials A and U will be those for the extended body. ThereCore. Equations (3.24) lo (3.26) are valid for an extended body with constant density and uniform magnetization. In terms oC fieJds, F'" -VA - -(M/rp)vg"

- (M/rp) V(VU· lit) (3.27a)

=- (M/rp) VU"

where U. - dU/da. For a component 01 F in tbe direction PI' this becomes

.. 47r/Lp

p is the nel positive poJe strength per unit volume at a point. We recal! that a field F produces a partial reorientation a10ng the fieJd direction oC the previously randomly oriented elementary dipoJes. This causes, in etrect, a separation oC positive and negative poJes. For example, the x component oC F separates pole strengths + q and - q by a distance t a10ng lhe x axis and causes a net positive poJe strength (qn dy dz - M" dy dz to enler the rear Cace in Figure A.2a. Because the pole strength leaving through the opposite Cace is {M" + ( iJ M,,/dx) dx} dy dz, the net positive pole strength per unit volume (p) created at a point by the fie1d F is -V • M. Thus,

Fit -

(M/rp) U..p

(3.27b)

In particular. iC M is vertical. (he vertical component 01 F is

z-

(M/rp)U.. - (M/rp)( iJg./éJz) (3.28)

These reIations are used to make pseudogravity maps from magnetic data.

3.3. MAGNETISM OF THE EARTH 3.3.1. Nature of the Geomagnetic Field

(3.22)

As Car as exploration geophyics is concerned. tbe geomagnetic field oC the Eartb is composed oC three parts:

(3.23)

1. The main fie1d, which varies re1atively slowly and is of internal origino 2. A small field (compared to (he main field), which varies rather rapidly and originates outside tbe Earth. 3. Spatial variations oC the main field, which are usually smaller than tbe main field, are nearJy constant in time and place. and are caused by local magnctic anomalies in the near-surlace erust • of the Earth. These are the targets in magnetic prospecting.

In a nonmagnetic medium, M =- O and

3.2.5. Poisson's Relation If we have an infinitesimal unit volume with magnetic moment M - Ma.¡ and density p, then at a distant paint we have, trom Equation (3.16), A - -M· V(l/r) - -M V(l/r) . el¡ (3.24)

From Equations (2.3a), (2.5), and (A.l8), the compo-

Magnetic merhods

68 x Geopapbic North

t--..,....-~---y Ea.

1 I

I

1 I I 1

1 1

1 1 r---r-

1:

I

Z.

I I I , _____ .)1,

Figure 3.5. Elemenrs of rhe Earrh's magneric fíe/d.

3.3.2. The Main Field (a) The Earth's magnetic field. If an unmagnetized steel needle could be huug at its ceuter of gravity, so lbat it is Cree to orient itself in any direction, and ir other magnetic fields are absent, it would assume the direction of the Earth's total magnetic field, a direcliOD that is usuaUy neither horizontal nor in-line with the geographic meridiano The magnitude oC this field, F", the inclination (or dip) 01 the needle from the horizontal, 1, and the angle it malees with geographic north (the declinatian), D, completely define the main magnetic field. The magnetic elements (Whitham, 1960) are illustrated in Figure 3.5. The field can also be described iD terms of the vertical component, Z,. reckoned positive downward, and the horizontal component, H" which is always positive. X, and are the components oC Hf , which are considered positive to tbe nortb and east, respectively. These elements are related as follows:

y.

F.,2

. .

_ H2

+ Z2

H, -

F" cos 1

x, -

H,cosD

tan D - y'/X,

_

X,2 + Z, -

y. -

.

, + Z2

y2

F" sin 1

H,sin D

tan 1- Z,/H,

(3.29)

F, - F,,'l - F,,( cos D cos Ji

+ sin D cos IJ + sin Ik) As stated earlier, the end of the needle that dips downward in northem latitudes is the north-seeking

or positive pole; the end that dips downward in southern latitudes is the south-seeking or negative poleo Maps showing lines oC equal declination, inclination, horizontal intensity, and so on, are called isomagnetic maps (Fig. 3.6). Tsogonic. isoc/inic, and isodynamic maps show. respectively. lines oC equal declination D, inclination l. and equal values ol F., H" or Z,. Note that the inclination is large (that is, Z. > H.) for most oC the Earth's land masses, and hence corrections do not have to be made for la titude variations of F, or Z, ( ... 4 nT/km) except Cor surveys covering extensive areas. The overall magnetic lield does not reflect variations in surrace geology, such as mountain ranges, mid-ocean ridges or earthquake belts, so the source of the main lield líes deep within the Earth. The geomagnetic field resembIes that oC a dipole whose north and south magnetic poles are located approximatelyat 7s o N,101 °W and 69°S, 145°E. The dipole is displaced about 300 km from the Earth·s center toward Indonesia and is inclined some 11.5 0 to the Earth's axis. However, the geomagnetic lield is more complicated than the field of a simple dipole. The points where a dip needle js vertical, the dip po/es, are at 7s o N, 101 °W and 67°S, 143°E. The magnitudes ol F, at the nortb and south magnetic poles are 60 and 70 liT, respectively. The mínimum value, - 25 liT, occurs in southern BraziJ -South Atlantic. In a lew locations, F, is larger than 300 p.T because of near-surlace magnetic features. The line of zero incllnation (magnetic eqtl4tor, where Z - O) is never more than 15 0 from the Earth's equator. The largest deviations are in South America and the eastern Pacifico In Africa and Asia it is sligbt1y nortb of the equator. (b) Origin of the main field. Spherical harmonic analysis ol the observed magnetic field shows that over 99% is due to sources inside the Earth. The present theory is that the main field is caused by convection currents ol conducting material circulating in the liquid outer core (which extends from depths al 2,800 to 5,000 km). The Earth's core is assumed to be a mixture of ¡ron and nickel, both good electrical conductors. The magnetic source is thougbt to be a self-excited dynamo in which highIy conductive fluid moves in a complex manner caused by convection. Paleomagnetic data show that tbe magnetic field has always been rough1y along the Earth's spín axis, implying that the convective motion is coupled to the Earth's spin. Recent exploration of the magnetic fields ol other planets and their satellites provide fascinating comparisons with the Earth's field.

,1

Figure 3.6. The farth's magnetic field in 1975. (From Smith, 1982). (a) Declination (heavy /ines) and annual rate 01 change in minutes/year (Iight lines)

'" - - - t o t a l IntenS&ty . _ - - annual chenoe

Figure 3.6. (Continued) (e) total fie/d strength in nanotes/a (heavy lines) and fate of change in nanotes/alrear (light ¡¡nes).

72 (e) Secular variations of the main field. Four hundred years oC continuous study 01 the Earth's field has established thal il changes slowly. The inclination has changed some 10° (75° 10 65°) and the dcclination abaut 3So (lOOE to 2SoW and back 10 10°W) duriog this periodo The source ol this wandering is thoughl 10 be changes in convection currents in the coreo The Earth's magnetic field has also reversed direction a number 01 times. The times 01 many ol the periodic field reversals have been ascertained and provide a magnetochronographie time sea/e.

3.3.3. The External Magnetic Field Most ol the remaining small portion ol the geomagnetic field appears to be associated with eleetric currents in the ionized layen of the upper atmosphere. Time variations of this portion are much more rapid than Cor the main .. permanent" field. Some effeets are: 1. A cycle ol 11 years duration that correlates with sunspot activity. 2. Solar diurnal variations with a period of 24 h and a range ol 30 nT that vary with latitude and season, and are probably controUed by action 01 the solar wind on ionospheric currents. 3. Lunar variations with a 25 h period and an amplitude 2 nT that vary cyclically throughout the month and seem to be associated with a Moon-ionosphere interaction. 4. Magnetic storms that are transieot disturoances with amplitudes up 10 1,000 nT at most latitudes and even larger in polar regions, where they are associated with aurora. Although erratic, they often occur at 27 day intervals and coerclate with sunspot activity. At the beight of a magnetic storm (which may last lor several days), long-range radio reception is affeeted and magnetic prospecting may be impractica1. These time and space variations ol the Earth's main field do not significantly affeet magnetic prospecting except lor the occ8SÍonal magnetic storm. Diurnal variations can be corrected lor by use oí a base-station magnetometer. Latitude variations (- 4 nT¡km) require corrections onIy lor high-resolution, high-Iatitude, or large-scale surveys.

3.3.4. Local Magnetic Anomalies Local changes in the main field result from variations in the magnetic mineral content ol near-surface rocks. These ;momalies occasionally are large enough to double the main field. They usually do not persist over great distances; thus magnetic maps generally do not exhibit large-sca1e regional features (although

Magnetic methods

the Canadian Shield, Cor example, shows a magnetic contrast 10 the Westem P1ains). Many large, erratic variations olteo mm magnetic maps extremely complex. The sources ol local magnetic anomalies cannot be very deep, because temperatures below - 40 km should be above the Curie point, the temperature (. SSO°C) at which rocks lose their magnetic properties. Thus, local anomalies must be associated with features in the upper erust.

3.3.5. Magnetism 01 Racks and Minerals Magnetic anomalies are caused by magnetic minerals (mainly magnetite and pyrrhotite) contained in the racks. MagneticaJly important minerals are surprisingly few in number. Substances can be divided 00 the basis oí their behavior when placed in an external field. A substance is diamagnetic ir its field is dominated by atoms with orbital electrons oriented to oppose the external field, that is, if it exhibits negative susceptibility. Diamagnetism will prevail on1y if the oet magnetic moment of all atoms is zero when H is uro, a situation characteristic oC atoms with completely fiUed eleetron shells. The most common diamagnetic earth materials are graphite, marble, quartz, and salt. When the magnetic moment is not zero when H is zero, the susceptibility is positive and the substance is paramognetic. lbe effects of diamagnetism and mast paramagnetism are weak. Certain paramagnetic elements, namely iron, cobalt, and Dicke1, have such strong magnetic ¡oteraction that the moments align within lairly large regions called domaiJU. This effeet is called ferromagnetism and it is - 106 times tbe effects of diamagnetism and paramagnetism. Ferromagnetism deereases with inereasing temperature and disappears entirely at the Curie temperature. Apparently lerromagnetic minerals do not exist in nature. The domaios in lOme materials are subdivided into subdomains lbat align in opposite directions so that their moments oearly cancel; although they would otherwise be considered ferromagnetic, the susceptibility is comparative1y low. Such a substance is antiferromognetic. The only common example is hematite. In some materials, the magnetic subdomains align in opposition but their net moment is not zero, either because one set 01 subdomains has a stronger magnetic alignment than the other or because there are more subdomains oC one type than oí the other. These substances are ferrimognetic. Examples 01 the first type are magnetite and titanomagnetite, oxides 01 ¡ron and 01 iron and titanium. Pyrrhotite is a magnetic mineral of the second type. Practically all magnetic minerals are ferrimagnetic.

73

Magnetism of the farth

3.3.6. Remanent Magnetism In many cases, the magnetization of rocles depends mainly on the present geomagnetic field and the magnetic mineral contento Residual magnetism (called natural remanent magnetization, NRM) often contributes to the total magnetization, both in amplitude and direction. The efrect is complicated because NRM depends on the magnetic bistory of the rock. Natural remanent magnetization may be due to several causes. TIte principal ones are: 1. Thermoremanent magnetization (TRM), wbich results when magnetic material is cooled below the Curie point in the presence of an external field (usually the Earth's field). Its direction depends on the direction of the field at the time and place where the rock cooled. Remanence acquired in tbis fasbion is particularly stable. This is the main mechanism for the residual magnetization of igneous rocks. 2. De/ri/al magnetiza/ion (DRM), wbich occurs during the slow settling of fine-grained partic\es in the presence of an external field. Varied c\ays exhibit tbis type of remanenee. 3. Chemical remanent magnetiza/ion (CRM), wbieh talces place when magnetie grains inerease in size or are ehanged from one Corm to another as a result of chemieal aetion at moderate temperatures, that is, below lhe Curie point. This process may be signifieant in sedimentary and metamorpbie rocks. 4. [so/herma! remanent magnetiza/ion (IRM), wbieh is the residual left following the removal of an external field (see Fig. 3.2). Lightning strikes produce IRM over very small areas. S. ViscoUJ remanent magnetization (VRM), whieh is produced by long exposure to an external field; the buildup of remanenee is a logaritbmie funetion of time. VRM is probably more charaeteristic of fine-grained than eoarse-grained rocks. This remanenee is quite stable.

Studies of the magnetic bistory of the Earth (pa/eomagne/ism) indicate that the Earth's field has varied in magnitude and has reversed its polarity a number of times (Strangway, 1970). Furthermore, it appears that the reversals took place rapidly in geologie time, because there is no evidence that the Earth existed without a magnetie field Cor any significant periodo Model studies of a self-exeited dynamo show sueh a rapid turnover. Many rocks have remanent magnetism that is oriented neither in the direetion of, nor opposite to, the present Earth field. Sueh results support the plale teetonics theory. Paleomagnetism helps age-date rocks and determine past movements, sueh as plate rotations. Paleomagnetic

laboratory methods separate residual from indueed magnetization, something that eanno! be done in the field.

3.3.7, Magnetic Susceptibilities af Racks and Minerals Magnetic susceptibility is the significant variable in magnetics. It plays the same role as density does in gravity interpretation. Although instruments are available for measuring suseeptibility in the field, they can only be used on outerops or on rock sampIes, and sueh measurements do not necessarily give the bu\k susceptibility of the Cormation. From Figure 3.2, it is obvious that k (hence p. also) is not constant for a magnetic substance; as H ¡nereases, k inereases rapidly at first, reaehes a maximum, and then decreases to z.ero. Furthermore, although magnetization curves have the same general shape, the value of H for saturation varies greatly with the type of magnetic mineral. Thus it is important in miling susceptibility determinations to use a value of H about the same as that oC the Earth's field. Since the Cerrimagnetie minerals, partieularly magnetite, are the main source of local magnetic anomalles, there have been numerous attempts to establish a quantitative relation between rock susceptibility and FCjO.. coneentration. A rough linear dependenee (k ranging from 10- 3 to 1 SI unit as the volume pereent oC FCjO" incceases from 0.05% to 35%) is shown in one report, but the seatter is large, and results from other areas ditrer. Table 3.1 lists magnetie susceptibilities for a variety oC rocks. Although there is great variation, even for a particular rock, and wide overlap between different types, sedimentary rocks have the lowest average susceptibility and basic igneous rocks have the highest. In every case, the suseeptibility depends only on the amount of fecrimagnetic minerals present, mainly magnetite, sometimes titano-magnetite or pyrrhotite. TIte values oC chalcopyrite and pyrite are typieal of many sulfide mineral s that are basically nonmagnetie. It is possible to locate mineral s oC negative susceptibility, although the negative values are very small, by means oC detailed magnetie surveys. It is also worth noting that many iron minerals are only slightly magnetic.

3.3.8. Magnetic Susceptibility Measurements (a) Measurement of k. Most measurements oC k involve a eomparison of the sample with a standard. TIte simplest laboratory method is to compare the deflection produeed on a tangent magnetometer by a

74

Magnetic methods Table 3.1. Magnetic 5u5ceptibiliies 01 various rocks and minera/s. Susceptibility X 101 (SI) Type

Range

Average

0-0.9 0-3 0-20 0.01-15 0-18

0.1 0.3 0.4 0.6 0.9

0.3-3

0.7 1.4 1.5

Sedimentary

Dolomíle límeslones Sandslones Shales Av. 48 sedimenlary Metamorphic

Amphibolite Schist Phyllíte Gneíss Quarlzite Serpentíne Slate Av. 61 metamorphíc

0.1 - 25 4 3-17 0-35 0-70

6 4.2

O-SO

2.5

'gneous

Graníle Rhyolíle Dolorile Augíle-syenile Olíví ne-diabase Oíabase Porphyry Gabbro Basalts Dionte Pyroxenite Peridotite Andesile Av. acidie igneous Av. basic igneous

0.2-35 1-35 30-40 1-160 0.3- 200 1-00 0.2-175 0.6-120 00-200 0-80 0.5-97

17 25 55

ro 70 70 85 125 150 160 8 25

Minerals

Graphile Quartz Rock sal! Anhydrite, gypsum Calcile Coal Clays Chalcopyríte Sphalerite Cassilerite Siderite Pyrite Umonite Arsenopyrile Hematite Chromite Frankliníte Pyrrhotite IImeníte Magnelite

0.1 -0.01 -0.01 -0.01 - 0.001 - - 0.01 0.02 0.2 0.4 0.7 0.9 1-4 0.05-5 0.5-35 3-110 1-6000 300-3500 1200-19200

1.5 2.5 3 6.S 7 430 1500 1800 6000

75

Field instruments for magnetic measurements

prepared sample (either a drill core or powdered rock in a tube) with that oC a standard sample oC magnetic material (oCten FeCI 1 powder in a test tube) when the sample is in the Gauss-A position [Eq. (3.lSa)]. The susceptibility oC the sample is Cound Crom the ratio of deftections:

Overton, 1981). They achieve great sensitivity because oC the bigh magnetic moments and low noise obtainable at superconducting tempera tu res.

3.4. FIElD INSTRUMENTS FOR MAGNETIC MEASUREMENTS 3.4.1. General

d, and dlld are the deflections for the sample and standard, respectively. The samples must be oC the

same size. A similar comparison method employs an inductance bridge (Hague, 19S7) having several air-core coils oC different cross sections to accommodate sampIes oC different sizes. The sample is inserted into one oC the coils and the bridge balance condition is compared with the bridge balance obtained when a standard sample is in the coil. The bridge may be calibrated to give susceptibility directly, in wbich case the sample need not have a particular geometry (although the calibration may not be valid for sampIes oC bighly irregular sbape). This type oC ¡nstrument with a large diameter coil is used in field measurements on outcrop. The bridge is balanced first witb the coil remote from the outcrop and then Iying on it. A calibration curve obtained with a standard relates k and tbe change in inductance.

,

1

i

(b) Measurement of remanent magnetismo Measurement of remanent susceptibilty is considerably more complicated than that of k. One method uses an astatic magnetometer, which consists of two magnets of equal moment that are rigidly mounted parallel to each other in the sarne horizontal plane witb opposing poles. The magnetic system is suspended by a torsion flber. The specimen is placed in various orientations below the astatic system and the angular deflections are measured. Tbis dcvice, in effect, measures the magnetic field gradient, so tbat extraneous fields must either be eliminatcd or made unifonn over the region oC the sample. Usually the entire assembly is mounted inside a thrcc-component coil system tbat cancels the Eartb's field. Anotber instrument for the analysis of the residual component is the spinner magnetometer. The rock sample is rotated at higb spccd near a small pickup coil and its magnetic moment generates alternating current (ac) in the coil. The phase and intensity o( the coil signal are comparcd with a reference signa! generated by tbe rotating system. The total moment of the sample is obtained by rotating it about different axes. Cryogenic instruments for determining twoaxes remanent magnetism have becn developed (Zimmerman and Campbell, 1975; Weinstock and

Typical sensitivity required in ground magnetic instruments is between 1 and 10 nT in a total field rarely larger than 50,000 nT. Recent airborne applications, however, have led to the development oC magnetometers with sensitivity of 0.001 nT. Sorne magnetometers measure the absolute field. a1though tbis is not a particular advantage in magnetic surveying. The earHest devices used ror magnetic exploration were modifications of the mariner's compass, such as the Swedish mining compass. which measured dip I and declination D. Instruments (such as magnetic variometers, which are essential1y dip needles of high sensitivity) were developcd to measure Z. and H., but they are seldom used now. Only the modern instruments, the ftuxgate, proton-precession, and optical-pump (usually rubidium-vapor) magnetometers, will be discussed. The latter two measure the absolute total field. and the ftuxgate instrument also generally measures the total field.

3.4.2. Fluxgate Magnetometer This device was originaIly developed during World War 11 as a sub marine detector. Several designs bave been used lor recording diurnal variations in the Earth's field, for airborne geomagnetics, and as portable ground magnetometers. The fluxgate detector consists essentialIy of a core oC magnetic material, such as mu-metal, pennalloy, or ferrite, that has a very high permeability at low magnetic fields. In the most common design, two cores are each wound with primary and secondary coils, the two assemblies being as nearly as possible identical and mounted parallel so that the windings are in opposition. The two primary windings are connected in series and energized by a low frequency (50 to 1,000 Hz) current produccd by a constant current source. The maximum current is sufficient to magnetize the cores to saturation, in opposite polarity, twice each cycle. The secondary coils, which consist oC many turos of fine wire, are connected to a differential amplifier, whose output is proportionaI to the difference between two input signals. The effect of saturation in the ftuxgate elements is iIlustrated in Figure 3.7. In the absence oC an external magnetic field, the saturation of the cores is

76

Magnetic methods B,. B.

H,-

H.

o

l1:li

O

B, -- -82

----1:""""'__- - H

lb)

Ma¡neliulion

Primary a.c. field --::::;;-.¡... curvo> for ~ lu ... IO coreo in Ihe 2 coil. ,----_B,. B.

I--'r---Ar--+--

(r)

(a)

H, "O B, .. -B,

8.+B, H," O (d)

dB

"di

j.;

I

L

Y

V

H, ... O

A

Fi8ure 3. 7. PrincipIe of the flux8ate ma8netometer. Note that H. - Fe. etc. (From Whitham. 1960.) (a) Ma8netization of the eores. (b) Flux in the two eores fo, F. - O. (e) Flux in the two eores for ~ ~ O. (d) 1) + ~ fo, F. ". o. (e) Ourpur volrase for F• .. O.

symmetrical and of opposite sigo near tbe peak of eaeh half-cycle so that the outputs from the two secondary windings cancel. The presence of an external field component parallel to the cores causes saturation lo occur earlier for one half-cyc1e than tbe otber, producing an unbalance. The difference between output voltages from the secondary windings is a series of voltage pulses which are fed into the amplifier, as shOWD in Figure 3.7d. The pulse height is proportional lo the amplitude oC the biasing field of the Earth. Obviously any component can be measured by suitable orientation 01 the cores. The original problem with this type 01 magnetometer - a IICk of sensitivity in the care - has been solved by the development and use of materials haviog suflicient initial permeability to saturate in small fields. Clearly tbe hysteresis loop should be as thin as possible. There remains a relatively high noise level, caused by hysteresis effects in the coreo The fluxgate elements should be long and thin to reduce eddy eurrents. Improvements introduced to inercase the sigoal-to-noise ratio inc1ude the foUowing: l. By deliberately unbalancing tbe two elements, voltage spikes are present with or without an ambient field. The presence of tbe Earth's fteld ineceases the voltage of one polarity more than the other and this dift'erence is amplified. 2. Because the odd harmonics are canceled fairly

F¡8ure 3.8. Portable fluxgate magnetometer.

77

Field instruments far magnetic measurements Earthts m"netic field

Malnetic

Fe Prtcession

Spin momentum

¿th

Magnetic tor'lu. on proton

E,rth',

,ravity tI.1d

Figure 3. 9. Proton precession and spinning-top ana/ogy.

well in a reasonably matched set of cores. the even harmonics (generally only the second is significant) are amplified to appear as positive or negative signals, depending on the polarity of the Earth's field. 3. Most 01 the ambient field is canceled and variations in the remainder are detected with an extra secondary winding. 4. Negative feedback of the amplifier outputs is used to reduce the effeet of the Earth's field. 5. By tuning the output of the seeondary windings with a capacitance. the second harmonie is greatly inereased; a phase-sensitive detector, rather than the differenee amplifier, may be used with tbis arrangement. There are several fundamental sources of error in the ftuxgate instrument. These incIude inherent unbalance in the two eores, thermal and shock noise in eores, drift in biasing cireuits, and temperature sensitivity (1 nT1°C or less). lbese disadvantages are minor, however, compared to the obvious advantages - direet readout, no azimuth orientation, rather eoarse levellng requirements, llgbt weigbt (2 to 3 kg), small size, and reasonable sensitivity. Another attractive feature is that any component of the magnetic field may be measured. No elaborate tripod is required and readings may be made very quickly, generally in about 15 s. A portable ftuxgate instrument is shown in Figure 3.8.

have a Det magnetic moment that, coupled with their spin, causes them to precess about an axial magnetic fieid. The proton-preeession magnetometer depends on the measurement of the free-precession frequency of protons (hydrogen nuclei) that have been polarized in a direetion approximately normal to the direction of the Earth's field. When the polarizing field is suddenly removed. the protons precess about the Earth's field like a spinning top; the Earth's field supplies the precessing force corresponding to Ihal of gravity in the case of a topo The analogy is ilIustrated in Figure 3.9. The protons precess at an angular velocity w, known as the Larmor precession Irequency, wbich is proportional to the magnetic field F, so that

(3.30a) lbe constant Yp is the gvromaglletic ratio 01 rhe pr%n, the ratio oC its magnetic moment lO its spin angular momentum. The value of Yp is known to an accuracy oí 0.001 %. Since precise frequeney measurements are relatively easy, the magnetic field can be determined to the same aecuracy. The proton, wbieh is a moving charge, induces, in a eoil surrounding the sample, a voltage that varies al the preeession frequency v. Thus we can determine the magnetic field from (3.30b)

3.4.3. Proton-Precession Magnetometer Tbis instrument grew out of the discovery, around 1945, of nuclear magnetic resonance. Some nuclei

where the factor 21T/yp = 23.487 ± 0.002 nT/Hz. Only the total fie\d may be mcasured.

Magnetic methods

18 O.CIIl."O. 01 kIIo_ft fr.~ ...c,

Po.,r 1""', to

Col"'" ,.

p.'" Ut

Ita ••

o,.. ,.t,

.U.r •• 011 500 cJe'"

... ,.,tlelll,.

...,.,1'

·'0 ....

o...

TIIft" to c,nt,ol •• !te"

Figure 3.10. Proton-precession magnetometer. (From Sheriff, 1984.)

The essential components oC this magnetometer inelude a source oC protons, a polarizing magnetic field considerably stronger than that oC the Earth and directed roughly normal to it (the direction oC this fieId can be off by 45°), a pickup coil coupled tightly to the source, an amplifier to boost the minute voltage induced in the pickup coi!, and a frequeneymeasuring device. The latter operates in the audio range because, from Equation (3.30b), " - 2130 Hz Cor F. = 50,000 nT. It must also be capable of indicaling Crequency differences of about 0.4 Hz ior an instrument sensitivity of 10 nT. The proton source is usually a smalI bottIe oC water (the nuclear moment of oxygen is zero) or sorne organic ftuid rieh in bydrogen, such as alcohol. The poIarizing fieId oC 5 to 10 mT is obtained by passing direct current througb a solenoid wound around the battle, which is oriented roughly east-west Cor the measurement. When the solenoid current is abruptly cut off, the proton precession about the Earth's field is detected by a second coil as a transient vollage building up and decaying over an interval of - 3 s, modulated by the precession frequency. In some models the same coil is used Cor both polarization and deteetion. The modulation signal is amplified to a suitable level and the frequency measured. A schematic diagram is shown in Figure

3.10. The measurement oC frequency may be carried out by actually counting precession eycles in an exact time interval, oc by comparing them with a very stable fcequency generalor. In one ground model, the precession signal is mixed with a signal Crom a local oscillator of high preclsion to produce low-frequeney beats ( .. 100 Hz) that drive a vibrating reed frequency meter. RegardIess of the method used, the frequeney must be measured to an aeeuraey of 0.001 % to realize the eapabilities of the method. Although this is not particuJarly difficult in

a fixed instalIation, it posses sorne problems in small portable equipment. The proton-precession magnetomeler's sensitivity ( ... 1 n1) is high, and it is essenlially free from drilt. The Caet that it requires no orientation or leveling makes it attractive Cor marine and airbome operations. It has essentialIy no mechanical parts. although Ihe eleetronie eomponenls are relatively complex. The main disadvantage is that only !he total field can be measured_ It a1so cannot record eontinuously beeause it requires a seeond or more between readings_ In an aireraft traveling at 300 kmjhr. the distance interval is about 100 m_ Proton-precession magnetometers are now the dominant instrument lor both ground and airbome applications.

3.4,4. Optically Pumped Magnetometer A variety of scientific instruments and teehDiques has been developed using the energy in translerring atomic electrons Crom one energy leve! to another_ For example, by irradiating a gas with light or radio-lrequency waves of the proper frequency. electrons may be raised to a higber energy level. If they can be accumulated in such a state and tben sud· denly retumed to a lower level, they release some of Iheir energy in the process. This energy may be used Cor amplification (masers) or to get an in tense Iigbt beam, sueh as that produced by a laser. The optica1ly pumped magnetometer is another applieation. The principie of operatioD may be understood from an examination oC Figure 3.11a, whi~ shows three possible energy levels, Al, Al' and B for a hypothetieal atom. Under normal conditions 01 pressure and lemperalure. the aloms oceupy ground state levels Al and A 2 • The energy difference between Al and A 2 is very small ( .. lO-a electron volts (eV)J, representing a fine structure due to atomic electron spins that normally are not a11 aligned in the

Field instruments far magnetic measurements

79

Figure 311. Optical pumping. (a) fnergv level transitions. (b) fffecl o{ pumplllg liShl Iral1smission.

J

•

.,¡

same direction. Even thermal energies ("" 10- 2 eV) are much larger than lhis. so Ihat the atoms are as likely to be in Ievel Al as in A 2. Level B represents a much higher energy and the transitions from Al or A2 to B correspond to infrared or visible spectral lines. Ir we irradiate a sample with a beam from which spectral line A 2 B has been removed. atoms in leveI Al can absorb energy and rise lo B. but atoms in A 2 will not be excited. When Ihe exciled aloms fall back to ground slale. Ibey may return lo either leveI. but if they fall 10 Al' they wiII be removed by photon excitation to B again. The resuII is an accumulation of atoms in level A2 • The tecbnique of overpopulating one energy level in tbis Casbion is known as oplica/ pumping. As the atoms are moved from level Al to A 2 by tbis selective process. less energy will be absorbed and the sample becomes increasingly transparent to the irradiating beam. When all aloms are in the A 2 stale, a photosensitive detector will register a maximum currento as sbown in Figure 3.llb. lf now we apply an RF signal. having energy corresponding to the Iransilion between Al and A 2. the pumping elfect is nullified and the transparency drops to a minimum again. The proper frequency for this signal is given by p - E/h. where E is the energy dilference between Al and A2 and h is Planck's constant [6.62 x 10- l4 joule-seconds). To make Ibis device into a magnetomeler. il is necessary 10 selecl aloms that have magnetic energy sublevels that are suitably spaced to give a measure oC the weak magnetic field of the Earth. Elements thal have been used for tbis purpose inelude cesium. rubidium. sodium. and helium. The first Ihree each have a single electron in the outer shell whose spin axis lies either parallel or anliparallel to an external magnetic field. These two orientations correspond to

011

the energy levels Al and Al (actually the sublevels are more complicated than this. but the simplification illustrates the pumping action adequately), and there is a dilference of one quantum of angular momenlum between tbe paraIJel and antiparallel states. The irradiating beam is circularly polarized so that the photons in the Iighl beam have a single spin axis. Atoms in sublevel Al Ihen can be pumped to B, gaining one quantum by absorption. whereas those in A 2 already have the same momentum as B and cannol make the transition. Figure 3.12 is a schemalic diagram of the rubidium-vapor magnetometer. Light Crom the Rb lamp is circularly polarized lo iIIuminate Ih.: Rb vapor cell. aCter which it is refocused on a pholocell. The axis oC this beam is inclined approximalely 45 0 to the Earth's field, which causes the electrons lo precess aboul the axis of Ihe fie1d at the Larmor frequency. At one point in the precession cycle the atoms will be mosl nearly parallel lO the light-beam direction and onehaH cycle laler Ihey will be more antiparallel. In the firsl position. more Iighl is Iransmitted through Ihe cell Ihan in Ihe second. Thus Ihe precession frequency produces a variable light intensity Ihal Hickers al Ihe Larmor frequency. lf Ihe pholocell signal is amplified and Ced back lo a coil wound on Ihe cell. the coil-amplifier system becomes an oscillalor whose frequency v is given by

(3.31) where Y. is Ihe gyromagnelic ratio 01 (he e/edron. For Rb. the value oC y./2." is approximately 4.67 Hz/nT whereas the corresponding frequency for F, - 50.000 nT is 233 kHz. Because y. for the eleclron is known lo a precision of about 1 part in 107 and because of Ihe relatively high frequencies involved, it

Magnetic methods

80

r--- - -- -:- - - - - - - - - - - - - - I

F.~Eanh'

ficld~Rb_reo" ~

I

I

1 I I 11 I

I

.

~/""

d

,/""'. Interf_ Cimd.. filter polamer

UD

I

r---- --, 1,..----,

I

1 I

- -

I

IlF feod ....t T

I I

_

- -:__

tJ- - -

r

...

pI'k

<00 .....11

11l·~iumf::- fl--fl.-P

---T;Il¡;~1

Len.

I

~I

I

L.. ____________________________

I J

Figure J 12. Rubidium-vapor magnetomerer (schemar;c).

is not difficult to measure magnetic field varialions as small as 0.01 nT with a magnetomeler of this Iype.

3.4.5. Gradiometers The sensitivity of tbe optically pumped magnetometer ís considerably greater tban normally required in prospecting. Since 1965, optically pumped rubidiumand cesium-vapor magnetometers have been increasingly employed in airbome gradiometers. Two detectors, vertieally separated by about 35 m, measure dF Idz, tbe total-field vertical gradíent. The sensitivity is reduced by pitcb and yaw of the two birds. Major improvements by the Geologieal Survey of Canada involve reducíng tbe vertical separation to 1 to 2 m and using a more rigid conneetion between tbe sensors. Gradient measurements are also made in ground surveys. The two sensors on a staft' in tbe Scintrex MP-3 proton-magnetometer system, for example. measure tbe gradient to ±O.l nT/m. Gradiometer surveys are discussed further in Seetion

3.5.5.

method employs a Helmholtz eoil large enough to surround the instrument. ThJs is a pair ol identieal eoils ol N turns and radii a eoaxialIy spaeed a distanee apart equal lo the radius. The resulting magnetic field, for a eurrent 1 ftowing lhrough lhe eoils eonneeted in series-aiding. is direeted along tbe axis and is uniform within about 6% over a eylinder oC diameter a and length 3014, eoncentrie with the coils. This field is given by

H'" 9.0Nlla

(3.32a)

where I is in mieroamperes. H in nanoteslas, and a in meters. Because H varies direetIy with lhe eurrent, this can be written

AH - 9.0NA1la

( 3.32b)

3.5. FIELO OPERATIONS 3.5.1. General

3.4.6. Instrument Recording Originally tbe magnetometer output in airbome installations was displayed by pen recorder. To aehieve both bigb sensitivity and wide range, tbe graph would be "paged back" (tbe referenee value ehanged) frequently to prevent the pen from running off lhe papero Today recording is done digitally, but generally an analog display is also made during a survey. Some portable instruments for ground work also digitally record magnetometer readings, station eoardinates, diurnal eorrections, geologiCal and terrain data.

3.4.7. Calibration of Magnetometers Magnetometers may be calibrated by placing them in a suitably oriented variable magnetie field 01 knOWD value. Tbe most dependable ealibration

Magnetic exploration is earried out on land, at sea, and in the airo For areas oC appreciable extent, surveys usually are done wilh tbe airborne magnetometer. In oil exploration, airborne magneties (along with surface gravity) is done as a preliminary to seismie work to establish approximale deptb, topography, and charaeter of tbe basement rocks. Since tbe suseeptibilities of sedimentary rocks are relatively small, the main response is due lo igneous rocks below (and sometimes within) the sediments. Within the last few years it has become possible to extraet Irom aeromagnetie data weak anomalies originating in sedimentary racks, such as result lrom the faulling of sandstones. This results from (a) the improved sensitivity 01 magnetometers, (b) more precise delermination ol location with Doppler radar (§B.S). (e) corrections for diurnal and other temporal

Field operations

lieJd variations, and (d) computer-analysis techDiques to remove noise effects. Airborne reconnaissance Cor minerals Crequently combines magnetics witb airborne EM. In most cases of followup, detailed ground magnetic surveys are carried out. The metbod is usually indirect, that is, Ihe primary interest is in geological mapping rather than the mineral concentration per se. Frequently tbe association oC characteristic magnetic anomalies with base-metal sulfides, gold. asbestos, and so on, has been used as a marker in mineral exploration. There is also, of course, an application ror magnetics in the direct search Cor certain iron and titanium ores.

3.5.2. Airborne Magnetic Surveys (a) General. In Canada and some other countries, government agencies have surveyed much oC the country and aeromagnetic maps on a scale of 1 mile to tbe inch are available at a nominal sumo Large areas in all parts oC the world have also been surveyed in the course of oil and mineral exploration. The sensitivity oC airborne magnetometers is generally greater than those used in ground exploration - about 0.01 nT compared with 10 to 20 nT. Because oC the initial large cost oí the aircraft and availability oC space, it is practical to use more sophisticated equipment than could be handled in portable instruments; their greater sensitivity is usefuI in making measurements several hundred meters aboye tbe ground surface, whereas the same sensitivity is usually unnecessary (and may even be undesirable) in ground surveys. (b) Instrument mounting. Aside from stabili7.alion, there are certain problems in mounting the sensitive magnetic detector in an airplane, because the latter has a complicated magnetic field oC its own. One obvious way to eliminate these effects is to tow the sensing element some distance behind the ai.craCt. This was tbe original mounting arrangement and is still used. The detector is housed in a streamIined cylindrical container, known as a bird, connected by a cable 30 to 150 m long. Thus the bird may be 75 m nearer the ground than the aircraCt. A pbotograph of a bird mounting is shown in Figure

3. 13 a. +-

An alternative scheme is to mount the detector on a wing tip or sligh tly behind the tail. The stray magnetic elrects 01 the plane are minimized by permanent magnets and soCt iron or permalloy shie1ding strip s, by currents in compensating coils, and by metallic sheets Cor e1ectric shielding oC the eddy currents. The shielding is a cut·and- try process, since the magnetic effects vary witb the aircraft and

81

mounting location. Figure 3.l3b shows an installation with the magnelometer head in the tai\. (e) Stabilization. Since proton-precession and optically pumped magnetometers measure total field, the problem oC stable orientation oC the sensing element is minoro Although the polarizing field in the proton-precession instrument must not be parallel to the total-field direction, practically any other orientation will do because the signal amplitude becomes inadequate only within a cone of about 5°. Stabili7.ation oC the fluxgate magnetometer is more difficult, because the sensing element must be maintained accurately in the Faxis. This is accomplished with two additional ftuxgate detectors that are oriented orthogonally with the first; that is, the three elemenls Corm a three-dimensional orthogonal coor· dinate system. The set is mounted on a small platform that rota tes freely in all directions. When the sensing ftuxgate is accurately aligned along the total-field axis, there is zero signal in the other two. Any litt away from this axis produces a signal in the control elements lhat drive servomotors to restore the system lo the proper orientation. (d) Flight pattern. Aeromagnetic surveys almost always consist of paTallel lines (Fig. 3.13c) spaced anywhere from 100 m to several kilometers apart. The heading generally is normal to the main geologic trend in the area and altitude usually is maintained al fixed elevations, the height being conlinuously recorded by radio or barometric altimeters. It is customary to record changes in the Earth's field with lime (due lo diurnal or more sudden variations) wilh a recording magnetometer on the ground. A further check generally is obtained by ftying several cross lines, which verify readings al line intersections. A drape suroey, which approximates constant clearance over rough topography, is gene rally Ilown with a helicopter. It is often assumed that drape surveys minimize magnetic terrain effects, but Grauch and Campbell (1984) dispute tbis. Using a uniformly magnetized model of a mountain-valley system, four profiles (one level, the others at different ground clearance) all showed terrain effects. However, Grauch and Campbell recommend drape surveys over level-flighl surveys because oí greater sensitivity to small targets, particularly in valleys. The disadvantages oC draped surveys are higher cost, operational problems, and less sophisticated interpretation techniques. (e) Effeet of variations in flight path. Allitude differences between flight lines may cause herringbone patterns in the magnetic data. Bhattacharyya (1970) studied errors arising from flight deviations

Compensali", plale

Magnetometer hcad

(b)

---Aipllincs

_

Conlrollincs

-

Total fiekl contoun

( e)

Figure 3.13. Ai,borne mdgnetics. (d) Mdgnetometer in d bi,d. (b) Mdgnetometer in d fail mounting. (c)Flight pattem and magnetic mdp.

Field operations

over an idealized dike (prism) larget. Altitude and heading changes produced field measurement changes tbat would alter interpretations based on anomaly shape measurements, such as those of slope. Such deviations are especially significant with higb-resolution data. The simplest metbod of localing the aircraft al all times, with respecI lo ground location, is for the pilot to control the flight path by using aerial pbotograpbs, while a carnera takes photos on strip film lo determine locations later. The pholos and magnetic data are simultaneously tagged at intervals. Over featureless terrain, radio navigation (see §B.6) gives aircraft position witb respect to two or more ground stations, or Doppler radar (§B.5) determines tbe precise ftight patb. Doppler radar increasingly is employed where high accuracy is required. (f) Aircraft localion.

(8) Corrections lo magnetic data. Magnetic data are corrected for drift, eIevation, and line location differences at line intersections in a least-squares manner to force tieso lnstrument drift is generally not a major problem, especially with prolOO and optieally pumped magnetometers whose measurements are absolute values. The value oC tbe maio magoetic fieJd of the Eartb is oClen subtracted from measurement values. The Earth's field is usually taken to be that of the [mernational Geomagnetic Re!erence Fie/d (IGRF) model. A stationary base magnetometer is often used to determine slowly varying diurnal etrects. Horizontal gradiometer arrangements help in eliminating rapid temporal variations; the gradient measurements do not involve diurnal etreets. Usually no atlempt is made lo correet for the large etrects of magnetie storms. (h) Advantages and disadvantages of airborne magnetics. Airborne surveyiog is extremely altrae-

live ror reconoaissanee because or low cost per kilometer (see Table 1.2) and high speed. Tbe speed not only reduces the cost, but also decreases Ihe etrects or time variations of the magnetic fleld. Erratic near-surrace Ceatures, frequently a nuisanee in ground work, are considerably reduced. The ftight elevation may be chosen 10 favor struclures oC certain size and depth. Operational problems associated with irregular terrain, sometimes a source or difficulty in ground magnetics, are minimized. Tbe data are smoother, which may make ioterpretation easier. FinalIy, aeromagnetics can be used over water and in regions inaccessible for ground work. The disadvantages in airborne magnetics apply mainly to mineral exploration. The cost for survey-

83

ing small areas may be prohibilive. The attenuation oC near-surfaee fealures, apt to be the survey objective, become Iimitalions in mineral search.

3.5.3. Shipborne Magnetic Surveys Both the fluxgate and proton-precession magnelometers have been used in marine operalions. There are no major problems io ship installation. The sensing eJement is towed sorne distan ce (150 lo 300 m) astero (to reduce magnetic effects of the vessel) in a watertight housing called a fish, which usually rides about 15 m below the surface. Slabilizalion is similar to that employed in tbe airborne bird. Use or a ship rather tban an aircraft provides no advantage and incurs considerable cost inerease unless the survey is carried out in conjunction with other surveys, sucb as gravity or seismic. The main application has been in large-scale oceanograpbic surveying related to earth physics and petroleum search. Much of the evidence supporting plate tectonics has come from marine magnetics.

3.5.4. Ground Magnetic Surveys (a) General. Magnetic surveying on tbe ground now almost exclusively uses tbe portable proton-precession magnetometer. The main application is in detailed surveys ror minerals, but ground magnetics are also employed in the followup oC geochemical reconnaissance in base-metal search. Station spadng is usually 15 to 60 m; occasionany it is as small as 1 m. Most ground surveys now measure the total field, but vertical-component ftuxgate instruments are also used. Sometimes gradiometer measurements (§3.5.5) are made. (b) Corrections. In precise work, either repeat readings should be made every few hours at a previousIy occupied station or a base-station recording magnetometer should be employed. This provides corrections for diurnal and erra tic variations of the magnetic field. However, such precautions are unnecessary in most mineral prospecting beeause anomalies are large (> 500 nT). Since most ground magnetometers have a sensitivity of about 1 nT, stations should not be located near any sizeable objects containing iron, such as railroad tracks, wire fences, dril!- hole casings, or culverts. The instrument operator should also not wear iron articles, such as belt buckles, compasses, knives, iron rings, and even steel spectacle Crames. Apart Crom diurnal effects, the reductions required for magnetic data are insignificant. lbe vertical gradient varies from approximately 0.03 nT/m at the poles to 0.01 nT1m at the magnetic equator. The

Magnetic methods

84 latitude variation is rarely > 6 nT¡km. Thus elevation and latitud e corrections are generally unnecessary. The influence 01 topograpby on ground magnetics, on tbe otber hand, can be very important. This is apparent wben tiling measurements in stream gorges, lor example, wbere !he rock walls aboye tbe station frequently produce abnorrnal magnetic lows. Terrain anomalies as large as 700 nT occur at steep (45°) slopes 01 only 10 m exlent in Corrnations containing 2% magnetite (k - 0.025 SI unit) (Gupta and Fitzpatrick, 1971). ID such cases, a terrain correctioD is required. bul it cannot be applied merely as a function 01 topograpby a10ne because tbere are situations (Cor example, sedimentary lorrnations ol very low susceptibility) iD which no terrain distortion is observed. A terrain smoothing correctioD may be carried out by reducing measuremenls from an irregular surface z - h(x. y) lo a horizontal plane. say z - O, ahove il. This can be done approximately by using a Taylor series (§A.5) wi!h two terrns:

Z(x,y,O) - Z(x,y.h) - h(az/aZ)._A (3.33)

3.5.5. Gradiometer Surveys The gradient ol F is usually calculated from tbe magnetic contour map witb the aid oC templates. There is, however, considerable merit in measuring tbe vertical gradient directly in tbe field. 1I is merely neeessary lO record two readings. one aboye the other. With inslrument sensitivity 01 1 nT, an elevalion dilference oC .. 1 m suffiees. Then tbe vertical gradient is given by

aF/az" (F2

-

Fi)/tu

where F¡ and Fi are readings at the higher and lower elevations, and tu is tbe separation distance. Discriminalion between neighboring anomalies is enhaneed in tbe gradienl measuremenls. For exampIe, the anomalies for two isolated poles at deptb h separated by a horizontal distance h yield separate peaks on a aF/az profile but tbey have to be separated by 1.4 h to yield separate anomalies on an F profile. The effect 01 diurnal variations is also minimized, which is especially beneficial in high magnetie latitudes. For most of tbe simple shapes diseussed in Section 3.6 (especially lor the isolated poleo finite-lengtb dipole. and vertical contact of grea! deptb extent). better deptb estimates can be made from the first vertical-derivative profiles than lrom eitber tbe Z or F profiles. For leatures 01 tbe first two types, the width of Ihe profile at (az/az)mu./2 equals the depth within a few per-

cen!. For tbe vertical contact, hall tbe separation between maximum and minimum values equals the depth. Gradiometer measurements are valuable in field cODtiDuation calculatioDs (§3.7.5). Ground gradiometer measurements (Hood and McClure, 1965) have recently been carried out Cor gold deposits in eastern Canada in an area where the overburdeD is only a few meters thick. The bosl quartz was located because ol its slightly negative susceptibility using a vertical separation oC 2 m and a station spacing oC ... 1 m. Gradiometer surveys have also been used in tbe search lor archeological sites and artilacts, mapping buried stone structures. Corges, kilns. and so forth (Clark, 1986; Wynn. 1986). Vertical gradient aeromagnetic surveys (Hood. 1965) are often carried out al 150 lo 300 m altitude. Detailed coverage with 100 to 200 m line spacing is occasionally obtained at 30 m ground c\earance. Two magnetometers horizontally displaced from each other are also used, especially with marine measurements where they may be separated by 100 to 200 m. This arrangement permits tbe elimination of rapid temporal variations so that small spatial anomalies can be interpreted with higher confidence.

3.6. MAGNETIC EFFECTS OF SIMPLE SHAPES 3.6.1. General Because ground surveys (until about 1968) measured the vertical-field component, whereas airborne sur· veys measured the total field, both vertical-component and total-fie1d responses will be developed. Depth deterrninations are most important and lateral extent less so, whereas dip estima tes are the least important and quite difficult. In tbis regard. aeromagnetic and electromagnetic interpretation are similar. In petroleum exploration the depth to basement is tbe prime concem, whereas in mineral exploration more detail is desirable. The potentialities of high resolution and vertical-gradient aeromagnetics are only now being exploited to a limited extent. As in gravity and elecU:QI!!l!!!Iet~, an2IDillk.ur.s..

~}E!lt~ wit!t"!!l~odels. ~"~~~:.~~!'~L

more di!i!~~!"t ~"~c~Jls.e..·~tt1ieJl~'!. charac~~-1!!~ '!la~~e"t~~."~~l
Magnetic effects of simple shapes

85

o I

(a)

Figure 3.14. M
the dip oC bodies and f3 Cor the strike angle relative to magnetic nortb (x axis). Note that depths are rneasured with respect to the rneasurement elevation (the aircraft elevation Cor aerornagnetic measurernenls).

3.6.2. The Isolated Pole (Monopole) AJthough an isolated pole is a ficlion, in practice il may be used lo represent a steeply dipping dipole whose lower pole is so far away tbat it has a negligible effect. The induced magnetization in a long, slender, near-vertical body tends to be along the axis oC tbe body except near tbe magnetic equator. Ir the length of the body is large, we bave, in effect, a single negalive pole - p located at (O, O, Z p)' From Equation (3.2) or Equations (3.9) and (3.11), we get Cor the field at P( x, y, O),

where r\ is a unit vector from P(x, y, O) toward the pole -p. Tbe vertical anomaly is (3.34a) Usually the field oC tbe pole, Fp , is much smaller tban the fie1d oC the Earth, F., and the total field

anomaly is approximately the component oC Fp in tbe F. direction. Using Equation (3.29),

F ... Fp

' '\

=

(p/r 3 )(

-xcos I +:p sin l} ( 3.34b)

[N ote that the total field anomaly F. which is only a component of Fp , may be smaller than Z. and that in general F,¡, (Z2 + H 2 )1!2.) Profiles are shown in Figure 3.14a Cor 1=45°; Zmax is located directly over the pole. The H profile is perfectIy asymmetric and its positive half intersects the Z profile nearly at 2 max /3. The horizontal distance between positive and negative peak s oC H is approximately 3zp /2. This profiJe is independent oC the traverse direction only ir the effect oC the pole is much larger than the horizontal component of the Earth's field. A set of total-field profiles for various values of 1 is shown in Figure 3.14c. Fmu occurs south of the monopole and Fmift north oC it. F is zero north oC the pole at x - Z tan l. The curves would be ref!ected in the vertical axis in southem latitudes. A total-field profile on a magnetic meridian becomes progressively more asymmetric as the inclination decreases (that is, as we move toward the magnelic equator). At the sarne time, the maximum decreases and the minimum increases and both are displaced progressively southward. The statement also applies

Magnetic methods

86 maa. N

-p (c)

F¡Bure 3.14. (Continued) (b) Contours of IB.. I - lB + H.I fO/ H_ - H. - 0.38. (e) F profiles for various inclinatíons. (""ter Smellie. 1967.)

Magnetic effects af simple shapes

87

to the southem hemisphere ir we interchange maximum and minimum. The maximum and minimum values of F in Equation (3.34b) oecur at XmU..DliD -

zp{ 3

± (9 + 8cot 2 l)1/2) /4cot [ (3.35a)

where the plus sign gives Fmu' The maxirnum and minimum values of F (recalling that the pole is -p. hence pis posi ti ve) are

response may also be obtained from these equations. repladng the inclination [ with the dip of the dipole E. Figure 3.15a shows the geometry. For a traverse in the dip direction, we find F. H. and Z by resolving F, and F, in Equation (3.14a) along the dipole. the vertical. and (he horizontal directions. respectively. Thus,

F = F,cos fJ - F, sin (J

-

(

- (m/r3){3cos 2 ( 1+

111/1'3) (3 cos 2 (J <1»

-l}

- (m/r S ) {(3cos 2 / - 1).1: 2 +(3sin2 {1

+ ( Xm... mm/Z,)

2} 3/2

( 3.35b)

-

[-

6.1::,.. sin leos [ 1):;,}

(3.37a)

Z = - ( F, sin <1> + F, cos <1> ) = -(m/r3)(2cosfJsinl/>

There are several relations between the profile characteristics and the pole depth. When Z = 2".../2. x1/2 - 0.75z, (Fig. 3.14a), and when Z ... Zm811/3. x1/3 ca zp' where xI/2 and xl /3 are the half-widths at Zm../2 and Zmu./3. respectively. Pole depth may also be estimated from Equations (3.35). For example.

1)

-

+ sin (J cos 1/»

.. (l1I/r S) {(2:;, - x2 )sin I - 3'>::m cO$l} (3.37b) H - F, cos 1/> - F, sin <1>

... ( m/r J )( 2 cos fJ cos 1/> - sin fJ sin 1/»

- (m/r S ) {(2x 2

-

z; )cos 1- 3xzm sin I} (3. 37c)

__ 2

Zp -

2(XDliD - x mu )/(8 + 9trur 1)

.. 4(xo -

1/2

(3.36a)

xmu )/{ tan [+ (8 + 9tan2 l)1/2} ( 3.36b)

It may be difficult to loeate xDlin and Xo in high latitudes, however, since the curves are practically symmetrical when [> 60°. An altemative estimate, good within 10%. is given by z, "'" 1.4XI/2' where x1/2 is the half-width of the F profile. A first vertical-derivative profile provides a good depth estimate. The width of the profile at (1/2)( aZ/dz)mu. is equal to zp to within a few percent.

3.6.3. The Oipole A small tbree-dimensional structure containing anomalous concentrations of magnetic materials and varying in section from rod-Iike to spherical often may be represented by a dipole model. The dipole field was developed in Section 3.2.3. Assuming that a structure is magneiized mainly by induction in the direction of the Earth's field. the dipole dip will be that of tbe inclination. and the magnetic response may be obtained (rom Equation (3.14). If the body's intrinsic field due to remanence is much luger Ihan !he external field (an unlikely case), the magnetic

where m - 2pl and :m is the depth oC the di poI e below the surface oC measurement. Profiles are shown in Figure 3.15b for 1 .. 45°. The dipole curves are somewhat sharper than lor the monopole. The width. x·. oC the Z curves in Figure 3.15b at - Zma.,J2 is .~. COI :m' The same relation holds Cor the F curves in Figure 3.15b. e in the range 30° !SO 1 !SO 90". For 1 = O. however. the profile is sharper and x· '" 0.7:", al Fmax /2. The F and Z profiles would be symmetrical on E- W traverses. with the ftanks asymptotic lo zero. The width oC a gradiometer profile peak al (1/2)( az/az)mu. gives a good estimate of z",. When the dipole ís polarized approximately vertically, which would be the case where I ~ 70 0 , we have

F"'" Z

=

m(2:! -

X2

)/r 5 and H =

-

3mx:",/r 5 ( 3.38a)

Near the magnetic equator. I "" O and

F .. H - m(2x 2

-

z;,)/r 5 and Z .. - 3mxz",/r' (3.38b)

Curves for these Iimiting cases are shown in Figure 3.15c and d.

B8

Magnetic methods

l.

"{~-1

f

"Z".

-P~

x

.1 P

:7

Surfaee

1

+p (d)

"\N / \\ \

x/Z.,

(b)

Figure 3.15. Magnetic effecls of an isolaled dipole, (a) Ceomelry, (b) Pro files for 1- 45·,

The Collowing relations hold Cor the vertical dipole: At x - O, Z, F are maxima: Zmu - Fmax -

2mlz!

At x - ±2z"" Z, F are minima:

ZmiD = Fmia

(3.39a)

-0.036mlz!

-

At x - ±z",,,2 Similar relations hold for the horizontal dipole: At x

os

O,

At x - ± 1.2z""

Hmia

-

Fmia = -miz!

Hmu - Fmu -

}

0.20mlz!

H-F-O (3.39b)

The direction oC dipole dip is toward the side oC the Z profiJe that has the steeper slope and negative taH. lbis tail is not pronounced, however, unless the dip ( < 50°. The F profiles are even more diagnostic oC dip. In Figure 3.15d the Z profile is asymmetrical, with peak and trough above the ends oC a long dipole for z",11 « 2. When z",l/ > 1, the peak and trough occur beyond the ends and depth cannot be estimated, although a steep slope at the zero crossover would indicate a shallow source. A finite dipole sorne times may be represented by a dipping sheet oC finite length and depth extent l&¡. (3.58») or by an infinite vertical dipping dike oC finite strike length l&¡. (3.49»).

3.6.4. Two-Dimensional Features (a) Ceneral. Clearly the strike oC a two-dimen· sional feature with respect to the earth's field wil1

89

Magnetic effects o( simple shapes

-1.0

Surface

,7

J

1I)(.t

ica I dipole

(e)

~

.:::. I!

2

'(

:2

.I!

u.

-2

",..-

t-x;;;tp

•

---

3 Mag. N X/l ..

Surrace

r

Zm

~orizontal dipolo

i

(d)

mago N

-1"•

'0

\

,

1_

o/ ' ..

z,.,. \

.'. 1

Oipolc

......_-2· .1. .... 1501 ,,_-

\1 ,

"

",:.../ . --..x_"" ,. .,

~

/

l.

.~

(e)

Figure 3.15. (Continued) (e) Profi/es (or vertical dipole. (d) Pro files for horizontal dipole. (e) F profiles for different inclinations of field and dipole. (Arter Smellie. 1 %7.)

r

Magnetic methods

,

,

F

I

2p,lz",

I 1

I ~

-- . -~

SW

"

",

;.o ,

.~.' _~&f!'

xlz",

-5

"

SE

1_0 0

/

. ...t:

- l· - -4-

.

-.:!-. _

-..._.-:;-:.: ... -'"

\.

' .............

,

","

NE or NW

,.. . . .

su,race

I

'pl

.-p

Figure j, 16. Tota/-fie/d profiles norma/lo a fine 01 po/es striking NW- SE.

control induced magnetization, so tbe strike direction fJ will be incorporated in the expressions lor various structures. Traverse direction is more critical in identifying a 2-D target. A profile 'Pproximalely along slme will be unproductive. For 2-0 models, it is customary to ewbit only principal profiles (normal to strike ol the bodies). As in gravity, a magnetic body generally is considered to be 2-0 wben its strike lengtb is at least 10 lo 20 times larger tban otber dimensions. This siluation is even less likely to be troe in magnetics tban it is in gravity, and lonnulas are olten modified Cor linite slrike lenglh (Rasmussen and Pedersen, 1979). In addition to using dircet magnetic analysis, 2-0 features may also be derived with relative ease from tbe corresponding gravity sbapes by using Poisson's relation (§3.2.5).

temporarily replace P(x',O) with r(x', z). Tben, r 2 _ (_x,)2 + (z", - z)2, ar/iJx - x'/r, and ar/az -lim ..... o{ -(z,,- z)/r} - -z",/r. Tben,

(b)' Une of poles (thin vertical dike of infjnite depth extent). An inlinite horizontal line of poles is an approximation to a long shear or fracture zone or thin dike, wbich bas appreciable susceptibility contrast and wbich extends to considerable depth. The magnetic potential is given by the logarithmic relation A - -2p,ln(1/r), where -p, is the pole intensity per unit lengtb [tbis equation comes Crom Eq. (3.9) following tbe procedure in problem 1, Chapter 2, and assurning infinitesimal cross section in Eq. (18»). We pass a vertical plane through P(x, y,O) perpendicular to tbe line ol poJes and take x' and z' axes in this plane such Ihat x' is horizontal, z' • z, and tbe line oC poJes intersects tbe z axis at a depth fJ is the angle between tbe x and -y' axes. The field is in tbis plane and is directed down from P toward tbe line of poles along tbe vector r - (- x'l' + z",k). To get derivatives oC r at P, we write r 2 in lenns of tbe components oC r and

where r 2

z",.

F",

F".

-VA'" -2p,v{lnr}

- (2p,/r 2 )( -x'i' + z"k) - (2p,/r 2 )( -x'sinfJi + z"k) (3.4Oa) Now tbe component along F. is

F - F" •

'1

- (2p,/r 2 )( -x'sin,B1 + z"k)

·(cosli + sin/k)

- (2p,/r 2 )( - x' cos / sin fJ + z", sin 1) (3.4Ob) -

X,2

+

zt,. Tbe vertical component is (3.4Oc)

The nortb-south component oC H is from Equation (3.4Oa):

H - -(2p,/r 2 )x'sin,B

(3.4Od)

Total-field principal profiles (nonnal to strike) are shown in Figure 3.16 Cor several inclinations and stme ,B - 45°. Obviously the Z protiles are tbe same lor any strike direction. The F curves in Figure 3.l6 bave tbe same cbaracter as Cor tbe single poleo altbough tbey are somewhat broader. For I < 30°, the balf-widtb of tbe protile at Fmu./2 is about equal to the depth. When I is smaller, tbe depth is roughly equal to halC the horizontal distance between FIIIU and FaD .


91 Z·profile ~ - 90'

~

\

\ 0·5

\

Z-prolile

\~P-lO' \

\ \

\ \

or-::l;-;-::,.....~--I.;------f¡_--..J~r:--~----""iz xlz""

z..,

~

"',

, -X'

Plan

(a)

I

xl:"., NEo. NW

zi ...,

~

O'lpote "'1

lb}

figure 3.17. Profiles normal to a horizontalline o( dipoles. (a) Vertica/-field profiles. I - 45°. (b) F profiles for fl - ± 45".

92

Magnetic methods

(e) Line of dipoles (ribbon). The opposite extreme to a line of poles is a magnetic stringer oC limited depth extent, which can be modeled by a line (ribbon) of dipoles, sometimes called a thin horizontal cylinder. We take the y' axis along the stme and derive the magnetic response along the principal profile (in the l' direction) using Poisson's relation [Eq. (3.26»):

where p, is the density per unit length and m¡ is the dipole moment per unit length in the direction 11) = cos 1 sin pI' + sin Ik. Then U .. - 2yp,ln(r) for infinitesimal cross section [Eq. (2.8»); we now write r 2 "" x,2 + (z",¡ - z)2, di/ferentiate, then set z = O. This gives

The magnetic potential becomes

A - {( -m¡jyp,)( -2yp¡)(x'l' - zm,k)/r 1 }

.

IX)

- (2m,lr 1)( x'i' - zm,k) . (cos I sin pi' + sin Ik)

- (2m,lr1)(x'cos Isinp -

zm¡ sin

1)

The field components are found rrom tbis (noting Ihat H is along the x' axis so that tbe component along the x axis is H sin P - see Eq. (3.41c»

-aAlaz - (2m,lr") x {( z;, -

directly above the center. As in the case or the dipole, the depth to the center oC the dipole line is approximately equal to the width of the profiJe at Zmu./2. Figure 3.17b displays total-field principal profiles for a line of dipoles striking NW (or NE) for inclinations 1- 90°.60°.30°,0°. When 0° ~ 1 ~ 15° and 45° ~ 1 ~ 90°, the full width of Fmu./2 is roughly the depth, whereas for 15° :S 1 :S 45°, the depth is approximately the distance between Fmu and Fmio' These profiles are also more diagnostic ol dip than Z measurements are.

3.6.5. Dipping Dike (Prism) (a) Ceneral case. Magnetic anomalies caused by intrusions, flows, or iron-rich sedimentary horizons are common features in regions favorable for mineral exploration. and there is Crequently a contrast in the magnetic mineral content of such features with respect to the host rock. Such fea tu res may often be simulated by a two-dimensional dipping dike (prism). A vertical dike is also commonly used in makíng basement depth determinations in oH prospecting. Direct applicatioD oC Poisson's relation is diffi· cult, so we proceed as Collows. We assume a dike with dip € and stme p, and we take the y' axis along the strike directioD. We assume that magDetic polarizatioD is in the F. direction, that is, M - k F,. The geometry is illustrated iD Figure 3.18a, Crom which we have tbe following relations:

Z-

r? - d 1 + (x + dcot€)2 X'2 )sin

r{ - D 2 + (x + Dcot0

1 - 2x'zm' cos 1 sin p)

rl - d 2 + (x + d cot € - b)2

(3.41a)

r1 - D 2 + (x + D cot ~ - b) 2

H - - aAlax' _ (2m,lr")

x {( x,2 - z;, )cos 1 sin P - 2x'zm/ sin I) (3.41b)

A -(Mjyp)g,- -(Mjyp)vU") (3.42)

... (2m/Ir")

- z;/)( cos 2 1 sirt P -

+ dcotn}

and so on. Slarting wilh Equation (3.26), we have

F - ( H sin p) cos 1 + Z sin 1 X { (x,2

2

sirt

1}

-4x'z""sinlcoslsinp} (3.41c) Two principal profiles for the vertical component are shown in Figure 3.17a, one where the dipole line slrikes E-W (P - '"/2) and one for a strike N300W (P - '"/6). When the dípole line ís in the magnetic meridian, p - O, the curve is symmetrical with Zmu

where ') = (cos 1 sin fji' (3.27a) Ibis becomes F

+ sin Ik). Using Equation

= -VA = (Mjyp) V(VU' ') ". ( Mjyp) V( Ux cos 1 sin p +

U. sin 1)

- ( kF.,jyp){ ( Un cos 1 sin fj + Uxz sin 1) l'

+ ( Un cos I sin fj +

u.. sin 1) k}

(3.43)

93


~.

0.4

'" ::::. 'O

~

S4S0E

O

D

1 (a)

E

-4

-2

/

6

O

---------...",

.lId

(b) Figure 3.18, Profiles (or dike model. L - 00 except for (d), (a) F, Z profiles for I - 60°, 45°, ( - 45", b - 2d, 0- 3.5d. (b) Z profiles for 1- 75°, fJ - O·, E- 45°E and

P-

~o,

b - 2d, D -

00,

Because U satisfles Laplace's equation (2.11a), Uu Differentiating Equation (2,9), we gel

- u,.,

...

Then, x'z'

Uxz

-

4ypf f - . dx' dz ' Xl

z' r

... 4ypf Z ' dz'f

x'dx'

(z'2 + x")

2

-1

x+:'cotE-b

J

- 4yp Z' dZ'{ 2( z'2 + X'2) } - 2yp We change x and z to x' and Z', the coordinates of a poinl inside the dike, ,2 becomes (X'l + z'2).

D{

~

x+t'cot(

Z'

z'2 csc 2 E+ 2z'x col E+ xl Z'

z"csc'( + 2z'(x - b)cot~ + (x - b)'

}

dz'

94

Magnetic methods

(c)

SE

(d)

FiBUfe 3.18. (Continued) (e) F, Z profifes for , - 60", fl - ~", ( - 4S"N and S, b - 2d, D - oo. (d) F, Z profifes for' - 75 0 , fl - ~", ( - ~o, b - 2d, 0- 00, 2L - 00 and 16d.


9S

Alter some manipulation. this becomes

If, in addition. the dike has vertical sides, and Equations (3.45) are simplified 10

flx. - 2yp sin H sin t In( '2')/'1'.) +Cost("'1 - ~ - ~ + ",.)} The value oC result is

u,. can be

+ cos 2/("'1 - "'2 - 4>J + cfJ.) }

Substitution oC tbe values of the derivatives in Equalion (3.43) g,ives Z - 2k~ sin t {(cos 1 sin ~ sin P

n

X("'1 - ~ - ~ + ",.)}

(3.44a)

H = 2k~ sin t sin P {(sin 1 sin t

-

cos l cos t sin p)ln( '2')/'.'1)

+ ( cos 1 sin hin P + sin 1 cos El ("'1 - ~ - ~ + +.)}

(3.44b)

F - 2kF, sin t [{sin 21 sin t sin P - cos t ( cos 2 1 sir?- fJ - sir?-

I) }

XIn( '2')/'.'¡} + { sin 21 cos hin P

+ sin te cos 2 l sinl P - sir?- l} } X(4)1 -

~ - 4>J + 4>.)] (3.44c)

The parameter values in tbese equations may sometimes be found from the interpretation oC ground surveys, but generally this cannot be done for airborne work. Monopole- and dipole-line approximations (§3.6.4b, c) may occasionally be distinguished from dike-llke models of considerable width in mineral exploration, but usually basement is so far removed from the aircraft in oil reconnaissance work that discrimination is impossible. The vertical dike is often used for basement depth determinations in the latter case. (b) E- W or N- 5 strike.

P-

When the dike strikes 90° and Equations (3.44a, c) become

Z - 2kF, sin t{ sine 1 + Elln( "'3/'.'1)

+oos(1 + t)( +t

-

~

- +J + ",.)}

(3.45a)

F - 2kF, sin H - cos( t + 2l)ln( "']/'.'1) +sin« + 21) x( 4>1 - ~ - 4>J + 4>.)} (3.45b) 1

! i

For N-S strike,

P - o.

Z - 2k~ sin t sin

(3 .46b)

so

I{ eos ~ ln( "']/'.'1)

-sin t( +1 -

+ sin 1 cos t) In( '2'3/'.'1) + ( cos 1 cos t sin P - sin 1 sin

E-W,

-sin /("'1 - ~ - ~ + 4>.)} (3.46a)

F - 2kF,{ sin 2l1n( r2 ,]/,.,¡} -sin~("'1 - ~ - ~ + ",.)}

X

90°

2k~{ cos Iln( '2'3/'.'1)

Cound the same way; the

u,. - 2yp sin t{ cos On( '2'3/'1'.)

X

z-

t-

+z -

~ +

cfJ.)} (3.47a)

F- 2k~sintsir?-/{(eost)ln(",]/r.'I)

- sin t( cfJ1 - +2 - 4>J + cfJ.)) (3 .47b) For a vertical dike with N-S strike, Equations (3.47) become

z - - 2k~ sin I( +1 F - - 2k~ sir?- I( cfJ1

- ~ - 4>J + cfJ.) -

~

-

(3.48a)

cfJ) + cfJ.)} (3.48b)

(e) Dike 01 limited length. Dike anomalies rarely satisfy the criterla for two-dimensionality (strike length ~ IOb, where b is width). For a more realistic model (sometimes ca11ed a prism model) having a strike length 2 L, D - 00, and t - 90°, equation (3.44c) beeomes

F-kI'( .n21.mp[ID( ('l + L')'" + L) -ln{ (,l + L2)1!2 -

L}

+ In{ (,i + L2)1!2 - L} -ln{ (rl + L2)l/l + - ( eos 2 I sin II X

L}]

- sial I)

[tan- 1 ( ~) - tan- I ( x ~ b)

_tan- I {

x(,l

Ld

}

+ L2)1/1

+tan-'( (x _ .)(~+L')"')]) (3.49) (d) Discussion 01 principal pro files. Principal profiles are shown in Figure 3.18. In Figure 3.l8a, the

96

Magnetic methods Eul

Wal

NOIIh

Soulb

Z,

F,

(b)

Figure 3.19. Po/e distribution in a dike.

dike strikes NE-SW and dips 45°SE. In high magnetic latitudes where tbe H component is small, strike direction is relatively unimportant. This is clear from Equations (3.44a, e) where, if 1 ... 90°, the expressions lor Z and F are practieally indcpendent of the strike dircction {J. Figure 3.18b displays profiles lor N-S strike. Figure 3.18e is for E~W stme. The asymmetry is less pronouneed for DOrtb dips than Cor south dips. In high latitudes a dike witb E-W strike and dip 1 gives a symmetrical Z profile and a nearly symmetrical F profile. Figure 3.18d is Cor a vertical dike with NW or NE strike; Z and F profiles for L - 00 are similar because the vertical component oC F predomina tes. Gay (1961) takes advantage oC these similarities and obtains a single Camily of curves Cor F, Z, and H over tbe whole range of clips and inelinations, defined by an index response parameler. Figure 3.18d also shows tbe total field response over a sbort dike. The shape is similar to lhe otber lwo curves but with lower amplitude. This profile is across tbe center 01 the dike and normal to the strike.

It is useful to provide a qualitative explanation for the character of the profiles in Figure 3.18 based on pole distribution where the magnetization is mainly induced by the Eartb's field. For a dae dipping east and striking N-S as in Figure 3.19a, Z. wil1 produce N and S poles along the footwall and hanging wall, respective1y, as can be seen by resolving Z. into eomponents parallel and normal to the dip. A similar explanation (Fig. 3.l9b) accounts for the more pronounced asymmetry in the profile of the E-W dike dipping south in Figure 3.l8c; the N poles on the footwall are produced by components 01 both H. and Z•. In faet, sueh a dike tends lo be magnetized lransversely because F. is praetieally normal lo the dip axis. Depth estimates based on width of profiles are not partieularly use fuI unJess the pro files are symmelrieal and thc width is no greater than the dcpth lo the top face. Under these reslrietions the rule lor hall-widtb at half-maximum gives the depth to within 20%, that is, x1/2 - d at Z .. ZD1.,./2. Several techniques based on profile slopes are effective for dcpth determination for the dike model (§3.7.11b). Direetion of dip is usually fairly obvious from the profiles


97

since we know the total-field direction. The situation is complicated, however, because we cannot determine in advance the presence and direction oC remanent magnetism and we bave difficulty in determining the zero line Cor a field profile, that is, in isolating a single anomaly. A solution to finding the zero line Cor the dike model is given in Section 3.7.8. The dike profiles in Figure 3.l8b, e, and d were simplified by assuming infinite depth extent (D (0). They are not greatly changed for finite depth extent unless the depth extent is less than five times the width 01 the top Cace, in which case the positive tails are puJIed down sligbtly. For very shallow dip, short strike length, and small depth extent (elfectively a ftat-lying plate magnetized transversely), the profiles becomes more symmetrical, with a broad maximum oC small magnitude aboye the plate and negative tails at the ftanks.

When the strike is E-W (3.50) become

(P - 90°), Equations

Z = 2klF.{ sine € + 1 + ( 2)/'2 - sin(( + 1 + 9\) /,d

(3.51a)

F = - 2klF,{ cos( E + 2! + ( 2)/r2

-cos( € + 21 + 9¡}/rd and when the strike is N-S

(3.51b)

(P = 0°),

Z - 2ktF, sin I ( cos( € + ( 2 ) /r2

-

cos( € + ( 1 ) /r¡} (3.52a)

F - 2ktF, sin2 l{ cos( ( + ( 2 )/r2

(3.52b)

-cos(€ + 9\)/'d

If the sheet is vertical, E-90° and Equations (3.50b), (3.51b), and (3.52b) simpliCy to

3.6.6. Dipping Sheet The expressions for Z and F profiles over a thin sheet may be derived from Equation (3.44) by replacing the horizontal width b oC the dipping dike model with I csc (, where 1 is the thickness of the sheet. The principal reason for considering the thin sheet is that the expressions are simpler than Cor the dike and are sufficiently accurate provided the thickness I is not greater than the depth to the top d. The thin sheet geametry is a1so common in mineral exploration areas. Far the geometry shown in Figure 3.20a, the result is

F= 2ktF.[(1/rz){ sin 21 sin P cos 92

+ ( cos 2 I siul P - siul 1) sin 92 } -(1/r1 ) { sin 21 sin pcos 91

+ ( cos 2 [ siul P - siul 1) sin 9¡ } ] (3.53a)

F- 2ktF,{sin(21 + ( 2 )/r2

-

sin(21 + 9¡}/r¡} (3.S3b) (3.53c)

z ... 2klF,[ (l/'l){ cos 1 sin p sin( ( + (2) +sin lcos( ( + ( 2 )} - (1/'1){ cos 1 sin p sin(( + ( 1)

+sinlcos(t+91)}] (3.50a) F - 2ktF,[ (l/'l){ sin 2l sin p sin( € + ( 2 ) - ( cos 2 1 sin2 P - sÍn2 1) xcos((

+ (2 )}

z ==

-(l/'I){ sin 21 sin p sin(( + ( 1 ) - ( cos /sin2 P - sin2 2

xcos«(

+ (1)} 1

The profiles in Figure 3.20 for I - 60° are similar to, a1thougb sharper than, those for the dike. Rougb dip estimates are possible when the strike of the body and total-field direction are known. Depth estimates from curve widths are fairly good when the curves are rougbly symmetrical, but not practical when the sheet extends lo great depth. The balfwidths at Zmu/2 for tbe short vertical and dipping models give Xl/2 .., 1.7d. When the depth extent is very great, r2 "" 00 and the sheet is elfectively a hall-plane. Then Cor Z and F we have from Equations (3.50),

- (2ktF./r1 ){ cos I sin P sine ~ + 9\)

+sin [cosa + 9¡)}

1)

(3.50b)

F ... - (2ktF./r¡){ sin 21 sin

(3.54a)

p sine € + 9d

- (cos 2 1 siul P - sin2 1) cos( € +

9d}

(3.S4b)

Magnetic methods

\ \

\~

\\\ \

(111

Venicl'

.hec.,

Dld - 3

I

,'\ ,

I

I

""":

'

, ,

I

'.

/Dip4soE

,

\~

I I

D-fIO

" '-. ...........

I I I I

-.,

I

O~---7----7---~--~~--~--~~--~~~~-

-2

"-._0

-o·, w

, '\¿_4'.

,I

E

d

D

"11 11

11 11 11 11

"11

1 ." (b)

Figure 3.20. Thin sheet; I - 6()0, D/d -.3. (a) F, Z profiles for ~ - 45WE, P - 60°. (b) Z profiles for N- S srrike (P - 0°), ,-4S"N and 90°, and effecr 01 deprh exrenr.

Magneric effecrs of simple shapes

99

r,

, , , ,,, , I ,

\

,

, ,, I

-.-

-

I

'"

,

I

I

\

I

\ / Dip4S'N. D/d - 3

,

,,'d

o ,

.....

-o·,

--

,J ........ -

'-,l1li'

-"~

Dip .,. S

Mal. N

S

f

d

1I D

l (c)

Figure 3.20. (Continued) (e) Z profi/es for f - W strike.

For tbis limiting case we can determine the depth and dip uniqucly. Sctting dZ/dx - dF/dx - O. we obtain tbe x vaJues ror the maximum and minimum values ror Z and F. This yields tbe foUowing relalions for Z:

t-

45"N and 45·5.

fl - ga".

F curve, we bave

x:"/d - 2( siol 21 siol f3

+ (siol 1 - cos1 / siol f3)

2} 1/2

/ { sin 21 sin f3 sin (

/( cos 1 sin f3 sin ( + sin I cos El (3.55a) x1/l1d

- { cos 2 1 siol f3 + siol / } 112

/(cos 1 sin f3 cos ( + sin I sin E) (3.55b) wbcre x.. - xlIIIlI - xaIIa and Xl/1 is the full width al half-maximum. Likewise. writing x:." xí/1 for \he

+ (siol I - cos2 / sinl f3)cos E} (3.56a)

xíf2/d - (siol 2/ siol f3 + (siul / - cosl I siol f3) l}I/2 /{ sin 2/ sin f3 cos (

+ (siol 1 - cos 2 1 siol P) sin ()

(3.56b)

Combining Equations (3.55), we obtain the dip

Magnetic methods

100

anglet

2x¡/2 cos Tsin fJ + x'" sin 1) /( 2x¡/2 sin 1- x'" cos 1 sin fJ)

d/r¡, cosB¡ - x/r\, sin 82 ... d/r2' and oos82 (x - 1)/r2' Eliminating 6\ and 82 , we get

tan E - ( -

(3.57a)

and the depth,

-

Z- -2ktF,[(I/rl)2(dcos/sinfJ + xsinI)

-(I/rl)2{ dcos Isin,8 + (x - /)sin I) ] 2

2

d - x",xld( x'" + 2Xl/2

)1/2

When the sheet is not two dimensional, we can modify Equations (3.50) Cor a length 2L. TIten the principal profiles for Z and F become

Z - 2ktLF.« Q + R)cos I sinfJ + (S + T)sin I} (3.58a) F ... 2ktLF,{ (Q + R)sin 21 sin ti)

-( S + T)( cos 2 1 si~ fJ - si~ 1)}

(3.58b)

where

Q - sin(E + (2)/{ r2(rl + L2 )\/2} - sin( E+

B,)/{ r$ rl + L2 )\/2}

R - ( x si~ Ecos E/( X2 si~ E + L2 ) X ( cot( E - ( 2 )/( rl

+

}

L2)1/2

-cot(E - B$/('12 + L 2 )\/2}

S - cos( E+ ( 2 )/{ '2(,l + L 2 )1/2}

- cos( E+ ( 1 ) /

{ '\

(rl

(3.58c)

+ L2) 1/2

hin E/( Xl ~ E+ L2 ) } X { cot( E- ( 2 ) /(,l + L 2) \/2

T - { X oos l

-oot(E -

(3.59a)

(3.57b)

BI)/(rl + L 2 )'/2}

The profile is reduced in magnitude but otherwise unchanged in shape.

3.6.7. Horizontal Sheet (Plate) When the sheet is horizontal (see Fig. 3.21a), E - O, d becomes the depth 01 the sheet, and Equations (3.SO) give

F- -2krF.[(1/r¡)2{ dsin2Isin,8

- x( cos 2 I sin2 ,8 -

si~

I} }

- (1/r2)2 { d sin 21 sin p - (x - 1)

x( cos2 T si~,8 - sin2 1) }] (3.59b) Figure 3.21 shows protiles for horizontal plates. In Figure 3.21a, a shallow plate striking north-south produces a symmetrical Z profile. TIte F profile (not shown) is the same as the Z profile but reduced in magnitude by the multiplier sin /. It is not possible to make good depth estimates from tbe width of these curves, but other techniques are available (see §3.7.8 and §3.7.1l). Over a horizontal thin sheet of finite strike length 2L, Equation (3.59b) becomes F - -2ktF,[ {d sin2lsin,8

- x( oos2 I si~ ,8 /r1(1 + rl/LZ )1 / 2

sin2 1) }

- (dsin2Isinp - (x-I) X ( cos 2 I sir?- P - sU;

/r2 (1 + rl/Ll)1/1]

1) } (3.60)

Total-field profiles for the thin plate, ilIustrated in Figure 3.21b for infinite strike length and for 2L 4/, are remarkably similar. (Tbis is alro true for gravity profiles over a thin plate.) Unless L < 1, the finite Jength does not alfect the curve more than 20%. Use of both the bottomless dike and the thin sheet models yields oúnimum and maximum depths, respectively, for d. Sharpness of the peak is characteristic of a shallow plate compared with the dike.

+ sinlcosB¡) -(I/r2)( cos Isin p sin O2 + sin 1cos '2)] 3.6.8. Semilnfinlte Horizontal Sheet: F - -2ktF, [(I/r\){ sin 21 sin JI sin 61 Fault Approximation - ( oos2 T~ P - s~ 1) cos Bd Ir rl (or rl ) approaches infinity, / becomes very large - (1/'2>( sin 21 sin Psin 82 and Equations (3.59) reduce to one term for a semi· 2 infinite sheet. Profiles for vertical component and - ( cos IsU; P - sU; 1) cos B2 } ]

Z- -2ktF,[(I/r\)(coslsinpsinB¡

where

rl-

X2

+ d 2 , rl-

(x -

1)2

+ d 2 , sin6\ -

total field are illustrated in Figure 3.22. In Figure 3.22a, the strike is N-S with 1- 60 D ; both curves

101


~ -2 .....--=::----""

--.... ....... " ,I

-

x/d

-0.4

-0.8

{a}

Figure 321. Thin horizanrill pIare af finite width. ~)". dll = 0.25.

1// - 0.125.

(a) Profiles lor

1-60°.

f3 - O· and

are antisymmetrical. The response in Figure 3.22b is similar to those from targets with stcep dip. Both E- W profiles provide good depth estimates; d equals half the horizontal distance between 2 max and 2 mm . (or Fmax and Fmill ). This measurement is 25% too large for the N-S prolile (Fig. 3.22a). It is necessary to traverse a considerable distance before the magnetic background is reachcd. For example, when d = 30 m, the survey should extend at least 800 m either way from the edge oC Ihe sheet. In practical situations trus often cannot be done because there are likely to be other magnetic features in the vicini ty. Ir we introduce another semiinfini te sheet al a different depth, as shown in Figure 3.23, we have an approximation to a fault. When the fault plane has dip E. Equations (3.59) give Z=

-2ktF.[(1IrlH deos 1 sin {3 + (x + d cot O sin l} -(llrl){ Dcoslsin{3 + (x + D cot E) sin l} 1

'.

F= -

2ktF. [( 1Ir? )(

rl = d 2 + (x + dcot~)2 rl =

(3.61a)

d sin 2l sin {3

D sin 2l sin {3

- (x + D eot El ( cos 1 sitr f3 - sitr !) } 1 2

(3.61b)

D2 + (x + Dcot~)2

For a vertical faull, 2 and F pro files are shown in Figure 3.23a. Responses from normal Caults are similar to these examples regardless of strike, bul a prolile over a reverse fault retlects the concentration oC anomalous material in the arca oC overlap and resembles the response of a steeply dipping target. An estimate oC the depth to the upper bed can be made in terms of XI/2' half the distance between 2max and Zmin: 0.5 ~ xl/2/d ~ 1.25. The lower limil applies when the lower bed is only slightly displaced; the upper limit applies when Dld is large. When Ihe fault-plane dip ~ is fairly sleep, ~ "" 90° and D can be estimated from

D ""

- (x + d cot El ( cos 2 1 sitr f3 - sitr !) }

- (llrl)(

where

XI/2[

Z",(1 + xt/2/d2)

/{ 2X I / 2 ( dZ/dx)max

- Z",( 1 + Xf/2/d2)} ,

(3.62)

where Zm = 2max - Zmin and (dZldx)max is tbe maximum slope. The fault approximation in Equations (3.61) is accurate lo witrun a few percent provided d is larger

Magnetic methods

102

2/. --4 I

-0·2'----7----':-----,~---~

....."':"O=----~---_i_

(bl

.

,. .; -'

~~J----~~----~~~-~--~~~---~~2----+·-01

-'

t

-0·2

-----

",.,.,.

..... "'-._._ . ....,....~----

_ ......

,

~I-·I-~~I (el

Figure 3.21. (Continued) (b) Pro files for 1- 75", fJ - 45", dll - 0.5. (e) Profiles for 1- 15", fJ - 45", dll- 2

than 21. When this assumption is not valid, it is necessary to use the dike model (§3.6.5). With '3 - '4 - 00 and 4>J - +4 - tI', the Z and F expressions for the horizontal slab are identical to Equations (3.44) to (3.48) with the terms in '3' '4' 4>J, and 4>4 omitted (sec Fig. 3.24). Figure 3.24 shows F profiles over a single horizontal bed with N-S strike and lace angles 01 45° and 135°. The curves are reftections oC eaeh other in bolh axes. To simulate a Caull, we add a similar slab at a difl'erent depth (as in Fig. 2.32), lor example, lor

E-W strike and strike length 2L, we gel Z - 2k~ sin UQ In( '2"/'1")

+R(.1 -

+z

-.7

+ +a)) (3.63a)

F - 2k~ sin El S In( '2'7/'1'.)

+T(4)1 -

+z -., + +a)]

(3.63b)

where Q, R, S, and T are as in Equations (3.S8c). [Note that ~ in Eqs. (3.63) and in tbe factors Q, R, S, and T is the slope of tbe fault plane.]


103

12

(al

\~

\~ \~

\,'!:

,~ 6().

-12

____ -8

'-.... 8 .... ---

JO

--- _.... - ... ,

4 x/d

Surrace

-00

(bl

Figure 3.22. 5emiin(inite horizontal sheet. F, Z profiles for (a) N - 5 srrike. / = 60°; (b) E- W strike. I = 60 and 30 c.

3.6.9. Contad between Beds of Different Susceptibilities A common magnetic structure results Crom the contact oC two slabs with contrasting susceptibility values (see Fig. 3.25). Because a uniCorm continuous slab creates no magnetic anomaly, the etrect oC the contact is tbe same as that oC the serniinfinite slab to the leCt with susceptibility fU = k' - k. From Equation (3.44), we have ,1

Z

+ sin 1 cos nIn( '2/rd + (cos I cos ~ sin fJ

llF =

(3 .64a)

F- ak F.[ sin E{ sin 2l sin ~ sin fJ - cos E( cos 2 I sin'- fJ - sin'- !) } In( '2/rl)

+ ( sin 2/ cos Esin f:l + sin Hcos2 1 sin'- f:l - sin'- J) }( f/ll

-

= 211kF.sin'-ltan- l (x/d)

( 3.65)

The ditrerence between the lilDiting value oC F at x-±oois

= 211k F. sin ~ { (cos 1 sin ~ sin fJ

- sin I sin ~)( cf>1 - ~)}

Figure 3.25 shows profiJes over vertical and dipping contacts oC considerable depth extent. When 'h = ",/2. Equation (3.64b) becomes, Cor a vertical contact striking N-S

Fmax -

Fmia = 2wtlok F. sirr 1

The maximum slope occurs over the contact and is given by (dF/dx),,_o = 2t:.kF.sirr l/d. We can ca1culate the susccptibility contrast and depth oC tbe bed:

~) 1 llk = llFsin'-I/2",F. and d

(3.64b)

=

llFjw(dF/dx),,_o

( 3.66)

104

Magnetic methods

NEor E

01--'" --..j p

I./~

t

D

1

r

I,/.(

t

~

,.., .l! N

:¡

u.

JI'\ -1

1, \

~ .!!

\ ~

.!I"

0.2

o

d1

(a)

0.6

0.4

Surface

elI

...<1.

---.....,

I

"" '..,,'I

Surface

TD 1

I

t

f (b)

Figure! 3.23. Thin-sheet fault approximation; D - 2d, I - 60·. (a) F, Z profiles for vertical faults striking N- S and Sf- NW (p - 0.,45°). (b) F profiles lor normal and reverse faults striking E- W; fault dip 45,135·.

This calculation is not simple in practice because long traverses are required to locate Fmu and Fmili and they are usually obscured by other anomalies. The curve in Figure 3.25a for E-W strike is similar to profiles over dikes dipping east (Figures 118b and 3.20b) and it would be difficult 10 recognize that it represents a steeply dipping contacto In Figure 3.25b, a contact with a slant lace produces a curve that gives some indication 01 the model. One curve (broken line) also resembles a dipping sheet; tbe other resembles a dipping dike. A gradiometer profile 01 dF/ dx defines the location of a vertical contact better Iban either Z or F

pro files. The depth is equal to the separation of maximum and minimum values.

3.6,10. Demagnetization In the preceding examples, we assumed that the induced magnetization is the product of k, the volume susceptibility of the body, and the external field F,. In faet this is troe only for rod-like shapes magnetized along tbe axis and having a cross section small in eomparison to their lengtb, such as the dipole of Equations (3.37). In general, the resultanl field inside lhe body is different from F,. This is


105

...

--........--

-----

Figure 3,24 F pro files for a semiinfinite horizontal slab striking N- S, 1= 45", dip of s/ab terminus 45 and 135°, O = 3d.

24

i

(a)

I

----

Ca ntaet 45"-SW - - ,. , """ 30°

!

l lb) Figure 3.25, F pro files for contacl between Iwo horizonlal slabs o( differenl susceplibill' lies: tH - k - k', 0 - 10d. (a) Vertical contdCt (~ - 90°), 1= 60°, P = O and 90°, (b) 5loping contdct (E - 45") for I - 30 and 60", p = 45°,

r

106

Magnetic methods

usually called demagnetization. The elfecl can be accommodated by replacing the susceptibility k by an apparent susuptibility k Q : kQ

-

k/(l + Nk)

o < N < 4".

(3.67)

Maximum demagnetization occurs in thin sheets magnetized normal to tbe lace; in this case, N ... 4".. For the sphere N .. 4"./3. The elfect is quite small unless k ~ 0.1 SI units. Demagnetization is signifi· cant only in massive pyrrhotite and in rocks contain· ing > 5-10$ magnetile. Sometimes an additional factor 01 (1 - cos 2 D cos 2 flI) is included 10 allow for tbe resultant magnetization being in a dilferenl direction from 1: fl 1 is tbe dilference in inclination and D is the declination.

3.7. PROCESSING AND INTERPRETATION 3.7.1. General Magnetic survey results are displayed as a set ol profiles or a magnetic contour map. In sedimentary areas there may be some similaríty between magnetic and gravily maps, bUI in general magnetic anomalies are more numerous, more erratic, less persistent, and of larger magnitude than gravity anomalies. Conse· quenlly, regional-residual separation is much more complexo Considerable success has been achieved with bandpass, matching, and nonlinear filter opera· ton. Downward continuation is not suitable in areas of complex shallow magnetics. characteristic of min· eral exploration regions. It migbt be used lor esti· mating the thickness of sediments in petroleum sur· veys. but it is not used much for this purpose. Instead, depths are determined by semiempirical depth rules or techniques like Wemer deconvolution. Second·derivative analysis is useful in mineral prospecting 10 enhance small·scale features near the surface, whereas upward continuation may be used 10 suppress them. Upward continuation may also be used to reduce topographic elfects in ground magnetic work. Equation (3.33) is a crude fonn 01 upward continuation. Aeromagnetic data are olten lreated as follows: l. Reduction ol data to a unifonn grid by one· dimensional interpolation perpendicular to ftight direction. 2. Preprocessing, which might involve continuation. calcu1ation ol derivatives, extraction of the verti· cal componenl, and so lorth. 3. Summation of several profiles 10 attenuate back· ground noise. 4. Filtering and setting a threshold to locate anoma· lous areas.

5. Analyzing the profiles lor the locations and orientations of anomalies. 6. Interpolating protiles normal lo strike and ceno tered on anomalies, for more detailed analysis. 7. Comparíng protiles with curves developed from models. Comparing field measurements with the results expecled for simple models. such as discussed in Section 3.6, is done to determine the location, depth, size, shape, attitude, ando possibly. the susceptibility of the magnetic bodies responsible for the anomalies. Although simplitied both geometrically and with re· gard to magnetization, matching curves (parametric analysis) with model curves provides reasonably rapid analysis and may be sufficient. especially where data are poor and/or ¡ncomplete. Considerable elfort has been expended to develope workable inversion procedures Cor magnetics. and, in spite of the nonuruque nature oC tbe problem, several elfective algorilhms have been developed, lo which numerous reCerences in the literature attesl (Bhattacharyya. 1964; Hartman, Teskey, and Friedberg. 1971; AI·Chalabi, 1971; McGrath and Hood, 1973; Barnett, 1976; Teskey, 1980). Wemer deconvolution (§3.7.10) is one such algorithm. The conventional starting point for magnetic data ioversion might be a leasl.squares fit, ridge regression (Leile and Leao. 1985), and so on, as in Section 2.7.9, but magnelic ¡nversion is more complex than gravity inversion because there are more variables.

3.7.2. Crude Interpretation and

Structural Aspects Because of the erratic and complex character oC magnelic maps. interpretation is oflen only qualitative. Indeed, interprelation is somelhing of a fine art. An interpreter experienced in magnetics can usually see structure merely by looking al a magnetic map, much as one can visualize surface features Crom the contours 01 a topographic map. Frequently magnetic features are rather directly related lo surface out· crops and a magnetic map may be a fair substitute for a surface geology map where surface reatures are obscured by alluvium. Often Ihere is a connection between magnetism and lopography, as well as with buried geologic structures, particularly in mineral exploratioD arcas. A visual study of the magnetic maps can be fruitful for preliminary interpretation. In this regard, experience is essential. Remanent magnetization. however, can produce significant eC· fecIs and lead to incorrect inlerprelation if overlooked. In sedimentary regions. particularly where the basement deptb exceeds 1,500 m, tbe magnetic con·

Processing and interpretation

tours are normally smooth and variations are small, reflecting tbe basement rocks rather than near-surface features. Tbe larger anomalies usually are caused by susceptibility variatioDS ratber than basement relieC. Consequently, anomaly magnitude is not oC much value in finding basement depth, and deptb calculations are usually based upon anomaly shape measurements, especially sharpness. Regions where igneous and metamorphic roeks predomina te. like the Precambrian Canadian Shield and tbe Appalachians, usually exhibit complex magnetic variations. Deep Ceatures are frequently camouftaged by hiper frequency magnetic effects originating nearer tbe surface. Techniques for separating deep and shallow anomalies are similar to tbose discussed for gravity features in Section 2.6. Magnetic anomalies often lie in trends. From a study 01 aeromagnetic maps of primarily sedimentary areas in westem and central North America and Venezuela, AflIeck (1963) found that the dominant direction witbin single magnetic-tectomc provinces is usually NE-SW or NW-SE and the trend normally terminates at tbe province boundaries. Moderate to weak features trending E-W or N- S olten are superimposed on these. These weaker trends frequently extend across province boundaries and are probably of more recent origino A cursory study of tbe Canadian Appalachian region (the Maritime provinces and eastem Quebec south oC the SI. Lawrence) and northem Saskatchewan and Alberta appears to confirm the trends. Large-scale northeast trends are obvious on the east and west flanks of the Canadian Shie1d.

107

We usually wrile relalions using two-dimeosiooal Fourier transforms f(x, y) ... F(u. v) (Eq. (A. 57» in the form

f(x, y) - (1/2,,)2 f f F( u, v) eJ2 or(U1l+.Y) dudv (3.68a)

F(u,v) - f ff(x,y)e- J2 .,(ux+oY )dxdy (3.68b) (x, y) are spatial coordinates and (u, v) are wave-

number coordinates. The important characteristic of transformations is that information is not lost in the process, and in many cases operations are easier to perform io the transform domain. For example, the output-input expression g(x, y) - f(x. y). w(x, y) for convolution in the spatial domain is (§A.I0)

g(x, y) = f f/(x - a. J' - fJ)w(a,p) dadP (3.69a)

where w(a. P) is tbe convolution operator (also called a weighting funetian or fi/ter). In the wavenumber domain, tbis becomes simple multiplication:

G(u,v) - F(u,v)W(u.v)

(3.69b)

The relations between sources and tbeir potential fields may be considered convolution operations, and transforms can be used lo determine source characteristics from field operations. as discussed in the following sections.

3.7.4. Derivatives 3.7.3. Data Processing Operations: The Fourier Transform As with gravity and seismic data processing. mathematical operations. 5uch as convolution and correlation. can accomplish filtering. residualizing. continualion, and so on. Operations can be performed in the spatial, or wavenumber, domain (often called the frequency domain because wavenumber is spatial frequency). Fourier transforms (§A.9) are particulady userul in magnetics for (i) resolution of specilic anomalies by downward or upward continuation. (ü) changing tbe effective field inclination (reduction to the pole) or conversion of total-field data to vertical-component data. (üi) calculation oC derivatives, (iv) general liltering - separatiog anomalies caused by sources of different size and depth, and (v) modeling (Bhattacharyya and Navolio 1976). For literature OD transformations oC poten ti al field data. see Dean (1958), Bhattacharyya (1965. 1966), Gunn (1975), and Spector and Grant (1985).

Derivatives tend to sharpen the edges of anomalies and enhance shallow features. First and second vertical derivative maps are the most common ones made. Derivative maps may be made by the same techniques used for gravity data (§2.6.5). The lirsl vertical derivative is also measured in gradiometer surveys.

3.7.5. Contlnuation Field continuation was discussed in Section 2.6.7 as it applies lo gravity. Adapting Equation (2.48) to magnetics, we have, for upward continuation (where z is positive downward),

F(x', y'. - h) h f f

- 2"

F(x, y,O) dxdy

{(x _ X,)2 + (y _ y')2 + h 2 } 1/2 (3.70)

108

Magnetic methods

Table 3.2. Coefficients for upward continua/ion. K (r;. 1)

K(r¡.2)

K(r¡.3)

K(r¡.4)

K(r¡.5)

O 0.11193 0.04034 1 0.32193 0.12988 0.06062 0.07588 '¡5 0.15206 0.14559 '¡8 0.05335 0.07651 '¡13 0.06586 0.09902 5 0.06650 0.11100 -150 0.05635 0.10351 {136 0.03855 0.07379 1274 0.02273 0.04464 25 0.03015 0.05998

0.01961 0.06592 0.05260 0.10563 0.07146 0.10226 0.12921 0.13635 0.10322 0.06500 0.08917

0.01141 0.03908 0.03566 0.07450 0.05841 0.09173 0.12915 0.15474 0.12565 0.08323 0.11744

0.00742 0.02566 0.02509 0.05377 0.04611 0.07784 0.11986 0.16159 0.14106 0.09897 0.14458

';

O 1

2 3 4 5 6 7 8 9 10

Thus, applying this resuIt and Equation (A.62), we obtain for the transfonn oC Equation (3.70),

n

Tbe left side is tbe total Held at tbe poínt P(x', y', - h) aboye tbe surface on which F(x, y,O) is known. Tbe calculation procedure is to replace the integral with a weighted sum of values taken on a regular grid. Tbe empírical formula of Henderson (1960) gives the field at tbe elevation h aboye the surface in terrns oC values F( ,/), tbe average value F( '¡) over a circ1e of radius '/ centered at tbe point (x, y,O):

~(u,v) =

(-2v/uv)-Fo(u,v).r(u,v) (3.73)

where $Oh(u, v) ++ F(x', y', - h), JOó(u, v) H F(x, y,O), and r(u, v) H w(x, y) - (h/21T)(X 2 +

y2 + h2)-1/2.

The continuation Hlter is

r(u,v)'" (h/21T)f f(x 2 + y2 + h2 )-3/ 2 X e- j2 .. (u" +vy) dx dy

_ (h/2.,,) e- 2trh (u 2 +o1)!/1

( 3.74)

For upward continuation, we know Fo(x. y.O) and the unknoWD is F,,(x. y, - h), whose transform is

Fh(U,V) -JOó(u,v)(h/2v) F(x,y,-h)-¿F(r¡)K(r(t-h) (3.71) where K(r" - h) are weigbting coefficients (listed in Table 3.2 for h - 1 to 5). Tbese coefficients give the upward continued Held witbin 2%. Anotber solution Cor continuation (in eitber direction) is by rneans of a Maclaurin expansion [Eq. (A.40»):

F(x,y,h) -F(x,y,O) +h8F(x,y,0)/8z +( h2/2!) 8 2F(x, y,0)/8z 2

+( h3 /3!) 8 1F(x, y,O)/8z 3 + ... (3.72) [compare witb Eq. (3.33»). For a first approximation, tbe first two terms involving F and 8 F/8 z are often sufficient, and tbe simultaneous measurernent of total field and vertical gradient provides these values. Tbe a2F/ dz 2 lerm can be found from rnaps of F, as indicaled in Section 2.6.5, and, ir nccessary, lhe a'F/8z 1 term can be Cound in a similar manner Crom maps oC aF/az. The Fourier transfonn provides anotber techruque for field continuation. Tbe integrand in Equalion (3.70) is tbe product of F(x, y, O) and (h/21T){(X - X,)2 + (y - y')2 + h2 }-3/l. Using tbe symmetry tbeorem [Eq. (A.60») and tbe convolution tbeorem [Eq. (A.67a»), we get

X(t)Y(t) ... 2".x( -w)- y( -w) - 2vx(w)-y(w)

xexp{ -21Th(u 2 + V2)1/2} (3.75) Tbus tbe calculation of F,,(u, v) is straightforward. Hanson and Miyazki (1984) use a continuation metbod tbat is effcctive wbere surface relief is large and rocks are bighly magnetic. As in gravity, upward conlinuation smootbs tbe data, whereas dOWDward continuation emphasizes high frequencies.

3_7.6. Spectral Analysis The Fourier transfonn expresses a rnagnetic fie1d as an integral oC sine and/or cosine waves, each defining a wave oC amplitude A{IC) and phase ~(IC), wbere 1C/2." - l/A is the wavenumber. Plotting A(Ie) gives tbe amplitude spectrum and A2(1e) gives tbe power spectrum. The expression for tbe field oC an anomalous body often can be wrilten as the product of three functions in tbe wavenumber domain (tbeir convolulion in tbe spatial domain): (i)

ID' amplitude factor, which is equal lo (41TM)2,

where M is the magnetic rnomenl/unit volume. tbe depth factor, exp{-2h(u 2 + if)l/l), where h is tbe pole deptb. (üi) IIJ' tbe field-orientation Cactor, {I cos fl + m sin fl)2 + n 2 - (lu + mv)2/(u 2 + if) + n 2, where fl is tbe angle between tbe body's orientation and rnagnetic nortb and /, m, and n are the direction cosines of the field F~. (ü)

A,

Processing and interpretation For bodies that are large compared to their depth, we require two additional factors: (iv) The size factor: for a rectangular prism, (sinuasinvb)/(ua Vb)2, wbere 2a and 2b are the prism dimensions. (v) The polarization-orientation factor involving the direction cosines of the polarization vector.

109 point aboye tbe midpoint of Ibe top of the dike. If we assume infinite depth extent so tbat r2 - '4 - 00, ~ = 4' we have Z = 2kF, sin H (cos 1 sin bin p

+ sin Icosnln(r3Ir¡) + (cos 1 cos ~ sin P

We thus write the field of a point pole or dipole in terms of factors (i) to (ili) as F(x, y,O) - ¡,,(x, y). Mx, y, h). /¡¡(x, y) (3.76a)

- sin 1 sin~)( 1 - 1 - coCl(x + b)/d, and
or, in the wavenumber domain,

Z - M{

.F(u,v,O) -~(u,v).F~(u,v,h)~(u,v) (3.76b)

The effect of any of these faclors may be removed by deconvolving in the space domain or by dividing in the wavenumber domain. Numerous other fi!ter operations can be used to separate deep from sballow, large from small, and tbree-dimensional from two-dimensional effects. Gunn (1975) discusses a solution for the magnetized rectangular prism. Habn, Kind, and Mishra (1976) estimate depth from Fourier spectra.

3.7.7. Reduction to the Pole This operation changes the actual inclination to the vertical. It can be performed (Baranov, 1957; Spector and Grant, 1985) by convolving the magnetic field with a filler whose wavenumber response is the product of a polarization-orientation factor and tbe field-orientation factor in items (v) and (ili) of Section 3.7.6. This transformation simplifies I total-field maps and is a relatively easy operation at high magnetic latitudes wbere Z "'" F, but becomes more difficult near the magnetic equator (Silva, 1986).

3.7.8. Use of Master Curves for Dikes of Creat Depth Eñent It is oflen difficult lo establisb a background or

datum level for magnetic measurements and to locate a dike with respect to the pro file. Hence, matching field results with profiles obtained from simple shapes can be difficult. An analysis (Koulornz.ine, Lamontagne, and N adeau, 1970) for prisms and dikes of infinite depth extent solves tbis problem with master (or characteristic) curves that give depth, dip, and width of a prism or dike. We rewrite Equation (3.44a) making the width 2b instead of b (Fig. 3.18a) and shifting the origin lo a

COI- l(

X + B) - cot- l ( X - B)}

+(NI2)ln[{(X- B)2 +

l)

I { ( X + B)2 + 1}

I

(3.77)

wbere M - 2kF.sin~ {(coslsinpcos~ - sin lsin~)}

and

NI2 =

2kF,sinH(cosJsinpsin~

+ sin Icos€)}

The first term is the symmetric component S and the second lerm is the antisymmetric component A. Over the cenler of the dike, S has a maximum and A ~ o. Ir we chose two conjugate points Xl and X2 on Ihe dike pro file such Ibat the sum of the Z values is equal lo 20, Ibe value of Z al X - O, that is, (3.78) Then, because

we have Al + A 2

'"

O (3.79)

For the antisymmetric component,

l} I { ( Xl + B)2 + 1}] + In[{ (X2 - B)2 + l) I { ( X2 + B)2 + 1}] ~ O {( Xl - B)2 + l){ ( X2 - B)2 + 1) - {( Xl + B)2 + 1){ (X2 + B)2 + 1} ln[ { ( Xl - B)2 +

Magnetic methods

110

t

z

Figure 3.26. T~dimensional dike of infini/e dep/h ex/en/. (a) Loca/ion of conjugate points and X-O.

z.....

Solving for Xl Xl' this gives (3.80) Initially we do not know either the location of the dike center. X - " - O. or the datum level Z - O. Two pairs of conjugate points. XI' X2 and X,. X4 • are chosen such that Equation (3.78) is satisfied. ando in addition. Z....,. - Z2 - ZI e and Zm"" - Z4 - Z, - ZmiD - E (Fig. 3.26a). Writing 1 - Xl - X4 • m - X, - X2 • n-XI - X" and using the relation Xl Xl - X, X4 (Eq. (3.74»). we find that

z..w. ..

+ 1)/(/ - m + n) X2 - -m(/- m)/(/ - m + n) X, - mn/(/ - m + n) X4 - (m -/)(n + 1)/(/- m + n) XI - n( n

(3.81)

We can now locate the point X - O and get 20. For the best accuracy, X, and X4 should be located close to the mídpoint 01 the anomaly, and Xl and Xl near the maximum and mínimum. Z(O) is the point on the profile located a horizontal distance Xl from Z,. X2 from ~, and so fortb. Thus the datum line Z - O can be drawn at a distance above ZnD equal to the vertical distance between Z....,. and 20. lbis

fol1ows from Equation (3.78) ir we pul Zl and Z2 - Zml1I' that is, - Zml1I - Zmu - 20· The analysis may now be carried further 10 establish the dike parameters. First, from the definitions of symmetric and anlisymmetric runctions. and S( X) - (1/2){ Z( X) + Z( -X)}} (

A( X) - (l/2){ Z( X) - Z( -X)}

2)

3.8

we can plot S(X) and A(X) by taking points that are equidistant either side of X-O. On these profiles we mark poinls 53/4 ' Sl/2' and AI/2 with corresponding abscissae X'/4' XI /2' and X,/2; a1so X. (Fig. 3.26b). By a deve10pment similar to thal used Cor Equation (3.81), it can be shown that

d- "1/2 ( ~2 -1)/2 - 2"1/2D

2b - "1/2 { 4 -

(~2 - 1)2} 1/2 -

2"1/2W

(3.83)

d - x,(l - "}2/2,, - 2x,!!J

2b ... x.{ 4,,1- (1 _

,,)4) 1/ 2/" .. 2","Y

where 11ft - Xl/~/"3/4' ,,- x'/"'/2' D - (1fil-1)/4, !!J - (1 - ")2/4,,, W _ {4 - (+2 - 1)2}1/2/2, "Y- (I/Z,,){4,,2 - (1 - ,,)4}1/1, "1/2 - X1/ 2d, and so rorth. Finally, we can find the dip angle f

111

Processing and interpretation

---

oF-~-----------4----4-!--~~+-----~==~==~x

\

\

\

\,...--..L.~_~ \

ZM'. \

"....... /

,

Figure 3.26. (Con/inued) (b) Symmetrie and an/is~'mmetric componen/s. (e) i\.1as/er curves.

112

Magnetic methods

from the relation ( -

fT -

cot

+ tan-

-l( H. I{

spectrum of tbe sougbt·for signal is known. A motched filter is a filter tbal has the same spectrum as the sougbt-for signal. One way to carry out matched filtering involves using the Hilbert transform (Sheriff and Geldart, 1983: §10.3.11) to sepa· rate the symmetric and antisymmetric anomalY components (§3.7.8). Both tOlal-field and gradienl data may be processed in this way (Naudy, 1971; Nabigbian, 1984).

sin fJ) Z.

A(X)ltIu

() S X_

I

4 tan- B

}

3.7.10. Werner Oeconvolution

Six masler curves involving functions oC d, b, and ( for the symmetric and antisymmetric components of the dike profile are shown in Figure 3.26c. The dip-angle functions P and gJ in Figure 3.26 are related to k.nown quantities in the foIlowing expan· sions of Equation (3.84): ( - ( fT -

coC 1(

H. sin fJ/Z.)}

- tan- I ( IP) or tan- I ( IgJ), (3.85a) wbere 1= A(X)D1u/S(X)II\U' 4tan- 1( W/2D)

Wemer (1953) proposed a method Cor isolating a magnetic anomalY Crom the interference produced by nearby anomalies. This led to automated procedures for interpreting magnetic data, now known as Wemer deconvolution (Hartman, Teskey, and Friedberg, 1971; Jain, 1976; IGlty, 1983). The magnetic anomaly for a dipping dike can be written in empirical form as

F(x) - (M(x - xo) + Nz}/{(x -

XO)2

+ Z2} (3.86a)

where Xo is the surface point directly aboye tbe center oC the top 01 tbe dike, z is the depth to the top, x is the point of measurement. and the x axis is normal to the strike. M and N are unknown Cunctions oC the dike geometry and mineralization. Rearranging Equation (3.86a) in the form

P - -:-:---.,:--,---.-.:_-

In{(1 - W)/(1 + W)}

4tan- ( '#'"/2~) gJ - ln{ (1 - '#'")/(1 + '#'")}

x 2 F(x) ..

l

00

+ 01X + boF(x) + blxF(x) (3.86b)

(3.85b)

Because Equation (3.83) gives W, D, '#'", and ~ in terms or ~ and ", and tbese in tum can be found from tbe curves, P and !J# are fully determined. We cán solve for the total-field anomaly in similar rasbion. The analysis for the dike or infinite deptb extent bas been extended to cover a prism of tinite length and depth extent. Because of the extra terms, it is necessary to provide more master curves, but the procedure is similar. Master curves for otber models are also availabele (Grant and Martín, 1966; Martin, 1966; Gay, 1967). The second reference contains the following models, in addition to the prism: horizontal slab, plate, rod, and dipping sheet. (The method can be extended to dikes or prisms in gravity interpretation.)

3.7.9. Matched Filtering Wbere the problem is locating a signal in a data set, matched filtering provides a powerful method if the

where ao - -Mxo + Nz. al - M, ~ - -x~ - Z2. and bl .. 2xo' we tind Ibat xo'" bl /2 and z( - 4ba - b~ )1/2/2. Thus we can determine Xo and z by measuring F at Cour slations and solving Equa· tion (3.86b) Cor °0' al' ba. and bl · Extending the problem beyond an isolated anomaly. Wemer assumed Ihat Ibe noise or interference caused by neigbboring magnetic anomalies could be talcen into accounl by extending tbe polynomial, so that the measured field ". becomes

where F(x) is given by Equation (3.86a) so that + 5) unknown quantities are involved. Usually the polynomial is first or second order only, so tbat six or seven stations are sufficient for a solution. The scope oC lhis analysis has been enlarged to inelude models other than dikes: basement topography, magnetic interfaces (wbich use dF/dx ratber

(n

113

Processing and interpretation Table 3.3 fmpirical depth estimation methods for magnetic anomalies.

Method

Half-width

Peak-to-Zero

Vertical grado

Flank slope

Componen! measured

F.Z,H

F, aF/az, Z, az/az

f,Z

F.Z

1.3x,/2 2x'/2 x,/2

l.3xpo lJ/x po xpo

Model Monopole Dipole Monopole line Dipole line General

2X'/2 S;

0.7

XpO

x,/2

S;

1.3

xpo

S;

2

··2F/(aF/az) -3F/(iJF/iJz) - F/( iJF/iJz) -2F/(iJF/iJz) -nF/(iJF/iJz)

0.5

S;

x, S; 1.5

Note: x'/2 is the fuI! width at half-peak amplitude, xpo is the horizontal distance from peak to zero-crossing. n is an pmpirically determined ondex factor. and x, is the horizontal distance over which slope is straigh! line.

than F), faults, and contacts. lbis type of analysis is a1so suitable ror gravity interpretation. There are limitations to Wemer deconvolution, such as resolution between neighboring bodies and lack of discrimination among parameters, leading 10 a relation belween, say, dip angle and susceptibility. The data are sensitive lo geological and measurement noise (signal/noise - 100 produces 20% scatter in depth and position estimates). However, the technique is attractive because of ease of access to the computer and consequent speed in handling large quantities oC data.

3.7.11. Depth Estimates (a) Smith rules fo, maximum depth. As in Section 2.7.12, which dealt with depth estimates for gravity anomalies. there are corresponding limiting values in magnetics derived by Smith (1961). If the magnetization M is parallel throughout a body, though not necessarily uniform or even in the same sense. and iI IMlmu' laZ/axl mu ' and laZ 2/ax 2 lmu are absolute values oC the maxima oC M and the first and second deriva ti ves oC F or Z along the x profile, Ihen the depth zu to the upper surlace is given by

For Z profiJes, where M is everywhere vertical and in the same direction (down or up), the numerical factors are reduced to 2.6 and 3.1, respectively. For two-dimensional magnetic Ceatures having infinite lenglh in the .v direction, in which the total magnetization is parallel throughout, the equivalent expressions become

Where the body is uniformly magnetized by induction, we may replace Mmu by kF. or kF./(1 + Nk) as in Equation (3.67). Because we do not normally have a value oC Mm... ' estimates obtained by combining the two limits are even cruder than the equivalent relations Cor gravity. For a semünfinite thin sheet. the result is within 50%. but it appears lo be even poorer Cor three-dimensional Ceatures. (b) Empirical depth rules. A number oC rules-ofthumb Cor depth estimalion have developed from practical experience in magnetic interpretation. These relate to profile shapes; Cor example, they often use horizontal widths at sorne fraction of the peak value for symmetrical curves and horizontal distances from peak-to-zero values for asymmetric curves. Pelers (1949) was probably Ihe first to relate depth to the horizontal extent of portions of sloping flanks, and variations of slope techniques are among the most popular. The vertical gradient is also used in such rules (Barongo, 1985). A summary of such rules is given in Table 3.3. Slope methods are widely used. especially Ior aeromagnetic interpretation. Graphical techniques use the sloping flanks of profiles to estímate depth (Neltleton, 1971; Spector. 1979). In Figure 3.27a. S is the horizontal extent of the portion of Ihe curve Ihat is nearly linear at the maximum slope. Two addilionalline segments have been drawn tangent to Ihe profile at half the maximum slope: the distance between the points of langency is P. The depth oC the source beneath these portions 01 the curve is given by h=k¡S

1.67:;:;k¡:;:;2.0

(generally k¡ .. 1.82) h - k2P

(generally k 2

""

0.63)

(3.89a) (3.89b)

and The use of both methods provides a check on the

114

Magnetic methods

,

I

l~' '

,'"

,

,,,

~/

"',4,' , ,t ".,--

.....

I I

""

f--S-l (a)

Fli¡ht Une Pllte

(b) Fi8ure 3.27. Determinin8 ¡/nomal)' depth from the slope of a ma8netic profile. (a) Mallimum-slope (5) and half-slope (P) measurements. (b) Maximum-slope measuremenfs on a thin piafe anoma/)'.

deptb estímates and the cate with which tbe graphical anaIysis is done. This method generally yields reasonable results lor horizontal basement models with steeply dipping contacts; thus, it is suitable in the analysis 01 airbome data. 11 is much simpler and raster and provides more depth estímates than analysis by model curve fitting. It can be carried Oul on original field profiles and so need not wail on map preparation; it can also be applied lo analysis 01 maps (Rao and Babu, 1984). Use ol slope techniques requires correctíons. When ftight lines are not normal lo the local geological strike, horizontal distances are too large and

should be multiplied by a cosine factor. Correctíon also has lo be made lor the flight elevation lo give values with respeet lo sea level (or to an arbitrary datum).

3.8. FIEtD EXAMPLES 3.8.1. Ground Surveys (1) The firsl example shows (be inherent complexity of ground magnetic dala and the difficulties in accurately interpreting tbem. Figure 3.28 displays magnmc contours and two vertical component profiles

,.,

aL

Line 7S

_ Field prolile --- Prolile for venial dipole, Equation (3.588) {J - 45·. I - 70· ~ - 90·.1" J. O .. 3,. L .. 21

NE

Une 73 6000nT

-

F"1C1d prollle

4000

F:"'+l

Rhyolitc

~porphyry

2000

~K_alin

k!..:!:.J

acidics COnlK1

-

Pyrir.e mincralizalion

Mineralizalioa

SW ZORe lOO m O.D.H. %pyr. (m) T-l 39 5 T-l 43 4 ___ Magnetic

o

c:onlours, nT

T-J

T-4 (a)

26 2S

4 7

"

NE ZORe

.

I +OONE Overbunlen

%pyr. (m)

35 27 9

6 5 2

+ +

•

(b)

Figure 3.28, Ground magnetic survey over pyrite mineraliz.¡tion. Barr.wte. northwest Quebec. (a) Magnetic map. (b) Attempt 10 match profiles on lines 755! and 735E.

116

Magnetic methods

z

E3 Volcanic::s

ID. A,lIesto. fibre zone ~ ~

Serptnl,nne. H,ghly carOOnalile
~Serpenlinitr. Moderately

D

carOOn."zed Massive serpentine

'--, I

,

I

Field profik Composil. Iheorclical profile

I~~S__L-~~~~____~~~______________________ N__

Figure 3.29. Vertical component ground magne/ic profile in an area of asbestos minero aliza/ion near Matheson. Ontario.

nonnal to the strike of pyrite mineralization. There are two parallel pyrite zones in acidic flows, near a contact between the lauer and rhyolite porphyry. 80th have a strike length greater than 300 m and the zone nearer the contact appears to pinch out on line 7S. Although the pyrite mineralization is clearly associated witb a magnetic trend in the area, the large magnetic anomalies on lines 73 and 75 could only be due to magnetite or possibly pyrrhotite, since the susceptibility of pyrite is relatively low (Table 3.1). However. there is no specific indication of these minerals in the drilllogs of holes 1 to 4. Because the overburden near the diamond drill holes was generally quite tbick (25 m al T-1, for example), it was originally assumed to be at least 15 m throughout the grid. However, a sballow seismic refraction survey carried out later on line 75 showed bedrock only 1.5 to 3 m below the surface in the vicinity ol the pyrite zones, dropping off abruptly to 15 to 2S m northeast oC tbe acidic ftow-rhyolite contact. Thus tbe magnetite sources may be very close to the surface and oC small depth extent. Tbe source for tbe single 13 p.T peak on line 7S appears to be a finite steeply dipping sheet at very shallow depth. Using Equation (3.58a) with fJ .. 45°, J - 70°, (- 90°, and Z~ - 36 p.T, and fitting the profiles al three points (including tbe maximum), we obtain a reasonable fit with t ... d ... 8 m, D ... 2S m, 2L - 30 m, and k .. 3 SI unít (See Fig. 3.28b). However, when we try lo match the double peak profile on line 73 by assuming two vertical sheets of identicaJ eross section separated by 50 m and inductive]y magnetized in the earth's field, Equation (3.58a) produces tbe following parameters: d ... t - 2.5 m,

D - 70 m, 2L ... 90 m, k¡ - 1.3 SI, and k 2 - 1.9 SI. Tbis results in a reasonable match of the central trougb and tbe northeast flank, but the southwest flank is much too large. A better fit (shown in Fig. 3.28b) was obtained with tbe two vertical sheets ilJustrated, but the trough between them is too deep. Also, the depth extent must be less than 120 m because the bodies were not encountered in holes T-l and T·3. Althougb this interpretation is certainly not definitive, it is c1ear that tbe magnetic sources are shallow, have linúted strike length, steep dip, and large susceptibility contrast. This last fact indicates higb magnetite content and possibly large rema· nence, which may be responsible for the disagreements (Green, 1960). (2) The magnetic method is particularly useful in exploring Cor asbestos because of its occurrence in ultrabasic intrusive rocks rich in magnetite. Wben olivine (Mg 2SiO.) is altered to serpentine (Mg)Si05 (OH).) and magnesite (MgCO) by the addition oC water and carbon dioxide, the asbestos is associated with higb magnetic susceptibility and massive serpentinite. Figure 3.29 shows a vertical component profile over an asbestos prospect near Matbeson in northem Ontarlo and tbe geologic section under a 15 m overburden. Higb magnetic re· sponses correspond to the asbestos and massive serpentine zones with lows over the voIcanics and highly carboruzed serpentite. A reasonable match to the field profile was obtained by assuming dikes of considerable depth extent using Equation (3.44a) with rl'" r., ~ ... ~., fJ - ,,¡2, and all contacts vertical except the left one, whicb dips 30°. The prescnce of asbestos in the massive serpentine zones can only be establisbed by drilling.

717

Field examples

lino

o,

2 km

(i) SI J.r.n A.roma.netie Slleel 16780

.1:>7

~Cf"l'

~,,"-~"'-o:::::---------::::::_~-'--------~

O ,

I

I

3 km I

mile.

P- -P Principal profile

(ii) Bel.,.il Aeroma,nelic Sheel 1674G

(a) figure 3.30. Mdgnetic data for threl' anomalous areas in Ihe 51. La...-rener IOll"/ands. (a) Maps, CI. - 100 nT.

3.8.2. Airborne Surveys (1) The Monteregian hiUs of the SI. lawrence low-

i

"

land region near Montreal were forrned by igneous intrusions into sedimentary rocks. These hills are magnetic as well as topographic anornalies because of their contrast with the low susceptibility sediments, Aerornagnetic rnaps (Canadian Government Aeromagnetic Series, St. Jean and Beloeil) show th.is clearly for Mt. Bruno, Mt. SI. Hilaire. Mt. Rougemont, and MI. SI. Gregoire, On the sarne sheet s we

also see two well-defined magnetic highs that are not topographic features: one about 5 km west of MI. SI. Gregoire and a larger one 11 km northwest of Mt. Bruno, One assurnes that they are igneous plugs that failed to reach the eminence of the Monteregian biUs. These two features and Mt. SI. Gregoire provide ellcellent exarnples of the vertical-prism rnodel comrnonly employed in aerornagnetic interpretation. Figure 3.30a shows the total-field contours, whereas profiles are displayed in Figure 3.30b. Two methods

MiJgnetic methods

118

2500

--Principal profiJe appro •. N-S' - - --V.rtocal prism (1-90-, .-150m le - 0.06, b _ 2/. _ 19U m

MI SI GrOJoir.

N

2700 -Principal profiJe N-S - - - - Vertical prism (1 - 90-, • - 300 m Ir - 0.04, b - 2/. - 1200 m

"nomaly .esl of SI Grelo;r.

N

Prism SCC1ion _ _ Principal profile NW-SE ----V.rlical prism (1 - 135-, • - 1200 m Ir - 0.06 b _ 4900 m 2/.- 12000 m

"nomaly northwclI ofMllruno

2500

NW

5

20 km

10

lb)

Figure 3.30. (Continued) (b) Principal profiles. 1- 60° and F~ - 60 1'1. Table 3.4. Interpretation of anomalies in Ihe Sto Lawrence lowlands.

Anomaly SI. Cregoire

I

k

(deg)

(SI)

60

0.04 0.05 0.06 0.025 0.03 0.04 0.08 0.055

75 Anomaly near SI. Cregoire

60 60 75

60 Anomaly near Bruno

75

60

z

b

2L

(m)

(m)

(m)

110 110 150 230 230 300 1,130 1.220

were employed to assess the magnetic characteristics. One used the models of Vacquier el al. (1951) and the other used Equation (3.44c) for a vertical prism, This aIlowed calcu1ation of tbe susceptibility contrast k, the depth z, slrike lengtb 2L, and widtb b by matching the principal protiles. The results, which tit reasonably well, are shoWD in Table 3.4 and in Figure 3,3Ob. If we assume 1 - 75 0 instead of 60°,

880 880

880

670 790 790 1,700 1.700 1.700 1.250 1,220 1.220 3.660 9.140 4,880 12.200

Source Vacquier (rig. A6O) Vacquier (rig. A70) Equation (3.44c) Vacquier (rig. A6O) Vacquier (Fig. A70) Equation (3.44c) Vacqier (rig. A7S) Equation (3.44c)

the curves have steeper slopes on the soutb or soutbeast flanks and il is necessary to increase the lateral dimensions to match Ihe field protiles, In practical interpretations, Ihe deptb lO the top of the prism is the mosl significant dimensiono Because ftighl elevation was 300 m, Table 3.4 pUIS the SI. Gregoire plug about 150-190 m above ground (MI. SI. Gregoire rises lo a heighl of 180 m above ground). Tbe lop of

Field examples

--

-

...... 1IW1C . . . . M

~ ~ :~e-&!

119

....

.......

"""1 IIUK' IIIftUIM . . . .

~

:. :'.!:::-'-,..

• " ..........,...,.U....,... •• ..

....... _11.

.. ...,\1'"

~ u..Illf.-' .. .. ... IMr..... UI ......

"

~ ....

~ .... 'lerU.

te .......U .... ...

". ..........,..rr. t.I

.............

ti

11 ........... .

EJ :. =:.:,::;.-""" nu. ti!

......

m.tIC "'~.ICS

r¡-;-J,.I;I. =~=: 'hI'r

I!.....:...JI

lit

..

..... _nl. ,r" ... d.

.. ...,....... ........ " ........ ""M C,"",

EJ :.•"

=!~.:rr.!!·t 'UI ... , .....

t"'.~

tr ........................

l-

E:] =!.~..,. ,nltl_ l- -1 ::.'-:!:!!,::-=:"

y ••. ,.....

~

, ..... ( __ ...... u - ' ) .

~

IIN''''_. .,..11.., ..".........

fa)

Figure 3.31. High-resolution aeromagnetic sun-ey, Timmins area, Ontario. (From Bhattacharyya, 1971.) (a) Geological map. (b) Cround vertical-intensitr map.

720

Mi/gnetic methods ..... '00-

.,. ,.'00"

...,.,..0-

...... 10' ......00"

(r)

•. -".'W -".,.,-

..

.'-.'·00·

..

"-"'00·

,~!'\".

"..

Ir ...

.'-1"10(d)

I.-M'OO-

Figure 3.31. (Continued) (e) Conventional aeromagnetie map. (d) High-resolution .leramdgnetie map.

121

Field examples Anomaly

In lerpreter choose. model

.'

List paramete" lo be varied by Powell algorithm

Search for minimum

correclion vector

Replace partial derivatives in Powell algorithm Calcula!e

Figure 332. Cf'nf'ralizl'd flow (harl of compulf'rized interpretation (From \lcCralh and Hood. ¡q7J)

.

l·

Ihe anomaly near MI. SI. Gregoire is jusi aboye tbe surCace wbereas the one near MI. Bruno is aboul 870 m below tbe surface. (2) The use of high sensitivily aeromagnetic data has becn described by Bhattacharyya (1971). In 1969, tbe Geological Survey of Canada arranged an experimental high-resolution survey in the Precambrian sbield of nortbern Onlario near Timmins tha! used a cesium-vapor magnetomeler wilh a sensitivity oC 0.02 nT. Control of the survey was much tighter than in conventional work at the time. Line spacing was 300 m al an average altitude of 250 m and flight paths were straight within lOO mover 24 km. Double baselines perpendicular to these were flown in opposite directions every 8 km. The total field was continuously recorded at a ground station. The following were recorded on the alrcraf!:

1. Total magnetic field in units of 0.02 nT. 2. Total field vertical gradient in units of 0.005 nT.

3. Terrain clearance in units of 60 cm. 4. Barometric altitude in units of 3 m. 5. Doppler-radar along-track and cross distances in units of 50 m. 6. Time in seconds. Data compilation ¡nvolved the following: 1. Check of in-flight digital dala and necessary correclions. 2. Calculation of coordinates. 3. Location of traverse and baseline intersections. 4. Adjuslment of intersection points. 5. Calculation of, and correction for, drirt. 6. Reduction of data 10 a common datum. 7. Reduction of corrected values for contouring.

A map oC a 10 x 10 km portion of tbis survey is shown in Figure 3.31d. Figure 3.31a, a provisional geological map, was prepared with help from an earlier ground vertical-

Magnetic methods

122 I~"

,

! II! \

··1

' I !. j ,A,

I,

l'

(

_ •• 1

¡

:

\

.

~ ;".i:

•

1'\'

¡ ,':.: : '. .

I

.

-1

¡

.

'.~

I

¡. .

1

~

••

'.

.,

.•

o

(a)

60600

BEST FIT

-~

u.

500

DATA '-...

400

1km 300

60200

A____-+.__~~~L~'G=H~T~L~IN~E~____~y~-B :Q

30~¡ 600

:1:

900

~ w

300m - - -n - . - -.-- -.PALEOZOIC SEOIMENTS - - - - - - -.

( e) FigurE' 3.33 BE'IE'c lakf> anomaly. Ontario. (from MeCra/h and l1ood, 1973.) (a) A(w)o magnetie map 01 the anomdly. (b) Profile AB and 'he anomilly eompu/ed lrom thp model. (e) Inlerred geologieal cro~~ 5pe/ion.

intensity map (Fig. 3.32b). The bedrock in lhis area, cut by numerous N-S diabase dikes, is an Archean complex ol gabbro, granite, and mafie and fe1sie volcanics. There are lhree major fault systems: The one striking N300w is the main conlrol for the diabase dikes, whereas the other two. trending WNW and NE, appear lo have affected the dikes by shearing and deflection. The ground survey map shows much detail. but lhe trends are broken up. The map from a conventional survey. Figure 3.31c, flown wilh a prolon-pre-

cession instrument (sensitivity 0.1 nT) at 300 m with 800 m tine spacing. obviously shows much less detail Ihan the high-resolution magnetic map in Figure 3.31d. SeveraJ pronounced anomalies. probably due 10 gabbro. are obvious on both aeromagnetic maps, whereas lhe ground map does not show them cJearly. The cost of the high-resolulion survey was about six times greater than the conventionaJ aeromagnetic survey. but the difference would be much less today: an equivalent ground survey on 120 m spacing would eost five lo six times as mucho

123

Field examples

(3) An example oC computer modeling followed Ihe procedure diagrammed in Figure 3.32. This modellng minimizes E. tbe dilference between observed. D(x. y). and model anomalies T(x. y). at m points through an iterative adjustment oI n model parameters, q\. q2' .... qll:

drilling measurements). The best-fit model showed an intrabasement magnetic zone al a depth oI 900 m, which corresponds to 600 m of sedimento The magnetic body is 1.730 m thick with a strike length of 14 km and dips 82° north: the susceptibility contrast is 0.029 SI. which is typical oC igneous rocks. The body has its polarization vector dipping 64° wilh declinalion 107°. The local magnetic inclination is 79°, which means tha! the body possesses significant remanent magnetization.

E(q¡.q2.···.q.) - E[D(x,y) - T(x.y.q¡.q2 .... 'qn)]2 Tbe minimum oI E may be Cound by the melhod oC Gauss. least squares. steepest deseent. or other techniques. Here it was Cound by a combination oC the Marquart and Powell a1gorithms (McGrath and Hood, 1973). [See §2.7.9 Cor a similar gravity proce· dure.) This example is oC modeling a basemenl anomaly in the Moose River basin oC Ihe Hudson Bay lowlands in northem Ontarío, which is shown in Figure 3.33. The model was a thick. steeply dipping plate. The Moose River basin contains about 600 m oC nonmagnetic Paleozoic sediments overlying a Precambrian crystalline basemenl (based on seismic and

Table 3.5. Vertical-companf'nt read;ngs in serpenline zanc.

z Stn.

(nT)

ON 1 2 3

275 220 224 230 185 185

11 12 13

155

I~

~

5 6 7

Stn

8N c:¡

35

.,

r

N

t •

i

~

c:r::>

ñc:iC-

-Road •

Building

Fence -

Po ... rhne

I

I

o

-~O

-lO

lO

i--

I

Z (nT)

100m

FigUfC' J.J.J. Vertical magneric ground SUf\·C'f'. Noranda ar"J. C ,. ~ 50 n T (Atl", 5f';81'1. 1957)

4-

. 15 100

150 220 220

Magnetic methods

124 Table 3.&. Traverse in Quebec Eastern Townships.

Z

Z SIn.

(nT)

SIn.

(nT)

17W 1& 1S 14

2.040 2,320 2,080 2,080 1,800 3,280 9,200 3.400 -9,500

8W

-7,000 -1,060 2,720 5,140 4,260 2,&80 2,220 2,240 1,940

13 12 11 10 9

7 & 5 4

3 2 1 O

2.

3.

Table 3.7. Vertical-component readings across zinc property. SIn. (fl)

& + 005 5 4 4 3 3 2 1

+ + + +

00 50 00 50 + 00 + 00 + 00

Z

SIn. (fl)

(nT)

O + 50S 0+00 O + SON 1 + 00 2 + 00 3 + 00 4 + 00

45 50 52 50 45 50

90

Z

(nT)

130 95 75 40

8 O

4.

-5

135

3.9. PROBLEMS 1. Chromite is found in serpentine in a certain district. A magnetic analysis ol several specimens indicates that there is less magnetite in the chromite-bearing serpentine Iban in barren ser· pentine. The Z·component readings in Table 3.5 were taken on a N-S line at 8 m stations. Assuming a two-dimensional E-W zone of min·

5,

eralization, estimate Ihe depth and cross-section of Ibe body causing magnetic anomaly from tbis profile. Figure 3.34 shows Z-component conlours obtained from a detailed ground magnetic survey in Ihe Noranda district, an area rich in sulfides and grapbite. The rocks to the south are rhyolites, rhyolilic breccias, and tuffs. To the north we find basic volcanics and tuffs with occasional rhyolite. Where would you expect to find anomalous sulfides and/or graphite? Are they shallow or deep? If they are sulfides, what varieties can be ruled out? Have the fence and power line affected the readings to any extent? Table 3.6 shows Z-component readings made 3 m apart on an E-W traverse in the QuebéC Eastem Townsrups region. The large anomaly was originally detected during a pace-and-compass exercise when tbe magnetic declination suddenly changed by about 110 0 , an effect that did not persist for any appreciable distance. In terpret the source with regard to location, depth, dip, lateral extent, and possible mineral character. Use a dipping sheet model ol considerable strike length to calculate and pi O! the total field F and vertical gradient BFfaz, given Ihat D - b - 10d and tha! the structure strikes (a) N-S and (b) E-W, in a region where I = 60°. By neglecting small terros, calculate the approximate maximum and minimum values of F and BF/az in (a) to check the N-S profile. The vertical component magnetometer readings in TabJe 3.7 are from a detailed survey of an bid mining property where the primary metal was zinc, wilb sorne Jow-grade copper and minor silver. Assume that the source of the weak mag-

z lin.450W

!OON

200N

300N

4UON

L

SOON

600N

o I

lOO

m

I

Figure 3.35. Vertical-compommt 8round ma8netic pro file, fast A frica.

Problems

125 I03E I

I

LIO E

LlO~E

N

IS8 •

1

IS7 •

------------~~~.8~V_---------LI~N

LI S6N---'-=?lr---lf---.::::..------'---~.......:::::J__I~-----

LIS6N U5 • 1000 I

3000 I

LIS2N 154· 100

(a)

102 (b)

Figure 3.36. fffect o( Jine spacing on magnetic data. (a) ConventionaJ magnetic map. c./. - 1.000 nT. (b) DetiliJed milgnetic milp centered ill 156N. 101E.

nelic anomaly is a dike of large strike length and depth extent and use !he method of Section 3.7.8 lo determine its parameters. 6. The vertical-component ground profile shown in Figure 3.35 is from a large-scale multiple-melhod survey Cor base metals io Tanzania. The geology is generally Precambrian metamorphosed sediments and volcanics associaled with granite. lo this region, F. .. 0.35 p.T, !he declination is 4°W, and the inclination is I '" 31°N. Sulfide bodies with large E-W extent are knowo in the vicinity. Ioterprel !he anomaly. 7. Tbe magnetic contours in Figure 3.36 show the effecl of line spacing (see also Bhattacharyya, Sweeney, and Godsoo, 1979). A small section Crom what would normally be considered a detailed ground survey is shown in Figure 3.36a. Lines were spaced 200 ft aparl N-S with statioo readings every 50 Ct (reduced to 20 ft near anomaJous vaJues). Tbe contours of Figure 3.36a are elongated N-S because !he line spacing is grealer than tbe station spaciog. Sorne of the

zones were resurveyed in followup work on SO fl grids with occasional readings 5 to 10 Ct apart because of the small laleral extent ol tbe anomalies. Three oC these detailed grids are shown in Figure 3.36b, e, d. The differences, particularly io lateral extent, slrike axis, magnitude, and anomaly localion, are very apparent. What are they? Other surveys have indicated massive sulfides al tbe centers ol Figure 3.36b. d but nOI al 164N,103E. Given tbis addilional information, would you conclude that the magnetic anomalies are direclly or indirectly related to the sulfides? Do they have any association with the sulfides? Would you reach the same conc1usion iC only Figure 3.36a were available? Estimate the depth, lateral exlenl, auilude, susceptibilily, and probable conten! of a Cew oC the anomalies in all Cour diagrams. Do they show evidence oC strong remanent magnetization? 8. The vertical-component ground magnetic contours in Figure 3.37 were Crom a survey over a

Magnetic methods

126

Ll60N

oI

16l·

161· 101

I I I o I I I

100 f\ I

2 / ,

lOO!"!

~

I

I

LIOlE

IOC

(e)

Idl

Figure 3.36. (Continued) (e) Detai/ed magnetie map eentered at (d) Detailed magnetie map eentered at 160N. 105E.

niclcel prospeel in norlhem Manitoba. Zone e is approximately 4 km NE oC zone A. There is considerable overburden lhroughout the area. E1ec:lromagnetie surveys showed that both zones were good conductors. One 01 them c:ontained ore-grade niclcel sulfides, tbe other was barren ol sulfides and graphite. Is it possible to distinguish the ec:onomie mineralization solely from the magnetic results? Estimate the depths ol the main magnetie anomalies in the two zones. 9. A c:opper deposit of Iimited extent in the Rouyn distriet ol Quebec: produc:ed the Z profiles in Figure 3.38. Match the profiles lo an appropriate model given that tbe E- W strike is very Iimited and the inc:lination I - 75°. What is tbe probable magnetie mineral? 10. Figure 3.39 sbows four vertical-component magnetie profiles from tbe Manitoba Nic:kel Belt, obtained during large-sc:ale base-metal apIoratiOD programs. Sulfides and graphite oc:cur in tbe Prec:ambrian racks below Paleozoie sedi-

164N. "IOJE.

ments and thiek overburdeD; the miDeralized zones frequent1y extend for miles. Diamond drilling has established that the mineralization associated with two 01 these profiles is pyri te and pyrrhoti te, a third is graphi te and pyrile, and the fourth graphite and pyrrhotite, and that tbey are loc:ated al rour dilrerent depths. With this informatiOD, use the magnetie data to loeate the mineralized seetions as prec:isely as you can. 11. The two ground magnetie con tour maps in Figure 3.40 iIlustrate the elreet oC irregular topograpby on magnetie measuremeDts (Oliver and Hinze, 1985). The areas surveyed in Figure 3.40 are only 60 miles apart. The terrain is quite rugged in both, as ean be seen from the dotted contours, but the geology is eDtirely dilrerent. In the former, the roc:ks are sedimentary to great depth; at the lauer site, there are granites in most of the north and west parts 01 the map and sediments in tbe lower ground at tbe south. It is

Problems

127

Ikm I

--

-------------------

ZoneC

Figure 3.37. Cround magne/ic con/our.'. nnr/hern Man//oba. C./.= 100 n T

Ihought Ibal the sediments extend for sorne distance up tbe hill in the lower left comer and the assumed contact between the granites and volcanic formations is somewhere in Ihe upper left portion oC the map. The uniform magnetk response over the sediments in Figure 3.40a (abou! 300 nT maximum) is to be expected because of tbe low susceptibility oC sandstone and Iimestones. There is no particular correlation between tbe topograpbic and magnetic contours, bence no need for a topograpbic correction. In Figure 3.4Gb tbe situation is quite dilferenl. A definite magnetic contrast exists between the granites and tbe sedimentary area, altbough !he map does not extend lar enough south and

southeast 10 indicate tbis c)early. However, a pronounced magnelic )OW follows the topography from north to south, then west to easl, starting in the upper lelt area. This is a clear refleclion ol the terrain elfect on ground magnetics. Using Equations (3.33) and (3.71), appty the terrain correction at a few se)ected poinls on the rnap of Figure 3.40a. For exarnp)e, the 100 nT )ow on the steep slope near the bottorn oC the rnap, midway between the east-west boundaries, ties on the 425 ft contour; if we choose the 600 ft e)evation for z = O, the value oC h will be 175 CI. Reasonable values for circJe radii would be r¡ ... 100 ft, r2 = 200 Ct, and so Corth. For other stations, one might select one at the top oC the

Magnetic methods

128

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Line 0+ ooE

I ION

SN

~~

:t SN

~

I ION

ISN

1\.,

Line I +ooE

I ISN

Une 2 + 00 E ISN

~g .~~

Line 3Z + 00 E I SN

I ~~ ION

I ISN

Line 4 + 00 E

t

b SN

ION

i ISN

I

H

I

100 rt Figure 3.38. Verticdl-component mdgnetic pro(iles, I?ouyn-Nordnda di~,rict. Qupbpc.

hill. one in the northwest comer. and one to the southeast. Do these modified Z values aid the magnetic interpretation in any way? Repeat the procedure for several strategically located slations on the map of Figure 3.40b. particularly in the area of the magnelic lows following lhe Slream gorge. (Obviously the beSI method for handling analysis of Ibis lype would be lo digitize the contoured data and use a computer_) Are the terrain corrections significant? Would they be more reliable iC vertical gradients had been measured? Why? 12. The two sets of conlours shown in Figure 3.41 illustrate the differences between airborne 101alfleld and ground vertical-component survey results. Only lhe relative vaJues are significant because there is no rdation between the absolute magnitudes. The airborne results show the ef-

fects 01 smoothing wilh altilude. The ground survey indica tes tive dislincl maxima. compared wilh a single symmetrical anomaly in lhe airborne contours. Furthermore. the largest of these ground maxima is displaced about 650 m from Ihe center oC the total-tield anomaly. The allitude of the aircra!t was 300. m and the ground is tlat. The magnetic inclination in the arca is 75°. Calculate the depths and approximate lateral extents oC the 6,000 nT and the larger oC the 2.000 nT ground anomalies as well as the airborne anomaly. With the aid of Equation (3.71) and Table 3.2, carry out an upward conlinualion of the ground data lo 300 m by choosing '1 - 100 m and h - 5. 13. Figure 3.42 shows a 9.5 x 6.5 km section from a Canadian govemment aeromagnetic survey in

Problems

129

l,""T

(1)

JIOO Z -L--~~--~~~~--~-L--~~--~O

o

200 m 200nT

(2)

100 Z

Figure 3.39. Vertical·component magnetic prof¡/es. Manitoba Nicke/ Be/t.

nortbwest Newfoundland. The rocks in tbe area are sedimentary, consisting of sandstones, shales. and limestones with some dolomite. In the upper balf and tbe lower left quarter of the section the topography is ftat; Ihe average elevation is - 100 m. A steep escarpment, in the shape of an inverted U with apex lo the nortb. occupies the lower middle portion oC tbe figure. It Collows the c10sed 200 nT contour on the leh, continues north and easl 10 overlap tbe east baJC oC tbe 100 nT low, and Ihen lums southeasl between tbe 300 nT contours on the lower rigbt. Thís scarp rise about 200 m, in places having a slope oC nearly 30°. As a result, the magnetic bigb in the lower part ol tbe diagram is on a 300 m plateau. Fligbt lines were easl-west, 300 m aboye ground leve\. With tbis inCormation, make an interpretation of the magnetic anomaly in the lower central

part of the section. Could it be entirely or partly the result of topography? Is it the reftection oC a single magnetic structure? Is it possible tbat tbe larger magnelic low area, contained in tbe 200 nT contour striking rougbly east-west, migbt represent a distinctly different structure? 14. The Z-component data in Table 3.8 constitute airbome and ground profiles along approximately the same line crossing a strong magnetic anoma1y oC great lengtb. striking rougbly E-W. The airbome magnetometer was a heavily damped vertical-component instrument al elevations oC 300 to 400 Ct aboye ground. The ground instrument was a conventional ftuxgate magnetome ter. Slation íntervals are in Ceet and airborne station 800N corresponds approximately lo a point between 400 and SOON on the ground traverse. Determine the depth. cross section, approximate susceptibility, and dírection oC mag-

(al

-- ....

20N

B.L.

lOE

lb)

Figure 3.40. Effeet 01 topography on magnetie measurements. (a) Elevation (dashed) and Z-eomponent (salid) eontours in ,ln are.! 01 sedimentdry raeks. (b) Eleva/ion and Z-eomponent eontours in .In afea o( granitic and sedimentary roch.

Problems

131

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Fisure 3.41. Comparison of sround ver/ical-componen/ da/a wilh airborne /o/al-')eld dala.

,"

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Fisure 3.42. To/a/-{ield aeromasne/ic con/ours, northwes/ Newfoundland. C.I. - 20 nT and fliSh/ alrilude 300 m.

.

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Magnetic methods

132 Table 3.8. Ground and airborne vertical·component survey. Airborne

Slnl.

ON 400 600 800 1.000 1.200 1,500

Ground Z (nT)

600 2,600 4,100 5,700 4,050 2,760 750

SIn.

ON 100

200 300 400 500

Z (nT) 4.600 7.400 13.700 28.600 40.000 40.000

Z

SIn. 6QON

700 800

900 1.000

(nT)

36,000 28.600 16.000 8.000 4,600

-

figure 3.43. TotaJ.field aeromagnetic con/ours, SI. tawrence lowlands. CI. - 100 nT.

netization 01 the source from each traverse. As a check on the results, continue the ground profile upward to find out il it matches the airbome profile. lS. A section trom Canadian govemment aeromagnetic maps oC the St. Lawrence lowlands sedimentary region is reproduced in Figure 3.43. There are al least three large structural features producing the magnetic anomalies. Two are well documented geologically. Can you distinguish any Cault zones? Any domes or plugs? Are these

anomalies produced by structures in the sediments or in the underlying basement rocks? AnaIyze this aeromagnetic section as precisely as possible, with particular emphasis on deplhs lo the sources. Altitude 01 the aircrafl was 300 m above ground level and the ftight lines were E- W. The lopography is essenlially Hat throughout. 16. Figure 3.44 shows a portion oC an E- W aeromagnetic profile. The fiducial maru (numbers at the bottom) are 2 km apart and the aircraft was

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Magnetic methods

734 Surfacr

Surface

f

f

d

d

(a)

(b)

Figure 3.45. Bilsement structures. (il) COn/ilc/ between s/ilbs o( different su~cf'ptibi/itv. (b) Uniform bed with il step.

flown al a constant barometric elevation oC 750 m. Analyze the profile using the methods oC Section 3.7.11 and Equations (3.89). 17. The schematics shown in Figure 3.45 represent two relatively common basement slructures: (a) a contact between beds oC great strike length and depth extent and (b) a uniform bed with a step. Assume D/d - 1.1 and a N-S strike Cor bOlh features. PIOI both profiles and compare the

maximum anomalies.

REFERENCES AIHeck. J. 1963. Magnetic anomaly Irend and spacing palleros. G~ophysic's 28. 379-95. AI-Cbalabi. M. 1971. Some studies relating lo nonuniqueness in Ihe gravity and magnetic inverse problem. Grophysics 36. 835-54. Baranov. V. 1957. A new melhod for inlerpretalion of aeromagnelic maps: Pseudogravimelric anomalies. Grophysics 22. 359-83. Barnett. C. T. 1976. Theorelical modeling of Ihe magnelic and gravilalional fields oC an arbitrarily shaped 3-D body. G~oph.ysics 41. 1353-64. Barongo. J. O. 1985. Melhod for deplh estimalion on aeromagnetic verlical gradienl anomalies. Geophysics 50.963-8. Bhattacharyya. B. K. 1964. Magnetic anomalies due to prism-shaped bodies wilh arbitrary polamation. G~hysics 29. 517-31. Bhattacharyya. B. K. 1965. Two-dimensional harmonic analysis as a tool for magnelic interpretation. Geophysic:s 30. 829-57. Bhallacharyya. B. K. 1966. Conlinuous speclrum of lolal magnetic-field anomaly due lO a rectangular prismalic body. G~h.vsics 31.97-121. Bhattacharyya. B. K. 1970. Some importanl consideralions in the acquisition and Ireatmenl of high-resolution aeromagnelic data. Bolletino di Geofoica Teorica ~ di Applicata 12. 21-44.45-6. Bhallacharyya, B. K. 1971. An aulomatic method of compilation and mapping of high-resolution aeromagnelic data. Geophysics 36, 695-716. Bhallacharyya. B. K .• and Navolio. M. E. 1976. A fastFourier transform method for rapid computalion oC gravity and magnelic anomalies due lo asbilrary bodies. G~hy$. Prosp. 24, 633-49. Bhallacharyya, B. K .• Sweeney, R. E., and Godson. R. H. 1979. Inlegration 01 aeromagnelic dala acquired al ditrerent times wilh varying elevalioDs and line spacings. Geophysics 44. 742-52.

Clark. A. 1. 1986. Archaeological geophysics in Brilain. Geoph.l'sÍC's 51. 1403-13. Dean. W. C. 1958. Frequency analysis for gravity and magnetic interprelalion. GeoplJysic's 23.97-127. Gay. S. P. 1967. Standard curves Cor inlerprelalion of magnelic anomalies over long tabular bodies. In Mining Geophysics. vol. 2. pp. 512-48. Tulsa: Sociely oC Exploration Geophysicisls. Granl. F. S.. and Martin. L. 1966 Inlcrprclalion of aeromagnetic anomalies by Ihe use of characteristic curves. G~P""'sÍC's 31. 13S-4M. Grauch. V. J. S.• and Campbell. D. L. 19M4. Does draping aeromagnelic data reduce lerrain-induced ctrecls? G~ophysic:s 49. 75-80. Green. R. 1960. Remanent magnetization and Ihe interpretation oC magnelic anomalies. Geophys. Prosp. 8.98-110. Gunn. P. J. 1975. Linear Iransformalions of gravily and magnetic fields. G~phys. Prosp. 23. 300-12. Gupla. V. K .. and Filzpalrick. M. M. 1971. Evaluation of terrain etrecls in ground magnelic surveys. G~ophysÍC's 36. 582-9. Hague. B. 1957. Alternating Currel/l Br¡d!?e Methods. New York: Putnam. Hahn. A.. Kind, E. G.. and Mishra. D. G. 1976. Depth eslimation of magnelic sources by mc:ans of Fourier amplilude speclra. Geophl's. Prnsp. 24. 287-308. Hanson. R. D. and Miyazki. Y. 1984. Continualion oC poten ti al fields between arbilrary surCaces. Geophysics 49,789-95. Harlman. R. R. Teskey. D. J.. and Fricdberg. J. L. 1971. A system ror rapid digilal aeromagnelic interprelalion. Geophysics 36. 891-918. Henderson. R. G. 1960. A comprehensive system or automalic computation in magnelic and gravity interpretalion. G~ophysÍ<'s 25. 569-85. Hood. P. J. 1965. Gradient measurements in aeromagnetic surveying. G~ph...sics 30.891-902. Hood. P.. and McClure. D. J. 1965. Gradienl measuremenls in ground magnetic prospecting. GeophysÍ<'s 30.403-10. Jain. S. 1976. An automatic method or direet interpretation or magnetie profiles. Geophysics 41. 531-41. Kilty. K. T. 1983. Werner deconvolution of prolile polential field data. Grophysics 48. 234-7. Kip. A. F. 1962. Fundamenta/s 01 f.'/eC'trici~l· und Magnetism. New York: McGraw-HiII. Koulornzine. T .. Lamontagne. Y.• and Nadeau. A. 1970. New methods ror dirccl interprelation of magnetic anomalies eaused by inelined dikes of infinite length. Geophysics 35, 812-30. Leite. L. W. B.• and Leao. 1. W. D. 1985. Ridge regression applied lo Ihe inversion of two-dimensional aeromagnetic anomalies. Geophysics 50:1294-306.

References Martin. L. 1966. Manual 01 Magnttic II/Itrpretation. Toronto: Computer Applications and Systems Engineering. McGrath. P. H .• and Hood. P. J. 1973. An automatic least-squares multimodel method Cor magnetíc interpretation. Geophysics 38. 349-58. Nabighian. M. N. 1984. Toward a three-dimensional automatic interpretation of potentiaJ field data via generalized Hilbert transCorms: Fundamental relations. Geophysics 49. 780-6. Naudy. H. 1971. Automatic interpretatíon of depth on aeromagnetic profiles. Geophysics 36. 717-22. Ncttleton. L. L. 1971. E/emenrary Gral'ity alld Magnelicslor Ge%gis's and SeismologiS/S. Tulsa: Society 01 Exploration Geophysicists. Oliver. R .• and Hinze, W. J. 1985. PotentiaJ fields in rugged topography. Geophysics. /he Leading Edge 01 E.~ploration 4. No. 4. 14-17. Paterson. N. R .• and Reeves. C. V. 1985. Applications oC gravily and magnetic surveys: the state-oC-the-art in 1985. Geophyics 50. 2558-94. Peters, L. J. 1949. The direct approach to magnetic interpretation and its practical application. Geophysics 14, 290-320. Rao. D. A.• and Babu. H. V. R. 1984. On the halC-slope and slraighl-slope methods oC basement depth detenninalion. Geophysics 49, 1365-8. Rasmussen, R .• and Pederson, L. B. 1979. End corrections in potential field modeling. Geoph,l·s. Prosp. 27,749-60. ReCord. M. S. 1980. History oC geophysical exploration. magnelic melhod. Geophysics 45. 1640-58. Seigel. H. O. 1957. Discovery oC Mobrun Copper LId. sulfide deposit, Noranda Mining District. Quebec. In Methods and Case Histories in Milling Geophysics. 6/h Commonwealth Mining and Metal/urgical Congren. Montreal: Mercury Press. Sherilf, R. E. 1984. Encyc/opedic' Dic/ionan' 01 Explora/ion Geophysics. Tu1sa: Society oC Exploration Geophysicists Sherilf, R. E.. and Geldart, L. P. 1983. Explorarion Seism%g;\!. vol. 2. Cambridge: Cambridge University Press .

./

135 Silva. J. B. C. 1986. Reduction to the pole as an ¡nverse problem and its application to low-Iatitude anomalies. Geoph,rsics 51. 369- 82. Smellie. D. W. 1967. Elementary approximations in aeromagnetic interpretation. In Mining Geoph.l'sics. vol. 2. pp. 474-89. Tulsa: Society oC Exploration Geophysicists. Smilh. P. J. 1982. The Earth as a Magnet. In Cambridge Encyelopaedia 01 Earth Scienus. D. G. Smilh. ed .. pp. 109-23. Cambridge: Cambridge Universily Press. Smith. R. A. 1961. Sorne theorems concerning local magnetic anomalies. Geoplrys. Prosp. 9. 399-410. Spector. A .. 1979. paper presented at the Canadian Institute oC Mining and Metallurgy. Montreal. April. Spector. A .. and Grant. F. S. 1985. Statistical models Cor interpreting aeromagnetic data. Geophysics 50. 1951-60. Strangway. D. W. 1970. His/ory ollhe Eartlr's Magneric Fie/d. Ncw York: McGraw Hill. Teskey. D. J. 1980. Computer based syslem Cor interpretation oC airborne gradiometer data with application 10 Key Lake area. Saskalchewan. Current Research. B. Geol. Surv. Canada paper 80-18. pp. 59-67. Vacquier. V .• Steenland. N. C .. Henderson. R. G .• and Zeitz. 1. 1951. Interpretation oC aeromagnetic maps. Geol. Soco Am. Memoir 47. Weinstock. H.. and Overton. W. C. 1981. Squid Applicarions ro GeophysÍL's. Tulsa: Societ)' oC Exploration Geophysicists. Wemer. S. 1953. Interpretation oC aeromagnetic anomalies at sheel-like bodies. Stoer. Gl!o/. Undersok. Seno. C. Arsbok 43. No. 6. Whitham. K. 1960. Measurement oC the geomagnetic c1ements. In MerllOds (md Tel'hniques in Geoph,l'sics. vol. 1. S. K. Runcorn. ed .. pp. 134-48. New York: Interscience. Wynn.1. . 1986. Geophysics in archaeology. Geoph.l'sics SI. 533-634. Zimmerman. J. E .• and Campbell. W. H. 1975. Tests ol cryogenic squid for geomagnelic field measurements. Gl!oplrysics 40. 269-84.

Chapter 4

Seismic Methods

4.1. INTRODUCTION 4.1.1. Importance of Seismic Work The seismic method is by far the most important geophysieal technique in terms of expenditures (see Table 1.1) and number of geophysicists involved. lis predominance is due to high accuracy, high resolution, and great penetration. The widespread use oC seismic methods is principally in exploring for petroleum: the locations for exploratory wells rarely are made without seismic information. Seismic methods are also important in groundwater searches and in civil engineering, especially to measure the depth to bedrock in connection with the construction of large buildings, dams, highways, and harbor surveys. Seismic techniques have found little application in direct exploration for minerals where interfaces between dilferent rock types are highly irregular. However, they are useCul in locating features. 5uch as buried channels, in which heavy minerals may be accumulated. Exploration seismology is an offspring of earthqua1ce seismology. When an earthquake occurs, the earth is fractured and the rocks on opposite sides of the fracture move relative to one another. Such a rupture generates seismic waves that travel outward from the fracture surface and are recorded at various sites using seismographs. Seismologists use the data to deduce information about the nature oí the rocks through which the earthquake waves traveled. E.xploration seismic methods involve basically the same type ol measurements as earthquake seis mology. However, the energy sources are controlled and movable, and the distances between the source and the recording points are relatively small. Much seismic work consists of continuol/S coverage, where the response ol suecessive portions of earth is sampled a10ng Iines of profile. Explosives and other energy sources are used to generate the seismic waves, and arrays of seismometers or geophones are used to

detect the resulting motion of the earth. The data usually are reeorded digitally on magnetie tape so that eomputer processing can be used to enhanee the signals with respeet to the noise. extraet the significant information. and display it Cor geological interpretation. The basie technique oC seismie exploration consists of generating seismie waves and measuring the time required for the waves to travel from the sources to a series oC geophones, usually disposed along a straight line direeted toward the souree. From a knowledge of traveltimes and the velocity of the waves, one attempts to reeonstruet the paths of tbe seismie waves. Structural information is derived prineipally from paths that CaU into two main categories: headwave or refracted paths, in which the principal portion oC the path is along the interface between two rock layers and henee is approximately horizontal. and rejfected palhs. in which tbe wave travels downward initially and at sorne point is reHeeted baek to the surface. the overall path being essentially vertical. For bolh Iypes oC path. the travellimes depend on the physical properties of the rocks and the attitudes of the beds. The objective oC seismie exploration is to deduce information about the rocks, especially about the atti tudes of the beds, from the observed arrival times and (to a lesser exlenl) from variations in amplitude, frequency, phase, and wave shape. Despite the indirectness of the method - most seismie work resulls in the mapping oC geological strueture rather than finding petroleum direetly - tbe likelihood of a suceessCul venture is improved more than enough to pay for the seismic work. Likewise, engineerlng surveys, mapping oC water resources, and other studies requiring accurate knowledge of subsurfaee strueture derive valuable inCormation from seismic data. We shall first give a brief outline oC the history oC seismic exploration and of the field methods used Cor acquiring seismic data. This will be followed by a

Introduction

brief diseussion of seismie methods that wiIl provide a background for the Collowing seetions. The subsequent seetions will then diseuss the theory oC seismie wave propagatíon, the geometry oC seismic raypaths. and tbe characteristics of seismic events. We shall tben examine, in more detail, the recording instrumentation and field techniques used for land and marine reHection and refraction surveys. Finally, we shall describe the processing of seismic data and conclude witb a discussion of interpretation techniques.

4.1.2. History of Seismic Exploration Much of seismic theory was developed prior to the availability oC instruments that were capable oC sufficieot sensitivity to permit significant measurements. Earthquake seismology preceded exploration applieations. In 1845, Mallel experimentedwith .. artificial earthquakes" in an attempt to measure seismic veJocilies. K.nott developed the tbeory of refleClion and refraction al interfaces in a paper in 1899 and Zoeppritz and Wiecbert published on wave theory in 1907. During World War l. both the Allies and Germany carried out research directed toward locating beavy guns by recording the arrival oC seismic waves generated by the recoil. Although this work was nol very successCul, it was Cundamental in the deveJopmenl of exploration seismology, and several workers eogaged in tbis research later pioneered the developmenl of seismic prospecting techniques and instruments. Among these researchers, Mintrop in Germany and Karcher, McCollum. and Eckhardt in the United States were outstanding. In 1919, Mintrop applied for a patent on the reCractíon method and, in 1922, Mintrop's Seismos Company Cumished two erews to do retraetion seismíe prospecting in Mexico and the GulC Coast area oC the United States using a mechanical seismograph oC rather low sensitivity. The discovery. in 1924, oC Ihe Orchard salt dome in Texas led lo an extensive campaign oC refraction shooting during the next six years. the emphasis being principally on Ibe location oC salt domes. By 1930 most oC tbe shallow domes had been discovered and the refraclion melhod began to give way lo the refleclion method. Whereas reCraelion techniques were ideal for locating salt domes, reftection techniques are more suitable for mapping other Iypes of geologic structures commonly encountered. Reftection seismic prospecting stemmed principally from Ibe pioneering work oC Reginald Fessenden about 1913. Tbis work was directed toward measuring water depths and detecting icebergs using sound waves. In tbe early 1920s, Karcher de-

137

veloped a reflection seismograph that saw field use in Oklahoma. It was not until 1927, however, that commercial utilization oC the reflection method began with a survey by the Geophysical Researcb Corporation of the Maud field in Oklahoma, wbich used a vacuum tube amplifier. Oklahoma preved to be particularly suitable for tbe application of refleetion methods, just as the Gulf Coast had been suitable Cor refraction techniques, and the reflection metbod rapidly grew in popularity until it virtually displaced tbe reCraction method. Although reflection has continued to be the principal seismic method, there are certain areas and types oC problems wbere retraction techniques enjoy advantages over reflection shooting, and so they continue to be used to a modest degree. A distinctive reflection was characteristic of the first reflection application in Oklahoma. Hence the first reflection work utilized the corre/alioli method whereby a map was constructed by recognizing the same event on isolated individual records. However, most areas are not characterlzed by such a distinctive reflector and so, in general. the correlation method has little application. In 1929, the calculation of dip from the time differences across several traces of a seismic record permitted the successful application oC reflection exploration in the Gulf Coast area where reflections were not distinctive oC a particular lithologic break and could nol be followed for long distances. Tbis method proved to be much more widely applicable than correlation shooting and so led to rapid expansion oC seismic exploration. As the capability oC recording the data from more geophones grew, recordings became spaced so closely tbat reflections could be followed continuously along lines oC profile, and continuous coverage became the standard seismic reftection method. Reflections from interfaces were interpreted on photograpbic recordings (Fig. 4.1) to map structure features. In 1936. Rieber published the idea of prooessing seismic data using variable-density record s and photocells for reproduction; however, widespread use of playback processing did not begin until magnetic tape became commercially available in 1953. Magnetie tape recording spread rapidly in the next few years, especially after digital recording and processing were introduced in the 19605. Magnetic tape recording made it possible to combine the data from several recordings made at different times and tbis made the use oC weaker energy sources feasible. Introduction, in 1953. 01 a dropped weigbt as a source 01 seismic energy was the forerunner of a series oC ditrerent kinds of seismie sources. Radar was one oC the outstanding technological advances oí World War 11 and it was widely used in

138

Seismic methods

Figure 4.1. 24-trilce seismic record for 12 geophone groups on either side al the 50urcepoint. The trace spacing i5 50 m, the heilV)' timing fines ilre 0.1 s apart, ilnd the finer timina fines 0.01 s aparto Traces 12 and 73 ilre 50 m (rom the shotpoint. (Courtesy Chevron Oil Ca.)

Introduction

the detection oC aircrart. However. noise Crequently interCered with the application of radar andconsiderable theoretical elrort was devoted to the detection of signals in the presence of noise. The result was the birth ol a new field of mathematics - information theory. Early in the 1950s a research group at the Massachusetts lnstitute of Teehnology studied its applieation lo seismie exploration problems (FIinn, Robinson, and Treitel, 1967). Simultaneously with this development, rapid advances in digital computer technology made extensive calculations Ceasible Cor the lirst time (Robinson, 1985). These two developments had a great impact on seismic exploration in the early 1960s and before the end of the decade, data processing (as the application is called) had changed seismic exploration dramatically, so much so that it came to be referred to as the "digital revolution." Most seismic recording is now done in digital form and most data are subjeeted to data processing before being interpreted. TIte common-midpoint method (also ealled eommon-depth-point and eommon-reHection·point) was patented in 1956. This method involves reeording data from the same subsurCace a number of times with varied source and geophone locations and then combining the data in processing. The redundancy oC data achieved with this method made practical a Bumber of schemes Cor the atlenuation of noise (ineluding multiple reftections) and improved data quality so mueh that most areas were remapped with tbe new techniques. Most seismic sourees are impulsive, that is, they develop a short, sharp wavefront. In eontrast, the Vibroseis method, developed in 1953 but not applied extensively until mucb later, generates a wavetrain tbat is so long that refteetions overlap extensively. Processing elrectively collapses the wavetrain back to tbat achieved witb an impulsive source. About halC of tbe land data is now acquired with the Vibroseis method. Because of eontinual improvements in instrumentation and processing, many areas have been resurveyed or reprocessed repeatedly; eaeh time better quality of data is achieved. New aequisition techniques, such as vertical profiling and tbe use of S waves, have becn developed. In areas oC special ¡nterest, tbree-dimensional acquisi tion techniques are employed that cover an area rather than merely aJong oceasional profile Iines. Interpretation techniques a!so have been improved continually. Rather than being limited merely to mapping struetural features, interpretation now involves studies oC veloc· ity, amplitude, frequency, and waveCorm variations so that information can be determined about the IitholoS)', stratigraphic features, and bydrocarbon aceumulatioDs. Applieations are extending beyond 10-

139 eating hydrocarbons to helping guide oil·field development and monitoring production. More on the history oC seismie exploration is given in Allen (1980). Bates. Gaskell, and Rice (1982), and Sherilr and Geldart (1982, pp. 3- 27).

4.1.3. OuUine of the Seismic Reflection Method To provide a background Cor the Collowing sections, a brief outline oC one of the many variations of seismic reftection technique will be given at tbis point (although the reasons for various steps will only be given later). Assume that a land erew uses an explosive as the energy souree. The first step in the field work is to drill a vertical hole at the sourcepoint (shotpoin/). the hole diameter being perhaps 10 cm and the depth between 6 and 30 m. A charge oC 2 lo 25 kg of explosive is armed with an electric blasting cap and placed near the bottom of the holeo Two wires extend from the cap lo the surface wbere tbey are conneeted to a blaster that is used to send an electrica! current through the wires lo the cap, which then explodes and delonates the main explosive (shot). Sourcepoints are usually spaced at equal intervals of 50 lo 400 m. Cables are laid out in a straight line extending away from the sourcepoint; each cable contains many pairs of electrical conduetorso Each pair oC wires is conneeted to an oudet and the outlets are spaced at intervals oC 2S to 100 m along the cable. Severa! geophones (seismometers) are connected to each of these outlets so that eaeh pair oC wires carries the output energy oC a group oC geophones baek to the recording instruments. Because oC the small spacing between the geopbones attached to one pair oC wires. tbe group is approximately equivalen! to a single large geophone located at the eenter of the group. Often 96 or more geophone groups are used. When seismíe waves Crom the explosion arrive, eaeh geophone group generates a signal Ihat depends on tbe motion oC the ground in the vicinity oC the group. The net result is signals Curnishing information about tbe ground motion at a number oC regularly spaeed points along a straight line passing through the sourcepoint. The electrica1 signals 1',0 to amplifiers that increase the signal strength and partially eliminate (jilter out) parts of the signal deemed undesirable. This information along with aecurate timing signals are recorded on magnetic tape. Thus the recorded data consist oC a number of traces, eaeh showing how the motion oC the ground at one geopbone group varied with time after the source instant (timebreak ).

140

Seismic methods :

Figure 4.2. Components of stress.

The arrival oC seismic waves produces systematic variations from trace to trace (ftJents). The trave/times. tbe intervals between tbe souree instant and tbe arrivals of tbe seismic energy (a1so known as the arriva/ times). of events believed to be rellections are measured. The location and attitude of tbe interface Ibat gave rise to each reflection eveot are ealculated from tbe traveltimes. The results from various souree localions are combined into eross seetions and eontour maps to represent the structure 01 geological interfaces. The presence of hydrocarbons or other minerals is inferred mainly from tbe structural information (sec, however. § 4.8.7). We have introduced a number of terms (indicated by italics) used in a specialized seose in seismic work. We shall follow the definitions for sueh terms given by Sheriff (1984).

4.2. SEISMIC THEORY 4.2.1. Theory of Elasticity (a) General.

The seismic metbod utilizes the prop-

agation of waves througb the earth. Beeause this propagation depeods on the elastie properties of the rocks, we briefly shall discuss the basie eoocepts of elasticity. The me and shape of a solid body can be ehanged by applyiDg forees to the external surface of the body. These external forces are opposed by internal forees that resist the changes in size and shape. As a result, the body teods to return to its origiDaI eondilion when the external lorees are removed. Similarly, a fluid resists· changes in siu (volume) but not changes in shape. This property of resistiog changes in size or shape and oC returniog lo the undeformed condilion when the external forces are removed is cal1ed e/afticity. A perfectly e1astic body is one that

recovers completely alter being deformed. Many substanees ineluding rocks can be considered perCeeUy elastic without appreciable error. providcd the defonnations are small, as is the case for seismic waves except near a seismic 10uree. The theory of elasticity relates the applied forees lO the resulting changes in siu and shape. The relations belwccn the applied forees and the deformations are expressed in terms of the concepts. stress and strain. (b) Stress.

Stress is defined as force per uníl area.

When a force is applied to a body. the stress is the ratio oC the force lO the area on which the force is applied. If the force varies from point to point, the stress a1so varies and its value al any point is found by taking an infinítesimally small element 01 arca centered at the point and dividing the total force acting on this area by the magnitude of the area Ir the force is perpendicular lo the area, the stress is said to be a normal stress (or prt!ssure). In this book, positive values correspond to tensile stresses (lhe opposite convention oC signs is also used Irequently). When tbe Coree is tangeotial lo the elemenl of area, the stress is a shearing stress. When the force is neither paralle1 nor perpendicular to the element 01 area. it can be resolved into components parallel and perpendicular lo the element. Hence any slress can be resolved inlo normal and shearin& components. lC we consider a small element of volume, the stresses actiDg on each ol the six faces 01 the elemenl can be resolved inlO components, as shown in Figure 4.2 for the two faces perpendicular to the x axis. Subscripts denote the x. y. and z axes. respectively, and O'"y denotes a stress parallel to the x axis acting on a surface perpendicular to the y axis. When the two subscripts are the same (as with 0'.... ). the stress is a normal stress; when tbe subscripts are different (as with O'"y)' th.e stress is a shearing stress.

Seism;c theory

141 O"d ¡¡y y

Ud"I

I I ~ r

----S'r-

-1- - -

I

-

-

-

-

,,

1

I

I

' /

Sr---~+-----------,R

I

16,'

t--I

'" r-

""

/

1I u -+1,1/

t..

R'

/

'

1 I

-

_---"1

/

-1

1

- -

~ I Q' ]

_ - ~ - -

lb,

rl-- ----p'----~'-" dx

J

~ dx ~Jt

H

-:-----'Q

x Figure 4.3, Analysis 01 (wo-dimensional strain.

When the medium is in stalic equilibrium, the Corees must be balanced. Thís means thal the three "y. . ' and acting on the Cace OA Be stresses must be equal and opposite to Ihe corresponding stresses shown on the opposite tace DEFG. with similar relations Cor the remaining four faces, In addition. a pair oC shearing stresses, such as "J"" constitute a couple tending lo rotate the elernent about Ihe z axis. Tbe magnitude oC the couple is

"x. . '

"u

(force X lever arm) - ( a,.. dy dz) dx

Ir we consider the stresses on Ihe olher four faces. we find tbat tbis couple is opposed solely by Ihe couple due to tbe pair of stresses a. y witb rnagnitude (axv d.... dz) dy. Because the element is in equilibrium, Ihe total moment musl be zero; hcnce axy = ay.' In general, we must bave

will undergo changes in siz.e andjor shape, and slrains will exist. Lel us assume Ihal u - u(x, y) and r - r(x, y). Then the coordinates of the vertices oC PQRS and P'Q' R'S' are P(x, y),Q(x + dx.y):

S(x. y + r./v), R(x + dx, y + o:v): P'( x + u, y + I!);

au dx, y + t' + -av dx );

Q' x + dx + u + -

(

8x

au d~'

S' x + u + -

(

R' ( x

ay .'

8x

Y + dv + .

au

+ dx + u + -ax

dx

(1

av

+ -a)'"dI'

).

au

+ -ay d~', .

au

al')

l'+d~'+I'+-dx+-dv

. (e) Strain. When an elastic body is subjected to Slresses, changes in shape and dimeosions occur, These changes, which are caIled strains. can be resolved into cerlain fundamental types. Consider a rectangle PQRS io the xy plane (see Fig. 4.3). When the stresses are applied, let P rnove lo P'; PP' have componenls u and 1'. If the olher ver tices Q. R, and S have the same displacemenl as P, the rectangle is merely displaced as a whole by the amounts u and v. In Ihis case, there is no change in siz.e or shape and no strain exists. However, iC u and I1 are dilferent for the different vertices, the rectangle

-

élx

ay .

In general, Ihe changes in u and 1I are much srnaller Ihan Ihe quantities dx and r./l'. Accordingly. we assume Ihal the lerms ( a uj él x), ( él u/ él y), and so on. are small cnough that powers and products can be neglecled. With this assumption. we see Ihat:

a

1. PQ increases in length by Ihe amount ( uj ax) dx

and PS increases by the amouot (iJll/ar) dy Hence. dU/aX and av/iJy are the fractional ¡ncreases in lenglh in the direction of Ihe axes. 2. The infinitesimal angIes 81 and 82 are equal lo éll,l/aX and auja}', respectively.

142

Se;sm;c methods

3. The rigll! angle at P decreases by the amount (8. + 82 ) = (av/ox + au/oy). 4. The rectangle as a whole is rotated countercJockwise througll the angle (8. - 82 )/2 - (ov/ox -

au/ay)/2.

Strain is defined as the relative change (that is, the fractional change) in a dimension or shape of a body. The quantitics au/ox and ov/ay arc tbe relativc increases in length in the directions of the x and y &Xes and are referred to as normal strains. Tbe quantity (ov/ox + ou/oy) is the amoun! by which a right angle in the ~v plane is reduced when the stresses are applied; hence, it is a measure of the change in shape of the medium, which is known as a shearing strain and is denoted by the symbol f xr The quantity (av/ax - ou/oy)/2, which represenu a rotadon or the body about the z axis, does not involve change in size or shape and hence is nol a strain; we denote il by tbe symbol 9•. Extending the aboye analysis lo three dimensions. we writc (u. v. w) as the components or displacement of a point P(x. y. z). The elementary strains thus are Normal strains

fu -

OU ax

Eyy -

oy

av

a;

tIC)' -

t)'IC -

av Shearing strains

OX +

aw

)"

-

E

eu

-

ex. -

,

.)' - -ay az

ou oy

av + -az

(4 .2)

OW

ou +

-a;

In addition to these strains, the body is subjected to simple rotation about the three &Xes. wbich is given by

,,_~(aw x

2

ay

_ OV) az

" _~(!.:!.a: _OW) ax 9 _ ~(av _au) ay )'

2

•

2

iJu

- -

ox

av

+ -

aw

+ -

aya:

(4.4)

(d) Hooke's law. In order to calculate the strains when the stresses are known, we musl know the relationsbip between stress and strain. When the strains are small, this re1ation is given by Hooke 's law, which states that a given strain is directly proportional to the stress producing il. Wheo several slresses exist, each produces strains independentJy oC the others; hence the total strain is the sum oC the strains produced by the individual stresses. This means that each strain is a linear function of all oC the stresses and vice versa. In general, Hooke's law leads to complicated relations but when the medium is iSOlropie, that is, when properties do not depend on direction, it can be expressed in the relatively simple form

(4.1)

aw

t" -

represented by 6. If we start witb a rectangular parallelepiped witb edges dx, dy, and dz in the unstrained medium. tbe dimensions in the strained medium are dx(1 + t,....). cry(l + ,,,,,), and d:(l + eu ); hence the increase in volume is approximately (E"" + E"y + E,,}dxdyd:. Because tbe original volume was (dx dy dz), we see Ihat

(4.3)

iJx

The changes in dimensions given by !he normal strains result in volume changes; the change in volume per unit volume is ca11ed !he dilalalion and is

i-x,y,:

(4.5)

i, j - x, y, :, i .. j

(4.6)

Equalion (4.5) states that a normal stress may produce stress in directions other than the direction of the stress; Equation (4.6) states thal a shearing stress produces only a shearing strain (no normal strains). The quanlities >" and p. are known as lAme eonSlanrs. If we write '1) - (olJ/p.), it is evident thal tI} is smaller the larger p. is. Hence p. is a measure of !he resistance to sheariog strain and is orten reCerred to as the modulus 01 rigidity or shear modu/us. When the stress is increased beyond an elastic Iimit, Hooke's law no longer holds and straios increase more rapidly. Strains resulting Coom stresses that exceed tbis limit do not entirely disappear when the slresses are removed. (e) Elast;c constants. Although Lamé constants are convenient at times, other elastic constants are aIso used. Consider a medium in whic:h all stresses are uro except 0xx' Assuming 0"" is positive (that is, a tensile stress), dimensions parallel lo o"" will iocrease whereas dimensions normal to o"" will decrease. This means that e"" is positive (elongation in the x direction) whereas E"y and 1,. are negative. From symmetry we can SCC Ibat Iyy - e l l • We now

Seismic theory

143

define Young's modulus and Poisson's ratio by the relations [see problem 1(a) and (b»). <1u

Young's modulus - E = -

+ 2¡.¡) A' + ¡.¡

¡.¡(3;\'

= ----

fu

( 4.7)

Poisson's ratio ~

-f

<1 _

--E'. [xx

(4.8) 7I.'/(A' + p.) is less than uníty). Values range from 0.05 for very hard, rigid rocks to about 0.45 for soft, poorly consolidated materials. Liquids have no resislance to shear and hence for them p. - O and a = 0.5. For most rocks, E, k, and p. lie in the range Crom 10 to 200 gigapascal (GPa) [10 to 200 X 10 9 newton/meter 1 (N/m2»); E generally is the largest and ¡.¡ Ihe smallesl of the lhree. Extensive tables of elastic constants of rocks have beco given by Birch (1966, pp. 107-73).

( 4.8)

4.2.2. Wave Equation and its Solutions The minus signs are inserted to make <1 positive. (The symbol a is more-or-Iess standard for Poisson's ratio; the subscripts should prevent any confusion witb a stress ai }") Consider a medium subjecled only 10 a hydrostatic pressure p, which is equivalent to the slatements

(a) Wave equatíon. Up to trus point we have been discussing a medium in static equilibrium. We shall now remove !bis res!rietion and eonsider what hap. pens when !he s!resses are nol in equilibrium. In Figure 4.2 we now assume Ihat the stresses on the rear face of ¡he element of volume are as shown in Ihe diagram, bu! that the stresses on the fronl face are, respectively,

aay" ay" + - - dx ax

Then, k is tbe ratio of the pressure to the dilatation: -p 3A' + 2/L bulk modulus - k - - & - . _3- - ( 4 .9)

The minus sign is inserted to make k positive. By eliminating different pairs oC constanls, many different relations can be derived to express one oC the five constants in terms oC Iwo olhers (see Sheriff and Geldart, 1982, p. 74). The preceding theory assumes an isotropic medium, but sedimentary and metamorphic roeks are frequently not isotropic; differences of 20 lo 25% have been reported. Ir one does not as sume isotropy, Ihe malhematics becomes complicated and physical insight is more difficult. Fortunately Ihe assumption of isotropy usually provides a reasonable explanation oC actual results. The next simplest situation aCter isotropy is transverse isotropy, where properties are the same in two orthogonal directions (usually the bedding-plane direetions) but different in the third. This situation is discussed by Sheriff and Geldart (1982, pp. 36-7 and 52-3). It can be shown tbat a layered medium composed oC isotropic layers behaves Iike a transversely isotropic medium when the seismie wavelengths are large eompared 10 the bed thicknesses. Interest in anisotropy is growing because Cracturing oC rocks induces anisolropy and because fracture porosity markedly affects hydrocarbon produetion. The elastíc constants are defined in such a way that they are positive numbers. As a consequence, " must have values between O and 0.5 [because in Eq.

"j

Because these stresses are opposite to those acting on Ihe rear face, lhe nel (unbalanced) stresses are

aa", --dx

aa"

-'-dx

ax

ax

These stresses act on a face tbat has an arca (dy dz) and they affect the volume (d... dy dz); hence we get for the nel Corees per unít volume in the directions of the x, y, and z axes the values

aa,." ax respectively. Similar expressions hold for the other Caces; hencc we find for the total force per unít volume in the direction of the x axis the expression

aa.", a a:.,. aa". ) -+--+-( -ax ay az Newton's second law oC motion states tha! the unhalanced force equals !hc mass times the acce1eration: thus we obtain the equation oC motion along the x axis:

a1u P--l = unbalanced Coree per unít volume

al

in the x direction

(Jau (Ja". aa", =--+--' +--

a...

ay

az

( 4.10)

Se;smic methods

144

where p is the density. Similar equations can be written lor motion along the y and z axes. Equation (4.10) relates the displacements to the slresses. We can obtain an equation ínvolving only displaoements by using Hooke's law to replace the slresses with strains and then expressing the slrains in terms 01 the displacements, using Equations (4.1), (4.2), (4.4), (4.5), and (4.6):

By subtracting the derivalive ol Equation (4.12) with respect to z from the deriva ti ve of Equation (4.13) with respeet to y, we get p

a2 (DW _ au)

iJt 2

iJy

_I'V 2

(aw _ DV)

az

ay

az

that is ( 4.15)

By subtracting appropriate derivatives, we ohtain similar results for 9y and 9,. These equations are different examples of the wave equation, which we can write in tbe general forro

o (OU + -iJu +iJW) -

ofl

-A'- +/,v 2 u+/,- ax ox iJx

ofl DX

- (A' + 1')- +

"V

2

8y

(4.11)

u

wbere V 2u - !.aplacían of u - (8 2u;ox2 + 2u; 8y2 + a 2u;az 2). By analogy we can write the equalioos for u and w:

a

a2v

iJ fl

+

p iJ,z - (A'

p

a2w

ot 1

")a; + /'v2v iJ fl

-

(A' + 1') a; + /,V 2w

( 4.16)

az

(4.12)

The wave equation relates a time derivative of a displacement (tbe left side) to spatial derivatives (the right side); the constant of proportionality is V2. (b) Plane-wave solut;ons. Lel us consider fint tbe case where ,¡, is a function only of x and t, so thal Equation (4.l6) reduces to

(4.13)

To obtain the wave equation, we differentiate these tbree equations with respeet to x, y, and z, respectively, and add tbe resutts together. This gives

( 4.17)

Any funetion of (x - Vr),

,¡, - f(x - Vt)

DU

+ /,v 2 ( -

iJx

au +DW) -

+ -

ay

az

that is,

or 2

a -

A' + 21' p

(4.14)

( 4.18)

is a solution of Equation (4.17) (sec problem 2) provided tbat ,¡, and its fint two derivatives have no discontinuities. This solution (known as d 'Alembert 's so/urion), lumishes an infinite number of particular solutions [for example, ek(J<- YI), sin(x - VI), (x - VI)J). The answer to a specific problem CODsists ol sclccting a combination ol SOIUtiODS tbat also satisfies tbe boundary conditions for tbe problem. A waue is a Itdisturbance" tbat travels through tbe medium. In our notation, the disturbancc ,¡, is a volume change whcn ,¡, ... l:J. and a rotation when ,¡, = 9". Obviously the disturbancc in Equation (4.18) is traveling along tbe x axis. We shall now show tbat it travels with a speed equal to the quantity V. In Figure 4.4, a certain part of the wavc has reacbed the point Po at the time lo. If the coordinate

Seismie theory

145

~

+

.!'

.!'

-"

-

.§"

E .;:

~'. O

·1·

x,

A"

~I

Figure 4.4. /IIustrating the velocity of a wave.

of Po is xo' then the value of >Ji at Po is '¡'o'" /(xo - Vto )' If tbis sarne portion oC the wave reaches PI at the time lo + al, then we have lor the value ol

• x'

'" at PI'

>Jil

=

f{

Xo

+ ax -

V(/ o +

al)}

But, because tbis is the same portion ol the wave that was at Po al time t o, we must have V-o - >Ji l , Ihat is,

1-

cos 8,

m - COI'3

" - cos la

Thus, the quantity V is equal to ax/at and is therefore the speed with wbich the disturbance travels in the positive x direction. A function oC (x + VI) denotes a wave traveling in the negative x direction. The general solution of Equation (4.17)

v-

-f(x - Vt) + g(x + Vt)

( 4.19)

represents two waves traveling a10ng the x axis in opposite directions with velocity V. Because the value oC >Ji is independent oC y and z, the disturbance must be the sarne everywhere in a plane perpendicular to the x axis. This type oC wave is called aplane wave. The quantity (x ± Vt) is known as the phase. The surfaces on which the wave motion is the sarne, Ihat is. surfaces on which the phase is constant, are known as wave/ronts. In the case we are considering, the wavefronts are planes pependicular to the x axis and the wave is traveling in the direction normal to the wavefronl. This holds Cor a11 waves in isotropic media. A line denoting the direction of lravel of lhe wave energy is called a raypath. lt is convenient to have an expression for aplane wave that is not traveling parallel to an axis. Assume

Figure -l.5. Wave direction not along an axis.

that the wave is lraveling along the x· axis that has direction cosines (1, m, n) (§ A.3.1.) relative to the x, y. and z axes (Fig. 4.5). Then, at a point Pon the x' axis at a distance x' from the origin, we have

x' - Ix + my + nz where the coordinates ol P are (x, y, z). Then,

v- -

f(lx + m)! + nz - VI)

+ g(lx +

m)'

+ nz +

VI)

(4.20)

(e) Spherieal-wave solutions. In addition to plane waves. we often use sphericaf waves where the waveCronts are a series of concentric spherical surfaces. We express the wave equation [Eq. (4.16)] in spherical coordina tes (r, tJ, cfl), where tJ is the colatitude

746

Seismic methods .

O~~--~r---------~~-----------4

Figvre 4.6. Relation between spherical and plane wilves.

and '" is tbe loogilude [Eq. (A.37»):

1 al",

v2 at2

1{ ",2

a( a",)

ar ,2a,

2

1 a (sinOa",) + -1- -a-",} (4.21 ) +---sin (} afJ

afJ

si¡¡ fJ a.¡.l

Wc consider only the special case wheo the wave motion is indcpcndent oC (} and .p, hence is a Cunction only oC r and t. Then we gel the simplified equation ( 4.22) Solutions oC Ibis equatioo are

,

'" - - f( r ± VI) and the general solu lioo is

,

So rar we have discussed only Ihe spalial aspeets or waves, that is, the way in whieh waves depend on space coordina les. However, '" is also a Cunction oC the time t. The simplesl form ol time variation is thal of a harmonic wave, that is, a wave involving sine or cosine expressions, such as (d) Harmonic waves.

1

1

As lhe wave progresses outward Crom the center, Ihe radius increases and eventually lhe portion of thc wavefronl near any particular point wiIl be approximalely plane. The error that we introduce when we replacc !hc sphcrical wavcfront PQR in Figure 4.6 wilh lhe plane wavefront P'QR' is due to !hc divergenee between the troe direction of propagation (the direetion oí the radius) and the direction normal to the plane. By laking the radius very large and/or lhe portion of the wavefront being considered very small, we can make the error as small as desired. Becausc plane waves are easy to visualize and aIso lhe simplcst to handlc ma!hematically, we generally assume plane waves. Also, curved wavefronts can be thought oC as a superposition of plane waves, wbich oflen allows us lo Ircal curvcd-wave problems in terms 01 plane waves.

1

,

"'- -f(r- Vt) + -8('+ Vt)

( 4.23)

in wbich the tin! term represents a wave expanding outward from a central poiot and the secood term a wave c:ollapsing toward the central point. When r and t are fixed, (, - VI) is constant and hence.tJ¡ is constant. Thus, at tbe instant I the wave has tlÍe same value al all poiots on the spherical surCace of radius r. The spherical surfaces are therefore waveCronts and the radü are rays. Obviously the rays are normal to the wavefronls.

'" - A cou(x - Vt) tJ¡ ... A sin K(lX + my

+ nz +

1/1= (B/r)coSfC(r- Vt)

(4.24) ( 4.25)

Al a fixed poinl, 1/1 varíes as Ihe sine or cosine 01 !he time, and so the motion is simple ha,monic. The values of 1/1 range from + A to - A lor the plane waves oí Equation (4.24) and from +B/r lo -B/,

Se;sm;c theory

147

for the spherical wave in Equation (4.25). The value IAI or IBITI is known as the amplilude of the wave .". For a fixed value of l. wbenever x in Equation (4.24) increases by (2""!K), the argument 01 the sine or cosine increases by 2'IT and henee the value of ." repeats. The distanee (2'IT/K) is cal1ed the wavelength, wbich is usually represented by Ihe symbol A. The quantity (/C/2'IT) is the wave Ilumber. the number oC wavelengths per unit length. Ir the space coordinates in Equations (4.24) and (4.25) are kept fixed and I allowed to increase, tbe value of ." repeats each time that I increases by tbe amount T where KVT- 2'IT = 2'IT(VTIA). Con sequently,

T= AIV

JI

= (liT) ... VIA

v = I'A ( 4.26)

where T is the period and JI is the frequency oC the wave. Another Crequently used quantity is the angular Crequency w, where w ... 2'IT1' = KV. Using the preceding symbols, we can write Equation (4.24) in the equivalent forms 2'IT ." - A eos/C(x - VI) - A cos-( x - VI)

A

- A cos( KX

-

(0)/) - A cos W(

= A COS21T(

~

-

I't)

~ - 1)

(4.27)

= A COS(KX - 2'171't)

4.2,3, Body Waves: P and S Waves Up to tbis point our discussion of wave motion has been based en Equation (4.16). The quantity .¡, has nol been defined; we have merely inCerred Ihal it is sorne disturbance that is propagated from one point to anolher with the speed V. However, in a homogeneous isotropic medium, Equations (4.14) and (4.15) musI be salisfied. We can idenlify the Cunclions A and 8" with ." and conc\ude that two types of waves can be propagated in a homogeneous isotropic medium, one corresponding lo changes in Ihe dilatalion ~, the other to changes in one or more components oí the rotalion given in Equation (4.3). These waves, wbich Iravel in the interior oC a medium, are cal1ed body waves. The firsl Iype is variously known as a dilatat;onal, longitudinal, irrotational. compressional. or P wat'e, the latter name being due to the Caet that Ibis Iype is usually the firsl (primary) event on an earthquake recording. The second type is referred to as Ihe shear, trallsverse, rotational. or S wave (be.

cause it is usualIy the sccond event observed on earthquake records). The P wave has the velocity Q in Equation (4.14) and tbe S wave has tbe velocity p in Equation (4.15) where a = {( A + 2p.) 1 p } 1/2 }

P = (111 p ) 1/2

( 4.28)

Because the elastic constants are positive, a is always greater than p. Writing 'Y Cor the ratio fJla, we see that (4.29) using Equalion (4.8). As o decreases Crom 0.5 to zero, 'Y increases from zero to its maximum value 1/.¡2; thus. Ihe velocilY of the S wave ranges from zero up to 70% of the velocity oC the P wave. For Huids, 11 is zero and hence p and "( are also zero. Therefore S waves do not propagate through fluids. Let us investigale the nature oC the motion oC the medium corresponding to Ihe IWO types oC wave mOlion. Consider a spherical P wave oC the type given by Equation (4.25). Figure 4.7 shows wavefronts drawn at quarter-wavelength intervals. The arrows represent the direction oC motion oí the medium at the wavefront. The medium is undergoing maximum compression at B (that ¡s. the dilatation ~ is a minimum) and minimum compression (maximum A) at the waveCront D. We can visualize the plane.wave situation bv imagining Ihat the radius in Figure 4.7 has becom~ so large that the wavefronts are praclically plane surfaces. The displacements are perpendicular to these planes so thal there is no convergence or divergence oC the parlicles oC the medium as they move back and forth paralle\ to the direction oí propagation. Such a displacement is longitudinal. wbich explains why P waves are sometimes calIed longitudinal waves. P waves are the dominanl waves involved in seismic exploration. To determine the motion of a medium during the passage oC an S wave, we returo to Equalion (4.15) and consider the case where a rotation 8.(x, t) is being propagated along the x axis. We have

Because

al'

au

al'

a.l:

ay

ax

8 ... - - - = -

:

Seismic methods

148

Figure 4.7. Displacements (or a spherical P wave. )'

/'

z ..

Figure 4.8. Molion during passage o( an 5 wave.

from Equation (4.3), we see that the wave motion consists solely of a displacement v of the medium in the y direction; v is a Cunction of both x and ,. Because v is independent of y and z, the motion is everywhere the same in a plane perpendicular to the x axis, that is, we are discussing a plane S wave traveling along the x axis. By Equation (4.19) the displacement v must have the form

v - f( x - P,) + g( x + P,)

We can visualize the preceding relations by using Figure 4.8. When the wave arrives at P, it causes the medium in the vicinity oC P to rotate about the axis 2'2" (parallel to the z axis) through an angle e. Since we are dealing with inftnitesimal strains, we can ignore the curvature of the displacements' and consider that points such as P' and P" are displaced parallel lo tbe y axis lo Ihe poinls Q' and Q". Thus, as the wave travels along the x axis, the medium is displaced transversely to the direction oC propagation, hence the name transverse wave. Moreover,

Seismic theory because tbe rotation varies from point to poinl at any given instant, the mediurn is subjeeled 10 varying sbearing stresses as the wave moves along. This accounts for tbe name shear wave. Because we might have chosen to illuslrate Oy in Figure 4.8 instead of O" il is c1ear that sbear waves bave 2 degrees of freedom-unlike P waves Iba! have only 1- along the radial direction. In practice, S-wave motion is usually resolved ioto components parallel and perpendicular to tbe surface of the ground. wmcb are known, respectively. a~ SH and SV waves. Because !he 2 degrees of freedom of S waves are indepeodeot, we can bave an S wave that involves motion in only one plane, for example. SH or SV motion; such a wave is said to be plane polarized. We can also have a wave io wmch the SH and SV motion have the same frequency and a flxed pbase differeoce; such a wave is elliplically polarized. However, polarization of S waves usually is nol important in seismic exploratioo. In tbe case of a medium that is not homogeneous and isotropic, it may no! be possible to resolve wave motion into separale P and S waves. However, inhomogeneities and anisotropy io the earth are small enough tbat assumption oC separa te P and S waves is valid for praclical purposes.

4.2.4. Surface Waves (a) Rayleigh waves. In an infinite homogeneous isotropic medium, on1y P and S waves exisl. However, when the medium does oot exlend lo infinily in a11 directions, otber types of waves can be generated. These waves are called surface waves because tbey are confined to the vicinity of one of tbe surfaees tbat bound the medium. In exploration seismology, tbe main type of surface wave of importance is the Rayleigh wave, oiten called ground roll. This wave travels along the surface of Ihe eartb and involves a combination of longitudinal and transverse motion witb a definite phase relation to each otber. The amplitude of this wave motion decreases exponentially witb depth. Tbe partic1e motion is confined to the vertical plane, which ¡neludes tbe direction of propagatioo of tbe wave. During tbe passage of tbe wave, a particle traverses an elliptical path and tbe major axis of the ellipse is vertical (near the surfaee). The direetion of parlicle molion around the ellipse is called retrograde (Pig. 4.9) because it is opposite to the more familiar direction of motion of particles in waves 00 the surface of water. The velocity of Rayleigh waves depends upon tbe elastic constants ncar the surface and is a1ways less tban the S wave velocity {J. When tJ - 1, tbe Rayleigh wave velocity is O.92{J. The

149

Fi8ure 4.9. Mofion durin8 pa55age of a Rayleigh wave.

exponential decrease in amplitude witb deptb depends on the wavc1ength of tbe waves. Because the elastic constants change with depth, the velocity of Rayleigh waves varies witb wavelength. A vmation of velocity with wavelength (or frequency) is called dispersion and it results in a change of the shape oC the wave train with distance (§ 4.2.6d). (b) Love waves. When a surface layer overlies a balf-space, another type of surface wave, called a Love wave, may exist. A Love wave involves transverse motion parallel to the surface of the ground and sometimes it is called an SH wave. Love waves have velocities intermediate belween the S-wave velocity at the surface and that in deeper layers, and they exhibit dispersion. Energy sources used in seismie work do not generate Love waves to a significant degree and hence Love waves are unimportant in ordinary seismic exploration. AIso, modero geopbones designed lo respond only to vertical motion of tbe surfaee would not detect any Love waves that might exist. Surrace waves, inc1uding Rayleigh, Love, tube, Stoneley, and channel waves are discussed in more detail in Sheriff and Ge1dart (1982, pp. 48-52 and 70-3).

4.2.5. Energy

o.

Waves

(a) Energy density; intensity. Probably the single most important feature of any wave is tbe energy associated with the motion oC the medium as the wave passes through il. Usually we are nol concerned with tbe total energy oC a wave, bul rather witb the energy in the vicinity of the point wbere we observe it. The energy density is the energy per uníl volume in the neighborhood of a point. Consider a spherical harmonic P wave for which the radial displacement for a fixed value oC r is given by u - A cos( wl + .p)

Seismic methods

150 where 41 is a phase angle. The displacernent u ranges Crom - A to + A. Since the displacement varíes with time, each element oC the medium has a velocity au/at and an associated kinetic energy. The kinetíc energy IJL contained witrun each element oC volume IJ 11 is

A.

TIte kinetic energy per unÍt volume is

IiL

1 2

(iJU)2

-=-p 811

at

1 --pt,lA 2 sin2("" + 4» 2

This expression varíes from zero to a maxirnum of p",lA1/2. TIte wave also involves potential energy resulting from the elastic strains created during the passage of \he wave. As lhe medium oscillates back and Corth, lhe energy is con verted back and forth from kinetic lo potential form and the total energy rernains fixed. When a partic1e is at zero displacemenl, the poten ti al energy is zero and \he kinelic energy is a rnaximurn, and when \he partic1e is al ilS extreme displacement, \he energy is all potential. Because the total energy equals \he maximum vaJue of \he kiDetic energy, the energy densily E lor a hannonic wave js

Figure 4.10. Dependence o( intensiry on disuJnce.

In Figure 4.10 we show a sphericaJ wavelront diverging from a center O. By drawing sufficienl radii we can define two portioos of wavefronts, Al and A 2 , of radii '1 and '2' such \hal \he energy that flows outward through the sphericaJ cap Al in 1 5 musl be equaJ 10 Ibal passing oUlward through \he spherical cap A 2 in 1 s (because tbe energy is moving only in \he radial direclion). The flow of energy per secoDd is the product 01 tbe iDtensity and the area, hence

Since tbe areas ~l and ~2 square of tbeir radii, we get

are proportionaJ to the

( 4.30) TItus we see tbat \he energy density js proportionaJ to \he first power ol the density oC the rnedium and to the second powers oC the Crequency and amplilude of \he wave. We are jnterested aJso in tbe rate oC flow of energy and we define tbe intensity as tbe quantity of energy tbal flows through a unit area normaJ 10 the direction oC wave propagation in unil time. Take a cylinder 01 infinitesimaJ cross sectíon area lid, whose axis is parallel to the direction oC propagation and whose length is equaJ 10 tbe distance traveled in tbe time /Jt. TIte total energy inside the cylinder at any instant t is EVlit/Jd. Al the time t + /Jt, aJI of this energy has Idt lhe cylinder tbrough one 01 tbe ends. Dividing by \he area oC tbe end oC lhe cylinder Bd and by the time intervalBt, we get \he intensity J, the amount of energy passing through unit area in unit time:

J- EV

(4.31)

Por a hannonic wave,·this~ ( 4.32)

Moreover. it follows from Equation (4.31) tbat E is proportioDaJ to J and hence

(4.33)

TItus, geomelrical spreading causes the inteDSity and the energy deDsity ol sphericaJ waves lO decrease inversely as the square 01 the distance lrom the source (Newman, 1973). This is called sphtrlca/ di-

ve,gence. (b) Absorption. We shall also consider two other mechanisms, absorption and partition at interfaces, which cause tbe energy density 01 a wave lO decrease. In the preceding sectiOD we considered varialiODS ol the energy distribution as a func:tion of geometry. Implicit in tbe discussion was the assumption tbat Done 01 tbe wave energy disappeared, thal is, was translormed into other forms of energy. ID

Seismic theory

151

reallty this assumption is a1ways incorrect because, as the wave passes through the medium. the elastic energy associated with the wave motion is gradually absorbed by the medium and reappears ultimalely in Ihe Corm oC hea\. This process is called absorptioll and is responsible for the eventual complete disappearanee of the wave motion. The meehanisms by which the elastic energy is transformed into heat are not understood c1early (Toksoz and Johnston, 1981). DUJing the passage oC a wave, heat is generated during the eompressive phase and absorbed during the expansive phase. The process is nol perfectly reversible beca use the heat condueted away during the compression is nol equal to the heat flowing baek during the expansiono Internal friction is undoubtedly involved, and many other mechanisms may contribute, such as IOS5 oC energy ¡nvolved in the crealion oC new surCaces (fracturing near an explosion), piezoelectric and thermoelectric elfects, and viscous losses in the ftuids filling the rock pores. The measurement oC absorption is very diffieult. Absorption varies with Crequency, and laboratory measurements, which are invariably made at high Crequencies. may not be applicab!e lo actual seismic waves. Field measurements must he eorreeted ror reflection or refraction elfeets. and the en tire path should be through the same homogeneous medium. Measurement difficulties have resulted in wide divergenee in absorption measuremenls. The 1055 oC energy by absorplion appears to be exponential with distance Cor elastic waves in rocks. Thus. we can write

( 4.34) wbere 1 and 10 are values oC the intensity al two points a distanee x apart and TI is the absorption coefficient. Other measures oC absorption are also used, such as the quallty Cactor Q ~ 'Ir /'11", where A is the waveJength. Experimental evidence indicates thal the absorption coefficient is proportional to frequency. that is, '11" and Q are rough!y constant Cor a particular rock. The inerease in absorption with frequency provides one mechanism for the loss oC high Crequencíes wilh distance. The consensus i8 Ihat Cor rocks. '11 is oC the order oC 0.16 to 0.02 dB per wavelength (or Ibat Q is in tbe range 20 to 150). To compare the 108s by absorption with the 10ss oC intensity by spherical divergence, we calculate the los ses in going Crom a point 200 m Crom Ihe source to various distances Crom the source assuming '11 0.10 dB/>. and V .. 2 km/s. The results shown in Table 4.1 were calculated using the following rela-

Table 4.1. fnergl' lusses bl' absorption and spreadil1g. " - O lO dBlw.:Jv('/cngth; V - 2,CXXJ mis. Distance from sourcepoint

(.~.)

Frequency • 1.200 m 2.200 m 4.200 m 8.200 m

Ahsorption

(Hz)

(dS)

(dS)

(dS)

(dS)

1

0.22

3

0.6~

0,.¡3 1.3

0.86 2.6

5.2

2.2 6"¡

10

30 SpH:!ad.ng

100

22

all

16

4.3

13

43

n

8.6

26 86 26

1.7 17

52 170 32

tions: Absorption: Loss in dO ~ 10 log(lo/ l)

= 4.3In( e U,IO>:/") = O.43( x, - 200)/" - O.4311( x, - 200)/2000 Spreading: Loss in dB - 10 log( 10//) - 20 log( x./200) where x, is the distance from the sholpoint. x ~

x, - 200. Table 4.1 shows tha! losses by spreading are more important than losses by absorption Cor low Crequencíes and short distances. As the Crequency and di);tance increase. absorption losses increase more rapidly Ihan spreading losses. and eventual1y become dominant. The more rapid loss of higher rrequencies results in change oC wave shape wilh distance, In addition to absorption and spreading, the partilioning of energy al interfaces is also responsible for Ihe decrease in the energy of a wave with distance. This is discussed in Seclion 4.2.7.

4.2.6. Wave Motion (a) Huygens' principie. This principIe is important in understanding wave trave! and is Crequently useCul in drawing successive positions of wavefronts. Huygens' prillciple states that every point on a waveCronl can be regarded as a new source oC waves. Given the location of a waverronl at a certain instanl, future positions oC the waveCront can be Cound by considering each point on the first wavefronl as a new wave source. In Figure 4.11. AB is the waveCront al tbe lime lo and we wish lo find the waveCront at a later time (to + .6. 1). During the interval At. the wave will advance a distance V.6.1 where V is the velocity (whicb may vary Crom point lo poinl), We select points on the wavefront. PI' P2 • Pl • and

Seismic methods

152

A

P,

P,

P,

r.

Figure 4.11. Using Huygem' principIe ro loeare new wavefron/s.

Figure 4.12. Reflee/ion and refrae/ion of aplane wave.

so on, from which we draw ares of radius V~I. Provided we select enough points. \he envelope of the ares (A'B') will define as accurately as we wisb the position ol the wavelront at tbe lime (r + tu). E.xc:ept on the envelope, the elemental waves interrere destructively so that their effeets cancel. (b) Refleetion and retraetion. Whenever a wave encounten an abrupt change in tbe elastic properties, as wben it arrives at a surface separating two beds, par! or the energy is reflected and remains in the same medium as the original energy. The balance ol the energy is relracled into the other medium with an abrupt change in the direction of propagation. We can derive the familiar laws of reHection and refraction using Huygens' principIe. Consider aplane wavefront AB incident on a plane interface as in Figure 4.12 (if the wavefront is curved, we mere1y take A and B sufficiently close together \hal AB is a plane to the required degree of accuracy). A B occupies the position A' B' when A arrives at tbe surface, and al thls instant, tbe energy al B' still must lravel the distance B' R before arriving al tbe interface. If B'R - VI ~t, then ~t is the time inlerval between the arrival of the energy al A' and at R. By Huygens' principIe, during .the time ~r the energy thal reached A' will have Iraveled either upward a distance VI ~I or downward a distance J-í ~t. By drawing ares with center A' and lengths equal to "í Al and J-í 4t, and then drawing the tangents from

R to Ihese ares, we locate the new wavefronlS RS and RT in the upper and lower media. TIte angle at S is a righl angle and A'S - VI ~I - B'R. Therefore, the triangles A'B' R and A'SR are equal with tbe result tbat the angle 01 incidence 81 is equal lo the angle 01 refleClion 8í. This is lhe law 01 reflection. For tbe refracted wave, the angle al T is a righl angle and we have

J-í ~t -

A'R sin8z

~I -

A'R sin6¡

and

JI¡ Hence

sin8z sin 81 -----=p VI Vz

( 4.35)

The angle 82 is called Ihe angle of relraclion and Equation (4.35) is Ihe law 01 relraelion, also known as Snell's law. The angles are usually measured between tbe raypaths and a normal lo tbe interface, bul these angles are the same as those belween the interface and tbe wavefronts in isotropic media. The laws of reflection and refraction can be combined in single statement: Al an interface the quantity p (sin 8¡)/ V¡ has the same value ror the incident, reflected, and rerracted waves. This generalized form of Snell's law will be understood in (uture references lo Snell's law. The quantity p is called tbe raypath

parameter.

153

Seismie theory

• A

i i l

! ! ! t 1 ! I

t

E

e

::E

~

B

'o + 261 1

= '. + /:;1

D

Figure 4.13. Oiffr;U-lcd wavcfronts. Oiffraclion al/ows seismic energy 10 reach regions forbidden by fa)' Iheory, such as Ihe shadow zone underneath Ihe wedge,

When the medium consists uf a number of paralle! beds, Snell's law requires that the quantity p have the same value everywhere for a11 reflected and refraeted rays resulting Crom a given initial ray, When "2 is less than VI' O2 is less than 0\. However, wben V2 is greater tban VI' (J2 reaches 90° when 81 - sin -1( VII V2 ), For this value of 9\. the refracted ray is traveling along the interface. The angle of incidence for wruch 82 = 90° is the critical angle 8<; obviously. sinO, ~ V¡/V2. For angles of incidence greater than Oc' it is impossiblc to satisry Snell's law (because sin 82 cannot exceed unity) and 10101 refleclion occurs (that is, the refracted ray does not exist). This situation is discussed in Section 4.2.7. SneU's law is very use fuI in detennining raypaths and traveltimes and in deriving reflector position from obscrved traveltimes, but it does not give information about the amplitudes of the reflected and lransmitted waves. This subject is also taken up in Seetion 4.2.7.

.

;

(e) Diffractíon phenomena. Seismic energy travels along otber paths besides those given by Sne\l's law. Whenever a wave encounters a feature whose radius of curvature is comparable lo or smaller than the wavelength, the ordinary laws of rcflection and refraction no longer apply. In such cases, the energy is diffracled rather Ihan reflected or refraeled. Because seismic wavelengths are large (often 100 m or more) compared witb many geologic dimensions, dilfraction is an important process. The laws of diffraction are complex, but at distances greater than several wavelengths from lhe dilfracting source, the diffracted wavefront is essentially that given by Huygens' construction (Trorey, 1970).

Figure 4.13 illustrates the method oC constructing dilfractcd wavefronts produced by a faulted bed. We assume aplane wavefront A B incident normalty on the faulted bed CO; the position oC tbe wavefront when it reaches the surface of the bed at t is CODo Al I - 'o + /:¡,I, the portion to the right of O has advanced to the position GH, whereas lbe portion to the lert oC O has been reflected and has reached the position EF. We might have constructed the wavefronts EF and GH by seleeting a large number of centers in CO and OD and drawing arcs of length V/:¡, l. EF and GH would then be determined by the envelopes oC tbese arcs. However, for the portio n EF there would be no centers to the right of O to define the envelope, whereas for the portion GH there would be no centers 10 the lert of O to define the envelope. Thus, O marks the transition point between centers Ihat give rise to the upward-traveling waveCront EF and centers that give rise to the downward-traveling wavefront GH. The are FPG with center O is Ihe dilfracted wavefront originaling al O and connecting the two wavefronts EF and GH. The dilfracted wavefront also extends into the geometrical shadow area GN and into the region FM. Dilfraction events will be discussed in Section 4.4,3. Sheriff and Geldart (1982, pp. 59-64) give an analytie lreatmenl of dilfraction.

'o

(d) Dispersion: group velocity. The velocity V, a, or p, which appears in Equations (4.14) to (4.29), is known as the phase velocity because it is lhe distance traveled per unit time by a point of constant phase, such as a peak or trough. This is not nccessarily tbe same as the speed with wruch a pulse of energy travels, which is the group velocily and will be

5eism;c methods

154

~--------U6/--------~~~

DirCClion B'

or

propapllon

--

(a)

:f..

1 ...·----6/.----~

lime

Oroup '''OCil, (b)

.. ,",l. ~~ -

U

~~ -

V

Phase .elocity -

Figure 4.14. Comp.lrison of group and phase velocities. (a) Defin;t;on of group veloc;ly U. (b) Arr;val of a dispersive wave al successive geophones.

denoted by U. Consider, Cor example, the wave train shown in Figure 4.14a. We could determine the group velocity U by drawing the envelope oC the pulse (lhe double curve ABe, AB'C) and measuring lhe dislance that lhe envelope lravels in unit time. Tbe relation between U and V is shown in Figure 4.14b, wbere V js given by the rate ol advance oC a ccrtain pbase (such as a Irough), whereas U is measured by the spccd oC the maximum amplitude ol the envelopc. Ir we decompose a pulse inlo its component Crequencies by Fourier analysis, we find a spcclrum of frcquencies. If the velocity is the same Cor all frequencies, the pulse shape wiIl remain the same and the group velocity will be the same as the phase velocity. However, il the velocily varies wilh frequency, the pulse changes shape as jI travels and the group velocity is different from the pbase velocilY, that is, lhe mcdium is dispersive. It can be shown

(see problem 3e) Ihal lhe group velocity U is U

=V-

dV

A- - V + dA

dV l/-

dI/

( 4.36)

where V, A, CIJ, dVId>', and dVId" are average values for the range 01 frequencies lhal makes up the principal parl 01 the pulse. When V dccreases wilh frequcncy, V js larger than U. This is callcd normal dispersion and is iIIustrated in Figure 4.14 where the envc10pc Iravels slower Ihan tbe individual cycles, which overlake and pass througb Ihe envelope and disappear as they reach the leading edge. When V increases witb frequency. the opposite is true. Dispersion js nol a dominant feature 01 exploration seismology because most rock! exhibit lilde variation of velocity wilh frequency in the seismic frequency range. However, dispersion is important in

5eismic theory

155 R

t

"SI

I

I I I I

R,jan

S'l

+x

G'II

I

I I

I I

;'

¡ I

S

"SI

Figure 4.15. Continuity 01 normal stress, figure 4.16. Waves generaled .1/ .in interface by .In inciden/ P "".H/e.

connection with surface waves and certain other phenomena.

4.2.7. Partitioning of Energy at an Interface

,)

When a wave arrives at a surface separating two media having different elastic properties, it gives rise to reflected and refracted waves as previously described. At the boundary, the stresses and displacements must be continuous. Two neighboring points R and S, which lie on opposite sides of the boundary as shown in Figure 4.15. wiIl in general have different values of normal stress. lbis dilference resu!ts in a nel force Iha! accelerates the layer between them. However, if we choose points closer and closer logether, the stress values musl approach eacb olber, and in the limit wben the two points coincide on tbe boundary, the two stresses must be equal. If Ibis were not so, the infinitesimally lhin layer al the boundary would be acted on by a finite force and hence have an acceleration lbal would approach infinity as Ibe two points approacb eacb olber. Because the same reasoning applies lo a tangential stress, we see that Ibe normal and tangential components of stress must be continuous (cannot change abrupt1y) at the boundary. likewise the normal and langenliaI componenls of displacement musa be continuous. If the normal displacement wcre not continuous, one medium would eitber separale from tbe other, leaving a vacuum in between, or else would penetrate into tbe otber so thal the two media would occupy the same space. If the tangential displacemenl were not continuous, Ihe two media would move dilferently on opposite sides of the boundary and one would slide'over the other. We rule oul such motion for rocks. and so displacement must be continuous at tbe boundary. The continuity of normal and tangential stresses and displacements at the boundary can be expressed by means of four equalions (boundar)' condition.f)

tbat tbe wave motion must obey at the interface. Assume aplane P wave with amplitude Ao incident on the boundary between two solid media. SneU's law fixes tbe angles 01 reflection and relraction whereas the amplitudes of the reflected and refracted waves are fixed by the rour boundary conditions. However, to satisfy lour equations we must have four unknown amplitudes; hence four waves must be generaled al the boundary. These correspond to reflected and rerracted P waves and reflected and refracted S waves. This is illustrated in Figure 4.16 where Al' A 2 , (JI' and (J2 are the amplitudes and angles of the reflected and refracted P waves and BI' Bz, ~I' and ~2 are the amplitudes and angles of the refiected and refracted S waves. Snell's law tells us that sin 8

sin (JI

sin Al

sin A

2 2 -~- - p a ~ ~

z

(4.37)

[This more general statement of SneU's law can be derived followiog the same reasoning used to derive Eq. (4.35).) The equations goveming the amplitudes were flrst given by Knott (1899), but he expressed Ihem in terms of potential funclions from which the displacemenls must be found by differentiation. The corresponding equations in terms of amplitudes were given by Zoepprilz (1919) in the following form (see Shcrilf and Geldart (1982, pp. 65-6) for derivations of Zoeppritz's and Knott's equations): Al cos

°

1 -

BI sin Al

= Ao COS (JI

+ Al COS (Jz + B2 sin ~2 (4.38)

Al sin 01 + BI cosA I - Al sin 8: + ~ COS~2 ( 4.39) - - Ao sin 81 Al21 ros ni - Bl"'í sin 2~1 - A: 2: cos 2Al - 8:W2 sinlA 2 - -Ao2lcoslAl (4.40) A1YIWI sin 291 + Bl"'í cos2~1 + A2YzW:z sin211z - BlW:cos2Al - AOyI W1 sin 2(J. (4.41)

Seismic methods

156 Table 42 fnergy reflec/ed al Ihe interface belween /wo media

First medium Interlace

Second medium

Velocity

Of>nsity

Velocity

2.0 lO

24 24

lO

24 2.4

2.1 4.3 1.5 1.5 1.5 0.5

2.4 2.4 1.0 1.0 1.0 1.5

2.0 2.3 4.5 1.5 3.0 0.36 2.0

Sandstone on limestone Limestone on sandstone Typical shallow interface Typical deeper interface "Solt" ocean bottom "Hard" ocean bollom Surface 01 ocean (Irom below) Base 01 weatheri ng

Oensity

24 2.4

2.0 25 0.0012

2.0

Z,/Z¡

R

E"

0.67 1.5 0.91 0.96 0.50 0.20 3500 0.19

0.20 -0.20 0.045 0.023 0.33 0.67 -0.9994 0.68

0.040 0.040 0.0021 0.0005 0.11 0.44 0.9988 0.47

Note: AIJ velocities are in km/s and densitics are in g/err?

where y¡ = fJja¡

Z¡

= p¡a¡

i

= 1,2

These equations govern the amplitudes or aH the waves that result from an interface. but they involve so many parameters that it is difficult to generalize Crom them. The products oC densi ty and veloci ty (Z¡ and W¡) are known as acoust;c ;mpedances. To apply these equations at an interface. we must know the density and velocity in each oC the media, hence Z\, L;, WI • H-í. 11' and Y2 are known. For a siven Ao and 8). we can calculate (J2' >-1' and >-2 Crom Equation (4.37) and the four amplitudes, Al' A 2 , Bl , and B2 , from Equations (4.38) to (4.41). Zoeppritz's equations reduce to a very simple Corm Cor normal incidence. Because the curves change slowly ror small angles oC incidence (say up to 20°), tbe results for normal incidence have wide application. For a P wave al normal incidence, the tangential stresses and displacements are zero; hence BI .., ~ - O and 81 - 82 - O, so Equations (4.38) to (4.41) reduce to

ZI Al

Al

+ A 2 - Ao

-

Z2A 2 =

-ZIA o

The solution of these equations is

Al

~

- ZI

Ao

~

+ Zl

R---

A2 2Z1 T--Ao Z2 + ZI

( 4.42)

These ratios usually are called the normal reflection and transmiss;on coefficients, but the fractions of tbe incident energy that are rel1ected and reCracted are

also somelimes called by these names. Writing EIf. and ET ror the fractions oC the incident energy retlected and transmitted. we lind, from Equations (4.32) and (4.42),

( 4.43)

(4.44) For a wave incident on an interface trom the opposite direction, we interchange ZI and Z2' nis will change the sign 01 R and the value of T. but leave ER and ET unchanged. Hence the partition of enersy does not depend on wbich medium contains the incident wave. When the impedance contras! vanishes, ER = O and a11 the energy is transmitted (note that tbis does not require that PI - P2 and al = a2)' As tbe impedance contrast approaches O or 00, T approaches zero and R approaches unity; thus, the farther the impedance contrast is from unity, the stronger the reflected energy. Table 4.2 shows how the reflected energy varies for impedance contrasts such as might be expected within the earth. Because both density and velocity contrasts are small for most of the interfaces encountered. only a small portion of the energy is reflected at any one interface; tbis is illustrated by the first four lines in Table 4.2. The sandstone-on-limestone interface is about as large a contrast as is apt to be encountered, whereas the typical shallow interface and the typical deep interface figures are more representative oC most interfaces in the earth. Hence, usually appreciably less than 1% of the energy is rel1ected at any interface. The major exceptions involve the bottom and surraee ol the ocean and the

157

Seismic theory

."

11

,yI

¡•

,

~

.

~

•l

.... 0 ... (

,

..

•

"

O"

(a)

lb)

" \

•

..

..

..••• ••

i

3

•

·,·

I

•

I

,

·,

( el

(d)

Figure 4.17. Partitioning af energy berween transmitted and refleeted wa\'es as d funetion of angle of incidenee for /hc caS(' ()f an ineiden/ P wave. TP - (raerion of energy in Iransmirrr>d P wave, I?P - (raetion in refleeted P wave, TS = fraetion in /ransm,tted 5 wave. and I?S = fraerion in reflectf'd S wa.·e. (From Tooley. Speneer, and Sagoci, 1965.) (a) CasI! wherr> ,'e/oei/}' in the incident medium is /arger: al/a¡ .. 0.5, flJ/ Pt - 08. o, - 03. dnd "; = 0.25. (b) Case where "elocilv in /he inciden/ med;um ;s sma/ler: al/a., = 20, P:l/ PI = 05, o, J. and "1 - 0.25. (e) Fraetion of energy reflectf.'d as P Wdve for \'drious P-wdve \'Plaeity ratios and P:l/Pt .. 1.0, o, - "2 - 0.25 (from Denham and Pa/meira. 1984). (d)Fraction af energy reflected as a P wave for var;ous densit~, ra/i05 and o;/a¡ - 1.5, o, - "l = 025.

o.

base oC Ihe wealhering (§ 4.2.8b), A rnueh larger proporlion of the energy can be rellected from Ihese and hence Ihey are especially imporlanl in the generalion oC multiple refteelions and olher phenornena Ihal we shall deal wilh laler. The land surCaee is usually oC less irnportance Ihan the base oC the weathering Cor rnultiple generalioD beeause increased Iravel in the wealhered layer iDvolves appreciable absorptioD. A Degative value oC R means Ihat Ihe reflected wave is 180 0 OUI oC phase wilh Ihe incident wave. Thus, (or an incident wave A o cos wt. the reflected wave is Al cos( WI + 'Ir). Phase reversal occurs when Zl exceeds Z2 (see Table 4.2). Turning now to the general case where Ihe angle o( incidence is not necessarily zero, we iIIustrate solutions oC Zoeppritz's equations with graphs Ihat sbow the energy partition as Cunetions oC the angle oC incidence Cor certain values of parameters. Many curves would be required to show the variations of energy partitioning as a function oC incident angle

beca use oC Ihe many parameters Ihat can be varied: incident P, Sil, or SV wave, P wave velocity ratio, density ratio, and Poisson ratio ror each medium or equivalent values (such as S- lo P-wave velocity ratios). Figure 4.17 shows several cases representative of tbe variety oC results possible. Figure 4.17a shows the partitioning oC energy when a P wave is incident on a medium oC lower velocity. For small incidenl angles, almost all oC Ihe energy is in Ibe reflected and transmitted P waves and hence hardly any S waves are generated, As the incidenl angle inereases, sorne oC the energy goes inlo reflected and transmitted S waves, and al intermedia te angles the reftected S wave carries more energy than the refteeted P wave, Such con verted waves (waves resulting (rom the conversion o( P waves to S waves or vice versa al an interface) are sometimes recorded al long olfsets (§ 4.S.2b) where tbey are evidenced by alignmenls Ihat disappear as one tries to foJlow Ihem to shorler olfsets, As grazing incidence ís approached, the energy oC the reftected

158

P wave inereases until at 90 0 aH of the energy stays in the P wave in lbe incident medium. The opposite situation is shown in Figure 4.17b where a P wave is incident in the low-velocity medium. Because the change in density is opposite to the change in velocity sucb that Zl = Z2' the P-wave refleetion coefficient is essentially zero for small incident angles. As the incident angle increases. S·wave energy increases. As the critical angle for P waves is approached, the transmitted P-wave energy Calls rapidly to zero and no transmitted P wave exists for larger incident angles. Also as the critical angle is approacbed, reflected P and S waves become very strong; such a buildup of reflection strength near the critica! angIe is called wide-angle reflection. Sometimes offsets are increased lo take advantage of tbis phenomenon to map reflectors Ibat cannol be followed at sbort offsets (Meissner, 1967). As the critica! angle for S waves is approached, the Iransmitted S wave falls to zero. Figure 4.17c shows the P-wave reHection coefficient for various P-wave veJocity ratios when there is no density or Poisson-ratio contrast. The reflected energy is zero for a velocity ratio oC unity (no impedance contrast) and increases as the velocily ralio increases or decreases. The peaks for a 2 /al > 1 occur al the critical angles for the P and S waves, respectively. Figure 4.11d sbows the energy of tbe refleeted P wave for various density contrasts. The graphs in Figure 4.17 generally sbow that tbe reflected amplitude deereases slight1y as the angle oC incidence increases, which is equivalent to saying that the P-wave amplitude decreases as tbe offset (source-to-geophone distance) increases. However, Shucy (1985) shows thcoretically that the amplilude may increase if Poisson's ratio cbanges appreciably. Such a change may occur when gas fills the pore space in a rock. Ostrander (1984) observed on field records such behavior associated with gas reservoirs. lbis behavior 01 amplitude with offset is used as an indicator oC hydrocarbon gas (§ 4.10.8).

4,2,8. Seismic Veloclty Equation (4.28) shows that the velocity of P waves in a bomogencous solid is a function only ol the elastic constants and the density. One might expect that tbe elastic constants, wbich are properties of the intermolecular forces, would be relalively insensitive lo pressure, whereas the density should inerease with pressure because rocks are moderately compressible. This would lead one 10 expect thilt the Dumerator in the cxpression for velocity would nOI change very much with increasing pressure whereas the deDominator . would get larger so that velocity would deerease with (a) Factors affecting velodty.

Seismic methods

deplh of burial in tbe eartb. In fact, tbis is contrary to actual observations. Birch (1966) shows wide ranges in the velocity of any given rock type, as illustrated in Figure 4.18. Whereas mosl rocks are mixtures of different minera1s, even if we were to eonsider only relatively .. pure" rocks, sucb as sandstones composed mainly of quartz or limes tones that are a1most pure calcite, we would encounter a wide range of velocity values, almost a11 ol lbem lower than tbe values for quartt or calcite. The mosl important aspeel in wbich sedimentary rocks differ trom homogeneous solids is in having granular struelure wilh voids between the grains. These voids are responsible for the porosity ol racks (§ 11.1.4) and porosity is the important factor iD determining velocity. Sheriff and Geldart (1983, Chapo 1) discuss tbis and other Cactors that affeet velocity. Gassmann (1951) derived an expression for lhe velocity in a model consisting ol tight1y packed elaslic spheneal parlicles under pressure such that lhe contacts between the spheres become areas rather than poinls. The elastic constants of such a pack vary with pressure, and the effeet is to make tbe P-wave velacily vary as tbe l/6th power oC tbe prcssure. Faust (1953) found an empirical (ormula Cor velocity in terms oC tbe depth oC bunal Z and the Cormation resistivity R: (4.45)

v is in Ceet per second when Z is in leet and R is in ohm-Ceet. However, the deviations oC individual measurements were very large, wbich iodieates the preso ence oC other Cactors tbat tbis equation dacs not talte iDto aecouot. An earlier lorm of Faust's law (Faust, 1951) aIso included the age of tbe rock as a factor in determino ing velocity. An older rack might be expeeted to have a bigher velocity, having been subjeeted for a longer time to pressures, cementation. and olher factors that might increase its velocity. In actual rocks, the pare spaces are filled with a Huid whose elastic conslants and density a1so aft'eet the seismic velocity. OH is slight1y more compressible tban water, so oil-filled pores result in slightly lower velocity tban water-filled pares. Gas is eonsiderably more compressible than water and so gas-filled pores olten result in much lower velocity. Even a small amount of gas may lower velocity appreciably (Domenico, 1977). These effeets are used as hydrocarbon indicators (§ 4.10.8). The fluid iD rock pore spaces is under a pressure lbat usually is different from that due lo lhe weight of the overlying racks. In Ibis situation, the effective pressure on the granular matrix is the difference

Seismic theory

159

o

Velocity (kft/s)

5 i

"""IT

10 i

,

i

,

,

i

¡

I

25

20

i

i

i

O Petroleum O Wale' c:l Mud

1~~sa~n~d~st~o~n~e~~===~~S% ~ Limestone i

Coal

20% Lr==:::::==~.:.. O o SaU Dolomite 20% CC::::::::::~.:.:-. O c=JGypsum and c==::J anhydrite Igneous I

O

2

4 3 Velocity (km/s)

Figure -l. '18. i\1easuremenl 01 i'eloot~ in different rock (From SlIerif; Jnd Ce/dart 1983)

between the overburden and fluid pressures. Where formation l1uids are under abnormal1y high pressures. sometímes approaehing the overburden pressure. the seismic velocity is exceptionally low, a fael that is sometimes used to predict almormal fluid pre,Uure from veloeity measurements (Bilgeri and Ademeno, 1982). Subjecting a porous rock to high pressure results in both reversible and irreversible changcs in porosily, that is, when tbe pressure is removed. a small parl of Ihe original porosily is regaincd whercas most is permanently lost, perhaps bccause of crushing oC the grains, alteration oC Ihe packing. or olher permanent structural changes. Empirical data suggest that the maximum deptb lo whieh a rock has been buried is a measure of the irreversible effect on porosity. In summary, porosity appears to be the dominant variable in determining tbe velocity in sedimentary rocks, and porosily in lum is determíned principal1y hy the existing differential pressure and Ihe maximum depth of huríal. The variation of velocity wilh deplh (Fig. 4.19). referred to as Ihe velod/y fU/le/ion. is frequently a reasonably syslemalic increase as we go to greater depths. Arcas oC moderately uniform geology. such as the U.S. Gulf Coast. exhihil relalively Hllle horizontal variation in vclocily from area lo area. Because oC seaward dip. as one goes seaward. younger section is encounlered al a given depth bul the velocity does nol vary greally borizontally: the maximum pressures to which the rocks have heen subjected are tbe exisling pressures. whicb depend mainly on depth. not age. On the olher bando areas subjecl 10 recent struclural deformation and uplirt. such as California, exhibit rapid horizontal variation

,

s

7

6

IlpPS

rpported

bl'

Birch (/966).

of veloeity from area lo area. Many of the California rocks have been buried lo greater depths and subjecled lo greater stresses than exist at present, resulting in rapid lateral changes in velocity, which profoundly affect seismic interpretation. The variation of velocily with density is shown in Figure 4.20. Tbe large range oC velocity tor any given lilhology (for example. shale velocities range from 1.6 to 4.0 km/s) lells the same story as Figure 4.18. Tbe overlap of ranges of velocity makes it impossible lo tell Ihe lithology oC a sample merely from its velocily. The range oC density values resuhs mainly from differenl porosíties. and the curves would look very similar iC velocity had been plotted against porosity. The dotted line in Figure 4.20 is sometimes used when a relation belween velocity and density is nceded. as in syntbetic seismogram manufacture, seismic log calculation. and other situations. The empirical time-al'erage equalion is often used lo relate vclocity V and porosity .p. It assumes that the travehime per uni! path length in a ftuid-filled porous rock is the average of tbe traveltimes per unit path lenglh in tbc matrix material 1/ V", and in the fluid l/V¡ where the traveltimes are weighted in proportion to tbeir respective volumes: 1

( 4.46)

This relationship is used extensively in well-Iog inlerpretation. Whercas the velocity oC S waves is generally about half that of P waves, the factor relating the two velocities varíes with the lithology and is

5eismic methods

160 Vcl~ity

3.0

I.S

O

(km/S>

8 ,

lO

6.0

4.5 12 (ltft/s)14

¡ · .••..N··N ............ _ •••• 0'_

16

-.....................

o • • • • • • • •-

......... "

18

20

I

r" .._._ ....... - ..... _.........._ ....~_......: I

2

.........-i.--o ..................._. ,

~/iI/Oi$lJasi" 1........_....... !

,

4 o • • • •_

. . . . _ _ _ _ . _ ._ _ . . . . . . . . _ . _ . _ . _ _ _ _

J¡

6

2 8

--

3 lO

E

....

.::

-

~

~

oC

c.

12

c!í

4 14

..,.\

.\ b\

5

..i1................ .

\\ .. \

"\

16

~ ..

,\

~\r---------------~

18

~~--------------------,

'9,\

\'

6

~

F¡8ure 4.19. Velocity- depth re/ationships from selected wells. (From Sheriff and Ce/dar/. 198.3.)

4

»

J.2i-----ir---r---i--T----...:r---T----:¡~----T----'r_--í

Figure 4.20. P-wave velocity- density relationships for different lithologies (Iog- log sea/e). The dotted line represents Cardner'S rule: p - aV1/ 4 • (From Gardner. Gardner. and Gregory. 1974.)

Seismic theory

161 Or---,----,------r----,r------,------r----,----,

I

I

I

I 1

I

\! A

~~

o,.

\

Figure 4 21. Finding maximum dep/h al buria/ Irom ve/oei/y. The shale ilnd limes/one regression Iines represenl rocks believed lo hilVe no/ been uplifted. (From Jankowsky. ~970)

..

occasionally used to determine lithology (Domenico, 1984). The velocity oC S waves is relalively insensitive to the nature oC the fluid tilliog rock pore spaccs, in contrast to that oC P waves. Thus a local changc in the S-wave lo P-wave vclocity ratio constitutes another hydrocarboo iodicator (§ 4.10.8). The irreversible change in porosily (and con sequently io velocity) with depth of burlal has beeo used to determine the maximum deplh at which a section fonnerly lay. lf the velocity-depth relationsbip Cor a gíveo lithology can be established in an area not subjected to upliCt, the maximum depth oC burlal can be ascerlained from Ihe observed velocily-depth relationsbip, and hcnce the amounl oC Ihe uplirt can be ioferred. lo Figure 4.21 the shale and limestone regressioo lioes (curves A and B) represent measurements on "pure" shales and limestooes Ihat are believed to be at their maximum dcpth oC burlal. Curve e, wbich is obtaioed from these curves by interpolation, is the predicted curve based 00 Ihe relative amouots oC shale and limestooe actually preseot and assumiog the rocks to be at Iheir maximum depth oC burlal. The displacemeot io depth required to lit tbis curve to Ihe actual measuremeots is presumed to iodicate the amouot oC upliCt that has occurred . Velocity and its elfecls are discussed more Ihoroughly in Sherllf and Geldart (1983, pp. 2-16) and eordier (1985). (b) The weathered or low-velocity layer. Seismic velocities that are lower than the velocity io water usually imply that gas (air or methane, probably

resulting Crom tbe decomposition oC vegetation) fills al least sorne of the pare space (Watkins, Waltcrs, and Godson, 1972). Such low velocities are usually Cound only oear Ihe surface in a zone called the wealhered layer or the low-veloci(v fayer, often abbreviated LVL. This layer, usually 4 to 50 m thiele, is characterized by seismic velocities that are not only low (usually between 250 and 1{)()() mis) but at times higbly variable. Frequently the base of the LVL coincides rougbly witb tbe water table. indicating that the low-velocity layer corresponds to the aerated zone aboye the water-saturated zonc, but tbis is not always Ihe case. Obviously the lerm "weathering" as used by geophysicists dilfers from the geologíst's "weathering," whicb denotes the disintegration oC rocks under the iofluence of the elements. The importance of the low-velocity layer is rourCold: (1) The absorption oC seismic energy is high in tbis zane, (2) the low velocity and the rapid changes in velocity have a disproportionately large elfcet on traveltimes, (3) the marked velocity change al the base of tbe LVL sharply bends seismic rays so that tbeir travel througb the LVL is nearly vertical regardless oC their direction of travel beneath the LVL, and (4) the very high impedance contrast at the base of the LVL makes ¡tan excellent reflector, important io multiple reftections and in wave conversion. Because oC the first factor, records from shots io thls layer oCten are oC poor quality and elforts are made to locate the shot below the LVL. Methods oC investigating the low-velocily layer are discussed in Sec- , tioo 4.5.2e and methods oC correcting for it in Section 4.7.1.

162 (e) Permafrost. Because the thermal conductivity oC most rocks is so small, seasonal changes in the surface temperature do nol significantly affect temperatures below a few meters. where the temperature approximates the average surfacc temperature. The result in arctic regions is a zone oC permanently rrozen rocks called permafrosl. Frozcn rocks generally bave very rugh velocities, often 3.0 to 3.8 km/s or higber. The permafrost may be very irregular in thlckness and often disappears completely under lakes tha! do not rrceze solidly during the winter. The laterally variable nature oC the permafrost results in time shifts and distortions that are often very difficult to remove. The very upper portion that is affected by surface temperature variations is called the active layer, and its velocity and other physical properties change seasonally by large amounts. Permafrost may even be present under tbe ocean, prcsumably having formed during a time oC lowered sea leve!.

4.3. GEOMETRY OF SEISMIC WAVEPATHS 4.3.1. Reflection Paths in a Constant-Velocity Layer (a) General. The basic problem in rellection seismic surveying is to determine the position 01 a bcd that gives rise lo a refleclion on a seismic record. In general, Ibis is a problem in tbree dimensions. However, the dip is oflen very gentle and tbe direction of profiling is lrequently nearly along either the direclion of dip or the direction oC strike. In such cases 2-0 solution is generally used. We shall discuss the 2-D problem in the next two sections and then the more general problem. The exact interpretation of reflection data requires a knowledge of the velocity at aJl points along the reftection paths. However, even ir we had such detailed knowledge, the calculations would be tedious and often we would assume a simple distribution of velocity that is close enough to gíve usable results. TIte simplest assumption is that tbe velocity is constant between thc surface and the reflecting bed. Althougb tbis assumption is rarely even approximately true, it leads to simple formulas Ibat give answers that are within the required accuracy in many instances. (b) Horizontal reflector: normal moveotit. The simplest 2-0 problem is that oC zero dip, illustrated in the lower part of Figure 4.22. The reflecting bed A.B is at a depth h below the source S. Energy leaving S will be reflected in such a direction tbat the angle of reflection equals the angle of incidence.

Seismie methods

Although the reflected ray CR can be determined by laying off an angle equal to ex at e, it is easier to make use ol the image point l. which is located on the same normal to the reflector as S and as far below the bed as S is aboye. Ir we join I to C and prolong the straight line to R, C R is the reftected ray (since CD is parallel to SI. making all the angles marked a equal). Denoting the velocity by V, the travel time t lor the reftected wave is (SC + CR)/V. However, se - el so that IR is equal in lengtb to the actual path SeR. ThereCore. t - IR/V and in terms of x, the source-to-geophone distance (offset), we can write

( 4.47)

or

Thus lhe traveltirne curve is a hyperbola as shown in tbe upper part 01 Figure 4.22. Thc geophone al R will also record the direct waue that travels along the path SR. Because SR is always less than (SC + CR), the direet wave arrives lirs!. The traveltime is t D - x/V and the traveltime curves are the straigbt lines OM and ON passing through the origin with slopes ol ± l/V. When the distance x becomes very targe, the dilference between SR and (Se + eR) becomes small and the reflection traveltime approaches the direct wave traveltime asymptotical1y. The location of the reflecting bed is delermined by measuring 'o' the travettime for a geophone at the source. Setting x - O in Equation (4.47), we see that (4.48) Equation (4.47) can be written

,2 =

x2

_

v2

4h 2

+_

VI

xl

= _

VI

+ t2

o

(4.49)

If we plot ,2 against xl (instead of t versus x as in Fig. 4.22), we obtain a straigbt line of slope (l/VI) and intercept I~. This forms the basis of a wel1·known scheme for detennining V, the .. Xl - TI method," wruch will be described in Section 4.S.Sc. We can solve Equation (4.49) for t, the traveltime measured on the seismic record. Generally 2h is appreeiably larger tban x so tbat we can use a binomial expansion as follows:

Geametry af seismic wavepaths

763

"

B

A I

I

I

\

1« /

\ r-,.

'r Figure 4.22. Geometry and !rave/time curve (or horizontal reflector.

The difference in traveltime Cor a given rel1ection Cor two geophone locations is known as moueout and it is represented by t1/. Ir ti' 12 , XI' and X2 are the Iraveltimes and offsets. we have lo the tirsl approximation (4.51 ) In the special case where one geophone is al Ihe source, tu is known as the normal mot>eout. which we shall denote by Atn' Then, ( 4.52) At times we retain another term in tbe expansion:

From Equation (4.52) we nole lhat Ihe normal moveoul ¡ncreases as the square of the offset x. invenelyas the square of the velocity. and inversely

as the tirst power oC the travellime (or depth; see Eq. (4.48»). Thus rel1ection curvature ¡ncreases rapidly as we go to more distanl geophones and, at the same time, Ihe curvature becomes progressively less with increasing record time. The concept oC normal moveout is extreme1y importan\. 1t is the principal criterion by which we decide whether an evenl observed on a seismic record is a reflection or not. If the normal moveout differs from the value given by Equation (4.52) by more than the a1lowablc experimental error, we are nol juslified in lreating the evenl as a reflection. One al Ihe mosl important quantities in seismic interpretation is lhe change in arrival time causcd by dip. To find Ihis quantity. we musl correct ror normal moveou\. Normal moveoul must also be eliminated befare .. stacking" (adding together) common-midpoint records (§ 4.7.8). Finally. Equalion (4.52) can be used 10 find V by measuring x, '0' and A'~, This forms the basis oC velocity analysis (§ 4.7.7). (e) Dipping reflector: dip maveaut. When the bed is dipping in the direction oC the profile. we havc the situation shown in Figure 4.23. where E is the dip and h is the depth (normal to the bed). To draw the raypath Cor the reflection arriving at the geophone R.

Seismic methods

164 Then 2h {

1=

V

1+

(X 2 + 4hx sin ~ )}1/2

x2

... ro ( 1 +

x

C'I

,C,' \

\,1,',h , , I

,

4h2

+ 4hx sin ~ ) 8h 2

(4.55)

using only the lirsl term oC the expansiono The simplest method of finding ( is Crom the difference in traveltimes Cor two geophones equally distant Crom. and on opposite si des or. tbe source. Letting x have the values + fax for the downdip geophone and - fax for the updip geophone and denoting the equivalent traveltimes by /1 and 12 , we get

'e

. ',

\"

I

Figure 4.23. Ceometry ;md traveltime curve for dipping reflector.

we join fue image poinl 1 lo R by a strai&ht line cutling fue bed at C. lOe path is Ihen SCR and , - (SC + CR)¡V. Because (Se + CR) - IR, applicalioD of fue cosine law to tbe triangle SIR gives

The quantity (A'd/Ax) is tbe dip moveoul (this term is a1so used witb a different meaning in sorne seismic processing). lbe dip is found from the equation sin~'"

V 2t 2

-IR 2 -

X2

.:. xl

+ 4h 2 - 4hx

cos( i + ~)

+ 4h 2 + 4hx siD ~

( 4.54)

On completing the squares. we obtain

+ 2h sin ~)l - 1 (2h cos E)2

(x

'Ihus, as befare, the traveltime curve is a byperbola, but tbe axis of symmetry is DOW tbe line x ~ - 2 h sin ~ instead of the 1 axis. This mean s Ihat I has diJferent values for geophones symmetrically placed OD opposile sides oC the source, unlike the case for zero dip. Setling x - O in Equation (4.54) gives tbe same value for h as in Équation (4.48). Note, however, that h is DOt the vertical depth here as it was in the earlier resul t. To obtain the dip we solve for 1 iD EquatioD (4.54) by asSUDÚng that 2h is greater than x and expanding as in the derivation oC Equation (4.50).

t.

V( -

-

2

l:J.l d )

Ax

( 4.56)

For smal! angles. ('" sin ( so that the dip is direcdy proportional to (lltd/l:J.x) under these circumstances. To obtain the dip as accurately as possible. we use as large a value of &x as tbe data quality permits. For symmetrical spreads. we measure dip moveout between tbe geophone groups at opposite ends or the spread. It should be noted tbat normal moveout was eliminated in the derivation of Equation (4.56). lbe terms in (&x)2 that disappeared in the subtraction represent the normal moveout. Figure 4.24 illuslrates diagrammatically the relation between normal moveout and dip moveout. lbe diagrarn al tbe leíl represents a reftection from 8 dipping bed; the alignment is curved and unsymmetrical about tbe source. Diagram (8) shows what would have been obsetvcd if the bed had been horizontal; the alignment is CUtved symmetrically about the source position owing lo the normal moveout. lbe latter ranges from O to 29 ms (1 millisecond 10- 3 S - 1 ms. the unit of time commonly used in seismic work) al an offset of 600 m. Diagrarn (C) was obtained by subtracting the normal moveouts shown in (8) from the arrival times in (A). The resulting alignment shows the eft'ect of dip alone; it is straight

Geometry of seismic waveparhs

165

Figure 4.24. Re/arion berween norma/ moveout and dip moveoul; lo V - 2,500 mis.

and has a time difference belween Ihe oulsidc curves oC 25 ms, Ihat is, tltd/tlx = 0.042 ms/m. Thus we find that the dip is sin -1 (2,500 X 0.021/1,000) = 0.052 rad - 3.0°. The method oC normal-movcoUI removal iIIustrated in Figure 4.24 was used solely lo dcmonstrate the difference belween normal moveout and dip moveout. If we require only the dip moveout fll d , we merely subtract the traveltimes Cor Ihe Iwo outsíde geophones in (A). We may nOI have a symmelrical spread and we find Ihe dip moveoul by removing the e(fcct oC normal moveoul. As an cxample, refer to Figure 4.24, curve (D), which shows a reflection observed on a spread extending Crom x = - 200 lo x = + 600 m. Let '0 - 1.000 S, ti ... 0.997 s, 12 = 1.025 s, V"" 2,800 mis. From Equation (4.52) we get, Cor tlt. at offsels oC 200 and 600 m, respectively, Ihe valucs 3 and 23 ms (rounded off 10 Ihe ncarest millisecond because tbis is usually the precision oC measurements on seismic records). Sublracting these values, we obtain, for the corrected Iravcltimes, 1I "" 0.994 s and t 2 - 1.002 s. Hence, the dip moveout is 8/400 = 0.ü20 ms/m. The corresponding dip is sin .. Id x 2,800 x 0.020/1,000) '" 0.03 rad ... 2°. An allemative lo the precedíng method is 10 use Ihe arrival times al x - - 200 and x = + 200 m, Ihus obtaining a symmelrical spread and eliminating the need {or calculating normal moveout. Howcver, doing tbis would decrease the effective spread length

~

1,000

s,

-----6x----------~

Figure 4.25. Finding rhe angle of approach 01 d wa~'e.

Crom 800 lo 400 m and thereby reduce Ihe accuracy oC the ratio (tlld/tlx).

Equation (4.56) is similar to the equation that gives the angle oC approach of aplane wave as it reaches Ihe surface. In Figure 4.25, A represents an upward-traveling plane wave at the instant when it arrives al the end of the spread, A. After a further interval 6.t, the sarne wave reaches the other end of the spread, B. Then, Be = Vtlt and

e

Be

sina = -

BA

tJ.1

( 4.57)

= V-

tlx

Tbis result, although similar in form to Equation (4.56) has a different significance because it gives the direction of travel of aplane wave as it reaches the spread. V is the average velocity between and the surrace. In Equation (4.56), V is the average velocity down lO the reflector and ~ is the angle of dip. The

e

166

Seismic merhods

I

I

1

I L\

~

1

\ 01

YI

\ 1

,1

•

I

Fisure 4.26. Tl1ree·djmensional

";I'W 01 a reflect;on patl1 lor.J dipp;ns bed.

two formulas &ive the same angle because V is constant down to the reflector and 2 tu in Equation (4.56) is thc same as Ax in Equation (4.57). Orten V will not be constant, as we shall see presently. (d) Cross dip. When lhe profile is nol perpendicular to the slriJce, the determination oC dip becomes a 3-D problem. In Figure 4.26 we talce lhe xy plane as horizontal wilh the z axis extending vertically downward. The line OP of length h is perpendicular to a dipping plane bed Ihal outerops (thal is. inlersects the xy plane) along the line MN iC sufficiently ex· tended. We write "1' "2' and Elor the an&les between OP and x, y, and z axcs. The cosines oC tbese angles (tbe direc:tion cosines of OP) have the values t, m, and n. Equation (A.8) sta tes that

in the derivation of Equation (4.55), we gel, Cor the approximate value of 1,

By subtracting tbe arrival times al two geophones located on the x axis at x - ±l1x, we find Al" ..

fAX) 'o ( -h-

..-Ul1x V

t-

COSOl ... -

V(

I1t,,) 2 I1x

( 4.58)

Ir we also bave a sprcad along the y axis (crou

spread; see § 4.5.2b), we gel 1be angle • between MN and the x axis is the dircclion of striJce of tbe bed whereas Eis the angle oC dip. The patb oC a reflecled wave arriving at a geophone R on the x axis can be lound usíng lhe image point 1. The lioc joining I lo R cuts the refleclor al Q: hencc OQR is tbe patb. Since OQ - QI, Ihe line IR - V, where t is the traveltime for the geophone al R. The coordinatcs oC 1 and R are, respectively, (2M, 2hm, 2hn) and (x, O, O). Henee we have V2,2

_IR 2 - (x - 2ht)2 + (O - 2hm)2 + (0·- 2hn)2

+ + + xl + 4h 2 - 4htx

_ xl _

4hl(t 2

m2

n2 ) -

4hlx

Whcn x - O, we obtain the same relation beas in Equation (4.48). Proceeding as tween h and

'0

V(11/,)

(4.59)

m-cos"l"2 l1y

where Al, is tbe time difference (eross dip) between geophones B distance 2 11 Y apart and symmetrical aboul the shotpoinl. Bccause

1+ m 1/2

n - cos E- {l - (1

1

)}

sin E- (1 - n1 )1/2 _ (t2 + m 1)1/2

-~ {(~~ f

+(

~; rf/2

(4.60)

When the profiJe liDes are nol perpendicular, for example, when one is along the x axis and the other a10ng tbe y' axis al an angle fj to the x axis, the solution is more complicated. Taking lhe lcngth of a

Geometry of seismic wavepaths

167

,., \

\

Figure 4,27. Re.so/urian af cras,s-.~pr('iJd informa/ion.

symmetrical spread along the y' axis as 2 A y'. the coordinates ol the ends oC ibis spread (relative to the x, y, and z axes) are (Ay'cos{l. Ay'sin{l, O) and (-t1y'cosfJ. -t1y'sinfJ. O). Then Vl,~ _

(2M± Ay'cosfJ)2 +(2hm ± Ay'sinfi)2 + (2hn)2

- (Ay,)l + 4h 2

± 4h Ay'(tcosfJ +

ni

sin

In

The moveout becomes

2Ay'

At' "" _·_(tcos{l + msinfJ) V

or

Figure' .¡ 28. Determina/ion 01 srrike.

(f cos fJ +

ni

At' ) sin fJ) _.v ( ---2 Ay'

( 4.61)

The measured moveouts. Al. and At'. give the values of I and (1 cos fJ + m sin {l) using Equations (4.58) and (4.61). Becaus!: fJ is known. nr can be found using Equation (4.60). The solution can also be found graprucally as shown in Figure 4.27 (sce also prob1em 5). To find the strike 4>. we start from the equation or aplane (that ¡s, the reflector) that has a perpendicular from the origin oC lenglh h and direction cosines (l. m. n). namely

Ix + my + nz = h Setting z = O gives the equalion oC the line oC intersection ol the reflector and the surface (MN in Fig. 4.26 or 4.28). This slrike line has the equation

Ix + my - h

The intercepts oC lrus line on the x and y axes are hj t and hjm. Referring to Figure 4.28. we flnd that 11

tan - m

when Ax = A l'. The strike can also be round using the constructi¿n shown in Figure 4.27.

4.3.2. Velocity Gradient and Raypath Curvature The assumplion oC constanl velocity is not valid, in general. because the velocity usually changes as wc: go from one poinl to anothcr. In petroleum exploration wc: are usually dealing with more-or-less ftat-lying bedding, and the changes in seismic vc:locity as we move horizontally are. Cor the most part, lhe result oC slow changes in (a) fffect of velocity variations.

Seismic methods

168

density and elastic properties oí tbe beds. These horizontal variations are gencrally much less rapid Iban the variations in tbe vertical direction where we are going from bed lo bed with consequenl lithological changes and increasing pressure witb increasing deptb. Because tbe horizontal changes are gradual. they can often be taken into account by dividing tbe survey area into smaller arcas within each of which the horizontal variations can be ignored and the sarne vertical velocity distribution can be used. Such areas often are large enough 10 inelude several slructures of the size oC inlerest in oil exploralion so tbat changes from one velocity function to another do not impose a serious burden on Ibe interpreter. (b) Equivalent average velocity. Vertical variatious in velocity can be taken into aecount in various ways. One of tbe simplest is to use a modification of Ibe eoustant velocity modelo We assume Ibat the actual seetion existing between tbe surfaee and a eertain refteeting horizon can be replaced witb an equivalent single layer of constant velocity V equal lo Ihe average velocity between the surface and the reflecting horizon. This velocity is usually given as a lunction 01 depth (or of 'o' which is nearly the same except when the dip is large). Thus the section is assigned a dilTerent constant velocity for each of the reflectors below il. Despite this ineonsistency, tbe method is useful and is extensively applied. The variation 01 the average velocity with lo is found using one oC the methods described in Section 4.5.5. For the observed values of the arrival time lo, we select tbe average velocity V corresponding to tbis reflector. Using the values of 10' the dip movcout fl.td/tu, and V. we caleulate the depth h and tbe dip E using Equations (4.48) and (4.56). (e) Velocity layering. A method tha! is commonly used to take into aecount velocity variations is to replace the actual velocity distribution witb an approximatc one that corresponds to a number oC horizontal layers ol difrerent velocities; the velocity is eonstant within caeh layer. Simple equations such as (4.48) and (4.56) are no longer appropriate because rays bend at each layer interface. We often replace tbe actual raypatbs witb a series of line segments tbat are straight within each layer but undergo abrupt changes in direction at the bouodaries between layers. Dix (1955) shows that the efreet 01 this lor a series oC horizontal parallel layers is lo replace tbe average velocity V io Equatioo (4.49) by its root-mean-square (rms) value VnDI , so that

( 4.63)

;

....

I I

\

i

\

I

\

\ - + - - -r-

\

....(r)

I

4 - I

\

I

\

I

- -

- -

-

-

-

-

-

--- -1--------I

..¡

I-tl.I'.

.... -1("

....(r)

......(d

Figure 4.29. Ri/ypi/lh where velocity vi/ríes with depth.

where

(4.64)

V¡ and I¡ are, respectively. the average velocity io and Ibe traveltime through, the ¡th layer (see a1so Shah and Levin, 1973). (d) Velocity functions. Al limes tbe assumption is made tbat tbe velocity varies in a systematic continuous manner and therefore can be represented by a velocity funetion. The actual velocity usually varies extrcmely rapidly over sbon intervals. as shown by sonic 10gS (§ 11.7.2). However. iI we inlegrate these ehanges over distances of a waveleogth or so (30 to 100 m), we obtain a Cunction. which is generally smooth except for discontinuities at marked lithotogical changes. If the velocity discontinuities are small, we are oIten able to represent tbe velocity distribution with sufficient accuracy by a smooth velocity Cunction. The path of a wave traveling in sucb a medium is tben determined by two integral eguations. To derive the equations, we assume tbat the medium is divided into a large number 01 thin horizontal beds in each 01 which tbe ve10city is constant. When we let the number oC beds go to infinity. the thickness 01 each bed beeomes infinitesimal and the velocity distribution becomes a continuous function oC deptb. Referring to Figure 4.29, we have, for the

Ceometry of seismic wavepaths

169

nth bed. sin i.

sin io

=p

v,.-v,,(z) ~x. ~I

=

~z"

tan in

~z"

•

= ---'-V.cos in

The raypath parameter p (§ 4.2.6b) is a constant that depends on the direction in which the ray leCt tbe shotpoint, Ibat is, upon io' In Ihe limil when n becomes infinite, we get

interface. Let us assume Ihal Ihese disturbances represented by the arrows reach the point P in Figure 4.30b al lhe time t. According to Huygens' principie, P then becomes a center from whieh a wave spreads out into the upper medium. Arter a further time interval 111. tbis wave has a radius of VI ~( whereas the wave moving along the refractor has reached Q, PQ = V2 111. Drawing the langent from Q to the arc ol radius VI Al, we obtain the wavefront RQ. Hence the passagc of the refracted wave along Ihe interface in Ihe lower medium generales aplane wave traveling upward in Ihe upper medium at the angle O, where

sinO sin; V

2

sin ;0

----p Vo

dx

dz

( 4.(5)

dz

Veos i z

x - ¡'tan idz

o

1=

dz

10 ~Vcos i

hence

•

VI

= -V

1

= sinfJ

e

( 4.67)

v = V( z) di

- tan;

t=

VI ~I

=V ~t

( 4.66)

d;:

1o V{l - (pV)2}

1/2

Since V is a function of z. Equation (4.66) furnishes two integral equations relaling x and 1 to the depth z. Tbese equations can be solved by numerical methods when we have atable of values of V al various depths.

4.3.3. Geometry of Refraction Paths (a) Headwaves. In refraction scismology we make use of waves that have be en refracted at the eri tical angle; these waves are often called Ireadwaues. In Figure 4.30a we see a P wave incident on the refracting hotUon at the critical angle Oc' After refraction it Iravels along Ihe interface in the lower medium. Tbis produces an oscillatory motion paralleI lO and immediately below the interface (as shown by the doublc·headcd arrow just below the interface). Because relative motion betwecn the two media is not possible, Ihe upper medium is foreed to move in phase with the lower medium. The disturbance in the upper medium travels along the interface with the same velocity 1'2 as the refracted wave just below the

Thus wc sce Ihat fJ = fJc ' so that the two inclined portions of the path are symmetrically disposed with respect lo lhe normal to the refractor. The preeeding discussion of the geometry of headwaves ignores an importanl point. wbich the alcrt reader may already have noled, namely that the Iransmitled energy. which is the product oC the intensity and [he beam width. is zero at fJc beeause the bcam widlh becomes loero (the amplilude does not become zcro). Consequently. the headwave carries no energy. However. at angles slighlly smaller than Oc, the narrow beams do carry finite energy. Because lhe vclocity below the interface usually ¡nereases slighlly with depth bc10w the interface, the refraeted energy will be bent back toward the surface. as in Figure 4.30c. and its travelpath will be almost the same as that along the interface, so that the result is nearly the samc as ir energy had been refracted along the interface. Headwaves do exist and frequentIy are very slrong. A more exact theory based on curved wavefronts (Grant and Wesl. 1965. Chapo 6) predicts Ihe existence ol headwaves with nomero inlensities and Ihe same geometrical relations as those predicted by plane-wave theory. Obviously the headwave will nol be observed al olfsets less Ihan ON in Figure 4.30b where

x. - ON = 2z tan Oc

is called Ihe critical distw!ce. As Ihe ratio "11 VI increases. Xc decreases. When V2/VI - 1.4, x. - 2z.

Xc

x'

J.:

o

.. t

VI

Vz

M

M

lal

V2

p

Vd:. I

Q

lb'

1',

Z

V; -

3

(~l

Figure 4.30. Heddw.JW!S. (.J) Motion .JI lile interfJce. (b) W.JVl'front emerging from refractor at critie../ ..ngle. (el eh,lOges in be.Jm widlh upon refraclion and bending of refracted raypaths becausf' of the vp./ooty gradif'nt in the high-Vf'/ocity medillm.

Ceometry of se;sm;c wavepaths

171

v• FigUfe! 4.31. Re!I.l/ion be/ween ref/e!c/ion ilnd re/rilc/ion raypa/hs and /riwcltime curves.

Henee as a rule oC thumb, refraclions are observed only at offsets ¡reater than twice the depth to lhe refraClor.

where

or (b) Single horizontal refractor. In Ihe case of a 'single horizontal reCracting horizon. we can readily derive a formula expressing the arrival time in lerms of the offset, the depth, and the veloci lies. In Figure 4.31, the lower part shows a horizontal plane refrac· tor separating two beds oC velocities VI and V2 , where Vz > V•. For a geophone at R, the palh oC the reCracted wave is OMPR. The Iraveltime 1 can be written

OM t - --

V¡

MP

+-

PR

+-

Vi

V¡

x - 2z tan Oc

-

Vi

OM

+ 2V¡

2:

+ VI COS 8,

V2

_~+

MP

,., -

Vz

2: (1.- VISíno) V¡ cos 8e Vi e

X

2zcosO.

Ji;

VI

- - + -_-.:

( 4.69)

where we have used the relation sin Oc - VII V2 in Ihe last step. 1ñis equalion can also be written X

1

= -V + ' 1 2

.

¡

( 4.70)

li -

(2zcosOe )/V.

Equation (4.70) represenls a straight line oC slope ti' 1ñis is illustrated in Figure 4.31 where OMQ and OMPR are two oC a series of refraclion paths and DWS is the correspondíng lime-distance curve. Note Ihat this straight-Jine equation does not have pbysical mean· ing Ior offsels less than Xc because the reCracted wave does nol exisl in Ibis region. Nevertheless, we can projecl Ihe Jine back lo the time axis to find t¡. The problem to be solved usually is to find the depth z and the Iwo velocilies VI and Vz. The slope oC Ihe direCI·wave time·-dislance curve is the reciprocal of VI and the same measurement for the refrac· lion event gives V2 • We can Ihen calculate the critical angle Oc from Ihe relation 8e - sin- 1 (VI /V2 ), and use the intereept time ti to caleulate z {rom Equation (4.70). In Figure 4.31 the time-distanee curves for the renection from the interface A P and for the direct path are rcpresented by the hyperbola eDE and the straight line OF, respectively. Since the path OMQ ean be regarded either as a reftection or as the beginning oC Ihe reCraeted wave, the reftcetion and refraetion tíme-distanee curves must coíncide al X ... Xc' thal is, at the point D. Moreover, differential· ing Equation (4.47) to obtain the slope of the

1/ Vz and inlercepl time

Seismie methods

172 T

..,--+- - - -

I Slope = I

I

v: '

I I I I

I

I

IR'

,.,"

1'.

FIsure 4.32. Raypaths and IfilVe/time curves for Ihe Iwo-refraclor case.

refleetion time-distance curve al x - xc' we tind

~I

-

[

oii?+QMQ]

However, part of lhe refraelion path is traversed at velocity V1 , so that as x inereases, eventually the refraetion wave will overtake the direct wave. In Figure 4.31 these two traveltimes are equa! al the point W. IC the offset corresponding lo W is x'. we have

~(tOQ)

=

V¡

OM

1

1

- -sinO - VI < "í We see therefore that the refleetion and refraetion curves have the same slope al D, and consequently the refraetion curve is tangenl to lhe rcHcelion curve at x - xc' Comparing reHected and refracled waves [rom Ibe same horizon and arriving al the same geophone, we note that the refraction arrival time is always less Iban the reflection arriva! lime (exeept at D). The intercept time t j Cor the refraetion is less than the arrival time t o Cor the reHeetion at the shotpoint because tj

-

2z -coslJ.

V.

2z t

o

-

-

VI

hence 1, < lo

Starting at the poinl Q, we see that the direct wave arrives ahead oC the reftected and refracted waves beeause its path is the shortest oC the three.

(4.71) lbis relation sometimes is used lo find z fram measurements of the velocities and the crossover distance x'. However, usua!ly we can determine ti more accurately than x' and hcnce Equation (4.70) provides a beUer method of detennining z. (e) Several horizontal refraetors. Where all beds are horizontal, Equation (4.70) can be generalized 10 cover the case oC more than one refraeting horizon. Consider the situation in Figure 4.32 where we have Whenever three beds of velocities VI' Vz. and V2 > VI. we have the refraetion path OMPR and

v,.

113

Geometry of seismic wavepaths

corresponding time-distance curve WS. just as we had in Figure 4.31. If r-; > V2 > VI. the deeper reCraction will eventually overtake the shallower re(raction. Tbe reCraction paths such as OM' M" P" P' R' are fixed by Snell's law: sin 8

sin 8

1

- -1- - -c= -

(d) Effect of refractor dip.

The simple situations 00 which Equations (4.68) to (4.73) are based are frequently not valido One oC the most serious defects is the neglect of dip because dip changes tbe refraetion time-distance curve drastically. The lower part oC Figure 4.33 shows a vertical dip section through a refracting horizon. Let I be the traveltime for the refraction path AMPB. Then, we have

where Oc is the critical angle for the lower honzon whereas 91 is less Ihan the critica! ang!e 8: for the upper horizon. The expression for the traveltime curve ST is obtained as before:

I

=-

AM+ BP

V¡ ZA

+

MP

+V:z

zB

- ._--- + VI COS Oc

AQ -

(ZA

+ zB)tan8c V2

+ P'P" ,- aM' VI+ R'P' +M'M" ------

( 4.74)

2z

2z + - -2V1 cos 81 V2 cos 8c

1 ----=-

x - 2z1 tan 01

-

Ir we place the shotpoint at A and a detector at B, we are "shooting downdip." In this ease it is convenient lo have t in terms of the distance from the shotpoint to the refractor ZA' hence we eliminate Z B using the relation

2z 2 tan fJ,

+---~-~-~-~

V]

- -X +

r-;

+ X

2z 2

(

V1 COS 9,

1 - -I-í sin fJ

r-;

)

<

2 (1 _ r-;V¡ sin fJ ) Z1

V] cos 9]

Writiog

I

2z 1

2z]

1'1

X

Thus the time-distance curve for Ihis refraction is aIso a straight line whosc slope is the reciproca! of !he velocity just below the refracting honzon and whose intercept is the sum of terms oC the form (2z;/ V¡ cos 0i); each bed aboye Ihe rcfracting horizoo cootributes one termo We can generalize for n beds:

+

1- -

Vn

n-I

2z

;-1

-'cosO, V¡

L

(4.73)

X 2zA + -cos Oc sin t + -cos Oc

V¡

VI

x

( 4.72)

X

for the dowodip Iraveltime. we obtain

xcos~ Id = - -

- - + -cosfJ + -cosO¡ V, V1 < VI

- -V, +, 2

Id

2zA

- -sin(Oc +~) + -cosO, VI V¡ ( 4.75) where

2zA

(.~ - --cosO v, < 1

The resull for shooling in the updip direction is similarly obtained by eliminating lA: X

tu = -sin(Oc where 0/ - sin-I(v¡/V.) (note that 0i are no! critical angles except for 0._ ¡j. This equation can be used lo find the velocities and thlcknesses of each of a series ol horizontal refracting beds oC constant vc1ocity, provided each bed contributes enough of the time-distance curve to permit it to be analyzed correctly. Then we can find al! of the velocities (hence the ang!es O{ also) by measuriog Ihe s!opes of !he various sections of the time-distance curve and get the thicknesses of the beds from Ihe ¡o lercepts.

V¡

0+

ts

(4.76)

where

Note that the downdip traveltime from A to B is cqual to the updip traveltime from B to A. This shotpoint-to-shotpoint traveltime is called the recíproca/ lime and is denoted by Ir'

Seismic methods

114

l.

---------x-------------~~

--

..tco.s:{-- -- --

Figure 4.33. Raypaths and tri/ve/time curves for a dipping refractor.

lbese equations can be expressed in the same form as Equalion (4.70):

( 4.77)

be found from the inlercepls using Equations (4.75) and (4.76). Equation (4.78) can be sjmplified when t js small enough that we can approximate by leujng cos E... 1 and sin E... E. Witb Ibis simplification, Equation (4.78) bccome5

V. --1 =

where JI: ti

V" VI

v. -

n

--:-:--=----,-5in(8e +

sin( Oc _ E)

~ { sin

(-H

-1 (

sin-

~)

;

= w

v., and Vy are known as apparent velocilies and are given by lhe reciprocals of the slopes oC the time-distance curves. For reversed profiles 5uch as shown in Figure 4.33, Equation (4.78) can be solved lor the dip ~ and tbe critical angle 8. (and hcncc for the refractor velocity Vz): '. _

v.

(4.78)

+ sin - I (

~)}

5in(

'e + U .. sin', + t cos '.

sin( '. - E) - sin ' .. - t cos '.

hence VI

V¡(1

1)

sin 8 - -- ... -- -- + -• V2 2 v., Vw so that

( 4.80) ( 4.79)

I

(

~)

-

Sin-

lbe distances to the refractor,

I

(

ZA

~)} and

ZB'

can then

An even sjmpler approximate formula ler Va (altbough slight1y less accurate) can be obtained by applying the binomial theorem (§ A.6) to Equation (4.78) and assuming that ( is small enough tbat

175

Characrerisrics of seismic events

higher powers of

E are

negligible:

VI Vd .. --:--0 (cos E + COlOr sin

O-

1

Sin <

hence

(4.Rl) Equations similar to Equations (4.75) and (4.76) can be derived for a numbe r of beds that have the same dip and strike or other specific situalions. but 5uch equation5 are of Iimitcd value in praclice. N 01 only do they involve a largc amoun t of compu lation. but also one usually is not sure Ihal they are applicable to a specific real situation. Morcover. where there are more than two refracting horizons. i t is orlen diffieult to identify equivalent updip and downdip segments. espeeially if Ihe rcfractors are not plane or iC the díp and strike change.

4.4. CHARACTERISTICS OF SEISMIC EVENTS 4.4.1. Distin guishi ng Features of Events The basic task of interpreting reflcction seclions is that oC selecting those events on the record that represent primary reflections. transla ting Ihe travel· times of these rcflections into depths and dips. and mapping the reflecting horizons. In addition. the interpreter must be alert to other types of events Ihat may yield valuable inform ation. such as multiple reflections and di!fractions. Recognition and identification of seismic evcnls are based upon five eharacteristies: (a) coherence, (b) amplitude stando ut. (e) charac ter: (d) dip moveout. and (e) normal moveout. The first of these is by far the most import ant in recognizing an event. Whenever a wave recognizable as such reaches a sprcad. it produces approximalely the same eITec! on cach geophone. If the wave is streng enough 10 override other energy arriving at the same time. the lraces will look more-or-1ess alike during the interval in which this wave is arriving. This similari ty in appear ancc from trace to trace is called coherel1ce (Fig. 4.34) and is a necessary condition for the recognition of any event. Amplilude stal1daur rders 10 an inerease of amplitude such as results Crom the arrival of coherent energy. It

is nol always marked . especially when AGC (§ 4.5.3e) is uscd. Character refers lO a dislinctivc appear ance of Ihe waveform tha! identifies a particu lar evento something Ihat makes one event look di!ferent from anothe r evento It involves the shape of the envelope. the numbe r oC cycJes showing amplit ude stando ut. and irregularities in phase rcsulting from interCerence among compo nents of the cvent. Moueout. whieh refers to a system atic di!ference in the traceto-trace traveltime of an event, has been discussed in Section 4.3.1b, C. Coherence and amplit ude stando ut teH us whcthe r or not a strong seismic event is presen t, hut they say nolhin g about lhe type of event. Moveo ut is the most distinetive criterion for identif ying the nature oí evenls.

4_4.2_ Reflections and Refrac tions Refleclions exhibit normal moveo uts that must Call within certain limils sel by the velodt y distrib ution. The appare nt velocity (distan ce betwee n two geophones divided by the di!ference in traveltimes) is ver;¡ large for refleetions. usually greater Ihan 50 kmjs. Reflection events rsrc1y involve more than two or three cyc1es and are oCten rich in frequency compo nents in the range 15 to 50 Hz. Deep refleetions may have considerable energy be10w this range. Refractions are relatively low frequency events and they usually oseillate for more cycJes snd have mueh smaller appare nt velocities than retlections. In-line refractions and refteeted refraetiolls (refrac ted waves that are refleeted back toward the spread : see Fig. 4.35a) generally have straigh t alignments (prior to norma l-move out eorrect ion) in contra st with the curved alignments oC reflectioDs and dílfractions. Broadside reflected refraetions (Fig. 4.35c) have normal moveout approp riate to the refract or velocity. Refrac tions Crom deep refractors are not observed on reflection records except where the o!fsets are unusuaJly long or when the oecasional retlected refraction is recorded. Reflected refractions of the type shown in Figure 4.35b are one oC lhe reasons why refraction wavetrains are so long. A powerful technique for distinguishing between reflections. di!fractions, reflected refractions. and multiples is to examine gathers (§ 4.7.8) after correeting for (a) weathering and elevation (slatie eorrectinns. hecause the correction is the same for al1 arrival times on a given trace (see § 4.7.1). and (b) norma l moveout (dynamie corrections, because the amoun t of correet ion deereases with inereasing traveltime). Provided the corree I norma l mOVeout was removed. reflections appear (Fig. 4.36) as straigh t

Seismic methods

176 Amplitud. lIandout ('

~I:: -- - -:

,--<

Envelope

,

PhaK break

Figure 4.34. Charaeteristies of seismic events.

y

Shotpoin.

(b)

Geophonn

1<'

Figure 4.35. Reflected refraetíons. (a) Ref/ected refractions from faults and salt dome. (b) Multiply refleeted refraetion. (e) Broadside ref/eeted refraetion (plan view).

alignmcnts whereas dilfractions and multiples still have sorne curvature (because their normal moveouts are larger than those of primary reflections), and refractions and other formerly slraight alignments have inverse curvature.

The amplitude decreases rapidly as we go away from trus point. Dilfractions usually exhibit distinctive moveout. In Figure 4.37, for al) shotpoint and geophone positions 5uch that the point of reftection R is lo the ¡eH of A, the reftection traveltime curve is given by Equation (4.49), tbat is,

4.4.3. Diffractions Dilfractions are indistinguishable (rom reHections on the basis oC character. Tbe amplitude oC a dilfraction is a maxirnurn at sorne point along Ihe diH'raction curve, that is, where a reflection cvent termina tes (where the reftection is tangent lo the ditfraction).

assuming tbat x is srnaller tban h. The reftection trave\time curve i5 a hyperbola as shown in Figure

Characteristics

o(

seismic events

177

d

1-4

1·8 L-_ _ _ _ _----L_ _-S._:L-_..1

(., Bcf'ore normal movcout correctionl

(b)

Arter normal moveoul correctlons

figure 4.36. Types of events on a If'ismic record. Identitip~ af events are: a - direct wave, V - 650 mis; b - refraetían al base of weatheríng, VH - 1,640 mis; c - refraetian fram flal refractor, V¡¡ - 4,920 mi S; d - ref/ection (rom refractor c, 1,640 mis; e - refleetion (rom flat reflector, v'v - 1,970 mis; f - reflee/ion trom (Iat reflector, 2,300 mis; g = refleelian trom dipping refleelor, 2,630 mi s; h - mulliple af d; i - mul/iple of e; i = ground roll, V = 575 mis; k ~ .lir wave, V - 330 mis; / - refleeted refraetion from in-/ine disruplian of the refractor e; m reflected refraclion from broadside disruplion of refractor c. After norma/-moveout eorrectíon, prím.uy refleelíons are straight. In processíng. data are usually muted. thal is, dala earlier than thal indicaled by Ihe dashed /ines are set lo zero 50 that rhe data in the upper right comer do not appear.

v,. -

v.. -

v.. -

4.22. For the case where the shotpoint is directIy aboye the diffraction source A. the diffraction Irave!time curve is given by (he equation

DllTraction

x

2h

.. - + V

x2

2Vh

( 4.82)

figure 4.37. Dif(raclion trave/time CuNe.

Thus, the dilfraclion curve is also a hyperbola, bul with twice the normal moveoul of a rcftcction. The refleclion corresponds 10 a virtual source al a deplb of 2h wbcrcas tbe diffraction comes from a source al deplh h. The earliest lraveltimc on a diffraction curve is for the trace lhat is recordcd directly over

Seismic methods

178

J l l-"-'f l ~$ i'fj 11 f' ~ !

1: l' 11 l' I

1

; I

, I

I

I

\ -:.>

I I-... I I

r- ~l:: ~ .... -... ......

.... .... ... .... .... , .... ....

"-

....

..... ....

1 figure 4.38 Reflpuion and diffraction response of a s{ep for sources dnd receivers coincident. (Afu', H¡{(errnan. 1970.)

Ihe diffracting pOiOI (excepl Cor situalions with uousual velocity distributions). Figure 4.38 shows the response oJ a mode! Ihat demonstrates Ihe major properties of diffraclioo events. Thc erest of the diffraclion curves locales thc discontinuities (in the absence of velocily complications). relleetions that termínate at the diffracting poinl are langent lo the dilfraction curve, Ihe relleetion amplilude decreases as the end oC Ihe refleclion is approached. and Ihe refleclion is continuous wilh Ihe diffraction. The .. forward branch" of the diffraction (the branch that tends lo carry the reflection forward) is of opposite polarity lo the .. baekward branch" that Iies underneath Ihe reflection, and Ihe amplitude oC Corward and backward branches is equal at equal distances from the poinl where the reflection is langenl to the diffraction curves. Diffractions are very important in determining Ihe appearance oC reflections where the refleclors are nol continuous or plane. Figure 4.39 shows the events that are caused by a sharply bent reflector. The reflection lo Ihe right of x ~ 10,000 gives rise lo BP'; the reflection to Ihe left oC x = 10,000 gives A P. Diffraction fills in the gap PP' and makes Ihe seismic event continuous without a sharp break.

4.4.4. Multiples Multiples are cvcnts that have undcrgone more Ihan one reftection. Because 'the amplitude of multiples is proportional to the product of the reflection coefficients for each of the reflectors ¡nvolved and because these are very small for most interfaces, only the strongest impedance contrasts generatc multiplcs strong enough 10 be recognized as events. We may distinguish betwcen two c1asses of multipies. which we call long path and short path. A

long-parh mulliple is one whose travelpath is long compared with primary reflections from the same deep interfaces and hence long-path multiples appear as separate events on a seismic record. A shortparh mulriple, on Ihe olher hand. arrives so soon after the associated primary reflection that it interferes wi th and adds tail to the primary reflection; hence its effect is that of changing wave shape rather than producing a separate event. Possible raypalhs for these two c1asses are shown in Figure 4.40. The only important long-path multiples are those that have becn reflected once at the surface or base oC the LVL (§4.2.8b) and twice at deeper interfaces with relatively largc acoustic impedance contrasts. Because ER is about 50% at the base of the LVL and perhaps 5% Cor the strongest interfaces at depth. the maximum effective ER for such multiples will be oC the order of 0.05 x 0.5 x 0.05 - 0.001. 1bis value is in the range oC typical reflection coefficients So that such multiples may have sufficient energy to be con· fused with primary events. Note that the relative amplitudes of these multiples depend mainly on the reflection coefficients at depth. The principal siluation wherc weaker long-path multiples may be observable is where primary energy is nearly absent al the time oC arrival oC the muItiple energy so that the gain of the recording system is very high. Short-path multiples that have becn reftected successively from the top and base of thin reftectors (Fig. 4.41 a), often called peg-leg multiples, are important in a1tering wave shape. A peg-Ieg multiple delays part of the energy. thus lengthening the wavelet. Most peg-leg multiples tend to have tbe same polari ty as tbe primary (because successive large impedance contrasts lend to be in opposite directions; otberwise tbe suceessive large changes in velocity would cause the velocity to excecd its allowable range). This effectively lowers the signal

~

,

~

•

I

<>'0110-100. _ .

• + + +--~-,~

..-~

'."--'

-

.•..

.~

•

H-

+--I-H--++-i

..

~

¡-

!

~.

.. '-

- . +. +-.

._-,

-1-.

I I

1--+- +- .-1--- .... -+._+ ._+ --4--+-4- +-

-rH-1 rrlT1·· -.L

1"1'

-1----1 . I l' l.' . I 1J . .-1. - 0 I

- .. +--1---

..

+ --+--+-1--1--+---1-+-+--+

I

I

. I

n·",..

......,

.. ~ J:.¡

+-

"lOO

·-t··- ~--4 ~

. ·1'

I

(t.lI'IO

0-«1"·

11'" .• : . ¡'lf' l" ..-":¡-'_ ..:' .: ¡:'. '~. . . . . !!~~=. . .~

.i

!

el

-+--+--+-- l' I 1. ..... . , -' .

1 1I

I

1:1..:.J-~1 .

--

• "1

1

...

~

'-*--:-++++--+++1 1 tti?·~,..

I-Im" ..

T-~

,

''''''........+._+,....

-.~' '-".

'

.....

==¡-'

,.

, .. ~

. . ¡.

lOO'"

,

!

I

--+-

L l:9F

':-'IT ~/~-

...... I

.. 1

1

..

i

1" ....

:

"

'

-1

.. ,

:::

.,

. '

,

.

,

. "- . -, ! ..- 1:' ........ .,. '--" l..

. •

! '

. I . I

.:.rr-':7r1. .,¡,!..

'.' :

l.

i:

'-y

MOot-

1 .. '.

. . ¡~~~ r(.:..... ; '.:': -¡!::.': . I I ~< f; I -+. =-,.'J" 1··111··.14-+·.··.··.·· ." .. ' '. . -" .... _-.~:..... .~ ... - _ ::': .. .' . ' ,: '8''#'' ~: ¡; ,< :, :': .,. . 'l"

, ....f- - ¡--f

"""'.'1

...., : . '

:

.,;

. '

r-, 11;.. > - - _. ...-

t .• , , '

':

'

;.

I!"

.!

.

..

o • . 'l, '

.•

~l

r.

:,.

~.,

i _.~!

:

:,: '

. , . t"" t'!~1 'r'H'". ,: . ";~~I"7: .. ,:¡ :(: ~. :'~:: :':0 ::~. " .

- -T-+·:

l'

l.

I .

"'1 ",' •.

.,¡, ",~.". •. " .

..

"'p' ','

......

:

·'I:.¡,,;.:.L':' .':. :', --:-T: ! I ! : ~ ; :í' '.': •

'1·'

~

~

¡

::P 'o"~

Figure 4.39. Ref1ectioru ..nd dif(radions from .. sharply bent reflector. The reflector dips 3 parts in 5 to the leh of x - 10,cn>, 1 part in 5 to the right. (Courtesy Chevron Oil Ca.)

180

Seismic methods Shorr-palh

lona-palh

.

.

mulliDI••

mullipl..

su,race

Other rcftec:lon

Figure 4.40. Types

\\ W.v.... in

a.

o{

mu(tiples.

O·6M6.

~ \\\\\\\ Wavelrain &11·372 S

(

..,

Afie, 0,686,

Ane, 2·744 s

o

I

o

~

100

I

I lOO ms

~

Ibl Figure 4.41. Changes in waveshape resulling Irom passage through a layered sequence. (Alter O'Doherly and AnSley, 1971.) (a) Schematic diagrdm showing peg-Ieg multiples. (b) W,¡velrains dlter different trilveltimes.

Characteristícs of seism;c evenrs

181 /,

",• \

1" \

I iI \ I

I

L.

\

;91

\

\

"

,,

I

/

"

\ \

\

G,

\ \

\

\

\

\

'1'

\~\

\

/,\,

\

/

'

I

/

\"

\

, \ , \1' ,.

\

,

\\ l/Ir /

,

1,

\

,

'f

\

I

I

/ I /

\'

\ 1 1 1

I I

I

I I I

\ \

I

/

\,

I

I

/

/

/

/

\1 I \11

...

1,

F/gure 442. I?aypalh of a mu/r/ple from J dipping bed.

frequency as time increases (O'Doherty and Ansley, 1971). Figure 4.41b shows how a simple impulse becomes modified as a resull ol passing it through a sequence 01 interfaces. lbe refteclion-seismic lechnique is based on Ihe assumplion oC simple waves sueh as those in Figures 4.22 and 4.23. Thus il is importanl Ihal long-palh multiples be recogn.iz.ed as such so Ihat Ihey wilJ nol be inlerpreled as reHcelions lrom dccper honzons, Because veloeily generally increases wilh depth. multiples usua11y exhibit more normal moveout than primBJ)' reflections wilh the same Iraveltime. This is the basis of Ihe attenualion of multiples in common-midpoinl proeessing thal will be discussed in Section 4.7.8. However, Ihe dilference in normal moveout often is nol large enough lo identify mUltipies. The elfect oC dip on multiples that involve the surface or tbe base 01 the LVL can be seen by tracing rays using the method of images. In Figure 4.42, we trace a mulliple arriving al syrnmetrically

disposed geophones G1 and G24 • The first image poinl l. is on Ihe perpendicular from S lo AB as lar bclow A B as S is aboye. We next draw tbe perpendicular from l. lo Ibe surface of the ground where Ihe second reflection oecurs and place 12 as far aboye the surface as I 1 is below. Fina11y, we loeate IJ on Ibe perpendicular lo AB as far below as 12 is aboye, We can now draw the rays lrom the source S lo the geophones (working backward from tbe geophones). The dip moveout is the difference between the path lengths I]G 24 and IJG•• Jt is about double Ihal 01 the primary (llG24 - IIG I ). The muttipte at the shotpoint will appear lo come from I J , whicb is updip from 11 , lhe image point for the primary, and 'JS is slightly less than twice 11S. Hence we can see Ihat if the reflector dips, tbc multiple involves a slightly different portion of the reflector than tbe primary and has a traveltime sligbt1y less tban double Ihe lraveltime of tbe primary. The latter facl makes identifying multiples by merely doubling tbc arrival time of the primBJ)' imprecise whenever

5eismic methods

182

appreciable dip is presen\. The arrival time of the multiple will be approx.imately equal to that oC a primary reflection from a bed at the depth of 11 , If the actual dip at I 1 is not double that at A B (and one would noto in general, cxpecI sueh a dip). then the multiple will appear to have annmalous dip. If the multiple should be rrusidentified as a primary, one might incorrectly postulate an unconformity or updip thinning that might lead lo erroneous geologie conc\usions. Ghosts are the special type oC multiple illustraled in Figure 4.40. Tbe energy traveling downward Crom lhe shot has superimposed on il cncrgy Ihat initially traveled upward and was then reflected downward at the base of the L VL (in land surveys) or at the surCace of the water (in marine surveys). A 180 0 phase shiCt, equivalent lO half a wavelength, occurs at the additional reflection, and hence !he elfective palh difference between Ihe dircel wavc and Ihe ghost is (V2 + 2d), where d is Ihe deplh of Ihe shot below the reflector producing Ihe ghos\. The interference between the ghost and the primary depends on the fraction of a wavelength represented by the difference in effective path length. Because the scismic wavelet is made up oC a range oC Crequencies, lhe interference effect will vary Cor Ihe different components. Thus, lhe overall elfect on Ihe wavelel sbape will vary as d is varied. Relatively small changes in shot deplh can result in large varialions in reflection character, creating serious problems Cor Ibe interpreter. Therefore the depth oC the shot below the base oC the weatbcring or the surCaee oC the water is maintained as nearly constant as possible. Ghosts are especially important in marine surveys because the surCace oC the water is almost a perCect reflector and consequently Ihc ghost interCerence will be strong. Ir d is small in comparison with the dominant wavelengths, appreciable signal cancellation will occur. At depths oC 10 to 15 m, interference is constructive Cor Crequencies ol 25 to 40 Hz, which is in the usual seismic range. The same clfeet occurs with respect to hydrophones at depth. Hence marine sources and detectors are oCten operated at such depths, A particularly troublesome type oC multiple produces the coherent noise known as singing (also called ringing or water reverberation) that is Crequently encountered in marine work (and oceasionally on land). This is due lo multiple refleclÍons in the water layer. The large reflection coefficients at lhe top and botlom oC this layer result in considerable energy being retleeted baek and Corth repeatedly; the reverberating energy is reinCorced periadícally by reflected energy. Depending on the water depth, certain Crequencies are enhanced, and as a result Ihe record looks very sinusoidal (Fig. 4.43).

Not only is the picking oC reflections difficult, but measurcd traveltimes and dip moveouts will probably be in error. 11lÍs type oC noise and its attenualion are discussed in Section 4.7.3d.

4.4.5. Surface Waves Surface waves (oCten callcd groulld roll) are usually present on reflection records. For the most part, these are Rayleigh waves with velocities ranging from lOO 10 1000 mis or so. Ground roll frequencies usually are lower than those oC reflections and refraetions, often with the energy eoncentrated below 10 Hz. Ground roll alignments are straighl, just as reCractions are, bUI they represent lower velocities, The cnvelope ol ground roll builds up and decays very slowly and oflen inc\udes many cyc1es. Ground rol1 energy gene rally is high cnough even in the retleetion band lo override al1 but the strongesl reflections. However, because oC the low velocity, diCrerent geophone groups are affecled al different times so that only a Cew groups are affected at any one time. Sometimes tbere is more than one ground roll wavetrain, each with different velocities. Occasionally wbere ground rol1 is exceptionally slrong, in-line offsets are used so that desired reflections can be recorded beCore the surCace waves reach Ihe spread.

4.4.6. Effects of Reflector Curvature Geometric focusing as a result oC curvalure of a ret1ector affects Ihe ampli tude of a reftection. Over anticlinal curvature reftected raypaths diverge, which results in reduced energy density. Strengthening oC reflections occurs over genlle synclines. Energy focusing as a result oC Ihe concave-mirror effect makes more oC tbe reftector surface effective Cor producing a ret1ection. If the center 01 curvature oC a reflector lies on the surCace oC lhe ground, lhe amplitude may be so large that the evenl will not be passed by the recording systcm. If the curvature oC a synclinal reflector is great enough, lhe energy focuses below tbe surCace oC the ground (see the two deeper reftections in Fig. 4.44) and a buried focus occurs. For a given surface localÍon, ret1ections may be obtained Crom more Ihan one part of !he reflector; tbe time-distance curve is no longer a simple curve, bUI has several branches, most commonly three. The two deeper reflections in Figure 4.44 involve buried Coci; each shows branches Crom each Hanlc oC the syncline plus a reverse branch Crom tbe curved bottom oC the syncline. Obviously Ibe likelihood oC occurrence oC a buried focus increases with reflector deplh.

183

Characteristícs of seismic events

(a)

(b)

Figure 4.43. Seismic record showing singing. (Courtesy Geosource Inc.) (a) Field record. (b) Same afler singing has been removed by deconvolution proces~ing (§4.7.3d)

,

The waves producing the reverse branch pass Ihrough a focus. which results in a 90° phase shift relative to waves thal do not pass through the focus (Sheriff and Geldart. 1982. p. 116); however, this phase shiCt is rarely useful in identifying buried-focus elfects. Nevertheless, it would alfect calculations oC reflector depth in the syncline if picking were done systematically on the same phase, Cor example, al-

ways in the troughs. The reverse branch is so named because tbe point oC reflection traverses the reflector in the opposite direction Crom the surface traverse. Thus, in Figure 4.44, as one moves from leCt to right on the surface, the reflection point Cor the reverse branch moves from right to left. Just as Iight can be focused by passing through a lens. seismic waves can also be focused by curved

Seismic methods

184

Figure 4.44. Reflections from curved reflector. In all cases. reflector radius of curvature - J.()(XJ m. V - 2lXXJ mis. Deplhs lo Ihe bottom 01 Ihe syncline are 800. 1,200. and 1.600 m. respectively, for the three reflectors. The traces are 100 m apart. (Courlesy Chevron Oil Co.)

velocity surfaces, which results in seismie rays being beot by refraction; such situations are oflen very complexo Curvature at the base of the weathering can be especially important because or the large velocity contrast usually associated with this surraee. Variations in permafrost thickness espeeially cause lens-type effeets.

4.4.7. Types of Seismic Noise Tbe reliability oí seismie mapping is strongly dependent 00 tbe quality oC the reeords. However, tbe quality oI seismie data varies tremendously. At one extreme we have areas where e¡¡cellent refleetions (or relractions) are obtaioed without any spedal measures beiog talteo; al the other extreme are those areas io which the most modem equipment, extremely complex fie1d techniques, and sophisticated data processing metbods do nol yield usable data (olten called NR oreas, that is. area~ oC no reflections). lo between these extremes lie the vast majority oC areas io which useCul results are obtained bul

the quantity and qualily oC tbe data could be improved with beneficial results. We use the term signa/ to denote any evenl on the seismic record Crom which we wish to obtain information. Everything e1se is noise, ineluding coherent events Ihat interrere with the observation and measurement oC signals. The signal-to-noise ratio, abbreviated S/N, is the ratio oC tbe signal energy io a specified portion of the record to the totaJ noise energy in the same portian. Poor record s result whenever the signal-to-noise ratio is smal); just how small ¡s, to sorne extent, a subjective judgmeot. Nevertheless. when S/N is less than unity. the record quality ís usually marginal and deteriorates rapidly as the ratio decreases Curther. Scismic noise may be either (a) cobereot or (b) incoherent. Coherent noise can be Collowed across at least a few traces, unlike incoherent noise where we cannot predict wbat a trace will be like trom a knowledge of nearby traces. Often the difference between cohereot and incoherent noise is merely a matter of scale and, if we had geophooes more

Character;st;c5 of se;sm;c evenrs

cJosely spaced, incoherent noise would he seen as coherent. Nevertbeless. incohercnt noise is defined with respect to the records being used without regard for what closer spacing might reveal. Incoherent noise is often referred lo as random noise (spatially random), which Implics not only nonpredictability but also certain statis(¡cal propertieso More often than nol the nOlsc 1$ not mil" random. (It should be noted that spaliaJ randomness and time randomness may be indcpendcnt: the usual seismic trace is apt to be random in time hecause we do nol know when a reHection wiU oceur on the basis 01 what the trace has shown previously, with tbe exeeption of multiples.) Coberent noisc is sometimes subdividcd into (a) energy that travels essentially horizon tally and (h) energy that reaches the spread more or less vertically. Anothcr important distinetion is betwccn (a) noise that is repeatable and (h) noisc that is nol; in other words, whether the same noise is ohserved at the same time on the same trace when a shot is repeated. The tbrcc propertics - cohercnce. trave! direction, and repeatability - form Ihe basis of most metbods of improving record quality. Coherent noise ineludes surface waves. reHections or reflected reCraclions from near-surface strucmres such as Cault planes or buried Slrcam channels, refractions carried by high-veloci Iy stringers. noise caused by vehieular traffie or farm Iraelors. multipies, and so Corth. AlI oC Ibe preceding exccpt multipies travel essentially horizonlally and all except vehicu)ar noise are repeatable 00 successivc shols. Incoherent noise, which is spalially random and aIso repeatable, is duc to scattering from ncar-surface irregularities and inhomogeneities such as bouldcrs, small-scale Caulting, and so forth. Such noisc sources are so small and so near the spread Ihat the oulputs oC two geopbones wiU only be the same when the geophones are placed almosl side by sirle. Nonrepe atable random noise may be due lo wind ~haking a geophonc or causing Ihe rools oC trccs 10 move. which generates seismic waves. stones eJccled by the shot and falling back lo Ihe earlh ncar a gcophone. occan waves beating on a seashore. dislant earthquakes, a person walking ncar a p,cophonc, and so on.

4.4.8. Attenuation of Noise

Ir Ihe noise has appreciable energy oulside Ihe principal frequency range of Ihe signal, frequency filtering can be used to advanlage. Very low-frequency components (such as high-energy ~urface waves rich in )ow frequencies) may be attenuated during Ihe initial recording provided the low frequencies are

•

185 sufficiently separated Crom the reflection Crequencies. However. Ihe spectrum oC the noise often overlaps the signal spectrum and tben frequency filtering is of Iimited value in improving record quality_ Witb modem digital recording, \he only low-Irequency filtering used in the field is oClen that resulting from the low-frequency response of the geopbones. Ir we add several random noises logether, there will be sorne cancellation because they will be out oC phasc with each olher. If they are truly random in the stalistical sense, the sum oC n random signals will be proportional to ¡ n, whereas the sum oC n coherent in-phase signals will be proportional to n so thal lhe signal-to-noisc ratio will be improved by the factor .¡ n (Sheriff and Geldart. 1982. p. 126)_ This principie is the basis oC the use of multiple geophones or multiple sources (ealled geophone or source arra¡;s: see §4.5.2c) to cancel noise. If wc connect together. for example, 16 geophones that are spaced far enough apart Ihat the noise is spatially random bUI still c10se enough together thal reflected energy traveling almost vertically is esscntially in phase at a1116 geophones, the sum oC the 16 outputs will have a signal-Io-noisc ratio 4 times greater than tbe output when the 16 geophones are placed si de by si de_ IC, on the other hand, we are attenuating coherent noise and the 16 geophones are spread evenly over one wavelength oC a coherent noisc wavetrain (for examplc, ground roll), then the coherent noise will be greally reduced_ Noise can also be attenualed by adding together traces shot at different times or differenl places or hoth. This forms the basis oC several stacking techniques inc\uding vertical stacking. common-midpoint stacking, uphole stacking, and several more complicated methods (§4.7.9 and §4.7.13a). The gain in record quality oCten is large because oC a reduction of both random and coherent noise. Provided the static and dynamic corrections are accuralely made, signal-Io-nose improvements for random noise should be aboul 5 Cor 24-Cold stacking_ Vertical stacking involves combining several record s for which both the source and geophone locations remain Ihe same. It is extensively used with weak surCace energy sourees (§4.5.3c). Vertical stacking usually implies that no Irace-to-trace corrections are applied but that corresponding traces on separate records are merely .added to each other. The eITect, therefore. is cssentially the same as simultaneously using multiple shots or multiple source units. In difficult areas, both multiple source units and vertical slacking may be used. In actual practice. the surface souree is moved somewhat (3 to 10 m) between the shots. Up 10 20 or more separate records may be verlically stacked; the stacking is onen done in (he fieId, sometimes in subsequent processing.

Seismic methods

186

Marine vertical stacking rarely involves more than 4 records because at normal sbip speeds the ship moves so far that data would be smeared when staeked. Smearing means that ehanges in the retleeting points alreet the arrival times so mueh tbal the signal may be adversely affeeted by summing (tbe effeet is similar lo using a very large geopbone or souree array). The common-midpoint teehnique is very elreetive in attenuating several kinds of noise. The summation traces comprise energy from several sbots using different geophone and sourcepoint locations. lbe field teehnique will be diseussed in Seelion 4.5.2a and lhe processing (which is almost always done in a processing center rather than in the field) in Seetion 4.7.8.

4.5. REFLECTION FIELD METHODS AND EQUIPMENT 4.5.1. Field Methods for Land Surveys (a) The programo Usually the seisnuc crew receives tbe program in tbe form of Iines on a map that

indicate where data are to be ohtained. Before beginning a sUTVey the following question sbould be asked: "Is it probable that the proposed lines will provide the requi red information?" Data migration (§4.7.12) may require that lines be located elsewhere than direetly on top of features in order to measure critical aspeets o( a strueture. Crestal arcas may be so extensively fauHed that lines aeross them are nondefinitive. The structures being sought may be beyond seismie resolving power. Near-surface variations may be so large that the data are diffieult lo interpret whereas moving the seismic line a short distance may improve data quality. Obstructions along a proposed line may inerease difficulties unnecessarily, wbereas moving tbe line slightly may achieve the same objectives at reduced cost. Where tbe dip is considerable, merely running a seismic line lo a wellhead may nol tie tbe seisnUc data to the well data Lines may not extend sufficiently beyond faults and other features to establish the existence of such features unambiguously or to determine fautt displacements. Lines may eross fentures sueh as Caults so obliquely tbat tbeir evidences are not readily interpretable. Laek of eros s control may result in features located below the seisnUe ¡ine being confused by (eatures to tbe side oC the line. (b) Permitting. Once lhe seismic program has been decided on, it is usually necessary to secure permission to enter tbe land to be traversed. Permission lO enler may involve a payment, often a lixed sum per source location, as compensation in advance for "damages lhal may be incurred." Even where tbe

surf ace owners do not have lbe right lo prevent entry. it is advantageous to explain the nature of the impending operations. Of eourse. a seismie crew is responsihle Cor damages resulting from their aetions whether or not permission is required to carry out the sUTVey. The survey crew lays out the lines to be shot, usually by a tr~it-and-chain survey Ihat determines the positions and elevations oC both the soureepoints and the centers of geophone groups. The chain is oCten a wire equal in length to the geophone group intervalo Suceessive group centers are laid out along the line, and eaeh center is marked by means of brightly colored plastie ribbon ealled flagging. The transit is used lo keep the line straight and 10 obtain tbe elevation of each group eenter by sighting on a rod carried by the lead ehainman. Many varlations from lbe aboye procedures are used depending on tbe sort of terrain being traversed. Electronie distance rneasuring (EDM) inslruments are generally used (§B.2; also Sherilr and Geldarl, 1982, pp. 134- 5). Plane tables and a1idades are occasionally used. Ties to benchmarks and wellhcads are oCten made by transit theodolite and rod rather than by chaining. Side features are often tied in by triangulation. The surveyor sbould indicate in bis data and maps the locations of aH imporlant features, sueh as strearns, buildings, roads, and fences. The surveyor also plans access routes so tbat drills, recording trucks, and so forlb, can get lO their required locations most expeditiously. In areas of difficult terrain or beavy vegetation, trail-building or Irail-eutting crews may be required. Tbese ofteo precede tbe survey crew bUI usually are under tbe supcrvision of the sUrveyor, wbo is lherefore responsible for the preparation of a straighl lraíl io the proper location. (e) Laying out the line.

The next unit 00 tbe scene is tbe drilling crew (when explosives are used as the energy source). Depending on the number and depth ol boles required and the ease of drilling, a seismic erew will gene rally have from one to Cour drilliog crews. Whenever conditions permit, tbe drills are truck-mounted. Waler lrucks are often required lo supply the drills witb water lor dril\ing. In areas of rough terrain, the drills may be mounted on traetors or portable drilling equipment may be used. In swampy areas, the drills are often mounted on amphibious vehicles. Usually the dril\ing erew places tbe explosive in the holes before leaving the site. (d) Shothole drilling.

(e) Reeording. The dril\ing erews are followed by Ihe recordiog uni!. lbis unit can be divided iD10

Reflection field methods and equlpmerrt

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three groups on the basis of primarv function: the shooting crew. who are responsible for loading the shotholes (ir the drillers have not alrcady loaded them) and for setting off the explosivc. the jug hustlers, who layout the cables. placc the geophones in their proper locations. and connec! them inlo the cables, and the recording crew. who do lhe actual recording of the signals. With common-midpoint recording. shotpoints are aboul 100 m apart, so high production amI high efficiency are needed to achieve a low COSI pcr kilometer. Redundancy of coverage has lessened the dependence on any individual record so that occa· sional missed record S can be tolerated. Also, the broad dynamic range oC digital recording has removed much of the need for filtcring in the field and Ihe need to tailor instmment settings to particular local conditions. Cost considcrations dictate that the recording operation must not wait on other units. ShothoIes may be drilled for the entire line before the recording crew begins so that il need m'ver wait on the drilIs. Extra cables and geophones are laid out and checked in advance oI the recording unit. A roll-along switch is used, whieh makcs it possible Cor the recording unit to be physically locatcd at a different place than where it is located electricalIy. The recording unit connecls to the scismic cable al any convenient location, 1m cl\ample. rhe intersection of a road and the seismic line. Thc roll-a1ong switch is adjusted so that the proper geophones are connecled and the shooters are ínstructed to operatc the bIas ter. Following the shot. Ihe shooters movc on to the next shothole (which is not very far away) and the observer (instrument operator) adjusts lhe rollalong switch so that the next geophoncs are connected. The time belween shots may be onlv a few minutes and the recording truck may no! movc all day long. Holes wherc misfires oceur are not rcloadcd and reshot. The shootíng unit olten walks the line because they need no equipment exeept the blasler and firing line and perhaps shovels lo fill in the shothole after the shot. Damagcs are redueed because less equipment traverses the lineo Thus othcr benefits accrue besides inereascd recording cm· ciency. When a seismic crew uses a surface energy source. the source units move into place and a signal from the recording truck activa tes Ihe somer trucks so that the energy is introduced into the ground at the proper time. Despite the Caet that an explosíve may not be involved, terms such as .. shot" and .. shotpoint" are still used. The energy from each surface source usually is small compared to tbe energy from a dynamite explosion so that many reeords are made for each source location and verlieally stacked to make a single record. The source units may advanee

187

a few metcrs hetween Ihe componenl subshots, which will be combined to make one record. It is nol uncommon 10 use 3 or 4 source trucks and combine 30 or so component subshots. A monitor record is usunlly made in Ihe field, either in parallel with the recording or by playback of tbe magnetic tape. These monitor records are cheeked to makc certain Ihat the equipment is funetioníng properly and also to determine weathering corrections (discussed in §4. 7.1). The magnetíc tapes are shipped lo a data processing eenter where correetions are applied and various proecssing techniques are used, ror example, velocity analysis. filtering, stacking. and migration (§4.7). The cnd result of Ihe data proeessing is usually record sections from which an interpretation is made.

4.5.2. Field layouts (J) Split-dip

and common-midpoint recording.

Virtually all routine seismic work consists of continuOILl' couerage (profilmg), that is, the cables and sourcepoints are arranged so that tbere are no gaps in Ibe data other Ihan thosc due to the fact that the geophone groups are spaced al inlervals rather than continuously spaced. Single eoverage implies Ihal each reftccting poinl is sampled only once, in contrast to common-midpoint. or redundam, coverage whcre each refteeting point is sampled more Ihan once. Areal or eross coverage indica les Ihat the dip components perpendicular to the seismic line have been measured as well as Ihe dip components along the line. Each of Ihese methods can employ various relationships between sources and geophone groups. Single coverage split-dip shooting is iIlustrated in Figure 4.45. Soureepoints are laid out at regular intervals a10ng the line oC profiling, often 400 to 540 m apar!. A seismic cable is laid on the ground with provision for eonnecting groups oC geophones al regular intervals (called lhe group illterval). Thus. witb sourcepoints 400 m apart and 24 groups, the group eenters are 36.4 m apart. With the cable strelched from 0 1 to ~, source (shot) ~ is tired, which gives subsurface control (for flat dip) between A and B, The portion oC cable between O) and ~ is then moved between 0 3 and O. and source ~ is shot; Ihis gives subsurface coverage between B and C. The travelpath for the last group rrom source OJ is the rcversed path for the tirst group from source ~ so that tbe subsurface coverage is continuous a10ng lhe lineo Common-midpoint (CMP) or rol1-along shooting is illustrated in Figure 4.46a (Mayne, 1962, 1967). We ha ve evenly spaeed geophone groups Ihat we number by Iheir sequence along Ihe seismic line rather than by the trace tbal Ihey represent on the

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seismic record. Geopbone groups 1 lo 24 are connecled 10 tbo amplifier inputs in tbe reeording truek and sbot A is fired, As~uming a horizontal reneetar, tbis gives subsurfacc coverage from a to g, Geaphone groups 3 to 26 are tben connccted to the amplifier inputs; the cbange is made by means of tbe ron-aJong switch rather than by physically moving

the seismic cable. Shot B is then fired, wbich gives subsurfaee coverage from b to h. Shot e is now fired into geophones 5 lo 28, which gives coverage from e lo j, and so on down tbe seismic line. Note tbat the reftecting point for tbe energy from shot A mto geophone group 21 is point /, which is aJso the renecting point for Ihe energy from B into geopbone

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group 19, from Cinto 17, from D into 15, from E into 13 and from Finto 11. After normal-moveout removal using a stacking velocity (§4.5.5c). these traces will be combined (stacked) in a subsequent data processing operations. Thus reHecting point f is sampled six times and the coverage is called sixCold recording. Obviously, the multiplicity tapers off at each end oC the lineo Most present-day recording uses 96 or more geophone groups and 24- lo 48-fold multiplicity. Occasiona1ly one oC the regularly spaced locations will not be a suitable place for a shothole (perhaps because 01 risk of damage lO nearby buildings) and an irregularly spaced shotpoint will be used. Thus if shotpoint E (Fig. 4.46a) could not be used, a shot might be taken at E' instead and then geophone group 14 (instead oC 13) would receive the energy reftected at f. To help keep track oC the many traces involved, stacking charts are used (Morgan, 1970). Figure 4.46b shows the stacking chart when E' is shot instead of E. Note how the six traces which have the common midpoint f line up along a diagonal; points along the opposite diagonal have a common offset whereas points on a horizontal !lne have the same shotpoint and points on a vertical line represent traces Crom a common geophone group. Stacking charts are useful in making static and dynamic correclions and to ensure that the traces are properIy stacked. (b) Spread types. By spread we mean the relative locations of the sourcepoint and the centers of the geopbone groups used to record the energy from the source. Several spread types are shown in Figure 4.47. In split-dip shooting the sourcepoint is at the center of a line of regularly spaced geophone groups. Placing the source c10se to a geophone grO\'p oCten results in a noisy trace (because of ground rol1 or truck Doise with a surface source, or gases escaping

from the shothole and ejection oC tamping material); hence the source may be moved 15 to 50 m perpendicular to the seismic lineo Often the geophone groups nearest the source are not used, which creates a sourcepoint (shotpoint) gap. OCten the source is at the end of lhe spread of active geophone groups lO produce an end-on spread, and in areas oC exceptionally heavy ground roll the sourcepoint is offset an appreciable distance (oflen 500 to 700 m) along the line from the nearest active geophone group to produce an in-line offset spread. Alternatively, the sourcepoint may be offset in the direction normal to the cable. either al one end oC the active part to produce a broadside-L or opposite the center to give a broadside-T spread. End-on and in-line offset spreads oCten employ sources off each end to give continuous coverage and two records for each spread. The in-line and broadside offsets permit recording ref1ection energy beCore the ground-roll energy arrives at the spread. Cross spreads, which consist of two lines ol geophone groups roughly al right angles to each other, are used to record threedimensional dip information. (e) Arrays. The term array reCers either to the pattem of geophones that feeds a single channel or to a distribution oC shotholes or surface energy sources that are fired simultaneously; it also ineludes the differenl locations oC sources for which the resuIts are combined by vertical stacking. A wave approaching the surface in (he vertical direction wi11 affect each geophone or an array simultaneously so that (he outputs wi11 combine constructively whereas a wave traveling horizontal1y wi11 affect the various geophones at dilferent times so that there wi11 be a certain degree of destructive interference. Similarly, waves traveling vertically downward Crom a source array will add constructively whereas waves traveling horizontally away from the source array will arrive at

190

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Fi8ure 4.48. Response o( arrays to 30 Hz signa/o The overalllength o( the array, which is the factor contro/ling Ihe width of Ihe (irst peak, ;s the same for all three arrays. The location o( the principal secondary (alias) peak is controlled by Ihe elemenl spacing. Weighting increases the attenualion ;n Ihe reject reg;on. The dotled curves indieate the array response lo a bell-shaped frequeney spectrum peaked al 30 Hz wilh a width of 30 Hz. (Courtesy Chevron Oil Co.) (a) Five in-line geophones spaced 10 m aparl. (b) Ceophones spaced 10 m apart and weighted 1,2,3,2, 1. (e) Nine geophones spaced 5.5 m aparto

a geophone with dilferent phases and will be partially cancelled, Thus, arrays provide a means of discriminating between waves arriving from dilferent directioos. Arrays are linear wben the elements are spread aJoog the seismic line or areal when the group is distributed over an area. The response of a geopbone array is usually illustrated by a grapb (sueb as Fig. 4.48) that shows the output of the array compared to tbe output of the same number of geophones coneen-

trated at one location. The response is usually given for a sine-wave input and plotted against a dimensionless variable, such as the ratio of the appareot wavelength to the element spacing (or some other key dimension of the array). Theoretically we get the same results by using 1 sourcepoint and 16 geophones as by using 1 geopbone and 16 sourcepoints spaced in the same manner; however, we use multiple geophones much more than multiple sources beeause the cost is less, al-

Reflection field methods and equipment

191

Figure 4.49. Noise analysis or walkaway. The vibroseis source Witll geophones spaced 1.5 m apart is offser 425 m ro rhe firsr geophone. Identificarion of evenrs: 1,890 mis arrival - re/raction Irom base 01 weathering; 530 and 620 mis - ground-roll modes; 330 mis - air wave; 3,140 mis - refraction evento (Afler Sheriff, 1984).

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though in exceptionally difficult areas, both multiple sources and multiple geophones are used at the same time, The canceling of horizontally traveling coherent noise by using geophone and source arrays presents a more challenging array design problem than the cancellation of random noise. In the case of random noise, the locations of the elements oC the array are unimportant provided they are not so c10se that the noise is identical. For coherent noise the size, spacing, and orientation of the array must be selected on the basis of the properties oC the noise to be canceled (Schoenberger, 1970). If the noise is a long sinusoidal wavetrain, an array consisting of n e1ements spaced along tbe direction of travel of the wave at intervals oC Aln, where Jo.. is the apparent wavelength, will provide cancellation. However. actual noise often consists oC several types that arrive Crom differenl directions; each type invariably comprises a range oC wavelengths. Moreover, the nature oC the noise may change from point to point along the line. One can apply the principIes oí antenna design to obtain maximum cancellalion Cor a band of Crequencies approaching Ihe spread Crom an arbitrary direction. and numerous articles have been written on the subject oC arrays. A review paper by McKay (1954)

shows examples of the improvement in record quality for dilferent arrays_ In addition to the difficulties in defining the noise wavelengths 10 be attenuated, actual field layouts rarely correspond with their theoretical design (Newman and Mahoney, 1973). Measuring Ihe location of individual geophones is no! practicable because oC Ihe time required. In heavy brush one may have lo delour when laying out successive geophones and oCten one cannot see from one geophone to another, so tha! even the orientation oC lines oC geophones can be irregular. In rough topography maintaining an array design might require that geophones be at different elevations, which may produce Car worse elfecls Ihan lhose Ihat the array is in tended lo elimina te. Similar problems arise where the condilions for planting the geophones vary within a group (Lamer, 1970), perhaps as a result of loose sand, mucky soil, or scattered rock outcrops. The besl rules for array design are oCten (1) to determine the maximum size Ihal can be permitted without discriminating againsl events with Ihe maximum anticipated dip and (2) lo distribute as many geophones as field economy will permit more-or-Iess uniformly over an area a Iiule less than the maximum size permitted, mainlaining a11 geophone plants and

192

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elevations as nearly constant as possible even iC this requires severe distortion oC the layout. (d) Noise .malysis. Systematic investigation oC coberent noise oCten begins with shooting a noise profile (also called a microspread or walkaway). This is a small-scale profile wi th a single geophone per trace, the geopbones being spaced as c10sely as 1 lO 3 m over a total spread length oC the order of 300 m or more. If tbe weatbering or elevation is variable, corrections should be made lor each trace. The corrected data, such as shown in Figure 4.49, are sludied to determine the nature 01 lhe coherent events, their frequencies and apparent velocities, windows between noise trains where reflection data would not be overridden by such noise, and so on. Once we have some indications oC the Iypes oC noises present, we can design arrays or olher field techniques lo attenuate the noise and then field-test our techniques to lee if the desired elreet is achieved.

(e) Uphole surveys. An uphole survey is one oC the best methods oC investigating the near-surface and finding tbe thieltness and velocity oC the low-velocity layer (LVL), Dw and VW , and the subweathering ve10cily VH • An uphole survey requires a shothole deeper than tbe base oC the LVL, a complete spread oC geophones, plus an uphole geophone (a geophone usually within 3 m oC the shothole). Shots are fired al various depths in the hole, as shown in Figure 4.50, beginning at tbe bottom and conlinuing unlil the shot is just below the surlace oC Ihe ground. Travel·

times are plotted against shot depth Cor the uphole geophone (Ihat is, the uphole time 'ub) as well as for several dislant geophones, incIuding two or more spaced 200 m or more apart, as shown in Figure 4.50. The plOI lor Ihe uphole geophone changes abruptly where the shot enters tbe LVL; tbe slope of Ihe portion aboye Ihe base oC the LVL gives Vw and the break in slope usually defines Dw clearly. For the distant geophones tbe plot is almost vertical at first because tbe patb lengtb changes very liltle as long as Ihe shot is in the high-speed layer. However, when the shot entees tbe LVL tbere is an abrupl ehange in slope and tbe traveltime inereases rapidly as the patb length in the LVL inereases. The reCraction velocily at the base of tbe LVL, VH , is oblained by dividíng the time interval belween tbe vertical portions oC the curves for two widely separaled geophones (~t17 in Figure 4.S0a) into tbe distance between the geophones. This velocity measurement may be different from that given by tbe slope oC the deeper portion oC the uphole geophone curve, partly because the lauer is less accurate (since Ihe time inlerval is les s than &/17 ), partly beeause the layering 01 beds oC different velocities has little elrcct on &/17 bul may afreet 'ub substantially.

4.5.3. Field Equipment for Land Surveys (a) Drilling. When explosives are used as the energy source, holes are drilled so tbat tbe explosive can be placed below the low-velocity layer. The boles are usually about 8 to 10 cm in diameter and 6 to

Reflection field method5 and equipment

193

Swi'el (mud is injecled inlo cenlre of Kelley and drill.tem) Draw.work. (for pullinS drillslcm from the borehole) Rotary table (turns Kelley and henee drillslem and bit) Pull down pulley (pUl. pre.sure on the drillslem and bit) Portable mud pil (collcets mud -----~~c.....---~f_-.-.:~=~;=~:;::::::~L,},:._J~ returnina up the annular 'pace around drillstem) Kelley

Tran5rcr case

Mud How. back lO surrace through annula, space bolween d,iIIslcm and hole wall. carrying Ihe cutlings with it

Kelley screwed inlo drill ,tem

'-'------"-Orill 51em

Dit scrcwcd onto drill 'Icm (mud emer,es Ihrou¡h bit)

ROTARY

DRILL

Figure 4.51. Rotary dril/. (from 5heriff, 1984.)

30 m in depth, althougb depths of 80 m or more are used occasionally. Normally the holes are dritted with a rotary drill, usually mounted on a truck bed, but sometimes on a tractor or amphibious vehic1e for working in difficult areas. Sorne ligbt dril!s can be broken down into uIlÍts small enough that they can be carried. Augers are used occasionally. In work in 80ft marshes, boles are sometimes jetted down wi th a hydraulic pump. Typical rotary-drilling equipment is shown in Figure 4.51. Rotary drilling is accomplished with a dril! bit al Ihe bottom of a drill pipe, the top of which is lumed so as to tum the bit. Fluid is pumped down through Ihe drill pipe, passes oul Ihrough the bil and retums lo Ibe surface in the annular region around tbe dril! pipe. The functions of the drilling fluid are to bring tbe cuttings to tbe surface, to cool tbe bit, and to plaster tbe drill hole to prevent the walls from caving

and formation fluids from flowing into the holeo The most common drilling fluid is mud, which consists of a fine suspension oC bentonite, lime and/or barite in water. Sometimes water alone is used and sometimes air is the circulating fluid. Drag bits are used most commonly in sort forrnations; these tear out pieces of the earth. Hard rock is usually drilled with roller bits or con e bits, which cause pieces of rock lo chip off because of the pressure exerted by teetb on the bits. In areas of exceptionally hard rock, diamond drill bi ts are used. (b) Explosive energy source5. Explosives were the sole source of energy used in seismic exploration until weight dropping was introduced in 1953. Ex· plosives continue to be an important seismic energy source in land work. Most explosives have a ve/ocity o/ detona/ion (that is, the ve\ocity with which the

194 explosion travels away from (he point of initiation in lhe explosive) around 6 to 7 kmjs. Conscquently, the seismic pulses generated have very steep fronts. This high concentration oC energy is desirable from the point of view oC seismic wave analysis bUI detrimental from the viewpoint oC damage to nearby structures. Ammonium nitrate and nitrocarbonitrite (NCN) are the dominant explosives used today. Explosives are packaged in tins or in tubes oC cardboard or plastic about 5 cm in diameter that usually contain 1 lo 10 lb (0.5 lo 5 kg) oC explosive. The tubes and tins are constructed so that they can be easily joined logelher end-to-end to obtain various quantities oC explosives. E1ectric blasting caps are used 10 initiate an explosion. These consist oC small metal cylinders, roughly 0.6 cm in diameter and 4 cm long. They contain a resistance wire imbedded in a mixture oC powder charges, one oC which ignites at a relatively low temperature. By means oC two wires issuing from the end ol the cap, a large current is passed Ihrough the resistance wire and the heat generated thereby initiates tbe explosion. The cap has previously been placed inside one oC tbe explosive charges so that the explosion 01 the cap detonates tbe entire charge. The current lhat causes the blasting cap lo explode is derived Crom a blaster, which is basically a device for charging a capacitor to a high vollage by means oC either batteries or a band-operated generalor, and tben discharging the capacilor through the cap at the desired time. Incorporated in tbe blaster is a device that generales an eleclrical pulse al Ibe instanl Ihal the explosion begins. This timebreak pulse fixes Ihe instant of the explosion, t = O. The timebreak pulse is transmitted lo Ihe recording equipmenl where it is recorded along with the seismic data. Several tecbniques are used at times to concentrate tbe energy traveling downward from an explosion. The detonating Cront in an explosive usually travels much lasler tban tbe Selsmic wave in tbe formation, so that the seismic wave originating Crom the top of a long explosive charge lags behind the wave from the bottom oC the charge even where the explosive is detonated at the top (which is the usual method). Explosives with low detonaling velocity are sometimes used, but tbey are made in long flexible tubes that are difficult lo load. Delay units are sornetimes used between several concentrated explosive charges to allow tbe wave in the formation to calch up with the explosive Cront; they may consisl oC delay caps (which introduce a fixed delay between the time the detonating sbock initiates tbem and the time they themselves explode) or helically wound detonating cord (so that tbe detonating front has to travel a longer distance). Expendable impact blaslers

Seismic methods have also been used; they detonate when tbey are actuated by the shock wave Crorn anolher explosiono Although explosives provide lhe most compact high-energy source, they have many disadvantages Ihat oflen preclude their use: high cost, Ihe time and expense involved in drilling holes, polenlial darnage 10 nearby buildings, wells, and so forth, as well as restriclions about where holes can be drilled and explosives detonated. (e) Surfaee energy sourees. Many allernative energy sources have been developed for use in bOlb land and marine work (Las ter, 1985). Discussion ol those Ihat are used prirnarily al sea and infrequently on land will be post poned until Section 4.5.4c. Without exception, the surface energy sources are less powerCul than explosives and Iheir use on a large scale has been made feasible by vertical stacking methods that permit adding Ihe effects 01 a large number of weak impulses to obtain a usable result. Sorne surface rnethods use explosive detonaling cords buried 10 lO 40 cm. A 100 m ol cord may be buried, oCten in a pattern, using a specia! plow, and then exploded by means 01 caps placed at intervals along the cord. Occasionally, in remole areas, explosive charges on sticks I to 2 m aboye the ground are used; tbis procedure is called aír shootíng. Aside Crorn raising a c10ud oC dust, it does no damage to the vegetation. However, it genera tes a strong airwave that can damage the ears 01 arumals within 100 rn or so oC Ihe explosiono The earliest nonexplosive source to gaín wide acceptance was lhe thumper or we;ght dropper. A rectangular steel pI ate weighing about 3,000 kg is dropped from a height oC about 3 m. The instant of irnpacl is delermined by a sensor on the plate. Weights often are dropped every lew meters and the results oC 50 or more drops composited into a single lield record. The time belween release of the weigbt and irnpact on the ground is nol constant enough to permit simultaneous use ol more than one source. Often two or three units are used in succession, one dropping its weight while the others Iift their weights into the armed position and move ahead 10 the next drop poi n\. The use of weight dropping is now largely restricted to desert or semidesert areas where tbe massive trucks can move about relatively lreely. Several variations of mechanicaJ sources are used in shallow-penetration work lor coa! exploration oc engineering objectives (McCann, Andrew, and McCano, 1985). Whereas the Coregoing are primarily surrace sources, gas guns, air guns (Brede et al., 1970), and olher devices are sometimes used in boreboles, especially in sort marsh wbere there is littIe risk of being unable to recover the equipment from the holeo The

Reflection fjeld method.1 and equipm ent

195

Conoco .) Figure 4.52. Vibrators mounte d for off-roa d survev. (Court ew

air guns used on land are modifications oí the guns designed for marine use, which are discussed in Section 4.5.4c. Air guns are sometimes used in bags of water set on the sur(ace of the ground; the coupling with the ground is generally good (Montgomery, 1984). Unlike otber energy sources that try to deliver energy to the ground in tbe shortest time possible, tbe Vibraseis source passes energy into the ground for 7 s or more. A vibrator (usually hydraulic) actuates a steel plate pressed firmly against the ground (Fig. 4.52). The output wavetrain consists of a sine wave whose (requency increases continuously from 6 to - 50 Hz during the 7 to 21 s "sweep." Each retuming reftection event is a similar wave train of about 7 to 21 s duration. Because reftections occur much doser together than tbis, the result is a superposition o( many wavetrains. Subsequent data processing (discussed in §4.7.4e) is necessary to resolve the data. In effect. the processing compresses each returning wavetrain into short wavelets, thus removing much of the overlap (see Fig. 4.82). Vibraseis sources. like most surface sources, produce low-energy density; as a result they can be used in cities and otber areas where explosives and other sources wou1d cause extensive damage. Vibroseis is now the most popular land seismic source. Seismic energy arriving at the surface o( the ground is detected by geophones, frequendy referred to as seismomelers, delectors, or jl/gs. Although many types have been used in the past, modem geophones are almost entirely of the (d) Geophones.

moving-coil electromagnetic type for land work and the piezoelectric type for marsh and marine work. The former will be described briefly here (for a more complete discussion, see Sheriff and Geldart. 1982. pp. 161-6) ; the lalter will be discussed in Section 4.5.4d in connection with marine equipment. The schematic diagram oC a moving-coil electromagnetic geophone in Figure 4.53 shows a permanent magnet in the form of a cylinder into wruch a circular slot has been cu t. The slot separates the central S pole from the outer annular N poleo A coil consisting o( a large numbe r o( tums o( very fine wire is suspended centrally in the slot by means o( light leaf springs A, B, and C. The geophone is p1aced on the ground in an upright position. When the ground moves vertically, the magnet moves with it but the coi1. because oC its inertia, tends to stay fixed. The relative motion between the coil and the magnetic field generates a voltage between the terminals of lhe coil. The geophone output ror horizontal motion is essentially zero because the coi1 is supported in such a way that it stays fixed re1ative lo the magnet during horizontal molion. The output vollage of the geophone is direct1y proporlional lo the strength oC the magnetic field o( the permanent magnet, the number of lums in the coil. the radius oC the coi1. and the velocity oC the coil relative to the magnet. Mode m high sensitivity geophones have an output of 0.5 lo 0.7 V for a ve10city of 1 cm/s of the ground. The geophone coil and springs constitute an oscillatory system with natural Crequency in the range from 7 to 30 Hz Cor reflection work and 4 to 10 Hz

196

Seismic methods

(a)

Figure 4.53. Moving-coil geophone (a) SchE'matic (b) Cutaway of a digital-grade geophone. (Courtesy Ceo Space Corp.)

197


for refraction work. Because the coil tends to oscillate after the ground motion dies away, it is necessary to dampen (attenuate) the motion. This is achieved in part by winding the coil on a metal "former"; eddy currents induced in the lauer when it moves in the magnetic field oppose the motion and hence produce damping. Additional damping is obtained by connecting a shunt resistance across the coil of the geophone; when a current Hows through the coil the interaction between the magnetic fields of the current and the permanent magnet further slows down the motion of the coil (the input impedance of the recording system is so large that it does not significantly affect the current and hence the damping). The geophone damping can be adjusted by varying the shunt resistance because tbis changes the current through the geopbone. A geophone with a bigh resistance shunt will oscillate foc some time after being tapped ligbtly. As the shunt resistance is decreased, the number of oscillations will decrease because of the increased damping until finally a point will be reached where a tap will just raíl to produce an oscillation. At this point, the geophone is critically damped. The response of a geophone to a harmonic signal depends on the relation between the frequency of the signal and the natural frequency oC the geophone as well as the degree of damping. Figure 4.54a shows curves of the amplitude of the output current as a function of frequency. The maximum velocity of the geophone is the same Cor all curves. Often the output is norma1ized with respect to (that is, expressed as a fraction oC) the output for high frequencies. The varíous curves correspond to different values of the damping; h is the ratio oC the amount oC damping relative to critical damping (h = 1). For zero damping (h - O), the output becomes infinite at the natural frequency; obviously this is merely a theoretical result sincc zero damping can never be acbieved. As h increases, the output peak decreases in magnitude and moves slowly toward higher frequencies. Somewhere between h - 0.5 and 0.7 the peak disappears and the range oC Hat response has its maximum extent. As h increases beyond tbis value, the lowfrequency response gradually falls off. The generally accepted choice of 70% of critical damping for geophones resuIts in more-or-Iess optimum operating conditioos with respect to amplitude distortion in the geophone output. The output of a geophone is sbifted in phase with respect to the input by the amounts shown in Figure 4.S4b. Phase shift is important because the seismic signal comprises a range of frequencies; ir the phase sbift does not vary properly with frequency, phase distortion occurs. The optimum phase shift is linear with frequency and with an intercept of "'Ir, that ¡s,

the sbift is equal to (kw + "'Ir) where k is a constant and " an integer. To show this, we note that an input signal of the form A cos wt will appear in the output as Bcos(wt

+ kw + "'Ir) - ±Bcosw(t + k)

Thus, the net effect is to sbift all frequencies in time by tbe amount k and to invert the pulse when n is odd, neither of wbicb results in cbange oC wave shape. Usually several c10sely spaced geophones are connected in a series-parallel arrangement to produce a single composite output. The en tire geophone group is considered to be equivalent to a single geophone located at the center of the group. However, the damping oC each geophone will be atI'ected by tbe presence of the otber geopbones because of tbe change in resistance of tbe circuito An exception is an arrangement of n parallel branches, each containiog n identical geophones in series, which has the same resistance as a single geophone and hence the same damping. The geophone signals are usually transmitted to the recorder by many pairs of wires in cables. Increasingly, tbe geopbone output is digitized at tbe geopbone group by a remote digitization unit (RDU) and the digital signal transmitted to the recorder. The signal may be sto red temporarily where it is digitized and subsequentIy transmitted to the recorder. perhaps along with the signals from other digitizing boxes, in a coded fashion over twin-Iead cable, coaxial cable, or fiber-optic cable; sometimes the transmission is by radio. At times the output for an entire day is stored on a magnetic tape in the digitizing box, lo be collected and combined with the data from other digitizing boxes at the end of the day's work. Except ror very strong signals arriving soon alter the sbot is fired, the output of the geopbone is too weak to be recorded without amplification. Also, the useful range of amplitudes of the geophone output extends from a few tenths oC a volt at the begioning of the recording to about 1 p.V near the end of the recording several seconds after the shot, weaker signals being lost in the system noise, a relative change or dynamic range of about 10 5 (100 dB). Besides amplifying weak signals, the amplifier usually is called on to compress tbe range oC signals as well as filter signals. Seismic amplifiers generally employ solid stale circuitry, wbicb a110ws them to be very compact. Although they are usually mounted in a recording truck or other vehic1e, they can also be carried where necessary. A block diagram oC an analog amplífier is shown in Figure 4.55. (e) Analog recording.

198

Seismic methods 10

(a)

haO \

\

.

~

\

.!:!

ñi

E

---:;~~ h = O.S ~

g

:..

:~

......h = O.

1.0

2

.

~

&

-

/h" 1.0 . /

IIJ ~

Q.

......

"

c:

o

&!

/'

/

Vi V

/h·2.0

'/ V

V

I

0.1 0.1

V

10

1.0

100

Relativo f,equency (w/w.)

. -i..j r

~ :::: ~~ / h·O.S ...... ....... h :O:r ¡;./ I ,/ V

Id

!

~

-:1

c:

v

,..

O

.D

V

~

:::-

V

-

h=jY ~2~0

--

V

~ e

,/

lO

f

/

..

VV

V

~

V V~

l/V V V // VlI

,/ ~V ~ V ~ F"-":: - itr

V

0.1

10

1.0

100

Relative f,equency (w/w.)

Figure 4.54. Ceophone response curves. (After Dennison. 1953) (a) Amplilude o, oulpUI re/ative lo input. (b) Phase o/ outpul re/alive 10 input.

Ptcampllritr OulpUI

tIIr

a,dance

ro<

lC'ophonc hi,h.fJnc

Amplificr

AmphtiC'r

Malnf:li

Low·¡,:ul

>...,~ Film.

fillu

AGC Neg31ivc rudbllck

conuol

hullal

!ouppruslon

MU''"I

from olher

"hlnnel.

Figure 4.55. Block diagram of ana/og seismic amplifier.

"pe ,ec:ordtr


The cable from the geophones may be connected to a balance circuit that permits adjustment of the impedance to ground so as to minimize Ihe coupling with nearby power lines, thus reducing pickup oC noise at Ihe power-Iine frequency (high-Iine pickup). The next circuit element usually is a filler to attenuate Ihe low frequencies that arise from strong ground ro11 and that otherwise might overdrive the first amplificalion stage and introduce distortion. Seismic amplitiers are multistage and have very high maximum gaín, usuaJly oC the order oC 10 5 (lOO dB), somelimes as much as 107 (140 dB): lOO dB means that an input oC 5 IN amplilude appears in the output wilh an amplilude of 0.5 V. Lower amplification can be obtaíned by means of a master gaín switch, which reduces Ihe gaín in sleps. The amplifier gaín may be varied during Ihe recording interval starting with low amplification during the arrival of strong signals al lhe early part oC the record and ending up wilh the high gaín value fixed by the master gaín seuing. This variation oC gaín with time (signaJ compression) can be accomplished with aUlomaric gain (volume) control, usually abbreviated AGC or AVC, which utilizes a negative feedback loop to me asure the average output signal leve! over a short interval and adjust the gaín to keep the output more-or-Iess constant regardless oC the input level. It is important in making corrections for nearsurface effects Ihal we be able to observe c1early the jirsl breaks, the first arrivals oC energy al the ditferenl geophone groups. (For a geophone· near the shotpoinl, the first arrival Iravels approximately along tbe straígbt line from the shot to the geophone: Cor a distant geophone Ihe tirst arrival is a headwave refracted at the base of Ihe low-velocity layer - see Fig. 4.76 and Ihe discussion of weathering corrections, §4.7.l.) lf we allow the AGC to determine the gaín prior

lo Ihe firs! arrivals, the low input level (which is entirely noise) results in very high gaio; the OUlput may !hen be noise amplitied to tbe point where it becornes difficult to observe the exact instant oC arrival of tbe first breaks. This problem is solved by using inilial suppression or presuppression. A highfrequency oscillator signal (about 3 kHz) is Ced into tbe AGC circuil, which reacts by reducing Ihe gaín so thal Ihe noise is barely perceplible; Ihe highfrequency signal is subsequently removed by filtering so Ihal it does not appear in the output. With the reduced gain, the relatively slrong firsl breaks stand out c1early. As soon as the fírst breaks have all been recorded, Ihe oscillator signal is removed, usually by a relay triggered by one oC the first breaks. Therearter, the AGC adjusts the gaín in accordance with tbe seisrnic signal leve\.

199

Seismic amplifiers are intended to reproduce Ihe input with a minimum oC dislorlion and hence the gaín (wilhoul filters) should be constant for Ihe entire Crequency spectrum oC interes\. For reHection work this range is about 10 to 100 Hz and Cor refraction work Ihe range is about 2 to 50 Hz: accordingly most amplifiers have Hat response Cor all Crequencies Crom - 1 to 200 Hz or more. Frequency jillering reCers lo the discriminalion agaínsl certaín frequencies relalive to others. Seismic amplifiers have a number of filler circuits, which permil us lO reduce Ihe range oC frequencies Ihat Ihe amplifier passes. Although delails vary, most permit Ihe selectioo oC the upper and Ihe lower limits oC the passband. Ofleo il is possible lo selecl also the sharpness of Ihe cUloff (Ihe rate at which the gaín decreases as we leave Ihe passband). Figure 4.56 shows Iypical filter response curves. The curves are specified by the frequency values at which the gaín has dropped by 3 dB (30% oC amplitude, 50% of power); Ihe curve marked "Oul" is the response curve of the amplifier wilhout filters. Seismic amplifiers may inelude circuilry for mixing or compositing, that is. combining Iwo or more signals to give a single outpu\. Mixing in etfect increases the size oC Ihe geophone group and is sometimes used lo attenuale surCace waves. The commonest form, called 50% mixing, is Ihe addition oC equaJ Cractions of the signals Crom adjacenl geophone groups. Magnetic lape recording has virtually eliminaled Ihe need to mix during recording because we can always mix in playback. The timebreak signal often is superimposed on one of Ihe amplifier OUlputs where it appears as a sharp pulse lhal marks the point I ... O for Ihe record. When explosives are being used, Ihe uphole signal (§4.5.2e) is also superimposed on one oC the outpuls; luh is important in correcting Cor near-surface effects. High resolulion or HR amplifiers are used in engineering and miniog problems to map the top 200 m or so. To get resolution oC a Cew meters, we musl use short wavelengths; accordingly these amplifiers have essentially uniform response up to 300 Hz, sometimes to 500 Hz, and Ihe AGC time constanls are correspondingly shor\. To permit recording very shallow reHections, small offsets are used and the initial suppression permits recording evenls wilhin O.OSO s or so after tbe first break. The recorded data must be presented in visual form for moniloring and for inlerpretation. This is done mosl commonly by an electroslatic camera. A srnall molor moves a strip of paper at constant speed (about 30 cm/s) during the recording period and a series oC gaJvanomelers, one Cor each geophone group, transCorms Ihe electrical signaJs corning out of Ihe amplifiers into spots oC Iight moving in accordance

Se;smic methods

200

10

6

20 Frequency (Hz)

Figure 4.56. Response of seismie (if/ers.

(a)

(b)

(e)

(d)

.' ..

..

.. :

.... :::: ~ s: :::: ~~ :::

:.:

~ ~

~

&

~

&

, f

~ ::::~ :::: :::: ~

~

:::: ::::

~ i

~

~

~

~ ~

~

~ ~ ~

&

.. ... .. ":::: :::::: ~ i . ~ § ::: ~ ~ ~ ~ ~ ~

:::!

::::

~

~

~ :::: ~ :::: :::: ~ :::: ~ ¡ ~

~

A

::: :::

::: :::

~:

~

~

~:: ::::

I !~ :

:e

~:!

~.

:~

•• 1 . . . . . . - "

:¡¡ ,.. ..

...... ...

Figure 4.57. Modes of displaying seismie data, (Courtesy Ceo Spaee Corp.) (a) Wiggle superimposed on variable area. (b) Variable area. (e) Wiggle. (d) Variable densi/y. (e) Wiggle superimposed on variable density.


.. " rl.

,IU1

201

lI \"

AootiD¡·poio.

AD

amplifier

o,.'on\ttlcr

Mil,nCtlt

lar e rt:cordtr

Figure 4.58. BlocK d,'agram of digital se¡'smic amplirier.

with the signals, producing .. wiggly" lines on the papero A timing device record s accurate timing marks on the record; the heart oI the timing system is an oscillating electric eircuit whose Irequency is accu· rately controlled by a crystal. Timing lines are usu· ally placed every 10 ms. Each individual graph, which represents the output oI a geophone group, is called a trace. Modes oC representation are compared in Figure 4.57. The uariable-area trace can be pictured as the result of passing the light from a galvanometer through a cylindrical lens whose axis would be vertical to give the result shown in the figure. This lens produces a vertical line oC light instead oC a point, as Ior the wiggly trace. As this line moves up and down witb the signal variations, tbe lower part is cut off by a stop. The variable-density trace is obtained by using a light souree wbose intensity is varied in accordance with the signal variations. For example, the intensity migbt inerease during signal peaks and deerease during signal troughs; the photographic record will then be darker for peaks and ligbter for Iroughs. Figures 4.57a, e show the wiggly trace superimposed on variable area and variable density, respectively; these have the advantage oC retaining the fine detail ar(orded by tbe wiggly trace and at the same time obtaining the graphic effects oI the variable·area or variable-densi ty displays.

I

t

(fJ Digital recording. Digital recording was first introduced in seismic work in tbe 1960s and is now almost universally used. Whereas analog devices represent the signal as a voltage (usually) that varies continuously with time, digital reeording represents the signal by a series of numbers Ihat denoles the geophone output at regular intervals, usually every 2 ms. DigitaJ recording is capable oí higher fidelity than anaJog recording and permits numerical processing 01 the data witbout adding appreciably lo the distortion. However, tbe beginning (geophone response) and end (display) of the recording process

continue to be anaJog. Anstey (1970) discusses instrument requirements Cor digital reeording and Pieuchot (1984) gives a comprehensive review oC seismie instrumentation. We shall discuss digital representations in tbe binary scaIe oC 2. The binary scaJe uses only two digit~, O and 1; hence only two different conditions are required lO represenl binary numbers, for exampIe, a switch opened or closed. Binary arithmetic operations are much like decimal ones, lor example, Decimal: 20873 Binary:

=<

2 x 10 4 + 8 X 10 2 + 7 X 101 + 3 X 10°

1011011 - 1 X 26 + 1 X 24 + 1 X 23 + 1 21 + 1 X 2° ... decimal number 91 Each pulse representing 1 or O is called a bit and the series oC bits, which give the vaJue oí a quanlity, is called a word. The block diagrarn of a digital recorder in Figure 4.58 can be compared with that oC the anaJog recorder shown in Figure 4.55. DigitaJ amplifiers usually have enough dynamic range so that they do not require low-cul filtering prior to the first amplification stage. Digital amplifiers are usually oC tbe instantaneous Hoating-point type: tbey measure the magnitude of each sample; each vaJue is expressed as a certain number of significant figures times 2 raised to the proper power, where both the significant figures and the power are recorded. The output of each preamplifier passes through an alias filter whose Cunclion will be explained in Section 4.7.3b. From the alias filter the signal passes to a multiplexer, which is in essence a high-speed electric switch. From the multiplexer onward, we require only one channel- one amplifier, one A/D (analog-to-digital) con verter , and so fortb, instead oC one ror each trace. The multiplexer connects each cbannel in tum to Ihe amplifier. Here the amplifier is eonnected to a X

Seismic methods

202

Figure 4.59. Conversion from digital to analog formo

sample-and-hold unít for about 1 ¡ts which is sufficient time to charge a capacitor lo tbe same voltage as tbe amplifier output at that instant. The amplifier is then disconnected and tbe A/D converler compares tbe capacitor voltage with a series oC standard voltages. lhe result of this comparison is a series oC pulses that gives tbe polarity and the value oC the amplifier output vollage (in tbe binary scale) at the sampling instant. Processing the data for each trace requires so little time that there is ample time to read each trace even at the fastest sampling rate (1 ms) ordinarily used. (For very large numbers of traces, digitization is usually done at the geophone so that tbese considerations are irrelevant.) The output oC tbe AjD converter is a word containing 14 bits (usually), the first of which gives the sign (plus or minus) of tbe signal and the remaining bits the magnítude. The series of pulses Crom the A/D converter passes to the formatter, the device that controls the sequence in which the various bits and words are recorded on the magnetic tape. In addition to the data from tbe A/D converter, the formatter also receives data identirying lhe profile, the timebreak, uphole information, a word lo mark the end of a record, and so on (all of tbis information is in digital form). 'Ibis series of numbers is written on halC-inch tape by níne recording heads. The rormatter distributes the various bits among the heads in a fixed pattem known as the formar (SEG 1980). The tape speed is adjusted so tbat the density of data along a single track is constant (often 6,250 bits/in.). Digital recording (and processing) involves a series of operations that take place sequentially on a time scale measured in microseconds. The entire sequence is controlled by an electronic "dock," a crystal-controlled oscillator that operates in the megacyc1e range, which furnishes a continuous series of pulses whose shape and spacing are accurately maintained. Time is measured by counting these pulses and the operating cycles of the component units (such as the multiplexer and the formatter) are controlled by circuits that count the dock pulses and operate electronic switches when the count reaches predetermined values.

Although digital data are ideal Cor versatile data processing, analog data are more suitable for interpretation and for monitoring the recording system to ensure that a11 units are Cunctioning properly. Accordingly, digital systems provide for reconverting Ihe digital data to analog form for recording by a camera. The D/A (digital-to-analog) conversion is carrled out by reversing the recording process. The bits coming off the lape are rearranged by a deformatter before going to the D / A converter. Usually only the seven or eight "most significant" bits specifying a signal value are used because the camera unit has a resolution oC only about 1% (or 1 part in 1100100 in binary). Smaller amplitude changes are undetectable on paper records. The D/A converter can be regarded as a series of batteries with vollages proportional to 26 , 2', 24 , 23 , 2l , 21, 2° units (when seven bits are used). The batteries are connected in series so that the total voltage is 1111111 (that is, 127 in the decimal system). Each "zero" disconnects the corresponding battery. The bit giving tbe polarity of the signal controls the polarity of the output. The result is a vollage at the output of the D / A converter equal in magnilude and sign to the original signal at the instant oC sampling. The output Crom Ihe D/A converter goes then lo a demultiplexer that connects each vollage lo a sample-and-hold circuit in the proper channel. The sample-and-hold output has a staircase Corm such as shown in Figure 4.59. The outpul goes through a low-pass filter that smooths out the steps and is then amplified to the voItage level required by tbe camera. Computers are part oC most recording equipment, taking over many test and diagnostic Cunctions as well as simple processing operations, such as vertical stacking and correlalion (Walker and Crouse, 1985).

4.5.4. Marine Equipment and Methods Marine seismic operations usually imply water that is sufficiently deep 10 allow Creedom oC movement Cor ships that are 30 to 70 m in length (Fig. 4.60). Such operations diffcr from operations on land and in shallow water primarily because oC the speed with which they take place. (a) Marine operations.

r


203

,

r

Figure 4.60. Seismic shlp rowing rwo
dre produced bv parav¡¡oP\ rhat pull ,trpanlprs off

I I

Normal production shooting takes place al a speed of the order oC 6 knols and can proceed on a 24 hour per day basis. Coverage of 250 km/day would be possible ir all the time were spent recording. Trus much production is never achieved because time is spent traveling to the line or from the end of one line to the start oC the next, waiting for good wcather. or because oC other factors. Praduction rates may be of the arder of 2 records/minule. each consisting of 2 to 4 component subshots which are then vertically stacked. The monthly cost of a marine crew is large. but the high production cuts the uní! cost of marine seismic data to about 10% of that of land data. The high production rate requircs special emphasis on efficiency in operations. Source and receiver uni ts are lowed into place and forward trave! does not stop during a recording. Althougb detailed monitoring of data quality is not possible. the relatively constant water environment surrounding the sources and re· ceivers and the general absence of a low-velocity weathering layer such as is usually presen I on land lessen variations in data quali ty. (b) Bubble effect.

An underwater bubble of gases

at high pressure, such as an explosion produces, tends to altemately expand and contract. As long as

the gas pressure exceeds Ihe hydrostatic pressure of the surrounding water, the net force wi\l accelerate the water outward. The net force decreases as the bubble expands and becomes zero when the bubble cxpansion reduces the gas pressure to the value 01 the hydrostatic pressure. However, at trus point the water has acquired its maximum outward velocity and so continues to move outward wrule decelerating beca use the net force is now directed inward. Eventually the water comes to rest and the net inward force now causes a collapse oC the bubble with a consequent sharp ¡ncrease in gas pressure, in effect a new energy release, and the process repeats ¡lseH. Seismic waves will be generated by each oscillation. With explosive charges of 7.5 kg, the effect is Ihal oC additional seismic records every 0.2 to 0.4 s superimposed on each other so that one canoot tell from which oscillation a reflection event comes. Although explosivcs are no longer used in marine operations, other types of sources also genera te bubbles.

(e) Marine energy sources. Marine seismic reflectíon work consists mostIy oC two types. commonmldpoint and profiler work. These differ considerably in cost, size of energy source, effective penetration, and various other aspects. We shall discuss here the larger energy sources commonly used

Seismic methods

204 Hílh-pres>un: .ir

Solenoíd valvc:

Hi,h-pr... un: .ir

e

8 - - - - Shullle

D

oor

8

(a)'

( b)

Figure 4.61. Air gun. (Courtesy 80/1 Associales.) (a) Ready for (iring. (b) Firing.

in eommon-midpoint recording: The smaller energy saurces used in proliling will be deseribed in Section 4.5.5í. The most widely used large energy source is Ihe air gun, a device thal diseharges air under very high pressure into the waler (Giles, 1968; SchulzeGattermann, 1972). Pressures up to 10,000 psi are used, although 2,000 psi is most common. The gun in Figure 4.61a is shown ín Ihe armed position, ready for liring_ Chambers A and B are filled with high pressure airo which entered A al the top lefl and passed into B through an axial opening in Ihe "shultle." The latter is held in the c10sed position by the air pressure (because flange e is larger than flange D, resulting in a nel downward force). To lire the gun, the solenoid at the top opens a valve that allows high pressure air lo reach the underside oC tlange C. This produces an upward force that is large enough lo overcome the force holding the shuttle in the c\osed position and, consequently, the sbuttle opens rapidly. This allows the high pressure air in the lower ehamber to rush out through ports into the water. The bubble of high-pressure air oseillales at a frequeney in the seismie range and so lengtbens tbe saurce pulse (rather Ihan generating new pulses). The upward motion of lhe shuttle is arresled before it strikes the 10p oC ebamber A because tbe upward force Calls off rapidly as the air enlcrs the water and lhe downward force of the air in the upper chamber inereases. The shuttle then retums lo the armed position and the lower chamber again fills wi th airo The explosive release oC the air occurs in 1 lo 4 ms and tbe entire discharge cycle requires about

25 to 40 ms. Usually several air guns are used in paralleL Because the dominant frequency of the pulse depends on the energy (that is, on the product oC the pressure and volume of air discharged), mixtures oC gun sizes (the gun size is the volume oC the lower chamber) from 10 to 2,(X)(} in? are usually used to give a broader frequeney spectrum_ One variation of the air gun (Mayne and Quay, 1971) allows Bir ftow into the bubble for sorne time after the inilial discharge to retard the violent collapse oC the bubble. This is achleved by dividing the lower chamber into two parts connected by a small orífice. The air in the lowermost chamber is delayed in passing through this orifice before discharging into the water_ Several types oC imploders are sometimes used. lmploders operate by creating a region of very low pressure; the collapse oC waler into the region generales a seismic shock wave. Water guns (Fig. 4.62) are the most common imploders. Space inside the gun is divided between an upper firíng charnber, which is filled wilh compressed air, and a lower chamber, which is filled with water (Salar, 1984). On tiring the gun, the compressed air Corees the shuttle downward, expelling lhe water into the surrounding water. The "slugs" oC water leaving the porls create voids behind them and lhe collapse ol water into tbese voids genera tes a seismic wave. OCten three water guns are used vertical1y aboye one another to decrease ghostíng effects. With the Flexichoct, an adjustable-volume charnber is eval;uated while Ihe walls oC the chamber are

t Trademark of Compagnie Générale de Géophysique.


205

(a)

Solenold - - - 1 - -

(b)

A"

supply

Upper chamber

Venled oir Shuttle

LOVler chomber

Gun por! --li-t-

Figure 4.62. Water-gun schemalic (From SaiJr. 1985.) (a) At beg1nnms 01 firing crelp. (b) At end oi firing crele.

kept fixed by mechanical Testrain\. On removal of the restraint, the hydrostatic pressure collapses the chamber and so generates a seismic pulse free of spurious bubbles. Alr is then pumped into the chamber to expand it again, whereupon the mcchanical restraint holds il open while Ihe air is evacuated, ready for the next collapse. With the Hydroseint, two pI ates are driven apar! suddenly by a pncumatic piston, creating bctween them a very low pressure rer,ion into which the water rushes. With the Boomer:j:, two pI ates are forced apart 5uddenly by a heavy surge of electrical current through a coil on one of the plates that generates eddy currents in the other plate, rcsulting in its being suddenly repelled. The Boomer produces Icss energy than F1cxichoc or Hydrosein. Many other types of marine sources have been used. Comparison may be made on the basis of energy or waveform shape (signature). Rayleigh (1917), while studying the sounds cmitted by oscillating steam bubhles, related hubhle frequeney to hubble radius, pressure, and fluid density, and Willis (1941), while studying underwater explosions, expressed the relationship in terms of source energy (the Rayleigh- Willis formula). The relalionship is ilIustrated in Figure 4.63. In general, large energy involves low frequency and vice versa.

(d) Marine detectars. Hvdrophones or marine pressure geophones are usually of the piczoelectric

t

Trademark of EG & G Intemational.

f Trademark of Compagnie Générale de Géophysiquc .

..

type, that is, they depend on the fact that. application pressure to certain substances produces an electrie poten ti al difference between two surfaees. Synthetic piezoelectric materials, such as barium zirconate, barium titanatc, or lead metaniobate, are generally used. Hydrophones are often arranged in pairs so that their outputs cancel for translational acce1erations but add for pressure pulses. Because hydrophones have high electrical impedance. impedance-matching transformers often are ineluded ror each graup. The hydrophones are mounted in a long streamer towed behind the seismic ship at a depth between 10 and 20 m (Bedenbender, Johnston, and Neitzel, 1970: Bemi, 1983). Figures 4.64 and 4.65 show a schematic diagram of a streamer and a pholograph of a portion of a streamer. Twenty or more hydrophones spaced at intervals oI - 1 m are connected in series (so the generated voltages add up) to form a single equivalent gcophone 10 to 50 m io length. The hydrophones and other sensors. connecting wires, and a stress member (to takc the straio of towing) are placed inside a plastie tube up to 7 cm in diameter that is filled with sufficient Iighter-than-water oil to make the strcamer neutrally buoyant, that is, so that its average dcnsity equaIs that of seawater. A ¡ead-in section about 200 m in lcngth is leIt between the stem of the ship and the first group of hydropbones to reduce pickup of ship noises. Dead scctions are sometimes included hetween the diffcrent hydrophone groups to givc the spread length desired. l11C last group is often followed by a tail section to which a buoy is attached. Visual or radar sighting on this buoy is used to determine the amount of drift of the streamer away Crom the track oC the seismic ship

Seismic methods

206 Equivalenl pound. of 60% dynomite ot 9 m depth

0.001

"11111

Ñ

~ ~ e

0.01

0.1

1I1Ir!

1 1I

I

"lit

10

1 I ft 11111

II ItllI

100

1111111

10

100

~

[

i!

i

e

.!/

:8

I!

'ii

6

-;;

.é

O 100 f1 Aquasc¡s (linea. explosiye)

100

10

10'

10'

10'

lO"

10'

10'

i

Ene.1Y in joules

Figure 4.63. [nNgY' frequency relationships for marine sources at 70 m depth. (From Kramer, Pelerson, and Walter, 1968.) Clbl ••••1 on " ••n of .hip

raU buoy wilh rada, .encelo.

D
'\30tiO:\' Group 1

Uve secuon containlftl ... 20-100 hydrophonrs in 12.S-100 meten I«nlth.

Croop I

f

Group 48 (0.96) Compl;"nt .. il .celion

Depth controlJer on dCld secho"

to bolltf rrom .til buoy jerkinl

Figure 4.64. Streamer. (Afler Sheriff, 1984.)

(caused by water currents). This buoy also helps retrieve tbe streamer iI it should be broken accidcntally. The total length oC streamer in the water is 1 to S km and may inelude up to SOO hydrophone groups. Sorne streamers digitizc the signals at various localions within the streamer so that the signals transmiued to the ship are in digitized formo When not in use, the streamer is stored on a large motor-driven reel on the stcrn oC thc ship. When the streamer is being towed, depth controllers and other devices keep tbe active part oC the cable horizontal at tbe proper depth. Depth detectors may be included at several places within the streamer to verify that tbe depth is correct. Water-break detectors are also included at several places along the streamer; these are high-frequency (SOO to 5,000 Hz) hydrophones

that detect energy from the source traveling through the water. Knowing the velocity of sound in tbe water permits converting the water-break traveltime into the offset distance. Magnetic compasses are also included to give the streamer's orientation. The signals from the sensors in the streamer may be digitized in the streamer and the digital signals relayed to tbe boat via wires or liber optics. When towing a streamer, a seismic ship must avoid stopping, making sharp turns, or even drastic reductions in speed; otherwise the streamer tends to drift, wruch may allow it lo get into dangerous locations such as into the srup's propellers. The depth controllers raise or depress thc cable by virtue of water ftowing by their vanes and thus they become ineffective when the streamer is not in motion.

207

Reflection field merhods and equipmenr

Figure 465 Photo of ,pl,mlc ,trpamN PIJ,ti( "pa(N, (a) arf' cOIln('Ctpd hl' three tensile cables (b) A bundle of eleclncal conductors (e) passe5 through hales in the centNs of the s{Jau'rs. A h~'dropll()np is at (d) A depth control/N (e) i5 clamped O\,I'( thE' strE'amE'r (Courtes\' Se/sm/e Engmeering.)

Consequently. if a shot is missed for anv reason. it cannol be repeated beca use the ship will have passed the location. If too many shots are missed, the ship must circle with a diameter larger than the slreamer length in order lo get the streamer in proper location to make up the missed shols. This is very time consuming and consequently very expensive. (e) Marine positionmg. Marine seismic navigation involves two aspects: (a) plaeing the ships al a desired position and (b) determining the actual location afterward so thal Ihe data can be processed and mapped properly. Absolute accuracy is importanl in tying marine surveys to land surveys and in relurning 10 a cerlain point latero fOf example. lo locale an olfshore well. Relative accuracy is important. primarily to enSUTe the proper location of one seismic proftle relalive 10 the next. Relative accuraeies of ± 10 m are desirable whereas absolute accuracies of ± 50 m are often suffieient. Thc actual accuraeies obtained in a survey depend upon Ihe system and equipment used. the configuration of shore slations, the position of the mobile stalion with respect to the shore stalions, varialions in ¡he propagalion oC radio waves. instrument malfunctioning, operator error. and so on. Systems capable of giving adequate aecu-

racy under good conditions may not realize su eh accuracy unless considerable care is exercised al all times. Many types of navigation methods are used, including radiopositioning. sanie devices, observation of navigation satellites. and so forth. Usually combinations oC systems are used so that the advanlages oC one system compensate Cor the disadvantages of anotheT, Positioning methods are discussed in Sections B.6 to B.8.

4.5.5. Measurement of Velocity (a) Conventional well surve\'s. Tbe mos! accurale methods of determining velocity require Ihe use of a deep borchole. Three types oC we/l surveys are used: .. shooling" a well. sanie logging. and vertical profiling (§4.11.4). Shoolillg a II'c/l consists oC suspending a geophone or hydrophone in the well by means of a cable and reeording the time required for energy to Iravel Crom a source near Ihe well down to !he geophonc (Fig. 466). The geophone is specially conslructed lo withstand immersion under the high temperalures and pressures encounlered in deep wells. The cable supports the geophone, serves 10 measure !he depth of Ihe geophone, and hrings Ihe geophone output to Ihe

208

Seismic methads -f.o-

x

---¡MI

t

Figure 4.67. Plat of average velocity from datum lo depth (V) and interval velocity ('1) for a well- veloClty survey.

Figure 4.66. Shaating J well far velaeity.

surfaee where it is reeorded. The geophooe is moved between shots so that the results are a set oC traveJtimes Crom the surCace down to various depths. The geophone depths are chosen to ¡nelude the most important geologieal markers, such as tops of formatioDs and uneonformities, and also iotermediate locations, so that the interval between sueeessive measurements is small enough to give reasonable accuracy (often 200 m apart). Results of a welJ survey are shown in Figure 4.67. The vertieal traveltime, t, to the depth z is obtained by multiplying the observed time by the factor ( : /(:1 + X2 )1/2} to correet for the slant distance. The average velocity between the surface and the depth : is then giveo by :/t. Ir we subtraet the depths and times for two shots, we find the interoal velocity V¡, the average velocity in the interval (z", zn), by means of the formula z". - z,.

V¡= - - -

while the survey is being run, the well must stand without drill stem io the hole and hence is vulnerable to cave-in, blow-out, or other damage. For marine well surveys, air gun energy sources are used (Kennett and Ireson, 1971). The air gUDS may be merely huog over the side of the drill platform or drill ship and hence only a small erew is required to obtain data at many depths. (b) Sanie logging. Sanie logging (§11.7.2), also called velocity lagging, yields a continuous-velocity survey. The sonie log measures the traveltime of a P wave between two sensors 2 ft (60 cm) apart to give the velocity, and the traveItimes are integrated to give a time-depth relation. The sonie log is rarely run all the way to the surface. The traveltimes to the top of the sonic log and to a number of other depths (incJuding total depth) are often determined by direet measurement Crom the surface to a borehole geophone (as discussed in §4.5.5a). The results of these cheek shots are used to remove the cumu)ative and other errors involved in integrating the sorne log. (e) X 2. r 2 merhad.

( 4.83)

1m - In

Shooting a well gives the average velocity with good accuracy of measuremeot. It ¡s, however, expensive because the cost ineludes not only the ooebalf to one day's time of the seismic crew but a1so the cost of standby time for the well (whieh often exceeds the seismic cost). Poteotial damage to the well is another factor that discourages sbooting wells;

The traveltime oC reflected energy depends not only on the reftector depth and the velocity aboye tbe reflector, but also on offset distance, a dependence that permits measuring the velocity. Equation (4.63) can be written ( 4.84) If we plot t 2 as a function oC x 2 , we get a straight line whose slope is l/v.2 and whose intercept is t~. Crom which we can determine the reflector depth.

Refraction field methods and equipment

209

The quantity V. is the stacking velocity (§4.5.2a) because it is used Cor normal-moveout removal in stacking. Velocity analyses (§4.7.7) are based on the normal-moveout concept. Sometimes spedal longoffsel profiIes are used to give better accuracy. An X 2_T 2 survey can give veIocities accurate witrun a few percent where (l) the data are of good quality and have a moderate number of reftections [rom nearIy horizontal. parallel reflectors, (2) accurate near-surface corrections are applied, and (3) the veIocity distribution is simple (Ibat ¡s, there is no lateral variation oC veIocity or complexity of strocture). Vrms and For borizonlal velocity layering, the interval velocity can be found between paraJlel refleetors. Writing VL for the velocity to the n th reflector and Vu for tbe velocity to the reflector aboye it, Equation (4.64) gives

v.,.,

n

n-1

E I-/l¡ - E 1

V¡2 1¡

+

v.,2t

"

n

=

vi E ti

1

Subtracting, we gel the Dix formula for the interval velocity in the nth bed:

2_ (V2~t- t

vn

L

J

-

( 4.85)

1

Note Ihat tbis equation requires parallel horizontal refteelors. The measurement of velodty is diseussed by Hubral and Krey (1980).

4.6. REFRACTION FIELO METHOOS ANO EQUIPMENT

4.6.1. Comparison of Refraction and Reflection Methods Refraction and reflection work are similar in many aspects and refleclion field crews sometimes do refraction profiling, though often not wilb the efficiency of a crew specifically designed for refraetion. The differences between reflection and refraetion field work mostly result from the long source-to-geophone distances employed in refraction. The encrgy input lo the ground must be larger for refraetion shooting, and explosives continue lo be the dominant energy source, although other sources are also used. The longer travelpaths result in the higber frequencies being mostly absorbed so that refraction data are generally oC low frequency. Consequently refraetion geophones have lower natural Crequencies than re-

flection geophones. a1though the response of the latter is often adequate for satisCactory refraetion reeording. Most digital seismie equipment can be used Cor refraction. Refraction shootíng is usually slower than reflection shooting because the largc offset distances involvc more moving time and create problems of eommunications and logistics. However, refraetion profiles are often nol as c10sely spaced as reftection Iines and hence the cost oC mapping an area is not ncccssarily greatcr,

4.6.2. In-Une Refraction The basic refraelion field method involves shooting reverscd refractíon profiles, a long linear spread of many geophone groups shot from each end; the distance is great enough that the dominant portion of the travelpath is as a hcadwave in the refractor or refractors being mapped. Usually it is not practical to simultaneously record many geophone groups spread over su eh a long distance, and hence refraction profiles are shot in segments. Rererring to Figure 4.68a, which shows a single refraclor, the spread of geophone groups might be laid out between e and D and shots al e and G fired to give two records; the spread then might be moved between D and E and shots fired at e and G as before, and so on, to develop the complete reversed profile CDEFG. The charge size is often varied for the different segments beca use larger charges are requíred when the offset beeomes greater. UsuaJJy one or two groups will be repeated for suecessive segments to increase the reJiability of the time tic betwecn segments. Thc shothole at e can also be used to record a profile to the lef! oC C and the shothole al G lo record a profile to the right of G. Note tbat the reciprocal time t r is Ihe same for the reversed protiles and Ihal the intereept limes for profiles shot in different directions from the same shotpoint are equal. These equali ties are exceedingly valuable in identifying segments of complex time-distance curves where several rerraetors are presento In simple si tuations, the reverse profiJe can be constructed without having to actuaJly shoot it by using the reciprocaJ time and intercept time information. However, usuaJly sítuatíons of interest are sufficientIy complicated that this procedure cannot be carried out reliably, The re[)ersed profiles shot from e and G allow the mapping of the refractor from L to M. The reversed profile to the left of C permits mapping as rar as K, but no coverage is obtained for the portian KL. Henee eontinuous coverage on the refractor requires an overlap oC the reversed profiles; a reversed profile between A and E (shown dashed in Fig. 4.68a) would províde coverage between U and V, thus

Seismic methods

210

, , ,, I ',1 A

O

E

F

(Q)

e

A

Su

7\

K

L

¿

G

E

V

(b)

1\

Figure 4.68. Reversed refracrion profiles. la) Time - dis/ance plol versed profiJing. (b) Seclion s!Jowing raypa/!Js for single refractor.

fUf

cunrinuvus re-

inc1uding the gap KL as well as duplicating the coverage UK and LV. Duplicate coverage does not yield new ¡nforrnation but in actual profiling i t provides valuable checks that increase the reliability of interpretarlon. If we have the two-refractor situation in Figure 4.69, first break coverage on tbe shallow refractor is (Q) obtaincd from L to K and from M to N when Ihe e G shots are at C and G. The corresponding coveragc on the deeper refractor is Crom Q 10 S and from R to P. If we are able 10 resolve tbe refraction events that p O R arrive later Iban the first breaks, called second arS (h) rivals or secondary refractions, we can increase Ihe coverage oblained witb a single profile. Howcver, il Figure 4.69. Rel'f'rsed refrae/ion profiles for two-refracfor is difficult wilh analog equipment to adjust the gaín case. (a) Time - dislance piar (b) Secfion showing rayto oplimize bOlh first breaks and second arrivals at paths for /wo refracrors. Ihe same time. If the gaín is too low, Ihe first breaks may be weak and ambiguities in timing may result, shotpoint D, F lo G with sholpoint E, etc. The whereas if the gain is too high, the secondary reCrac- portions of the time-distance curves attributable 10 lions may be uDpickable. Because of tbis difficulty, Ihe refractor being mapped are then translated paralprior to magnetic-tape recording, refraction mapping IcI to themselves until they connect lo make a comwas generally based on first breaks only. With mag- posite time-distance curve such as that shown by the netic-tape recording, each event can be displayed dashed line. The composite curve may differ from under optimum condítioDS. the curve that would actually have been obtaíned Cor The portions of the time-distance curves Ihal do a long profiJe from shotpoint C because oC refraction not add information necessary 10 map the refractor events from other horizons. ol interest oCten are not shot where tbey can be predicted reasonably accurately. Thus, Ihe portions 4.6.3. Broadside Refraction and Fan Shooting CP and GQ oC tbe reversed pro/ile in Figure 4.68a In broadside refraction shooting, sbotpoints and can be o~tted. Where a single refractor is being followed, a spreads are located along Iwo parallel lines (Fig. series oC shoet reCraction profiJes is often shot rather 4.71) selected so tbat tbe desired refraction event can Iban a long pro fiJe. ID Figure 4.70 geophones from C be mapped with a minimum of inlerference from to E are used wilb sholpoint C, from E lo F with olher events. Where Ihe refraclion event can be

=

~

~;

¿-'S

V

=

Refraction field methods and eqU/pment

- --

....-

-

211

..- ..-'

F

()

Figure 4.70. Unreversed re/raclion profiles for a sing/f' refraclor. showing projectiolJs back lo the intercept time (short dashes) and compositing /or shot br upl\'ard Iranslation al segmenl$ of the curves.

e

o,

O,

O,

A

I

I

,

O. ¡

O,

O,

I

I

I \

\

4--+

,--

I

-8

I

I

\

f

I

I

) (j

F

El I

I

c~

-- -- --

.L-

\

I \

--+--t-

I

-D

I

\I I O',

o,

I O'

I O'

,

,

F

(

I O'

I

•

O',

I

O',

z

Figure 4. 71. Bro~dsid" r"fraClion profiling

c1early distinguished rrOm other arrivals. il provides a very economical melhod of profiling beca use all the data yield information about the refractor. However. usual1y the criteria for identifying the refraction event are based on in-line measurements (such as the apparent velocity or Ihe relationship to other events), and these eriteria are nOI available on broadside records where the offset distance is essentially constan!. Thus ir the refraclor should unexpectedly change ils depth or if anolher refraction arrival should appear, one might cnd up mapping the wrong horizon. Consequently, broadside refraction shooting is often combined with oceasional in-line proliles to check the identity oC the honzon being mapped. The first extensive use oC refraction was in searchjng ror salt domes by Ihe fan-shooting technique. A sall dome inserts a high-velocity mass into an otherwise low-velocity seclion so Ihal horizontally traveling energy arrives earHer than if the saIt dome were not present; the difference in traveltime between that actualJy observed and that expected with no salt dome present is called a [ead, In fan shooting (Fig. 4.72), geophones are located in different directions from the shotpoint at roughly the same offset dis-

tances. The desire to maintain constant offset distance usually is sacrificed in favor of loeations Ihat are more readi1y accessible. The leads shown by overlapping, fans Ihen roughly loeate the high-velocity mass. This method is nol used Cor precise shape definition.

4.6.4. Engineering Surveys on land The shallow refractions used in engineering applications, such as in determining the depth to bedrock, do not require large energy sources or complex instrumentation. Energy sourccs are usually very simple, for example, a hammer striking a steel plate on the ground. The instant oC impact is determined by an inertial switch on the harnmer. Sometimes the energy is obtained by a hand-operated tamper, by a weight dropped on the ground (§4.5.3c), or by a small explosiono Such sources are al so used Cor reflection engineering surveys (Meidav. 1969). The energy is usually detecled by moving-coil geophones similar to those already described. Often only a few channels are used, perhaps six, because otherwise the spread layout becomes complicated.

Seismic methods

212 Geophone IOCíllions

ApprolCim3.te oUlline

o" . . all domf: responsible ror h:ads

Graph 01"

time lead,:Ill~~§2~~~:~~i__~~r:-~~-A Normal

rrotn sholpoint A

pr0lik f ..l ~n

\\ hcrc no dOI1le' , .. rrc ..cnt ~~Iahh .. hl'''' rwrnul tlll1l~ di,I:1I1n: rdatIt 1 " .. hlp

e

8

Gr'lrh \11' linte Icad,; (r\1I11 ,h0I1"\)IIl! 8

Figure 4.72. Fan shoorlng. (Afrer Netrleton. 1940.)

The amplifiers and the camera generally weigh only a few pounds and often are contained in asma)) metal suitcase. In sorne systems, (he recorded data are displayed on a small oscilloscope tube and photographed with a Polaroid camera so Ihat a permanenl record is obtained. In other systems, lime counters are started al Ihe instant the energy is delivered lo the' ground and slopped when the first-break energy arrives al the geophones, thus giving direct readings of Iraveltimes.

4.6.5. Marine Refraction Work Because refraction recording requires Ihal there be appreciable distance belween the source and (he recording locations, Iwo ships havc usually been required for marine refraction recording. To shoot a reversed refraction protile in one Iraverse requires Ihree ships - a shooting ship at each end and a recording ship that travels between them. Por the shooting ships to travel the considerable distances between shotpoints takes appreciable time because oC the relatively low maximum speed of ships, and hence the high production rates thal makc marine refteclion work economical are not realizcd in marine refraction. The sonobuoy (Pig. 4.73) permits recording a reCraetion profile with only one ship. The sonobuoy is

an expendable listening station that radios tbe information it receives back lo the shooting ship. The sonobuoy is merely thrown overboard. The salt water activales batteries in the sonobuoy as well as other dcvices that cause a radio antenna to be extended upward and one or two hydrophones to be suspended beneath the buoy. As the ship travels away from tbe buoy, shots are tired and the signals received by the hydrophones are radioed baek to tbe ship where they are recorded. The arrival time of tbe wave that travels directly through the water Crom Ihe shot to the hydrophone is used to give the offset distance. After a given length or time lhe buoy sinks itself and is not recovered. Sonobuoys make it praelical lo record unreversed refraction profiles while earrying out reflection profiling. The only additional equipment cost is tha! oí the sonobuoys.

4.6.6. Refraction Data Reduction Refraetion data have to be corrected for elevation and weathering variations, as with reflection data. The correction methods (§4.7.1) are essentially the same except tbat oCten geophones are loo Car from ¡he shotpoint to record the refraction al the base of tbe LVL and Ihus there may be no weathering data a10ng mucb oC the line. Additional shots may be taken Cor weatbering information.

-

Hydrophone output relayed back to ship by radio

Antenna

(

~ Energy sou rce

--\.

\.:. "-1( /-

\

~ ~.,"'''''',o .

~~

U pon immersion in water _ (1) Antenna is raised (2) Hydrophoncs are droppcd (3) Batterics are activatcd

-----------------

Figure 4.7]. Sonobuoy oper¡¡tion.

Seismic methods

274

Where complete reCraction pro fiJes from zero offset to large offsets are available, playback oI the data with judicious selections oC tilters and AGC may aJlow one to correlate reflection events with reCraction events, thus adding useful information to each type of interpretation. Often the most prominent reflections will not correspond lo tbe mosl prominent refractions. Another useful technique is lo display the dala as a reduced refraction section where arrival times have been shiCted by tbe amount x/VI!' wbere VI! is near tbe refractor velocity. If VR were exactly equal lo tbe refractor velocity, the residual times would be the delay times (wlúeh will be disellssed in §4.9.3), and relief on the reduced refraction section would correlate with refractor relief (altbough displaced from the subsurCace location of the relief). However, cvcn if VI! is only approximately correct, the use oC reduced sections considerably improves the pickability of refraction events, especially secondary refractions.

Figure 4.74 iIIustrates a method oC obtaining the eorrection for lo, the shotpoint arrival time. Ed is the elevation of the datum, E, the elevation of tbe surface at the shotpoint, D, tbe depth oC tbe shot beJow the suríace, and t uh is the uphole time (§4.5.2e). The deviation of reflection paths írom the vertical is uSllally small enough that we can regard !he patbs as vertical. Therefore, the time required for Ibe wave to travel from the source down to Ihe datum is /};.I" where

( 4.86) Similarly, the time for the wave to travel up Crom the datum to a geophone on the surface at B is /};.Is whcre

AIII = Al, +

( 4.87)

luh

The correction Alo for the traveltime for a geophone at the sourcepoint is then

4.7. DATA PROCESSING 4.7.1. Data Redudion Variations in tbe elevation oí tbe surface atrect traveltimes and it is necessary to correet for sueb variations as well as for cbanges in tbe near-surface low-velocity-Iayer (L VL). Usually a reference datum is selected and corrections are calculated so tbat, in etrect, tbe shotpoints and geopbones are located on tbe datum surface, and it is assumed that conditions are uniform and tbat there is no LVL material below tbe datum leve!. The reference datum is usually horizontal, but where elevation variations are large, a ti/red dalum or a ftoaling dalum (one having the generalized relief oC the surface but witb smaller magnitude) may be used. Many methods exisl Cor correcting for nearsurface etrects. These schemes are usually based on (1) uphole times, (2) refractions from tbe base oC the LVL, or (3) tbe smoothing of retlections. We shall describe several oí tbese metbods tbat are simple to apply and adequate to cover most situations. Automatic statics-correction schemes, which usually involve statistical metbods oí smootbing retlections, will be discussed in Section 4.7.5d. We shall assume !hat Vw and VH , the velocities in tbe LVL and in tbe layer just below it, are known; they can be found írom an uphole survey or tbe refraction first breaks, as will be discussed later in tbe section. In what fol1ows we assume tbat tbe sbot is placed below the base oC !he LVL; if Ibis is not true, modifications bave to be made in !he equations in this section (see problem 10).

/};.t o =

=

Al,

+ Al, = 2 At, + tuh

2( E, - D, - Ed ) VH

+/uh

( 4.88)

Subtraction of Ato' from tbe arrival time lo is equivalent to pladng the sbot and the shotpoint geophone group on !he datum plane, !hereby eliminating the effect oC !he low-velocity layer ir !he shot is beneath the LVL. At times tbe shot may be so Car below the datum plane !hat Al, will be negative. When Equation (4.56) is used to calculate dip, tbe dip moveout must be corrected Cor elevation and weathering. The correction to tbe dip moveout, Al r , often called the differential weathering correctiQn, is tbe difference in traveltimes at opposite ends of a split-dip spread for a retlection Crom a horizontal bed. Referring to Figure 4.74, tbe raypatbs Crom the shot B down to a horizontal bed and back to geophones al A and e have identical traveltimes except for the portions A' A and CC from the datum to tbe surface. Assuming as before that A' A and CC are vertical, we get for At. the expression

Ale = (Al,) e - (Al,)

A

- (Al, + luh)C - (&t, +

'uh)A

(4.89)

If we take tbe positive direction oC dip to be down from A toward e, then (&tc/&X) must be subtracted algebraically from the observed moveout to obtain tbe true dip moveout. The Collowing calculation iIIustrates tbe etrect oC !he correction. We take as datum a horizontal plane

Data proeessing

215

B Low ,,·t:locity

E,

v,

lo)er

- -(E,-V,-E,I

Datum plan e

E,

e

.4'

Figure 4. N. ellel/lation of weathPrillg íorrr'r/ions.

Table 4.3 Calculation of difierential weathPring

we can write the approximate relation

(orrer/ion

A'B' Shotpolnt

Shotpoint 8

Shotpoinl

244 13

257 20

tuh (ms)

248 15 48

44

53

Calculated !l/, (ms) !l/5 (ms)

16

15

64

59

18 71

!l/o (ms)

BO

74

89

e

E, (m)

r\'easured

D, (m)

200 m aboye sea level; VH is 2,075 m/s. Table 4.3 gives data Cor three successive shotpoints, A, B, and C. at intervals of 500 m (such as those in Fig. 4.74). Let us suppose that a reflection on a split profile from shotpoint B gives the following data: (o = 2.421 s, lA - 2.419 s, and (e - 2.431 s. Then the eorreeted value or is 2.421 - 0.074 = 2.347 s and the eorrected dip moveout is

'o

~v~x

- {2,431 -

AB

+ 2tw '" ---;- + 2(w ~lI

A

- 7

!l/e (ms)

'AG + f SG '" - VH

2,419 - ( - 0.007)} /0.5

where t w is the traveltime through the weathered layer at G. Thus, (w'"

+'BG-(AB/VH )}/2

(4.90)

Subtraeting t w from the arrival times in effeet places lhe geophone al the base oí the L VL. To correet to datum we must subtract the additional amount (Eg - EJ - Dw)/V/{, where Eg is the elevation oC the geophone group and Dw is found by multiplying llV by V w · Oecasionally special refraction pro files are shot to obtain data for making correetions Cor intermediate geophones. These profiles may be oC the standard type using small charges placed near the surCaee or a nondynamite source on the surface; they are interpreted using standard mcthods such as Wyrobek's (§4.9.3e) to lind the depth and Iraveltime lo the base of the L VL. Alternatively. a shot may be plaeed just below Ihe L VL as in Figure 4.75, in which event we must modify Equation (4.69) beca use the shot is at the base rather than lhe top of the upper layer. Thus,

= 38 ms/km t

Ir (te - fA) had been negative, for example - 10 ms, then the dip moveout would be {- 10 ( - 7)} /0.5 - - 6 ms/km, so that the eorreetion can change the direction of dip as well as its magnitude. Therefore accurate corrections are essential. Corrections are often required ror geophones in between shotpoints, hence uphole times are not available and the first breaks are frequently used in Ihis case. In Figure 4.75 G is a geophone intermediate between adjacent shotpoints A and B. Let I..fG and IBG be the first-break times ror the paths A'CG and B'C'G. Almost always GC and GC" are within 20° of the vertical and CC" is therefore small. Thus,

{tAG

.'( - Dw tan Oc

Dw

.\'

VII

VW cos Oc

VII

= ----:-:--- - + - - - = -

+

Dw cosUe VII'

( 4.91) Most near-surface eorreetion methods require a knowledge oí VH and sometimes of V", as well. The Cormer can be determined by: (1) an uphole survey as described in Section 4.5.2e, (2) a special refraction survey as described aboye, or (3) analysis of the first breaks for distanl geophone groups (because these are equivalent lo a refraelion profile su eh as that shown in Fig. 4.76). The weathering velocity V w can be found by (1) measuring the slope oC a plot of the first breaks for geophones near the shotpoint (correcting distanees for obliquity), (2) dividing D, by

Seismic methods

216 G

Ba .. 01 LVL

Velocily - V w

~

B'

Velocity - VH Ollum plane

Figure 4.75. Da/um correc/ion for geophone between shOlpain/5.

Figure 4.16, Refractian weathering profiJe. t!lb Cor a shot placcd near the base of the LVL, (3) an uphole survey, or (4) firing a cap at the surface and measuring the velocity oC the direct wave. Of these, (3) is clearly superior.

4.7.2. Introduction to Digital Processing: Fourier Transfonns Most seismic processing is done in digital form (Robinson and Treitel, 1973; Schultz, 1985) and in tbe following we treat seismic data as time series (whereas Appendix A treats much of the same material as continuous functions). Data processing is bascd on the application oC information theor)' and we present here a simplified version oC its concepts; a more complete account is given in Sheriff and Geldart (1983, Chapo 10). Usually we think oC seismic data as tbe variation witb time (measured from the source instant) of tbe amplitudes oC various geopbone outputs. When we talte this viewpoiot, we are thin.king in the time domai", that is, time is the independent variable. We aIso sometimes find it convenient to regard a seismic wave as a superposition oC many sinusoidal waves differing in frequency, amplitude, and phase. Tben the relative amplitudes and phases are functions of frequency and we are tbinking in the frequency doma;n. The frequency dornain approach is ilIustrated by electrical systems that are specified by their effects OD the amplitude and phases oC sinusoidal signals ol different frequencies. For example, graphs of filler characteristies usua1ly show amplitude ratios

or phase shifts as ordinates with frequency along the abscissa. A Faurier /ransform (§A.9.2) in our context involves transforming functions from the time domain to the frequency domain and an ¡nverse Fourier transform transforming from the frequency domain to the time domain. The important point with transforms is that no information is lost in transforrning. We can, thus, start with a waveform in the time domain, transform it into the frequency domain, and then transform tbe frequency-domain representation into a waveform that is idcntical with the original waveform. TIris maltes it possible to do part of our processing in the time domain and par! in the frequency domain, tiling advantage oí tbe faet tbat sorne processes can be executed more economically in one dornain than in the other. We also gain additional understanding from baving the viewpoints oC botb domains. lf we have a reasonably "well-behaved" function 8, and its transform G., then [compare with Eq. (A.53)] ( 4.92) ( 4.93)

Equation (4.93) gives the Fourier transform oC g, wbereas Equation (4.92) gives the inverse transform g,. rEqs. (4.92) and (4,93) are often written in other equivalent forms.] We refer to K, and G. as a trans-

Data processing

217

form poir and the relation is expressed in the form

8,_ n

g, .... G.

For actual waveforms, g, is real and usually causal (§A.9.3). In general, G. is complex [Eq. (A.56)], so G - A ej··

•

(4.94)

•

where A. is real and positive and is called !he amplitude spectrum; <1>. is also real and is called the phase spectrum. Substitution in Equation (4.92) gives g, -

EA. e

j (2 17 "

Time invariant:

+ •• )

( 4.95)

• When g, is real (the usual case), i! equals the real part of Equation (4.95): g, - LA.cos(2".vt + <1>.)

( 4.96)

•

--+

1system 1-- !, - n

=

L~.:-~.:_~~~jo, fl ' f2 •... ] n zeros

In the last bracket on the right. the first output different from zero is fo amI occurs at !he instant t - n/l. Obviously any input that consists of a series oC sampled values can be represented by a series oC unít impulses multiplied by appropriatc amplitude factorso We can then use the aboye two properties to find the output Cor cach input impulse and by superimposing these we gel the output for the arbitrary input. 11lls process is called convo/ulion. We sha11 illustrate convolution by considering the output Cor a tilter whose impulse response !, is [Jo. 11' h] = [1, - 1, When the input x, is [xo. XI' x 2 l = [1.!. we apply to the input the series oC impulses [B,. i B'_I' - ! 8'-21 (the last two subscripts mean that the impulses are delayed by one and two sampling intervals. respective1y) and obtain the output

H H

4.7.3. Convolution Let us now conO. sider the time-domain operation called conoo/ution (§A.I0). Assume that we (eed into a system data sampled al regular inlervals, Cor example, a digital seismic trace. The output 01 the system can be calculated ir we know the impulse response (§A.13) oC Ihe system, Ihat is. the response of tbe syslem when Ihe input is a unir impulse 8, (§A.9.3). The impulse response 01 the system will be zero prior to r = O and then will have the values fo. 11' 12 .... at successive sampling intervals. We represen! tbis process diagramatically thus: (a) The convo/ution operation.

r

, ;

•

Most systems with wbich we deal are linear (§A.l3) and time-invariant (or very nearly so). A linear system is one in which the output is directly proportional to the input whereas a time-invoriant sysrem is one in which the output is independent oC the time when the input occurred. Writing 8,_. for a unít impulse that occurs at 1 - n/l. where /l is the sampling interval. we can iIlustrate linear and timeinvariant systems as follows: Liner.r:

[1, - 1.~1 P'-l ..... [O,í, - Ll] B, ....

- tB'-l .... [0.0, -

L!, -l]

By summing we find tbe outpUI

Convolution is ilIustrated in Figure 4.77. Th.is operation is equivalent to replacing each element oC the input by an appropriately scaled version oC the impulse response and then summing e1ements that occur at the same times. If we call the output z, and denote the operation oC taking the convolution by an asterisk, we can express this as ( 4.97a)

z, = x,.!, = "'[X'-kfk k

- [xo/o • xtlo

+ xo/l , xdo + xtll + xo/2" .. ] (4.97b)

Note that we would have obtained the same result if we had input /, into a filler whose impulse response is x,; in otber words. convolution is commutative: x, • !, - !, • x, - "'[x'-kfk "" L!,-kXk (4.98) k

k

The convolution theorem states Ihat the Fourier transform oC Ihe convolution oC two Cunctions is

218

Seismi c metho ds

r,

Input

Fiher

I

·1 '

-->-~----r-¡ -~'"I _-1

~

O

~

O

~

_t.-- --l

L-

I

.t,

Oulpul

I 1'_--J1 L~ :,

fr

~0-'--r¡-_-!---l)>-iL._ _

I

I

I I I

-,

, t'

ti

¡-l

ti

O

¡-! +-1

_..J. O-...........""'-.... .--

-1 -1 Figure 4.77. Filtering .15 an eXdmple o( convolu tion.

equal lo the produc t oí Ihe transío rrns of Ihe individual Cunclions. We can slate the theorern as

of a cornb is also a cornb: comb( t) .... k¡ comb( JI)

X, ....

X(,,)

-1 X( JI) 1eJ··(')

/, .... F( JI) =IF( JI) X, • /, ....

=

1 ejo~,(,)

X( JI) F( ,,)

[1 X(,,) 11".1+·(,) HI F( JI) 1e J·,(·) I

.... 1X(,,) 11 F(,,) I eJ[t.(,)+ ¡(.)]

(4.99)

where IX(JI)I and IF(")I are Ihe amplilu de speclra, and cf>A JI) and are Ihe phase spectra. This rneans Ihat iC two seis of data are convolved in the lime dornain, the effect in the frequency dornain is to rnultiply their amplitu de speclra and lo add Iheir phase spectra. Because oí symme try proper ties oí Ihe Fourie r transío rm [Eq. (A.60»), il can be shown Ihal

"'1 (,,)

X,!, .... X(,,). F(,,)

( 4.100)

(b) Sampling and aliasing. In Ihe analog-Io-digital conversion, we replace the continu ous signal wilh a series oí values al fi¡¡ed inlervals. It would appear that we are losing inform ation by discard ing the data between the sampli ng instants. The transfo rm relationship in Equati ons (4.92) and (4.93) can be used lo unders land sampli ng and Ihe situalio ns in which inCormation is nOI lost. We rnake use oC the eomb or sampling fune/ion, which consists oC an infinile sel of regularly spaced uníl impulses (§A.9.3 and Fig. 4.78b). The transfo rm

( 4.101)

where k¡ depend s upon the sampli ng inlerva l (see proble m 12b). If the comb in Ihe time domai n has eJements every 4 rns, tbal ís, the sampli ng Crequeney is 1/0.00 4 '" 250 Hz, the Iransfo nn is a comb with spaeing 250 Hz. We shall also make use of the boxcar (Fig. 4.78d), a funetio n Ihat has a consta nt value over the range ± "o and is zero everywhere else. The Iransfo nn of a boxear is a sine funetion: sin 2""01 bo¡¡ca r(,,) .... k 2 sinc(2'ITI'o f) - k 2 --'2'ITJlot ( 4.102) where k 2 is the area oC the boxcar (see proble m 12c). Figure 4.78a shows a contin uous, real, causal functio n y(t) and its arnplit ude spectru m IY(")I; the lalter is symme tric about zero, so negaliv e Crequeneíes give the same values as positiv e frequencies. The sample d data Ihal represe nt y(l) can be Cound by multip lying the contin uous Cunclion by tbe comb (hence the name "samp ling funetio n"). If we are sarnpli ng every 4 rns we use a comb with elements every 4 rns. Aecord ing lo Equati on (4.100),

Convo lution is equiva lenl lo replaci ng each data elernent [each impuls e ¡" comb( ,,) in Ibis instanc e] with Ihe other funclio n Y(,,) (prope rly scaled). This is ilIuslra ted in Figure 4.78c. Note Ihat the Crequency

Data processing

219

-

101

~~V'

?

t

:

muhiph4:d

,:

-toi

r-- 0-004 ..

.

,L '1 ~

o

.""" +

1;.-1 1 ),

o·

: k 2 sine

, t

-1

Sptt'tril

1\, ,(\.

,

t

lHultiJ'llicd

~'~'$"

1+

1

Id)

--------- ~~ -LI------L-____~~______~.~-----L

W(-

-+l f*- 0004

--J

~V:X:L.W;>(i.'\/ -250 -llS O 115 250 Ilz

2'''''0'

__ AA_

= 250 Hz 4

.jo

~

1 0004

A.lia~

y,.lds

í\, /(\

Conyolved wíth

,,

l'

1

...

j

!'opet.:lra -+-1

I

Ju 4--

Ali,b

I

,, 1:,rr"l'

125 HI

•

. . 1 . . . - _ - 1 -_ _ _

+

,

O

+ ~,lf\\ohtd wi'h
/11/11/1///1///1/111111111

i

Hz

b)' ~o,n" (1)

1

I

-12~

~

-15ft

-125

O

115 H1.

.¡.

• ••

yitld~

vitlds

.¡.

,

,

~ ~ _~I~ O ,-,~"'--"""""r::7"----250

fold, back

____

-U~L-~~__L-~ ~ ~

-125

__

o

125 Hz

__

v

Figure 4,78, Sampling and reconstitUling,

i

r ,

spectrum of the sampled function differs from the spectrum of the continuous function by the repetition of the spectrum every 250 Hz. We can recover the spectrum of the original function by multiplying the spectrum of the sampled function by a boxear. The equivalent time-domain operation [Eq. (4.99») is to convolve the sample data with the sinc Cunction. As shown in Figure 4.78e, this restores the original function in every detail. The sinc function thus provides the precise "operator" for interpolating between sample values. In the aboye instance no information whatsoever was lost in the process oC sampling and interpolating. However, if the continuous function had had a spectrum (shown dolted in Fig. 4.78a) that included frequency components higher than 125 Hz (in this example), then the time-domain multiplication by the sampling function would have produced an overlap of Crequency spectra (dotted curves in Fig. 4.78c) and no longer would we be able lo recover Ihe original spectrum from Ihe spectrum of the sampled data; hence we would nol be able to recover the original waveform. Whether or not the original waveCorm is recoverable depends, therefore, on whelher or not the original waveform con!ains frequencies lúgher than half oC the sampling frequency. The relationships demonstrated in the foregoing texl are summarized by the sampling theorem: No

information is lost by regular sampling provided that Ihe sampling Crequency is greater than twice the highest frequency componen! in the waveform being sampled. This is equivalent to saying that there must be more Ihan two samples per cycle for the highes! Crequency. The sampling theorem thus determines the mínimum sampling we can use. Because this minimum sampling allows complete recovery of the waveform, we can further conclude that nothing is gained by using a finer sampling. Thus, sampling Tates of 2 and 4 ms permit us to record data faithfulIy provided none oC the signal speclrum lies aboye 250 and 125 Hz, respectively. Half the sampling frequency is called the Nyquist frequency. Any frequency present in the signal that is greater than the Nyquist frequency "n by the amount Il" will be indistinguishable from the lower frequency "n - /l". In Figure 4.79 we see that a sampling rate oC 4 ms (tbat is, 250 samples/s) will allow perfect recording oC a 75 Hz signal but 175 and 250 Hz signals wiII appear as (that is, will alias as) 75 and O Hz (which is the same as a direct current), respeclively. Alias signals Ihat fall within the Crequency band in which we are primarily inlerested will appear to be legitimate signals. To avoid this, aliasing jillers are used before sampling to remove frequency components higher Ihan the Nyquist frequency. With filters having 72 dB/octave slope, we

Seismic methods

220

(a}

(b}

Id

Figure 4.79. 5ampling and aliasing. Differenr frequencies sampled ar 4 ms inrervals (250 rimes per second). (il) 7S Hz signil/. (b) The 77S Hz signal yields rhe same sample values as 75 Hz. (e) The 250 Hz signal yields samples of eonstant value (de).

musl begin fihering an octave lower Ihan the Nyquist frequency to be SUTe that frequencies tbat might otherwise alias are reduced by at lea~t 72 dB before sampling (Pig. 4.56). This must be done before sampling because afterward the alias signals cannot be distinguished. Alias filtering also has 10 be done before any resampling operation that may be performed during data processing. Aliasing is an inherent property of all syslems that sample and thus applies not only to time sampling but also to other situations. such as where we use geopbones to sampIe the earth motion (spatial sampling). (e) Filtering by the earth. We can lhink ol tbe earth as a filter of seismic energy. We might consider the wave resulting from an explosion as an impulse k8" Chal is. the wave motion at the SOUTce oC Che explosion is zero boCh belore and aIter the explosion and differs rrom zero on1y in an extremely short interval (essentially at t - O) and during this infinitesimal inlerval Che motion is very large. Ideally, the signal that we record would be simply k 6(t) con volved with the impulse response of the earth.

The result would be zero except for sharp pulses corresponding to the arrivals oI different reHections. If Ibis were so, we could determine easily from the recorded data the complete solulion to the seismic problem. However, in practice, the waveform is strung out and modified by filtering due lo absorplion and other causes so tbat reflection waveforms overlap, and several types oC coherent noise and random noise are superimposed. The waveform that we finally record as a seismic record is Ihe result of the successive convolulions ol the shot impulse with Che impulse response ol the various porlions of the earth Chrough wbich Ihe wave travels. We can arrive al an approximate picture by considering Ihe earth to be divided into zones: 1. The zone near the shot where stress levels and Ihe

absorption oC the highest frequencies are very sevcre. We write s, Cor Che impulse response of tbis zone. 2. The rel1ecting sequence of beds whose impulse response e, is the .. message" information Chat we are seeking to discover by OUT seismic exploration.

Data processing

221

3. Changes in propagating through the section (P,) because oC absorption, peg-Ieg multiples, and other causes. 4. The near-surIace zone thal exercises considerable filtering aclion in changing the waveshape. We write n, Cor the impulse response oC this last zone. Neglecting additional filtering effects. we thus write the seismic trace z, as the expression z,

= k 8, • S, * e, * P, * n,

w, -

[1. - 2r,3r 2 • - 4r 3 ,5r 4 , ... ]

= (1.0,- 2r.O,3r 2 ,O, - 4,3, ... ] (4.105) - (k 8, • S, • Pr • II r ) • er (4.103)

The factor (k 0, • s, • p, • n,) is called the embedded !'.'ave/el.

When we use a Vibroseis souree, the inpuI lo the earlh is a long wavetrain v, and the seismie trace z; which results is

Z: -

ing thus, we see that a hydrophone will detec! successive signals of amplitudes 1, -2" 3r 2 • -4,3, 5,4, ... arriving at intervals oC na. We can therefore write ror the impulse response of water layers of depths d = (n fj,) V /2. where V is the velocity in the water and n = 1, 2, 3, respectively:

(v,.s:. p,.nt) * e,

(4.1 04)

(where we write s; rather than s, because the filtering processes near the Vibroseis souree may be diCferent Crom those near a shol owing lo the different magnitude oC tbe stresses involved). (d) Water reverberation and deconvolution. Let us examine Ibe effect of multiples resulting from reftection at tbe bottom and top of a water layer (Baekus. 1959). We write na for the round trip traveltime from top to bOllom oC the water and back where n is an integer and 6.. is the sampling intervalo We assume that the reflection coefficients at the surface and bollom of the water layer are such that the ratios oC the reftected to incident amplitudes are -1 and +', respectively. where the minus sign denotes phase reversal at the water-air interface. We assume also that the amplitude of a wave retuming directly to a hydrophone after reflection at a certain horizon (without a "bounce" round trip between top and bOllom of Ihe waler layer) is unity and Ihat ils traveltime is 1. A wave that is reflected at the same horizon and suffers a bounce either hefore or after its travel down to the reflector. will arrive al time I + na wilh the amplitude - r. Because there are IWO raypaths with the same Iraveltime Cor a single-bounce wave, one tha! bounced before traveling downward and one Ihat bounced after returning Crom depth, we have in efrect a wave arriving at time 1 + n fj, with amplitude - 2,. There will be three waves that suffer two bounces: One that bounces twice before going downward to the reflector, one Ihat hounces twice on return lo the surface. and one tha! bounces once before and once after its travel downward; each of tbese is of amplilude ,2 so that their sum is a wave of amplitude 3,2 arriving al time I + 2n a. Conlinu-

= [1.0.0. - 2r.0.0.3r 2 ....

]

If we transforrn lhis to the frequency dornain, we find a large peak (the size oC the peak increasing with increasing ,) at the lrequency 2/n 6.. and at multipies of tbis Crequency. These are the frequencies !hat are reinforced a! lhis water depth (Ihat is. the frequencies Cor which interference is cons!ructive). The result of passing a wavetrain tbrough a water layer is the same as multiplying the amplitude spectrum ol the waveCorm without the water layer by !he spectrom of the impulse response oC the water layer. Whenever Ihe reflection coefficient is large (and hence r is large) and the frequency (2/n 6..) (or one oC its harmonics) lies within the seismic spectrum, the scismic record will appear very sinusoidal with hardly any variation in amplitude throughout the recording period (Fig. 4.43b). Because oC the overriding oseillations, it will be difficult to interpret the primary refleclions. A filter " that has the property tha! w, • i,

= 8,

( 4.106)

is callcd the im'erse filler oC w,. If we pass the reverberatory output from the hydrophones through the inverse filter (in a data processing center), we will remove the effect oC the water-Iayer filter. The inverse oC the water-Jayer filter is a simple filter with only three nonzero terms. Cor example, i, = [1.2r. r 2 ] ti

=

1}

= [1.0,2r.0. r 2 )

n=2 (4.107)

= [I,O,O,2r,O,O. r 2 ]

11

= 3

and so forth (see problem 13). Figure 4.36b shows the result of applying such a filler. The process of convolving with an invcrse filler is ca1led decoll1>olurioll and is one of Ihe most important operations in seismic data processing (Middleton and Whiulesey. 1968; Webster, 1978; Ziolkowski, 1984). Whereas we have iIIustrated deconvolution as removing Ihe singing efrect oC a water layer, if we know enough about the filters and the

222

Seismic merhods

signal, we could also deconvolve tor other filters whose efreets we wish to remove.

4.7.4. Correlation (a) Cross-correlation. The cross-correlation ¡unclion is a measure oC the similarity between two dala seIS. One sel is displaced relalive to tbe otber, corresponding values of the two sets are multiplied together, and the products are summed lo give tbe value ol the cross-correlation. Wberever Ibe two seIs are nearly the same, tbe products will usually be positive and bence the cross-correlation is large; wberever the sets are unlike, sorne oC tbe produclS will be positive and sorne negative, and hence the sum will be smal!. If the cross-correlation Cunclion has a large negative value, it means that the two data sets would be similar if one were inverted (tbat is, Ibey are similar except that they are oul oC phase). Obviously, Ihe cross-correlalion is a runction oC the relalive shift belween the seis. By convenlion we call a shift positive ir it involves moving Ihe second function lo the lelt with respect lo Ihe lirsl Cunction. We express the cross-correlation of Iwo data seIs x, and Y, as

( 4.108) where T is the displacement oC y, relative lo x,, [Note that cjozy( T) is a data set rather than a continuous function, because X and y are dala sets.] Let us illustrate cross-correlation by correlating the IwO funclionsx , - [1, - l,íland y, - [l,L - íl,shown in Figure 4.80. Figure 4.8Oc shows the two funclions in their normal positions. Figure 4.80a shows Y, shifted two uníts to the right; corresponding coordinales are multiplied and summed as sbown below the diagram to give cjozy( - 2). Figures 4.80b, c, d, e show Y, shifted varying amounts wbereas Figure 4.80l sbows tbe grapb of cjoZy(T). The cross-correlation has its maximum value (the functions are most similar) wben Y, is shilted one uníl to the lefl (T - 1). Obviously, we gel the same results ir we shift x, one space lO Ihe right. In other words,

Hence cross-correlation can be perCormed by reversing the lirst dala set and convolving. If Iwo dala sets are cross-correlated in the time domain, the efrect in the frequency domain is the same as multiplying the complex spectrum ol the first data set by the conjugate oC the complex spectrum oC the second seto Because Corming the complex conjugate involves only reversing the sign of Ihe phase, cross-correlation is equivalenl to multiplying tbe amplitude spectra and subtracting the phase spectra. In mathematical terms, X,

++

Y,

++

x_.

++

cf>xy( .,) ....

-1 X( JI) 1eJ··<·) Y( JI) -1 Y( JI) 1e H ,(') X(,,) -1 X(,,) 1e- J··<·) X(;) Y(,,) -1 X(,,) "Y(,,) 1eJc +,-+.) X( JI)

( 4.111) We note that changing lhe sign 01 a phase spectrum is equivalent lo reversing the trace in the lime domain. (b) Aurocorre/arion. The special case where a data sel is being correlated with i tseU is called autocorrelation. In lhis case, Equalion (4.108) becomes

( 4.112)

Autocorrelation Cunctions are symmelrical because a time shift to the right is the same as a shift to the leCt, that is, from Equation (4.112), ( 4.113) The autocorrelation has its peak value at zero time shift (that is, a dala set is most like ¡!seU before it is lime-shifted). IC the autocorrelation should have a large value al sorne time shift /lt .. O. it indicates Ihal the set tends to be perlodic with the perlod /lt. Hence the autocorrelation function may be thought 01 as a measure of the repelitiveness ol a lunction.

( 4.109) The similarity between Equation (4.108) and the convolution equation (4.98) should be noted. We may rewrite Equation (4.108) in the form

+..y( T) -

t/>yz(

( 4.114)

-T) - L)icXk-_ k

- LYkX-C.-k) - Y. • k

(e) Norma/ized corre/arion. The autocorrelation value al zero shift is called the energy 01 the trace:

X_.

(4.110)

(This terminology is justified on the basis that x, is usually a voltage, current, or velocity, and hence x~ is proportional to energy.) For the autocorrelation

Data processing

223 (a)

Sh,ft of -2

Shift

(h)

I

~ ~ +1

I

I

O

x/_,

O

-1

t

+1

o t-I

I

--~~'--li-

O

T -j

0/>,,1-21-0+0+] = +~

+1

(d) Sh,ft of

+ t )', -----I-I-J-L-iro t-j

+1

t o

1

1

t+!

t+!

0/>,,( - 1)

I

--:

s

o- ) + 1

++\

>, -----.,~Tr-L-

-1

t+

j,

Ir) Shift ofO

I

+1

X 102

or -1

t+ l

I

"'--~-~'--T-

4t,. (O)

-1 -

+-l

~ -

l

- +1

(,) Sh,fl of +2

--+e l

," •• 1

+l

O

+1 +~

-1

t+

1

'+! , , ---''--''-itr-,....O -1 f,,,( + 1)

O+ ! + ) - +1

~

+!

t

+2 t -Jf,,, - - ' - -t, , - - l L -'-r--

t

-2

+1

l

o

t+l

.... (+2) =

• l

o+ o- !

= - ~

Figure 4.80. Caleulating the cr05S'correlalion o( Iwo (uneliom.

Cunctíon, Equation (4.111) becomes (4.115) Beeause the z.ero-shiCt value oC the autoeorrelation Cunetion is the energy of the trace, (x(t»)2 is the energy per unit oC time or the power oC the trace and [X(" »)2 is the energy per ¡ncrement oC Crequency, usually cal\ed the ellergy dellsity. We often normalize the autocorrelation Function by dividíng by the energy: ( 4.116) The cross-corre\ation function is normaliz.ed in a similar manner by dividing by the geometric mean oC the energy oC the two traces:

~yy('T)Dorm= [

() ()JI/2 (4.117) )'y O

Normalized correlation values lie between ± 1. A value oC + 1 indica tes perfecI copy; a value oC - 1 indicates perCect copy if one oC the traces is ¡nverted. (d) Automatic statics. Cross·correlation affords us a means oC determining the amounl of time shiCt that

wi1l result in the optimum alignment of two seismic traces. lf one trace has been delayed with respect to another, Cor example, in passing through the nearsurface layers, the delay equals the shiCt that maximizes the cross-correlation, that is, that produces the optimum alignment (match) oC the two traces. The magnitude oC the cross-correlation indicates quantitatively how much improvement such a shiFt will produce. Cross-correlation is a powerful tool and is especially useful when the data quality is poor. It is used in many processes to determine static corrections and the amounl oC normal moveout to introduce to align traces from different offset s before stacking (Hileman, Embree, and Pl1euger, 1968; Disher and Naquin, 1970). Criteria can be set that permit such shifts lO be determined and applied automaticaJly. provided tests are incorporated to ensure that the shifts so introduced are consistent (for example, to ensure that the same corrections are a!ways assumed for the weathering beneath any par· ticular location). Figure 4.81 illustrates the improvement in a CMP stack resulting from the use oC an automatic statics programo (e) Vibroseis analysis, The signa! z: that Ihe system records when we use a Vibroseis source [Eq. (4.l04») bears little resemblance lo e" the impulse response of the earth. To obtain a meaningful record, the data are correlated with the Vibroseis sweep

...C1J

5!0--

~

~

--

"(

~ c:: .2 t

-

-m-

.... -

.-

--

...~

8

.- -

-

.~

~

!!!

'"

~

..2 C1J al

-... ~ -... ~

~

~

~

·2

~

Ce

:...

~

t: ~

a

--

c:: .g

-E I.J

~ o

I.J

.\;1

!:l

.,

'"

.l:,!

o "5

.

....'"o C1J

'"

}c:: ;: .2

N

"'-í-

..:~

~6

..,. I.J

Q

... Q

~.~ ~

.~!!

... '"

· ,"" .

'

mr

I\\\\~I.~~,I!,. (

IH

,~

\ <'í: -

"

Seism;c methods

226 signal

v,.

The recorded signal

z;

is

z; - v, • e: where we let e; = s; • e, • p, • n, in Equation (4.104). Using Equation (4.110), we Iind, lor tbe cross-correlation ol tbe sweep and tbe recorded signal,

- e; •
( 4.118)

(The next to the last step is possible because convolution is commutative.) Hence tbe overall effect is that of convolving the eartb function with the autororrelation of the Vibroseis sweep signal. The autocorrelation function
4.7.5. Phase Considerations Equation (4.96) represents the adding together of cosine waves ol different frequencies and different phases. IC the same components are added together with different phase relations. different waveforms result. Changing the waveform changes the location 01 a particular peak or trough, and hence measurements of traveltimes are affected by variations in the phase spectra. Because seismíc exploration primarily involves determining the traveltimes oC events, preservation oC proper phase relationships during data processing is essential. Out oC all possible wavelets with the same amplilude spectrum, the wavelet whose energy builds up the fastest is called tbe minimum-delay wavelet. lts phase is always less tban tbe otber wavelets with the same amplitude spectrum, and hence it is also called minimum phase. The simplest wavelet (except for an impulse) is a data set tbat contains only two elements, tbe set [a, bj. The amplitude spectrum of tbis dala set is identical with that of the set [b, aj, but no other dala set has the same spectrum. Ir lal > Ibl, energy is concentrated earlier in tbe wavelet in the set [a. b) than in the set [b, a), and hence [a. b) is mínimum phase (or mínimum delay). Larger wavelets can be expressed as the successive convolution of two-element wavelets; a large wavelet is minimum

phase ir all of its component wavelets are minimum phase. The impulse response oC many 01 the natural Iiltering processes in the earth are minimum phase. Sorne filtering processes require that assumption be made about the phase 01 the signal; general1y minimum phase is assumed (Sherwood and Trorey. 1965). Thus deconvolution based on autocorrelation information has to assume the phase because the phase information of the waveform was lost when its autocorrelation was Cormed. Tbis can be seen Crom Equation (4.115) where we note that the autocorrelation function
4.7.6. Frequency Filtering (a) Least-squares (Wiener) (iltefing. Sometimes we wish to determine the fiIter lhat will do the beSl job of converting an input into a desired oUlput. The fiIter that most ncarly accomplishes tbis objective in the least-squares sense (§A.8) is called the leastsquares filter or the Wiener filter. occasionally the optimum filter (Robinson and Treitel, 1967). Let the input data set be x" the filter that we have to determine be ¡" and the desired output set be z,. The actual result oC passing x, through this filter is x, • ¡, and the "error", or difference. between the actual and the desired outputs is (z, - x, • j,). With the least-squares method, we add together the squares of the errors, Iind the partial derivatives oC the sum with respect to the variables J, (the elements oC j,), and set these derivatives equal to zero. This gives the simultaneous equations where z, and X, are known:

a a'

-~(z ~, JI

I

-x, ./,) ,

2

-o

i-O.l.2 •... n ( 4.119)

One such equation is obtained for each oC the n + 1 elements in j" and solving for the unlcnowns ¡" we Iind the filter j, that minirnizes the sum oC the errors squared. Manipulation leads lo the so-called normal equations (Sheriff and Geldart, 1983, pp. 41 and 151), wbich are more convenient than Equation (4.119):

"

L ,¡,,,A'T - j) 1; '"
1-0,1.2 •... n

j-O

( 4.120)

227

Data processing

These equations can be used to cross-equalize Iraces, Ihat is, lo make traces as nearly alike as possible. Suppose we have a group of traces to be stacked, 5uch as the components ol a common-midpoinl stack. After the normal-moveoul corrections have been made, the traces may still ditfer from each other because they have passed through ditferent portions of the near surlacc. The normal equations can be used to find filters that will make all the traces as nearly as possible like sorne pi/ot trace, such as the sum of the traces. This procedure will improve the quality of the stacked result. The normal equations are also used lo design deconvolution operators. The earth impulse response e, is assumed to be random, that is. knowledge of shallow reflections does not help to predict deeper primary reflections. Consequently, the autocorrelation of e, is negligibly small except for a shift oC zero time and we can write

4>•• ( '1")

( 4.121)

"" ka,

The geophone input 8, is regarded (Eq. (4.103») as the convolulion ol e, with various filters (the most important of which usually results from near-surface etfects), and the overall elfect is represented by the single equivalent filter n;; g, ~

e, * n;

The desired output z, is the earth's impulse response e, (which can be shown 10 be mínimum phase); henee using Equation (4.110) we can write

4>,z('I") -z.*g_. = e r .( e • n' ) -T

-T

... (e f' • e -.,. ) • n'- , .

= kIJ. • n~. =

kn'-.,.

( 4.122)

n;

is causal, thal is, it does nol yield an The filler output until after there has been an input; hence = O Cor '1" < o. Thus

n;

4>,z ( /)

= O for t < O

( 4.123)

ThereCore, iC we concem ourselves only with positive values of /, we have the values required to solve Equation (4.120) for Ihe deconvolulion filler. (b) Frequency filtering and deconvolution. The use oC deconvolution lO removc Ihe filtering elfect of a water layer and the near surface has a1ready been discussed. Although the water-Iayer filler was presented in a delerministic way, the proper choice of paramelers is usually not obvious. Slatislical and empirical ways oC choosing filter parameters are sometimes used (Kunetz and Fourmann, 1968). Deconvolution by Wiener filtering (using Eq. (4.123)]

has a1so been discussed (Peacock and Treitel, 1969; Robinson, 1972). One deconvolution assumption is that the amplitude spectrum should be Hat, that is, all frequency components should be present in equal amounts. It is argued that Ihe Earth's reflectivity is etfectively random (the same argument thatjustified Eq. (4.121)) and hence should contain equal amounts of al1 frequencies. This assumption is called whitening, in analogy lO white light, which contains al] frequencies in equal magnitude. lt is also called spiking deconvofu/ion because the amplitude spectrum of a spike (8,) is white. Whitening can be accomplished by Fourier transforming a trace, flattening the amplitude spectrum but not changing the phase spectrum, and then inverse transCorming. Whitening can also be done in analog processing by passing the signal through a number of narrow bandpass filters, making Iheir oulputs equal in magnitude, and then recombining. Whitening tends to inerease the noise iC the signal level is below the noise level Cor any frequency components. The values of a correlation function Cor t';' O me asure the predictability involved. If a trace were nonpredictable (Ihat ¡s, random), Equation (4.123) would hold. If a11 reHections involve the same embedded waveshape (as implied by Eq. (4.103)] and it is known, then Ihe early part of a reflection can be used lo predic! the values that Collow. If the refleclion waveshape has the length n and ir tbis waveshape is the only predictable element, the aulocorrelation will have nonzero values between ± n and the autocorrelation spectrum will be the square 01 the spectrum oC the wavelet. If multiples are generated by a reflector associated with the travellime m, then the traveltimes oC the muItiples can be predicted, which will cause Ihe trace autocorrelation lo have nonzero values for '1" > m. Predictive deconvolution utilizes these facts. Setting rl>gg ('1") = O for T > n effectively shortens the waveshape to the length n. Using the values of 4>f8( T) Cor T > m gives the predictable effecI 01 the multiples, which can be subtracted from Ihe trace to produce a result that shou1d be free of Ihe multiples. This is caBed gapped deconvolution because the autocorrelation values in the gap '1" < m are not involved. Wavelet processing is a Iype oC deconvolution Ihat attempts lo acbieve a short wavelet of symmetrical waveshape, a waveshape that facilita tes interpre!ation. The spectrum oC the embedded wavelet can be found from the spectrum of the trace autocorrelation, as previously indicated. Usually the autocorrelations oC a number of traces are summed to average out trace-to-trace noise ditferences. lf the wavelet phase speclrum can be assumed or determined, then Ihe embedded wavelel is given by the inverse Fourler

Seismic methods

228

RHS VELOCITY (FT/S) .1.

,. ~...

':'1

.'

....

:ro :_ ,'1 , .. ,",\ " ! '::< .:.al

,~

D'

,1

'

.

;¡"

-,

-'1 .1

o

.;. J•

• 0 ......:

01--+--+......

•

.,

.... ..:.

"l(

.:w": l'Il Ji.L·

",. :'

,. Ifi w:

". " , :

., P",

OT ,. -"~

~

....a

.,.

• "I!'

'T:

no .re .''''" .......

~

;¡; :¡:-.,::--.. >ti 'rIl lo' 11 ":¡¡ 11 ......."j.

"

lO~I!..""

óI~ ~.I ~.'

)

'"

'"

(b)

(e)

(d)

Figure 4.83. Veloeity ilnillysis. (Courtesy Grant·Norpac.) (a) Portion of seismie seetion, (b) Veloeity analysis af data ar righr side o( (a). (e) Maximum semblanee at eaeh record time. (d) Peak amplitude at eaeh record time.

transformo Once the embedded wavelet is known, an operator can be found to replace it with sorne other desired waveshape.

(e) Time- varíant filtering. Deeper reftections have a higber percentage of low-Crequency energy tban shallow reftections because oC the greater attenuation oC

the higher frequencies as a result of absorption and other fihering mechanisms. Hence, time-variant filtering is used in which the passband moves toward lower frequencies as record time increases. One method oC achieving time-variant fihering is to use separate gates (time intervals), Cor example, shallow and deep, so that the deconvolution operator varies with record time (Clarke, 1968),

229

Data processing

4.7.7. Velocity Analysis The variation ol nonnal moveout witb velocity and record time has already been discussed in connection with Equation (4.52). Several techniques utilize tbe variation of nonnal moveout with record time 10 find velocity (Garotta and Michon, 1967: Schneider and Backus, 1968; Cook and Taner, 1969; Taner and ~oehler, 1969). Most assume a stacking velocity ¡V. In Eq. (4.84)], apply normal-moveout corrections as a lunction ol arrival time and offset, and then measure the coherence (degree ol match) among al1 the traces available to be stacked. Several me asures of coherence may be used and they are discussed further in Seclion 4.7.13 [Eqs. (4.125) and (4.126)J. Another stacking velocity is then assumed and the calculalions repeated, and so on, until the coherence has been determined as a function oC bolh stacking veloeity and arrival time. (Somelimes normal moveout is the variable rather Ihan stacking velocity.) A velocity-analysis display is shown in Figure 4.83. This is a good analysis because tbe data involved are good. Higlts on tbe con tour plot correspond to events. The locations ol the higlts yield the velocities (or normal moveouts), that oplimize the stack. (hence the name stacking velocity Cor V.). Mulhples as well as primaries give rise to peaks and hence tbe results have lo be interpreted to determine the best values to be used to stack the data (Robinson, 1983a). In many areas where the velocity more-or-less monotonically increases wi th dcpth, the peak~ ~sociated with tbe higltest reasonable stacking velOClhes are assumed to represent primary relleclioos and the peaks associaled with lower velocities are attributed to multiples of various sorls. In other areas the relalionships are nol as obvious, and even where the velocity relalionships are gene rally regular difficulties will be encounlered. ' The major objective of velocily analysis is to ascertain the amount oC normal moveoullhat sbould be removed lO maximize tbe stacking of cvents thal are considered to be primaries. This does not necessarily optimize the primary-to-multiple energy ratio and beller stacks can be achieved with respect to identifiable multiples. This is not often done. how(ver. An auxiliary objective oC velocity analysis is identiCying lilhology; tbis is discussed in Section 4.10.7.

4.7.8. Common-Midpoint Stacking Common-midpoinl slacking is probably the most importanl application of data processing for improving data quality. The principIes involved have already beco discussed along with Ihe field procedures used lo acquire the dala. The component dala are sorne limes displayed as a gather: a common-midpoint

ga/her has tbe componcnts fOf the same midpoint arranged side by side and a common-offser garher has the components for which the offset is Ihe same arranged side by side. Arter correcting for nonnal moveout, Ihe data are slacked into a single outpul trace for each midpoint. [f reflectors dip, the rellecting point is not common Cor common-midpoint traces and coosequently the stacking result involves smearing and degradation of data quality. Thc degradation can be avoided by migrating before slacking (which is expensive) or approximately bul relatively cheaply by several methods. Sometimes partial slacks, each of traces over a limited offset range, are made and migrated to cut down on the amount oC data lo be migrated. Dip-moveout (DMO) processing transCorms a sel of prestack common-midpoint gathers so that each gather contains events from the same reflecling poiol (Deregowski, 1986). Ir the velocity is constant, the locus Cor equal traveltimes is an ellipse with the source and receiver locations as Coei; all reftectors, dipping as well as horizontal, are tangenl to such an ellipse. DMO uses the differences belween the midpoinl and the points where perpendiculars to the ellipsc inlercept Ihe surfaee lo creale commonreflecting point gathers. These galhers can then be stacked and migrated without rellecting-poinl smear. The constant-velocity assumption provides a reasonably satisfactory approximation where velocity varies vertically. First-break data and the refraclion wavetrains that follow Ihe first breaks usually are so slrong that tbey have lO be excluded Crom the slack to avoid degrading Ihe quali ty oC shallow rcflcclions. This is done by mu/ing, which involves arbilrarily assigning lero values to traces during the period when the firSI breaks and foIlowing wavetrains are arriving. Thus the multiplicity of a stack increases by sleps, with tbe shallowest data often being only a twoCold slack slightly deepcr data being a fourCold stack, and s~ on, until the Cull multiplicity of Ihe stack is achieved afler the muted events have passed beyond the most distant geophones.

4.7.9. Apparent-Velocity (Apparent-Dip) Filtering The apparent velocity ol an event, ~, is found by dividing the dislance between two points on the surface of the ground by the difference in traveltime ror the same event at geophones located at the ~oints. II. is Ihus the reciprocal oC the quantity /l///lx ID EquatlOn (4.57): VA = /lx/Ilr- V/sina

( 4.124)

where V is the veloeity with which a wavefront

Seismic methods

230 approaches the spread and a is the angle between the wavefront and the spread. Apparent velocity is an entirely dilferent quantity from the stacking velocity or the velocity used to convert traveltimes to reflector depths. A reflection that arrives from vertically beneath the spread has an infinite apparent velocity (after correction for normal moveout) without regard for the depth oC the reflector or the velocity with which the refleetion energy has traveled in the earth. Apparent velocity generally decreases for dipping reflectors, becoming smaller as the dip increases, but usually it is still rnuch larger than seismic velocities. Horizontally traveling wavetrains (rnainly ground-roll and refractions) have low apparent velocities cornpared with reflections and so can be discriminated against on this basis. This forms the basis oC velocity-filtering rnethods (Treitel, Shanks, and Frasier, 1967; Sengbush and Foster, 1968; Christie, Hughes, and Kennett, 1983). The filtering can be achieved in the time domain by mixing signals in such a way that events with certain apparent velocities are added out oC phase and so cancelled. Filtering can also be done in the (""'1() domain (Christie, Hughes, and Kennett, 1983) after twodimensional Fourier transformation [Eq. (A.57)]. Apparent-velocity filtering is sometimes done before stacking but usually afterward.

4.7.10. The p-r Transfonn The axes of a seismic record (or section) are olfset (location) and traveltime. The same data can also be represented by a plot of the slope of events p against tbe intercept on the time axis '!' (Diebold and Stolfa, 1981). [For reflections, p is the raypath parameter of Eq. (4.65)]. Whereas the Founer transform represents data as a superposition of harmonics, the P-'!' plot represen!s the same data as a superposition of straight-line events; curved wavefronts become a superposition of plane wavefronts. Straight-line events, such as the direct wave, headwave events, ground roll, and air waves, transform into points wbereas hyperbolic renections become ellipses in the p-'!' domain. As with other transCorms, one can transform back into the time-space dornain witbout Ioss of information except that due to the interpolation between sampled values and to boundary elfects. Filtenng and otber operations can be done in the P-'!' domain as with apparent-velocity and frequencydomain processing.

4.7.11. Relative-Amplitude Processing Most oC the inCormation Cor structural interpretation is determined from the traveltimes of events, and it is desirable to see as many events as possible. This is

better achieved by minimizing amplitude dilferences between events, and so sections for structural interpretation objectives often do not preserve relative amplitude. However, for stratigraphic interpretation and hydrocarbon indicator purposes, maintaining correct relative trace-to-trace amplitudes for each event is important. Some amplitude variations, such as spherical divergence, can be corrected based on theory. Sorne, such as absorption and peg-Ieg multipie elfects, vary so slowly that they can be approximated by gradual exponential amplitude correction. Sorne, sueh as variations near the source or geophone, can be corrected by a surface-consistent amplitude modeI where the corrections are statistically determined frorn the redundancy in data (Taner and Koehler, 1981). After correcting for as many factors as possible, remaining amplitud e variations are usually attnbuted to reflectivity variations. Relative amplitude data are sometimes displayed at very low gain so that only the strongest events are apparent; these then are considered as possible hydrocarbon indicators (§4.10.8).

4.7.12. Migration or Imaging Common-midpoint seismic sections show reflections (and other) data onented with respect to midpoints, that is. with respect to where tbe equivalent coincident sources and geophones are IocatOO. Our goal, however, is to locate renectors and dilfracting points in the subsurface. The process of moving data elements from midpoint locations to subsurface locations is called migration. It is also called imaging becausc its objective is to produce a c1ear image oC the subsurface (Robinson, 1983b; Brower, Douma, and Helbig, 1985). Migration implies that the seismic data being migrated are either prirnary reflections or dilfractions. Migration of other types of events as if they were reflections or dilfraetions smears them out and creates noise (migration noise). Large local bursts 01 energy get smeared into smiles, which have the general shape oC wavefronts (Fig. 4.84). Almost every migratOO section shows some smiles, especially deep in tbe section and near the ends of the sections where noise is high and data are incomplete. Migration to the correet location requires knowledge 01 the velocity distribution bUI, in structura11y complex areas where migration is most required, velocity information is apt to have large uneertainty. However, migration is fairly tolerant ol errors in vertical variations in velocity so that migration with the wrong velocity usually belps to clarify structure even though events are nol located correct1y. Changes in velocity in the horizontal direction produce distortions unless tbey are allowed for correctly. Migration

.... '"

;;:;

, i ¡

,1

~-

,

~-I {

i

~ -1

:I !I,III!Ium:

~-l'

,I ,I• .

o 6

o o

N

232 tbat attempts to allow for horizontal velocity changes is called depth migration (Lamer et al., 1981). Iteralive ray tracing may be used in complex areas; tbe model ol velocity and dip values resulting from one iteration provide tbe input information for the next iteralion. Events from off to tbe side of tbe line generally are migrated incompletely because tbe migration deals only witb the apparent dip in tbe in-line direclion. Thus diffractions from faults tbat are not perpendicular to the line will collapse only partially. However, even ir sorne events may be undermigrated, interpretation is usually made easier by tbe migration. When velocity varies only witb deptb (tbat is, not laterally), tbe traveltime curve for a diffraction (diffraetlon curoe) depends only on the velocity aboye tbe diffracting point and tbe deptb ol tbe diffracting point. (The situation for sources off tbe line, diffracted reflections, diffracted refractions, and other more complicated paths, is more complex.) The energy diffracted by a point can be found by summing tbe energy along tbe diffraction curve for which tbat point is at tbe apex (Hagedoom, 1954). If tbe apex is not at an actual diffracting poinl, the values along tbe diffraction curve wi1I not be systematic, and Desalive and posilive values will tend to cancel. If tbe section is searched along all possible diffraction curves and tbe sums ol tbe energy found along each is positioned at tbe crests of tbe curves, all diffraclioos wi1I be migrated correct1y. Because the same physical processes are involved in generating reflectioos and diffraclions, one can think of a reflector as many closely spaced diffracting points and a reoecIion as tbe interlerence composite of tbeir diffraclions (Huygens' principIe). Thus if reHection elements are migrated as if tbey were diffraction elements, tbe reflections will be migrated correctly (providing tbe cross-dip is zero). This principIe Corms tbe basis oC SOrne computer migration processes (Klrchhoff migratlon). A result is sbown in Figure 4.84. The wave equation expresses bow waves move in space and time and can be used to "move waves backward." If we assume coincident source and geophone (as a common-midpoint section implies), tben a wave moved backward to where it was at half tbe traveltime should be localed at the reflector or diffracting point. This coDcept forms tbe basis for wave-equalion metbods oC migration. The migration is sometimes done in tbe time domain using finite differences to ~pproximate the derivatives in tbe wave equation, continuing tbe wavefield dOWDward step by step (Berkhout, 1981). It is sometimes solved in tbe Crequency-wave-number domain after a twodimensional Fourier transform [Eq. (A.5?)] converts

Seismic methods tbe data to the new domain; tben tbe Crequeacydomain equivalents of downward conlinuation are performed (Chun and Jacewitz, 1981), aCter which the data are transformed back to tbe space-time domain for display oC tbe migrated results. Sornetimes combinations of domains are used or operations are performed partially in one domain and partially in another. The results oC all types of migration are eonceptually equivalent, but in practice, weaknesses in one type (mainly because of the approximations involved) or the ease oC aeeommodating special considerations may Cavor one metbod or anotber. More inCormation on migration can be found in Gardner (1985) and in Oaerbout (1985).

4.7.13. Measures of Coherence Trace-to-trace eoherence as defined in Section 4.4.1 can be givea a quantitative significance in several ways. For two traces, one could use tbe cross-correlation as a me asure oí coherence. For a large number ol traces, we could mue use ol tbe faet that when we stack several channels together the resulling amplitude is generally large wbere the individual channeIs are similar (coherent) so tbat tbey stack in-pbase and small wbere they are unlike (incoherent). lhe ratio oC tbe energy of the stack eompared to tbe sum oC tbe energies oC the individual components would therelore be a measure ol the degree 01 coherencc. If we let X'I be the amplitude of the individual channel i at the time t, then the amplitude of tbe stack at time t will be L/X,I and the square of this will be the energy. If we call E, tbe ratio of tbe output energy to the sum oC tbe energies of the input traces, we may write

EI

(E,XI/)2

EI ( x~)

( 4.125)

We expect a cohcrent event to extend over a time intervaI; hence a more meaningful quantity than E, is tbe semblanee ~ (Neidell and Taner, 1971), which denotes tbe ratio of tbe total energy oC tbe stack of N traces within a gate of lengtb ~I to N times tbe sum ol tbe energy of tbe component traces within tbe same time gate. Using tbe same terminology as before we can write. ( 4.126)

The semblance will not only tend to be large when a coherent event is preseat but the magnitude of the semblance is also sensitive to wbetber or not all traces contrlbute equally. Tbus strong events will

•

Basie geologieal eoneepts in petrole um explor ation

233

exhibit large semblance and weak events will exhibit moderate values of semblance whereas incoherent data will have very low semblance. Semblance and otber coherence measures are used to determine tbe values oC parameters that will optimize a stack. The semblance is calculated for various combinations of time shifts between the component channels, and tbe optimum time shifts are taken to be those tbat maxioUze the semblance. Semblance therefore can be used to determine static corrections or normal-moveout corrections.

sorne times calculated and displayed superimposed on tbe seismic data (Taner, Koehler. and Sheriff, 1979). Amplitude data are sometimes converted to acoustic impedanee or synthetic sonie-Iog forms (tbe processing is called im'ersion) (Lindseth, 1979). Modeling (§4.1O.2) oC both stratigraphic and structural fealures is done lo aid in interpretation (Hilterman, 1970, 1982). 4.8. BASIC GEOL OGIC CONCEPTS IN PETROLEUM EXPLORATION

4.7.14. Other Types of Processing 4.8.1. Basic Conce pts (a) Diversity staeking. Much data processing is far ing the objectives oC seismic interpreless eltotic than suggested by the mathematical rela- Before diseuss review sorne basic concepts that are tionships expressed in tbe foregoing pages. Sorne oC tation, we shall petroleum exploration. these processes merely involve eltcluding certain ele- fundamental in is Petroleum the result oC the deposition of plant ments oC the data, such as the muting operation, or animal matler in areas that are slowly subsiding. whicb bas airead y been discussed. usually in the sea or a10ng its mar· Diversity stacking is another techruque used to These areas are lagoons or marshes and occasionally achleve improvement by excluding noise. Records in gins in coastal swamps. Sediments are deposited high-noise areas, such as in cities, often show bursts in lakes or inland the orgamc matter. and the rate of depoof large amplitude noise whereas other portions oC along with nts must be sufficiently rapid that the record s display relatively little noise distortion. sition oí the sedime the orgaruc matter is preserved by Under sucb circumstances, amplitude can be used as at least parl of destroyed by decay. As time goes a discriminant to determine which portions are to be burial before being continues \O sink slowly [because of excluded. This can take tbe form of merely excluding on and the area nts deposited or because of a11 data wbere the amplitude exceeds sorne threshold, the weight of sedime forces], the organic material is or perhaps sorne form oC inverse weighting might be regional (Iectoruc) and hence is exposed to higher temused. Such noise bursts often are randomly located buried deeper pressures. Eventually cherrucal changes on repeated recordings so that sufficient vertical peratures and generation oC petroleum, a complex, stacking after the weighting tends to produce record s result in the highly variable mixture of hydrocarbons, including relatively free from the high-amplitude noise. both liquids and gases (part of the gas is in solution use of the high pressure). Ultimately the subsi(b) First-break staties. The first arrivals (or lirs! beca and may even reverse. breaks) on a seismic record are usually a headwave dence will stop Sedimentary rocks are porous; porosity is the from the base of the weathered layer for geophones of the rock occupied by cavities or sorne distance from the sourcepoint. The first-break Cractional volume s in these cavities and íntercollect traveltimes are oCten interpreted by standard reCrac- pores. Petroleum the remairung water that was buried tion metbods to give the thickness and traveltime mingles with When a sigrulicant fraction of through the weathered layer for tbe purpose of mak· with the sediments. nnected so that f1uids can pass ing static corrections. The first breaks may be picked the pores is interco rock is permeable. Permeability the rock, automatically and static time shiCts may be caleu- through the oil, and water to separale partially lated (Hatherly, 1982; Farrell and Euwema, 1984). permits the gas, differenl densities. The oH and gas This is usually done to give first-order static correc- beca use of their they eventually reach tbe surface of lions, and second-order corrections (residual statics) tend to rise, and are dissipated unless they encounter a are made by a surface-consistent program that relies the earth and their upward migration. Such a on cross-correlation between elements of a com- barrier Ihal stops barrier produces a trap. Figure 4.85 ilIustrates the mon-midpoint gather. most important types oC traps. The anticline shown in vertical cross section in (e) Specialized proeessing. A variety oí other types is a common type of trap and often the oC seismic processing are perCormed for special pur- Figure 4.85a In the diagram, bed A is impermeposes. Attributes (measurements based on seismic easiest to map. reservoir rock B is permeable. Oil data such as amplitude oí the trace envelope, instan- able whereas the collect in the reservoir rock oC the taneous phase, or instantaneous írequency) are and gas can (

Seismic methods

234

M-------------------------

("

(fJ

(b)

! '.,{' ".

,.

~

f

.., .'"

'~

. . ,' .i .. : ~ .......... H,I$

2, '1. .:-.... ó•.• iJj

(rJ

(h)

(dI

(n

Figure 4.85. Sedimentary structures Ihat produce hydroc.ifbon traps. Permeable beds are do/ted; hydrocarbon accumulations are in blaek. (a) Ver/ieal seelion through anticline along Jine MN in (b) (b) Map of /he top of the permeable bed in (a) with thf' spill-point contour dashf'd. (e) Vertical section through fault traps. (d) Map of the lower permeable bed in (e). (e) Possible traps associated with thrust faulting. (f) Slratigraphie traps produeed by Jithologic ehange and pinchout. (g) Unconformity traps. (h) Trap in a ree! and in draping over the reef. (i) Traps associa/ed wi/h a sal/dome.

r

I I ,

I I

r

235

Refraction interpretation

anticline until the anticline is filled to the spill point. Although the diagram is two-dimensional. similar condilions must hold for the third dimension, the structure Corming an inverted bow1. The conlour through the spill paiot, the c10sing con/our (- 2,085 m in Fig. 4.85b), defines the maximum area of hydrocarbon accumulation. Figure 4.85c shows a fault trap in which permeable beds overlain by impermeable beds are faulted against impermeable beds. A trap exists iC lhere is also c10sure parallel to the Cault; an example is shown by the contours in Figure 4.85d. Obviously Caults do not consti tute traps if the rocks across the fault are permeable or if hydrocarbons can percolatc up the fault planeo Pinchouts and unconformities (Figs. 4.85f and g) provide traps only when the adjacent roca are impermeable and there is closure at right angles to the diagram. Figure 4.85h shaws a limestone reef that grew upward on a slowly subsiding platform (§4.10.S). The reel is composed ol coral or other marine animals with calcareous shells, which grow prolifically under the proper conditions oC water temperature and depth. As the reef subsides, sediments are deposited around it. Eventually the reel stops growing, perhaps because of a ehange in the water temperalure or the rate ol subsidence, and the reeC may be buried. The ree! material is usually highly porous and often covered and surrounded by impermeable sediments. Hence the reef may form a trap for petroleum generated in the reer itself or flowing into it from another bed. Figure 4.85i represents a salt dome formed when a mass ol salt ftows upward under the pressure resulting from the weight oC the overlying sediments. The salt dome bows up sedimentary beds and seals off disrupted beds and so provides traps over and around the sides of the dome.

4.8.2. Objectives of Interpretation The primary objective of a seismie survey Cor hydrocarbons usually is to locate structures such as those shown in Figure 4.85. However, many structures that provide excellent traps do not contain oH or gas in economie quantities. Because drilling wells is very costly, we try to derive from the seismic data as much inlormation as possible about the geological history of the area and about the nalure oC the rocks in an effort to form an opinion about the probability oC encountering petroleum in the structures that we map. Unconlormities oCten show up c1early on seismic sections, especially on long regional lines that give sufficient sense oC perspective to allow an interpreter lo distinguish between regional and local features

and between reasonably consistent geologic information and superimposed noise. Unconformities often indicate changes oC eustatic sea level that can be correlated with specific times in geologic history; their recognition thus provides information lor agedating sediments. Pattems in the seismic data somelimes indica te the eovironment in which the rocks were deposited. The velocities oC rocks are sometimes a clue to their lithology and origino Drawing conc1usions from these types oC observations is an objective of seismic stratigraphy (§4.10.6). The velocity, reflectivity, and other properties oC a rock are sometimes altered noticeably because of changes in the fluid that fills the rack pores. Thus the effects of hydrocarbon accumulations can sometimes be secn (§4.1O.8). Seismic methods are also increasingly used for nonhydrocarbon objectives (Dobecki and Romig, 1985). Water resources are sometimes controlled by earlier topography or by faulting. Heavy minerals sometimes accumulate in channels on old topography, and mineral s may be associated with rock contaets. Faulting that interrupts eoal seams affect the planning oC mining operations. In many mining areas, old mine drifts are not mapped accurately and knowing their location is es sen ti al to avoid eutting into one that is water-filled. Nuclear waste disposal requires reasonably detailed knowledge oC Caults and other geologic features. Seismie methods often provide the eheapest way of mapping such features with reasonable resolution. Seismie methods are also used inereasingly for engineering purposes. Tbe integrity of foundation rocks must be established; cavities in the rocks or zones of weakness due to faulting or fraeturing need to be known before large struetures are eonstrueted. In planning road cuts and other engineering projeets involving earth removal, the cost of exeavating depends to a significant degree on rock hardness; thís can be estimated from seismie veJocity.

4.9. REFRACnON INTERPRETA nON 4.9.1. Interpretation of Refraction Records The identifieation of headwave events is usually simpler than for reflection events. Traveltimes are usually available for a relativeJy long range of offsets, and hence it is easy to separate reflections and diffractions with their curved alignments from the direct wave, surfaee waves, and headwaves with tbeir relatively straigbt alignments. Tbe direct wave and surface waves are easily distinguished Crom headwaves because of the lower velocities ol the former. Usually the only problem is in identifying the different headwaves when several refractors are present.

Distance (km)

Figure 4.86. Marine refraction pro file. (Courtesy Compagnie Générale de GeÓphysique.)

Refraction interpretation

Record sections are especially useful in studying second arrivals. The refraerjon record secrjon (also called a refraction profi/e) in Figure 4.86 shows the direct wave as the first arrival near the shotpoint; refractions from successively deeper refractors become the first arrivals as the offset distance ·increases. Following the first arrivals, the continuations oC various events are seen after each has been overtaken by a deeper event. Numerous other events are also seen in the zone of second arrivals; most oC these are either refractions that never became Hrst arrivals or multiply-reflected refractions (see Fig. 4.35b). The simple equations (4.68) through (4.81) can be used when the data are easy to interpret and limited in quantity. Often the cbief failure oC these equations (and of most refraction interpretation techniques) is in the assumption of VI' the veloci ty or tbe section aboye Ihe refractor. Most methods assume straighlline raypaths from the refractor upward lo the surfaee. This is usually nol true because the overburden velocity is rarely constant. The biggest improvement in the results obtained wben using tbe simple equations to calculate refractor depths oCten is the result of using a more realistic assumption for VI based on information other than that obtainable from the refraction dala tbemselves (Laski, 1973). Problems sometimes result from a hidden zone, a layer whose velocity is lower Ihan thal of the overlying bed so Ibat it never carries a beadwave. Energy tbat would approach it at the critical angle cannot get through the shallower refractors and hence there is no indication of ils presence in tbe beadwave arrivals. The low velocity of the hidden layer, however, increases the arrival times oC deeper beadwaves relative 10 what would be observed iC the hidden zone had the same velocity as the overlying bed, wbich results in exaggeratioD oC the depths of deeper refractors. Another siluatioD, which is also referred to at times as a "hidden zone," is that of a layer whose velocity is higher than those of ¡he overlying beds bul thal never produces first arrivals despite this because the layer is too thin and/or its velocity is not sufficiently greatcr than those of the ovcrlying beds. Such a bed creates a second arrival but the second arrival may nol be recognized as a distinct event. Refraction interprctation often is based solely on first arrivals, primarily because tbis permits accurate determination of the traveltimes. When we use second arrivals we usually have to pick a later cyc\e in the wavetrain and estimate traveItime from the measured time. However, velocities based on second arrivals will be accurate, and much useful information is available through thcir study. Several additional considerations affect refraction interpretalion. Refraction traveltimes are corrected

237

to datum in thc same manner as reflection travel· times. Therc is one diffen:ncc. however: Travelpatbs aboye the refractor are inclined and so the datum should be near the surface lO minimize the effects oC ¡he inc1ined paths on the corrections and the effective shotpoint- geophone distance. If enough data are available. interpretational ambiguities often can be resolved. However, in an effort to keep survey costs clown, only the minimum amount oC data may be obtained (or less than the rninimum), and sorne of the eheeks that inerease certainty and remove ambiguities may not be possible.

4.9.2. Refraction Interpretation Methods Three types of approach are made to refraction interpretation: 1. Application of Equations (4.68) to (4.81). 2. Delay-lime methods. 3. Wavefront reconstruction methods.

Simple multiple-Iayer equations are generalizations of Equations (4.69), (4.75), and (4.76). These equations generally demand that the refractors be nearly planar over the arca being studied, that is, the refractor relief can be ignored in calculations of depth, dip, and velocity. Refraction interpretation often involves "stripping," which is in effect the removal of one layer at a time. In this method the problem is sol ved for the first refractor, after which the portions of the time-distance curve for the dceper refractors are adjusted to give the result that would have been obtained if the shotpoint and geophones had been located on the first refracting homon. The adjusIment consists of subtracting the traveltimes along the slant patbs from shotpoint down to the refractor and up from the refractor to the geophones, and also decreasing the offsets by the componenls of the slanl paths parallel to the refractor. The new time-di stance curve is now solvcd for the second refracting layer afler which this layer can be stripped off and the process continued for deeper refractors.

4.9.3. Delay-Time Methods (a) General. The concept of delay time, introduced by Gardner (1939), is widely used in routine refraction intepretation, mainly because the various schemcs based on the use of de1ay times are less susceptible to the difficulties encountered when we altempt to use Equations (4.69) to (4.81) witb refractors that are curved or irregular. Assuming that the refraction times have been corrected for elevation and weathering, the de/ay time () associated witb the path SMNG in Figure 4.87 is the observed refraction

Seismic methods

238

~I·~-----------x------------~~~I

s

G

figure 4.87. lIIusrraling de/ay lime.

figure 4.88. Determining sourcepoint and geophone de/ay times.

time at G, '" minus Ihe time required lor tbe wave to travel lrom P to Q (lhe projection 01 the path on Ihe refractor) at Ihe velocily V2 • Writing 8 for Ihe delay time, we bave

PQ 8-,, -VI _ ( SM + NG + MN) _ PQ Vl

"2

VI

_ (SM ~ NG) _ (PM ~ NQ) =

(SM _ PM) + (NG _ NQ) Vl

"2

v"

VI

- 8, + 8,

(4.127)

wbere B, and 8, are known as the shotpoint de/ay time and Ihe geophone delay time because tbey are associated with Ihe portions 01 Ihe palh down from Ihe sbot and up to Ihe geophone. An approximate value of 8 can be found by is assuming Ihat Ihe dip is small enough Ihat approximately equal to Ihe geopbone offset x. In this case,

PQ

x

8 ... B, +8, ""t, - "2

( 4.128)

Provided Ihe dip is less Ihan about 10°, this relation is sufflciently accurate lor most purposes. If we substitute Ihe value of t, obtained from Equations (4.70), (4.75), and (4.76), we see that 8 is equal to the

intercept time Cor a horizontal refractor but not for a dipping refractor. Delay- time metbods are subject to certain errors that must be guarded against. As tbe shotpoint to geophone distance increases, tbe reCraction wavetrain .becomes longer and energy peak shifts to later cyeles. There is tbus tbe danger Ihat different cycles will be picked on different profiles and that the error will be interpreted as an increase in shot de]ay time. If sufficient data are available, the error is usually obvious. Variations in refractor velocity manifest themselves in local divergences of the offset totaldel ay-time curves for pairs of reversed pro files. However, if sorne data that do not represent refraction travel in the reCractor under consideration are aecidentally included, the appearance is apt to be the same as if the refractor velocity were varying. In situations where several refractors that have nearly the same velocities are present, unambiguous ínterpretation may not be possible. Many interpretation scbemes using delay time have becn given in the lilerature, Cor example, Gardner (1939, 1967), Barlhelmes (1946), Tarrant (1956), Wyrobek (1956), and Barry (1967). We shall describe only the latter two. The method described by Wyrobek is suitable Cor unreversed protiles whereas that oí Barry works best with reversed profiles. (b) Barry's method. The scbeme described by Barry, like many based on delay times, requires that

we resol ve the total delay time 8 into its component parts 8, and 81f' In Figure 4.88 we show a geophone

Refraetían ínterpretatíon

239 Dí,lance (CI x lO')

I

1

30

40

-

..E

'"u

~

¡:

¡:

E

r~

:e i:~~

¡:

210 2·14 2·18

2·14 2·18

_ _ __ _

¡:

:E.

~

"~mes

\

..

DePlh:

1·06 1'10

Average off,el delay lIme

'

~~ o.98~ (fl) 1·02 9000 ¡:

"E

~

---

Offset deliY

~

..

~

= -1

=-----

g 9OOO~O1{)2 98 .., fr lOooo

----10.000

___'1.. -'

";l

~

I·~ ~ 1.10

¡:

Figure 01.89 The del,¡y-time method of interpreting reversed profiles. (Afler Barry, 1%7)

R for which data are recorded from shots at A and B. The ray BN is reflected at the critical angle, and hence Q is the tirst geophone to record the headwave from B. Let 8"M be the shotpoint delay time for shot A, 8NQ and 8p 1I. the geophone delay times for geophones at Q and R, and 8AQ and B"R the total de1ay times for the paths AMNQ and AMPR. Theo

we have Z

BQ

=

V¡8BN

=--

Neos 8.

( 4.130)

2z", tan 8.

( 4.131)

BAM + BNQ

BAQ

-

BH

= 8AM + 8n

tJ.8 - BAQ

-

B,,1I.

= BNQ

-

8p 1l.

For !he shot at B, the shot delay time 8BN is approlÓmately equal to 8NQ provided the dip is sm al!. In this case,

.,. : ( 8BR

...

j( 8BR

+ tJ.8) } -

(i) The corrected traveltimes are plotted. (ii) The total deJay times are calculated and plotted at the geophone positions. (üi) The geophone offset distances (PP' in Fig. 4.88) are calculated using Equation (4.131), and, assuming PP' - BQ, the delay times in (ü) are shifted toward the shotpoint by these amounts. (iv) The shifted curves in (iii) for the reversed profiles should be parallel. Any divergence is due to an incorrect value oC Vi, hence the value oC Vi is adjusted and steps (ii) and (iii) are repeated until the curves are parallel (wi th practice onJy one adjustment is usually necessary). (v) The total delay times are separated into shotpoint and geophone delay times; the latter are plotted at the points oC entry and emergence

!

The geophone delay times are now given by

8NQ 8PR

The shot delay time 8BN is assumed to be equal to half the intercept time at B; this a110ws us to calculate an approximate value oC BQ and thus determine the delay times for a11 geophones to the right oC Q for which data from A and B were recorded. The interpretation involves the following steps, which are illustrated in Figure 4.89:

( 4.129)

tJ.8)

Thus, it is possible to find the geophone delay lime al R provided we have data from two shots on lhe same side and we can find point Q. Ir we assume that the bed is horizontal at N and is at a depth ZN

Seismie methods

240

f

Slep

(i)

(uaveltimes)

:;.;.-------/- -----

6

¡

Stop

(ii)

(Iolal delay lime.)

<:ompositt deJay-time

curve

I 1',

¡ ¡

1

Slep (i;;) (halr.inltr""pl lime.)

-

Step (iv) (deplh)

Figure 4.90. Wyrobek's melhod using unreversed profiles. (Afler Wyrobek, /956).

from the refractor (S and T in Fig. 4.88). The delay-time scale can be convcrted into depth if required using Equations (4.130) with 6PR in place of 6BN •

(e) Wyrobek's method. To ilIustrate Wyrobek's method we assume a series oí unreversed profiles as in the upper part oC Figure 4.90. The various steps in the interpretation are as follows: The corrected traveltimes are plotted and the intercept times measured. (ii) The total delay time 11 is calculated for each geophone position for each shot and the values are ploued at the geophone position (if necessary, a value of J.í is assumed). By moving the various segments up or down, a composite curve similar to a phantom horlzon is obtained. (iii) The intercept times divided by 2 are plotted and compared with the composite delay-time curve. Divergence between the two curves indica tes an incomet value of J.í (see below); hence the value used in step (ii) ís varied untíl the two curves are .. parallel," after whieh the half-intereepl time curve is completed by interpolation and extrapolation to cover the sarne range as the composite delay-time curve. (iv) The half-intercept time curve is changed to a depth curve by using Equation (4.70), narnely,

(Note Ihat we are ignoring the dilference between the vertical depth z and the slant depths ZA and ZB in Fig.4.33.) Wyrobek's method depends on the fact that the curvc oC () is approximately parallel to the half-intercept time curve (see problem 15). Wyrobek's method does not require reversed profiles beeause the intercept at a shotpoint does not depend on the direction in which the cable is laid out.

(i)

4.9.4. Wavefront Methods (a) Ceneral. Wavefront reconstruction, usually by graphical rneans, forms the basis of several refraction interpretation techniques. The c\assic paper is one by Thomburgh (1930); other important articles are those by Gardner (1949), Baurngarte (1955), Hales (1958), Hagedoom (1959), Rockwell (1967), and Schenck (1967). Figure 4.91 iIluslrates the basic method oC reconstructing wavefronts. The refraction waveCront Ihat reached A al t = 1.600 s reached B, e, . .. at the times 1.600 + tJ.tB , 1.600 + tJ.tc ••. , • By drawing ares with centers B, c, ... and radii Vl~tB' Vl~tc",., we can establish the wavefront Cor r - 1.600 s (A Z) as accurately as we wish. Sirnilarly, olher refraction waveCronts, such as that shown Cor t - 1.400 s. can be constructed at any desired traveltime intervalo The dircct wavefronts from the shot S are oC course the cirdes shown in the diagram.

Retraetían interpretation

241

z

F'gure 4.91. ReconSlruclion o( wavefronls.

Figure .J. 92. Fir~l'drrival wdl'l,fronls. CoincidenHime bu rgh.193o.J

In Figure 4.92 we show a series of waveCronls chosen so that only waves that will be first arrivals are shown (all secondary arrivals have been eliminated in the ¡nlerest of simplicity). Between Ihe shotpoint S and the crossover point C [Eq. (4.71)j the direct wave arrives firsl. To the right oC C. the wave refracted al the firsl holizon arrives first until. lo the right of G. the refraction from the deeper horizon overtakes the shallower refraction. The two systems oC waveCronts representing the direct wave and the refracted wave from the shallow horizon. intersect atong the dotted line A Re. This line. called the coincidell/' time line by Thornburgh. passes through the points where the intersecting wavefronls have the same traveltimes. The curve DEFG is a coincident-time curve for the deeper horizon. The coincident-lime curves are langent to the refractors at A and D where the incident ray reaches the critica! angle (see problem 16) whereas the points at wruch the coincident-time curves meet

CUNes

are dotted. (Afler Thorn·

the surface are marked by abrupt changes in the slopes of the time-distance plol. Since the coincident·time curve is tangent to \he refractor. the latter can be found when we have one profile plus other data - such as the dip. depth. critical angle - or a second protile (nol necessarily reversed) because we now have two coincident-time curves and the reCraclor is the common tangent to the curves. When reversed protiles are available. the construction oC wavefronts provides an elegant method of locating the refractor. The basic principIe is iIIustrated in Figure 4.93. which shows two wavefronts, MCD and PCE. from shots at A and B intersecting at an intermediate point e. Obviously the sum oC the Iwo traveltimes from A and B to C is equal to the reciprocal time between A and B. 1,. If we had reconstructed the two waveCronts from the time-distance curve without knowing where the refractor RS was located. we would draw the wavefronts as MCN

242

Seismic methods A

s

""

Q

N

D E figure 4.93. Determining refractor position from wavefront inlersections.

~ ,

"

,• , ,.........<] ~ ....

-': .... )

,..... . .... ~<]

"'
S
'minus' value=r. - 106
figure 4.94. The plus- minus method. (After Hagedoorn, 1959.)

and PCQ. not MCD and PCE, Therefore. ir we draw pairs of wavefronts from A and B such that the sum 01 the traveltimes is 1,. the refractor must pass through the points of intersectioo oC the appropriate pairs ol wavefronts in Figure 4.93. (b) Plus- minus method. The plus-minus metbod, devised by Hagedoom (1959). utilizes a construction similar lo that just described. Wben the refractor is horizontal. the intersectiog wavefronts drawn at intervals ol Il ms lorm diamond-sbaped figures (Fig. 4.94) whose borizontal aod vertical diagonal s are equal to J)1l and V¡ll/cos Be. respectively. If we add together tbe two traveltimes at eacb intersection and subtract tr • the resulting "plus" values equal O on tbe refractor. + 21l on the horizontalline through the flrst set 01 intersections vertically aboye those defining the refractor. + 41l on the next line up. and so on. Because the distance between each pair of adjaceot lines is V¡ll/cosBc ' we can use any oí tbe plus lines to plot tbe refractor. The difference between

two traveltimes at an intersection is called tbe "minus" value; it is constant along vertical lines passing through the interseclions of wavefronts. The distance between successive minus lines as shown in Figure 4.94 is V2 1l; hence a continuous check on J) is possible. Although dip alters the preceding relations, Ihe changes are small for moderale dip, and Ihe assumplion is made thal Ihe plus Iines are SlilI parallel lo the refractor and the minus lines do not converge or diverge.

4.9.5. Engineering Applications Refraction methods are commonly applied in mineral-exploration and civil-engineering work lo measure depth of bedrock. With the arrangement showo in Figure 4.95, shots are fired from tbe end points oC the spread, A and B, and lhe midpoinl C. (The "sbot" is usually a bammer blow for sballow overburden or a blasting cap for deeper.) Let t,fB be tbe surface-lo-surface traveltime from A to B, and so

243

Reflection interpretation

e

A

B

_\-L--.&~L~Z_ Figure 4.95. Refraction profile for determining deplh lo bedrock.

forth. TIten (see problem 17) Z

e

= (/ CA +

I CB -

2

I AB )

V1 V2

(vl-vn

1/2

(

4.132)

where VI is the overburden and V2 is the bedrock ve1ocity. Frequently "í » Vi and we can replace the velocity terms by VI: ( 4.133) The error in ze is less than 6% iI V2 > 3V¡. This method assumes that the overburden is essentially homogeneous, the depth variation is smooth, the dip is small, and the velocity contrast is so large Ibal tbe perpendicular distanee lo bedrock is roughly equal to the vertical distanee. Depth calculations by this teehnique are gene rally good becausc they depend on the measurement of only one velocily, VI' and three traveltimes.

4.10. REFLECTION INTERPRETATION 4.10.1, Interpretation Techniques

.,.,

(a) Mapping refleeting horizons. Reftections are usually ideotified with bedding planes based on correlalions witb observations in boreholes, velocity inlormation, synthetic seismograms (§4.10.2), or previous experience in the area. The borizons that we draw on seismic sections provide us with two-dimensional pietures only. A three·dimensional picture is necessary to determine whether c\osure exists. the area within the elosing con tour. the location of the highest poinl on Ihe structure, and so on. To obtain three·dimensional information, we usually shoot a number of lines. and most refteelion surveys are earried out along a more· or·less rectangular grid oI Iines. Horizons are first mapped on cross sections and the sections are compared at line intersections to identify the same horizons on alllines; identification is made on the basis ol character and traveltimes. Tbe horizons are carried along a11 Iines in the prospeet area 10 the extent that the quality oI the data permito

When a horizon is carried a11 the way around a c10sed loop, we should end up with the same travel· time with which we started. This c10sing 01 loops provides an important check on reliability. When a loop fails lo close wilhin a reasonable error (which depends mainly on the record quality and the aceuraey of Ihc slatics corrections). the cause of the misclosure should be investigated carefully. Migrated sections have to be tied by finding the same reflec· tion on intersecting sections. Such tie points will be displaced from the vertical Ihrough the sourcepolnt by the amount of the migration on each oI the lines. Often misclosure is due to an error in correlating from line to line, possibly because of inaccurate corrections, change in reflection character. or error in correlating across faults. When the dip is different on the two sides of a fault or the throw varies along the fault. an incoreect correlation across the fault may result in misclosures (but not necessarily). After the sources oI míselosure have been carefully examined and the final misclosure reduced lo an acceptable level. the remaining misclosure is distributed around the loop. Afler horizons have been carried on tbe sections, maps are prepared. For example, we migbt map a shallow horizon. an intermediate horizon at TOughly the depth at which we expect to encounter oil if any is present, and a deep horizon. We map 00 a base map. which shows the locations of the seismic lines (usually by means of small circ1es representing sourcepoints) plus other features. such as oil wells, rivers. shorelines, roads, land and political bound· aries, and so on. Values representing the depth of the horizon bclow the datum plane are placed on the map (posted), usually at each sourcepoint. Other information relevant to tbe horizon being mapped (depths in wells, locations of gravity anomalies, releo vant geologic information, etc.) is also posted. Faults Ihat have been identified on the record s or cross sections are drawn on the map and depth values are then contoured. lsopach maps. which show tbe thickness of sedi· ments between two horizons. are useful in studying structural growth. They can be prepared by overlay· íng maps of the two horizons and subtracting the con tour values wherever the contours on one map

244 cross the contours on the other. The dilferences are recorded on a blank map and then contourcd. If the contours show a treod toward increased thickness in a certain direction, it may suggest Ihat Ihe region was tilted downward in this direction during Ihe perlod of deposition or that the source of the sediments is in this direction. Uniform thickness of a Colded bed indicates that the Coldiog came afler the deposition whereas if the thickness increases away from the crest oC an anticline, deposition probably was contemporaneous with the growth of the slructure. Growth during deposition is usually more favorable for petroleum accumulation because il is more Iikely Ior reservoir sands lo be deposiled on Ihe flanks oI structures wi Ih even sligh I reJief. (b) Structural style. Slructural traps, such as anticlines and Cault traps, and struclural leads (possibilities oC traps that require more work to define them completely) are usuaJly evident Crom examination oC the maps. Traps eesulting Crom pinchouts and unconlormilies are more difficult lO recognize and nonseismic evidence oflen musl be combined with seismic dala lo define such features. Nevertheless, careful study oC Ihe maps, sections, and record s plus broad experience and ample imagination may disclose variations of dip or other elfects that help locate traps of these types. The orientation and type oC structural features depend on the stress fields to which they have been subjecled. The underlying system of structure is caJled structuraJ or tectonic style. The structural style of an area provides a guide Ior interpreting what otherwise might be ambiguous definilion of structural features, especially where data are scarce. For example, il a well-defined Cault is seen on one horizon but is nol clear on other horizons, it might not be evident whether the Caull movemenl was normal, reverse, or strike-sJip and what the attitude ol the fault plane is. However, the structural style, if known, helps to decide the most probable type of faulting, fault plane dip and orientation, and so on. Examples of structuraJ style in seismic dala are shown in Bally (1983-4).

ACter the structuraJ information has been extracted, the next step is to work out as much as possible oC the geological bistory 01 Ihe arca. Fundamental in tbis connection is the determination oC the ages of the different horizons, preCerably aceording to the geological time scate, but at least relative to one another. Olten seismic lines pass clase enough to wells to permit correlating the seismic horizons with geological horizons \ in the we1ls. Refraction velocities (ir available) may help to identify certain horizons. Un(e) Working out geological history.

Seismic methods

conformities associated with maJor time gaps are apt lo be among the most prominent reflectors. Occasionally a parlicular refleclion has a distinctive character Ihat persists over large areas, permitting identification not only oC it but also oI other events by Iheir relation lo it. Notable examples of persistent identifiable refleelions are Ihe low-Irequency reflections sometimes associated with massive basement and the prominent reflection Crom the lop of the Ellenburger, a limes tone encountered in Nortbem Texas. The unraveling of the geological history oI the area is important in answering questions such as: (a) Was the trap Cormed prior lO, during, or subsequent lO the generation 01 the oil and gas? (b) Has the trap been tilted sufficiently to allow trapped oil to escape? (e) Did displacement ol part of a structure by faulting occur before or aftee possible emplacement oC oil? Whereas the seismic data rarely give unambiguous answers to such questions, often clues can be obtained that, when combined with other information, such as surface geology and well data, permit the interpreter to malee intelligent guesses that improve the probabiJity of finding oi!. A1ertness to such clues is the "art" of seismic interpretation and often the distinction between an "oil finder" and a routine interpreter. (d) Drawing conclusions (rom reflection data.

Dcducing geological significance lrom the aggregate of many minor observations nol only tests the ingenuity of an interpreter, it also tests bis in-depth underslanding 01 physical principies. For example, downdip lhinning of reflection intervals might resull from a normal increase of velocity with depth as wel\ as from thinning of the sediments, and flow oC salt or shale may cause illusory structure on deeper horizons. Geometric focusing produced by reflector curvature can produce various elfects, especially ir the migration is not correct, and energy that comes from a source localed off to one side of the line can interCere with the pattems oC otber reflection events to produce elfects that might be interpreted erroneously unlcss their true nalure is recognized. Improper processing Iikewise can creale opportunities for misinterpreting data (Tucker and Yorsten, 1973). When the interpretation is finally completed, a report is usually prepared, oCten bolh Cor submission in writing and for oral presentation. In sorne ways tbis is (he most difficult and most important task of the interpreter. He must present bis findings in sueh a way that the appropriate course oC action is defined as clearly as possible. The important aspects should not be obscured by presenting a mass ol details nor should they be distorted by presenting carefully selected but nonrepresentative maps and

245

Refleetion interpretation

sections. Evidence to support significant conclusions should be given. Alternate interpretations should be presented and an estima te given oC tbe reliability oC the results and conc1usions. Finally tbe interpreter should recommend wbat further action should be undertaken. Good references on seismic interpretation inelude Sherllf and Geldart (1983), BaBy (1983-4), McQuillín, Bacon, and Barclay (1984), Badley (1985), and Grles and Oyer (1985).

4.10.2. Modeling: Synthetic Seismograms (a) General. The effects oI passage through a sequence of layers with given ve10ci ties and densi ties is expressed by e, (Eq. (4.103», in clfcct a list of the traveltimes and reHection coefficients for each reftecting interface. The embcdded wavelet, Hi, • s, • p, .", in Equation (4.103), can be used along with e, to calculate a synthetic seismogram, that is, what the recorded wavcform should theoretieally be. A wave is assumed to impinge on the first interface where its encrgy is partitioned among transmitted and reftected waves. Each of these waves is then followed as il trave1s to other interfaces where additional wavcs arc generatcd, and so on. The resulting seismic record ís simply the superposition of those waves that are ultimately observed at Ihe recording station. Because Snell's law determines raypaths and Zoeppritz's equations determine energy relationships, the problcm is completely delermined and the solution is straightforward if we know the spatial distribution of the elastic properlies and densities. However, actually solving the problem is a formidable task, even for modern computers, hccause of the tremendous number of waves generated lor a realistic sequen ce 01 layers; thus, simplifications must be made. (b) Normal incidence synthetlc selsmograms

which represent multiples. Figure 4.96a shows a sonic log plolled to a time scale (ralher than the usual deplh seale) and Figure 4.96b shows the synlhetic seismogram thal would result, assuming a cerlain initial wave shapc and neglecting multiples and cbanges in density. Figure 4.96c is a field recording made in Ihe same arca; sorne events, such as B, D, and J, correlale well wi th synthetic events but elsewhcre the correlalion ranges from fair lo poor. Figure 4.96d differs from Figure 4.96b in that simple multiples are incJuded; Ihe principal ditrerences are the appearance of a strong mulliple at K and con· siderable reduclion in Ihe amplitude of F, presumably because of interference with multiples. This synthetic seismogram was made without shallow information; sonie logs are often not run in the upper part of a borehole, and consequently many of the mosl importan! effeels cannol be modeled correctly. A sonic log and a synthetic seismogram fail lO have a one-Io-one correspondence not only because of the approximations made in the calculation, but also because Ihe seismic wavelengths are so much longer than the distances over which the acoustic properties can be assumed to be constant that the actual seismie waveform is lhe interference composite of many small events, and because the sonic log used to ca1culate the reflectivity is also subject to errors. An important use of synlhetie seismograms is in studying the elTect of changes in the layering on the seismic record. One might, for example. assumc that a shale passes laterally into a sand and determine how such a change would alTect events on the record, possibly altering the number of ¡egs in a refteetion event or changing sorne olher characteristic. This mighl then provide a c1ue in looking for ancient slream channcls or other features oC interest. SynIhetic seismograms are important in indicating the reatures Iha! may help lo identify stratigraphic Iraps.

af-

Ien horizontal bedding is assumed and only the raypath normal to the reftecting interfaces is Iracked. Density variations are Irequently ignored or assumed lo have a definite relation to velocity so that the reftection and transmission coefficients can be based on velocity changes only. Often small velocity variations are ignored and only the major contrasts are eonsidered, or else the small changes are lumped logether into larger steps. Often multiples, especially short.path multiples, are ignored. In many areas the synthetic seismogram is a reasonable approximation to actual seismic records and is therefore useful in correlating reflcclion evenls with particular horizons. Comparison of the actual and synthetic seismograms may also hclp to determine which events represent primary refteclions and

(e) Two-dimcnsional synthetie seismograms.

A

series of one-dimensional synthetic seismograrns are often made where the model is modified slightly for successive traces in arder lo simulale stratigraphic or structural changes along a seismic line, and the rcsult is displayed as a two-dimensional synthetic section. A true Iwo-dimensional section to simulate unmigraled seismic data would show dipping features in dilfercnt )ocalions and diffractions. Such synthetic seismograms are sometimes made using a wave-theory a1gorithm aceording to Ihe scalar wave equation (whieh does not allow for mode conversion). (d) Raypafh modeling. Whcre the structure andjor horizontal velocity variations are complicated, itera· tive ray tracing through a model may be used to

L_

400

500

600

700

800

900

1000

1100

1200

1300

1400

\500

1600

\700

1800

1900

Two-way time (m/s)

(al

(b)

(dI

Figure 4.96. Synthetic seismogr,¡ms. (Courtesy Compdgnie Génér,¡/e de GeÓphysique.) (a) Sonie log plotted in time. (b) 5ynthetic seismogram of prim,¡ry refleetions only. (e) Field record after normal-moveout correction. (d) Synthetic seismogr,¡m with simple multiples added.

247

Reflection interpretation Veloclty (ft/s)

Depth (ft) 0000._ 2000 4000

(a)

6000 8000 10,00012,000

(h)

12,000 __

00OQ

. !Il'M'ln

ffl

i\

2000 400O

1\ \ \

i\\\

600O

(e)

I

Hh

\\

8000

\

,

1

10,o6
I

o"'"

\\\\\~

. k~;'9

d

12;

\6~~o

,tfizooo

rt\~H!r\hp~o

0.00

AOO

-.&i-•.

(dl

6000

,lOO l200

...

ltlOO 2000 2MlO

111

------------------- ------------------

~

-~ ~I:0001JOO i 12.000

--~--/

--¿-::-=_-.--.. _ _ 1 2

~

.....

3

----

~

"'000

"lo

OEPTH

CO .... ON 'ROUfrtD POINTS

FEET O

-0-- . REF'LEC TlNG

.2000.

HOIIUrON!

------

_6000.

----._-

.Io.~-

IZPOQ.

Figure 4.91 Rdl-Iraee modeling 01 iJ CMP seclion Rd)'S pPrpendimlar lo reffeelors are benl aeeording to 5nell's law as the)' pass through inten'ening interfaces. (from Taner. Cook. and Neidell, 7970) (a), (b), (e) Tracing three refleetors (or a North 5ea model. (b)/ (e) are Ihe top/ haS/' 01 iJ sall la ver. Id) The predicled CMP section (e) Ra)' Iracing lo delermine staeking lelocil)' values,

•

248

Seismic methods

2

3

4

(a) Figure 4.98. Section across a thrust (ault in the Oregon Basin, part o( the Big Horn Basin of Wyoming. (After 5tone, 1985.) (a) 5eismic section.

determine a model that is compatible with the seismic observations. The usual assumption is that reftections mark tbe boundaries between layers, each of wrnch has constant velocity. The procedure oCten is to first map a shallow reflector, assuming a laterally constant velocity function. One then maps the reflection that marks the second interface, between layers 2 and 3, by tracing rays obeying Snell's law at the first interface. The interface and raypaths are varied iteratively so that tbe model time section matches the actual time section lor each successive interCace. The process is repeated at each interface. Examples oC ray-trace modcling are shown in Figures 4.97 and 4.98. Irregularities on one interface will distort stacking velocity measurements Cor deeper reflections, and a

further check on ray-trace modeling is provided by matcrnng the model stacking-velocity calculations with those observed (Fig. 4.97e).

4.10.3. Evidence of Faulting Ideally reflection events terminate sharply as the point oC reftection reaches tbe Cault plane and resume again in displaced positions on tbe other side of tbe fault, tbe reflections having sufficiently distinctive character tbat the portions on opposite sides of tbe fault can be recognized and tbe fault throw determined. In practice, diffractions usually prolong events so that the location of the fault plane is not c1early evident, although occasionally it is possible to observe sharp terminations. Sometimes tbe same re-

249


Figure .)98, (Con/mued) (b) Ral' Iraórlg/hrough J depth model (depth.s in "f/ 10 3).

.1

fteelion ean be identified unequivocally on opposite sides oC the fault. but in Ihe majority of cases we can make only tentative correlations. The two record sections in Figure 4.99 join al their north and west ends at right angles. On the N-S seetion. the refteetion bando which consists of four strong "Iegs" (cycles) marked ~. can be readily correlated across the normal fault. which is downthrown to the soulh by about 65 ms al 1.6 s. At a velocity oC 2.300 mis. this represenls a vertical throw oC aboul 75 m. Thc event near 2.3 s (marked X) il1dicates a throw of aboul 120 ms. At a velocity of 3.000 m/s. tbis represenls 180 m of throw so that the fault appears to be growing rapidly with depth. Although the cvidenee suggests that the fault is a simple break in the shallow seelion. at greater depths there seems lo be a fault zone or a subsidiary fault (shown dashed in the figure). If the deeper correlations across the faull(s) are correcto the downthrown event rz al 3.5 s is found around 2.9 s on Ihe upthrown side. and assuming a velocity of 3.500 mis at tbis depth, we gel a vertical throw oC 1.000 m. The correlation across the fault for the shallow event is based on reHeetion eharacter; for the deeper evento it is based on intervals between strong reHections. systematic growth of throw with depth. and time ties around loops. Sometimes the displacement oC an unconformity or other recognizable feature will indicate the amount of throw. Often. however. the

Ihrow canno! be determined c1early from Ihe seismic data. The component of fault-plane dip in Figure 4.99a is around 53° [using Eq. (4.56)]. A fault that is nearly straight on a deplh seclion (a record section whose vertical scale is linear in depth) is concave upward on a time seclion (whose vertical scale is linear in traveltimc for a vcrtically traveling wave) because 01 the increase in velocity with depth. Ir the fault surface is actually concave upward (the usual situation). the curvature will be accentuated on a time section. The fault has no! completely died out by the north end of the line. and henee the fault should appear on the interseeting Une (Fig. 4.99b). As picked on the E- W section. the fault oHsets the event ~ al 1.6 s by only about 30 m. which indicates that the fault is dying out rapidly toward the east. The fault plane has nearly as much dip in the E-W seetion. so the strike of the Cault near the intersection of the two lines is NE and Ihe fault plan e dips aboul 60° to the southeast. The apparent dip on sections is always less than the tfUe dip. Fault indications are not evidcnt below 2.0 s on the E- W section. so the fault appears to have died out al depth. Several diffractions can be se en along the fault trace in Figure 4.99a between 1.9 and 2.5 s. and changes in the refleclÍon dip are seen on both sides 01 the fault trace; these are common evidences of

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Seismic methods

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Caulting. Another feature that is olten observed (but which is nol c1early evident on these sections) is distortion 01 events whose raypaths passed through tbe fault plane and experienced bendíng at the lault plane. TIte effect is often accompanied by deterioralion in data quality that sometimes is so great Ihat reflections may be almost entirely absent beneath the fault, which causes a sbadow zone. Occasionally the fault plane itseU generales a reftection, bul unless the data are migrated it may nol be cIear that the fault-plane rcflection is associated with the fault. TIte normal Cault in Figure 4.99 is the most common type of lault encountered; il is associated with

extension. The Iaull in Figure 4.98 is a thrust lault, which is produced by compressíon. Figure 4.100 shows three successive thrusts buried beneath the plain oI the Po River. Folding associated with the laulting provides Iraps lor several oil fields.

4.10.4. Fold and Flow Structures When subjecled lo slresses, rocks may fault. fold, or ftow, depending on the magnitude and duration ol the stresses. the strength of the rocks. the nature ol adjacent rocks, and so forlh. TIte folding oC rocks

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into antielines and domes provides many oC the traps in whieh oH and gas are found. Figure 4.101 shows a migraled seismic seetion across an antic\ine. Sorne portions, such as A, that are composed of the more competent rocks (for example Iimestones and eonsolidated sandstones), lend to mainlain Iheir thiekness as they fold. Other porlions, sueh as B, that eonlain less eompetent rocks (often shales and evaporitc:s). tc:nd to Ilow and slip along the bedding, resulting in marked variations in thickness within short distances. Geometry places Iimits on the amount of folding that is possible and folded structures almost always involve Caulting. NOle al e how a fault is involved with the folding. Arehing places sediments under tension so Ihal often they break alongnormal faulls and pro-

duce graben-type features on the topo AnticJinal eurvature tends lo make seismic reflections weaker as well as increase the like1ihood oC faulting and flow, so lhat dala quality eommonly deleriorates over antielines. Salt flow often produces antic\ines and domes. In many parts of the world thick salt deposits have been buried fairly rapidly benealh relatively uneonsolidaled sedimenls. The sedimenls compacl wilh depth and so increase their density, whereas the salt density remains nearly constan\. Thus, below sorne critical depth Ihe salt is less dense Ihan Ihe overlying sedimenls. Salt behaves Iike a very viscous fluid under sufficient pressure. and buoyancy may result in Ihe salt flowing upward lo form a sall dome. arehing the overlying sedimenls and somelimes

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piercing through them. Grabens and radial normal faults (whose throw decreases away from the dome) often result lrom such arching oI the overlying sediments, thus relicving the stretcbing that accompanies the arcmng. Salt domes tend to form along zones 01 weakness in the sediments. Figure 4.102 exhibits several portions oC a seisnllc line in the North Sea. The horizontal scale has been compressed SO as to display a long line on a short section, wmch produces considerable vertical exaggeration. Tbis line shows deep salt swells that have not pierced through the overlying sediments (Pig. 4.102a), salt that has pierced through sorne oC the sedimentary section (Fig. 4.102b), and also salt that has pierced all the way to the sea floor (Pig. 4.l02c). Tbe reflection Crom the base oC the salt is generally continuous and unbroken, but distortions produced by the variable salt thickness aboye it al times interrupl tbis reflection. Because the salt velocity is greater

than Ihat oC the adjacent sediments, the base oC the salt event appears lo be pulled up where the salt is thicker. In olher areas where the salt velocily is lower than that 01 Ihe surrounding sediments, ftat reflectors beneath the salt may appear to be depressed where the overlying salt is tbicker. Shallow salt domes are apt to be so evident that they can scarcely be nllsidentified. Because oC the large impedance contrast, the top of lhe salt dome (or the cap rock on top oC the dome) is olten a strong reflector. Steep dips may be seen in the sediments adjacent to the salt dome as a result oC these sediments having been dragged up with the salt as it flowed upward. The salt itself is devoid of primary reflections, although multiples may obscure tbis Ceature. Defining the ftank oC a salt dome precisely is orten econonllcally important but seismically difficulto Hydrocarbons may be accumulated in a narrow belt adjacent to the ftank oC the dome, but because

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the lIank is usually nearly vertical, it rarely gives rise to a recognizable rellection. Fortunately the ve\ocity distribution is oCten only slightly alfected by the growth oC the dome (except Cor the ve10city in the salt and the cap rock) so tbat the steep dips of the sediments adjacent to the flanks can be migrated fairly accurately and the flank outlined by the terminations oC these reflections. Nevertheless, there remains much art and experience in defining salt·dome Ilanks. Three salt domes can be seen in Figure 4.103. The salt in a salt dome generally has come from the immediately surrounding region. The removal of the salt from under the sediments around the dome has thus a110wed them to subside, which produces a rim syncline. Local thickening oC portions of the section in the withdrawal synclines indicates when the salt was moving out from undemeath and can be used to date the salt movement. Withdrawal synclines, which show fairly clearly in Figure 4.103, a1so help to provide c10sure in neighboring areas where the sediments continue to be supported by the residual salt. Occasionally shale or other substances a1so form Ilow structures that resemble salt domes. Overpres· sured shale is an especially common diapiric material. The water laid down with c1ays (or shales) needs to escape as the c1ay comes under greater pressure because of additional rock deposited on top oC them, but the very low permeability may prevent su eh escape. In tbis situation, the interstitial fluids become overpressured, the shale loses its shear strength, and it behaves like a viscous liquido Often the instability that results produces growtb faulting with shale moyo ing from undemeath the downthrown side or the rault and up on the uptbrown side. Overpressured shale is often found on the upthrown side ol normal faults in young sediments; it usually shows as a zone relatively devoid or reflections, and it can be con· fused with the shadow rone that is oflen seen be· cause of the erratic bendiag 01 raypaths as they pass through the fault.

4.10.5. Reefs The term "reef' as used by petroleum geologists comprises a wide varicty of types, ineluding both extensive barrier reefs that cover large areas and small isolated pinnaele reefs. It ineludes carbonate structures built directly by organisms and aggregates comprising Iimestone and other related carbonate rocks, as well as banks of interstratified carbonate (and sometimes a1so noncarbonate) sediments. Reef dimensions range from a few tens of meters to several kilometers; large reefs are tens or kilometers in 1ength, a few kilometers wide, and 200 to 400 m or more in vertical extent. Because recrs vary so widely,

257 the evidence ror reers shown by seismic data is extremely varied. We shall describe a model reer so that we may develop the general criteria by which reefs can be recognized in seismic data, keeping in mind that deviations from the model may result in large varia· lions from these criteria. Our model reer develops in a tectonically quiet area characterized by flat-Iying bedding thal is more·or-Iess unirorm over a large area. The uniformity or the section makes it possible to altribute significance to sub tI e changes produced by the reer, which might go unnoticed in more active areas. The reef is the result oí the buildup of marine organisms living in the zone of wave aClion where Ihe water, light, and temperature are suitable ror sustaining active growth. The site of the reer is usually a topographic high that provides the proper depth. The topographic high may be due to a hinge line or structure in (he underlying beds, such as a tilted fault block, but more often it is provided by a previous reef. As a result, reefs tend to grow vertically, sorne times achieving thicknesses of 400 m or more, thereby accentuating their elfects on the seis· míe data. For the reer to grow upward, the base must subside as the reer builds upward, maintaining its top in the wave zone as the sea transgresses. The reer may provide a barrier between a lagoonal area (the backreef) and the ocean basin (the forereef), so that sedimentation (and consequently the reflection pat· tem) may be dilferent on opposite sides or the reer. The surrounding basin may be starved, that is, nol have sufficient sediments available to keep il filled al the rate at which it is subsiding. Al times only one si de, more orten the ocean side oC the reeC, may be starved. Altematively, the reer may not be a barrier to movement or sediments, and in this case it will be surrounded by the same sediments on both sides. Erosion or the reef oCten provides detritus Cor depo· sition adjacent to the reeC, resulting in foreset beds with dips up to 20 c . Eventually the environment ror the reer organisms will change so that they can no longer continue to live and build the reeC; this might come about because oC changes in the water temperature, an increase in the rate or subsidence so that the organic buildup cannot keep pace (called drowning of the reer), or various combinations of circum· stances. Subsequently the reeC may become buried by deep-water shales, which may provide both an impermeable cap to the porous reeC and sufficient hydrocarbons so thal the reer beco mes a petroleum reservoir. Additional sediments may continue to be deposited; their weight compacts the sediments Ihat surround the reer more than they compact the rela· tively rigid reer and thus the overlying sediments that were deposited lIat may develop a drape over the reer.

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Based on the foregoing model, we might hope to see diffractions from the top and/or flanks of the ree!. Abrupt termination of reflections from the surrounding sediments may indicate the location ol the reef. If the reef provided a barrier to sedimentation, tbe entire reftection pattem may differ on the two sides of the ree!, reflecting the different sedimenlary environments. Overlying reflections may show sniall relie! (usually only a few milliseconds in magnitude) because 01 Ihe differential compaction. The yelocity difference belween the reef malerials and the surrounding sediments may produce pscudostruclure on reftecting horizons below Ihe reef. Usually the velocily in the reef limes tone will be greater than Ihal in tbe surrounding shales so that there will be a pseudohigh under the reef, often less Ihan 20 ms. Sometimes. however. the reer will be surrounded by calcareous shale, anhydrite, or other rock Ihat has a higher velocity than Ihe porous reer limes tone, so tbat the time anomaly is reversed.

Figure 4.104a shows a barrier reer. The reef lies on a hinge in the underlying sediments; this can be seen by laying a straight edge along reftections from undemeath the reer. The place 10 look for a reer is often aboye sorne underlying feature that rnight have provided the setting where a reef could grow. Sorne drape can also be seen aboye the reer. This is produced by differential compaction because !he sediments around the reef compacted more under the weight or oyerlying sediments !han did the relatively slrong red. The reflection paltems on opposite sides or the reer are different, showing that tbe reer was a barrier separating different depositional environments. Somewhat similar evidences indica te the reef on Figure 4.105. Reef evidences are often so small and subtle lhat seismic mapping of reefs is feasible only in good record are as. or first importance is geological information about the nature of the sediments and transgressive periods oí deposition, so !hat one knows

262 beforehand in what portion of the section reefs are more likely to occur. Similarities between reds and salt features cause problems at times. The lagoonal areas behind reefs may provide conditions for evaporite deposition so tbat sal! may be present in the same portion of the sedimentary column. Dilferential solution of salt beds foJlowed by the coJlapse of the overlying sediments into the void tbus created may produce seismic features tbat are similar in many ways to those that indica te reefs.

4.10.6. Unconformities and Seismic Facies Pattems Unconformities are often among tbe best seismic reftectors. They often are fairly easy to spot because ol an angularity between families of reftections. An unconlormity reftection may result from erosion or nondeposition, and angularities may occur aboye andjor below tbe unconformity. The nature of such a reftection may change laterally as dilferent beds subcrop against tbe unconformity or onlap onto it, and consequently the reftection often changes character along a line, sometime even completely reversing tbe polarity. Channels cut ioto unconformities sometimes provide channel sand or point-bar sand deposits that represent ooe type of stratigraphic trap. Channels are also sometimes fiJled witb impermeable day to seal the movement of hydrocamons. A channel can be seen on Figure 4.106. This channel is cut into tbe coal bed that produces tbe strong reftection at about 0.150 s. Coal beds often have lower velocity and density than the overlying or underlying rocks, and consequently often produce strong reftections. Unconformities subdivide a section into depositional uníts that are oflen dilferent from adjacent unÍts and are distinguished by distinctive seismic character (seismic facies). Certain pattems characterize depositional environments so that deltas, foreset bedding, reefs, sandbars, turbidite fans, periods of nondeposition, periods of tectonic activity, and so on, may be identified by the aggregate ol subtle evidences. From seismic facies studies one may be able to suggest tbe environment of deposition of tbe rocks and hence something about the stratigraphy. UsuaJIy seismic data of excellent quality are required for facies analysis. The amplitudes of reftections, especially lateral changes in amplitude, provide information for stratigraphic interpretation (Payton, 1977; Sherilf, 1980; Berg and Woolverton, 1985). Strong amplitudes result from large changes in acoustic impedance, such as may occur at basement or an unconformity, or because of a change from dastic to carbonate rocks. Strong amplitudes may also be the result of interfer-

Seismic methods

ence, focusing, and other causes. Gas accumulations may appreciably lower the density and velocity in porous sedirnents and hence may be located through amplitude elfects (see Fig. 4.107).

4.10.7. Use of Velocity Information With common-midpoint data, which have a high degree of redundancy, and velocity-analysis programs (§4.7.7), interval velocities can be calculated from Equation (4.85) al many points io the section - in fact, almost on a continuous basis. After due allowance for uncertainties in the measurements, systematic variations might be interpreted in stratigraphic terms (Hofer and Varga, 1972). Carbonate and evaporite velocities are sufficiently higher than c1astic velocities (especially in Tertiary basins) so tbat they can oflen be distinguished. The analysis of velocity data constitutes an important interpretation problern. As with other interpretation problems, sorne interpretations can be ruled out because they imply impossible or highly improbable situations. From experience we know that velocity does not vary in a "capricious" manner. It is unreasonable to expect the velocity to vary other than in a slow systematic way unless the seisrnic section shows significant structural or otber changes that suggest why the velocity should change rapidly. Two velocity analyses might show some dilferences between portions oí the section that are separated by a fault, whereas one expects little velocity variation in portions that appear to be conlÍnuous. One must be cautious about interpreting velocity data. Srnall errors in normal-moveout measurements can produce sizable errors in stacking velocities, and these in tum cause large errors in interval-velocity calculations when the intervals are smal\. Where the reflectors are nol parallel, interval-velocity calculations are meaningless (Taner, Cook, and Neidell, 1970). Velocity measurements sorne times are severely distorted by interference elfects, noise of various kinds, distortions produced by shallow velocity anomalies, or weathering variations, and care must be exercised that such elfects are not token as indications of actual changes in the velocity of the rocks.

4.10.8. Hydrocarbon Indicators Hydrocarbons in tbe pore space of a rock lower the velocity and the density compared to water in the pore spaces. Oil lowers the velocity and density slightly, but gas has a considerable effect. A small percentage oí gas may lower the velocity more than eitber a larger percentage oí gas or zero gas. Hydrocarbons thus change the contrast in acoustic impedance with tbe over1ying and underlying rock and hence the reflectivity. The consequent change in am-

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264 plilude (and somelimes oC polarity) of the reHections from the reservoir rock often is large enough to be seen. In clastic sections, tbe lowering oC the acoustic impedance oC a reservoir often produces a highamplitude reHection caBed a brighr spot, which is the most common hydrocarbon indicator (HC!). Seismic sections are sometimes displayed with low gain so that only the bright' spots stand out. When the acoustic impedance of a water-tiJled reservoir is appreciably larger than that of tbe adjacenl rock, as in a limes tone reservoir capped by shale, the lowering of the acoustic impedance by hydrocarbons produces a dim spor. Where a waterfilled reservoir's acoustic impedance is only slightly larger than the adjacent rock, the lowering by hydrocarbons may reverse the renection polarity. Thus a bright spot HC!, a dim spot HCI, and a polarity reversal HCl al1 have the same cause. The lowering of velocity also increases the traveltime oC deeper reHections, producing a velociry sag, another Hel. A horizontal gas-oiJ, gas-water, or oil-water contact may produce a distinct reHection, especially where the reservoir is thick; such a rellection is called a fiar spot HC!. Overlying changes in gas column thickness may tilt a Hat spot so that it is no longer horizontal. Almost all section displays employ an equalizing scheme whereby the gain on a trace is adjusted so that its average is the same as the average Cor adjacent traces. The increased amplitude oC a bright spot which causes the gain oC a trace to decrease lowers the amplitude oC deeper and shallower reHections and produces an amplitude shadow. Sometimes immediately undemeath a reservoir tbe dominant Crequency is lowered. Gas lealdng from a reservoir may permeate overlying Cormations enough to alTect their velocities and transmission qualities, producing gas-chimney elfects. HCI elfects usually indicate gas, and most elfects attributable to oil accumulation are too weak to be observable. Virtually all the HCl elfects can be produced by situations other tban hydrocarbons so that observation oC any one HCl may not indicate a hydrpcarbon accumulation. The case Cor an accumulation is strengthened considerably when several indicators are presento HCI may be sufficiently weak that none are detectable. In general, HCI are useful in young (Tertiary) c1astic sediments and become less useCul wi th increasing age, consolidation, cementation, or depth oC burial oC Ihe rocks.

4.11. SPECIALlZED METHODS 4.11.1. Profiling Marine protiling may employ as Cew as one hydrophone group, and shooting and reeording may take place at such short intervals Ihal a continuous

Seismic methods record section is obtained. The technique is similar to the continuous recording of water depth using a fathometer (echo sourider). It dilfers from convenlional marine surveying in that it employs smaller ships and weaker energy sources, and hence is much cheaper. Profilers also have relatively small penetration and cannot discriminate between events on Ibe basis of normal moveout where only a single hydrophone group is used. Profiling is extensively used in engineering studies (Fig. 4.108) lo map the bottom sediments and to locate bedrock. 11 is also widely used in oceanographic work lo survey large arcas cheaply (Fig. 4.109), 10 loca te pipelines buried in mud, and so on. The energy sources most commonly used are high-powered transducers, eJectric ares, air guns, and imploders. High-powered Iransducers are usually piezoelectric devices that employ barium li tanate or lead zirconate. Such materials not only generate electric tields when compressed (as when used as hydrophones), but they also change dimensions when subjected to an electric field, that is, they transform electrical energy to acoustic energy and vice versa. Profiling transducers operate at lower frequencies and higher power levels than Cathometers used Cor water-depth measurements; Crequencies in Ihe range 2 to 10 kHz and power levels of roughly 100 W are commonly used. A repelition rate oC 2 s and penetration oC 20 to 100 m are gene rally achieved. Retlec· lion character can sometimes be interpreted lo indio cale the nature of the sediments, Cor example, lo find sand layers that can support structurcs erecled on pilings. Electric ares (sparkers) utilize the discharge of a large capacitor to create a spark between two electrodes located in the water. The heat generated by the discharge vaporizes the water, creating an elfect equivalent to a small explosion. Several sparker unils are oCten used in parallel. Modern sparker arrays deliver as much as 200 kJ at 50 to 2,000 Hz and achieve penetrations or 600 m or so. A variation oC tbe sparker oCten used in fresh water involves connecting the electrodes by a thin wire that is vaporized in !he discharge. This inereases the duration of the bubble and consequently its low-Crequency content. The air guns used in profiling are similar lo Ihose used in convenlional marine work except that they are smaller; they involve as little as 1 in. J oC air at 1,000 psi and a dominant frequency of 250 Hz. Imploders used in profiling ¡n elude Ihe Boomer al· ready described, which delivers about 200 J oC energy Crom SO Hz to a few kilohertz. Profiler data are sometimes recorded on e1ectrosensitive paper using a strip recorder, but most commonly they are recorded on magnetic tape, often in digital formo

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J"~.!:;'¡;L~~~;.r:

:,,7;m.,.''''' ¡"~ "'," t.·..:.::::..: ;'1..; ,,' i ..I.·:.~: lo"':.. /

'.. ;.,(,..: ...t. ...._ ... ..:.~~~...

.: ,.,., .•••••." /. :.'. ..: •

~,'

.j..' •• :

~ .. .yi ~ ;':',i ~.

,.,>~ •••. ,~. ~"f;

; .•__ , • ; ••: ,., .•.4.' ... : .•

,//

~I

(a)

r

¡

( b) Figure 4.110. Side-sc,ln sonar. (Courtesy Compagnie Générale de Géophvsique) (a) Schematic dia8ram. (b) Record showing reflections (rom sea- floor relief. There is a blind zone under Ihe ship's track.

Multiples of the sea ftoor often are very strong and make data arriving after them unusable (Allen, 1972). In engineering work where interest is concentrated in the relatively thin layer of unconsolidated sediments overlying bedrock, such as shown in Fig. 4.108, this usuaIly does not create a problem; where the unconsolidated sediments are thick, the sea bottom is apt to be 50ft (not involving a large acoustic impedance contrast) and hence the bottom multiple is relatively weak. In deep-water oceanographic work, a long period ol time (a wide window) eJapses before the ocean-bottom muItiple arrives (as in Fig. 4.109) so that appreciable data are recorded without ambiguity. The power and complexity of profilers are sornetimes increased to such an extent that the difference rrom conventionaI marine methods virtuaIly disappears. They may emp)oy arrays of sources, streamers

containing many hydrophone groups. and common· midpoint methods. Profiler surveys often employ severa! types of sensors, possibly towing magnetometers and sniffers (devices that sample and anaIyze the seawater Cor hydrocarbons or other materials). Side-scan sonar (Fig. 4.110) is sometimes used, which utilizes highfrequency transducers to record energy reftected back Crom sea-t1oor relieC to the si de of the ship. Sometimes the deep-tow method is employed, that is, sources and sensors are towed near the sea t100r in deep water.

4.11.2. Three-Dimensional Methods (a) Acquisirion. Most seismic data are recorded along lines oC traverse, and variations perpendicular to the seismic line are inferred Crom comparison with

1I

'" 100 m ---'~I¡..'----- '" 200 m ----.0-11

, I

Porl paravane

I I

I

GE¡Q4iH~ /

I

- -- - - - - - - - -- - - - - - - -

~-

- - - --

Port source

.1~~ ~,~~~ --- ~-:;~~:;;::, Line of midpoints

, I

I

'" 100m

--¡ -

1 ~~ ~ ~~~t~

pinger signal

_ _ _ _ _ _ _ _ _

Starboard

"" 100 m

sourc':...OE~~R !~'.'~ _________________1 ___

Slarboard paravan.

(a)

0-1 o·

""100m

o o o o

o .. D ........ .

•••••••••• 0.'

::0::::::::: •• oo' oo.

O"

_.1

-. T '" 50 m

,.

::0::::::::: ::0:::::::::

::9::::::::: ::9:::::::::

'" 100 m

H

::0::::::::: ::0::::::::: ••••

o ••

o ••

O"

::0:::::::::

::0::::::::: ............. ::Q::::::::: ............. ::0:::::::::

o

o o

lo. Geophone group centers o Sourcepoint locations

o o o o o ( h)

Figure 4.111. Arrangemenls for Ihree-dimensional surveying. (From Sheriff and Celdart. 1982.) (a) Use of paravanes lo pull source units lo Ihe side of Ihe ship's 'rack 50 Iha, Iwo parallellines of coverage can be obtained by allernating sources. PdrdVdneS dre .1150 used 10 record wilh /wo s'reamers simultaneously. (b) (and three-dimensional data are usudlly recorded wilh Iines of geophones (usually wilh several pdrdllel geophone lines used simu/laneously) perpendicular lo Ihe line of sourcepoinls.

Specialized methods

parallellines or cross lines. This is oCIen done during conlouring, after inlerpreting the individual lines in a grid oC lines. Three-dimensional methods involve acquiring dala over an area rather Ihan in linear Cashion. Obviously 3-D data cost more than 2-D data, but the added cost will be justified ir the removal oC interpretation ambiguities is sufficiently importan\. Most 3-D data have been acquired after hydrocarbons have been discovereG in an area and before field development. Most often the increased costs are more than offset by savings due to fewer dry development holes. Also, more precise maps of a field may result in locating wells so as to leave less hydrocarbons in the ground, which effectively increases the reserves discovered. Ideally, element spacing in both directions should be the same - that dictated by spatial-aliasing considerations. These depend on the maximum dip to be recorded without ambiguity. The required spatialsampling interval is often less than 50 m, but such small spacings are rarely used because of cost considerations, and typical spadng is about 100m. Complete uniformity also requires that each element of dat:!!. have the same multiplidty and be composed oC the same mix oC offset distances, so that it will have the same signal/noise ratio. Although uniformity is usually not achieved, interpretability is still improved because 3-D data elements have more neighboring values than linear data and so do nol require tbe same uniformity. In tbe marine environment most equipment is towed into place and usually the ship cannot stop without losing control oC the towed equipment. This constrmns marine 3-D acquisition to a series of c\osely spaced parallel lines. Towing dual streamers offset to the side, and/or the use of dual sources (Figs. 4.60 and 4.111a), also offset to the side, make it possible to obtain two or more lines of midpoints on a single traverse. Long streamers do not necessarily track tbe srup, however. Magnetic compasses located throughout the streamer and radar sighting on the tail buoy help determine the streamer's orientation, and water-break detectors help determine distances from the source locations. Streamer drift to tbe side because of a cross-curren I is sometimes used as a device to obtain areal coverage, though at the price of a nonuniform mix oC offset distances. Land 3-D acquisition is most often acrueved using lines of geophones and sources at right angles to each other (Fig. 4.111b). Tbis arrangement provides coverage over a block. Often several lines of geophones are used, especially with systems that can record large numbers ol separate traces, to produce a swath of coverage. However, distortion is introduced because the direcúvity oC arrays is usually different in the in-line and cross directions. Another arrange-

269 men! sometimes used. especially where the center of an area cannot be reached beca use of rulls, lakes, and so on, is the loop method wherein both geophones and sourcepoints are arranged completely around a loop. Other systems are used to adapl to specific local access restrictions. (b) Proeessing. Data must be located on a regular grid for almost all processing applications, so the area of coverage is divided up into rectangular cells called bins and traces are put into the bins in which the midpoints He. Displays may be made of the number of traces in each bin as a check on the uniformity of coverage. Data may be interpolated from neighboring bins when bins have insufficient traces. With land 3-D, many bins are not aJong Iines of traverse where near-surface data are available and because the multiplicity within each bin is apt to be small and irregular, poorer control on static time shifts may result. Likewise the control Cor velocity analysis is apt to be poorer than with CMP data. Oflen CMP data in the are a are used as the starting point for corrections. and additional CMP lines may be shot in connection with a 3-D survey to provide this information. Migration is usually approximated by first doing a 2-D migration of the data in one direction and then migrating this intermediate result in !he direction at right angles. The result is nearly tbe same as would be achieved by a true 3-D migration and it is considerably cheaper.

(e) Display. The 3-D data sel can be thought oC as a volume oC data (Fig. 4.112) that can then be sliced in various ways. The data can be sliced vertically in various directions to provide cross sections in any direction; they can even be sliced along z.ig-zag lines to provide fence diagrams to connect well locations. The data can also be sliced horizontally to provide time slices (Fig. 4.1l2b), wruch are especially useful because a phase lineup on a time slice represents the same event at the same traveltime, tbat is, a time contour, and tracing the sequence of phase aligomenls on successive time slices genera tes directly a time-con tour map. The data may also be sliced aJong reHecting horizons (a horizon slice; see Fig. 4.1l2c), so that variations in amplitude can be studied. Tbis is a useful tool in studying stratigraphic changes and in mapping hydrocarbon accumulations where the hydrocarbons change the horizon's reHectivity. Sections and slices are often displayed in color, using one color (often black or blue) to indicate peaks and another color (often red) 10 indica te troughs. Such a display usually makes significantly more information available to tbe interpreter !han

Sejsmic methods

270

___,,_ TDp Or "clion shDwn in (b)

(a)

(b)

( e)

~igure 4.112. Three-dimensional data obt.lined from a set of c/osely spaced N-- S lines. (a) Isometric djagram of the volume these data occupy. The easternmost N -- S section is shown along with dn E-- W sec/ion made from the southernmost traces on eaeh N -- S line. (b) The data set with the top portion removed. The top now eons/j/u/es a tíme-slíee. (e) The da/a sljeed along one reflee/íon eons/i/u/es a hor¡zo~sliee. Sueh maps show reflectivitv varia/ions along the same horizon such as may indjcate strari. 8raphie or f1uid-content ehanges.

does the common variable area display where often the trough information is lost. Sometimes an additional color border is used with slice displays to clarify which direction is down- or updip. Color codes are also used to indica te amplitude or other attribute measurements (Sheriff and Geldart, 1983, pp. 73-4). (d) Interpretatíon. The major problems in the interpretation oC 2-0 data sets oCten involve decidíng what goes on between the lines oC traverse, how to connect up-Cault evidences, whether there is a local high between lines, and so on. The interpreter's imagination is exercised trying to figure out the most optimistic possibilities in between the lines oC coverage. With 3-D data, questions of tbis sort usually do not arise because the answers are clear Crom the data, and tbe questions Cor the interpreter deal with mQfe subtle matters. Horvath (1985) and Brown (1988) show many examples of the interpretation of 3-D data.

reHection occurs at the layer boundaries; tbis may happen ir the velocity contrast is exceptionally high (as at a free surface) or if the angle of incidence exceeds the critical angle (Sheriff and Geldart, 1982, pp. 70-3). Channel waves (also called guided or normal-mode waves) can travel in a water layer overlying a bigh-velocity sea Hoor and in low-velocity members, such as coal, that are sandwiched between high-velocity members. Channel waves are used to determine the continuity oC beds in coal exploration (Buchanan et al., 1981). A source in a gallery generates waves in a coal seam that can be detected in neighboring galleries iC the coal seam is continuous, that is, not interrupted by intervening Caulting. Sometimes source and geophones are located in the same gallery to detect reHections from fault faces. Channel waves are generally dispersive, with diCferent frequency components traveling at different velocities. The resuIt is that an impulsive input becomes a long wavetrain (as in Fig. 4.113) after traveling for some distance.

4.11.3. Use of Channel Waves Seismic energy can sometimes be Irapped within a low-velocity layer. Then the energy from a point source will decrease with distance according to cylindrical rather than spherical divergence, that is, at a slower rate. This will happen when total or near-total

4.11.4. Vertical Seismic Profiling Velocity surveys in boreholes (§4.5.5a) involve placing a geophone at several depths and measuring the traveltime of the first energy from a source near the wellhead. The geometry for vertical seismic profiling

Specialized methods

271 2.•

2.5

40 H.

48+ 250 Hz

S6 H.

Figure 4.113 Dispersive wal'c/rain such as Ihal produ{'ed by clJanne/ waves. rhe burs/ 01 high' frequency energy slarling aboul 2.66 s IS superimposed on Ihe /ow-frequenCl' wave. bolh ending abrup//y al aboul 2.13 s: Ihis is known as Ihe Airr phi/se. (From Clal' and Medwln. 1977)

(VSP) is similar except tbat tbe entire wavetrain is recorded (Balch and Lee, 1984; Cassell, 1984; Hardage. 1985). The geophone locations in the boreholes are usually closely spaced, typically about every 50 m, and the results are usually displayed as in Figure 4.114. The wavetrains inelude not only direct waves. bUI also reflections and multiples of various types. The downward- and upward-traveling wavetrains can be separated almost complelely in processing. The downward-traveling wavetrain provides the information needed for deconvolution. The upwardtraveling wavelrain after deconvolution usually shows predominantly primary reftections and is useful in correlaling reftection events wilh well horizons. The VSP is also useful in "seeing ahead of the bit," that is, in showing refiecting horizons that tbe well has not yet penetrated. These show up with greater ciarity than in surface data because the waves have not had as far to trave!. If the source is moved sorne distance from the wellhead, then reftecling points will be localed farther from the well, the Carther the reftecting horizon is from the well geophone. Having recordings al many geophone depths results in a profile to the si de oC the wellbore. VSP records are thus useful in seeing features that the borehole missed, such as faulls or olher changes in reftectors. VSP surveys are also used in directional holes and in olher situations as in terprelational aids.

4.11.5. Shear Waves in Exploration AlIhough most exploration is done with P waves, S waves depend on different elastic parameters and thus provide independenl information. Appreciable effort has been expended in recenl years lo use S-wave dala in conjunclion with P-wave data to define lithology, as a hydrocarbon indicalor (Ensley, 1985), and in fraclure delection. The ratio of S-wave lo P-wave velocities differs with lilhology, and hydrocarbon accumulations, especially gas, oflen

change the P-wave velocity significanlly but have Hule effect on the S-wave velocity (Tatham, 1982). Fractures affect velocities differently depending on the raypath orientation with respect lo the fractures. Severa! methods preferentially generale S waves, and geophones oriented lo detect horizonlal motion can be used as S-wave detectors. P waves generate SV waves upon conversion al inlerfaces and vice versa, which leads to confusion in interpreting results. However, most S-wave exploration is done wilh SH waves that do not convert.

4.11.6. Variation of Amplitude with Offset Reftections generally decrease in amplitude wilh increasing angle oC incidence, that is, with increasing offset. However, when gas fills the pore spaces, the amplitude may increase with offset (Oslrander, 1984). Although Ihe situation is complicated, the variation oC amplitude with offsel may be useCul as a hydrocarbon indicator.

4.11.7. Cross-hole Methods Pladng a seismic source in one borehole and geophones at various depths in another borehole provides data for a number of raypaths, the more so iC the source is successively located at a number oC depths. The traveltimes and amplitudes oC the multilude of raypaths provide tomographic data Ihat hopefully can be used to discover how velocities and factors causing amplitude loss are distributed Ihroughout the region between the boreholes (Peterson, Paulsson, and McEvilly, 1985). Cross-hole methods are presently handicapped by limitations oC the strength of the source thal can be placed in a borehole; this limits the distance over which signals can be detected. However, the method offers promise as a field-development and production-monitoring 1001.

3000

0.0

Deplh (mI IKOO

600

-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII!!IIIIIIIIIIIIIIIIIIII

3000

0.0

Deplh (m) 1800

Velocily (mis)

~ §~

- .., ...

6OO-..in.-

~"IIIIII¡""""""mllllll""III""""IIII11I11l1.HIIIlIIIIlI!IIIIIIIII~

1T1

0.0

I

1.0 _11I1I1111I11II1II1I11I1II11II1II11I~~"""'-"""".-'!:""",i;;¡(':~J

1.0 ..JIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIUIU/UUIIlU/UllllIIIIIUIIUIIIIIlIIIIIII/:..o-

!

¡

I

I

600hf! lI 1.0

,,

lC2

I+~-':

!

..c:

Do

~

§

~

~.O

;; .~

< 3.0

3.0

(01

4.0 (b)

IC)

(d)

Figure 4.114. Vertical seismic profile. (Courtesy SSe.) (a) Each trace ;5 recorded at iI st.ltion in a boreho le using .ln .lir gun source at the surface. (b) Same exeept eaeh trace has been shifted by the one-w. ly tr.lvelti me to the surf.lce, thus align;ng reRections (upcom ing events) horizontal/y. (e) Portion of reflecti on record shot aerOS5 the we/lhe ild (d) Sonic log in the well.

273

Problems

4.12. PROBLEMS 1. (a) By substituting

6',

m_ V -

O in Equation (4.5), show that fyy - fu and veriCy the relation Cor Poisson's ratio, Equation (4.8). (b) By adding the three equations for 0n' ayy ' and o"' derive the relation Cor Young's modulus, Equation (4.7). (e) Substituting 0xx - a yy - o" - - p in Equation (4.5), derive the relation for the bulk modulus, Equation (4.9). 2. (a) Verify that \ji in Equation (4.18) is a solution of the one-dimensional wave equation [Eq. (4.17)J. [Him: Let t = (x - Vt) and show that éJ\jI/éJx = (d//dn(aUdx) = d//dt = /" and so on.J (b) VeriCy that .¡, in Equation (4.20) is a solution oC the wave equation, Equation (4.16). (e) Using the same teehnique as in parts (a) and (b), show that \ji - (1/r)/(r ± Vt) satisfies the spherieal wave equation, Equation (4.22). 3. A pulse eonsists oC two Crequency eomponents, 1'0 ± Av, oC equal amplitudes. For the two eomponents we write 0n

> O and

= 1'0 + Av, 1'2 = 1'0 - Av, ko = 1/'\0 = "o/V, k l '" ko + Ak '" (l'o + Av)/V, and k 2 '" ko - Ak '" (l'o - Av)/V. (a) Show that the pulse is given approximately by the express ion where

VI

where B = 2A eos2wAk(x - (Av/Ak)t). (b) Why do we regard B as the amplitude? Show that the envelope of the pulse is the graph of B plus its refleetion in the x axis. (e) Show that the envelope moves with the group velocity U where A.. dI' dV "" V - , \ U = - '" Ák dk d'\

6)

y

0yy ... 0zz -

dV

.. V+...,d...,

4. Assume three geophones oriented so that one records only the vertical component oC a seismie wave, another record s only the horizontal component in the direetion oC the sh0t, and the third reeords only the horizontal eomponent at right angles to this. Assume a simple wave shape and draw Ihe responses oC the three geophones Cor the ColJowing cases: (i) a P wave traveling directIy Crom the shot to the geophones; (ü) a P

-,-.

" 11

., Figure 4115. Combining dip componen/s.

Table 4.4.

Depth

Two'way time

(m)

(s)

1.000 2.500 2.600 4.600

1.0 2.0

2.1 3.1

wave reftected from a deep horizon; (iü) an S wave generated by refteetion oC a P wave al an interCace; (iv) a Rayleigh wave generated by the shot. 5. Using Figure 4.115, show that the construction oC Fig. 4.27 gives the same result as Equation (4.61). [Hint: Express OB in terms of n-sin e, and use equation (4.61).] 6. (a) Given the time-depth inCormation in Table 4.4, ealeulate interval ve10ei lies and average velocity to each depth. Plot veloeity against depth and velocity against time, and determine the equations oC straight Iines that approximate interval velocity and average velocity against time and depth (Cour equations). What are sorne oC the problems involved in miling Cunctional fits to data? (b) Using the Cunction derived in (a) tor the average velocity as a Cunction of time, calculate the depth 01 reflections with zero-dip moveout and traveltimes oC LO, 2.0, 2.1, and 3.1 s. How mueh error has been introduced by approximating the ve\ocity by a function? 7. (a) Assuming equivalent average velocity as indicated in Section 4.3.2b, the results Crom part (a) oC problem 6, and a dip moveout of 50 ms per 1,000 m, calculate the dip of reflectors corresponding to traveltimes oC l.0, 2.0, and 3.0 s. Plot the locations oC the reftecting points.

274

Seismic metho ds A

B

'"..,

-

~

~

.~

-

-- _. f--

.- 1---

.. -

~

--

r-_.

~ .-- f1-

-

--

~--

~

.-

-- 1--

_.- .-

....,

~3

1--. O~

0,.\

-- - -r-..

.-- -

f--

04

--f---

-

-

ff--

~¡?= 1::-- --

=--

.-

-

.- . . . L_

05

--~¡::;o<

=-,...-- 1--- 1--

f-

I-+--:

06

=-

,.......

_. -

' - f--

-

----¿-

__ o

1--t--.

..

f--

.

f--

~

- 1--- 1- 1---

- r" - 1-- --.:. --- 1- ..- -_. --- - r=- ~ -:.... f-- . - f--- f--._- :::-.::. f-= 1= '--- ¡--- f-__ -

'Jo

-

=~

01

r-f-:- 1-- ¡-- ¡-- r-. 1--- 1-:-" ::::-

-

i--

-

f---

'"

;:; I~

1--. 1--- 1- 1--

1- f--

.-- f-.St-. ..

~

,.oc- ,.= ,.o- ~-

--

-.- i--f

r-

'Jo

F'--s. 1---1-

r-.

1---'

- - ,.,. ~

o

- -:::iII:

..

--

'-- 'x

--- F-' .... -.. f-- r--

1--~-

..,

VI

EI~\la1lon!.

- ,.- ,.- -- - o ~

,. - - ,. ,. ,.'" 3 S '" '"

-

B

EIC'\-.lllon'i

'r=11--- 1-.

.- 1-- --

-

=

- - i-i--

-

Figure 4.776. Firsl breaKs and d reflecri on on reverse d end-oll spreads.

(b) Assume constant-velocity layers as follows: Oto 1,000 m 1,000 to 2,500 m 2,500 to 2,800 m 2,800 to 4,800 m

2,000 m/s ~,ooo m/s 6,000 m/s 4,ooo m/s

Verily that this gives the time-depth data ol Table 4.4. By ray-tracing through these layers for a dip moveout ol 50 ms per 1,000 m, find the dip and rellecting points lor rellectors for which the acrival times are l.0, 2.0, and 3.0 s. Compare witb the results Cor part (a). 8. The correction methods discussed in Section 4.7.1 assume that tbe shot is below the base of the LVL. What changes are required in the equations oC this section il this is no! the case? 9. Figure 4.116 shows the first arrivals at geophone stations 100 m apart Crom shots 25 m deep at each end of the spread. (There are actually 11 geophone stations with the shotpoints at the first and eleventh stations; however, the geophone group at each shotpoint is not recorded because oC hole noise.) The uphole geophone is recorded on the third trace from tbe right. The weathering velocity is 500 m/s.

(a) Estimate Ihe subweathering velocity V by H averaging the slopes oC lines approximating the first breaks. The valley midway between the shotpoints produces a change in the first-break slopes, as ir two refractors are ¡nvolved, which is not the case. How can one be sure of the latter? (b) Determine the weathering thicknesses at the two shotpoints Crom the uphole times. (c) What corrections !llo should be applied to rellection times at the two shotpoints Cor a datum oC 1,100 m? (d) Calcula te the weathering thickness and the statiC time correction for each geophone station. 10. (a) Two intersecting seismic spreads have bearings N100E and N140oE. If the tirst spread shows an event at '0 = 1.760 s with dip moveout of 56 ms per 1,000 m while tbe same event on the second spread has a dip moveout oC 32 ms per 1.000 m, find the true dip, depth, and the strike, assuming that (i) both dips are down to the south and west and (ii) dip on the first spread is down to the soutb while the other is down to the southeast. Take the average velocity as 3 km/s. (b) Calculate the migrated position for each spread as if the cross-information had not been

275

Problems D.plh

V.lociI}'

.,

-----------------r---------------r------------------Ofi 6000 ni. --------------;-----------------I~

-------------H//tHlII\\------ _____ 1.. 6800

- lSOO

g~

------------~HH~~----------_1-----------------22oo

I

I I I I I

9600 3200

11.400

1 -----4400

I I

: 12.600

I

------+-+ -+ +--+--+--+-+-+-+ -+------t---- --·-·-·------·5900

Figure 4.117 5impli(ied wavefront eharr formerly used ro pIar cross seerions on a rramparenloverlay. Charr shows rays traeed through a series of eonstanl-veloeity layers for t:.f,j values of O, ± 0.010. ...• ± 0050 s, t:.x - 1000 fl. Wavefronts are shown for lo - 0.4 to lA s assuming Ihat Ihe rays are reflecred upward along the downward parhs. Plolted reflector ;5 for lo = 1.285, t:.ld - 0.033 s.

available and eaeb bad beeo assumed to indicate total moveout. Compare witb the results of part (a).

11. Consider a refteetion witb an arrival time at tbe shotpoint of 1.200 s and arrival times at geophones 1,000 m away on opposite sides oC the sbotpoint equal to 1.162 and 1.237 s, respectively, where statie and dynamie correetions have been applied to all traveltimes. (a) Using the simplified wavefront chart and velocity distributiOD shown in Figure 4.117, plot the migrated position oC the reftection. (b) Ir straigbt-ray plotting were used at the angle of approaeh, wbere would tbe refteetion be plotted7 Velocity just below datum - 5,500 Cl/s. (e) Using straigbt-ray plotting and assuming that V.v - 12,600 fl/s, the velocity at tbe refteetor, what is tbe migraled position? (d) The average velocity for a vertical traveltime of 1.200 s is 8,600 h/s. How can tbis be delermined from tbe data given in Figure 4.1177 (e) Assuming the average velocity 8,600 fl/s and straigbt-ray travel, wbat is the migrated position?

(1) On the adjoining record, wbich has a shotpoint 1,500 ft away, wbat is the arrival time oC tbis reftection for a geophone at the shotpoint (assume aplane reftector)? 12. (a) Because 8(/) is zero except for 1 = O where it equals + 1. Equation (4.93) now gives

8(1) .... +1 show that

(b) The comb can be written +00

comb(l)

=

L

n-

8(1 - nl o )

-00

the transform of Ibis expression is c1early +00

comb( 1)

....

S(,,) -

L

I! -

j2ft"'o-

Se;sm;c methods

276

]

-aE

.

..

II

.~

E ~

o

Z

OL-________

~

________

O

~

__________

~

______

2~1

Frequrncy

Figure 4.118. Spectrum of water-Iayer fIIter for water-bottom reflection coefficient af 0.5. If h - water depth and V - water ve/aeity, " - V/ 2h.

Show (Papoulis, 1962, p. 44) that this represents an infinite series of impulses of beight 2'IT /10 spaced 2'IT/lo apart, that is,

++

2'IT)

(

-,-

o

+ 00

I:

(

2'ITm)

8 2'ITp- - , "'--00 o

or eomb( 1)

++ Co.\¡

eomb( w)

(e) Sbow tbat a boxear of beight h and extending from - Po to + Po in tbe frequency domain has tbe transform

boxear(p)

++

the "singing frequeney." Sketch the amplitud e spectrum of the inverse filter. [Hinr: Timedomain eonvolution sueb as sbown in Equation (4.106) corresponds to frequeney-domain multiplication [Eq. (4.99)J; the frequency speetrum oC (he unit impulse is + 1, Le., tlat-J (e) Verify your sketch of the water-reverberation inverse filter by transforrning Equation (4.107):

sin 2'ITpol A sine(2'ITPot) - A - - 2 'IT Po'

where A - 2hpo = area of the boxear. 13. (a) Verify that Equation (4.107) is the inverse filter for water reverberation by convolving Equation (4.105) with (4.107), that is, by substituting tbe expressions given by Equations (4.105) and (4.107) in Equation (4.106). (b) The speetrum oi tbe water-Iayer filler is shown in Figure 4.118; tbe large peaks occur at

14. (a) Convolve [2,5, - 2, 1J with [6, - 1, - 1J. (b) Cross-eorrelate [2, S, - 2,lJ witb [6, - 1, 1J. Por what shift are tbese funetions most nearly alike? (e) Convolve [2,5, - 2,1) witb (-1, - 1,6) and compare witb the answer in (b). Explain the dilference. (d) Autocorrelate [6, - 1, - 1) and (3, - 5, - 2J. The autocorrelation of a funetion is not unique to that Cunction, Cor example, other wavelets tbat have the same autocorrelations as the preceding are [-1, - 1,6) and [-2, - 5,3). Whieh member oC the set is the minimum delay wavelet? (e) What is the normalized autocorrelation of (6, - 1, - lJ? What is the normalizedcross-eorrelation in (b)7 What do you eonclude from the magnitude oC tbe largest value of tbis normalized eross-correlation? 15. Prove that tbe half-intereept curve referred to in tbe discussion of Wyrobek's method in Section 4.9.3c is parallel to tbe curve of the total delay lime 8 (Pig. 4.119). Note that the reciprocal time

277

Problems

_----1!:O~l~al~d~el~.Y~l~il1\~C~(~~l~-----l L '"

(,. -

~,)

r--L-~~I

Figure 4.119. Demonstraring rhe para//plism of rora/-de/ay and ha/f-inrercept time curves

s sin

Rerractor

/

,,

/'

"-

v, v,

.....

/

/

......

.....! V,

Coincld~nl·tlmc

"-

-V' I /

l' f} -

.....

1)'

......

......

, "-

,,
......

......

"

"o

Figure 4. 120. Deriving the properties of the coincident-time curve.

can be written [Eqs. (4.77»)

(, = ~2 {(!:.... V + d

I Id )

+

(-~ V •

+

I lu ) }

16. Using Figure 4.120 show that: (i) DE, the wavefroot for I "" O, is at a depth of 2h = SD =

r

2z cos (J (note that CD '" SA = z/cos 8); (ü) each poiot 00 the coincident-time curve is equidistant from S and DE, that is, the curve is a parabola; (üi) taking DE and SD as the x and y axes, the coincident-time curve has the equation 4hy - x2 + 4h 2 ; (iv) the slope of the coincident-time curve at A is tan (J, hence the curve is tangeot to the refractor at A.

Seismic methods

278 Table 4.5. JI

Table 4.6. t (ms)

(m)

15

19 29 39 50 59 62

30

45 60

75 CJO

JI

(m)

105 120 135 150 165 180

t (ms)

'- Cms)

10 20

10 20

30 40

30 40 46 51

76 78

60

75

50

83

90

60

105 120 135 150 165 180

65 69 73 77 81 85

"1 -

'. - 1000R

v. - -10.000 nI'

ti - 1000 n

v. - 5000 nI.

1

f.4 (ms)

15

'A

t

(m)

65 68 72

17. Prove Equation (4.132) assuming tbal the surlace is horizontal and me refractor is plane between tbe two shotpoints. 18. To find tbe deptb to bedrock in a dam-site survey, traveltimes were measured from tbe shotpoinl lO 12 geopbones laid out at 15 m intervals along a straight line through tbe shotpoint. The offsets x range from 15 lo 180 m. Determine tbe depth of overburden from tbe data in Table 4.5 19. To determine tbe tbickness 01 the surface layer in a certain area, tbe readings in Table 4.6 were obtained from refraction records. Shotpoinls A and B are localed al me end 01 a 180 m east-west spread 01 13 geophones where A is west 01 B and and t. are tbe traveltimes al shotpoints A and B. The ground surface is Hat. No data were obtained from the geopbone al the shotpoint. Using tbe data in Table 4.6, find tbe velocitics in tbe upper and lower heds, tbe dip, and the vertical deptbs to the refractor at A and B. 20. Show that the two geological sections iUustrated in Fi¡ure 4.121 produce the same refraction timc-distance curve. Wbat is tbe apparent deptb to the Iowcr interface (obtained from tbe rerraetion data) if Jo) .. Vi in the section at tbe lelt, lor example. Vi - 8.20 kft/s, Jo) - 8.60 kit/s, and 4.10 H/s, and tbe hed tbicknesscs are as shown in the figure? 21. Thc time-distance obscrvations in Figure 4.122 constitute an cnginecring refraction problem. (a) Using Equations (4.77) and (4.79), show tbal tbe finl laycr dips about 1° and ranges in tbickne5S from 9 lo 11 ft bctwccn points 63 and 69.

t

It

30

45

69 74 80 85

(b) Show that the second and tbird layen have velocities 01 about 11,500 and 18,000 ft/s respectively, witb tbe interface betwccn the two layen dipping about 6°. (c) Determine tbe thicmess of the second layer by stripping off tbe shallow layer (§4.9.2). 22. Assume horizontal layering as shown in Figure 4.123 with a sbot at interface A that generates a wave tbat has amplitude 1 when it reaches interface B.
". - 10,000 n/l

y. - 20.000 R/I

y. - 20,000 R/I (,,)

57 63

(6)

FiBure 4.121. Two different Be%gie sections that B;ve the same refraetion timedistance curve.

Problems

279

Figure 4.122. Engineering refrdction profi/e.

Suríace

Deplh (m)

S~~~~~--------~~~---O

V-l.60km/s

p - 1.45 g/cm)

• Shol A - - - . . . ; ; . ; . . - - - -....---=~----IO

25.

v- 2.40 km/s P - 2.35 ./cm l 8-----------------------------810

v-

3.20 km/s

p - 2.68 g/cm)

26.

e -----------------------1610

v- 3.40km/s p - 2.70 g/cm) •

00

27. Figure 4.123. Horizontallayering situdtion.

28. 29.

" 30. Figure 4.124. A minimum-phdse wdvelet.

makes the shale-to-gas sand reftection coefficient -0.15 and tbe gas-to-water sand rellection coefficient + 0.20. What is the reftected wave shape1 (d) Repeat (c) where 20 m oC the sand is tille
31.

(b) Assume that your time-velocity pairs are pieked lo an accuracy oC 2%. What is tbe maximum error in the calculated interval-velocity values? From the sCÍ5mie record shown in Figure 4.1, determine tbe following: (a) The deptb oC shot, assuming a near-surface velocity of 500 mis. (b) The vdocity oC the subweathering by plotting the tirst breaks. (e) The stacking velocity from the measure
Seismic methods

280 REFERENCES ABen, F. T. 1972. Sorne characleristics oC marine sparker seismic data. Geophysics 37, 462- 70. Allen, S. 1. 1980. History oC geophysical exploration: SeiSDÚc method. Geophysics 45, 1619-33. Anstey, N. A. 1970. Signal characteristics and instrument specitications. In Seismic Prosp~c/ing Instrumenu, vol. 1. Ikrlin: Gebruder Bomtraeger. Backus, M. M. 1959. Water reverberations- their nature and eliminalion. Geophysics 24, 233-61. Badley, M. E. 1985. Prac/ical Seismic Interpre/a/ion. Boston: Intemational Human Resources Development Co. Balch, A. R, and Lee, M. W. 1984. Ver/ical Seismic Projiling: Technique, Applica/ions, and Case His/ories.

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40-5. Robinson. E. A .• and Treitel. S. 1967. Principies of digital Wiener fillering. Geopnys. Prosp. 15. 31l-D. Robinson. E. A.. and Treitel. S. 1973. Tne Rohinson- Treirel Reader. Tulsa: Seismograph Service. Robinson. 1. C. 1972. Computer-designed Wiener filters for seismic data. Geophysies 37. 235-59. Rockwell. D. W. 1967. A general waveCront method. In Seismie Refrae/ion Prospecring. A. W. Musgrave. ed .. pp. 363-415. Tulsa: Society oC Exploration Geophysicists. Safar. M. H. 1984. On the S80 and P400 water guns: A performance comparison. Firsr Break 2. no. 2. 20-4. Schenck. F. L. 1967. ReCraction solu:ions and wavefront targeting. In Seismic Refraerioll Prospectillg. A. W. Musgrave. ed .• pp. 416-25. Tulsa: Society 01 Exploration Geophysicists. Schneider. W. A .. and Backus. M. M. 1968. Dynamic correlation analysis. Geophysics 33.105-26. Schoenberger. M. 1970. Optimization and implementation of marine seismic arrays. Geophysies 35. 1038-53. Schultz. P. S. 1985. Seismic data processing: current industry practice and new directions. Geopn.vsies 50. 2452- 7. Schulze-Gattermann. R. 1972. Physical aspects oC the airpulser as a seismic energy source. Geophys. Prosp. 20. 155-92. SEG 1980. Digital Tape Standards. Tulsa: Society of Exploration Geophysicists. Sengbush. R. L.. and Foster. M. R. 1968. Optimum multichannel velocity filters. Geophysics 33.11-35. Shah. P. M .. and Levin. F. K. 1973. Gross properlies oC time-distance curves. Geoph.vsies 38.643-56. Sheriff. R. E. 1976. Inferring stratigraphy from seismic data. Bul'. A. A. P. G. 60.528-41 Sheriff. R. E. 1980. Seismic Stratigraphy. Boston: Intemational Human Resources Development Ca. Sheriff. R. E. 1984. Enqclopedic Dietionary of Exploration Geophysics. 2nd ed. Tulsa: Society of Exploration . Geophysicists. Sheriff. R. E .. and Geldart. L. P. 1982-3. Explorarioll Seismologv (in 2 volumes). New York: Cambridge Universily Press. Sherwood. J. W. c.. and Trorey. A. W. 1965. Minimumpbase and related properties of the response oC a

horizontally stratified absorptive earth to plane acoustic waves. Geophyslcs 30. 191-7. Shuey. R. T. 1985. A simplilication of the Zoeppritz equations. Geopnysics 50. 609-14. Stone. D. S. 1985. Geologic interpretation oI seismic profiles. Big Hom Basin. Wyoming. In Seismic Explorarioll ofrne Rocky Moantaín Region. R. R. Gries. and R. C. Dyer, eds., pp. 165-86. Denver: Rocky Mountain Association oC Geologists and Denver Geophysical Society. Taner. M. T .• Cook. E. E.. and Neidell. N. S. 1970. Limitations oC the reflection seismic method; lessons from computer sirnulations. Geopnysics 35. 551- 73. Taner. M. T.. and Koehler. F. 1969. Velocity spectra - digital computer derivation and applications of velocity functions. Geopnysics 34, 859-8l. Taner. M. T .• and Koehler. F. 1981. Surface consistent corrections. Geophysics 46, 17-22. Taner, M. T., Koehler. F .• and Sheriff. R. E. 1979. Complex seisrnic trace analysis. Geopnysics 44. 1041-63. Tarrant. L. H. 1956. A rapid method of determining the Corm oC a seismic refractor from line profile resuIts. Geophys. Prosp. 4. 131-9. Tatham. R. H. 1982. Vp/V, and Iithology. Geophys;¡-s 47.

336-44. Thomburgh. H. R. 1930. Wavcfront diagrarns in seismic interpretation. Bull. A. A. P. G. 14. 185-200. Toksoz. M. N .• and Johnston. D. H. 1981. Seismic Waue . A rtenuatioll. Tulsa: Society oC Exploration Geophysicists. Tooley. R. D .• Spencer. T. W .• and Sagoci. H. F. 1965. Reflection and transmission oC plane compressional waves. Geopnysics 30. 552- 70. Treitel. S.. Shanks. J. L.. and Frasier. C. W. 1967. Sorne aspects 01 fan lillering. Geophysics 32. 789-800. Trorey. A. W. 1970. A simple theory Cor seismic diffractions. Geopnysics 35. 762-84. Tucker. P. M .• and Yorston. H. 1.1973. Pirfa/ls in Seismic Interpretarion. Tulsa: Society ol Exploration Geophysicists. Walker. c.. and Crouse. B. 1. 1985. Field processing in the ·80s. Geophysies. Tne úading Edge of Explora/ion 4. no. 3. 41- 70. Watkins. J. S.• Walters. L. A.. and Godson. R. H. 1972. Dependence oC in-situ cornpressional-wave velocity on porosity in unsaturated rocks. Geophysics 37. 29-35. Webster. G. M. (ed.) 1978. Decollvolution (in 2 volumes). Tulsa: Society of Exploration Geophysicists. Willis. H. F. 1941. Underwater explosions - time interval between successive explosions. British Report Wa-47-21. Wyrobek. S. M. 1956. Application of delay and intercept times in the interpretation oC rnullilayer refraction time distance curves. Geophys. Prosp. 4. 112-30. Ziolkowski. A. 1984. De<"OlIvolurion. Boston: lntemational Human Resources Development Co. Zoeppritz. K. 1919. Über reflexion and durchgang seismischer wellen durch Ünstetigkerlsflaschen. Berlin. Über Erdbebenwellen VII B. Nachrichlell der Koniglic'herr Gesellschaft der Wisserlschafterr za Corringen. nwrn-phys. KI. pp. 57-84.

1

Chapter 5

Electrical Properties 01 Rocks and Minerals

5.1. ClASSIFICATION OF ELECTRICAL METHOOS Electrical prospecting involves the detection oC surface effects produced by electric current flow in the ground. There is a much greater variety of techniques available than in the otber prospecting methods, where one mues use ol a single field ol force or anomalous property - gravitation, magnetism, el asticity, radioactivity. Using electrical methods, one may measure potentials, currents, and e1ectromagnetic fields tbat occur naturally - or are introduced artificially - in tbe earth. Furthermore, the measurements can be made in a variety of ways to determine a variety oC results. Basically, however, it is the enormous variation in electrical conductivity found in different rocks and minerals that makes tbese lechniques possible. Eleclrical methods ¡n elude self-potential (SP), telluric currents and magnetotellurics (MT), resistivity, ineluding mise-a-la-masse, electromagnetic (EM), ine1uding AFMAG, and induced polarization (IP). They are often c\assified by the type of energy source involved, that is, natural or artificial. On this basis the first three and AFMAG aboye are grouped under natural sources and the remainder as artificial. Such a classification can be made for prospecting methods in general. Hence gravity, magnetics, and radioactivily are included in the natural source methods, whereas seismic requires artificial e~ergy. In the following chapters we shall study the eleclrical methods in a sligbtly different ~equence, groupiog three natural source methods together but considering AFMAG with EM, because the field techniques are quite similar. For the same reason IP will be considered immediately after resistivity.

5.2. ELECTRICAL PROPERTIES OF ROCKS AND MINERALS 5.2,1. Electrical Potentials Several electrical properties of rocks and minerals are significant in electrical prospecting. They are natural electrical potentials, electrical conductivity (or the inverse, electrical resistivity), and the dielectric constant. Magnetic permeability is also an indirect factor. Of these, e1ectrical conductivity is by Car the most important, whereas the others are of minor significance. Certain natural or spontaneous potentials occurring in the subsurface are caused by electrochemical or mechanical activity. The contralling factor in all cases is underground water. These potentials are associated with weathering oC sulfide mineral bodies, variation in rock properties (mineral content) at geologica! contacts, bioelectric activity oC organic material, corrosion, therma! and pressure gradients in uoderground fluids, and other phenomena of similar nature. There are four principal mechanisms producing these potentials; the first is mechanical, the lauer three chemica!. (a) Cenera ,.

(b) f/ectrokinetic potential. Also known as streaming potential, tbis is observed when a solution of electrica! resistivity p and viscosity 11 is forced through a capillary or porous medium. The resultant potential difference between the ends oC the passage is

r /lPkp 4'IT1J

( 5.1)

E/eetriea/ properties of rocks and minera/s

284

r

where is !he adsorption (zeta) potential, flP is tbe pressure difference, and k is tbe solution dielectric constant. The quantity l" is tbe potential 01 a double layer (solid-liquid) between tbe solid and solution. Altbough genera1ly 01 minor importance, !he streaming effcct may be tbe cause ol occasionallarge anomalies associated witb topography. It is a1so observed in self-potential well logging, where !he drilling ftuid penetrates porous formations (§U.3.l). (e) Liquid-junetion (diffusion) potential. This is due to tbe difference in mobilities oC various ions in solutions ol different concentrations. The value is given by

(5.2a) where R is tbe gas constant (8.31 I/oq, F is !he Faraday constant (9.65 X lO· C/mol), 9 is tbe absolute temperature, n is !he valen ce, l. and le are !he mobilities oC anions and cations, and el and e; are tbe solution concentrations. In NaCI solutions, I./Ie - 1.49, hence at 25°C, (5.2b)

E. is in millivolts. (d) Sha/e (Nernst) potentia/. When two identical metal electrodes are immersed in a homogeneous solution, tbere is no potential difference between tbem. If, however, tbe concentrations at tbe two electrodes are different, !here is a potential difference given by

(S.3a) For n - 1, 8 - 298 K, this becomes (E. in millivolts) E, - - 59.1 log( el/e;)

( 5.3b)

The combined diffusion and Nemst potentials are known as tbe electrochemical, or static, self-potentia/. For NaO at rc, tbe electrochemical self-potential (in millivolts) is E - -70.7 e

(T+273) 273

(el) e;

log -

(5.4)

When tbe concentrations are in tbe ratio 5: 1, Ec ±SO mV at 25°C.

(e) Minera/izarion porenria/. When two dissimilar metal elcctrodes are immersed in a homogeneous solution, a potential difference exists between tbe electrodes. This electro/y tic contact potemia/, a10ng witb tbe static self-potential. considered in Section 5.2.1 b, e, d is undoubtedly among tbe basic causes 01 tbe large potentials associated witb certain mineral zones and known as minera/ization potentia/s. These potentials, which are especially pronounced in wnes containing sulfides, graphite, and magnetite, are much larger tban tbose described in tbe preceding sections; values of several hundred millivolts are common and potentials greater tban 1 V have been observed in zones 01 graphite and a1unite. Bccause of tbe large magnitude, mineralization potentials cannot be attributed solely to tbe electrochemical potentials described earlier. The presence of metallic conductors in appreciable concentrations appears to be a necessary condition; nevertheless, tbe exact mechanism is not entirely clear, as will be seen in tbe more detailed discussion of mineralization potentials in Section 6.1.1 in connection witb !he seH-potential prospecting metbod. Otber sources of electrical potentials in tbe earth should be mentioned. From Equations (5.2a) and (5.3a) it can be seen tbat tbe magnitude ol tbe static self-potential depends on temperature; this !hermal effcct is analogous to tbe pressure difference in streaming potential and is 01 minor importance. Obviously metal corrosion - of underground pipes, cables, etc. - is a local source oC electrochemical potential. Large-scale eartb currents (§6.2.1) induced Crom tbe ionosphere, nuclear blasts, tbunderstorms (see AFMAG, §7.4.2e), and tbe like create small, erratic earth potentials. Currents ol bioelectric origin flowing, for instance, in plant roots are aIso a source ol earth potentials. Negative potentials of lOO mV have been reported in this connection, in passing from c1eared ground to wooded areas. Most of the earth potentials discussed above are relatively permanent in time and place. OC !he variable types, only telluric and AFMAG sources have been employed in prospecting. When measuring static potentials !hese ftuctuations cause a background noise and may be a nuisance.

5.2.2. Electrical Conductivities (a) Genera/. E1ectric current may be propagated in rocks and minerals in tbree ways: electronic (ohmic), electrolytic, and dielectric conduction. The tirst is tbe normal type ol current ftow in materials containing free electrons such as tbe metals. In an electrolyte the current is carried by ions at a comparatively slow rateo Dielectric conduction takes place in poor conductors or insulators, which have very Cew free carri-

285

Electrical properties Table S.l. Resistivities of minerals Resistivity (Om) Mineral Bismuthinite Covellite Chalcocite Chalcopyrite Bornite Pyrite Pyrrhotite Cinnabar Molybdenile Galena Millerile Stannite Slibnite Sphalerite Cobaltite Arsenopyrite Niccolite Bauxite Cuprite Chromite Specularite Hematite limoni te Magnetite IImenite Wolframite Pyrolusite Quartz Cassiterite Rutile Uraninite (pitchblende) Anhydrite Ca Ici te Fluorite Siderite Rock salt Sylvite Diamond Serpentine Hornblende Mica Biotite Bitum. coal Anthracite lignite Fire clay Meteoric waters Surface waters (ign. rocks) Surface waters (sediments) SoU waters Natural waters (ign. rocks) Natural waters (sediments) Sea water Saline waters, 3% Saline waters, 20%

Range

Formula Biz~

CuS

CU~

CuFeSz CUsFeS. FeSz Fe~

HgS MoSz PbS NiS C~FeSnSz

S~~

ZnS CoAs5 FeAs5 NiAs Alp,· nHp C~O

FeCrzO. Fe2Ü] FezÜ] 2Fe zÜ] . 3HzÜ Fe,O. FeTiÜ] Fe,Mn, WO. MnO, Si02 5nO, Ti02 UOz CaS04 CaCÜ] CaF, Fe2(CÜ]), NaCl KCI C

18- 570 3 x 10- 7 -8 X 10- 5 3 X 10- 5 -0.6 1.2 x 10- 5 - 0.3 2.5 x 10- 5 - 0.5 2.9x1 0- s -1.5 6.5 x 10-'- 5 x 10- 2 10- 3 _10' 3X10 - s -3xl 02 10- 3 -6 X 10' 10 5 _ 1012 1.5 - 10 7 3.5 X 10- 4 -10-' 2 X 10- 5 -15 10- 7 -2 X 10- 3 2 X 102 -6 X 103 10-'-3 00 1-10'

Average 2 X 10- 5 10- • 4X10 - 3 3 X 10- 3 3 X 10- 1 10- 4 2 X 107 10 2 x 10- 3 3 X 10- 1 5 X 10' 102 10- 3 2 X 10- 5 30

6 X 10- 3

3.5 x 10- 3 -10 7 103 _10 7

5 x 10- 5 -5.7 X 103 10- 3 -50 10-105 S X 10- 3 -10 4 X 1010 _ 2 X 10'· 4 X 10- 4 _10 4 30-100 0 1- 200

30-1013 1011 _10'2 lO_lO '· 2Xl02 -3xlo J 2Xl0 z -10' 9 X 10'_10 '4 2 X 102 -10' .,. 0.6-10 5 10- 3 _2 X 105 9-200

0.2 500 109 2 X 1012 8 X 10" 70

30

30-103 0.1-3 x1oJ 10-10 0

100

0.5-15 0

9

1-100

3 0.2 O.lS 0.05

Electrical properties of roeks and minerals

286

ers or none at al1. Under the influence oC an external varying e1ectric field, the atomic electrons are displaced slightly with respect to their nuc1ei; tbis slight relative separation oI negative and positive charges is Itnown as dielectric polarization oI the material and it produces a current Itnown as the displacement curre"r. (b) Eleetronie eonduetion. lbr electrical resistivity oI a cylindrical solid oC lengtb L and cross section A. having resistance R between tbe end Caces. is given by P - RAIL

(5.5)

If A is in square meters, L in meters, and R in

ohms, the resistivity unít is the ohm-meter (Om). For dimensions in centimeters tbe unít becomes the ohm-centimeter (Ocm): 1 Om - 100 Ccm. The resistance R is given in terms oC the vollage V applied across the ends ol the cylinder and the resultant current 1 flowing through it, by Ohm's law:

R - VII where R is in ohms and the units of V and 1 are volts and amperes. lbe reciprocal ol resistivity is tbe co"ductivity (1, wbere the units are siemens per meter (S/m). lben (1-

where ~ is the lractional pore volume (porosity), S is tbe Craction ol the pores containing water, Pw is the resistivity ol water, " .. 2, and a, m are constants, 0.5 ~ a ~ 2.S, 1.3 ~ m ~ 2.5. For example, suppose S - 1, a - 1.5, and m - 2, then p,lpw l.51;f} and lor values of ~ - 0.01, 0.1, 0.3, 0.5, p,1P w beoomes 1.5 X 10 4 , ISO, 17, and 6, respectively. Water conductivity varies considerably (see Table 5.1), depending on the amount and conductivity ol dissolved chlorides. sulfates. and other minerals present. The geometrical arrangement ol the interstices in the rock has a less pronounced effect, but may make the resistivity anisotropic, that is, having different magnitudes for current flow in different directions. Anisotropy is characteristic of stratified rock that is generally more conductive in the bedding planeo The anisotropy effect depends on the ratio of maximum to minimum resistivity, may be as large as 2 in sorne grapbitic slates, and varies from 1 to 1.2 in rocks sucb as limes tone, shale, and rhyolite. As an example, oonsider the layered formation shown in Figure 5.1, having resistivities PI and P% whose respective fractional volumes are v and 1 - v. Here the resistivity in the horizontal direction - a stack ol beds effectively in parallel- is

(5.8)

IIp - LIRA - (IIA)/(VIL) - JIE (5.6)

wbere J is the current density (A/nr) and E is the electric field (V1m). Because most rocks are poor conductors, their resisti'¡jties would be extremely large were it not for the Cact that they are usually porous and the pores are filled with ftuids. main1y water. As a result the rocks are electrolytic conductors, whose effective resistivity may be defined as in Equation (5.5), wbere the propagation oC CUTrent is by ioníc conduction - by molecules baving an excess or deficiency oC electrons. Hence the resistivity varies with the mobility, ooncentration, and degree oC dissociation of the ions; the lalter depends on the dielectric constant ol the solvent. As mentioned previously, the current ftow is not only slow compared to ohmic conduction, but represents an actual transport oC material, usually resulting in chemical translormation. lbe conductivity oC a porous rock varies with the volume and arrangement oC the pores and even more with the conductivity and amount oí contained water. According to the empirical formula due to Arcbie (1942),

In the vertical direction, the beds are in series so that

(e) Eleetrolytic conduction.

(5.7)

Then the ratio is

-~ - (1 - 2v + 2v 2 ) + (PI - + -~) v(l - v) ~

Ph

PI

If u « 1 and ~/pI » 1, tbis simplifies to Pu ~ - ... 1 +-10 Ph

(5.10)

PI

If the layer ol resistivity PI is for water-saturated beds, this ratio might be quite large. (d) Dielectric conduction. The mechanism of dielectric conduction - the displacement current - was described briefly at the beginning ol this section, where it was pointed out that the displacement current flows only in nonconductors when the external electric tield changes with time. The significant parameter in dielectric conduction is the dielectric consta"t k, sometimes called the specific inductive

Elecrncal properties

287

fit---+----------..,.r---.<

~r4----P,

)"

Figure 5.1. Anisotropic resistivity as a result of horizontal bedding.

capacity of the medium. lo analogy with magnetic quantities M, H, k, B, and Il (§3.2.1) we have an electrostatic set: eleetrie polarizatiol1 (eleelrie dipole moment/ul1;t volume) P, eleelrie jield strength E. eleetrie suseeptibility "'1, electric displacemenl (flux/unit area) D, and dieleclric conslant k. In

electrostatic units, the relations between tbese are

P = T/E

D

=

E + 4,"P = E(l + 4'"71) = kE (5.11)

whereas in mks units, P

= T/E

D = EoE + P

= E(to + lJ)

= tE

(5.12)

f'

and the dielectric constant k = 1 + ·,,/EO - E/Ea. In electrostatic units, P, E and D are volts per centimeter and 71 and k are dimeosiooless. lo mks units E, Ea, and 71 are io farads per meter, P, D are in coulomb s per square meter, E is io volts per meter, and k is agaio dimensionless and the same io either system. The dielectric coostant is similar to the conductivity in porous formations in that it varies with tbe amount of water preseot (note that water has a very large dielectric constant; see Table 5.5). We sball see in Section 6.2.3 that displacemeot currents are of secondary importance in earth material s because electrical prospecting methods geoerally employ low frequencies.

5.2.3. Magnetic Permeability Where EM sources are employed, the voltage induced in a subsurface conductor varies not only witb tbe rate of cbange of magnetic field, but also with the magnetic permeability of the conductor. From Maxwell's equation,

aH

"\i'xE--,,-

al

we see that currents induced in the ground are enhanced by the factor p.. Practically, however, the permeability rarely is appreciably greater tban unity, except for a few magnetic minerals (§5.4.3); consequently it is oC no particular significance in electrical work, except when F~03 is present in large concentration.

5.2.4. Polarization Potentials Where a steady current is passed through an electrolytic conductor conlaining mineral partic1es it is possible. as described in Sectioo 5.3.1, to determine the elfective resistivity. If a curreot is suddenly switcbed 00 or off io a circuit containiog an e\ectrolyte, a finite time elapses before the potential ¡nereases to a fixed value or drops to zero. The delayed buildup or deeay oC curreot is cbaraeteristic of electrolylic conduction, and is due lo accumulatioo oC ions at interfaces between the electrolyte and mioeral partic1es. As a result, a poteotial opposing

flectrical properties of rocks and minerals

288 A,ea =

T I

1 Figure 5.2. Simplified sehematie of equipment far measuring resistivity af eare samples.

the normal current ftow is developed across the interface. A similar efl"cct is observed at the contact between electtolytes and elay partic1es. TItese are known as polarization potentials; the process is called the induced po/arization effect. Induced polarization (IP) prospecting involves these interface potentials. Tbey wiU be considered in more detall in Section 9.2.

5.3. MEASUREMENT OF ELECTRICAL PROPERTIES OF ROCKS ANO MINERALS 5.3.1. Laboratory Measurement of Resistivity In order to measure direcUy the troe resistivity of a rack, mineral, eJcctroJyte, and so forth, it is necessary to shape the sample in some regular form, such as a cylinder, cube, or bar of regular eross section. An experimental arrangement is shown in Figure 5.2. lbe main difficulty is in miling good electrical contact. particularly Cor the current electrodes. For this purpose tinfoil or mercury electrodes may be used and it is generalJy neccssary to apply pressure to the current elcctrodes; sometimes the ends oC the sample are dipped in soft soJder. From Figure 5.2 and Equation (5.6) the resistivity is given by p - AV/LI

TIte power source may be dc or preferably Jow frequency ac (400 Hz or Jess). lbe possibility oC anisotropy can be checked by measuring the resistivity in two dircctions, provided the shape is suitable for this. Obviously one can malee these measurements in the fieJd as well, on drill core, grab samples, even outcrop. ir the electrode contact is reasonabJy good. Estimates oC resistivity, made on samples by using an ohmmeter and merely pressing or seraping the terminals oC the leads against the surface however, are not very trostworthy.

5.3.2. Measurement of Dielectric Constant An ae bridge may also be used to measure the resistivity of soils and electrolytes. At audio frequencies any reactive component - norma1Jy capacitive - must be accounted for in order to get a good bridge balance. Consequently the measurement determines the efl"ective capacitance, as weU as resistivity, of the specimen. Since capacitance varies with the dieJectric constant of the material, it is thus possible to determine the latter by substitution. TIte Sehering capacitance bridge is suitable for this measurement in the laboratory (Hague. 1957).

Typical values of electrical constants

289

Table 5.2. Resistivities of various ores Ore Pyrite 18% 60% 95% Pyrrhotite 41% 79% 95% Sb~ in quartz FeAsS 60% FeAsS

Other minerals

2% (chalco) 5% (ZnS) + 15% 5% (ZnS)

FeS 20%

80% 20%

300 0.9 1.0

59% 21% 5%

2.2Xl0-· 1.4 X lO-S 1.4 X lO-S 4 X 10)-3 X 101 0.39 10-.-10- 2 3 X 10-) 7 X 10- 2 103 _10 1 0.8 0.1-300 2.5 x 103

20%

sial

C~FeS.

CUsFeS.40% Fe.Mn. WO. PbS. near massive FePI Fe2ÜJ. massive Iron Fep4 6O% 75% brown iron oxide fe)O. Zinc 30% 80% 90% Graphitic slate Graphite. massive

60% Si02 CoAsS

25% 5% Pb5. 15% feS 10% PbS. 10% FeS 5% PbS

5%

2% FeS

8% Si02

50%

MO~

Mn02 colloida! ore Cu;¡S CuFe~ Cufe~

90% FeCr20 4

5.4. TYPICAL VALUES OF ELECTRICAL CONST ANTS OF ROCKS ANO MINERALS 5.4.1. Resistivities of Rocks and Minerals OC all the physical properties oC rocks and minerals,

electrical resistivity shows the greatest variation. Whereas the range in density, elastic wave velocity, and radioactive content is quite small, in magnetic susceptibility it may be as large as 1O~. However, the resistivity-of metallic minerals may be as small as lO-s Om, that oC dry, close-grained rocks, like gabbro as large as 107 Om. The maximum possible range is even greater, from native silver (1.6 X 10- 8 Om) to pure sulfur (1016 Om). A conductor is usually defined as a material of resistivity lesa than 10- 5 Om, whereas an ¡mulator is one having a resistivity grealer than 107 Qm. Between these limits tie the semiconductors. The metals and grapbile are a1I conductors; they contain a large Dumber of free electrons whose mobility is very great. The semiconductors also carry current by mobile electrons but have fewer of them. The insulators

p (Cm)

Gangue

45 2Xl0·-8x10 5 5 X 103 -8 X 10J 0.75 1.7 X 103 130 0.13 10- 4 -5 X 10- 3 2 X 10 2-4 X 10) 1.6 3 X 10- 2 10-· -1 0.65 103

are eharaeterized by ionie bonding so that the valence electrons are not free to move; the charge earriers are ions that must overcome larger barrier potentials than exist either in lhe semiconductors or eonduetors. A further difference between conductors and semiconductors is found in their respective variation with temperature. The Cormer vary inversely with temperature and have their highest conductivities in the region of O K. Tbe semiconduclors, on the other hand. are praetically insulators at low temperatures. In a looser e1assification, rocks and minerals are considered to be good, intermedia te, and poor conductors within tbe following ranges: (a) Minerals oC resistivity lO-a lo about 10m. (b) Minerals and rocks of resistivity 1 to 107 Om. (c) Minerals and rocks of resistivity above 107 Om. Group (a) ineludes the metals, grapbite, the sulfides except for spbalerite, cinnabar and stibnite, all the arsenides and sulfo-arsenides except SbAs2 • the antimonides excepl for some lead compounds. the

Electrical properties of rock,s and minerals

290 Table 5.3. Resisriviries of vario'.1s rocks and sediments Resistivity range (Om)

Rock type Granite porphyry Feldspar porphyry Syenite Diorite porphyry Porphyrite Carbonatized porphyry Quartz diorite Porphyry (various) Dacite Andesite Diabase (various) Lavas Gabbro Basall Olivine norite Peridotite Hornfels Schists (calcareous and mica) Tuffs Graphite schist SI ates (various) Gneiss (various) Marble Skarn Quartzites (various) Consolidaled shales Argillites Conglomerates Sandstones limestones Dolomite Unconsolidated wel clay Marls Clays Oil sands

4.5 )( 103 (wel) -1.3 x lO' (dry) 4 )( 103 (wet) 102 -10' 1.9 X 103 (wen - 2.8 )( 10' (dry) 10 - 5 )( 10' (wel) - 3.3 )( 103 (dry) 2.5 x 103 (wet) - 6 )( 10' (dry) 2 X 10' - 2 )( lO' (wet) -1.8 X 105 (dry) 60-10' 2 X 10' iwet) 4.5 X 10 (wet)-l.7 X 10 2 (dry) 20-5X10' 102 -5 X lO' 103 -106 10-1.3 X lO' (dry) 103 - 6 X 10' (wet) 3 X 103 (wet) - 6.5 X 10 3 (dry) 8 X 103 (wet)-6 X 107 (dry) 20_10' 2 X 103 (wet) _10 5 (dry) 10-10 2 6xl0 2 -4X 1 0' 6.8 X 10' (wet) - 3 X 106 (dry) 10 2 - 2.5 X 108 (dry) 2.5 X 10 2 (wel) - 2.5 X 108 (dry) 10-2

X

108

20-2 X 103 10.- 8 X 102 2Xl03 -10' 1-6.4 X 108 SO-lO' 3.5 X 102 -5 X 103 20

3 -70 1 -100

4-800

tellurides, and some oxides such as magnetite, manganite, pyrolusite, and ilmenite. Most oxides, ores, and porous rocks containing water are intermediate conductors. The common rock-forming minerals, silicates, pbosphates and tbe carbonates, nitrates, sulfates, borates, and so forth, are poor conduetors. The following tables list characteristic resistivities Cor various minerals and rocks. The data are from various sources, including Heiland (1940, Ch. 10), Jakosky (1950, Ch. 5), Parasnis 0.956, 1966, Ch. 6), Keller (1966), and Parkhomenko (1967). Resistivities oC tbe variOI1S metals in pure form, from antimony to zinc, vary by only about 2 orders of magnitude. (Bi '" 1.2 X 10- 6 Om, Ag '" 1.6 X 10- 8 Om). Tellurium is an exception ( .. lO- 3 0m). Two otber elements oI common occurrence are

Table 5.4. Variarion of rock resistiviry wirh water content Rock Siltstone Siltstone Coarse grain SS (oarse grain SS Medium grain SS Medium grain SS Graywacke SS Graywacke SS Arkosic SS Organic limestone Dolomite Dolomite Peridotite Peridotite Pyrophyllite Pyrophyllite Granite Granite Granite Diorite Diorite Basalt Basalt Olivine-pyrox. Olivine-pyrox.

%HP 0.54 0.38 0.39 0.18 1.0 0.1 1.16 0.45 1.0 11 1.3 0.% 0.1 O 0.76 O 0.31 0.19 O 0.02 O 0.95 O 0.028 O

p

(Om)

1.5 X 10' 5.6 X 108 9.6 X 105 108 4.2 X 103 1.4 X 108 4.7 X 103 5.8 X lO' 1.4 X 103 0.6 X 103 6 X 103 8 X 103 3 X 103 1.8 X 10' 6 X 106 lO" 4.4 X 10 3 1.8xl06 1010 5.8 x lOS 6 X 106 4 X lO' 1.3 X 108 2 X lO' 5.6 X lO'

graphite (5 X 10- 7 to 10 Om range, "" lO- 3 0m average) and suIrur (10 7 _10 16 Om range, ... 1014 Om average). The variation in resistivity of particular minerals is enormous, as can be seen from Table 5.1. Among tbe more common minerals, pyrrhotite and graphite appear to be the most consistent good conductors, whereas pyrite, galena, and magnetite are often poor conductors in bulk form, althougb the individual crystals have higb conductivity. Hematite and sphalerite, in pure form, are practically insulators, but when combined with impurities may have resistivities as low as 0.1 Om. Graphite is oCten the conneeting link in mineral zones, which makes them good conductors. The range of resistivities oI various waters is notably smalier than for solid minerals; tbe actual resistivities are also lower than tbose of a great many minerals. Table 5.2 from Parlchomenko (1967) lists resistivities for a variety of ores. In general it appears that pyrrhotite in massive Conn has tbe lowest resistivity, tbat tbe resistivity oC zinc ores is surprisingly low (possibly due to the presence oC lead and copper Cractions), and that molybdenite, chromite, and iron ores have values in the range oC many rocks. Table 5.3 lists typical values for rocks and unconsolidated sediments. The ranges are quite similar to tbat Cor water, which is the controlling Cactor in many rocks.

291

Typical values of e/ectrica/ constants

Very roughly, igneous rocks have the highest resistivity, sediments tbe lowest, witb metamorphic rocks intermedia te. However, tbere is considerable overlapping, as in other physical properties. lo addition. the resistivities oC particular rock types vary with age and lithology, because the porosity oC the rock and salinity oC the contained ':vater are aJfected by both. For example, tbe resistivity range oC Precambrian voicanics is 200-5,000 Om, wbereas Cor Quaternary rocks oC the same kind it is 10-200 Om. The effect oC water content on tbe bu1k resistivity oC rocks is evident Crom Table 5.3. Further data are listed in Table 5.4, wbere samples with variable amounts oC water are shown. In most cases a small change in the percentage oC water affects the resistivity enormously. As the depth oC penetration oC electrical methods is increased with new and refined equipment, it is found tbat tbe signi/lcance of water in lowering bu1k resistivity oC crustal rocks gradually decreases with increasing deptb, wbereas tbat oC temperature and pressure increases. Hermanee (1973) carried out deep sounding resistivity and magnetote!luric surveys in Iceland that indicated crus! resistivi ties decreasing from 100 to 100m in the depth range 2 to 12 km. Because this is a geothermal area straddling tbe Atlantic Ridge, one would expect anomalous low resistivities at sballow « 2 km) deptb. However, modeling oC the data suggested tbat water persisted to 8 to 10 km deptb, wbereas solid conduction in dry crustal rocks at high temperatures (700 to 1,OOO°C) and pressures (1 to 4 kb) became dominant below lhis.

Subsequent laboratory studies on dry granites, basalts, and gabbros in tbe tem:oerature range 500 to 1,OOO°C by Kariya and Sbankland (1983) provided rough agreement with the results of Hermanee and showed a 2-order decrease in resistivity over the 500°C temperature change.

5.4.2. Oieledric Constants of Rocks

and Minerals As mentioned previously, the dielectric constant is a measure oC the electrical polarization resulting Crom

an applied electric /leld. TIús polarization may be e1ectronic, ionic, or molecular. Thc /lrst type is characteristic oC all nonconductors. Ionóc displacement occurs in many rock-forming minerals, whereas water and the hydrocarbons are the oaly common materials that exhibit molecular polarization. Because oC the relatively slow mobilities oC the charge carriers, molecular polarization - the largest oC the tbree eJfects - and ionic polarizatioo are insignificant at very high frequencies. Thus the dielectric constant, whicb is proportional to the degree oI

Table S.S. Die/eetrie eonstants of rocks and minera/s Rock. mineral Galena Sphalerile Cassiterite Hematite Fluorite Calcite Apatite Barite Peridotite Norite Quartz porphyry Diabase Trap Dacite Obsidian Sulphur Rock salt Anthracite Gypsum Biotite Epidote Plagioclase feldspar Quartz Granile (dry) Gabbro Diorite Serpentine Gneiss 5andstone (dry to moist) Packed sand (dry 10 moist) 50il (dry to moist) Basalt Clays (dry to moisl) Petroleum Water (20· C) Ice

Dielectric const.

18 7.9-69.7 23 25

6.2 - 6.8 7.8- 8.5 7.4-11.7 7 - 12.2 8.6 61 14 - 49.3

10.5 - 34.5 18.9 - 39.8 6.8- 8.2 5.8-10.4

3.6 - 4.7 5.6 5.6 - 6.3 5 - 11.5 4.7 - 9.3 7.6 -15.4 5.4-7.1 4.2 - S 4.8-18.9 8.5 - 40 6.0 6.6 8.5 4.7 -12 2.9-105 3.9 - 29.4 12 7 - 43

2.07 - 2.14 80.36 3- 4.3

Table 5.6. Magnetic permeabi/ities

Mineral Magnetite Pyrrhotite Titanomagnelite Hematite Pyrite Rutile Calcile Quartz Hornblende

Permability

S 2.55 1.55

1.05 1.0015 1.0000035 0.999987 0.999985 1.(XXl15

polarization, varies inversely with Crequency. It is also indicative oC the amount of water present, because water has a dielectric constant of 80 at low Crequencies. Table 5.5 lists dielectric constants Cor various mioerals and rocks. Most oC the measurements have been made at frequencies oI 100 kHz and up. For very low frequencies the values would be generally

Electrical properties of rocks and minerals

292

higher by about 30%. In exceptional cases - one example being certain ice samples - the results have been larger by several orders oC magnitude.

5.4.3. Magnetic Penneability of Minerals The etrect oC l' on electrica1 measurements is very slight except in the case of concentrated magnetite. pyrrhotite. and titanomagnetite. From Equation (3.7), magnetic penneability is related to susceptibility by the expression lA' - 1

+ 4".k' in cgs uníts

l' - 1 + k

in SI units

" and lA' are dimensionless. Generally k is too small 10 change " appreciably from unity. Table 5.6 liSIS maximum permeabilities of some common minerals.

REFERENCES Archie, G. E. 1942. The elcctric resistivily log as an aid in determining some reservoir characteristics. Trans. ArME 146, 54-62. Hague, B. 1957. Alternati", Current Bridge Methods. London: Pitman. Heiland, C. A. 1940. Geophysical Exploration. New York: Prenliee-Hall. Hermanee, J. F. 1973. An elcctrical model lor !he subleelandic crust. Geophysic$ 38, 3-13. lakosky, l. J. 1950. Exploration Geophysia. Newport Beach, CA: Trija. Kariya, K. A .• and Shankland. T. 1. 1983. E1ectrical conductivity 01 dry lower crustal rock!. Geophysia 48. 52-61. Keller, G. V. 1966. In Handbook of Physical Constan/s. S. P. Clark, Ir., ed. GeoI. Soco Ana. Memoir 97, 553-76. Parasnis. D. S. 1956. The elcctncal resistivily ol some sulphíde and oxide mineral s and !heir ores. Geophys. Prosp. 4, 249-79. Parasnis, D. S. 1966. Mining Geophysics. Amslerdam: E1sevier. Parkhomenlto, E. I. 1967. Elrclrical Proprrlirs o/ Rocks, G. V. Keller, Irans\. New York: Plenum.

Chapter 6

M ethods Employing Natural

Electrical Sources

6.1. SELF-POTENTIAL METHOD 6.1.1. Origin of Potentials

..,

Various spontaneous ground potentials were discussed in Section 5.2.1. Only two of these have been considered seriously in surCace exploration, although the self-potential method is used in a variety oC ways in well logging (§11.3). Mineralization potentials produced mainly by sulfides have long been the main target oC interest, although recently exploration for geothermal sources has inc1uded self-potential surveys as well. The remainder of these spontaneous potentials may be c1assified as background or noise. This also means that geothermal ahomalies become noise if they occur in the vicini ty of a sulfide survey and vice versa (§6.1.4). A mor~ detailed description of these sources follows. Background potentials are created by fluid streaming, bioelectric activity in vegetation, varying electrolytic concentrations in ground water, and other geochemical action. Their amplitudes vary greatly bul generally are less !han 100 mV. On the average, over intervals of several thousand feet, the potentials usually add up to zero, because !hey are as likely to be positive as negative. In addition !here are several characteristic regional background potentíals. One is a gradient of Ibe order oC 30 mV Ikm, which sometimes extends over several kilometers and may be either positive or oegative. lt is probably due to &fadual changes in diffusion and electrolytic potentials in ground water. Sometimes a more abrupt change will result in a baseline shift of background potential. Another regional gradient oC similar magnitude seems to be associated with topography. lt is usually negative going uphill and is probably caused by streaming

potential. These background effects are nol dífficult to recognize. Potentials arising from bioelectrlc activity of plants, trees, and so forth, sometimes are as large as several hundred millivolts. They bave been observed as sharp negative anomalies - when passing from open ground into bush - !hat are quite similar to those appearing over sulfide zones. Long perlod telluric currents (> 1 min) may also produce background potentials, as large as several hundred míllivolts per kilometer over resistive ground, which are more difficult to detect, because the self-potential readings are made at a much fas ter rateo Self-potential (SP) anomalies apparently generated by thermoelectric and/or electrokinetic coupling processes have been reported in Ihe course of surveys for geothermal sources, an applícation of the method which has become attractive since the late 1970s (Corwin and Hoover, 1979). The thermal mechanism is not well understood, but may result from differential thermal diffusion of ions in pore fluíds and electrons wi!h donor ions in the rock matrix: The ratio of voltage to temperature difference {j, VI {j, T is known as the rhermoelecrric coupling coejJicient. The electrokinetic coupling coejJicient, Ekl{j,P in Equation (5.1), depends on fluid flow, which may be due to the thermal as well as the pressure gradient. Analysis of the coupling processes is presently not developed sufficiently to provide quantitative comparison of the two effects. Corwin and Hoover (1979) describe two SP surveys over geothermal sources produced by shallow coal fires. At Marshall, Colorado, a well-defined negative anomaly of 140 mV peak was centered over the bum area, which was overlain by 10 m of sandstone. At the second site, Acme, Wyoming, a 30 mV

Methods employing natural electric sources

294 ~

- -

Currenl ftow

Nepli•• centre

-

/

I

,--

~=--

/ , ,,- - - - - ,

",,' -ti '" /

'"

\ .1.

---

:: "";)o;:¡. -. L" /7 ...
- ::.::: --

- - _ .............. ---<".." .. ",'" _- .... '\,"'~_--- .... ,', '

~".

-- ....

, \\11' I ... _

...." ........

'\

/~ ~//:/>-:"("' . . - t 11- . . \'\ \\ '\ \, .f /

/

I

.,' I"

,"

II I

I

I

I \

\ +-\~ \

+,,

¡'/~

f "

"

II : I I '

I

~

I

II

1/1)1) 11/ 1// /1, I

/

J.

.,

\

SUIHdCI /

,,6

/l(

__ /

I 1

I

I

,

I

l

!

~

II

/ //

I

I

1

I

I

I

/

/

"

I,

/

I

/

/

I

I

I

I /

"

/..,. 1.,. / "

~

II

I

/, /

/

\

,

I

I I

1+

1

I

I

I I

I

figure 6.1. Oxidizing sulfide zone as a galvanic cell.

positive anomaly was recorded where the bum was about 3 m below surface. Larger potentials were measured over tbicker overburden nearby; they suggest thal elcctrokinetic effects were increasing the response. Mineralization potentials have usually been the main intereSl when prospecting with the self-potential method. Thcy are associated with lhe sulfides oC the melals, with graphite, and sometimes with the metal oxides such as magnetite. The most common mineralization potenlial anomalies occur over pyrite, chalcopyrite, pyrrhotite, sphalerile, galena, and graphite. Amplitudes range lrom a Cew millivolts to 1 V; 200 mV would be considercd a good SP anomaly. The potentials are almost always negative near the upper end oC the body and are quite stable in time. !be mechanism oC spontaneous polarization in mineral rones, like the geothermal effect, is not completely understood' although several hypotheses have been developed to explain it. Field measurements indicate that some part ol the mineral must be in a zone of oxidation in order that SP anomalies may appear at lhe surface. The original explanation, bascd on tbis evidence, was that the body behaved like a galvanic cell with a potential difference being created betwcen the oxidizing zone (generally the uppcr sur-

face) and the remainder. The action ol tbis cell is illustrated in Figure 6.1. There are several weaknesses in tbis explanation. Grapbite frequently is the source of large SP anomalies, although it does not oxidize appreciably. On the other hand, cxtensive oxidation, such as could occur in most metal sulfides, would leave the upper surlace oC the body with a net positive charge due to the loss ol electrons. In fact the charge is negative. Another hypothesis suggests that pH variations aboye and below the water table could provide tbe current flowing around the source. There is considerable evidence that the solutions aboye sulfide bodies, and witbin tbe water table, are highly acidic (pH 2-4), whereas those below the table are slight1y basic (pH - 7-9). !bere is probably a close relation between pH and mineralization potentials, but a diCCerence in pH alone is not sufficient to move electrons in and out of the mineral zone and maintain the flow ol current. A reasonably complete explanation oC mineralization potentials is that proposed by Sato and Mooney (1960). Thcy postulate two electrochemical hall-cell reactions 01 opposite sign, one cathodic aboye the water table, the otber anodic at depth. In tbe cathode hall-cell there is chemica1 rcduction ol the

Self-potential method -

295

-

-

~ Current ftow

-

0,

,a.

Surf.«

,,/

I

I I

"-

,,

/"

H,O

,

0, di..oI ••d\

I I

,

~.

1

I..!!ter !!!!! \

\

"

\

H,O,

\

I ---1 OH"

I I

\ \

I I

/

Figure 6.2. 5e1f-potential mechanism in pyrite. (From Sato and Mooney. 1960.)

substances in solution - lhat is, they gain elecIrons - while in the anode ce)) an oxidalion reaction lakes place and electrons are lost. The mineral zone ¡lseU functions only to transport electrons from anode to cathode. The magnitude ol the overall SP e/fect is determined by the di/ference in oxidation potential (Eh) between the solutions at the two halCcells. This mechanism is iIlustrated in Figure 6.2, showing the flow ol electrons and ions that leave the upper surCace negatively charged, the lower positively. This hypothesis, a1though a considerable improvement on previous explanations, still Caíls to account for some observed anomalies. For instance, Sato and Mooney give maximum possible potentials for various sources, such as graphite (0.78 V), pyrite (0.73 V), and galena (0.33 V). For surface measurements tbis would imply a maximum no grealer than tbese values, even wben tbe body outcrops. Potentials as large as 1.5 V, however, bave been reported over graphite. A field study in whicb potentials were measured in drill holes penetrating a sullide zone. as well as on the surCace over the zone, gave surCace anomalies oC approximately the same size as those encountered in the sulfide itselC, even though the lalter was well below the surface. These abnormally large SP results may be due lo combinations of anomalies lrom adjacent mineralized zones, or enbancement by coincident background potentials.

Otber unusual field results are discussed in Section 6.1.4. Most oC the sulfides are good conductors, witb the eltception ol sphalerite, cinnabar, and stibnite. Seupotential anomalies have. bowever. been observed over sphalerite and in drill holes that passed through sphalerite bodies. The Sato-Mooney theory assumes that Ibe sullide zone must be a good conductor lo transport electrons Crom deptb to tbe oxidizing zone near surface. Thus the case oC sphalerite is puzzling, a1though it may bebave as a semiconductor and in many occurrences it is closely associated witb otber conductive sulfides. Recent reports by Roy (1984) and Corry (1985) disagree with the Sato and Mooney hypOlhesis oC mineralization potentials. Botb autbors show field results thal indicate the measured potential is simply ~E, the oxidation potenlial dilference between the electronic conductor (sulfides) and eitber the borehole fluid or a surCace e1ectrode outside the mineral zone. That is, without tbe borebole or a wire connecting the surCace electrodes. no current will flow. There are .additional arguments Cor tbis mechanism and against tbe Sato Mooney version; these include the obvious long time stability oC sulfide deposits in various climates. the lack 01 evidence for a positive pole in tbeir vicinity, the absence 01 surlace SP anomalies over high1y oxidized mineralization, tbe presence oC unusually large surlace SP (in excess 01


296

1.----

Terminal

t I in. PVC lube

Appro l 3fl

.

Copper lube j in. diam.

T

Porcelain pOI-

5 in.

upper 5urface

,Ial.d. nos.

porous. ',5 in. diam.

Saluraled

- - CuSO. S,olulion

CuSO, cry51al5

figure 6.3. Walking-s/iek SP elee/rode.

1 V negative), and large depth of penetration (~ 1 km).

6.1.2. Self-Potential Field Equipment The SP method goes back to 1830, when Robert Fox used copper-plate electrodes and a string galvanometer as a detector in an attempt to find extensions oC underground copper deposits in Comwall. Since 1920 it has been employed in base-metal search, usually as a secondary method. The equipment required is extremely simple, consisting merely of a pair of electrodes connected by wire to a núllivoltmeter. There are, however, two restrictions on the electrodes and detector that are most important. If one were to use metal slakes driven into the ground as SP electrodes, the resultant electrochemical action at the ground contacts would create spurious potentials of the same size as those being measured. Furthermore these contact potentials are quite erratic in different ground and at different times, so that it would not be possible to make a fixed correetion. ConsequentIy nonpolarizing electrodes are essential. These consist of a metal irnmersed in a saturated solution of its own salt, such as Cu in CuSo~, Ag in AgO, and so on, and contained in a porous pot that aIlows the solution to leak slowly

and make contact with the ground. A good electrode of lhis type is the waIking stick arrangement shown in Figure 6.3. The main requirement of the millivoltmeter is Ihat its input impedance should be large enough that negligible current will be drawn from the ground during the measurement. This was formerIy achieved by using a potentiometer, now a smaII digital dc meter with an input impedance greater than lO' n. Such instruments, with ranges from 10 mV to 20 V full scale, are readily available. It is sometimes necessary to encIose the meter in a shield can to prevent erratic readings caused by contact of the instrument case with the body or ground.

6.1.3. Field Procedure The two porous pots should be filled from a uniform batch of salt solution. OtherwiSe the pots can be partly filled with salt crystals and water added; the first method is obviously preferable. When the loaded pots are standing side by side in a hole in the ground with the meter connected between them, the reading should be less than 2 mV. If not, the pots should be cIeaned and recharged with fresh solution. Generally they can be used for a couple of days before fUnning dry.

297

5elf-potential method

Where possible, traverses aT:! carried out normal to the strike of suspected SP anomalies. Station intervals are usually not greater than 30 m and may be as small as 3 m. One of Iwo electrode spreads may be employed: either one e\ectrode is fixed at a base station while the other moves to successive stations along the line, or bolh electrodes are moved while maintaining a fixed interval belween them. The firsl arrangement, recommended for long Iraverses. requires a ree\ witb ~everal kilometers of cable. The meter may be at either e\ectrode, but is usually al the base station. The advantages oC Ibis layout are that the potential is measured continually with respect to a fixed point, located. iC possible, in a barren area; at the same time small zero errors between the electrodes do not accumulate. The onIy disadvantage is the long cable that inevitably slows down the measurements. The fixed-electrode spread is maintained by moving the rear electrode up to the front pot hole and the forward electrode to a new station after each measurement. If the in terval is smali' tbis is essentially a measurement oC potential gradient, dV/ ds, at a point midway between stations, where ds is the electrode spacing. Alternately the mccessive values of dV may be added algebraically to give the same potential profile as in the first metbod. This arrangement is faster than the other electrode layout, but has the disadvantage that tbe zero errors add up as the traverse progresses. To reduce tbis cumulative error the pots should be cbecked side by si de in the same hole every 300 m or so. An altemative procedure for the fixed-electrode spread is to leapfrog tbe electrodes in moving from station to station. lf the rear pot is carried beyond the forward pot to the new staLion, cumulative zero errors are eliminated. The re\ative polarities are reversed at successive stations in tbe process; this must be kept in mind to produce the potential profile. Since the poten ti al between the r.Iectrodes will be randomly positive and negative, the use of a centerzero meter is a great advantage. Al the same time it is essential to maintain a sign convention between tbe pots, tbat is, forward pot with respect to rear, or moving pot with respect to base poI. On completion of a closed grid, the algebraic sum of potentials should be zero. This is obviously easy with a fixed base station, but may require sorne care in measuring witb two moving electrodes. In all SP field work the individual traverse lines must be hed together by measuring tbe potentials between ea;;h lineo In general, the procedures outlined in the foregoiog tex t are sufficieot for sulfide exploration, where anomalies are frequently large and distinct. In geothermal surveys more care is required, because tbe sources may be deeper and more exteDsive. Sev-

eral additional background effects may be troublesorne in these circumstances, such as variations in soil moisture caused by watering the electrodes for better ground contact, spurious polarization from e\ectrode contarnination, differential driCt, and temperature. The Ag-AgCl e\ectrodes are better than the usual Cu types in these situations. With care, reading errors may be held within ± 5 mV.

6.1.4. Interpretation of Self-Potential Data The end resuIt of an SP survey is a se! oC profiles and possibly a con tour map of equipotentials. A typical profile and set of contours are ilIustrated in Figure 6.4. Note that the negalive maximum lies directly over the sulfide mass; where tbe topography is steep, the center may be displaced somewhat. It is possible to calculate the potential distributions around polarized bodies oC simple shape, such as the dipole, sphere, and ellipsoid, by miling sorne simplifications and assumptions concerning the potentials on the surfaces oC the sources themselves. For exarnple, consider the polarized rod in Figure 6.5. The potential at a poinl P on the ground aboye is given by

(6.1) where ± q is the charge at either end of the rod. Because r, - (x 2 + zf)1/2 and, r2 = {(x - 0)2 + zi }112, where a = I cos a, I is the length oC rod, and a is the dip angle, this expression becomes

v==

q[1/(x 2 + Z?)1/2 -l/{(X -

a)2

+

zn

1/2

]

(6.2) Because of the air-ground interface, the rod has an eIectrical image aboye surface, which could make this potential twice as large (§8.3.3 and §8.3.4). Typical profiles are plotted in Figure 6.5. It is apparent that the characteristic SP curve is fairly symmetrical unless the dip angle is quite shallow. The polarized sphere is ilIustrated in Figure 6.6. To simplify the analysis, the sphere is assumed to be on the sliced in two with a constant potentialupper half and zero on the lower. To calculate the potentials off the vertical axis it is necessary to employ Legendre polynomials (§2.7.4 and §8.3.5). Althougb these simple shapes give results that are similar to profiles obtained in tbe field, tbey are seldom used in SP interpretation, which is mainIy qualitative. The shape of an anomaly and its extent are indicated by the contour map or by a set of profiles normal to strike. An estimate of deptb can be made from the shape of tbe profile. IC xI/2 is the

va


298

o SP (mV)

Profil. ,f-A

Suñl"

-

Figure 6.4. Typical SP profile and contours over sulfide body.

total width ol the profiJe at half the (negative) maximum, then the depth to the top 01 the body is oC the order oC hall this distance. From the sphere in Figure 6.6, this is obviously a very crude rule, and judging from half a dOlen random field examples, the estimate may be within ± 100%. In particular, if the anomalous profile is wide, the source is also wide, rather than deep, because the depth of detection in SP is usually not greater than 60 m. A rough idea ol the attitude of the body may also be obtained from the lack of symmetry oC the profile, that is, the steep slope and positive tail should be on the down-dip side. It is oCten desirabJe to remove regional effects from the SP profiJes in order to clarify the anomaly shapes. lbis can be done by inspection, to take out large-scale gradients, baseline shifts, effects of surface vegetatioAl, known geoJogic structure, and the like. The type of overburden apparently has a pronounced effect on surCace SP. Figures 6.7a, b show surface SP pro fiJes over two suJfide bodies. Both have been drilled and the SP and core logs are also

ilIustrated. In Figure 6.7a sulfides at 300 ft gave a good surface SP anomaly, whereas in Figure 6.7b the mineralization at 300 and 4-500 ft did not show up at all on surfacc. The topsoil in the vicini ty of the first was sand, in the second clay. From other exampIes as well, the absence of surface SP seems to be associated with a clay cover. Figure 6.7a is also surprising for another reason. No sulfides were encountered above a depth of 300 ft; the surface SP anomaly is presumably due to mineralization between 300 and 500 ft. This is well beJow the water table in the area. Self-potential measurements have occasionally been made offshore, to locate deposits in shallow water, to determine whether a known land anomaly extends offshore, and lo locate un.k:nown deposils in rugged shoreline terrain. Corwin (1976) describes a survey carried out by boat in Penobscot Bay, Maine, where sulfides had produced near-shore SP anomalies. Although the saline water generally reduces the SP amplitude, noise level is aIso greatly reduced at the same time « 0.3 mV), so that anomaJies of a

299

Self-potential method

..... I

I "

I I

V'I/
\

\

I

I I 1- lz,

I

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.•

P

r~7 figure 6.5. SP profiles over buried po/drized rod.

VI V,

t,

o

Ef' Figure 6.6. SP profiles over buried polarized sphere.

"l.,

Surface

Methods employing natural electric 50urces

300 -lOO ¡

100 .. v

-100

i

j

DDH R42

H"I,,' der th ( ftl

Core

log

sulfides E:< sulfides E:' sulfides !2 s'Jlfides t2 sulfides ~ Low sullides 1:::

10% 50-80% 30-80% 20% 60-80%

R42

-':

o

200

800ft

600

400 I

Surface trlilv('rse

(o)

-200 I

o

-100

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r

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q. I

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Surrate Ira verse

(b)

Figure 6.7 Surface ard drill- hale SP lar diflerent overburdens. (a) Sand overburden. (b) Clay averburden

few millivolts were c1early cletected below 12 m 01 water. Special Ag-AgO eleetrodes are necessary Cor this type 01 work, in whichthe near electrode is located one or two boat lengths astero and the other 10 to 100 m beyond thls_ Tbe larger electrode separalion produces better sensitivity, but increases the

noise level. particularly in the vicinity 01 irregular shorelines_ The discussion 01 background or noise potentials in Section 6.1.1 and elsewhere was based on the assumption that any potentials not generated by the target souree constituted noise. This is correet as lar

Self-potential

method

301

l' 8·00 40·

11'"45

JO·

SE

B'

U

I

WEST Z

~ KllOMETERS

I

EAST

2000

.c/) Za: 1800

Qw 1-1
1600

>~ W

1400

W

1200

-1

Z

O

-1

< ¡::

Z>

·200

~E

O

~

·400

U.

-1

W

C/)

·600 '--~---±---~--±---~0"'----±---~---:!6

t REFERENCE ELECTRODE KILOMETERS FROM REFERENCE ELECTRODE Figure 6.8. SP profile, line 8-8', Kyle Ho, Springs, 8uena Vista Valley, Nevada. KY-1 and KY-3 are dril/-hole locations. (Afler Corwin and Hoover, 1979.)

as it goes, but the recent use of SP in geolbermal exploration has sometimes re1egated minera1ization potentials lo the category of noise. Although the converse is also true, the resultanl noise elreel is less or a problem, because mineral anomalies are usually larger. The firs! siluation is iIIustraled in Figure 6.8, which shows a huge negalive anomaly of 550 mV peak exlending over sorne 5 km of a 14 km profile measured on sloping ground al Kyle Hol Springs in

Nevada. Originally thoughl lo be produced either by a geothermal source associaled with the hot spring or a slreaming potential due lo the 800 m slope, or a combination of the two, Ihe lest holes KY·l and KY -3 penetrated an extensive seetion of conductive graphite with pyrile, continuing downward from 40 m deptb. Furthermore, the heat ftow in the holes was normal ror the area. In lhis eonlext the mineraliza· tion represents an extremely large source of Doise.


302 1)5'

EllO'

45'

W I3S'

fO' lO'

'11)'

,.,. lO'

O'

.

MitlnÍlh\

Noon ,

Miclnip\ ,

Fjgure 6.9. Worldwjde telluric-currenl syslem on Mercator's projeclion. (Afler Dobrjn, 1960.)

Self·potential has played a minor role iD geopbysical exploratioD. This is mainly due to the diffi· culty in making significant interpretation ol the results - which are frequently quite erratic - and partly because the depth 01 penetration has generally been assumed to be sballow, although this matter is not at all clear. It is, bowever, a simple, fast, and cheap metbod tbat is useful in rapid ground recon· naissance for base metals when accompanied by magnetics, EM, and geochemistry. Aside from tbe possibility 01 detecting sulfides, it is useful in map· ping shallow structures Iike faults, shear and fracture zoncs, and contacts, and appears to have some applicatiOD in tbe search lor geothermal sources.

6.2. TELLURIC ANO MAGNETOTELLURIC METHOOS 6.2.1. Origin and Charaderistics of Magnetotelluric Fields and Telluric Currents In this section we shall consider techniques that employ certain large-scale (generally low.frequency) magnetic fields and tbe terrestrial current systems induced by tbese fields. The terms oc magnetotelluric" and .. teUuric" are generally used to designate tbese fields and currents' respectively. These topics are included in this chapter because they are naturalsource electrical methods, like self-potential. Such magnetic fields, however, are identical with those discussed in SectiOD 7.2.

The existence of naturallarge-scale earth currents was first established by Barlow in 1847 in the course ol studies on the first British telegrapb system. Long-term records ol teUuric currents were made at Greenwich, Paris, and Berlin in the late nineteenth century; nowadays they are recorded at various observatories around the world. 1be source ol tbese currents has been fairly deflnitely located outside the eartb. Periodic and transient f1uctuations can be correlated with diurnal vario ations in the eartb's magnetic field, caused by solar emission, aurora, and so fortb. 1bese activities have a direct influence on currents in the ionosphere; it is tbought tbat tbe telluric currents are induced in the earth by ionospheric currents, 1be inductive mecbanism is an electromagnetic fteld propagated with slight attenuation over large distances in tbe space between tbe ionosphere and eartb surface, somewhat in tbe manner ol a guided wave between parallel conducting plates, 1bat is to say, it proceeds by bouncing back and fortb between these boundaries and hence has a large vertical com· ponent. At large distances from tbe source this is a plane wave of variable frequency (from about 10- 5 Hz up to tbe audio range at leást), Obviously these magnetotelluric (M1) fields can penetrate tbe earth's surface to produce tbe telluric currents. The pattern ol tbese terrestrial current systems is shown in Figure 6.9. TIte huge whorls cover millions of square kilometers, are fixed witb respeet to tbe Sun, and rotate altemately c10ckwise and counterc1ockwise. In mid-latitudes there are two maxima

Telluric and magnetotelluric methods

303

MAGNETICS

~'OE

"NO

~

F1L TEREO

TELLURICS WIDE BAND

FILTERED

- - - - - - - - -__ TIME

-------4...

Figure 6.10. Magnetic and telluric field data before and after filtering.

and two minima per day, tbe average direction being mainly in tbe magnetic meridiano Near tbe equator (Peru, Madagascar), on tbe otber band, there appear lo be only one maximum and one minimum per day, (he amplitudes are considerably smaller, and tbe average direction is east-west. For signals in tbe period range 10 to 40 s (Pe type), tbe current intensity is much larger on the dayligbt side of Eartb, as well as in aurora latitudes compared to lemperate. The electric fields related to these currents are of tbe order of 10 mV¡km, whereas the associated magnetic fields are in tbe milligamma (picotesla) range. Superimposed on Ibis average telluric field are random fluctuations whose intensities vary with elec-

tri cal disturbances in the ionosphere. These pulsations occur at frequencies as high as lOO kHz, a1though most are much lower. As a result the telluric record consists of erratic variations in potential, as iIIustrated in Figure 6.10, which a1so sbows Ihe raw signals after filtering. One source of the higher-frequency current fluctuations is electric storms. A1though their location is to some extent random, tbere are tbree major storm centers, a11 located in equatorial regions - Brazil, Central Africa, and Malaya. Sorne of the thunderstorm energy is converted to electromagnetic fields tbat are propagated in the ionosphere-Earth in terspace. The weak currents induced by these fields in

•

••

•

Telluric and masnetote/luric methods

•••

...

,..

. ,..

305

,

******"******** lOO

"'

UG

1..

...

..

••

MI

....

'111'

...

....

'W

111.

******* na.

.,.,

,..

u.

11M

.t41

110.

******* ******* ******* _. ... .. ... 13-11

IUO

114'

14"

MI'

"SO

M4'

,."

tllt

".0

"4'

....

....

,...

... ,

170.

'71,

'uo

'7"

'lO.

.",

******* ******* **;~;;:// ,

••••

..

,

••••

;:}{,///// //777// #)t/}r*// J"

".

14S

....

41.

...

.4.

/;rJV%%;f/

... ...* .,. -*

*'

**

..

... ... *

'*

_ _o

Figure 6.12. Anisotropic te/luric response. Vale Perkins, Quebec. May 8- 9, 1975. Frequency 145 Hz.

the subsurface are useful in tel1uric and magnetotelturie prospecting, partieularly because they have amplitude peales at several distinct lrequeneies - 8, 14, 760 Hz, and so on. 111ese same electromagnetie lields are also empl~ed in the AFMAG method (§7.4.2e). Information concerning audio and sub audio telturie and MT signals may be found in severa) reports (Slankis, Telford, and Becker, 1972; Strangway, Swift, and Holmer, 1973; Goldstein and Strangway, 1975; Hoover, Long, and Senterfit, 1978). To investi-

gate the diurnal amplitude and azimuthal variatioDs ol tellurie signals at 1, 8, 145, and 3,000 Hz, four telluric receivers connected to four pairs of electrodes were set up at a site free rrom power·line disturhances in the Appalachian region about 150 km east 01 Montreal (Telford, 1977). Eaeh electrode pair spacing was 30 m, the orientatiODS being ap. proximately 343°, 28°, 73°,118° with respect to troe north. 111e tellurie uníts, described in Section 6.2.6a, witb their gaios equa1ized, were simultaneously read

306

Methods employinS natural electric sources

Figure 6.13. fleclric dnd mdgnetic fields 01 fqudlions (6.3) and (6.4). (After erdnt dnd West, 1965.)

every quarter hour lor the lour lrequencies over a 24 bour periodo Figure 6.11 iIlustrates the telluric response from the north-south electrodes; the data have been normalized lor each frequency and plotted on a log scale. The 3,000 Hz signal abruptly increases and decreases at sunset and sunrlse, respective1y, on all four orientations; in the 28° (- NNE) azimuth the lower three Irequencies are very similar to this. However, for the north, northwesl, and east eleclrodes, the 1, 8, and 145 Hz levels are generally low from 21:00 hours througb the night. In this respecl these frequencies resemble the Pe signals mentioned previously, whereas the response in the north-northeasl azimuth is reversed. The explanalion for tbis is nol c1ear, altbough the general regional strike (Sulton anticlinorium) is approximatcly north-northeast. Figure 6.12 shows the directional response al 145 Hz, wbich is practically isotropic during daylight hours and becomes stronger north-northeasl from about sundown lo sunrise, that is, 20:45 lo 5:15 hr (these signals bave becn normalized at each frequency and measurement time lor the four orientations). For the other frequencies 3,000 Hz is strongly maximum along the 28° axis througboul the entire day, 1 and 8 Hz only during the night.

6.2.2. Elementary Electromagnetic Theory An elementary development of electromagnetic theory can be employed to describe magnetotelluric wave propagation. To understand the propagation and attenuation ol such waves il is necessary lo use MaxweU's equations in a form relating the electric and magnetic fteld vectors:

aB

vxE---

a,

ao

vxH-J+-

a,

density (teslas (A/m), and

mI, H

is the magnetic fte1d intensity

o is the electric displacement (C/rrr).

Equation (6.3) is a mathematical statement of Faraday's law that an electric field exists in the region of a time-varying magnetic field, such that the induced emf is proportional to the oegative rate of change of magnetic flux. Equation (6.4) is a mathematical statement of Ampere's law (taking into accouol Maxwell's displacement current aDiar), namely, that a magnetic field is generated in space by current flow and that the field is proportional to lhe lotal current (conduction plus displacement) in (he region (Fig. 6.13). Using the vector identity V o V X A - O (Eq. (A.24») we get for lime-varying fields V

o

aB

a

ar

al

V X E - -V, - - - -(V

o

B) - O (6.5a)

that is VoB-O

(6.5b)

Similarly, V oJ

+V

8D

.-

al

a

+-

- V oJ

al

(V o O) -

o

(6.Sc) We also know that the divergence of current density is equivalent to the rale of accumulation of charge density, Q, or from Equation (6.5c),

V oJ -

aQ

-Tt - -

a

a,(V 00)

(6.6a)

(6.3) hence

(6.4)

where J is the current density (A/nh E is the electric fteld intensity (V1m), B is the magoetic flux

V 00-

Q

(6.6b)

In regions of finite conductivity, charge does nol accumulale 10 any exlenl during current flow (omit-

Telluric and magnetotel/uric methods

ling electrolylic conduclors), hence Q ..

v . o .. EEOV

V·J-O

•

307

o so Ihal

E .. O (6.7)

Besides the relation between displacement and electric field, we also have the following relation between B and H [Eq. (3.7a)J: ( 6.8) In Equations (6.7) and (6.8), ¡J. is Ihe relative magnetic permeability of the medium, E is the relalive dielectric permittivity, 1'0 is the permeability of free space = 471' X 10-' H/m (Tm/A), and EO is the penniltivity of free space - 8.85 x 10- 12 (F /m). Furlhermore, in homogeneous isolropic media, we can express these relations, together with Ohm's law,

as

o -eE

B-¡J.H

( 6.9)

J - aE

where a is the conduclivity and we have eliminated for convenience by using mks unilS. We can simplify Equations (6.3) and (6.4) as

1'0' EO

aH/a, v xH=aE+eaE/ar v

E .. -¡J.

X

(6.10)

v

X

H=

~

+ aE + e aE/at

(6.l1b)

Taking the curl oí Equations (6.10) and (6.11a) and using Equation (A.25), we finally gel [note tbat V • H - O - V • E from Eqs. (6.5b) and (6.7)}

aE

a

2

a2 E

v E - l' a,(V X H) .. ¡J.aTt + ¡J.e at 2

( 6.12a)

v 2 H - -a(v -

X

a

E) - e-(V

at

a2 H ¡J.a- + ¡J.e-at a,2 aH

X

E) (6.12b)

If we choose sinusoidal time variations - which is generally done in MT work - we can write

E( t) - Eo ejw1

V 2 E - jw¡taE -

2

¡J.fE

(6.13a)

V 2 H .. jW¡J.aH - "l¡J.eH

(6.13b)

W

the first and second lerms on the right-hand side being related lo the conduction and displacement currenls, respectively. These are the, electromagnetic equalions for propagation of electric and magnetic field vectors in an isotropic homogeneous medium having conductivity a, relative permeability ¡J., and relalive dielectric permittivily E.

6.2.3. Attenuation of EM Fields The wave is attenuated in traveling through some media but not in free space. This can be shown as follows. Considering the relative magnitudes of the parameters e, ¡t, w, and a, we can say tbat tbe maximum normal value of e occurs in water where E - 80; for rocks, E is generally less than lO. Similarly, ¡J. s 3, even in ferromagnetic minerals; normally the value is unity. Thus we have

( 6.11a)

If, as in some situations, there are independent current sources ~, not related lo the magnetic field (from SP, power devices, etc.), Equation (6.11a) becomes •1

where w = 2'/TI is the angular frequency of the field. Thus Equations (6.12) are simplified to

e" 10Eo" 9 X 10- 11 F/m ¡J. "" 1'0" 1.3 X 10- 6 H/m The periodic frequencies employed in MT work (and in EM methods as well, as we shall see in Ch. 7) are usually less than 3,000 Hz, hence w S 2 X 104 • The corresponding wavelengths, which are given by

A .. 2'fTc/w

=

2'fT X 3 X 10 8/w m

are greater than 90 km. Because the distances involved in field layouts are usually less than 1 to 2 km, tbe phase variation resulting from propagation is negligible. In tbe air a .., O. e - eo. and ¡J. = ¡too Thus the factor w 2¡J.t in Equations (6.13) is of the order of 5 X 10- 9• that is, there is no attenuation of the wave in airo The conductivity of rocks and minerals, however, varíes enormously, as we have seen in Section 5.4.1. In rocks of low conduclivity we might have r10eo, ¡J. - /lo' and a ... 10- 3 S/m, so tbat, for w 2 x lO".

H( t) - Ho e jw1

aE Tt - jwE

aH

Tt

-jwH

However, in regions oí high-conductivity (massive sulfides, graphite, and tbe like) a ... 103 S/m and V 2 E .. ( -4

X

10- 8 + 25j) E ... 25jE

JOB


Comparison 01 Equations (6.13) sbows tbat identical relations hold for H abo. Thus in all cases tbe real part 01 tbe right-hand side 01 tbe equation (which corresponds to the displac:ement current) is negligible. As a result, in air and in poorly conducting rocks, we have

or

m - ±(1 + j)'¡(IJp.a/2) - ±(l + j)a wbere a - (lJI'af2)I/2. Because H must be finite wben : - + 00, we discard the plus silO and obtain the solution

(6.14) whereas within a good conductor tbe imaginary part of the expression is significant, and Equations (6.12) tben are written

aE

V 2 E .. I ' a - .. jlJI'aE

al

v

2H

aH

.. p.a- .. jlJp.aH

al

Taking the real part as the required solution, we bave (6.16b)

( 6.15a) ( 6.15b)

This is the difrusion equation, which reduces lo Laplace's equation (Eq. (6.14)) in the air and in rocks of low conductivity. Equations (6.15) are generaIly diflicult to solve; however, there is one important case in which a salution is readily obtained, that in which the wave is plane polarized. Assume the wave is propagating along the : axis so that the xy plane is the plane oC polarization. We can then solve Equation (6.15b) by assuming the form

The second part of the expression represents simple barmonic motion with a phase shift wbereas tbe exponential is the attenuation 01 the wave with propagation distance. This attenuation term may be written (taking p. - /A-o - 4". X 10- 7 ) (6.16c) Taking a Cew numerical examples, we get values as in Tables 6.1 and 6.2. A commonly used criterion lor the penetration oC electromagnetic waves is the skin depth, the distance Table 6.1. Attenuation of CM wa.-es.

wbere H is the magnitude oC H. Then,

v 1H - (a 2H,/a: 1 )

_

f (Hz)

p (Om)

IH,/Holfor z- 30m

z for IHy/Hol- 0.1 (m)

loJ loJ loJ loJ loJ 10 102 lO· 106

10-· 10- 2 1 102 lO· 10 10 10 10

0.00 0.00 0.15 0.83 0.96 0.94 0.83 0.15 0.00

O O 37 370 3,700 1,160 370 37 3.7

m2H

and

(aH,lat) - jlJH Substitution in Equation (6.15) sbows that we must bave

Table 6.2. Skin depth variarion wirh frequency and resistivity.

f (Hz)

p-l0-·0m z, (m)

10- 2 Clm z. (m)

100 0m z. (m)

102 0m z, (m)

lO· Om z. (m)

10-) 10- 2 10-1 1 10 10 2 loJ lO· 106

160 SO 16 5 1.6 0.5 0.16 0.05 0.005

1,600 500 160 50 16 5 1.6 0.5 0.05 0.005

1.6 x lO· 5,000 1,600 500 160 50 16 5 0.5 0.05

1.6 x lO' 5 X lO· 1.6 X lO· 5,000 1,600 500 160 50 5 0.5

1.6 X 106 5 X 105 1.6 X 105 5 X lO· 1.6 X lO· 5,000 1,600 500 50 S

10&

309


in wbicb tbe signal is reduced by l/e, tbat is, to 37'1>. This is given by z, - l/a in Equati on (6.16b), tbat is,

z, "" 500 (p/f)I /l m

( 6.17)

From tbese tables it is quite obvious tbat if tbe resistivity is low, or tbe frequency bigb, or botb, tbe magnetic field will not penetrale Ihe ground lo any extent. As a crude rule of tbumb we can say tbat if

z.¡(f/p ) > 10 3 tbe attenuation will be large and vice versa. For tbe same plane polarized wave in Equati on (6.16b) we can also find tbe currenl, using Equations (6.9) and (6.11a). Thus we bave (neglecting tbe term 8E/8t because WE « a)

v X" - aE - J J.-l. • -O y

aH.

a az { Hoe-· ' COs( wl - az)}

- aHoe- "'{cos (wt - az) - sin(w l- az)}

- .¡2aHoe-'" cos( wt - az +

¡)

n X (El - El) - O

electric field tangential to interface js continuous. n X (", - "l) .. O magnetic fieId tangential to interface is contin uous. n'(a,El-~E2)-0

_ (w/1a )'/2 Hoe-" (""./2) X COS{ wl - z( w;a f/2

As in dc resjstivity tbere are several bound ary conditions for EM fields Ihat must bold at interfaces wbere (and possibly /1) change abruptly. These can be derived from Equati ons (6.3), (6.4), (6.7), and (6.9) as follows (Fig. 6.14):

°

and

Tz - -

uniform tbroug bout tbe volume of the conduc tor but wi11 be concenlrated toward tbe outside. Because it is nol generally possible lo determ ine tbis curren t distribution, even for simple sbapes, tbe analytical solu- . tion of most problems by electromagnetic tbeory is out of the question.

6.2.4. Boundary Cond itions

Hence

J" - -

Figure 6.14. Boundary conditi ons on EM fields at an interface.

+

¡}

curren t density norma l to interface is contin uous. ( 6.18)

This sbows tbat tbe amplitude of tbe current is (w/1a y/2 times tbat of the magnetic field at all points. A1so, bccausc J" is propor tional to Hy , tbe current flux exhibits tbe same sitio effect as tbe magnetic fleld and in a good conductor, tberefore, it is concentrated neaf the surface. The pbysical result is tbat when (wl'o/ 2)'/l is small, tbe magnetic fteld wi1l propagate tbrougb tbc medium without mucb attenua tion and in tbe process will fail to induce any appreciable curren t flow in it. Conscquently tbcre will be vcry liUle secondary magnetic field generated. On tbe otber band, wben ("'/10/2)1/2 is large, tbe large surface curren t creates a large seeondary magnetic fic1d, out of pbasc witb tbe original, which partially or completely cancels tbe primary field. Wben tbe medium bas intermediate conductivity tbere will be some sccondary magnctic field developcd. Even bcre tbe curren t density will not be

n . (1'1"' - /12"2) - O magnetic flux norma l lo interface is contin uous. These four condit ions are valid when tbere is no free charge or curren t on tbe interlace. For tbis case, the potent ial V is also contin uous across tbe interlace, bccause no work is done in carrying a charge from one side of jt to tbe olher. AlI electromagnetic fields must satisfy tbe preced ing condit ions at all interlaces.

6.2.5. Magnetotelluric Fields To adapt tbe wave equati ons to magnetotel1urics, it is nccessary 10 make certain simplifying assumplions. Certainly tbe frcquencies are so low that displacement curren ts are negligible. Next, for plane waves oC tbis type, it is clear tbat borizontal variations in E and " are small compa red witb vertical variations. Furtbe rmore, we will consid er only periodic frequency variations, bccaus e the fieIds are so

310


erratic that it would be difficult to do otherwise. Taking the xy plane as horizontal and : positive downward, these conditions can be expressed mathematicaJIy in the form

aD

--o al

a

a

ax- 0 -ay -

a

al

and

T p"'-

E

2

"

2ftl' H,

(6.22a)

Clearly the x and y axes can be interchanged, hence these expressions can be stated in the more general form

- -jw

(6.21b)

If the wave is polarized in the xy plane and traveling in the z direction, we talten the magnetic vector as Ho at an angle 6 to the x axis so that the magnitudes of the magnetic components are H"o = Hocos 6 and HyO - Ho sin 9. We can write

p=

~1112 2ftp. .K

(6.22b)

where Ij.Tt' is equal to either E"jH, or E,jH". Setting l' ... 1'0 - 4," X 10-', substituting Equation (6.22b) in Equation (6.12b), and changing uruts to millivolts per kilometers for 1, gammas (n1) for JI{', and kilometers for t?}, we get finally

From Equation (6.11a), 1

E" - - (x component of V ti

x H) - -1 ( - aH) -'

a:

ti

1

- - -( Ho sin9)e-·'{ -a cos( wl

-

ti

az)

t?}

=-2,"1 (5pT)1/1 km

(6.21c)

(6.22c)

+asin(wI - a:)} - v'2;( Ho sin 9) e-·· cos( wl - az +

¡) ( 6.l9b)

Similarly,

E, - v'2;< Ho

cos 9) e-'" cos( wl -

az +

¡) (6.19c)

Dividing Equations (6.19b) and (6.19c) by Equation (6.19a), the squares of the ratios of the amplitudes become

(6.20)

If we assume ti to be the effective conductivity in a penetration depth !JI, we can find approximate values of!JI and ti by replacing aja: by 1ft?} and w by 2ftjT; Equations (6.19) and (6.20) then give 1 H, !JI- - .. ti

E"

1

tI( W/'P )1/1

-

(Wl'P )1/1

wl'

- -

T

E" -

2ft/' Hy

( 6.21a)

The application of magnetote1\uric theory to determine the electrical conductivity within the earth was originally described by Cagruard (1953). These relations are similar, excepl that the penetration depth is 70% oí Cagruard's value. By measuring the amplitudes of orthogonal horizontal components of the electric and magnetic fields at the surface, for various frequencies, one can determine the variation of resistivity with depth. This is an apparent resistivity (§8.5.2). The potential advantages in using these natural fields and currents are immediately obvious. With a relatively smalI electrode separation (100 to 600 m) it should be possible to determine the depth and resistivity of horizontal beds. Furthermore the depth of penetration can be very great if low frequencies are selected. In practice, however, the possibilities are limited by the nonuniformity of the subsurface and by the fact that the signal is rarely sinusoidal so that measurements of E and H for a particular value 01 T are not easily achieved. The magnetote1\uric survey requires detection of both magnetic and electric field components. In the telluric method it is only necessary to measure the electric field associated with the earth currents. Thus the lalter techruque is simpler and requires less equipment. However, the amount of information derived from tellurics is considerably less than frolll MTwork.

311

Te/luric and magnetote/luric methods

PREUP

llOO

...-----1 lOl 11 01 S(

80,110 Hz REJECT

STE' AHEII .

UIIDPASS AMP.

RECT. I lllTEC.

Figure 6. 15. 5chematic of telluric unir for audio and 5ubaudio frequencif'.~.

6.2.6. Field Equipment and Operations (a) Te/luric current equipment. Because the currents cannot be measured direcdy, it is necessary to measure the potential gradients between electrodes planted on surCace or possibly in drill holes. As in SP work, nonpolarizing electrodes should be used to reduce erratic potentials at the surface contact; lead plates, which are Cairly inert chemically, might be suitable. However, metal (stainless steel, brass) stakes driven into the ground are more commonly used and are quite acceptable at frequencies aboye 1 Hz. The electrodes are connected to an amplifier (bandwidth dc to 100 Hz, gain 2,(00) tbat will drive a strip chart or magnetic tape recorder. If specific frequencies are of interest, various bandpass and reject tilters are incorporated in the amplifier section. Also, sta tic potentials between the electrodes, which may be several hundred millivolts, must be balanced out; tbis is done with a potentiometer, or capacitance input, the latter having a time constant considerably longer than the maximum period to be recorded. Because of large variations oC signal amplitude, with time, two electrode spreads are necessary, one as a base station monitor, the other for the moving station. Because the signals also vary in direction with time, the base and field stations normally have two pairs oC electrodes each, laid out perpendicular to each other, say north-south and east-west, or parallel and normal to regional strike, if the laUer is known. Thus continuous records of two horizontal components are obtained at each station. With this arrangement one can - at least in theory - compare the horizontal components oC electric field variations between the base and field station, with regard to frequency, phase, and amplitude. This is the method used in oH exploration applications. A simpler field method may be used when tellurics (usually in the sub audio and audio range) is applied to mineral exploration. A single pair oC electrodes is set up at each station (one fixed base, the other moving), all electrodes being in a traverse

line or perpendicular to il. The signals at the two stations are integrated over the same time intervals, using an integrating circuit and meter readout in place oC the recorder, and Ihe two compared Cor amplitude. In addition the amplifier has a narrow passband, for example, (8 ± 0.5) Hz. A block diagram oI the telluric unít of tbis Iype is displayed in Figure 6.15. The preamplifier galn is 100 to 200, with a bandwidtb sufficient lor (he desired overall frequency range. The fundamental difference between tbis receiver and the wide band sets used Cor deep sounding is that the former contains severat narrow-band channels to amp1ify. rectify, and integrate selected frequencies whose outputs are read from a meter or recorded. For signals at frequencies 8 Hz and bigher, an integration time oC about 30 s is sufficient. Signals are normally averaged Cor three or more successive measurements at each station. Looking again al Figures 6.11 and 6.12. it is evident that fluctuations in signal amplitude and direction are relatively small (± 50%) during a 6 to 8 h period centered about midday. (Of course when there are local tbunderstorms, signal strength increases and fluctuates greatly so that work generally must be suspended.) Since we are looking for conductivity variations in the subsurface much targer than this, it was possible to dispense with the base station entirely in most surveys. Tbis increases 1he speed oC operations to a poinl where the method is raster than resistivity and induced polarization and comparable to ground electromagnetic metbods. Electrode spacings for deep sounding structural studies and oil exploration are usually 100 to 600 m. For mineral searcb the spread can be much smaller, 30 m or less being reasonable. In both cases the field station is moved with respect to the base. ir the latler is used. (b) Magnetote/luric equipment. Equipmenl Cor MT work is more complicated tban for tellurics alone. The electric field detector is similar to that described in Section 6.2.6a; two components are


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313

Figure 6.17. AMT survey with dipale saurce. Shaded areas represent afeas with mini-

mum coupling between Y-oriented transmitter (center) and E,-Hy receiver orientatian; datted lines shaw approltimate limits af strong caupling for Ey-H, receiver directions. (After Galdstein and Strangway, 1975.)

, )

r

measured at each station. bUl no base station is required. A schematic of an MT sel is seen in Figure 6.l6a; the block diagram is shown in Figure 6.21. Although at extremely long perlods it is possible to measure the magnetic fteld with a fluxgate magnetometer, the sensor for this purpose is normally a coil of many tums (~ 50,(00) on a large frame, or a long solenoid wound on ferrite or other high permeability core. The coll, or several sections of il, must be able to detecl the complete frequency band desired, say 0.00001 lo 1 Hz. Three magnetic components are measured at each station: two horizontal, in the same directions as the tel\uric components, plus the vertical as an indicator of two-dimensional structures. MT equipment designed for the frequency range 1 Hz lO 10 kHz requires smaller coils with fewer tums to reduce the self-capacitance and permit resonanl tuníng to the frequencies selected in the bandpass sections described in Section 6.2.6a. Alternatively a coil witb wider passband (1 lo 1,000 Hz) has been used successfully. Because tbe magnetic variations are in tbe milligamma (pT) range, tbe sensitivity requirements for tbe magnetic unít are higher than for tbe telluric section. Tbe coil is a critical component in MT work. Generally it is necessary to install it in a shallow treoch, because very slight motiODS create noise voltages, particularly troublesome in wooded areas. The coil actually record s aHI at rather tban variations

of H; a portable ac magnetometer would be an improvement, but no suitable instrument is presently available. A furtber modification of tbe MT technique in tbe audio range (AM1) was produced witb the introduction of a controlled grounded electric dipole source (Goldstein and Strangway, 1975), similar lO that formerly used in the grounded Turam transmitter (§7.4.3b), a1though considerably shorter. lbis 50 ft (15 m) source produced 1.5 A at various frequencies up to 10kHz. To simulate normal conditions for MT work (plane wave from a remote source), various theoretical, model, and field tests were carrled out. Oearly over a homogeneous area the 111Jf"1 ratio must be reasonably constant for tbe plane-wave assumption to be correet [Eqs. (6.22»). This was found lO be so, provided the dislance betwccn transmitter and receiver was at least tbree skin depths (§6.2.3, Table 6.2) relative to the highest ground resistivity in tbe area, for two orthogonal orlentations of tbe receiver sensors with respecl to the transmitter. The geometry involved is clarified in Figure 6.17, where tbe large square represents a uniform area to be surveyed and the inner circ1e radius is three skin deptbs. With tbe dipole source centered along tbe y axis, tbe shaded segments correspond to areas tbat may be surveyed witb tbe receiver oriented Ex-HY' Response witbin tbe circ1e varies as 11r rather than 1/r 3 and is too large, whereas in tbe corners of tbe

314

square it becomes too small wilh Ihe E,,-H, alignmento Tbe comer segments are mapped successfully wilh tbe receiver oriented Ey-H" and Ihere is some overlap of Ihe Ex-Hy data. Wilh Ihese restrictions MT surveys may be performed over complex ground witb good results, which may be analyzed using standard interpretation techniques. (e) Field operations. Until recently most MT ficld work, intended for crustal sounding and oil exploration, has been done on a large scale using very low frequencies (
Methods employinS natural eleetrie 50urces

because huge erratic sigoals at random times prevented operation without a base station. Tbese were certainIy nol due to local thunderstorms. nor did tbey appear to be associaled witb seismic activity. Obviously the simple telIuric equipment of this type can be improved by the addition of another channel with coil input for AMT surveys (Strangway, Swift, and Holmer, 1973; Strangway and Koziar, 1979) with or without an artificial source. Tbe H-field measurement slows tbe survey somewhat, bul the extra quantitalive data are welt worth this disadvantage. AMT reconnaissance surveys have been carried oul in a number of geolhermal areas (Hoover, Frischknecht, and Tippens. 1976; Hoover, Long, and Senterftt, 1978; Sandberg and Hohmann, 1982), recording two orthogonal E- and H-field responses, with a frequency range 7.S Hz to 18.6 kHz. Tbe geothermal sources are resistivity lows, produced by high temperature and salinity ol the water, usually surrounded by a conductive zone ol larger volume. In one area where double-dipole resistivily surveys had also been perCormed, the AMT proved somewhat less expensive, faster, and provided better resolution. However, there were problems with natural source sigoals falling to low levels in the frequency range 2S0 to 5,000 Hz during the winter season.

6.2.7. Interpretation of Telluric Data If the ground were quite homogeneous at both base and field slations, the only difl'erence in electric fie1d sigoals between tbe two could be a slight phase shift, if they were far enough apart. However, any nonuniform geologic structure lhat dislorts the currenl ftow al one slation will produce an anomaly in Ibis field. An antieline or dome of high resistivity in the basement would cause such distortion by crowding the currenl lines over the apex, as shown in Figure 6.18. The efl'ect of certain simple geological struelures on the electric field can be computed theoreticaJly. These inelude two-dimensional slructures, such as the anticline, basement step, and horizontal cylinder, and three-dimensional shapes like tbe sphere and ellipsoid. Examples oC the firsl three, solved by using conforma! transformations, are given in Kell,:r and Frischknecht (1966). In these examples the current ftow is assumed lo be normal lo the anomaly strike. In field situations, however, the currents tend lo ftow parallel to strike, lhal ¡s, they ftow in the good conductor rather Ihan across it. Furthermore, because most rack structures are anisotropic, the ftow will nol usually be uniform in any case. The record s may be Curther complicated by near-surface efl'ects oC overburden and erratic electrode contacts.

315

Telluric and magnerorelluric merhods Surracr

..

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-

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Figure 6.18. Distorlion LeoniJrdon. 1948.)

o(

Current lines

telluric curre nI flow by anlicline. (Afler Boissonnas and

Model profiles over a vertical dike of finite depth ex!enl in a uniform host rock are shown in Figure 6.19a. The E field measured normal 10 slme is defined as the E J. or H polarization; when lhe electrodes are maintained parallel lo strike along the same traverse, we have the EII or E polarization, as in Figure 6.l9b. Signals are normalized and plotted on a log scale. 80th diagrams have been plotled for two frequencies, 100 Hz and 10 kHz. There is only a 30% difl'erence between the minima in the E J. examples, the lower frequency being larger; !he contras! in E 11 response is considerably greater, the higher frequency being more pronounced. Although the EII arrangemenl produces twice tbe anomaly of tbe otber in tbis example, il does nol define tbe tbin conductor as well. Furtbermore, the electrode arrangemenl (parallel to stme while traversing across slme) would be quite difficult excepl in open ground. Figure 6.19c shows the EJ. response at 8 Hz over tbe same type of dikes dipping 60 and 30°. The profiles c1early become asymmetric over bodics with shallow dip, with a morc pronounced minimum down dip and positive overshoot on tbc footwall side. The modcl curves in Figure 6.19 may be produced by several numerical metbods: finite difl'erence, impedance network, finile elemenl (Forsytbe and Wasow 1960; Swift 1967; Silvesler and Haslam 1972). These lechniques are well suiled lo analysis of two-dimensional struclures. Taking the y axis parallel to slrike (ala y - O) and z axis posi tive down-

ward, Equations (6.10) and (6.11a) become, for E.1 polanzation (Ey =- const.),

iJE.liJx - iJExliJz = jWIJ.oHy - aHy laz - oE%

which may be combined lo give Ihe scalar diffusion equalion in Hy , analogous lo Equation (6.15):

a2H

ax: +

iJ 2H az/ - jWIJ.ooHy - O

(6.23a)

The boundary condilions al the air-ground interface come from the Cacts that a - O in air and displacemcnt currents are negligible. Thus J. ).-0 - O and E,),_o - iJHyliJx),_o - O, which means that Hy is invarlant along the ground surface. Thus ir we measure Ex and By simultaneously at two slations, Equation (6.22b) gives us PI - TIE%/HyY/2wl'o, where i - 1,2; from tbis we find tbat ( 6.24) Hence for tbis orientation we oblain relalive values of Pa witbout measuring H al al\. Similarly, for EII polarization we have

316


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800

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Figure 6.19. Theoretical resistivity pro files over vertical dike [(a) and (b)) and dipping dike (e). (a) E.1 polarizarion. (b) E" polarizarion. (e) E.L polarizarion.


The boundary conditions are not as simple for E polarization. because Hx. H•• and Ey are all continuous across tbe air-ground interface. Consequently. the horizontal H field is not constant everywhere aboye ground in tbe vicinity oC a lateral inhomogeneity. Thus it is necessary to consider the air layer as well as tbe subsurCace structure in attempting to get numerical solutions for E polarization. This requires an upward extension oC the model cross section to the air-ionosphere interface. which has no lateral changes in conductivity. Then H. = O and Ey is constant. because aEy/ ax - - jWIJ-o H,. Equations (6.23) may be solved numerically using linite dilrerences by dividing the geologic section into a nonuniCorm mesh whose spacing is small in the vicinity oC conductivity discontinuities - zones where the MT or telluric fie1ds change rapidly - and increases witb distance from these interfaces until the mesh sections are undisturbed in homogeneous isotropic host rack. Using appropriate boundary conditions. values oC Hy and Ey at interior mesh points are computed iteratively, using overrelaxation factors (Wachspress. 1%6) to calculate their real and imaginary components by successive sweeps through the mesh, with values adjusted after each pass to bring the expressions closer to zero. The impedance network numerical version introduces voltages and currents, in a five-element (four impedances Z. one admittance Y) circuit, as analogs to tbe parameters in Equations (6.23). Apart from using a matrix solution ratber than the iterative procedure, tbe sub sequent operation is similar to tbe otber techniques and has certain advantages. In the finite element numerical technique, tbe section mesh is divided into triangles of various sizes, which permit better matching oC irregular boundaries. a particular advantage when computing complex shapes. The ftexibility oC tbe numerical methods thus allows solutions Cor a wide range of geometrical sections. Because only a limited number oC models can be sol ved analytically, the technique is a powerfuI tool for interpretation in tellurics and MT; it is used frequently in resistivity and IP as well. Equations (6.19) tell us tbat in homogeneous ground the electric field leads the magnetic component in phase by 45°. The presence oC anomalous structures will change this value. It may be shown Ibat the conductor geometry has more elrect on tbe phase than on amplitude response in certain cases. Figure 6.20 illustrates this feature. The amplitude response at 10 kHz over the block model is negligible because the sltin depth in tbe host material is only about 25% oC the depth to its topo From Figure 6.20b we see that the phase shift varies Crom about 1° at 10 Hz to a maximum of roughly 7.5 0 al 1.000 Hz and then decreases at higher frequencies. Figure 6.2Oc

317

emphasizes the phase sensitivity still more c1early by showing the sharp dependen ce on skin deptb in the host rock. Thus it would be useful to me asure phase as well as amplitude in MT work Although this might be difficult with natural source fields. it would be an attractive test with a controlled source. The phase measurement might also help to explain sudden large phase shifts - up to 180 0 as reported by Slankis (1970) and others - when crossing high1y conductive zones during E.I. surveys. Although developed and employed before MT, the telluric method has not been used to any extent in petroleum prospecting in America, in spite oC considerable application and sorne successes in Westem Europe, North Africa. and the USSR. nor has much been done with the relatively speedy and simple audiofrequency telluric technique in mineral prospecting, although it has produced sorne promising and interesting results.

6.2.8. Interpretation of Magnetotelluric Data (a) General. The end result of a conventionallowfrequency MT survey is a paper and/or magnetic tape record of two electric and three magnetic component field variations. similar to the examples shown in Figure 6.10. To determine the general type oC structure (l-D, 2-D, anisotropic. and so on) plus the impedance Z and resistivity p values associated witb it requires that we perform a complicated analysis of the raw data. The processing involves power-spectrum analysis and various forms oí filtering. A typical up-to-date instrumeotation system for MT data analysis is shown in the block diagram of Figure 6.21. This represeots a single acquisition board oí the 10 illustrated in Figure 6.16. Input írom one of the sensors passes by one of two routes through the various blocks to be filtered, amplified. and deposited in the sample-bold amplifier. The lowCrequency path receives signal data al 0.001 10 100 Hz, the other from 100 to 20,000 Hz, with heterodyne demodulation to reduce higher frequencies to 100 Hz. The multiplexer-A/D converter digitizes tbe signal. after which the digi tal computer deve10ps the power spectra by standard methods, followed by analysis to determine the MT parameters. Several MT systems are now available equipped with a computer, eliminatiog the necessity for storing raw data; these are evaluated and may even be interpreted in tbe field. Various other information, such as station and sensor locations and calibration data, is also Ced into the computer. The analysis, of course, becomes more complex with the type of structure that has becn

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FREQUENCY (Hz)

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"F SKIN DEPTHS IN HOST MEDIUM (m) /12 SS 11 , , ,

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Figure 6.20. (Continued) (e) Phase differenee versus frequeney.

surveyed and should be done stcp by stcp, partieulady wbere tbere are several routines 8vailable betwee1i input and solution (Hermanee, 1973). 11 is also advisable to monitor tbe original data along !be way. (b) One-dimensional structures. The MT metbod should perform best over uniform, isotropic, more or less borizontal layers in wbicb tbe resistivity varíes only witb dcpth. An expression Cor apparent resistivo ity measured aboye two beds, sucb as a top layer over basement with resistivities PI and P:z and tbiclcnesses z and 00, respectively, was given by Cagniard (1953). Somewbat modified, tbis relation becomes

a2e2" + 2ae" cos y + 1 PI - ~e2" - 2ae"cosy + 1 P.

(6.25a)

wbere a - (~

+ ,91)/(~ - ,91)'

Y - 2Z(CIII'O/2PI)I/2. O.OO4z(f/PI)I/2 - 2z/z"

f

js tbe frequency, and z, is the skin dcpth in tbe upper bed. The phase angle, rcpresenting the lag of H with respect to E, is

Master curves in P.. and 4t, developed from Equations (6.25) for a two-Iayer earth, are shown in Figure 6.22. The phase curves are not much osed, exccpt Cor verification of results from tbe resistivity data; tbis is mainly due lo tbe dimeulties in aequiring reliable phase measurements. 1ms is unfortunate because MT phase jnformation js quite oseful in resistivity, just as it is in EM and IP worlc. lt should be easier lo obtain with controlled-source equipment. The original master curves of tbis type, which may be found in Cagniard's paper and elsewhere,

Te/luric and magnetotelluric methods

321 "

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CALClK.ATE MT PARAMETERS

Figure 6,21. B/ock diagram o( a wide-band MT system with computerized data processing, (After M'cho/s, 1987.)

were ploUed with (P../Pl) or .p as ordinate and .¡T signal period) as abscissa, both on log scales, lor Pi - I nm, z - 1 km, and a large range oC values oC P2. The master curves in Figure 6.22 are more suitable for AMT and certain EM survey work (§7.7.6b), because the horizontal-axis log scale is frequency (Hz) correspondíng to an expansion of the lelt-band portion of tbe .¡T scale in the originals, whereas Pi is 100 nm and z only 10 m. However, tbey perform the same function, lor shallow ratber than deep soundíng. To use either version ol such curves, it is necessary to plot fie\d results in the lorm P. versus / or .¡T on tbe same scale log paper as tbe master curve and matcb the plot to one oC tbe tbeoretical curves of tbe master, maintaining the ordinate and baseline axes parallel. Sometimes it may be necessary to interpoJate between two of the latter. When the superposition has beeo made, we obtain a value of P.. OD tbe field plot overlying or correspondiog to p" - I Om on the Cagniard curve or p" - 100 Om on the curves of Figure 6.22, wbichever are beiog used. This gives the value of PI lor tbe survey, wbereas P2/Pi on tbe master yields the value of P2 lor tbe bottom layer. Finally, the tbickness of the lOp layer may be calculated. From (T ..

Equalion (6.25a) we see that when p" - Pi' COS Y - O, and l' = 'Ir /2. Thus we can write

z'" 250Y(Pl/f)1/2 ... 400(Pl/f)1/2 where / is the frequency al which y - 'Ir/2 (marked with a vertical bar at 154 kHz in Fíg. 6.22). For tbe Cagniard curve it is necessary to substitute T for 1/1 in the aboye relation and use the correspondíog abscissa point A marked on the master curves. Theoretically it is possible to extend the I-D problem lo 11 beds. The procedure is lo 8tart lrom the bottom interface and work upward, one layer at a time, using a recursion formula given by

where

t) e-l«' / + 1),

~ .. {( p,,/p )1/2e-iI -

{( P./P )1/2 e-J'

a - ("'1'017/ 2) 1/2( I - j),

and 8 - .p - 'Ir/4. The parameter ~ is constant for any bed. AJso tlle boundary condítions (§6.2.4) lor E and H across eacb interface must hold. Coosequently the value ol

322

Methods employing natural eleetric sources

i-

i

S

a.

(.)

Figure 6.22. Master curves for MT sounding over two-Iayer earth. p, - 100 12m and 10 m. (a) P2 < pI.

Z, -

P. at tbe bottom of a layer must be tbe same as that at the top of the layer below it. Figure 6.23 shows tbe gcometry and parametcrs Cor tbe multilayer section, togcther witb an cxample of a typical MT sounding curve, wbich appears to bave a relativcly sba110w rcsistive hed, an intcrmcdiate conductive sectiOD, and a rcsistive bascment. values may be Thus tbe succcssivc p.. and fOUDd from Equation (6.26) by cquating thc real and imaginary parts at eacb interface, beginning at the top oC tbe bascment, wbere ,,/4 «(I~ O) and POI. - p... Procecding upward to tbe next and sballowcr interfaces, it is Dccessary to establish values for P"(N-l)' (1"_1' and so fortb, using data from the

+

+-

-

sounding curve. Generally tbis is best done by an invcrsion process. Practically the preparation of master curves for more than three beds is a formidable task, just as in resistivity soundings (§8.6.4), because of tbe enormous range of possible z and P eombinations. Thrce-Iayer master curves, bowever, are available (Srivastava, 1967). The matching proccdure is analogous to that used in resistivity interpretation, altbougb not as highly developed. In dealing with tabular geometries in Seetion 6.2.7, whetber 01 one or more layers, we found tbat tbe horizontal c1ectrie (e) Two-dimensional struetures.

Tellur;c and magnetotellur;c methods

323

1 0 0 r - - - -_ _~-

451-_....- '

10)

100

10

FREQUENCY (Hz)

(b. F;gure 6.22. (Cont;nued) (b) P1 > Pr.

and magnetic field components were laterally invarianl (al ax - al ay - O) and the vertical components E, and H, were uro (Eqs. (6.21) and (6.22)). 1f we define an impedance Z - E,'; Hy ' it is c1ear that Z is complex (because of the pbase difference belween E and H), thal it bas units of ohms, and Ihal in tabular structures it is ¡ndependent of the measurement direction, that is, it may also be written Z - Eyl H" or whatever. In the presence of 2- or 3-D structures (faults, veins, etc.), bowever, the impedance Z is not invariant, but depends on the distance of the point of measurement from the structure and tbe angles between the stme and the coordinate axes. Tbus, E"

varies nol only with Hy but is affected by the H" component as well; the same holds for E,. Tbererore, the scalar impedance Z lor the 1-D structures becomes a tensor impedance lor 2-D structures; tbe tensor relation can be written E" - Z"" H"

+ Z"y Hy }

(6.27a)

Ey - Zy;C H" + Zyy Hy Tbe simple impedance Z is changed to lour tensor components Z¡j" To determine these, the first step is to record two horizontal E and H compo-

324

Methods employíng natural electric sources

z, ------------------------------na í

e,

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z

a

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(.n. m 1..

,,~------~~-------~-------'---.-..;"...!----'..., '.1 "lfl Figvre 6.23. MiJgnetotelfvric sounding over mv/tiple beds.

nents. (This is normally done in MT surveys, bUI A marked improvement in this regard was recently obviously it is not necessary when surveying a struc- obtained by using a remo te souree, located a few ture known to be one-dimensional. However this kilometers Crom the survey station, whieh record s operation is still not sufficienl to solve Equations referenee fields H,,,, H,y sjmultaneously (Gamble, Goubau, and CJarke, 1979; Labson, et al., 1985). (6.27a) because we have four unknown quantities. A common procedure for processing the recorded Although these measurements also contain noise, it dala lO get the tensor impedance components is:
Te/luric and magnetotel/uric methods

ea Z

~

60 (ohm s)

40

20

o -20

/

,",

,

I

/

~+, 1'N~

'.' ,(

, ,, I

,

-40

eo

325

,,

'

,-

'{ ,

I

,

,

I

V' 1\

,

,

1

,,

I

--' '"

!

Principal Direction

¡

Figure 6.24. Rotation ofaxes for twa-dimensional model with Z;y - 100

z;. - 10 n.

is unlikely that we would know the azimuth oC either the source wave or the structure, tbe survey axes will normally be at an arbitrary angle to both. The series of measurements produces data to fit Equations (6.27a). By an analytical rotation oC the survey axes we now align the components in Equations (6.27a) parallel and normal to the structure. 1bi.s procedure, known as location 01 the principal axes, produces relations similar to Equation (6.24) by decoupling the four tensor impedances so that Equations (6.27a) become E'" - Z'"y H'y )

(6.27b)

E'y - Z'y"" H'

where the primes define the axes parallel and perpendicular lo strike and the principal impedances Z:y'

n

and

Z;.. are related to the tensor impedances as follows: Zu

=

Zyy -

H Z;y + Z;,,)sin28 } - H Z;y + Z;.. )sin28

Z",'

(6.27c)

8}

Z"y - Z;,y - ( y + ZY,'.. ) S.irr Zy .. = Zy .. - (Z"y + Zy.. )sllr8

(6.27d)

where 8 is tbe clockwise rotation angle between tbe survey and the principal axes. Clearly we have

Z.... + Zyy - O Z ..y - Zy" ... Z;y - Z;..

) (6.27e)

... constant for a1l (J During a rotation oC 1800 , the off-diagonal elements Z.., and Z,.. each go through two maxima

326


(O°. 180°) and one minimum (90°). The diagonal eIement Z"" has two minima (-45°.135°) with a maximum at 45°. whereas is the exact converse. When the axes ol measurement are parallel to and normal lO strike. Z,," - Z,.,. - O. The condition that Z"" - - Z,.y [Eq. (6.27e)] has been shown to hold a1so lor a stack of anisotropic horizontal beds (Vozoff. 1972). Sims and Bostick (1969) have reported that Equation (6.27e) is a1so valid for 3-D structures; however. the analysis is very difficult for such features. Figure 6.24 illustrates the axial rotation plot for a 2-D model having principal impedances Z;,. - 100 O and Z;" - 10 O. One oC the principal directions is obviously e-90°. where Z"" - Z,.)' - o and X",.. Zy" are mínima; the other is normal to tbis, at O°. In a practica1 case. using best estimates of the impedances from generally noisy data. the values oC e will not be exactly 0° and 90°, that is, (Z"" + Z,.y) .. O. nor will (Z",. - Z,.,,) be constant over the range ol 9. A measure ol this discrepancy. called the skewness or skew ratio. is

Z,.,.

e-

S should be minimum (theoretically S - O). Devialions lrom zero indicate the reliability ol the results. A large skew ratio may also be an indication that the structure is not truly 2-D, at least not in the frequency range chosen for the Z estimates. Another parameter tha. serves as a check on the proper rotation angle 9 is called the tipper (see tbe summary at the end 01 this section. also §6.3.2, Example 3). We may now determine the apparent resistivities in the principal directions from the corresponding impedancesj thus, p'",. - 0.2TIE,,/H.l- 0.2TIZ;,.l l (Om) (6.28a) ~,,- 0.2TIE,./H"l l

-

If the beds are randomly anisotropic, the survey resuIts resemble those for a 2-D strueture to some extent and analysis involves tensor impedances Z/J; thus, the direction in wbich E and H components are measured is significant. However. Z"" - - Zyy. H, - O. and Z",. ojo Z)'". 2-D structures. Lateral diseontinuities produce the same effect as random anisotropy. ando in general. Po varíes with measurement direction as well as frequency. If the structure is known reasonably well, the survey (telluric or MT) may be performed on traverses normal to strike. This allows measurements to be made either in the H polarization (EJ.) or E polarization (En) orientation, the first being more practical. OnIy scalar impedances need be considered. regardless ol the source-field direction. because E and H fields may be resolved into components normal and parallel to strike (a/ a y - O). This setup allows us to find resistivities using Equations (6.28) and then solve Equations (6.23) by the varíous numerical methods outlined in Section 6.2.7a. If the stme is nol known, the survey ol necessity is carried out at an arbitrary orientation. Five components must be measured. namely, E". E,.. H". Hy • and H,. to provide data for estimating the lour tensor impedances ZIj in Equation (6.27a). It is then possible to determine the stme by an analytic rotation of the survey axes (Ibis could be done physically, but only with great elfort) until one of them coincides more or less with a principal direction normal to or parallel to strike. We can then use Equations (6.28) to ca1culate tbe scalar principal impedances and resistivities. If noisy data and/or complex structure obscure the precise orientation 01 the principal axes, we may indicate the deviation by means of the skew ratio mentioned earlier. A second check is provided by a transfer tensor relation between vertical and horizontal magnetic components. Tbe tipper. T. defined by the relation

0.2TIZ;,,1 2 (Om) (6.28b)

H.( "') - T,,( "') H,,( "') + T,,( "') Hy ( These P values are sca1ars. p'",. being the resistivity for H polarization and ";.,, for E polarization. We can summarize the precedíng díscussion ol the interpretation of telluric and MT data over varíous structures as lollows. keeping in mind Equations (6.21) and (6.27). l-D structures. If the ground is isotropie, orientation problems are eliminated in the survey work (because a/ax - a/ay - O) and the parameters ol the subsurlace bed(s) may be determined either by tellurie or MT soundings earried out over a range ol frequencies in any horizontal direction. Tensor impedances are reduced to scalars and Z,," - Zyy O and Z,,)' - - Zy,,'

"')

(6.29)

is a complex funetion ol frequency (Vozoff. 1972; Labson et al .• 1985) related to tbe ratios H,/HIt and Hz! Hy lor 2-D structures (Fig. 6.28). It is a1so a good indicator ol noise sourees (Labson et al .• 1985. p.657). 3-D structures. Apart from features witb pronounced symmetry like the sphere and ellipsoid. no entirely successfuI interpretation procedures have been developed to date. E-polarization end effects on a slab of limited strike length are particularly troublesomej apparently the 2-D approximations lor Ibis model with H polarization are more reliable.

327

Field examples

Dislance (1'1) Or-------~------~~~

__~._----------------Provtn ~---

mineraliz&1ion

Figure 6.25. SP profile across massive su/fides. Senneterre Area, Quebec.

6.3. FIELO EXAMPLES 6.3.1. Self-Potential Figure 6.25 shows an SP profile oblained over a massive sulfide body in tbe Senneterre area of Quebec. The mineralization is pyrite and pyrrholite, averaging about 30% for tbe entire zone, 40 to 70% in the more strongly mineralized sections. The bost roeks are melasedimentary breccias and lulfs, interbedded witb lava ftows. Twenly-five diamond drill holes outline tbe sulfides iD some detail. Altbough tbe mwmum SP anomaly is very large (600 mV), it is also surprisingly narrow, appearing to reftcel one of the sulfide zones, rather than a com· bined elfcet. Nortb of lhis peak tbe Iwo shallow sulftdes produce very little surface pOlential, whereas the one lo the soutb is Dot detceted al all. The Degative peak al 200S coinciding witb a low swampy surface is not explained.

6.3.2. Tellurics and Magnetotellurics l. Results of an 8 Hz telluric survey made over a massive sulfide body in nortbem New Brunswick are shown in Figure 6.26. The zone, located in diorilerbyolite bost rack, has been well outlined by dia· mond drilling. It subcrops below the overburdco lo the soutb and plunges gently to a depth of 400 ft at tbe north cod.

Conlours are apparent resistivity values determined from relative telluric field strength measuremenls as in Equation (6.24). The sulfide zone is c1early indicated, with the lowest resistivities al Ihe south end. The exlension of lhe contours beyond the southem extremity of the sulfide oulline is due lo furlher shallow mineralization belween lines 13 and T4 • The lelluric anomaly extends lo line 1930S in tbe norlhem part of the mineralized zone, which is over 200 ft deep at Ibis point. 2. AD example of magnetotelluric deep sounding in a relatively simple geologic area is given by Reddy and Rankin (1971), who carried out measuremenls in the period range 1 lo 1,000 s (1 to 0.001 Hz) al 16 stations in Alberta. Their resulls are surnmarized in Figure 6.27, which shows a geologic section lor a southwest-nortbeasl line tbrough Edmonlon extending from the Rocky Mounlains for 350 miles lo the Saskatchewan border. Sediments- in the central Alberta plain vary in thickness from 4,000 ft in tbe east to more tban 15,000 fl where they abul tbe deep-rooled, deformed Precambrian mounlain sediments in the southwest. The basement is composed of crystalline racks oC Precambrian age. The magnetolelluric fields are controlled by the stme of the contacts of these plains sedimenlS witb the olher lwo sections, both of which have relatively high resistivities. As a result tbe currents at depth in the more conductive sedimentary basin are polar· ized northwesl-soutbeast to produce a pronounced

328


mE

D

SuJllclucac

-lOO-- Apparcnl rnistivily

1- I Hz

Va/llel (Oml

,

o

,

500R

Figure 6.26. Telluric data (rom 8 Hz survey over milssive sulfides, New Brunswick.

anisotropy in tbe apparent resistivities, tbat is, tbe values are generally parallel to strike for !he longer perlod signals. The faet that tbere is no apparent anisotropy at short perlods (10 s or so), on !he other hand, would indieate that the basin sedimeots are reasonably homogeoeous. Figure 6.27 shows a set of smoothed curves of P" versus perlod from the 16 stations, taken along the major axis of anisotropy, as weU as theoretical curves ror a two-Iayer earth model in whieh the thickness (ti) and resistivity (PI) of the top layer are varied. Clearly both parameters are variable in the field area. It is possible to produce more complex threeand four-Iayer sections for individual stations that match the measured results very well, although these models are not unique. m~mum

Although the results are satisfaetory in the exampIe ol Figure 6.27, in general the agreement between fleld results and simple layer theory has not been particularly good. Discrepancies are often eaused by anisotropic ground and lateral discontinuities in conductivity. The theory assumes vertical currents to be negligible. In faet large vertical current components extending over distances oC more than 130 km have been reported in the Iiterature. 3. Figure 6.28 shows an 8 Hz magnetotelluric profile over a contact between Precambrian metasediments and Paleozoic shales, sandstones, Iimestones, and dolomites. The area is about 20 miles west ol OUawa, north of the Ottawa river. The apparent resistivities in Figure 6.28a are obtained rrom the ratio E~/HII , that is, the teIJuric field was measured

329

Field examples

r-SO

milc5...f

P. curves alonl major u.is or anisotrop)'

Cenlral Albefla

p. (U m)

100

(h)

-7- .moothed curvo ror stalion 7 T (S) 100

1000

P.

10m)

Modol

:~W&;Wk

1<)

p, - 5000 11m

-

1, == 3 km. PI va.riable

..... =. \liu¡IIMe. PI

-

10 Um

T (s)

100

FiBure 6.27. MiJgne/o/elfurie deep soundings in Central Alberta. (After Reddy and Rankin, 1971.) (a) GeoloBieal seetion. (b) p. curves along major axis of anisotropy. (e) Theoretical p. curves far /wa-Iayer earth.

¡

rougbly normal to the contact, the magnetic field paralleJ lo it. The agreement between the measured profiJes and the theoreticaJ ones, originally derived from a vertical contact oC great depth witb resistivity contrast of 100, is Cair, The actual geologic profile is Dol so simple because the Paleowic sediments (tbe low resistivity section) are onIy 600 ft thick as illustrated in Figure 6.28f. The MT profile, however, reftects tbe contact c1early. Measurement oC the teUuric field at several azimutb angles otber tban E.l. showed that the apparent resistivity became progressively more anisotropic as the contact was approached from tbe north and that tbe minimum P" was paralJel to slrlke (Fig. 6.28b).

The Precambrian-Paleozoic contact is indicated on all profiles excepl that in Figure 6.28c, where tbe HII field theoretically should remain invariant. The field components change gradually acrass the contact, suggesting a z.one of variable resistivity belween tbe resistive igneous and conductive sedimentary racks; in faet there is an outerop oC Precambrian age about 0.5 mile south of the main contaet. The model tipper profile in Figure 6.28e is a reasonable match witb the vertical contact model, considering the shallow character of the actual section. The next two examples show several pseudodepth plots from subaudio and audiofrequency MT surveys, a type of display popular Cor IP data (§9.5.1). It may also be employed in resistivity, tel1urics, MT,

330

Methods employing natural electric sources ~

OBSERVED THEORETICAL ( a)

Apparent resistivity

104 .

(nm) El.

10'

{\::....

. .-

8AS€ SlAT'ON

. \ ......,..... :...". .•.•..-:\.o."

"~-.....:.."

lO· •

...

•••••••

/

.'. .'·1

"

./

•••..•

'-".,1

".

\,

"'- ..... ' .1

10' .

'.~

........... -_..;:\_ .....

(b)

(e)

.~ ........ _..... _.......... ,.,,-._...-, .J\.

Apparent resistivity (nm) El

Relative HA

~·--./\//

:~~ -----------~:~:>::::::"C.:-:-~___._.\1

_._ '\./'\

O.6L _____~·--------~·----~·----~I--------~I----~·--~

......

(d)

Relative HJ.

oo•.• oo••• o •• _•• o •• o. _•••.. \....

(H.)

•

--.--. ,.

... v.."'=.~.~ .................... . ...

(e)

.

-

."..- .....

H,/HJ.

1000'

( f)

Geologic section

500'.

OTTAWA

-. ",v,. o' "1~·

-500"

X

T-"''' ;;n»fF'-' ( ? 7.Z~'. I

'4UOIO.C-./

ssw

'/tIC""'.'." I

l!

DlSTANCE (MILES)

Xl.

"

NNE

Figure 6.28. MT profiles over Preeambrian- Paleozoie eontaet. near Ottawa. (a) Al based on fJ.' (b) Al based on f. (e) Relative H •. (d) Relative HJ.. (e) Hz/HJ.. (f) Ceologie section.

and certain types of EM work. The only difference between tbe MT and IP plots is in the vertical scale; this is logarithmic in period or frequency lor MT, linear in distance for ¡P. Thus tbe deptb or penetration in the first is relaled lo skin deptb, in the second primarily to eleclrode spacing. Readings ror tbe pro-

file and conlour plots in Figures 6.29 and 6.30 are reckoned al tbe midpoints 01 the electrodes. 4. Figure 6.29 shows a pseudodeptb MT plot over a conductive zone bounded by two outcropping faults, (F, and f2), seen in tbe geologic section below. This illuslration is taken from a survey caro

r, Field examples

331 PSEUDODEPTH PLOT

WEST

EAST

1000

100

>-

U

Z

""...5 a: lo.

20 .-o. seALE : O--_..... =

97

15

CONTOURS IN n-M

GEOLOGICAL SECTION F,

Ompo~~~~~~O:~~~~~~~~'--1r

1 100m

/

r

./

I

;:J::.:OVERBURDEN ~ :FAULT ::. .. :FRACTURE ZONE , :DDH

METAMORPHIC 1 : 1.0WER SERIES

II :INTERMEDIATE SERIES

Figure 6.29. Magnelotelluric pseudodepth plot fo, conductive fracture zone, Northern Saskatchewan.

(a'

STATION SMt-1

(M

II

¡·DModel

Sürilce

~

E e

-

i.~

~tit~ ~.I.."

~

~,

y \'¡, ~t •

4OO0m

0.05 km

1000 Om 0.030m

0.45 ± 0.1 km 0.180 km

1.00m

7 ± Hm

3OO0m

2.5 km

SOOOOm

140 km ac

•

l.

10

JICOI

r (s,

(d

~

~ID

'""

•••

•• "'.L.:~-: ~rtvr! •••

ll)¡

.

"

Q/

..

ID

r(ll

Figure 6.30. P. results near Ste. Mathilde, Quebee. (a) Map shawing elevatiam, locatians a( profiles 1- J plus p. eontours. (b) flesults (or station SMt·1: 1\ curve, tensor data in the principal axis o( anisotropy from 0.03 to 10,000 s, and sealar data from 0.0tXIB to 0.13 s; dols and triangles are p. values for the majar and minar axes o( an;sotropy, respective/y; error bars show maximum seatter from O.roJB to 100 s, two standard deviations (rom 100 lo 10,000 s: salid curve ;s for Ihe 1·D model. (e) Skew ratios.

I000O

Field examples

333

NW_

•

I

t

¡

¡

..

1 -. DIST~Nct

Z 400 DISTANCIE ' .....,.1 _

[ .......1 -

Prolila 2 pSludo·slICIÍon.

Pro"l. 1 pS.Udo·section.

2'

20

700

600

200

1200

'400

OISTANCE (m"....') (d) Figure 6.30. (Continued) (d) AMT pseudodepth plots (mm profiles 1, 2, and 3.

ried out in northem Saskatchewan in the area of Colt~ell Dome, where uranium mineralization is sometimes associated with conductive fracture zones witbin the rcsistive Precambrian formations. The low resistivity section is more c1early evident from tbis form ol MT plot, both horizontally and vertically, than from conventional MT oc resistivity profiles.

5. Figure 6.30a shows an anomalous bigh conduc· tivity zone of limited lateral elttent located near the village of Ste. Mathilde, Quebec, on the lower north shore of the Sto Lawrence River. 'Ibis feature is in a regíon of bigh1y complelt geology, witbin a few kilometers oC Logan's Line, a major tbrust fault separating the Grenville Province from the Appalacbian;

JJ4


Table 6.3.

SP Stalion

OW

(mV)

1

O -37

2

-100

3

5 6 7 8 9

-108 -158 -236 -138 -210 -290 -335

10

-258

11 12

-170 -120

4

13

-73

14

15 16

-40 -21 -17

17

-7

the zone is adjacent to the east rim of a large Paleozoic impact erater and near the northeast edge of an active seismic zone along the Sto Lawrence. On a smaller scale a granite body about 2 km by 0.6 km, surrounded by a wide migmatite zone injected by pegmatites and overlain by frequent outcrops of Precambrian rack, appears to be roughly centered on the anomalous zone. The cause of this extremely conductive feature is not known. It is tbought to be a volume of highly fractured rack filled with conductive aqueous solutions, possibly ineluding graphitic, sulfide, or ferrous mineralization (although lhere is no particular indication of lhe latter on local aeromagnetic maps; see Kurtz el al., 1980). The depth to lhe top of this feature, determined from 1-D modeling, is between 0.25 and 1.0 km, lhe· vertical extent being 4 to 7 km. The structure. no more than a few square kilometers in eross section, trends northwest-southeast and plunges northwest. Figure 6.30a sbows a map of lhe area plus P. con-

L20N

Lt8N

LI6N

Lt4N

Lt:.!N

LtON

UN

L6N

UN

Figure 6.31. SP survey in Northern New Brunswick. Conlour values in millivolts.

335

Problems B.l.

Figure 6.32. SP survey in fasrern Nm'a Sco/ia.

tours. Figure 6.30b shows Po values obtained Irom tbe field data plus a sounding curve for lbe l-D model shown. Figure 6.3Oc gives skew ratios for (b). Figure 6.3Od displays tbree AMT pseudodepth plots from profiles 1 to 3 (Fig. 6.30a). The pseudodepth plots, tike the Po contours in Figure 6.30a, enhance lbe small dimensions and sharp boundaries oI this odd Ieature.

6.4. PROBLEMS 1. The self-potential readings in Table 6.3 were oblained on a detailed traverse. Stations are 10 ft aplkt and SP readings are given with reference to statron O. Make an interpretation oC this anomaly based on the limited data available. 2. Figure 6.31 shows a set of SP contours for a prospect in northem New Brunswick. The area is

mainly wooded with sorne open ground rougbly parallel to, and slightly west oC. the baseline between lines lON and 20N. What interpretation can be made oC tbis prospect - particularly tbe large SP negalive cenlers - lrom the data? Is any additional work warranled and ir so what would you recommend? 3. The SP profiles shown in Figure 6.32 were the result oC a survey carried out on a large geochemical anomaly in eastem Nova Scotia. These profiJes are part of a much larger SP survey, extending Curther in all directions except east, in wbich the general background SP is 140 mV more positive Ihan the zero values shown. Convert the profiles into contours by adding -140 mV to all readings and make any interpretations you can 01 the result. 4. Readings from a self-potential survey made over suspected sulfide mineralization in southeastem


336

8 -111 -121 -156 - 13 a o o a o e o -120 -109 LineI9+50N-~-I20 -1)2

-113

-ISS

-18

-26J

-as

-161

-141

-10

UMI6N'oo--~O~~O--~Q=-~Q~Q~~Q~~C~~C~~o~~o~~a~oo~~Q~a

83

LiMI2N

Line I N

-339

-109

-53

-77

-126

-106

-37)

-110

-61

-138

-136

-50

-131

-20

~a~~o~~o~o~~o~~o~~o~~o___~o--~a~oa~~a___a~~a~-Oa

-29

-JI

-140

-77

-227

-118

-64

-S8

-206

-lIS

-112

-m

-38

-64·

-40

c>a--~o:-&D--~D~a_~o~~o_-clo~-clo";"'... a ___oa~<1'a~o.a;.....o~-40

-36

-70 a

Line4N

,

-109

-127

-65

-175

-65

-$4

-106 -79 -110 -65 -62 -117 a o o a a o a e a o a a o -102 -77 -1S8 -49 -71 -72 -42 I

20W

ISW

Figure 6.33. SP survey in

H lron

I

10W

Southe~stem Ont~rio. Re~dings

in mi1livolts.

Table 6.4. SIn

1 Hz

8Hz

32 Hz

145 Hz

20W

120 69 97 81 62 37 37

110 140 140 155 126 56 40 39 44

282 270 265 307 243 117 88 81 70 133 140 160 393 565 845 715

655 590 550 763 flJ7 256 242 242 127 190 305 205

19 18 17 16 15 14 13 12 11 10 9 8 7

6 5

46

45 62 29 48 143 156 207 223

84

71 92 257 375 510 445

Ontario are mown in Fig. 6.33. By drawing prolila and c:ontouring tbese data, makc an intcrpretation lor !he area. S. Tbc tdlurie ficld strcngtb readings in Tablc 6.4 wcrc obtaincd during a traversc ovcr a prospccl in eastcm Nova Scotia Four frequencies, 1, 8, 32, and 145 Hz, are mcasurcd by intcgrating

660

970 1700 1580

signals, obtained from 100 lt electrode spreads, lor 30 s. Normalize tbese readings lor eaeh ehannel, by taking tbe averages of alI slalions to obtain a common background of unity, plOI on a Jog scale, and interpret the rcsuIt. (Note: Presumably one can make use 01 tbe faet tbat deptb oC

Problems

337

IJ

-

8Hz 32Hz ••••. 145 Hz

.I!

__ o

i

·I-! 0·1 ar: 0.01

~

____~____~____~____~____~~~~~~-L____-L__ line~S

IlOOE

IOOOE ,

I

Fisure 6.34. Multifrequency telluric profiles from Soulheaslern Quebec. f/ectrode spac· ;ns 50 h.

5SW P•••

lO'

(11m' 10>

I

I

I

50 I

4S

I

,

1

40I

I

I

35 I

I

JO

I

25W I

,

I

+------., .-"-:.~7"_.5~~,c:=::;;~:_::7L:'::.""7~~~~)o¡e;;;;Jl,/-'

IO·1-------------------~~--------~~----------------------LineO

10:~::::::::::::::::::::::::::==::::::::::::::::::~~::::=:

lO' P.rof'

\UmIIO·+'"7'.......=.--"""'~::::"._-I-~_-....--~.",.-l.+:_:-1~=~~.....,.~~

.-',-,

""_.-._

"

.\\; ..,,,..; IO>1-~--~~~--------2---------~~-----------------------Lineo 25 20W 40 JO 25 35 50W 4' 10

I

I

I

I

I

I

I

I

I

I

I

I

,

I

I

,

,

I

I

I

--8Hz -'-1 Hz

,

!

O

I

,

I

,

I

I

,

100 200m

Fisure 6.35. Telluric profiles al 1 and 8 Hz, Northeastern Brazil.

penetration varies inversely with frequency in some fasmon.) 6. Figure 6.34 shows three profiles of multifrequency (8, 32, and 14S Hz) tel1uric field strength over a zone of sulfide mineralization in southeaslem Quebec. As in problem S, the signals

were integrated for 30 s, while !he electrode separation was SO ft. Malte an interpretation of the results based on tellurics alone. 7. The profiles shOWD in Figure 6.35 were part of a multifrequency reconnaissance telluric survey. OnIy two of !he four frequencies measured


338

--------~~~~~--r_+_--------~------~~--+_------ ~N

..eN

40N

B.L. ,

I

!

o

200

,

!

400

600 o

Figure 6.36. 8 Hz telluric data, normalized and contoured for large-scale interpretation.

10'

)(- - -)(- . ~--t1._

i i

0·5 O'l

10'

I.~

0'1

10" X-'-)( TeUuric{EJ 100 fleleetrodes

'"JI 0-05

j

MIl

10'

,

0--0 Ma,neloleUuries (,.)

Appa.n:nt

\1 .-.:.,

mlSllvlly

10 (Om)

\

0-01

,, I 1../,1 r; )(

"'.... .,' f-·~

Di.l&nce (O)

Figure 6.37. 8 Hz magnetotelluric profife, Northern Quebec.

(1 and 8 Hz) are reproduced bere. Spacing between the two lines sbown is 400 m. Relative telluric field readings bave becn converted to apparent resistivities, based on resistivity measurements made al several slations in tbe area. Make an ioterpretation of these linúted data. 8. An experimental 8 Hz telluric survey was made over an area previously covered by IP in eastern

Canada. 'I'he relative telluric field contours are shown in Figure 6.36. Interpret the broad features of this area with no other data available. 9. 'I'he magnetotelluric profile ilIustrated io Figure 6.37 was obtained by measuring E.J. and H" (electric field roughly normal, magnetic field parallel, lo slrike 01 the mineralization) al 8 Hz over a sulfide showing in northem Quebec. 'I'he tel-

Problems

339 Table 6.5. SIn

OSO 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 1,000 1,100 1,200 1,300 1,400 1,450 1,500 1,600

8 Hz

145 Hz

1,000 Hz

3,000 Hz

0.83 1.00 1.20 1.28 1.50 1.26 1.05 0.83 0.72 0.80 0.80 0.78 0.73 0.77 0.78 0.67 0.62 0.72 1.00 0.93 0.80 0.85 0.82 0.81 0.82 1.00

1.00 1.10 1.25 1.30 1.40 1.07 0.90 0.57 038 037 0.38 0.40 0.43 0.42 0.40 036 0.35 0.37 0.42 0.47 0.78 1.00 0.72 0.63 0.82 1.22

1.40 1.28 1.10 1.00 0.94 0.90 0.55 0.30 0.24 0.22 0.23 0.22 0.25 0.27 0.22 0.21 0.25 0.26 0.27 0.78 1.28 0.96 0.74 1.00 1.50

1.50 130 1.14 1.06 0.96 0.<)2 0.55 0.29 023 0.19 0.16 0.15 0.12 0.11 0.14 0.17 0.18 0.18 0.22 0.75 1.40 1.00 0.81 1.26 1.70

luric profile for E J. is also shown. It indicates that the telluric measurement corresponds very c10sely to the magnetotelluric result, although the apparent resistivity values, oC course, cannot be determined. What crude interpretation can be made Crom this profile? 10. During a routine reconnaissance ground survey witb four-frequency tellurics and SP in eastem Nova Scotia, the readings in Table 6.5 were obtained over a part of a long traverse. Station readings are in Ceet, SP in millivolts, and the telluric readings bave been norma1ized (as in problem 5) to produce a relative telluric field strength (RTFS). Tbe upper layer oC overburden carries anomalous lead and zinc values. Overburden depth is not generally known, but appears to be as much as 50 Ct from nearby trenches; it also contains numerous fractured boulders laced with sulfides. Plot these profiles and interpret them with regard to possible base-metal anomalies and their deptbs, geometry, and commercial interest. n. Figure 6.38 sbows an area of potential base-metal minerallzation on tbe Canadian east coast; earlier prospecting had exposed promising Cu showings and MoS¡ samples were common along the rocky shoreline. An extensive geochemical soil survey had also established a large-scale anomalous z.one that included Pb and Zn. Ear-

SP 20 10 6 7 +8 -74 -119 -50

-7 +25 33

33 31 19 O 24 34 31 35 20 33 37 25 19 40 62

lier, magnetic and IP surveys were carried out to establish structural trends and disseminated sulfide minerallz.ation, without marked success. MT and telluric work were done in an attempt to determine wbether the latter, cheap and rapid compared to MT and IP, was a suitable substitute method. Tbe MT profiles displayed in the upper section oC Figure 6.38b were obtained several years after the telluric results shown below and simultaneouslywith EM16R measurements of apparent resistivity (§7.4.2r; §7.7.6b), shown dotted in the upper halC oC Figure 6.38b. Consider the multifrequency MT and telluric profiles carefully. Do tbey correlate sufficiently tbat you would employ tellurics with confidence for raster and cheaper coverage'l Is Ibis correlalion as good between EM16R (17,800 Hz) and tellurics at 3,000 Hz.? Are there visible trends in conductive and resistive struclure, both borizontally and vertically? Is the EM16 source (Cutler, Maine, roughly west of the area) welllocated for the honz.ontal trends? 12. A novel expression oC ground geophysical measurements over a well-mapped working·mine subsurface is displayed in Figure 6.39. Tbe steep profile line, striking roughly east-west, passes over a large section oC the ore body, inc1uding tbe edge of the worked-out "Glory Hole" around


340

5W

~~

DC2

____________

2E

~~LINE2S

tw

lE

oS'~

.

OA '.". ,.~

('''' .... ~

..........

(a)

el 5 ¡"

4 3

2 11 DC2 lE 2

i'

¡

i

3

11"

4 5 i

6

1

8

9 lOE 11 12 13E as,

i""

r:-:-::-::------,....7-f'"------ .. ·.. ·3000 Hz LlNE

...........

.-- 145

+00$ ~;.:::.:.--

32 8

RTFS--~

(b)

SI

NORMALIZED TELLURICS

OC2

lOE

o,

Fisure 6.38. TeIluric. MT. and VLF results. Canadian east coast. (a) Plan survey area. (b) Top two sets 01 curves: p. profiles Irom MT and VLF (fM16R) measurements; bottom two sets: re/afive tel/urie f;e/d strensth (RTFS) profiles.

Bl

.'.

I

2

3

I

I

4

5

---------.--~

..

7

8

9

I

I

10

n

I

12

13

I

14

15

I

16

I

18

11

19

20 21

22 23 24

4~t

=t

MAGNET1CO

'" "- .... f 1 '\:'---J'o.

/~.-

TEI.UAICO

<"'r-··J

--*

~.~--

I

k~~.".>¡---b{t\:k~;f/F:·~.t+ 1 ~ I "1-':';"-Y'~ .• --"j¡.{:;1' I ---¡--, ·'''---~T-_r···~ 'r" l' ,- í I f ' I ,....••

- -.- -32 H.

d'Y

.•• 1_---'

m

-------lOOO ................ 8

".

[Z]

POAFIOO (fa""",ble par.. la m_MllilClClón)

ng,~~.:t

ANOESITA (medla""mente favorable

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l'

0

ANDESITA

rffij

FII.ON

O:..... r-'" I_.J

OAE 9001

"

............

para lo minerahlGc.on)

BASAI.TICA

--" -\'.... --'~\'~-'-

. ''''... """ ........ ~\:~ -:;::. ....... ,. .' . .7.t., ...... ... . , .. t¡--¡ ,,-. -. ",'" ..... ..-, -t' ... " ,. .... ,"

VACIO

ANOESITICO

'.

'/~~I

•

•• '

;"-1-.," '.::.'.'; ...~.:::_r.,o,

I

¡;.¡:,

~'.j (;LOA't

_

:.. : ... 1" ......... "\: ..~!¡.. \

:.:':;~~.:.':.\

, ... J.;¡.: .... ~,:(.

•. :·.·Ii

:.·.·.;: ...1

.:'.::: :.' ~:."::''; •••••• ~

,

..

,

\

/'

r

/ : - ..., ........ : •• _,

.·.t :.,'./j \ /.':,i-!:: '. ' . -,~,;,' ,.,,'~', ~ ': . ./-' ...../,:' 14"1" ., .. ,:,,:/', l.:

,

\ I

"

I

'

',-

.

•

,'/"

.'

,,--,..

'"....,'l'*. I.:-i,'¡'

,1.... 1

1

~,

l.

4;:11.,.. ....... ......

", ... -\-

SANTA ....... e LAR'"

":::.~J: """ . . 4-

-'"

-\-'.

\.%' . . ...,::...... . . , . . . . ...... '. ..-.~~ ) /:'~'-

\

,~.-;,:/..,

•

I

/.;;

\' r"~,~',:'/ ~" , , ¿ ;.... : ...• {"' , .. , " /,"~': :'11'10' , •.

',1

. . • '1

'

,_ \' /#J"I."'1 •. . .r l '''' ,

.,':. ,,."

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I ,', . -

............

. . . . . . . . . . . .............\ ~

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HOI.E ;. '.'.' ..... .- ",_.,' ."',: .~"... ,J

·::~.··.··.:··:i'

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-

k

'

'-'

Elcala ',2500

•

ti ..';

Figure 6.39. Geolog;c seclion wilh magnelie and lel/une surfaee profiJes over mine ./rea. Chile.

...... ,

-t

342

Methods employin8 natural electric sources

stalion 15. A tellurie base located near station 5 was oceupied during tbe traverse to reduce noise eaused by erratie signals. Study tbe magnetie and four-frequeney tellurie responses tbroughout the promes. Do they reflect tbe known section properly7 Draw a tellurie pseudodeptb plot, as in field Examples 4 and S, and compare it with tbe geologie section seen here. Does this display enhanee tbe tellurie response with respect to frequeney versus penetralion depth? Is there evidence for a terrain effect in any of the diagrams?

REFERENCES Se/f-Potentio/ Corry, C. E. 1985. Spontaneous polarization associated with porphyry sulfide mineralization. Geophysics 50, 1020-34. Corwin, R. F. 1976. Ofl'shore use oC Ihe self-potential method. Geophys. Prosp. 24,79-90. Corwin, R. F .. and Hoover, D. B. 1979. The self-potential method in geothermal exploration. Geophysics 44, 226-45. Roy, J. 1984. Electrical metbods in mineral welllogging. Ph.D. thesis, McGiIl Univ., Montreal. Sato, M., and Mooney, H. M. 1960. The electrochcmical mechanism of sulfide self potentials. Geophysics 25, 226-49.

Tellurit:s Boissonnas, E. and Leonardon, E. G. 1948. Geophysical exploration by lelluric currents wi th special reference to a survey oC Ibe Haynesville Salt Dome, Wood County, Texas, Geophysics 13, 387-403. Doborzynski, Z. B. 1973. Prospecting witb multi-Crequency telluries. M.Eng. tbesis, McGill Univ .. Montreal. Dobrin, M. B. 1960. Introduc/ion/o Geophysica/ Prospecring. New York: McGraw-HiII. Gamble, T. D., Goubau, W. M., and Clarke, J. 1979. Magnetotelluries with a remote reference. Geophysics 44,53-68. Keller, G. V., and Frischknecht, F. C. 1966. Electrica/ Me/hods in Geophysical Prospec/ing. Oxrord: Pergamon. Slankis, J. A. 1970. Telluric and magnetotelluric surveys at 8 Hz. Ph.D. thesis, McGiII Univ., Montrcal. Slankis, J. A., Telford, W. M., and Becker, A. 1972. 8 Hz telluríc and magnetotelluric prospecting. Geophysics 37, 862-78. TelCord, W. M. 1977. Characteristies oC audio and sub-audio telluric signals. Geoph.ys. Prosp. 25, 321-33.

Magneroreflurics Cagniard, L. 1953. Basic tbeory oC the magneto-telluric method of geophysical prospecting. Geophysics 18, 605-35.

Forsytbe, G. E., and Wasow, W. R. 1960. Fini/e Differenc~ Methods lor Par/ia/ Differen/ial Equorions. New York: Wiley. Goldstein, M. A., and Strangway, D. W. 1975. Audio frequency magnetotellurics with a grounded electrical dipole saurce. Geophysics 40, 669-83. Grant, F. S., and West, G. F. 1965. Interpretot/on Theory in Applied Geophysics. New York: McGraw·HiIl. Hermanee, J. F. 1973. Processing oC magnetotelluric data. Phys. Ear/h and Planer. In ter. 7, 349-64. Hermanee, 1. F., and Thayer, R. E. 1975. The telluricmagnetotelluric method. Geophysics 40, 664-8. Hoover, D. B., Frischknecht, F. c., and Tippens, C. 1976. Audio-magnetotelluric soundings as a rcconnaissance ellploration technique in Long Valley, Calif. J. Geophys. Res. 81, 801-9. Hoover, D. B., Long, C. L., and Senterfit, R. M. 1978. Audiomagnetotellurie investigations in geothermal arcas. Geophysics 43, 1501-14. Kurtz, R. D., Niblett, E. R., Chouteau, M., Scott, W. l, and Newitt, L. R. 1980. An anomalous electrical resistivity zone near Ste. Mathilde, Quebec. J.

Cafladian Soco Explor. Geophysics, 56-67. Labson, V. F., Becker, A., Morrison, H. F., and Conlí, U. 1985. Geophysical exploration with audiorrequency natural magnetic fields. Geophysics SO, 656-64. Niehols, E. 1987. Personal communication. Pbam Van Ngoc, Boyer, D., and Chouteau, M. 1978. Cartograprue des" pseudo-resistivités apparentes" par profilage tellurique-tellurique associe l la magnetotellurique. Geophys. Prosp. 26, 218-46. Reddy, 1. K., and Rankin, D. 1971. Magnetotelluric measurements in central A1berta. G~ophyslcs 36, 739-53. Sandberg, S. K., and Hohmann, G. W. 1982. Controlled source audiomagnetotellurics in geothermal exploration. Geophyslcs 47, 100-16. Silvester, P., and Haslam, C. R. S. 1972. Magnetotelluric modeling by Ibe finite ele~ent method. Geophys. Prosp. 20, 872-91. Sims, W. E., and Bostick. F. X., Ir. 1969. Methods of magnetotelluric analysis. EGRL Tech. Rep. # 58, Univ. oC Texas, Austin. Srivastava, S. P. 1967. Magnetotelluric two and three layer master curves. Dom. Observo (Ottawa, Canada) Pub. 35, No. 7. Strangway, D. W., and Kaziar, A. 1979. Audiofrequency magnctotelluric sounding - a case rustory at the Cavendisb geophysical test range. Geophysics 44, 1429-46. Strangway, D. W., SwiCt, C. M., Jr., and Holmer, R. C. 1973. The application oC AMT to mineral exploration, Geophysics 38, 1159-75. Swift, C. M., Ir. 1967. A magnetotelluric investigation oC an electrieal conductivity anomaly in lbe southwestcm United Statcs. Ph.D. thesis, Depl. of Geo!. and Geophys., MIT, Cambridge, MA. Vazofr, K. 1972. The magnctotelluric method in the exploralion of sedimentary basins. Geophysics 37, 98-141. Wachspress, E. L. 1966. l/eru/iue So/u/ions 01 Ellip/ie Systems. Englcwood C!itrs, NI: Prentice-Hall.

Chapter 7

Electromagnetic M ethods

7.1. INTRODUCTION AND HISTORICAL BACKGROUND

.\,

,

;f

\

With the exception of magnetics, the e1ectromagnetic (EM) prospecting technique is the most commonly used in mineral exploration. In its usual form the equipment is not suitable for oH search, because it responds besl to good electrical conductors at shallow depth. Nor has it been much employed in civil engineering work, a1though it is used occasionally lO locate buried pipe and cable, for the detection of land mines, and for mapping surficial areas infiltrated by contaminants. As the name implies, the method involves the propagation of continuous-wave or transient e1ectromagnetic fields io and over the earth. There is a c10se analogy between the transmitter, receiver, and buried conductor in the EM fie1d situation, and a trio oC eleclric circuits coupled by electromagnetic induction. In a few EM ground systems the source energy may be inlroduced into the ground by direct contact, although generally inductive coupling is used; invariably the detector receives its signal by induction. The EM ground method was developed during the 19205 in Scandinavia, the United States, and Canada, regioos where the detection of conductive base·metal deposits was Cacilitated by their large co~trast with the resistive bost rock and generally thin overburden. The airbome version was introduced some 30 years latero Until the early 1960s, practically a11 EM equipmen! transmitted and received continuous1y on one frequency at a time. Sucb a continuous wave system is said to be operating in the frequency domain (FEM or FDEM). Although several attempts were made, datiog back to the 1930s, to transmit transient pulses and detect the ground response during off-time (Statham, 1936; Hawley, 1938), the first successfu1 applications of this type did not appear until 1962. These were the airbome Input (Barringer, 1962), the MPPO·l grouod transieot system in the USSR, and the EMP pulse grouod equipment ol Newmont Ex-

ploration (Dolan, 1970). Since the early 1970s, there has been a dramatic increase in the development oC such time-domain systems (TEM or TDEM). Almost aH EM field sets inelude a portable power source. However. limited use has also been made oC radio transmission stations io the Crequency range 100 kHz to 10 MHz and particular1y in the very low frequency range (VLF), 15 to 25 kHz. One other field method that can be ineluded wilh EM. AFMAG, makes use of atmospheric energy resuIting from wor1dwide thunderstorm activity (§6.2.l). A great advantage oC lhe inductive coupling is that it permits the use of EM systems in aircraft. Airbome EM. usualIy in combination with other aeromagnetic methods, has been wide1y applied in mineral exploration reconnaissance and recently in detailed surveys.

7.2. ELECTROMAGNETIC THEORY 7.2.1. Vector and Scalar Potentials The propagation and attenuation of electromagnetic waves were discussed in Sections 6.2.2 to 6.2.5 in connection with the magnetotelluric method. Although the frequencies employed in EM prospecting are somewhat higher Ihan in most MT work, the general theory, limiting assumptions (negligible dis· placemenl current and spatial phase shift), and boundary conditions are identical in the two methods. In general pOlential theory il is usualIy easier to solve problems by starting wilh Ihe pOlential and obtaining the field vectors by appropriate differentiation. The same rule applies in electromagnetics, where it is convenient to introduce certain potentials from which both electric and magnetic field vectors may be derived. We define the vector magnetic potential A in lerms oC the magnetic induction

vxA==B

(7.1)

344

Electromagnetic methods

Still anotber potential, tbe Hertz ~c'or potmtia/ II, is available to define tbe EM field. It is defined in terma of A and tbus:

TheD from Equation (6.3) we have

+

v x (E + aA/a,) - o Tbe vector inside the bracket is irrotational [see Eq. (A31») and can be expressed u tbe gradieat of a scalar potential .:

E + aA/a, -

A

-,,,alI/at+ I'alI}

. - -V·II

(7.8)

Following manipulation similar to that COl A and ., we arrive at tbe expression (Ward, 1967)

-v+

or (7.2) 1be term - aA/a, is tbe induced em! portion of E while - V." is tbe potential gradieat due to current ftow in a resistive medium. Using Equations (7.1) and (7.2) along witb Equations (6.4) and (6.9), we bave

V X V X A + I"{

aZA/a,2 + V( a+/8,)} - I'J (7.3a)

[If external somees are present, J must be replaced by J + 4-see Eq. (6.l1b).] Tbe electric field E in Equation (7.2) produces a CUJ1'eDt in a conductíng medium such that (see Eq. (6.9»

7.2.2. Oescrlptlon of EM Flelds; Bjot - Savart Law

J - eJE - -eJ( aA/a, + V.,,) Substitutíng lOl J in Equation (7.3a) and using Equation (A2S), we obtain

V(V . A) - V 2A + I'e{

a2A/8,2 + V( a+/8,»)

+ I'a( 8A/a, + V.) -

o

(7.3b)

Equation (6.6b) states tbat V • D - Q, Q being the cbarge density. Using tbis lo eliminate E in Equation (7.2) gives V~

+ V . (aA/a,) - -Q/e

(7.4)

We now malee use ol the Lorentz condition (Ward, 1967): V .A-

-(,,,8.,,/81 + I'a.,,)

(7.5)

(this forces botb A and • lo satisfy tbe same wave equation u H and E). Substituting Equation (7.S) into Equations (7.3b) and (7.4) we get

v 2A -

1" 8 2A/8,2 -

I'aaA/8, - O V 2+- 1',8 2+/8,2 - I'aa+/8, - -Q/e

wbere K - - P /e, or - M, or zero. P, M are tbe respective electric and magnetic-dipole momenta per unit volume. 1be value 01 K depends on tbe conditions of tbe system. Although tbese potentials do not have tbe pbysicaJ signiftcance of tbe scaJar potentiaJ in gravity or electrostatics, tbey provide convement matbematicaJ tools for determining various EM fields, as we sban see in tbe lollowing sections. Tbe similarity in form between Equations (7.6), (7.7), (7.9), and (6.13) is wortb notíng.

(7.6)

(a) General. 1be primary or source fields used in EM prospecting are normaJIy generated by pusing altemating or pulsed current tbrough long wires or coils. For simple geometric configurations such as

these tbe resultant fields can be calcu1ated exactly for pointa in the surrounding regían, although this is not generaJIy possible. Witb FDEM one must measure tbe disturbing fteld iD tbe presence of tbe original primary field, hence it is oftea necessary lo caJcu1ate tbe latter at the receiver iD order lo e1iminate, or al least reduce, ita effect. Witb IDEM tbe primary field is elimioated by source cutoff. la botb cases the secondary fields of interest are smaJI in comparlson witb the primary ftelds. (b) 8;ot- Savart law; magnetic fiefd 01 a long wire. Original1y stated lor slatic magnetic fields, tbis law is valid also ror low-frequency ac, provided the linear distances involved are much less than the wavelengtb (§6.2.3). From Equation (3.4) and Figure 7.1 we bave

AH - (1 di)

(7.7)

la scaJar form this becomes

Tbus we bave a pair of potentials, one vector and tbe otber scalar, tbat in homogeneous media satisfy the same wave equation as tbe fields.

AH - lp ( sec 2 • sin( ,,/2 -lcos+d+/471'p

X f 1/471'r 2

- +)} d+/4,,'; sec2 + (7.10a)

Eleetromagnetie theory

345

'p

dH (oul orpaper)

p

mitter sourees in free space and over a conductive halC-space. The assumption of free space is generally valid because Ihe host rocks surrounding the conduclor often are highly resistive. Ward and Hohmann (1988) give an excellent theoretical treatment of electromagnetic fields in EM prospecting. Tbe discussion in Section 7.2.3 is based largely on their papero (b) Long straight horizontal wire. We take the y axis along the wire. The field is now given by Equation (7.10e) where ,; - xl + z2. and H is a vector perpendicular to p at the point P(x, y. z) in tbe direction given by the righthand rule (Fig. 7.1). The x and z components are

I

Figure 7.1. lIIusrraring Ihe Biot-Savarr law.

Inlegrating over a straighl wire, the result is H - (T/4"p)(sin~ - sin.1 )

H, - lx/2ft'; (7.1Od) (7.10b)

.1 --

If Ihe wire is elttrcmely long (infinite lengtb), ~ ,,/2, ff/2, and

H -1/2fTp

(7.lOe)

(e) Vector potential of a eurrent element. To get tbe potential A for a current element I di, we simplify Equation (7.3a) by neglecting all curren!s (including displacement currents) eltccpt tbose induced in tbe conductor. Thus, we set IU a1A/at 1 - O (tbis eliminates displacement currents-see discussion of cqs. (6.13b) and (6.14», and we also sea • - O. This reduces eq. (7.3a) to

There is also an electric component (Ward and Hohmann, 1988) given by (7.10e)

Ey - -jwp.IKo(jkp)/2fT

where Ko(jkp) is the modified Bessel function of the second kind oC order zero and k is the propagation constant given by

in free space C1 = O and

V X V X A - p.J

e being the velocity of light in free space. When kp

BUI V . A - O from Equation (7.5) when '" - O,

is small, Ko(jkp) "" -ln(jkp/2) (Abramowitz and Stegun, 1964: 375) and Equation (1.10e) reduces to

hence Equaton (A.2S) gives

Ey .. jwp.lln(jkp/2)/2'IT

This equation resembles Poisson's equation in gravily and magnetics. It has tbe foUowing solution for a current element I dI A-("/4,,.)

f/dv/r - (,,/4fT)~ldl/r

(7.11)

wherc tbe line integral (§A.3.4) is over a dosed path encircling the element di or its prolongation, A is tbe potential at P{x, y, z), and r is the distance from P lo di.

7.2.3. Fields in the Frequency Oomain (a) Ceneral. In this section we consider propagation of alteroating fields from several common trans-

(7.10f)

while Equation (7.10d) is unchanged. When the long-wire source lies on the ground (tbe usual case), Equations (7.1Od, e, f) are modified because tbe propagation constant becomes kl_ - jWP.C1 (Ward and Hohmann, 1988). For (kp) small, tbe components become H" = jkl/2.;2.", H, .. -(l/'lTx)ln(jkx/2)

Ey ..

O}

(7.10¡)

When the current is alteroatíng, l in Equations (7.10) should be replaced with [e- j ." but in practice the exponential factor is understood and nol written out (however it must be taken into account when time derivatives are involved). Also, we assume that the FDEM fields are H(w), E(w) in contrast to tbe


346 I

e

F

B

lb)

<11>

Figure 7.2. Geometrical parameter5 in volved in calculating the magnetic field o( a rectangular loop. (a) Calculating rhe field .lt an internal point; (b) Calcula/ing the field at an ex/ernal poin/.

TDEM fields H(I), E(I) to be considered later (§7.2.6). (e) Large reetangle. The geometry is shown in Figure 7.2. Inside the rectangle the field (whicb is normal to the paper) at P, produced by the currenl in segment AE, is (rom Equation (7.10b) witb 4>1 - O,

wbere Jil1 is tbe area of tbe rectangle witb diagonal 'l' Adding tbe fie1d H(AH),

H(AE) + H(AH) _ (1/4"'I Ji11) {( HP)2 + (EP)2} - (I/4")('I/JiI.) Adding tbe fields of tbe four subrectangles, we get !be total field 4

H == (I/491')

E (rn/Jiln)

(7.12a)

"-1

Wben P is outside tbe rectangle, we find

H' - (I/4,,)( ,{/JiI{ + rílJil{

considerably less than the distance to tbe Car side. It is important to note that the field in the neighborhood oí tbe long wire, or outside a large reclangle and close to one side, faUs off inversely as the distance, a relatively slow decrease in intensity. The preceding analysis is for a loop in free space. The case of a rectangle Iying on a bomogeneous half-space has not been solved up 10 tbe present (see also §7.2.6d). Both the long wire with and without the ends grounded and the large rectangle or square have been extensively used for generating EM primary fields in FD systems such as Turam, and also (or pulse transmission (UTEM, Newmont EMP, SIROTEM, etc.). Dimensions are generally several hundred meters. (d) Small horizontal circular coil (vertical magnetic dipole). By using tbe vector potcntial we can calcu-

late tbe field at a point in the neighborhood of the loop, not necessaríly in its plane or on tbe axis. The cylindrical coordinate system js shown in Figure 7.3. The cross section oC tbe winding on tbe loop is assumed to be very small with respect to its radius. Because tbe current js confined to a circular path there is only one component ol A, A •. Then dv a d4> dp dz, J. - l/dp tiz, and Equation (7.11) simplifies to

-r;¡JiI{ - rJ/JiI¡) (7.l2b)

Within the loop tbe field varíes about 40% over a rectangle concentric witb ABeD and one-quarter the arca, being a mínimum at the center. Outside the loop the field will be mainly determined by the near side oC tbe rectangle, provided tbe distance (rom it is

" f. cos 4>J.( p) dv

A-•

491'

V

R

,,1 ~2.. -

a cos 4> d4>

-

491' o (l +

Z2

+ a2

-

2apcos4»

1/2

347

E1ectromagnetic theory

O; inserting the time factor exp( - jwt), we have

E.

=

-aA./al

_ jwp.J8..PJ1pe- j "'/4.,,( p2 + z2)3 / 2 (7.14d)

--------~~~~

~-------+------y

However, its effect is small compared to the magnetic fields. AlI three components may also be expressed in spherical coordinales as H" H" and E. [Ihe last being identical lo E. in Eq. (7.14d»). Because H,2 + Hi ... Hp2 + H} and z = r cos (J, p == r sin O, we gel H, - 2Hz/(2cosO - sinO tan O) ~ 2 Hp /3 sinO

H, = H,/{ 2 cos (J cot

(J -

sin O)

=

Hp /3 cos (J

x

Thus, Figure 7.3. Field of a small circular eoil ar a poinr outside Ihe plane of Ihe loop.

If we assume that 1 + denominator, we obtain

z2

H, = I8..PJ1 cos O/2."r 3

(7.14e)

= 18..PJ1 sin O/4."r 3

(7.l4f)

E. - jwp.1 B..PJI sin O/4."r 2

(7.14g)

H,

» a2 and expand the

There are three limiting cases of interest in regard to the H fie1ds:

(i)

p == O, so O = O and the field is axial:

Hz == H, "" I8..PJ1/2."z3

(ü) z ... O, so

(J -

.,,/2 and the loop and field

are coplanar:

(7.13)

Hz = - H, = -IB~/4."p3 Now we can get the magnetic field using Equation (A.36) (see §A.4)

H _ yo

X

" ..

A • ~ {_ aA.

"

10 2

4(1 + z2)

az

1 + ~ a( pA.) I } P

p

ap

These are approximations because we took (p2 + the error, however, is less than 3% if either z or p is larger than 7a. Replacing the laUer in the original expressioo for A. and setting p - z - 0, we find tbe field at the eoil center to be

I

I)i,} (7.14a)

where 11' and 1, are unit vectors along tbe p and z axes. Tbus the magnetic field has two components: one in tbe p direction and the other in the z direc-

tion: H, - 3IB~pz/4.,,( 1 + z2)5 / 2 H,.18d(2z 2 - p2)/4,"(1 +

(7.14b) / Z2)5 2

(7.14i)

Z2) » 0 2 ;

( ili) 5/2 {3pzi p + (2z2 -

(7.14h)

(7.14c)

where Bd- "'0 2 , the area of the loop. Tbcre is also an electric field component E., obtained from Equation (7.2) with the potential <1> -

H, - 1/20

H, - O

(7.14j)

Clearly the small coil is equivalent to an oseillating magnetic dipole lying in the z axis at the origin with magnetic moment giveo by m = 1 B..PJI e- jw ,. Furthermore its shape is not significant, provided a < 0.14p (or 0.14z); for a square loop (H.>,_o .. 18d 4 "'V. It is also or interest that the z componcnts in Equations (7.14h) and (7.14i) resemble the Gauss A and B positions (§3.2.3) with m in Equation (3.lSc) replaeed with I8~/4." .• The dipole fie\d intensity, then, falls off with the inverse cube of the distance; compared to the longwire systems, the intensity decreases much raster. However, it should be kept in mind that both are approximations. The straight wire is assumed to be considerably longer than the perpendicular distance to the station at which the field is measured, whereas

348

Electromagnetic methods :

the closed-loop dimeDSions are considerably smaller than its distance from the field station. If tbe source loop, instead ol being in lree space, is lying on homogeneous ground, tbe tleld components in Equations (7.14b, C, d) become (Ward and Hohmann, 1988:211-2) in cyclindrical coordinates

H, - - (I8.Afk% /4'11'p){ JI (ljkp) KI ( Vkp) -Jz( Vkp) Kz( Vkp)} (7.14k) H, - (J B~/2'11'k2';) ( 9 - (9

-4k zPZ

+ 9jkp J'

_jk3~)e-Jk,}

(7.141)

..

E. - -(IB~/2'11'0"..){ 3 - (3 + 3jkp - k 2PZ) e- jkp }

(7.14m)

where the propagation constant (§7.2.3b) k - (¡,l"e - jw,,0)1/2 - (_jwl'0)1/2 over homogeneous ground, Jft(!jkp) ud K.. (!jkp) are modified Sessel functions ol tbe tlrst and second \dnds ol order 11 (Pipes and Harvill, 1970). For (kp) .. O, tbe aboye equations become

H,." -( 1B~kz/16'11'p)

(7.1.:n)

H," -(IB~/4wp3)

(7.140)

E• .. (IB~k2/4'11'1J¡')

(7.l4p)

Using reasonable values such as p - 100 m, o 0.01 S/m, we find tbat tbe magnitudes 01 all three components in Equations (7.14n, o, p) are smaller tban tbose in free space by a factor of aboul 10- 4 • The vertical magnetic dipole is widely used in ground systems. (e) Horizontal magnetic dipole.

This type of

source is commonly used in vertical-loop fixed. transmitter and broadside ground units (§7.4.2b, c) and in airborne systems. The results for propagation in free space are easily obtained. We take tbe coil in tbe xz plane witb its center at tbe origin; tbe expressions for the components are tben obtained by replacing z in Equations (7.14b, c, d) with y. When tbe coil is on homogeneous ground, the components are (Ward and Hohmann, 1988) H~ - 3IB~xy/4f1';

Hy

-

J8.Af(2y% - x 2)/4.",r

H, - -jwl'oIJIB~y/16f1PZ

(7.14q) (7.14r) (7.14s)

where Pz - x% + Z2. In a\l tbe preceding magnetie field sources we have also assumed only one turo of wire. If tbere are

Figure 7.4. Field o( a short vertical wire at a distant poinl.,

turns, tbe calcu1ated fields are increased by a factor of 11 in all cases.

11

(fJ Vertical straight wire (vertical electric dipole). One otber artificial source oí EM waves tbat has been employed in prospecting should be considered here. This is the high power VLF (very-Iowfrequency) transmission in the range 15 to 25 kHz, whieh is normally used lor air and marine navigalion. There are, ol course, many RF stations available as well, but tbe frequencies are considerably higher (500 kHz and up) and the power lower than the VLF sources, so that tbe range and depth of penetration are limited. The VLF antenna is effectively a grounded vertical wire, several hundred meters high. Consequent1y it is much shorter tban a transmission wavelength, which, lor a frequency of 20 kHz, is 15 Itm. Whereas the small loop is equivalent to a magnetie dipole, tbe short wire behaves as an dectrle dipole. There are several possible modes of radíalion from tbis type of antenna, but in the low-frequency range and at distances considerably greater than a wavelengtb, tbe propagation is a combination 01 ground wave and sky wave. The tormer travels over the earth's surface, whereas the sky wave is refracted and reftected by tbe ionized layers in tbe upper atmosphere (SO Itm and higher) to return to ground. At large distances from the antenna tbe VLF waves appear lo be propagated in tbe space between the spherieal retleeting shell formed by tbe earth sudace and tbe lower ionosphere. lbe attenuation is comparatively small in botb surfaces. From Figure 7.4 it is apparent lbat tbe electric dipole is quite like tbe magnetie dipole ir we interchange tbe E and H components 01 the wave, tbat is, tbere are two components ol electrie field, E, and E, in spherieal coordinates, and one magnetic com-

flectromagnet;c theory

349

ponent H. in the azimuth. TIte vector potential of a currenl elemenl 181 can be Iound from Equation (7.11); in spherical coordinales, A - p./lJl e- j .. ,ol,/4,"r

- p./81 e-¡"'·( cos 81, - sin 01,) /4,"r where the currenl flow in the dipole lengtb 81 is along the z axis, 1* - 1- ,/c ~ l - r(¡a)!/2, and c is the velocity of light - 3 X 108 mis. TIte scalar portion,
-/SlcosO( w/cr + 1/r2) e-}wr·/4,"EW.

Using Equations (7.1), (7.2), and (A.38), we find E - -V
aA/a,

- -( a~'/ar + iJA,/iJI)i, -( iJ~'/réJ8 + éJA./BI) 1,

(7.15a)

H=(V xA)/p.

- [íJ(,A,)/ar - íJA,/aO]I./p.r TItese expressions produce one magnelic and two electric components: H. - 181 sinOe-¡"'·( j",/er

+ 1/r2) /4,"' (7.1Sb)

E, -IB/cos8e-j ..,· x(l/er 2

-

j/",r 3 )/2wt

(7.l5c)

consider only the first term inside the brackets in Equalions (7.1Sb, d) and assume that E, .. E, ., O at great distance. TIte preceding development may be carried out Cor Equations (7.14c, r, g) (Slratton, 1941; Smythe, 19S0). Apart from tbe dipole moments and a phase sbifl oC ± 7T/2 (indicated by ±j; see §A. 7), for all lerms, Equations (7.14g) and (7.15b) are identical, and Equations (7.1Sc) and (7.1Sd) are the same as Equations (7.14e) and (7.14f) if the latter are multiplied by (l/"'E) and H and E interchanged. However, because the magnetic dipole is very rarely used Ior transmission beyond a few kilomelers, only the near-field term is significant. Because the amplitude oI VLF fields decreases only as l/r and the slalion outpUl power is large (100 to 1,000 kW), it is possible to detect these sources over continenlal distances, occasionally nearly half way around the world. Al greal distances from the source, E, is negligible and E would appear to be nearly vertical; at the ground-air boundary, however, there is a considerable horizontal componenl in the direction of propagation. The magnetic field lines are horizontal circ1es concentric about the antenna; al distances of several hundred kilometers tbis field is practically uniform over, say, a few square kilomelers, and is al rigll' angles to the station direction. Figure 7.5 compares the magnilude of primary fields from the various sources described in this section: VLF transmitter, long wire, square loop, and circular coi!. These were calculated from Equations (7.10b), (7.14), and a modification of Equation (7.1Sb), foIlowing, that allows for attenuation:

E, -IBlsin8e-j ..,·

x( j",/e2 r + 1/er 2

-

j/wr 3 )/4'ITt (7.15d)

(7.1Sh) TIte three components may be converted to cylindrical coordinates as in Section 7.2.3d. For example, using Equation (A.36) and neglecting lerms in 1/r2, 1/,3 (note that ,2 - ,; + z2 in Fig. 7.3), Ep" 3jwp.llJlzpe-j "'·/4'IT(p2 + z2)3/2

(7.15e)

E, .. O

(7.lSC)

H. _jw(p.e)1/2llJlpe-¡"'·/4'IT(p2 +

Z2)

(7.1Sg)

TItese formulas are more complete and more complex than those for the magnetic dipole, and they contain terms in l/r, 1/r 2 as well as 1/r 3• Clearly the VLF system is designed for long-distance transmission; the so-called radiation jields or far fields, varying as 1/r, are significant when the induelion and statie jields (neor jietds), varying as 1/r 2 and 1/r3 , have become negligible. Consequently, we

wbere A, r, and SI are in kilometers. The curves are drawn for the following parameters: 1. VLF transmitter power - 10 6 W, frequency - 20

kHz, antenna currenl - 5,000 A, and heigbl300 ft (100 m). 2. Long-wire power - 1,000 W, current - 3 A, and length ... 4,000 ft (1,200 m). 3. Square-loop power - 300 W, current - 3 A, seclion area - 36 ft l , (3.3 nr), and luros of wire 100. 4. Circular-loop power - 5 W, currenl - lOO mA, diameler - 3 fl (1 m), and lums 01 wire - 1,000. These values correspond roughly to (1) VLF, (2) Turam, (3) vertical-loop dip-angle, and (4) horizontal-loop systems used in EM field work.

f/ectromagnetic methods

350

10-'

Magnellc field (ampere-tums pe1'

meler) 10-'

10-

1

~....-r-nrTmrr--r---r-ñ.--r---rLn'-"""T""",,-1;n---r-''''''rc...,..~-'TT!

10

10'

OiSlance rrom souree

Figure 7.5. Comparison of magnetic fields produced by various sources.

7.2.4. Combinatlon of FO Fields (a) Ceneral. So far we have described the propagatiOD, atteDuation, and generation ol a1temating magnetic fie1ds. We have seen tba! such fields can be iDitiated by various current configurations and alten· uated more or less dependiDg on their lrequency and the conductivity (and permeability) ol the medium tbrough which they travel. In Section 6.2.3 it was aIso noted that the EM fie1d was shifted in pbase on encountering a rela· tively good conductor. In fact, tbis conductor be· comes the source of a secondary fie1d, which difl'ers in phase lrom the primary field, while having tbe same lrequency. Hence a suitable detector in the viciDity wil1 be energized by both tbe primary and secondary flelds simultaneously. The existencc of the secondary field, indieating the presencc oC a subsur· face conductor, may be established with respect lo the primary field by a change ol amplitude and/or phase in tbe normal delector signal. Some EM 5yS· tems measure both quantities; sorne respond to one or the other. (b) Amplitude and phase relations. The character of the secondary magnetic field is best illustrated by a consideration of the coupling between ac circuits. We assume a trio 01 coils having inductance and resistance and neg.ligible capacitance; the first is the primary source, the second is equivalent to tbe con·

1" ...-_11,.. kn -_...¡

2 Fi8ure 7.6. Electric-circuit analogy for EM system.

ductor and tbe third is tbe detector (Fig. 7.6). The

p~ EM field at a poin! n~ar the ~n~uctor (coi1

2), resulting from a current " coil, is given by

ftOW1ng 10

the !irst

H, - Ki, - KI, sin/llt where K depends on tbe geometry oC the system, the area and number 01 tums of tbe primary coil, ud attenuation ol the wave. As a resuh of this field, coil 2 has an emf induced in it tbat lags behind tbe primary field by ,,/2; thus,

di, e - - M - - -/IlMI eos/llt • dt ' - /IlMI,sin(/Ilt - ,,/2)

... -j/llMH,/K

flectromagnetic theory

351

Figure 7.7. Vector diagram showing phase shift between H, and Hp .

(§A.7) where M - Mrc - mutual inductance (see §7.2.5) between coils 1 and 2. TIten the current ftowing in coi! 2 will be i. -

e.lz,· e./( r. + jwL.)

where z, - (r, + jwL,) is the effective impedance oC the conductor oC resistance r., and inductance L •. The secondary field near the detector (coi! 3) as a result oC this current will be -K'jwMHp ' K ( + jwL.)

H ... K'i .. ,

The phase difference between primary and secondary fields is

---'---~

r.

where tan q. - wL.I r.. The lag in phase oC '/T12 is due to the inductive coupling between coils 1 and 2, whereas the additional phase lag q. is determined by the properties of tbe conductor as an e1ectrical circui t. Tha t is,

-K'MHp(jwr. + w2L.}

H. ~ K'I,sin{w/- (w/2 +
K( r.1 + w L;) 2

-

-K'MHp ( Q2 + jQ) KL.( 1 + Q2)

= -

(7.l6a)

where K' is a constant similar to K and Q - wL.lr. is the figure 01 merito TIte primary field at the detector coi! will be Hp' - K"i p - K"lp sinwt - K"HpIK

where K" is similar to K and K'. Thus the relative magnitude oC the fie1ds at the detector is H.

H'p

¡

K"i p

I

K'M { Q4 K"L, ( 1 + Q2)2

---

The phase sroCt is most c1early illustrated by the vector diagram in Figure 7.7. (In this diagram tbe magnitude of H. with respect to Hp is greatly exaggerated.) The resultant oC Hp and H, is H,. From tros diagram and Equation (7.17), it can be seen that when we have a very good conductor, Q - wL,lr, -+ 00 and <1> -+ '/T/2. In this case, the pbase of the secondary field is practically 180° ('/T) behind the primary field. For a very poor conductor wL.lr. -+ O and <1> -+ O; tbe secondary field lags '"/2 behind the primary. Generally H, is somewbere between w/2 and w (90° and 180°) out oC phase with

H,.

K '·1,

=--

-

K' T, cos( wl - <1»)

K'M

1

K"L,

(1 + 1IQ2)1!2

(7.16b)

Because the ratio K' MI K" L. is generally very small, the ratio H.I H; is small, regardless oC the value oC Q.

The component of H, 180 0 out oC phase with Hp is H. sin q., whereas the component 90° out oC phase is H. cos <1». In EM parlance, tbe 180 0 out-of-phase Craction oC H. is called the real or in-phase component. The 90 0 out-of-phase fraction oC H, is called the imaginary, out-phase. or quadrature component. These terms originated in ac circuit theory and, in fact, there is nothing imaginary about the quadrature component. From Figure 7.7 we get the important relation [see Eq. (A.47a») (7.18)

Eleetromagnetie methods

352 (e) Elliptie polarization. 1be detector in an EM fte1d system, generally a sma1l coi1 with many tums of fine wire, measures the secondary fteld procluced by a subsurface conductor, in the presence of the primary fteld. Consequently, the detected signal is a c:ombiDatioo or the primary and ooe or more secOlldary ftelds. In general the combination is a magnetic fte1d that is e1Iiptically polarized. From the previous sectiOll we can write

H, - A sin

r.I'

and

H, - B cos(

r.I' - .)

where A and B are fuDctions of the geometry of the transmitter, conductor and detector. Because

cos(

r.I' - .) - ces 111' ces. + sin 111' sin • - (1 -

H;/A

2t'1 cos.

Consequently the superposition of ftelds produces a single field that is elliptica1ly polarized, the vector being finite at all times [altbougb H, and H, become uro at 1111 - nfl and (2n + 1)"./2, respectively) and rotaling in space with contmuous amplitude change. Its extremity sweeps out an ellipse. This ellipse may lie in any space plane, althougb the plane will normally be only sligbtly tilted off horizontal or vertical. This is because the major axis 01 the ellipse is determined by H, - because jt js usually much larger than H. - and tbe primary field is normally either horizontal or vertical in EM systems. 1bere are two special cases of Equatioo (7.19) of considerable importance. Figure 7.7 is agaín helpfu1 in visualizing tbese situations. (i) • - "./2. Equation (7.19) tben reduces to

- O or (-H,A - -H.)2 B

+ H,sin./A -H,/B we gel

BR, - AH .- O

wbich is a straigbt line tbrougb tbe origin of tbe coordinates, having a slope + B / A. lbis case corresponds to a very good conductor, because • - tan- 1 r.lL,/r, - "./2

that is, or, bccause tan. -

00,

r,-O (7.19)

Tbis equatiOll is 01 the lorm Lz2 -

2Mxz + Nx 2

-

The ellipsc of polarization has collapsed into a straigbt line. (ü) • - O. The ellipse equation simplifiea to

1

wbich is the equatiOll 01 an ellipsc. We bave made two simplilying assumptiODS in obtaining the cquatiOD. The fint is that H, and H, are orthogOllal in space, wbich is not generally true. However, iI the angle between H, and H, js ex .. fIf2, these vectOR may be resolved in two orthogoDal components, say

H, - H,

+ H, ces ex and H" - H, sin ex

in whicb case the expression for H, and H" is more complicated and has constant terma, but is stil1 the equatiOll 01 an ellipse. 1he second assumption was that H, js due to the current in onIy ODe conductor. 1his is not necessarily the case; however, a combination 01 vectors of diflerent amplitudes, directions, and phases, resulting from currents in severa! conductors, can be resolved into a single resultant for H•.

which signifies a poor conductor because r, ::1> IIIL. when • - O. In tbe unlikely event tbat A - B as we1l, tbe combination 01 H, and H. results in circular polarization. Obviously a detector coil can always be oriented so tbat it líes in tbe plane 01 polarization, when a true null signal would be obtained. Some of the early EM metbods were based 00 tbis fact; the djp and azimutb oC the polarization ellipse and ita major and minor axes were measured. On tbe otber hand, il tbe detector coil is rotated about its vertical or horizontal diameter, it will not always be possible to find a perfect null position, because tbe plane 01 tbe coil will not, in general, coincide witb tbe plane ol tbe ellipse. There will, however, be a minimum signal at one coil orientation.

Electromagnetic theory

7.2.5. Mutual Indudance (a) Ceneral theory. lt was noted in tbe discussion of phase shift that the inductive coupling between electrical circW ts is proportional to the coefficien t of mutual inductance M. This parameter can be used to some effect in determining the signal amplitude at the receiver due to both the transmitter and conductor. It has already been employed to estímate the current induced in the conductor as the result of the primary fteld. If we can simulate the transmitter and receiver coils and the conductor by simple electric circuits, it may be possible to ca1culate the mutual inductances that coupte them. Consider the coil system iIIustrated in Figure 7.6, in which the mutual inductances between transnUtter and conductor, conductor and receiver, and transmitter and receiver are, respectively, M TC , Melt , and M rR . It was shown previously (§7.2.4b) that the current i, induced in the conductor by the transmitter is related to the transmitter current by the expression

where Q - wL,/r, was a figure of merit for the conductor circuit. Current i., in turn, will induce an emf in tbe receiver coil given by

353 ter loop inductance, and Lit is the receiver loop inductance. Then we can write Equation (7.20a) in the form

Although this eliminates L, in the first part oC tbe expression, it does not simplify the first ratio much because the k values, like the M values, involve complicated geometry of the system. Equation (7.20b) does indieate, however, tbat this ratio, sometimes called tbe coupling parameter, is usually a very small quantity because kTIt witl tend to be much larger than the two coefficients in tbe numerator. That is to say, the transmitter and receiver are coupled through air, which means the auenuation is practically zero. In sorne FDEM field layouts, tbe source and detector coils are purposely oriented to reduce the direct coupling, whereas in others the decoupling is accomplished by electrical means. In any case, the mutual inductances between the various components within the range 01 the magnetic field are a controlling factor in EM systems. Consequently il would be useful lo determine M for simple geometrical configurations that simulate field situations, as an aid in interpretation. The mutual inductance M 12 between two circuits 1 and 2 is defined as the total flux ~12 through. circuit 1, produced by unit currenl in circuit 2. Thus,

At tbe same time the primary fie1d induces an emf in the receiver

Because the secondary or anomaJous field is mea-

where Sl is any sudace terminating on circuit el' and the last result came from Stokes' tbeorem [Eq. (A.29c)). From Equation (7.11) we have

sured in the presence 01 the primary fteld, we have ",i 2 ~

A ·4", 2

Mutual inductance may also be written in terms of the coupled seJf-inductances:

d(2 -r

This gives the general Neuma,.n formula for mutual inductance:

Mclt - k clt ( L. Lit) 1/2 MTC - k rdL,L r )l/2

cosl - - '" ~~ --dl¡d(2 4", r

(7.21a)

M T11 - k rlt ( LrLIt) 1/2

wbere kclt is the coupling coefficient between conductor and receiver and SO lorth, LT is the transmit-

where dll , dll are elements of lengtb in circuits 1 and 2, r is tbe distance between dl1 and d12 , and I is tbe angle between dl1 and d12 •

354

Efectromasnetic methods (,,)

(b)

I

-....,ff----t -~ I

I I

I I

t

I T -I I

I I

(e)

(d)

Figure 7.8. Ca(culating mutual inductance o( various geometrical figures. (a) Two parallel straight Unes. (b) Coaxial eire/es. (e) Coplanar cire/es. (d) C;rc/e and long straight wire.

In many cases it is necessary to integrate numerically to get a particular answer from this general formula. Howevcr, several simple cireuits can be worked out exactly. These are illustrated in Figure 7.8 and the formulas are given in the following text. Units are microhenrys and meters. (i) Two parallel wires 01 equal length. Let the length be ( and the distance apart s. Then,

M-

O.U[In{ (/.1' + (1 + (2/s2)112} -(1 + .1'2/(2)112 + S/(]

(7.21b)

When (/.1' > 1, this can be modified to give

(üi) Two coplanar circles. When r» a, b,

M ... -0.1'11'a 2wb2/r 3

..

-0.1JJ1d1/r 3

..

-a 2 b2/r' (7.2ld)

Again, more complicated arrangcments of the cireles are dealt with in Grover. (iv) Circle and long straight wire. Let a long straight wire intersect at right angles the extcnsion of a dianteter of the eircle oC radius a. If the plane 01 the circle mues an acute angle a with the plane through the dianteter and the long wire, and iC s is the distance between the wire and the center of the cirete, then

M-

4w X lO-'{ s see a

- (.1'2 see 2 a _ a 2)112) (7.2le)

and when s/ a
MMore complicated forms of straight conductors may be found in Grover (1962). (ü) Two coaxial circfes. M is a funetion of a, b, and s, the radü and scparation, which varies with a paranteter k, given by

M - 0.2f1'a 2f1'b 2/s' - 0.2JJ1d1/s' .. 2a 2 b2/s'

- --sseca

(7.2lf)

(b) Self-inductance. Values oC L for the straight wire and circle are given by

Lw - O.U[tn(U/p) - 0.75] Le" 4"

which is found in tables (Grover, 1962). When s
sseca

X 1O-'a[tn(8a/p) -

(7.22a) 2] (7.22b)

where p is the wire radius, and (, a are as sbown in Figure 7.8. Self-inductance for several regular figures may be written

L - O.21.[ln( 4t./p) -

xl

(7.22c)

(7.2le) JJI, 91 being areas of the cireles.

where 1, is the perimeter oC the figure and X is a constant relatcd to the shape; generally X < 3.

355


In a1l these formulas the values of M are inereased by NI N2 and L by N 2 iC these are the number of tums on the various eireuits. Although M and L are easily determined Cor the regular figures of the transmitter and receiver antennae, it is a diffieult problem to simulate the conductor. Beeause we normally do not know the eurrent-tlow eross seetion, it is neeessary lo oversimpliCy the equivalenl cireuit. (e) Numerical example. To ilIuslrate the magnitu de oC the coupling factor, (MCR Mrc )/( M TR L,), in Equation (7.20a), eonsider tbe case oC a horizontalloop system (§7.4.3c) straddling a long, thin vertical eonducting sheet that outcrops at the surface as in Figure 7.9. We assume that the transrnitter and reeeiver coils are identieal (eross section - A), the distance I between their centers being less than t, the length oC the sheet, and that the ratio t/ p .. 2,500. The principal effect of the sheet is due lo its upper edge; hence to a firsl approximation we can consider tbe sheet as a horizontal wire of length t at the surface. Using Equations (7.21d, f), and (7.22a), we gel for the coupling factor in Equation (7.20a)

- (O'~~~r( O.:~l ) x( o.u{ln(2t~p) _

Figure 7. 9. Coupling factor of horizontal· loop system over a long vertical sheet conductor.

When Q is very small, both real and imaginary parts 01 the Cunction are very small. The ratio of secondary to primary response in the receiver will be

This is the case of a poor conductor. As O ¡ncreases, the imaginary part increases at a Caster rate at first and its magnitude is larger than the real Craction until Q - 1, when they are both equal to 0.5. Beyond tbis point the imaginary part decreases until, at large values oC O, it is again zero. Meanwbile, the value oC A incceases to an upper limit oC unity when Q is large, or

3/4} )

.. 1O-4( lit) < 10- 4 Thus the signal response has been reduced by the factor 10 4 or more. (d) Conductor response. Retuming to Equation (7.20b), the second factor on the right-hand side depends only on the conductor and the lrequency (because Q - ",L,/r,). In this situation Q is known as the response parameter of the conductor, whereas tbe complex ratio (Q2 + jQ)/(l + Q2) is called Ihe response function or induction number. Plotting the response function against Q, we get Iwo curves Cor the real and imaginary parts oC the Cunction:

and

wbieh is the maximum value for a very good conductor. When the value oC Q is quite small the phase angle of Ibis funclion is 'fT/2; when Q - 1, it is 3'fT/4 after which it inereases to '1T for a very good conductor, thal ¡s, the secondary signal is opposed to the primary. In the range O :;; Q :;; 1 the imaginary or quadrature component is larger than the real component, whereas from 1 :;; Q :;; IX) the reverse is true. Thus the ratio of in-phase to quadrature components is somewhat diagnostic of the conductor. lt is also clear that if one measures only the imaginary component in an EM system, a very good conductor will give a very poor response.

7.2.6. Fields in the Time Domain where A and B are real. This plot is shown in Figure

7.10. This example, 01 course, is oversimplified because it represents a wire loop. However, more realistic models of a sphere, !hin sheet, or halC-space are quite similar.

(a) General. The time-domain EM transmitter generates repetitive signals ol a transient or pulse character in various forms: half sine-wave, step, ramp functions, and so Corth. Al\ of these have a broad frequency spectrum that results in a secondary fie1d time-decay curve beginning immediately following

356

Electromagnetic methods RaJand

1....11&.,. pulloI

0-. ;::: f1"

14-I

f1" + JQ I + f1" - A +JII

Rapo_ IIIncllon _

+ f1"

and Q

11-I

+ f1"

Response perametcr, Q

F¡Bure 7.10. Response (unetion of

.óI

conductor in

.óln

ae field. (After Grant and West,

1965).

the transmitter culoff aud in which thc frequcncy decreases witb time. Material for Section 7.2.6 is talten, to a great extent, from Ward and Hohmann (1988) and Irom the c1assic papen 01 Wait (1951&, c; 1960a; '1971). 11 is interesting tbat the theoretica1 work was done so long before tbe serious devclopment 01 TDEM. ID Sec:tion 7.2.3 we denoted FDEM fields by H and E; in this section we use h and t for TDEM ftelds.

Prom here 00 we shall oeglect displacement currents because we are considering propagation in a conducting medium; tbis eliminates terms in e in all the equations aboYe, producing a diffusion equation as discussed in Section 6.2.3. Then a solution lor Equation (7.24a) is (Stratton, 1941, Section 8.3)

Development in the time domain ana1ogous lo that in Scction 7.2.3 for the frequency domaiD is best accomplished by using Laplace transforms (§A.l2) which are well suited to discussion of transient fields. Taking Laplace translorms ol EquatioDS (6.3) and (6.4), and using Equation (A.78a) with n - 1, we obtaiD

where the integration is pedormed over a volumc V containing the source of current, whereas '!fes) is determined at a point at a distance r outside it. The source is a step function given by I(t) - lu(t) [Equation (A.79»). From Equation (A.80) we have lu(,) ... l/s. Having found 11(S) from Equation (7.24b), we find e(s), h(s) from EquatiODS (7.25), then transform back to the time domain to get e(t) and h(t) for a step input. A simplifed version of the above approach is given by Ward and Hohmann (1988); they consider the PD field relatioDS as Pourier transforms, then translate these into Laplace transCorms 01 the ID response lo a step input. This method will be discussed in Section 7.2.6e.

(b) Method of TD analysis.

v V X

e(s) - -,,,,b(s) h(s) - (o + u)e(s), X

(7.23a) (7.23b)

wbere e(s) ... e(t), and so tortb. Gencrally, potential

functions such as those discussed in Sec:tion 7.2.1 are used. If we use the Hertz vector potential, we write for Equation (7.9) (Wait, 1951a), { V

2

-

("u 2 + "os) } 1f( s) - - j( s) /( a + es) (7.24a)

Equations (7.2) and (7.8) give e(s) whereas h(s) is

given by Equatioos (7.1) aud (7.8); the results are e( ,) - V (V . '!r( s)} - ("OS + "u 2) '!f( , } (7.25a)

h(s) - (o + u)V X .(,)

(7.25b)

'!f(') - (1/4".47)

J"j( s) [exp{ - r( "as )1/2} Ir] dv (7.24b)

(e) Long straight horizontal wire. Ward and Hohmann (1988) give relatioDS for the TDEM field for tbis source in free space. When the wire is aloag the y axis,

ey - - ¡Solt-,lti'/4".t h _Ie-,lti'(zl - xk)/2trpl

(7.26a) (7.26b)

ah/at - 18 2e-,1ti'(zi - xlt)/2".t (7.26c)

357


where 8 - (1'00/41)1/2, ,; - x 2 + z2, and 1 is the decay time of the transient aCter current shutoff. (Tbe time derivative oC h is given here because it is Crequently the measured parameter in ro surveys.) Tbe x and z components of h and ah/ a, are easily found from Equations (7.26b, c). Strictly speaking, o - O so that the exponentials in EquatioDS (7.26) are unity. When tbe wire lies on homogeneous ground, tbe formulas are modified and we have

e, - l( 1 -

e-""')/fTOX 2

(7.27a)

h" - l{ 8 2 x 2 F( 8x) - 9x} /.,,)/2x h. -

-l{ 1 + 92x2( e-l'''' -

(7.27b)

is at the center oC a circular transmitter loop oC radius a similar to that used in the Sirotem coincident-loop equipment (§7.4.4.d) and in EM deptb sounding (§7.7.6). We have for tbe fteld at the center (Ward and Hohmann, 1988)

h.

=

(I/2a) { 3e-"Q'/1"8D

+ (1 - 3/202a 2 ) erf( ~a)} (7.28a)

ah./ar - -(I/l'ocra 3){3erf(Oa) _ ( 2:a) e-"Q'(3 + 28 2a 2 )}

(7.28b)

1)} /2'frx (7.27c)

ah,,/al -

l{ (1 +

where erf(8a) is the error Cunction (§A.12.3). At late times oC the transient response, for o .. O, lj9 2 x2) F(8x) - 1/8x} /.,,3/2X1 these expressions become (1.27d)

ah./al -l{ ~(-1)"+1n(9x)2"/(n + 1)!}/2fTXI

h. "" 1(l'ocr)3/2 a 2/ 30{ .,,(3)1/2 (1.28c)

ah./ar ... l( 1'00 )3/2 a 2 /20( ",') 1/2 (7.28d)

(7.27e) where F(9x) is Dawson's integral (Abramowitz and Stegun, 1964). Retaining only the first term in the series expansions of EquatioDS (7.27d, e), the expressions for the time derivatives become

•

ah,,/at .. (l'oO)1/2 1/ 6( .",)3/2 8h./81 .. /Loolx/16"/ 2

ro fields for tbe long straigbt insulated wire lying on a conductive balf-space bave been discussed in severa1 reports (Wait, 1971; Kauahikaua, 1978; Oristaglio, 1982). Tbe second paper quoted discusses !he effect of grounding the eDds of the wire; obviously this introduces galvanic currents into tbe balfspace. According to Kauahlkaua, this atrects various field components: e, and h" are modified, h" e", and e. components are introduced by the grounded ends, whiJe onIy tbe h. field is entirely due to tbe insulated Jength. (d) Large rectangle.

..

This geometry, much used in

TDEM systems as well as in Turam, is discussed in Section 7.2.3c. Fundamentally it is similar to the magnetic dipole in Section 1.2.3d, apart from tbe dimensions of tbe loop relative to its distance from tbe detector. Nevertbeless tbe equations are so difficult to solve tbat no analytical solution is currently available for tbe general case 01 a Turam-type loop 00 homogeneous ground. However, a solution is available for tbe transient response wben tbe receiver

11'1 a well-known paper, Nabighian (1979) described tbe downward and outward diffusion from the dipole oC a transient EM field through a conducting half-space, the velocity and amplitud e decreasing with time very much like a smoke ring in airo Oristaglio (1982), using two parallel line sources, illustrated a similar effect in which tbe two current pattems move away from each llne at an angle of about 25°. Tbree SectiODS drawn for current densities at successive times in tbe ratio 1 : 2 : 4 are displayed in Figure 7.11. Nabighian and Oristaglio (1984) noled that at late decay times the response feU off as ,-15 in both systems, provided the rectangular source was oC reasonable size. The velocity V, radius R, and diffusion distance d (tbem éqúfv8:tent of fue skin deptb-see §6.2.3) of the current whorls are 'of considerable significance. They are given by tbe relations

' l

V - 2/( "1'00')

1/2

.. 1/1"9,

(1.29)

R - (4.37'/1'00 )1/2 _ 1.05/9

(1.30)

d - 2,,(21/1'00)1/2 - .;2.,,/8

(1.31)

Tbe diffusion distance locates the center oC a wborl in terms of the decay time and conductivity. At late times the eddy currents reach large distances from the source; lor a fixed time interval, tbe increase in d wiU ~~.!~!. th.~..~L~i~~~~i,Üb~L!'-t!ºr!s ,tM~ !()II$~~,t(),!rll.v.~I,,~, ,gi~~~~di~,t.~_c~,-~!!j.§•.~~,J.e.~@in longer in higb conductivity beds. ,.":".-", ... ,..,.-...",-.-.".,,,",---,

358


o I

20

40m

Daubll Linl Sau,,,

I

. . . . •• 1 , .l'dIlI {pIP1.1'1jiP¡ li' !"" .rl "'" '; ... ·:.'HiI· :':'1" ,'1 . ... -1 ; t': • . ,. ¡1 i . . ,-U:I.::. ."i l' ' , ' ' : ' . ·,¡,U· . ....; .. ~¡1'1 i! I :: . -:1'; i ¡. . 1 I I ~'" . " ~I"I'

~'I:

1_

~

1,

~1

~I

•

~rfl.:¡¡. l" l ' • i : : •. 1:: 1:

Idi,:,... " ¡: ¡ ¡ ¡ ¡ ii':'....

"." .: .,: ¡1~~, ., 1 1 '.1 , l'" -.¡I! II ¡: 11, ¡

., l.:

: I 1: 1'!¡~

. "lr!!l'il " "

1-"'' '",

~

"-,

..

...•..Ti '1 1//1• ¡:: I. =1' . '.1 l' 1I11' I/nl·IIT. ~! j .rijl! :4. ,1 !H!ll1il. 11 •••• , 11• ,

al'.: ·1,'·,11 ',' ',', -" ,1, ¡""T.' ~i j , ¡.::, !¡ji''¡I''l

........ 11 ' 1 1

/"'1'11'1

.1..1.

: :jI! 1I

. ¡! 11 !! . ':" j.1111 1'·11,

•

il'¡V . :1 .:~. ~l! !¡¡!l·... ~ ~ . . ~ ¡'¡¡,'¡IPi! d. El 11. .. 1o¡¡¡¡¡J.J. .. ! 1,! ª! ': i!~' . . . . ~1ril', ¡HIli ¡I ~:,:Ij:::

1

il =j 5: E! :1

I

~:,

'1'

'i:¡',Tj~ . , ...• ~iT'i:j'il ,¡¡(ll,iTj~i'~~~'r::¡iqi\li,i

1'11, 1,,, \,,1" ' !:¡!:l!1

"j·.II'·j·I·, il:'I:II .. ii!"I':,!': :¡I!i!!!!!

1',11'1. i ,,11 11 i11! ,.1I1 .. ': :',:1 " :ql' jJlpiiJi¡ .: I :.1::

i ' 5\ iiii!:ilil:'¡lill:i::i;II,lill i §j ¡¡j'¡jit'ljj'jll!'¡il':jj',li':', ':jj'¡¡ ':

:1

~

·I··II'·P·'II".I',·,:'¡,' " ,!I:illlll!I!I! ! !':i!':H':'!;!I':!!;!': 1!jj.lII!li!l ¡II!I .1

::¡ : I::¡:::: 1:: 11 : : : I I : : : : , 11 I :

1I

r

¡'i ¡ ,,,

I1 :

1IEl .j!ijlilll:! !!¡j¡¡j:!¡¡:¡¡¡H!ji ~ ¡ ; ¡ ¡,.; ¡¡.;: ¡ j.; l·; ¡ l·; i j.; i !.; i i ¡; i ¡ ¡ :,',L'jl:

i!

j.; j.! ~l¡·:!!·!H,!¡¡,:¡¡,~

I f :

!Hl·!¡¡,;i¡·; .;

:.,¡ :'. : :"

:

I

; 1:::::: 1: i i ji ¡ d ¡ :

'"''

:

:

:

¡

1:::::: : in:':i!': :

: : Li i L1! l.i ! l""""" • i¡ Jii,!!!.!;!J¡!.!!¡) U¡ljiiJli.l J ..i J1" i .1'"11 J 1i ; :: ::11:1::1:1:::1: 1il::III::: : 1: 1111 1I : :: :;:::::::::::::: :::::::::::, : P il·; Ji ; ~I j i J ! !J1!Ji ! =1'11'111111''''': :.. :: ,,1, ..... : l.ll! . .. , " . ' ,. '1' •• ' ,1"

11'1'11111: 1:1,.1" "

l'

ji!n!)!lH!}!!) lJtlJ¡!}¡¡H f,::

,

COIII", LIVIIs (lO-S ...,./",2) 8 - 3.D

e-

2,0

D - 1.0

E - 0,0

H - -3,0 G - -2,0 F - -1.0 (/1 )

FiBure 7,11. Plots of subsurface current density, Current flow 1 A, into page at ., out at O, Current shut-off time t Con tour intervills 10 - 5 Alm} in (a) ilnd (b), 10- 6 Al m} in (e), (Afte' OristaB/io, 1982), (a) Plol fo, Val' - 101 ni,

o.

(e) Small horizontal coil (vertical magnetic dipole),

'Ibere is no airbome ro source of this type in current use. As for ground systems, although Input uses a horizontal-loop transmitter, the shape is rougbly triangular and the loop is considerably larger than the conventional small horizontal loop, However, PEM and SIROTEM Slingram-type ground eqwpment use relatively small vertical magnetic dipotes (see §7.7.4b and Table 7.3). The ro field response in free space for this source can be written (Ward and Hohmann, 1988) h,. - (3/ BJIf"pz/4".r')( 1

+ 49 3r 3 /31") (7,32a)

h. - ( 1 BJIf"/4".r')( 2z 1 -

e. -

X{1-48

¡;) r ¡;/1"(2z1 -¡;)}

3 3

(7.32b)

(jwl'ol BJIf"p/4".r]) X {l - erf(9r)

+ 28re-,·,2/1"}

Ove, homogeneous ground the ID components can be obtained from Equations (7,14k, 1, m), For a homogeneous conducting medium, k - (-jWl'0)1/2 where l' and o are constant. Thus, at a fixed point (that is, p also constant), tbe rigllt hand sides of Equations (7.14k, t, m) are functioDS of jw, that is, they are Fourier transforms of the fie1d responses. Assuming the system is linear (§A.13) we see from the discussion of Equation (A.87a) that these expressions are transforms of the unit impulse responses. Moreover, Cor the Cunctions involved in these equa· tions, we can set the covergence factor o in Equation (A.75b) equaI lo zero, that is, a - jw. When we replace jw with a, the Founer transCorms become Laplace transCorms (§A.12), Writing o: - ("a)1/2p , we have jkp - j( - jw"a ) 1/2 P _ (jw) lfl a _ as lf2 ;

(7,32c)

k 2¡;

_ -a2a;

jk 3,i

_ _ a3a3/ 2

Substituting these relations in Equations (7.l4k, 1,

359

flectromagnetic theory

o I

20

4Dm I

•

;

o

.

Conlour Levels ( lO-s .mpl/m l , 8 - 1.1

e-

1.0

o-

0.9

E - 0.8

F - 0.7

G - 0.6

H - 0.5

X - -1.1 W - -10 V - -0.9 U - -0.8 T - -0.7 S - -0.8 A - -0.5 I - 0.4

J - 0.3

K - 0.2

L - 0.1

D - -04 P - -0.3 0- -0.2 N - -0.1 (!J)

Figure 7.11. (Continued) (b) tjl1JJ. = 2 X 101 m l

m). we gel the Laplace transforms of the urut Impulse responses. Dividing by s gives us the transforms of the unit step responses (Sheriff and Geldart, 1983:174-5) in Ihe form

h,(.s) - (l Bdl'a/47Tp) { IlOas 1/l)K 10aF2) -12( í as l/2 ) K2 ( í a sl/2 )}

h,(s) - -(IBd/2'ITI'a~) {9/s 2

-

(9/s 2

ficu1t; details are given in Ward and Hohmann (1988:216). The final results are

x (1¡08 2p2) -

12 ( íIPp2)}

(7.32d)

h, - -( J8d/47T,f){(9/2821)erf(8p)

+erfc(8p) - (48p + 9/8p)e-,'j /I"} (7.32e)

e. = - (J Bd/2 7Tap·){ 3 erf( 8p) -(28p/I")(3 + 2821)e-,2p2) (7.32r)

The last two are readily transformed to the time domain using Equations (A.84b) and (A.85a, b. e, d). Transformation of the first expression is more dif·

where erfc( 8p) = 1 - erf( 8p) (§A.12). To gel the time derivatives of the field responses, we multiply the Laplace transforms by s (see Eq. (A.78a) with n - 1, g(O +) = O), then transform to the time dornain. The results for the magnetic field

Efectromagnetic methods

360

,

o

,

20

40In

o

:: ' , . , : , :Al~11llI11!'r : ~lll'j -'

....... ~ l'

-

•

.T. ji

'1'I

: tllllp': '1

Jj • T"

11

'

,

:_i~iillljllj •f

!

DI1 jll)1 j: j'

11 )III) 1... J'1 1 I I J,-

ji' I . 111 JI' '-I'j ,lli,h' :¿.~. l j' .• l· \ . .: . . . , l I¿ , , , . ,11!1 . !.~ 11 . " I'}I, i ! ,'11 , , . ,1 I l. 11I 11 1 1I 1 1 I 1

Tíll·'" d i l' , ·l111HjTjTI' 1'1 r i % ' , • AL' . . 1 -. ¡, il'" .. ~m! l· . 1 !. l¡ 111 1 l' ,.! j I í!' . i11 1j . ¡¡1. í,' . Ii 11 1.1!!"1jll'l' 1r1i " i., . , , ..... :"I'lllil' ·.n I"lIPI" -¡ 111 1 PI ¡ l ' l' , 11' '.·lllr1h,· 'l'I'I¡!,'; <¡¡¡i'I,'" ill Ijl i i JI J, l · 1 ~ '",I"I V--: ' '.' , :¡"lflll!lllilli "1 111 ,': 111111'" -~!l! ¡jlli í I li_!l--~ •

--.. •

I

U¡'

l

o ••••

,

•

,

·,

JI

,

~ :¡ll l!'lrl'-PI'li lilPIF,H I!i¡thll~: : .lillll¡l

"1\1I 1"1.1. ' 1'1i 1'" .. I¡ ¡lli _ .. ¡.¡ \I 1I1 a ~ 1: : 111 . _..•~ ¡¡¡¡¡¡Umm '· . . . TI"I'1 i"jil"j _.,~

- .. , 7"j1 1i !lllll '.1 l', , . . . , . . , ,. 'Till¡I,'!

~

-

~ :li~-~~-_:

": 11'1111 11 ' II 11l" 1': 1•

: : : :">I~ijL!)i1Hi.! ¡)¡jl

; , IJIIJlWI",iiTW:"i!'111 JIIJIi.!II!!i! ¡Jli! 1111111 !!III I If IIlljlllllll:ll!! l'lli

~lI::IIIIHlltr"

'--~!!l!_l--~--'

3,0

::

l'

::

1 ' ~~¡~¡¡)l1)l¡)¡P¡I)l1) ÜU~l¡~: III I

·I·II·III"!·"·I\I·I·"· e-

.

: lo 1'1' . 1'1 ,f, , " . ~!ljl'I'I:I'i'i!I!'llil!~"~'I~'fi'l!'I! 111 : , . ~1 111 ¡ i) .! I':!'; !H i \1'1 1'.1 ,'1" i' i lll 11'ill¡l . . ¡i lI·I.!·I '.: 1 , 11111'1' 11 1 111..1. I )11' 11I 11' -

•

~. !1 :::.'1.:1.':::: 1111 'II·II\!'I\ 1 :1 11 11 1 : l.,'11.:dd:rl.::.' :1 1: 11 "'11: I 1 Con'.r LIYIfI (10'"

5

. 1'1 i 11 ft ' . , , . . . . . :

~ 'll lh' ~.

.• .•

11 ::.1.

B - 4.0

I

-

• ~ =

"'' ' 111, D - 2.0

E - 1.0

J - -4.0 I - -3.0 H - -2 n G - -1.0 (t")

Figure 7.". (Continued) (e) t/a". - 4 X

are (Ward and Hobmann, 1988)

ah,Jat - (13#8 2/2"pt) e-,2h2 X {.( 1 + 8 2",)

-(2

loU82",)

+ 8 2", + 4/8 2",) 1108 2",)} (7.32g)

ah,/al. -(IB.Af/2,,#,o~){gerf(8p) -(28p/y'II')(9 +

6,2'" + 494p")e-,2~)

(7.32h)

At late time, EquatioDS (7.32d, e, g, h) become

7al m2.

Figure 7.12 illustrates theoretical responses for h" and h, and their time derivatives for thc vertical magoetic dipole. TIte decay amplitude is the value at a poiot 100 m from the transmitter over a 100 Om homogeneous earth. TItus the curves show maximum values of h and ah/a, at the surface lor the circular currents or "smoke riogs" (Nabighian, 1979) as they diffuse during the decay cycle (Fig, 7.11). Note also that the curtents change sigo on 3 of the 4 plots, following a sharp CUsp or crossover. In Figure 7.12a the hp curve is positive througbout with a peak of _10- 7 A/m at about 10 #,5 after current cutoff. At later time h" decays at ,-2, the curve being at an angle of about 63 0 to the horizontal. TIte ah,,/ar curve changes sigo abruptly at -10 ¡U and subsequent1y falls off as ,-' at n°. Prom Figure 7.12b it is seen that the early-time maximum 01 h, (10- 7 #,A/m) persists to -10 #,5 where it changes sigo and decays as ,-3/2 at an angle 01 56 0 ; ah,/a, also is constant (-10 mA/m.s) througb early time to - 20 #,S after which it decays as ,- 5/2 at an angIe ol 68 0 (Oristaglio, 1982),

."

EM equipment

361 lO"

r_----------------, ------- ... , \

, \

-•• '" ..'1-..,.

10. 11

I

-•

-

-

10'" .....

-..

E

-.....

oC

oC

IO·lr

'-

~

-oC

"

oC

,, ...,

" ,.312

?S6.3 \

,

\

10'

time (ms)

1

,,

time (ms)

FiBure 7.12. rD Iransienl decay curves al a poinl100 m (rom a vertical maBnetic dipole on 100 Dm homoBeneous earth. (From Ward and Hohmann. 1988.) (a) h, and ah,lat. (b)

h, and ah,/ ato

(1) Horizontal magnetic dipole; vertical electric dipole. A1tbough Wait (1951a) has discussed tbe ID version oC the electrie dipole on homogeneous

VLF and AFMAG, make use of remote power sources and consequently do not need a transmitter.

ground. neither of these sources has becn developed Cor either airbome or ground TD surveys.

7.3.2. Power Sources

7.3. EM EQUIPMENT 7.3.1. General The measuring equipment for EM systems iDeludes a local ae power source operatiDg at one or several recurrence frequcDcies. transmitter and receiver coils (which may be one and tbe same iD sorne ID sets). receiver amplifier tuned to the transmitter Crequeney (FO units) or wide-band (- 40 kHz in TD reeeivers). and 10 indicator. such as headphones. meter. digital readout. or recorder. Sorne FO field sets require in addition an ac potentiometer (or phase and amplitude compensator) for comparison ol primary and secondary field sigoals. lbere is very little difference in these components whetber they are used for ground or airbome sets, except that the latter are more elaborate and bu1ky. Two fie1d metbods tbat properly come under the heading of EM, namely

Formerly the power supply for EM transmitters was normally eitber a gas-driven altemator or a small, light battery-powered oscillator witb a power amplifier having a low impedanee output. The choice between these depended on the type of field set, that is, whether the transmitter was only semiportable or continually moving. In the long-wire, the large hori7.ontal-loop. and the vertical-loop fixed-transmitter systems the larger power souree would be used. whereas for the various eompletely mobile transmitters, sueh as horl7.ontal-loop and vertical-loop broadside, the small unit was necessary. Actual output from the semiportable power supo plies varies between 250 and 2,500 W. The moving sources range from 1 to 10 W. Weight ol tbe equipo ment, ol course, inereases with tbe power output and may be anywhere from 2 lo lOO kg. In recent EM equipment power supplies have been modified to reduce weighl and me. For portable units the transmitter coil is an integral part of the

362 oscillator, eliminating fue low-efliciency power amplifier. High-power sets employ a type of .. flip-ftop" switching unit to feed the coil directIy for the same purpose. The transmitter output, sinusoidal in FD equipment, is in the lower audio range, 100 to 5,000 Hz. With mEM the periodic transient frequencies are low (3 to 300 Hz), consisting 01 balI-sine, squarewave, or ramp-type (sawtooth) pulses, al1 of alternating polarity. The off time may be cqual to or several times longer than the on time. One mEM unil, the UTEM system (West, Macnae, and Lamontagne, 1984), uses a triangular waveform with zero off time. Formerly some FD power sources were dual Irequency, one low and one relatively high, for exampie, 875 and 2,200, 1,000 and 5,000, and 400 and 2,200 Hz. Recent ground FDEM equipment bas a range from 111 to 3,555 Hz in steps 01 2 (approximately). Frequency range in one operatiog airbome system is 900 to 35,000 Hz. The advantage io using two or more frequencies lies in discriminating between shallow and deep conductors and/or an indication 01 conductivity of the anomaly and the surrounding medium.

7.3.3. Transmitter Loops In order to generate the desired electromagnetic field, the OUlput of the power source must energize the ground by passing a current through some wire system. In the semiportable field sets this is done by coupling power into a long straight wire grounded at each end, a large (usually a single tum) rectangle or square laid out on the ground, or a relatively large vertiealloop supported on a tripod or bung from a tcee. lo the first two arrangemeots, the dimensions are 0.5 km or more. The vertical loop, which may be single- or multiple-tum winding, may be triangular, square, or circular, and 01 necessity has an area oC onIy a few square meters. Some means must be provided for orienting this coil in any desired azimuth. The completely mobile FDEM transmitters often employ multiple-tum coils (100 tums or more) wound on insulating frames 01 1 m diameler or less. Sometimes the coil may be merely a single tum of heavy conductor; in this case, a matebing transformer may be neeessary in the source oulpu\. An alternative to this type of aireore coit, in whieh the wire is wound as a solenoid on a ferrite or other high-permeability core, is now used in many EM systems. Ir the winding is distributed proper1y, it is possible to generate a field equivalent to a eoil wound on a much larger frame, because the value of H increases with core permeability to compensate for the small


area enc1osed. Because the value of fA. for certain ferrites is about 1,000, the cross section can be greatly reduced. Many FD transmitter systems have a capacitance in series with the coit, the value being chosen to resonate approximately with the coit inductance at the source frequency. Because the coil has low resistance, this permits maximum current (within tbe limits of the power supply) to flow in fue coil.

7.3.4. Receiver Coils In FD systems, these are generally small enough to be entirely portable, that is, 3 ft (1 m) diameler or less, and have many tums of fine wire. Smaller coils with bigh-permeabilily cores are also used. The coi! may be shunted by an appropriate capacitance to give parallcl resonance at the source frequency. The resulting high impedance across tbe amplifier input acts as a bandpass filter lo enhance the signal-to-noise ratio. Receiver loops, and usually the portable transmitter loops as well, are electroslatically shielded to eliminate capacitive coupling between coil and ground and between coil and operator. The shielding is obtained by conductive paint or strip s of conductive foil over the winding; the shield, which is split around the perimeter to permit emission and receplion of the signal field, is then connected to the main circuit ground. Generally the receiver coil must be oriente4 in a certain direction relative to the detected field. In some ground systems tbis merely means that the loop is mainlained approximatcly horizontal or vertical. In otbers it is necessary to measure inclination and/or azimuth at each station. In airbome EM systems it is often a difficult problem to maintain a fixed orientation between transmitter and receiver coils. In some TDEM syslems the same coil may be employed both for lransmitting and receiving (obviously this is not possible with continuous transmission). In such cases the loop size may vary from a few meters to several hundred; hence the coil is not completely portable.

7.3.5. Receiver Amplifiers Amplifiers are of fairly standard designo The overall voltage gain is usually between 104 and 10'. One or more narrow bandpass filters, tuned to the sourcc frequency or frequencies, are incorporated in the FD amplifier. A network of tbis type, called the Twin-T, which uses only resistors and capacitors, is illus-

r

r

363

EM equipment

e,

e,

R,

Figure 7.13. Twin- T network for fM receivers. (,,21/(2C{R,R2 ) - 2/(C,C2Rl). Cenerally R2 ... 2R" Cl .. 2C, fa, convenience in design.

value, or they could be the percentage change in amplitude and phase required lo null tbe signal, tbis change being compared to a normal or background null. Because Ihe readings are continuous in airbome EM, a recorder oC sorne type is required. These were Cormerly oC the strip-chart type, but digital recording is now widely used as well. As in other geophysical methods. the computer revolution has led far beyond tbis to digitized EM systems, particularly airbome versions, in which the processing and presentation of data are automatic.

trated in Figure 7.13, This eircuil presents very high 7.3.7. Compensating Networks impedance at either end to a single (requenc~ la! Unless the receiver loop is purposely oriented to given by the formula in the legend. When the TWID- T minimize coupling of the primary wave in FD equipis eonneeted across an amptifier stage, the feedback ment, the secondary signal will be swamped by the is practieally zero at this frequeney and in.creases primary as we have seen from the numerical example rapidly either side of it. Sometimes band-reJect fil- in Section 7.2.5c. Because many EM systems, both ters, particularly for power tine Crequencies, are in- ground and airbome, use transm~tter-re.ceiver l.oop c1uded in both FD and TD receiver systems, geometry in which the coupling IS m8Xlmum, It IS The amplifier used in time-domain sets has a necessary to cancel the primary signa! by sorne other large bandwidth to handle the frequencies from be- means. This is aecomplished by introducing al the low the transíent recurrence rate up to 30 to 40 kHz receiver input an artificial signal of the same freal the high frequency limit. This introduces noise quency and amplitude but opposite in phase.. problems from power lines and their harmonics, Compensation of this sort would be sufficlent to VLF, and other manmade signals, as well as sCeric permit measurement of an amplitude, that is, the real noise (due mainly to lightning discharge; see §6,2.1 component, of the secondary fie1d. However, from and §7.4.2e) over the amplifier spectrum. The artifi- Section 7.2.4 and Figure 7.7, it is apparent that Hp cial noise sourees may be greatly reduced by suitable and H generally differ in phase as well as amplitude digital band-rejeet filters, whereas synchronous de- and tbat, furthermore, tbis phase sbift is diagnostic teetion and signal averaging (staeking) enhanees the of tbe conductor. Thus sorne provision foc changing signal-to-noise ratio by reducing sferics and other phase should also be included in the compensator. natural sources as well as the cultural interference. The primary-field cancellation is achieved by a Thus the wide-band ID receiver, a1though suscepti- signal derived from the transmitter current, for exble to noise not present in FD equipment, performs ample, by means of a small single-tum eoil on or quite as well as the latter (Maenae, Lamontagne, and near the transmitter loop. The amplitude and phase West, 1984; McCracken, Oristaglio, and Hohmann , shift may be adjusted for mínimum in a barren or 1986; Beeker and Cheng, 1988). background region. Relative amplitud e and phase changes caused by secondary fields at other locations may tben be measured direct1y, by using a syn7.3.6. Indicators chronous detector with digital readout. In many ground FDEM sets measurement is made Referring again to Figure 7.7 we see that a vector by nulling or at least reducing the receiver signal to a equal in amplitude and opposite in direction to H, mínimum - sometimes by ehanging the orientation will cancel tbe receiver signal. From the geometry of oC the receiver loop, sometimes by manipulation oC the vector triangle, when H.jHp « 1, it is easily e1eetrical components as in balancing an ae bridge. shown tbat The indieator is normally a set oC sensitive headphones on the output oC the amplifier. Occasionally a HZ ) H H, "" Hp ( 1 - H: sincjl + 2~; suitable meter may be used, but in the audio range tbere is no particular advantage in the visual indicatoro In any case, the significant parameters are noted and wben the minimum signal is obtained. These paramH. eters might be the dip or azimuth angle of the sin a '" - cos cjI Hp reeeiver loop in degrees or percent of a maximum

364


Tbus tbe required vector has approximately tbe same amplitude as H, and is sbifted in phase by (r - el). For a very good conductor,

H,. (H, - H.) and «. O wbereas lor a very poor one,

H,

«. -

H,

7.4. EM FlEtO SVSTEMS FOR GROUNO SURVEVS 7.4.1. General A great variety ol metbods is available for EM fieldwork. Tbese can be divided into ground and airborne systems and subdivided according to type, PO or TO, and actual measurement made, such as polarizatioo ellipse, intensity and phase components, and so oo. Tbere are in addition many techniques deve10ped 30 or 40 years ago tbat have gone out of style or have been superseded by improved versions; these win not be considered lO any extent. An enormous amount ol informatioo on state-of-the-art EM equipment may be found in tbe annual summaries by Peter Hood in tbe Canodian Mining Joumal since the late 19605 (Hood, 1967 and lollowing years).

7.4.2. Frequency-Oomain Systems; Oip-Angle Measurements (a) Cenera ,. Tbere are several field systems tbat measure, in effect, tbe direction 01 tbe combined primary and secondary ftelds at a receiver station. Whether tbey employ a natural or artificial source lor the primary field and whetber this source is fixed or movable, tbey all come under tbe heading oC dip-angle measurements, because tbe tilt 01 the detector coi] about a horizontal axis is recorded as tbe stalion reading. Furthermore, all tbe systems employ a primary field that is approximately horizontal. Tbe dip-angle systems remain very popuJar in EM work, in spite 01 their IimitatioDS, primarily because the equipment is inexpensive and simple lO aperate and the technique is rapid and works quite well over steeply dipping sheet-Iike conduclOrs, which are common geoJogical features. Tbe fixed-transmitter unit and AFMAG are also capable ol a reasonably large penetration depth. (b) Fixed vertical-loop transmitter. This is the oldest 01 the methods, developed in tbe 19205 and still used quite wideJy. Tbe transmitter coi], which may

be square, triangular, or circular, usualJy has a Cew hundred turns with effective area oC the order of 2 rrí'-. Tbe coil stands vertical and is free to rotate in tbe azimutb. The pOWer source usually delivers several hundred watts. Tbe receiver coil, consisting ol many tums of fine wire wound either on an open lrame SO cm in diameter or on a ferrite core, is connected to a tuned high-gain amplifier witb headphones, or occasionally a meter, in tbe output. Provision is made lor measuring tbe tilt angle of the coil. Figure 7.14 shows the operating procedure. Traverses are made by moving the receiver along liDes approximately normal to geologic stme. Stadon intervals are usualJy 15 to 60 m. For each receiver setup, the transmitter coi! is rotated to point al tbe receiver station (that is, its plane is in the transmitter-receiver liDe so that tbe primary field at tbe receiver is horizontal), either on a prearranged time schedule or on receipt ol a signal given by shouting or by walkie-talkie. Tbe receiver is tben tiJted about the T-R axis lor a minimum signal and the tilt angle is recorded. OperatioDS may be speeded up by havin¡ two receiver sets; in tbis event, tbe second operator must occupy a station on tbe same axis al !he same time as the first receiver (Fig. 7.14). It is apparent that in tbe absence of conduclors the minimum will be obtained witb the receiver coi] horizontal, because tbis represents zero-coupliDg geometry witb respeet to the transmitter coiJ. 1bis wouJd aIso be true when the receiver coil was directly OVer a rather narrow conductive zone, because the secondary field would have no vertical component. Characteristic profiles over tbis type ol conductor are shown in Figures 7.30 and 7.31a. Tbe tilt angle either side ol the conductor is such that the coiJ axis points toward tbe conductor untiJ the receiver has moved a considerable distance away lrom it. Range ol receiver operation depends mainly on the size ol the transmitter loop and power sourcc. In practice tbe maximum T-R separation may be 200 to 400 m. Tbere is also a mínimum separation ol about 60 to 120 m; at smaJler spacing it is difficult to obtain a minimum signal. Obviously there will be other situatioDS as well when the minimum wilJ be poorly deftned, because there is no arrangement for balancing out tbe quadrature component. Tbe profiles in Figure 7.30 contain considerable information about the conductor. Tbe crouOlJer poinr (tbat ¡s, tbe point where tbe dip angle changes sign) locates the top oC tbe body, the slape near thc crossover is an indication of its depth, as is tbe maximum dip angle, plus or minus. Tbe symmetry 01 the profilc is a c1ue to its dip, as can be seen in Figure 7.30.

365

EM field systems for groun d surveys Vertical loop lrammiu er pointing

at rectlVer stat!on

Rece,ver coil

tilted about T-R

/

aXIs

(/

¿-~----/ Figure 7.14. Dip-ang le sys/em, fixed transmi//er.

For reconnaissance and ground Collowup oC airbome EM, particularly where the strike is not known, the fixed-transmitter field procedure is modified. First the transmitter is set up roughly in the center oC the area 01 interest and pointed at successive receiver positions alang the perimeter of the area. Dip angles are recorded al, say, 50 m intervals in this Cashion. When a proper crossover (§7.7.3b) is Cound, the Iransmitter is moved to this station and dip angles measured on a traverse approximate1y across the ceoter oC the area with the Iransmitter loop lined up on each station. If a second crossover is loeated, the transmitter is moved lo this station and the original crossover checked. Usually this point will be changed somewhat Crom the original perimeter crossover, unless the first transmitter loeation was Cortuitously on 10p oC the conductor. When, as is often the case, more than one crossover has becn found during reconnaissance, several interchanges of the transmitter and receiver may be necessary to establish the strike. Having c1early defined the latter, detailed dip-angle or other EM surveys may be carried out on suitable lines. If multiple conductors are present, usually the sharpest crossover (that is, the steepest slope or largest maximum tilt angle) will be obtained when the receiver is on the conductor nearest to or directly be10w the transmitter, because the coupling is then a maxi-

mum. TIte transsimultamoved is and le portab mitter is compl~tely along ding proeee neously with the receiver, the two parallellines. Readings are taken at intervals or 15 to (e) Broadside (parallel-line) method.

60 m, with the transmitter coil pointed at the receiver ror each stalion reading. TIte receiver eoil, normally horizontal, is then rotated about the T-R (also written Tx-Rx ) axis to obtain a null. Tbe transmitter-receiver line is maintained approximately paralle1 to geologic strike where possible, the T-R spacing being usually 100 to 200 m. This arrangemenl is shown in Figure 7.15, and typical profiles are given in Figures 7.32 and 7.33. As in the fixed-transmitter method, two or more receivers can be used provided all are kept in line with the transmitter. The source power is inevitably lower than in the fixed-transmitter arrangement and is normally a battery-driven solid state osci1lator oC 1 to 10 W output. Comparing the profiles oC Figures 7.30 and 7.32, we see that the crossover is aboye the top of the conductor in both instances, whereas the slope oC tbe curve near the crossover is somewhat steeper in Figure 7.32. TIte maximum dip angle is mucb more clearly defined by the parallel-line layout, because, as might be expected, the dip angle becomes uro again a relatively short distance off the conductor axis. A modification oC this field metbod is oCten used in preliminary ground reconnaissance work. The transmitter and receiver are moved along the same traverse Une with the transDÚtter coil pointing al the receiver station 60 to 120 m away. Dip-angle measurements are recorded as described previously. The traverse lines are nol usually perpendicular to slrike, but rather at about 45°, because the purpose is merely to loeate the conductor and perhaps get an idea of its extent. One of tbe standa rd dip-angle (or other) EM surveys is then carried out in detail.

366

Electromagnetic methods R.

Second receiver lino

\

T

Transmiuer lino

\

\ \

\ \ \

\

~

Reteiver lino

Fi8ure 7.15. Díp-iJn8/e system, broiJdsíde orientatíon.

(d) 5hoot-back method. In very billy terrain il is difficult lO mainlain correet alignment of tbe transmilter and receiver coils, and, as a result, false dip angles are oflen obtained. The shoot-back method, developed by Crone Geopbysies, was intended lo overcome tbis problem. The coil conflguration resembles a modification of an early metbod of Mason (1927) [sec also Eve and Kcys, 1956: p. 176) ratber tban tbe present dip-angle sets. Thc fleld procedure is the ,ame as tbat described in tbe preceding tcxt for rcconnaissance with tbe portable transmitter. Howevcr, tbe shoot-back system requires a receiver and transmitter at each stalion; for this purpose tbe coi)s are convertible. The spacing is usualIy 50 lo 60 m and tbe axis, ratber than tbe plane, of tbe transmiltcr coi! is poioted toward the receiver station. Consider tbe situation shown schematically in Figure 7.161. Witb unít 1 transmitting, tbe axis of coil1 is directed toward coil2 but dipping 15° below horizontal. Coil 2 is tben rotated about a horizontal axis normal to tbe traverse line to get a minimum. Then a second reading is taken for tbe same station witb transmitter and receiver interchanged. Coil 2, now tbe transmitter, is oriented so tbat its axis is directed al coil 1, but inclined 15° above tbe horizontal, while coil 1 js tilted lor a minimum. In botb setups, tbe possibility of misalignment and of obtaining an incorrect dip angle are eliminated by tbe relative orientation 01 tbe lWo coils; tbe axis ol tbe transmitter coil, ratber tban its plane, determines the rotation of the receiver coil about an axis normal to, rather tban coaxial with, tbe T-R lineo In homogeneous ground the differeocc between tbe two titt angles will be zero. This will be true

regardless of the relative elevations of the two coils. However, witb a conductor present, tbe secondary fleld wil1 atrect tbe tilt angles at tbe two receiver positions in tbe opposile SeDse, as can be secn belter from the distorted field lines in Figure 7.16b. A profile obtained over a sheet-like conductor is also iIlustrated in Figure 7.16c. Normally tbe differencc between the two dip angles is plotted al tbe midpoint of tbe two coils. The equipment uses lWO frequencies, 480 and 1,800 Hz. The latter is used alone for reconnaissancc work. The profile in Figure 7.16c shows the resultant (a2 - al) positive over tbe conductor. A dipping sheet results in an asymmetric profile tbat is positive over tbe upper end and crosses zero lo a negalive maximum down dip. Flat-lying conductors produce a negalive anomaIy symmetric about the midpoint. (e) AFMAC method. The initials denote audiofrequency magnetic fields. Tbis is a natural-source dipangle metbod, introduced by Ward (1959b). The main origin oí the primary field is ligbtning discharge (sferies) associated witb worldwide tbunderslorm activity as in audiofrequency MTwork (16.2.1). There are otber minor sources of energy such as corpuscular radiation interaction with the earth's magnetic field and manmade noise. This EM energy is propagated between tbe eartb surfacc and tbe lower ionosphere as in a waveguide. The frequencies associated with AFMAG are in the ELF range, from 1 lo 1,000 Hz, with the best reception apparent1y between 100 and 500 Hz. Because the sferic sources are random, tbe signal is effectively noise witb seasonal, diumal, and shortperiod variations in intensity. Over tbe ELF range an

Unitl

Unit2

~

-t

Travcnelino lIS"

--

. ·r Tr.... T-R fiud spacin,

Ie

O~

+

~ Rec'r ~

I

Traverse lino

Roe'r

~ T

"'" ,'o ' •

.'~ ~ ~

Tram·r

30m

/'«.

ClJ: -

R¡j"_\

-

~.' .~ • /' AIfII!I'f

\.'~' ~7·

.. _ ., - O

T

fI.,

H

;¡;7t.......--

. , / Barmlground

"""---...

(a)

.' ."

(ii)

(í)

~~ Cond-~_ _o

,,-.,>0 (b)

pn:scnl

____

T

~~ R~. O ; " ."~' .

\ ~ I., ~. ..'-\

.~'" .

(e)

Figure 7.16, Crone shootbdck system. (After Grant and West, 1965). (a) Transmitter-reeeiver arrangcments, (i) and (ii) representin8 interehan8ed positions of the transmitter and receiver for successive measurements at the same station. (b) Operdtion in rugged terrdin. (e) Typieal profiles with T-R Spdcin8 oi 50 to 60 m.

368

Electromagnetic methods Sicnal

coil S

Plan

(rmi .. cores)

MN

Rererence ..,il R

Azimulh

anale

o

s + R

(b)

Noplive

P",ili..

Zero ti..

e.",so...

,. !777II

'

n-r" ~ I L

Figure 7.17. AFMAG system. (a) AFMAG equ;pment (sehematie) and measurement 01 azimuth. (b) Measurement 01 ti//. (e) Vector plot where az;muth i5 not in traverse /ine.

AFMAG record is quite similar to the telluric current record shown in Figure 6.10. Generally the vertical component is small compared to the horizontal, acept in the vicinity of a good conductor. Hence the AFMAG field may be detected by a titt-angle technique. The receiver, however, is modified from the conventional dip-angle detector because the random variations in primary field intensity malee it impossible to locate the minimum with a single coll. Two mutually perpendicular coils, wound on an insulating frame or ferrite core, are mounted on a stand that aIlows rotalion about vertical and horizontal axes. One oC the coils is first connected to the receiver amptifier and rotated about a vertical axis to find the rougb azimuth 01 the horizontal field (Fig. 7.17a). Tbis azimuth, oC course, is the direction oC the horizontal component and is often quite fuzzy and erralic. One oC the orthogonal coils supplies a reference signal in the tilt-angle measurement. Using ferritecore coils, as in the illustralion of Figure 7.17, this

reference coil is usually nearly horizontal and in the azimuth direction. The other (vertical) coil is now connccted to the amptifier along with the reference coil and the pair are tilted about a horizontal axis normal to the main azimuth to get a minimum. Posilive and negative tilt convention is illustrated. Measurements are generally made at two frequencies, 140 and 510 Hz, with two narrow-band filters in the amplifier. The field procedurc is otherwise quite similar to the fixed-transmitter method, with the transmitter considered to be at an infinite distance. Traverses are made at rigbt angles to gcologic strike where possible. If the AFMAG azimuth is Dot roughly along the traverse line, it is preferable to me asure the tilt angles in the azimuth direction. The resultant crossover profiJes may be plotted exactIy as in the fixed-transmitter method, or they may be plotted as vectors (Fig. 7.17c) ir the minimum IZimuth direction is distinctly different from that of the traverse line or if the azimuth varles appreciably over a sbort time intervalo In the plot ShOWD the length of each vector is proportional to the dip angle

EM field systems fo, gfOund surveys

and tbe direction is that oC tbe azimutb mínimum witb respeet to tbe traverse. The crossover is then indieated by the reversal ol tbe arrows. AFMAG has several real and potential advantages over tbe artificial source metbods. No transmitter is required. The frequency is comparatively low and bence tbe depth oC penetration is probably greater tban for a local source. Because the primary field is uniform, at least instantaneously, over the survey area, all tbe conduetors are energized uniformly. At times this may be a disadvantage, bowever, because it may empbasize large-scale, relatively poor conduetors at the expense ol smaller coneenlrated bodies. There are two specific disadvantages witb AFMAG. The first is the effecl of large random changes in lbe amplitude and direction of the inducing field, that produce corresponding variations in the signal strengtb as well as changes in anomaly shape and size. Tbe second is tbat the random ftuetuations in direction may make it very difficult to locate the azimutb oC the horizontal field. Recent work with more sophisticated equipment and controls (Labson et al., 1985) appears to have reduced or eliminated tbese limitations in AFMAG. They constructed new field sensors (coils) sensitive enough to make year-round measurements (tbe AFMAG signal is weak in winter and at high latitudes) and incorporated digital acquisition and processing lo provide results in the field, reducing noise by a remote relerence souree (Gamble, Goubau, and Clarke, 1979). These improvements produced relatively stable noise-Cree measurements oC tbe ratio of vertical-to-horizontal H-field components (tbe .. tipper" in MI work; see §6.2.8c). (f) VLF method. 1be use of VLF signals broadcast by certain marine and air navigation systems as sources Cor EM exploratian has becn mentioned in Secrlon 7.2.31. 1be main magnetic-field component is horizontal like the AFMAG signal and tbeoretica1ly is tangent to cireles concentric about tbe antenna masto Hence it is much less ereatic in direction than AFMAG. A worldwide network of high-power VLF stations was planned lor marine navigation. The sites are arranged so that at least two stations can be detected anywbere over the Earth's surlace. At present suitable transmissions lor EM prospectíng in North America are located at Cutler, ME, Anoapolis, MD, Boulder, CO, Seattle, WA, and Hawaii. 1be useful ranges are surprisingly large, because tbe Scattle slatíon is easily detected on tbe east coast 01 Canada However, tbe coverage is much less complete in the Eastem Hemispbere, wbere on1y three large transmitters - Rugby, England, North Cape, Australia, and Moscow (undependable) - are currently avail-

369 able. The reception is best in tbe moming, but adequate all day. The receiver for detecling VLF signals measures a tilt angle and a quadrature component by means oC two mutually perpendicular coils wound on ferrite cores. The coil whose axis is normally vertical is first held in a horizontal position and rotated in azimuth to find a minimum. This direction is in line with the transmitter station and is usually well defined. The same coil is next held vertically and tilted about a horizontal axis parallel to the direction of propagatíon. The second coil, whieh is rigidly mounted al right angles to the first and so is approximately horizontal initially, is similar to tbe reference coil in tbe AFMAG receiver. Its signal is shifted in phase by 90° and, connected in series with tbe vertical coil signal, is fed in to the receiver. The amplitude of this signa! is adjustable on the quadrature dial, whieb reads percent plus or minus. A clinometer on the instrument allows tilt angle measurement. By tilt and quadrature adjustments, a good mínimum is obtained. The receiver amplifier incorporates two plug-in units tuned to frequencies oC two VLF statíons that can be detected in tbe survey area (It is uselul to have extra units Cor otber stations available, in case a particular statíon either is not operatíng, or its signal is weak, or the station direction is such that tbe azimuth minimum is not roughly normal to the direction of the traverse.) Tbe mínimum signal indication is obtained on beadphones or from a smaD speaker (the transmítter carriers are audiomodulated). Tbe receiver is illustrated schematically in Figure 7.18a. An addition to the VLF instrument manufactured by Geonics (EM16), shown in Figure 7.18b, appeared about 1973. Known as the EM16R, it is mounted on the EM16 unít and coupled e1ectrically to it, while a pair of 5 m leads terminating in two high impedance electrodes pushed into the ground are connected to the R-unit box. Tbe orientation is c1arified in Figure 7.18b. Tbe combined unit, restíng on tbe ground, permits measurement of apparent resistivity p" of the subsurface and relative phase angle between the observed e1ectrlc and magnetic fields by adjusting the p" dial (identical to tbe quadrature dial in EM16 operation) and a pbase dial lor mínimum. The values 01 P. and ." obtained by delecting Ehor and H. (§7.2.3f) are essentiaDy equivalent to those in Equations (6.25), using an artificial source at higher frequency. This additional inlormation increases the usefulness ol tbe instrument considerably. Clearly the VLF tilt-angle system is similar to AFMAG, with the advantage that the primuy fie)d direction is fixed and the signal leve) lairly unilorm. The deptb of penetration is not too welJ establisbed,


370 111' ,hin and atlen',

z

/ / / remto COR

coils

VLF

ampIi. fier

~''It-----' Z-Z Recei,er coil detecu H.' X-X Quadrature
(a)

...

5. ELECTRODE

S.

o

ELECTRODE

01 .'...DIAL 11M" OUADRATURI)

PHAIE DIAL

0·-'0·

(b)

FiBure 7.18, VtF receivers. (a) Schematic. (b) Schemafic o( fhe fM16R unit.

bul seems lo be somewhal less than that of dip-angle units using local power. The field procedure and pro file plotting are identical with AFMAG. The equipment is small, light, and conveniently made, and readings can be taken rapidly. The faet that the source is at infinity provides the same advantages and disadvantages in energizing the conduetors in the survey area as described for AFMAG in the previous section. One drawback seems lo be that it is not always possible to use a transmitting station approximalely on geo· logic strike in the area, thus obtaining a primary field vector approximately across 5trike (that is, maximum coupllng). The high frequency of the source is aIso an inherent weakness. AIl the dip-angle methods have certain attractive Ccatures: simplicity, spced, and relatively low price. They have one common disadvantage as well: TIte distinction betwcen anomaly conductivity and depth is often difficult. Measurement at two frequencies should hc1p in this regard. However, the higher freo quency seems to enhance suríace reatures (conductive overburden, groundwater concentration, and the like) more than would be expected.

7.4.3. FD Systems for Phase-Component Measurements (a) General. AlI the ground EM sets discussed so lar record only a part 01 the available information. As we saw in Section 7.2.5d a measuremenl ol both in-phase and quadrature components or the secondary fic1d would provide us with some knowledge

ol the electrical propcrties of the conductor itself whereas the methods described so far are capable only of locating and outlining it. To record the additional data, it is necessary not only lo cancel most oí the primary field but to measure the phase as well as amplitude 01 the secondary field with respect to the primary. This is done with some form 01 compensating or ratiometer network. Two ground units 01 this type wiIl be described. (b) Turam method. TIte transmitter system consists of alto 2 kVA source operating at 220 or 660 Hz reeding a long grounded wire or a large rectangle as shown in Figure 7.19. The long-wire transmitter is seldom used now because it introduces terrain current-channellng effects and other complicatioDS (sce also §7.2.6c). Traverses are made normal lo the long dimension with a receiver unít consisting oC two identical coils spaced 15 to 60 m apart, joined by cable. Measurements oC amplilude ratio and phase dilo ference between the two coils are made at each slation (the midpoint 01 the two coils is reckoned as the station location). With DO conductor present the phase differencc will be zero, while the amplitude ratio e¡/e2 decreases with distance from the transmitter wire; multiplying the amplitude ratio at each station by d"jd1 • the ratio of the distances lo the far and near coils, one obtains a constant amplitude oC uníty and a constant ~~ oí uro lor all stations under these conditions. With a conductor near the receiver system, both parameters are changed - see Figures 7.37 and 7.38

EM field systems for ground surveys

/

371

..-

;'

,/

/' /

/

/

/'

/

/

/

/

I

/

/'

I

,/ ,/

/

/

/

I

,/

/ I

I

I W.COill I

/

/

Coil2

/

I Turam system

/ /

Fisure 1.19. Turam field layout.

in Section 7.7.3g. The amplitude ratio is plotted in values greater or less than unity and the phase in degrees plus or minus. The profile is typical oC a conductor of steep dip, its long axis roughly in line with the transmitter cable. Because the two receiver coils measure, in effect, the horizontal gradient of amplitude and phase of the vertical component ol the secondary field, the profiles are horizontal derivatives of those obtained with the compensator equipmento Sensitivity is about 0.5% for Ihe amplitude ratio, 0.2 0 in phase. Thus Turam provides Ihe extra information available when both real and imaginary components are measured, acbieving a good null balance in the process. An altemative mode of Turam operation has been described by Duckworth and Bays (1984) in wbich Ihe transmitter is rotated 90° to lie on the conductor, roughIy normal to its strike, rather than adjacenl to the conductor and parallel to its strike. The receiver system is then moved parallel to the transmitter-loop long axis, that is, across strike. The orientation is said 10 have several advantages over the original Turam layout: 1. a larger area oC operation for one setup, hence the

2. 3.

4. 5.

possibility oC reconnaissance as well as detail surveys; larger receiver coil spacing resulting in greater depth ol penetration; reduction of conductive hosl-rack and overburden effects beeause the teceiver traverses are parallel, rather tlÍan normal, lo the Iransmitter loop; consistenl indication of targel dip (§7.7.3g); conversion oC original readings lo reduced amplitude ratios and zero phase differences is unneees-

sary because they are already unity and zero, respectively, except over an anomaly. In tbis orientation, however, coupling of the primary field to the sheet conductor should be very weak compared to the standard layout. fe) Moving souree (horizontal-loop) me/hod.

Known also as Slingram and Ronka EM, tbis system, like so many otbers, was developed in Sweden and has been popular in North America since abouI 1958. The field layout is iIlustraled in Figure 7.20. Both transmitter and receiver are moved, a fixed spacing oC 100 to 1,200 ft (30 lo 360 m) between them being maintained by a cable. TIte transmitter is low power (1 to 10 W) and the transmitter coil is about the same size as the receiver. In sorne sets the coils are wound on insulating frames - 1 m in diameter; in otbers, lerrite-core coils are employed. The coils are coplanar and almosl always oriented to detect the vertical component, although this is not a necessary requirement. In at least one model, the conneeting cable is replaced by a radio link; but the cable serves the additional purpose, on reasonably level ground, of maintaining correet spacing, which is quite critical. Following procedures outlined in Section 7.3.7, alter obtaining primary-field compensation in a barren area, the in-phase and quadrature components expressed as percent of the seeondary field may be read off visual indicators. Sensitivity of both measurements is about 1 to 2%. Traverses are made perpendicular to strike where possible and the readings plotted lor the midpoint of the system. Typical protiles are shoWD in Figures

372


--------~

__~-~~===~-_-~~2~~\u25

TraJllmllter

---- T

Cable

~Compe.nsalor ,-IVU

R------

Figure 7.20. Horizontal'Ioop system.

7.36 aud 7.41 in Sections 7.7.3f aud 7.7.3i. As discussed later, the interpretation of auomalies with horizon.tal-loop (HLEM) systems is generally simpler thau Wlth other EM field sets. However, tbe chieC advautage is tbat tbe fixed relative positions oC the receiver aud transmitter maintain a constaut mutual indUCtaDce MTR [Eq. (7.2Id»). Thus tbe direction oC traverse is immaterial, tbat is, we cau interchauge tbe receiver aud trausmitter aud get the same reading at the same stalÍon. There are also some drawbacks to tbe horizontalloop unit. The deptb of penetration is inevitably limited by the portable low-power trausmitter. Maximum deptb for detecting a good conductor is often conside.red to be hale tbe coil spacing; although separations as large as 350 m are available it is unlikely tbat the corresponding deptb wouid be 175 m. Botb tbe spacing aud orientation of tbe coils also are critical. Decreasing a 60 m interval by 1 m will produce au appreciable in-phase auomaly (6%), aud a relalÍve tilt oC 100 between tbe coils will give a 1.5% error or greater, depending on whether tbe rneasurement is made in tbe presence of a good conductor. Care must be talten in hilly ground to maintain botb proper spacing aud tilt. For instauce, on a slape tbe coils must be parallel ratber thau horizontal, because tbeir elevations are different. CorreclÍon may be necessary in this case because tbe total vertical component is not being measured. Again if tbe coils straddle a steep hilltop, tbe correct spacing may not be maintained. Sorne horizontal-loop sets aperate at two frequencies (e.g., 875 aud 2,200 Hz) with a view to rustinguishing shallow auomalies tbat may mask better conductors at deptb. One popular unít, MaxMin, provides six frequencies.

7.4.4. Time-Oomain EM Ground Systems (a) Ceneral. The USSR, very active in electrical prospecting since early connections witb the SchJumbergers, pioneered in transient EM techníques for ground aud downhole work from tbe early 19605. Development aud use oC TDEM ground systems has increased in the Westem world only since about 1973. Their popularity is based on several advantages over FDEM. It appears that botb tbe maximum deptb oC penetration and ability to detect targets through conductive overburden are superior to tbe latter; the first feature is attraclÍve anywhere aud tbe second particularly so in tropical regions where surface terrain is often high1y conductive. Results from FDEM base-metal surveys in Australia, for example, were disappointing prior to about 1976 and led to the development of tbe SIROTEM equipment in that country (Buselli and O'Neill, 1977). AlI TDEM systems (except UTEM-see §7.4.4f) use a trausmitter tbat produces a sharply terminated primary-field pulse aud a detector tbat samples any resultaut secondary-field transient at a number oC preset time intervals (channels) alter tbe primary field cutoff. AlI systems detect the time rate of change oC the secondary fleld (dH/ di) because an induction coi! is used as the sensor (but see §7.4.5). We will outline several ground ID systems in tbe following sections. (b) MPP.4. Developed by VITR Leningrad and aperational since 1981, this is a Soviet ground and borehole IDEM system tbat may be used eitber with a single square loop (usually 200 X 200 m maximum) Cor trausmitting and receiving or witb a portable multitum fenite-core receiver coillinked by radio to the transmitter for synchronization and


373

CURREHT "'-__I___~ MONITOR r-

DATA

JlP UNIf

IUS ZOY. 5A

l1li1

7 liT DATA]

3 lIT (XP. [ 1 IU SIGN.

,..------, JI AMP

TI TRICCER CHANNnS

ind TURN 0f4 TI: 50 Hz. SYNCH....+.....;;,.;.;.-----11 ....

SAMPUS 2"

PR(-AMP

.5

L.P. 'llT[R

•1

ANALOC SIGNAL CAl" e [

12"]

PRIHTER CO.URCl.

'Nl(R~LLY

SWITCHlD

Figure 7.21. Simplified block diiJgram of S/ROTfM. (Afler Buselli and O'Neill, 1977.)

communication. Transmitter current is about 20 A maximum, the square pulse being 20 to 40 ms duralion with the same off time. Transient decay is sampled and averaged in 10 to 20 channels, commencing about 1 ms after currenl cutoff; the output is read on a meter. Tbe portable receiver is used lor more detailed targeting by traversing grid lines either inside or outside the large transmitter loop. Whether this survey method is more sensitive to conductors of limited dimensions is nol clear; the single-loop arrangement is said to be rather insensitive to small conduclors, deep or shallow, giving bes! response for bodies whose dimensions are rougbly the same as or gualer than the large loop (Kleinkopf el al., 1974; Zietz et al., 1976; Buselli, 1980). Originally designed by Crone Geophysics and Newmont Exploration, tbis equipment first appeared in 1972 as a semiportable horizontal-loop unit. The multitum transmitter coi! is 6 lo 15 m in diameter laid out in a rougb circle on tbe ground. Tbe recurrence frequency is either - 23 Hz for a 10.8 ms pulse with equal off time or - 12 Hz for 20.9 ms pulses with equal off time. In tbe original model the pulse turo-off was a 1.4 ms portion 01 a cosmc wavc, later changed lo linear ramps of 0.5, LO, and 1.5 ms duration; the tum-on was cxponential with 1.0 ms lime conslant. This model was subsequcntly modified several limes. In 1975 a larger Turam-type transmitter loop (e) PEM ("Pulse" EM).

was introduced a10ng with a small receiver coil used for surface coverage outside the transmitter loop; a borehole receiver unit was inc\uded as well. Another version called Deepem appeared in 1977 with a 100 X 100 m transmitter loop. The receiver, which traversed outside tbe loop al distances of SO to 350 m from the loop edge, measured tbe vertical and one horizontal component or H. About 1979 this system was provided with more transmitter power (2.5 kW, 20 A), energizing larger loops of 1,000 X 300 m. The PEM system has becn widely used in Arabia and Australia as well as in North America, and appears to have good depth oC penetration. For example, in the logging mode the receiver is capablc of dctecting large conductors 150 m to one side of the borehole or 300 m below il. Surface survcys over resistive ground have defined conductor depth, position, and strike as well as partial shape. On conductive overburden, surface currents tend to disguise the target geometry and two transmitter loop positions are usually necessary lO define it bettcr. However, the penetration is said to be al least 200 m in resistive rock and 150 m under conductive overburden. The equipment now incorporates a field computer ror data storage and analysis. (d) SIROTEM. Tbis time-domain equipment was dcveloped during tbc period 1972 to 1977 by thc Commonwealth Scientific Industrial Research Organization (CSIRO) in Australia (§7.4.4a). Tbe decision to switch from FDEM to TDEM was taltcn in

flectromagnetic methods

374

900\'" X

(b)

over the range 0.25 to 150 ms are available with widths lrom 400 p.s (early time) to 25.6 ms (late time); up to 4,096 pulses may be stacked in digital memory, maximum measuring time is 4 mio/station, low noise leve1 for smal1 signals, suppression 01 power line and VLF interference, simultaneous measurement of channels, and common-mode suppression of 1,000: 1. The complete battery-operated instrument weigbs 16 kg, operates 10 hours on one charge, and wi11 deliver 10 A maximum to the transmitter coit. Either a coincident loop, 100 x 100 m, or two loops, each 25 X 25 m with two tums and 100 m separation between centers, may be used ror field measurements. As in the PEM system, the two loops provide much beuer target definition tban the single version. In 1979 a 4.3 kg logging probe was added. (e) fM37.

(e)

FiBure 7.22. EM37 TDEM system. (After Callagher, Ward, and Hohmann, 1985.) (a) Field layout. (b) Trans· mitter-current waveform. (e) Time derivative of current waveform.

spile 01 the difficulties in data inversion encounlered in the laller (more troublesome at that time) and because 01 the practica1 advantages resulting from elimination of the large primaty fields duriog measurement, superior extraction of small signals from noise, and less sensitivity lo topography. A block diagram of the SIROTEM set is shown in Figure 7.21. The unit incorporates a microprocessor with 4K memory and PDP-8 language, controlling the transmitter, storage and averapng of data, measurement, and output sequence, and it will print out data as fJ.V/ A, apparent resistivity, or other suitable parameter. Several additional improvements over earlier TDEM systems are the following: up to 32 channels

Manufactured by Geonics Ltd., this system is similar to the Crone PEM with a Turam-style transmitter loop of variable size up to 300 X 600 m and a 1 m diameter air-core receiver coi!. The lalter wi11 measure three components of aH/a, both inside and outside tbe transmitter layout over a range of 10 to 1,500 m (Fig. 7.22a). It first appeared about 1980. The transmitter has a bipolar 30 A maximum output and operates at three recurrence frequencies, 3, 7.5, and 30 Hz, with equal on-off times. Figure 7.22b shows the current waveforms, with a slow exponential tum-on and fast ramp shutoff; the time derivative, dl/d, is displayed in Figure 7.22c. Transient response is measured at the receiver (which has a 40 kHz bandwidth) in 20 logarithmica11y spaced windows, tbe first of these coming on 800, 320, or 80 p.s after cutoff, corresponding to the respective 3, 7.5, and 30 Hz repetition frequencies. The receiver oUlput may be read on a digital meter with a 20-position rotary switch; T-R synchronization is obtained with a quartt crystal oscillator, direct wire link, or Crom the primary field. (fJ UTfM. Lamontagne and West developed this TEM system at the University oC Toronto over the period 1972 to 1980 (West, Macnae, and Lamantagne, 1984). It uses a conventional Turam field layout with a transmitter loop 011 X 2 km in resistive terrain, 300 X 300 mover conductive ground, with corresponding receiver distances up to twice the loop dimensiono Measurements are made oC H" sometimes 01 Hbof and E hor aIso, the latter by means of grounded electrodes about 25 m aparto The geometry is shown in Figure 7.23a. Unlike the other time-domain systems, the UTEM transmitter genera tes a continuous triangular waveform with no off time (§7.3.2). Thus tbe receiver


375

-TRANSMTTER - - - - - - - - -............----RECEIVER - - - - - - - - - - -

H.E LARGE l.OCf'

TRANSMlTTER

(a)

ITRANSMITTER

CURRENT

I

--+-----~~----~------~~-----t

SECONOARY FIELO

~~~~======~-------, (b) l'

Figure 7.23. UTEM time-domain sysrem. (Afrer West. Macnae, and lamontagne, 1984.) (a) Block diagram. (b) Transmitrer and receiver waveforms.

response in free space would be exactly a square wave; in tbe vicinity oC conductors tbe square wave is distorted. The UTEM receiver measures average amplitudes over 10 del ay times spaced in a binary geometric progression between discontinuities on tbe triangular waveform. Hence tbe distortions are revealed in tbe varlous windows. Effectively tben. UTEM measures tbe magnetic-field step response (response to a step in tbe primary field), whereas all

other TDEM systems measure impulse response (§A.13).

Transmitter and receiver waveforms are displayed in Figure 7.23b togetber with a few sampling windows. The latter are numbered in reverse, tbe first window beiog 1 cycle duratioo, the second 1, tbe tbird f¡, and so on. Dilfereoces io response of tbe UTEM system, compared to tbose from step-functioD transmitter


376

TRIANGLE TRUSIIITTU CURREIT

~ STEP

I

RECEIYER CDll VDlTACE

STEP

"'-

IMPULSE

IPRIIIAI,I

T

+

'ti

~I ~ ~t ....

VARIATlOI Of SECOIDARY YDLTACE IITM COIDUCTOR 'lj TIllE COISTUT

(e)

Figure 1.23. (Continued) (e) Comparison of signals for tri.mgular and step-funetion inputs.

systems, are lurtber illustrate
R

Figure 1.24. Feedback circuit to eonvert SH/St signal to H.

tometen. It is expected lbat me maximum current may be increased by a factor of 10.

7.4.5. Measurement of H EM systems invariably employ a coil to detect secondary siguals for the receiver. Tbis is DO problem in FD, but because the coil measures aH/a" it enhances short time-constant response lor TD siguals. A wide-band ac magnetometer, measuring H,«(oI), would make a better sensor, but none is available al present (1988). Aa altemative approacb is provided by beavy feedback in a receiver-amplifter stage. Figure 7.24 sbows a circuit for this purpose; lbe receiver coil is coupled to the input and we bave lor tbe receiver output k aH/a, - jwkH - tia' With negative feedback across tbe stage whose gain is G, tbe feedback vollage is -jwMI- jwMto/R. The input is now jw(kH - MtolR), so t

o - Jt..JG( kH - Meo/R)

and eo - jt..JkH/(l/G

+ jt..JM/R)

Airborne EM systems

If G is very large, we have

eo" (kRjM)H Thus the time derivative oC H at the input is converted to a direct measurement of H.

7.4.6. Assessment of EM Ground Methods It would be attractive to compare the various frequency-domain EM ground sets in a sequence of increasing sophistication, so that we would arrive al the best possible equipment for field work, aCter consideration of simpler ver· sions. This is not really possible, however, because there are inherent advantages and weaknesses in al1 the presently used systems. The criteria for judging tbe worth of a particular set inelude source power, reliability, speed and simplicity in field operation, information obtained, and ease of interpreting the results. In a rough summary we can say that the depth of penetration increases with source power and bence the large transmitting loop systems have an advantage. By the same token they are less attractive for fast reconnaissance; in this area the numerous dip-angle techniques are particularly suitable. Finally the units that measure both in-pbase and quadrature components provide more information about the anomalies, but at the same time are more expensive, usually slower, and rcquire more competent operators. (a) Frequency doma in.

It is very difficult to rate the presently available TD ground systems, particularly on the same basis as in the preceding section, because there is considerably less variety among them. For example, the apparent advantage in using a single loop for transmitter and receiver is greatly reduced by its lack of mobility and poor discriminalion, nor is the superiority of UTEM's continuous triangular waveform over pulse input e1early established. Thcre are, bowever, several obvious differences between time- and frequency-domain systems. The former have the advantage of wider frequency range, greater depth of penetration, and ability to see through conductive overburden. On the other hand, FD is more suitable for fast reconnaissance and detail with light-weight, portable, cheap units, proba· bly produces better anomaly resolution, and the interpretatioD of field data is better developed. Because TD applications are relatively new, however, and are being actively investigated, some of these comparisons will soon be out of date. (b) Time domain.

377

7.5. AIRBORNE EM SYSTEMS 7.5.1. General A prime altraction of EM prospecting, as mentioned before, is that reconnaissance exploration can be done from the airo Only magnetics and radioactivity, among the other metbods, can be used in this way. A great variety of airbome EM systems has been developed to take advantage of this fact. Tbey will be considered in the order in which they appeared, an order that corresponds roughly to the development of more complete and complex equipment. Tbe frequencies employed in FO systems are the same as in ground EM, lower frequencies generally being used with bigher power and greater altitude. The height of ftigbt also determines the line spacing, which may vary from 300 ft to ! mile (100 to 800 m). Position of tbe aircraft is usually determined from continuous strip photography, occasionally by radio navigation, which, of course, adds considerably to the cost. Recording oC data is continuous, now generally digital. Originally airbome EM surveys were performed with small fixed-wing aircraCt. Now both FO and TO systems have becn modified for helio copter, which is more suitable for detailed work and rugged terrain. With either carrier they are normally combined with airbome magnetics, sometimes witb airbome radiometrics andjor additional EM surveys.

7.5.2. Quadrature Method Tbe Hrst airbome installation used on any scale, this system measured only pbase shlft between primary and secondary fields. It was updated in the mid 1970s as the McPhar Quadrem to be carried by fixed-wing aircrdt or helicopter; it had five frequencies (instead oC two) to extend the range of conductor response. Otherwise, it suffered from the same limitations as the earlier models, and is no longer used to any extent.

7.5.3. Turair System Originally used in Russia and Westem Europe, this is essentially a ground Turam transmitter unít with two helicopter-bome receiver loops measuring the gradient of either borizontal or vertical H fields on flight lines normal to the long dimension of the loop. The North American version is the Scintrex Turair. Parameters measured are the same as with the ground equipment. There are two aUractive features ol this arrange· ment, one being a greater depth 01 penetration from

Electromasnetic methods

378 Transo coil

Ilec. coi!

QT~r.~n.~·r]-_~-
...tin, .011

A/Dconv.

Fi8uTe 7.25. Block dia8Tam of the airborne phase-component system. (From Keller and Frischknecht, 1966.)

the ground transmitter, the other that immediate ground followup may be carried out in more detail.

7.5.4. Airbome VLF Numerous versions of airbome VLF equipment have become available since about 1970; these inc1ude sets manufactured by Barringer, McPhar, Geonics, Scintrex, Sander, and Hen. The Barringer Radiophase and E phase, among the earliest of these, appeared around 1970 (Barringer, 1970; Arcone, 1978). A pair of whip antennas (orthogonally mounted dipoles) mounted 00 an extension of the aircraft nose cone measure E. and Ex, with the line of flight normal to transmitter direction. Only the quadrature phase component of Ex with respect to E, is measured, the latter being the phase reference. This gives the wave tilt in the presence ol ground conductors in the form Wq - E"q/ E" where q and i refer to quadrature and in-pbase components, respectively. Hence it is possible lo determine ground apparent resistivity from the relation Pq -

2(E"'1/ E.,)2/w!Q.

The McPhar KEM system carries a pair of orthogonal coils undemeath the wing tip to measure total-field tilt angle (± 30· max) and displays horizontal-component H field and tilt angle on conventional meters, with provision for analog recarding.

Geonícs EM-18 and Scintrex SE-99 equipment both measure in-phase and quadrature components of H, with respect to total horizontal H field in a similar fasbion to the earliet airborne AFMAG unit (Becker, 1979). The Hen Totem-1A (Hood, 1979), a lightweight 5 kg unít, appears to be otherwise similar to these. Sander's EM-ll VLF system, reported in Hood (1978), incorporated three orthogonal receivet coils to provide a11 amplitude and phase components. A later 1982 Hen model, Totem-2A, measures multiple parameters on two channels simu]taneous]y, inc1ud· ing amplitude of the total field and vertical quadtature. It uses advanced circuitry to acbieve ]ower DOise; for example, the system automatically corrects for aitcraf! pitch, yaw, and rollo VLF systems at their present stage oC develop. ment seem capable of performing fairly detailed shallow resistivity mapping, particularly in resistive environments, and have been used extensively in indirect exploratioD Cor uranium and ~old.

7.5.5. Phase-Component Measurements There is a variety of these airbome systems, moUDted either on a Iight aircraft or helicopter. They include the Kenting-Scintrex Tridem, Geonícs EM-33, Barringer Aerodat, Dighem, and others. All are similar

Airborne EM systems

379

to the horizontal-loop movíng-source ground set, except Ibat the coils more oflen are vertical, sometimes null-coupled; several frequencies are available. Flexure of the coil mountíngs caused by turbuleot air ís quite serious witb tbis type oC equipment. For a coil separatíon of 15 m, a cbange in distance of a Craction of a millimeter is sufficien t to change the receiver loop signal by 10 ppm, although only the in-phase component is afl'ected. Introduction in 1977 oC the Aerodat low-noíse bird or boom structure, made oC ligbt, higb-rigidity plastic, reduced tbese mechanical problems. Tbis type of button-on mountíng holds the transmitter and receiver eoils at a fixed spacing of 7 to 10 m and reduces noise level to - 1 ppm. The block diagram 01 a phase-component airborne unit is shown in Figure 7.25. Obviously it is mueh more eomplex Iban the ground unit. The primary field and the fixed anomaly 01 the aireraft are caneelled at the receiver as completely as possible; any additional signals above noise level are recorded as anomalous conduetors. In effect we are detectíng Hr , which is made up of all the signals arriving at tbe receiver loop: the primary dipole field, the effect oC the aireraft, and whatever seeondary field may also be present; that is,

I

t

Cancellation 01 tbe last term, H¡', by means of the bueking coil al the reeeiver, gives us Hs , wruch is measured in lerms oC H¡'. Thal is,

H. H¡'

Hr

- --1

H¡'

where tbe ratio is generally expressed in parts per million. Figure 7.26 ilIustrates three coil arrangements used on aireraft and helieopters. The coils are eítber coplanar or coaxial with tbeir axes in tbe line of ftigbt. All tbree configurations are basically similar, because tbe primary field al tbe receiver is given by Equations (7.14h, i) in Section 7.2.3d. That is, for eitber of tbe coaxial mounts on tbe helicopter,

and for the coplanar system on the wing tips, '·1

where N, i, and a are the number of turns, current, and radius of the transmitter coil and I is the dislance between centers of the two coils, wruch varies from 20 to 80 lt (6 to 24 m), depending on tbe aircraft.

Frequencies used in the fixed-separation systems range Crom 300 to 50,000 Hz, the choice having to do witb the aircraft type, which in tum determines the ftigbt altitude, Helicopler carriers can fty as low as 30 m and generally use tbe higher frequencies. Fixed-wíng aifcraCt maintain an altitude of 300 to 600 CI (90 lo 180 m) depending on the terrain. Noise (other than mechanical) may be filtered out with tbe aid of digital signal processing. Depth of penetration ís lower Cor in-board and helieopter boom mountíng than with towed bírd systems, but more data are obtained. The Dighem helieopter-borne equipmenl produces a large amount of data from three orthogonal receiver coils shown in Figure 7.26d. These are maximum-coupled (MC), null-coupled horizontal (NH), null-coupled vertical (NV); the first record s in-phase and quadrature components at 2 and S ppm sensitivity, whereas the otbers show quadralure only at 2 ppm. The Aerodat AEM system ineludes two vertical coaxial pairs at 955 and 4,536 Hz and two horizontal coplanar pairs at 4,132 and 33,000 Hz. The latest Dighem unit carries three coil pairs, two coaxial and one coplanar. Dighem data from an area eontaining numerous conductors are shown in Figure 7.27. AlI ehanne1s respond over the southern conductors, while the null-coupled pair are weak on the northern reatures. Model sets of curves for half-space, horizontal and vertical sheets, and two layers have been prepared lor interpretation. MC data are analyzed Cor complex eonductivity, assuming a superposed dipole system (altitude » T-R spacing). The NV eoil is sensitive to ftight direction and may be used to correet the MC anornaly for oblique strike, whereas the NH coil indicates target dip. Profiles and contours of apparent resistivity may also be developed from tbe models.

7.5.6. Transient (Input) Method As we have seen from the previous descriptions, tbe fundamental problem in airborne EM is lhe isolation of very small secondary responses in tbe presence oC a very large primary field. lbis difficulty, or course, applies to ground systems as well, but to a mueh lesser degree. One way oC getting around tbe problem is lo use a pulsed - ratber tban eontinuous - primary field and attempt lo measure seeondary response during transmitter off-time. Tbis principIe is tbe basis of tbe Input (induced pulse transient) system (formerly ealled INPU1) developed by Barringer (1962). Tbis was the original airborne time-domain system, and the transmitting and reeeiving method had some resemblanee to the induced-polarization time-dornain operation.

380

Electromagnetic methods I"'~R

T

R (G)

Altilude

-lOOR

I· · 1

Surfacc

(b) Tralllmiller

l.

I-~I\

150ft

~

(e)

lOA

_1

Surfacc

TRANSMmER COIL (900 lu I 5 RECEIVER COILS

(d)

Figure 7.26. Airborne double-dipole fM sy51ems. (a) Fixed-wing. eoplanar. (b) Helieopler on-board coaxial mounling. (e) Helieopler boom mounling. (d) Dighem multicoil bird.

Airborne EM systems

381

CHANNEL

l,dt.1+ 1... ,1, ",1, ,] '" '" 1'" .l1Y!.b.

1

I~+nlllll 1....lr::. '

IrFB&1111 , 1..."II!. '

PftN?tf t:fucliij. · 1

I

r'Hi I I I I

IWD+ H

1

1 1

I""~i:.' ~I

+.

II 11 11¡ 11 ~d:l~. kHl fElll t@', SOUTM

NORTH

Figure 7.27. Dighem multicoil record over widespread conductors. (After Fraser, 1978.)

'lbe transmiuer loop, strung horizontally about a relative1y large aircraft, is energized by half-sine-wave pulses ol alternately opposite polarity. The on- and off-times were 1.5 and 2 ms, respectively, in an early model, resulting in a recurrence frequency of about 285 Hz; these parameters have since been modified over a small range lor various applicalions. Large peak transmitter currents produce dipole moments ol roughly 2-5 X 105 Arrf-. The receiver loop is usually vertical with its axis in the ftight line; it may also be mounled witb a vertical axis, particularly for resistivity mapping surveys. In either orientation it may be lowed in a bird at the end of a 330 ft (100 m) cable in lixed-wing Input, or carried in the boom lor a more recent helicopter version. Duriog transmitter-off perlods the receiver amplilier samples the decay curve at several points (lour in tbe first Input syslem, six and eleven io later models) for iotervals ol 100 p.s or longer, as seen in Figure 7.28d. These signals are inlegrated and recorded, lormerly on a multichannel strip charl, now in digital form for automatic data processing. The sequence ol magnetic lield and voltage pulses is shown in Figure 7.28.

The ll-channel results in Figure 7.28e are from a test survey in tbe vicinity ol Oltawa, Ontario (Dyck, Becker, and Collett, 1974), which was performed with the receiver coil horizontal. Minimum T-R coupling is obtained when the line between aircraft and bird is about 36° (Fig. 7.26). The lirst channel comes on about 220 p.s aíter current shutoff; the widths oC successive gate intervals become progressively larger, with no off-time belween them. The chief source 01 noise is lhe spurlous secondary field lrom the aircraft. The effecl 01 this lield is eliminated to a large exlent by introducing a reference signal from the primary lield voltage in the receiver coil, lo cancel this signal in each channe1 ol the receiver; relative molion of the bird is compensated al the same time. Other noise sources, 8uch as atmospherics and power lines, are more difficult to suppress, although data processing in recent models has improved this. The Inpul method has certain attractive {eatures. The depth of penetration appears to be larger (possibly as great as 300 m) than most airbome EM, and the multichannel record reveals the character oC conductors. Multichannel recording, however, is a neces-


382

(a) I

I

'1'

~ 1.S ms

1

2 ms

---l'"

1 1

1

(b)

(t)

1

I

O

(d)

.~ 450

1250

850

1650

2000

¡JS

2

I~

Channels

....91.1 u

....

~t. t

""

e

(tI

le.

a

~

...

~~

gu

..5

~u 1234

•

~::....:

!l1 1

•

U

•

~ 10

'Im.1

r1 ti

Channel. tnt.,nte
(fl

Flight path_

Figure 7.28. Input airborne EM sysrem. (a) Primary magnetic fie/d, Hp ' (b) Reeeiver-eoi/ va/tage due ro Hp when H, - O. (e) Receiver-eoil va/tage due to Hp + H,. (d) Decay signa/s in the four sampling ehannels. (e) l1-channe/ sampling with zero off-time berween. (f) Four-channel record over Texas Gu/f Su/phur, Timmins, Ontario.

Interpretatían

sity as well as an inherent advantage, because in a pulsed system the coil detector, which record s dH./dt, enhances the fast decay fields, wbereas good conductors usually produce a secondary field tbat decays slowly (however, see Section 7.4.5). Being the only TD airbome system available and having establisbed a higbly successful record over 25 years, Input is used widely in a variety of applicarions. Tbe latest units ftown by Questor and Geoterrex incorporate digital acquisition directly at the receiver-coil preamplifier, so that a11 subsequent signal processing becomes digital. This results in rejection of sCerics and improved ease oC computation.

7.5.7. Cryogenic EM System A higbly interesting single-coil airbome EM system (Morrison, Dolan, and Dey, 1976) detects minute changes in resistance oC a large coil (- 3 m di ame· ter) immersed in Iiquid belium in a dougbnut-sbaped cryostat hanging vertically from a helicopter. Because the coil winding is superconducting and energized at a low lrequency 01 40 Hz, it responds to variable ground conductivity by mutual coupling and sbould have a large depth oC penetration. UnCortunately, development is presently suspended on this novel equipment.

7.5.8. Assessment of Airborne EM It is apparent from the discussion that airbome EM is considerably ditrerent in detail from ground methods, a1though the fundamental principIes are the same. The equipment is more eIaborate, there is more of it, the requirements for background noise rcduction are much more stringent, depth of penetration and discrimination between conductors are reduced, and the interpretation possibilities restricted. The survey price, 01 course, is much increased, al· thougb not the unít cost (about S60jkm in 1987). In spite of these Iimitations, reconnaissance EM is invariably done lrom the air whenever the survey arca is large enougb and finances permit it. For fairly large-scale search, especially when accompanied by aeromagnetics, it becomes quite inexpensive per line·ki1ometer and is a powerful tool in mineral exploration. There are, however, c1ear-cut differences among the present AEM systems. The VLF method is simple, cheap compared lo other air surveys, and provides limited data for shallow depth. The semiairborne Turair lurnishes phase-component data to considerable depth, but with higher mobilization costs. Input, the most popular airbome method Ior some years, yieIds rather rudimentary data with good

383 deptb of penetration. Phase-component systems supply the most detaiIed information with some loss ol penetration. Finally, there is an obvious choice between fixed and rotary wing carriers, the latter baving an advantage in rugged terrain, in detail and discrimination, bUI at higber costo

7.6. EM FIELO PROCEOURES Tbe standard field procedure is profiling a10ng straigbt Iines. Except in sorne ground reconnaissanee, tbe surveying is done across geologic strike witb tbe line and station spacing dictated by the amount ol detail required. Procedures for tbe various ground and airbome systems have a1ready becn discussed in tbe previous sections. EM may be used lor vertical (depth) sounding in a manner similar to vertical resistivity sounding (§8.5.4b, §8.6.3, §8.6.4). This can be accomplished either by increasing the transmitter-receiver separation while maintaining a constant frequency, or by varying the frequency with fixed spacing. The latter has the advantage that lateral changes in resistivity do not affect the readings. As in resistivity, however, ir there are several horizontal layers oC ditrerent conductivity, more than one spacing may be necessary even when the frequency is varied. Several ol the ground EM methods have been used for depth sounding. The long-wire transmitter systems have a greater depth potential than, say, tbe horizontal-loop set; however, the Iatter is more attractive lor interpretation because oC the symmetry. Apart from the use ol several Crequencies and T·R spacings in Slingram surveys, however, there were no EM sounding applications until about 1973. The growtb oC TDEM has since provided a stimulus, and tbe technique, discussed in Section 7.7.6, has developed considerably. EM methods have been used to some extent in drill hole logging, particularly with TD equipment; this application is found in Section 11.5.

7.7. INTERPRETATlON 7.7.1. Introduction As in otber geophysical methods, the interpretation oC EM field resuIts is done by comparison with the calculated and/or measured response ol the same type of equipment to conduclors of various simple shapes and conductivities. Theoretical calculations for this purpose are Iimited to very elementary geometry. For instance, it is possible to solve the following configurations (Grant (a) Ceneral.

384

E/ectromasnetic methods

and West. 1965):

1berefore,

1. Condueting spbere (cylinder) in uniform ac and dipole field. 2. Conducting infinite borizontal thin sbeet in uniform and dipole field. 3. Conducting infinite balf-space in uniform and dipole field. 4. Condueting semiinfinite half-plane in dipole field. This is a limited set 01 anomalies and the solutions are not at al] simple. An alternative and more elementary theoretieal approacb is to assume the conductor to be a lumped circuit having resislance, self-inductance, and mutual induetance witb respect 10 transmilter and receiver. Here again the number of geometrical sbapes is quite limited, being confined 10 circular and straigbt line elements - in effeet the edges of thin conduetors. lbe solutions, however, are comparatively simple. (b) Ana/os mode/ systems. For more complex geometry and variable conduetivity, it was former1y necessary to resort to analog model measurements lO match field results. This tecbnique was used more in EM interpretation than for otber geophysical metbods. We shall discuss briefty tbe tbeory of sca1ing for model systems. From Equation (6.15), Section 6.2.3, we had tbe diffusion equation. wbich described tbe propagation of EM waves in tbe field in tbe form

p", •

I ... p. ... ( /¡p.,

p,

Im)2 1,

(7.33a)

Thus, tbc ratio plp.fl2 has the same value in both systems. Now we generally measure EM effects in dimensionless form, for instance, tbe response ratio H.IHf or something similar to it; thus ir tbe ratio p/p.fl has tbe same value in tbe two systems, the response ratio will be reprodueed in going from one lo tbe otber. Practically, we may dispense witb tbe permeability ratio, because magnetic permeabilities do nOl vary lo any extent. lbus if we put (/",11,) lln, where n ::. 1, we get

(7.33b) This relation means lhat we can vary eitber p or to satisfy tbe aboye requirements. As an example, suppose we want lo model a massive sulfide conductor (say 10- 3 Cm) on a dimensional scale of 1/500. We can make I...I/¡ - p,lp". - 500. Ir tbe field equipment has a frequency of 1.000 Hz, tbe model parameters would be

1, or botb,

P, -

10em - SOm

1m -

500kHz

P... - 2 X 10- 6 Cm In order tbat a model system may exact1y simulate tbe field situation, botb must satisfy this equation. Using 5ubscripts m and I for model and field pararneters, ir / is a leDgtb and I a frequency and we scale distance and time linearly, tben the following relalioos must bold:

and

t",lt,· /¡II...

These values, however. are unsatisfaetory for a practica] model, partIy because tbe frequency is too high, but mainly because it is difficult to vary tbe resistivities of suitable model conductor materials more tban 2 or 3 orders of magnitude. ID fact, it is preferable to choose the p". value first ando if possible, to maintain the same frequency in tbe model as tbe field system, because tbe field-set receiver may be used for tbc model measurements (much bigher frequencies may introduce UDwanted capacitive effects, hence displacement currents). In tbis case, ir tbe mode1 conductor is aluminum (p .. 2.8 X 10- 1 (lm). we have

Also.

henee

'1H • ( 1,)'1 2H _

V",

I'V' '"

(¡. .

a"')

p. ...

zH

IV,

~p.,~

whicb makes tbe dimensional scale 10 cm • 20 m. As previously meDtioned, tbe choice 01 model conductors is Iimited. Resistivities range tbrough aluminum, brass lo stainless steel (7 X 10- 7 Cm). The only otber solid material useful for models is commercial graphite (10- 6 lo 10- 5 Cm). Oosed loops of copper or alumiDum wire may be used as mode)s for

Interpretatíon

385 Plan

I Shccl ) conduclor.

Elevalion

R , - - - -~rJ

H'

Ien8lh (

--_./r---.'

«(> h)

k ""TOPar

conduelor

(a)

(b)

Figure 729. Oip'angle (;,ted transmitter over steeply dipping sheet. (a) Plan view. (b) Elevation showing receiver signa/s.

good conductors, as well as solid metal, because the induced currents do not penetrate the solid conductor to any extent. The wire loops have tbe additional advantage that the geometry may be changed easily. Ir the host rack is a poor conductor it is permissible to measure the model conductor in airo To simulate the etrect of a conductive overburden, horizontal sheets of aluminum foil may be placed over the model orebody, possibly with an electrical connection between the two. Where the long-wire transmitter - which introduces currents directIy into the ground - is being used, or where the host rack has appreciable conductivity, the EM model rnay be irnrnersed in a water tank (§8.6.2). The conductivity of the liquid is variable over a wide range by the addition of salt or acid. In the tank model it will usually be necessary to increase the frequency to maintain the scaling ratio. Obviously the EM model equipment should be scaled the same as the conductor. Practically this may not be possible, because a 1 m diameter receiver coil becomes impraclically small when scaled 1,000/1. But if the model coil is very large with respect to the stalion spacing, or receiver-transmitter spacing, it is preferable to adopt a smaller scale ratio. Coils may be conveniently wound on small diameter (2 to S mm) ferrite rods for model work; theoretically this limits the dimeDSÍon ratio to about 200. However, considerable latitude is permissible in this respecto (e) Numerical modeling. As a result of computer advances, the application of inversion techniques and other approaches have created small librarles or EM data for more complicated models. Several pro-

grams have been developed for determining EM response over 2-0 structures. Digital-analysis methods inelude finite difference, transmission-line analog, and finite-elernent modeling (§6.2.7). Integralequation rnethods require solulions of the equations for the EM fields or their current distributions (Parry and Ward, 1971; Hohmann, 1971). Computer analysis has replaced sca1e modeling to a great extent, even thougb computer solutions ror 3-D structures are extremely difficult, as in MT interpretation.

7.1.2. General Interpretation Procedure In discussing interpretation oC ground EM we shall Iimit the types oC frequency-domain field methods lo dip-angle (fixed-transmitter, broadside, shootback. AFMAG, and VLF) and phase-component (Slingram and Turam). Tirne-domain systems iDelude PEM, SIROTEM, EM37, and UTEM. For airbome methods, we will describe elemeDtary interpretation applied to data from quadrature, VLF, phase-component, and Input surveys. The models that are amenable to interpretation are simple and Cew in number. By far the most popular is the conductive sheet in various attitudes, because it is a common and excellent target for EM. Response from spherical (3-D) and layered (l-D) structures will be considered more briefty.

7.7.3. Ground Systems¡ FDEM over Dipping Sheet A common configuration for conductive zones is a thin sheet, long in the strike direction, with variable dip and depth extent. If the conductiv(a) General.

J86 ity is large or tbe frequency high, tbe induced current might be assumed to ftow mainly along the top edge, vertically at tbe ends, and return at deptb. That it does not lo)]ow tbis patb has been shown by model studies (Koefoed and Kegge, 1968; Koefoed and Struyk, 1969; Annan et al., 1975). However, model work has proved a great aid for interpreting tbe response ol common ground EM systems to tbis target. (b) Dip-angle measurement; fíxed vertical-loop Iransmítler. The coil geometry witb tbis type ol

conductor is shown in Figure 7.29. The transmitter coil, located if possible at a point direct1y over tbe top ol tbe conductor, is pointed at successive re· ceiver stations and a minimum is obtained by tilting tbe receiver coil about tbe T-R axis. 'Ibis measurement is tbe ratio ol the vertical component to tbe total horizontal component at the detector. The lormer is entirely due to the secondary field, whereas the horizontal is the sum of the secondary component and the primary fie1d (which of course is horizontal). Then we have

where H~ is the total horizontal component. Because will be zero wben the receiver coil is directly over the top ol the sheet and will change sigo as we move in either direction across strike (Fig. 7.29), it is clear that the dip angle profile is asymmetric. Using tbe sign convention that the dip angle is positive to the lelt, negative to the right, 01 the sheet as the traverse proceeds lrom left to right, we obtain profiles as in Figure 7.30a. The slope ol these, positive to negative from left to right, defines a real or praper crOS30ver at tbe zcro dip angle; the latter maro quite accurately the location of a thin dipping conductive body surrounded by resistive host rack. (TIte sigo convention lor tbis definition could as easily be in the opposite sense, but must be consistent to avoid confusion.) Figure 7.30b displays several proflles over vertical sheet models; these are perfectly asymmetric, tbe dip angle increasing to two peaks equal and opposite in sigo eitber side ol the crossover, then tailing off gradually for larger xlz. As the dip ol the sheet decreases from 90° to 30° in Figure 7.30a, the positive peak to the leCt (footwall or updip side) increases, whereas the negative on the right (hanging wall or downdip side) decreases. Beyond these peaks the footwall-side dip angle falls off at about the same rate as the vertical sheet, whereas on the hanging wall the decrease is more rapid and may eross zero, indicating a fa/se or revene crOS3over, which in tbis example is merely a reftection ol the bottom 01 the

H:


sheet. Reverse crossovers, however, may also be produced by resistive structures and multiple conductorso It should be noted that tbe real crossover is displaced slightly downdip as tbe sheet lies more nearly horizontal. Thus the deviation of tbe type curve from perfect asymmetry is diagnostic 01 the conductor dip. Similarly, the curve slope near tbe crossover tells us sometbing of its deptb and/or conductivity. TIte laner quantity is contained in the response parameter (§7.2.5d, §7.7.7a), which lor the thin sheet is given by p.wat/, where al is tbe thickness-conductivity product (TCP), also called conduclance, and I is tbe T-R spacing. Consequently tbe conductor response should increase for proflles obtained on traverses Curther removed from tbe transmitter, provided the sheet is long enough and tbe eddy currents induced in it are less tban saturation. That tbis is so is apparent Crom tbe pair 01 curves in Figure 7.JOe, lor profiles obtained at two T-R separations over tbe same model conductor. The scale ratio is 1/200. TIte upper profile, carried out - 250 m from the transmitter, shows a positive peak some JO% larger than the one below it which was 125 m away; in Caet, the entire upper curve is shifted upward with respect to the lower one. TIte dip-angle curves in Figure 7.30b, obtained with a model vertical halC-plane conductor, illustrate the effect 01 variable deptb. Over a range of 50 Cor z, tbe peak values 01 B ehange from 3 to - 43 o and tbe peaks practically disappear at deep and very shallow depths. Depth extent ol the sheet conductor is not very significant, except lor some spreading oC the profiles on tbe hanging wall side Cor different clip angles. If the transmitter is offset with respect to the top edge of a dipping sheet, the crossover is still located almost exact1y aboye the lop (ratber tban slight1y downdip) but tbe profiles are changed considerably, as can be seen in Figure 7.31a. TIte offset reduces peak dip angles in alllocations. When it is downdip, the positive and negative maxima are more nearly equal than in figure 7.JOa and again are more sharply defined downdip. If tbe transmitter is updip, response is almost zero on that side. When tbe sheet is horizontal (Fig. 7.31b), transmitter location produces stiU grealer changes in dipangle response. TIte profile from a centrally located transmitter is similar to that from a thick horizontal slab (Fig. 7.31c). If it is near one edge, tbere.are large peaks in tbe same sense witb steep slopes near eaeh edge 01 tbe sheet and no crossover al all. For an offset complele1y beyond the sheet, the dip angles are extremely small. EM systems olten use two lrequencies, say 1,000 and 5,000 Hz, to aid in assessing conductor geometry

387

Interpretation

30"

z/d - 0.1. dip .. 30°

20 1&1

-'

10

z e

O·

CP

z/d - O.l.dip - 60° Falle croslover \

Il.

-10

2i

o

,' .... __ .. .,. .... ,.," ...... .'

\\

DO -20' Z

-10 -8

-6

-4

-2

o

4

6

a

10

(a)

t 100

---... ... -.......JE. o::

........

80

-~

""

::: ~ 40

....

••

~.c:

"'10 .~..

80

100

8 12 18 20 24 28 x/z

-28 -24 -20 -18 -12

20' 1&1

= e .. -'

-o

....

10

xlz

O·~~~-,~-r-r~~~~~~~~~~-r~-

-10' 20'

-8

-5

-2

........ -.-

._ ••• ..1 0

L

o

1 .. 125 m

DO

-

30'

••• 90'

(e)

Figure 7.30. Response 01 dip-angle fixed-transmitter system to dipping sheets. 1- T·R. (After Ward, 1967.) (a) Sheets 01 depth extent d dippinS 30 and 60°. (b) Effeet al variable depth 01 vertical sheet. (e) Effect al T·R separation.


388

20'

w 10 o z e O' a.. Ci ·10

...

----------- ... "

••• z / d - 0.1, dip - 45°, transmitter otIset dlstance d to rlght - z / d = 0.1, dlp - 45°, transmltter otIset dlstance d to left

'falte

cronover

·20'

(a)

SOOO Hz ------------- ... ....... 1,000 Hz

"

t _____-_2_D_____-~~____-~w~__~~~=='=-~~~----~w~----~----lD~---25~x/1

(c)

Firure 7.31. Effeet of transmitter loeation and frequency on dip-angle fixed·transmifter results. 1- T·R. (After Ward, 1967.) (a) Sheet of depth extent d dipping 45°. (b) Horizontal sheets of width d, various Tx locations; zll- 0.1, dll - 1.2. (e) Responses at 1,000 and 5,000 Hz to a eondueting s/ab of fin;te width (rraphite in the model).

and discriminating between depth and conductivity. Figure 7.31c displays two 5uch profiles for the fixed·transmitter unít over an inhomogeneous slab. Although both frequencies give about the same size maxima and indicate a wide body, the 5hape 01 the curve for 5,000 Hz suggests a width less than halC that for 1,000 Hz. The strike 01 a long sheet conductor is Cairly wett determined by joining crossovers on successive dipangle profiles. In the presence oC broad or multiple conductors, this is never as simple as it sounds. Additional knowledge ol the geology is essential. Because tbe fixed-transmitter system will give anomalous profiles on traverses beyond the ends ol tbe conductor, it is necessary to relacate the trans-

mitter on strike, but several hundred meters beyond the end oC the conductor, lO determine its strike lengtb. The traverses near the transmitter will tben be barren until the end ol the conductor is crossed. With other EM sets, strike length is quite well marked by the absence of tbe anomaly on traverses beyond the ends of the conductor. The efl'ect of conductive host rack and overburden can be very significant in reducing response with all EM systems, particularly FD types. In all discussions hitherto tbe assumption has been that the conductors were immersed in a medium oC very high resistivity. If the host rack and overlay are homogeneous and of relativ~ly good conductivity, the aUenuation witl be appreciable, resulting in profiles ol

Interpretatían

389

...

/,X" .\

-

I

,

I \ I -I

, i ',

\

\I

......'"a: ~

,I -I

o

w

-LO

o

I - II

~

z

--LO

- I

I I je lA

W

..J

. ""'"

/'/,..

-0.5

-1

e

I- ,I

L

. I I ,1 I I

Q

i' ! \' . , II

,

\

.t' /

~. Figure 1.32. Response 01 the dip-angle broadside system over dipping sheets 01 finite depth extent. (After Ward, 1961.)

decreased amplitude. As mentioned before, tbis situ, alion may be simulated in model work by making the measurements in a tank ol suitable liquid; theoretically the bomogeneous conducting medium can be allowed for as well. However, when the overburden is a good conductor, lying as a horizontal slab over the anomaly source, the problem is more complicated. Field situations exist where swampy overburden of good conductivity (1 to 50 Om) has apparently masked out any response lrom metallic conductors lying no more than 15 m below surface, In one location of this type in northem Quebec dip-angle, horizontal-loop, and Turam EM, as weU as induced-polarization methods, aIl failed to give any significant response. It is possible to test the effect of overburden in a model. The result 01 placing a conductive slab over the conductor 01 interest is to decrease the amplitude and shilt tbe phase of the profiles, so tbat the anomaly appears lo be deeper and 01 different conductivity \han it actually is. Where two Crequencies are employed, tbe ratio (that is, oC dip angle, quadrature,

20' 111

10

..J

o 0·~~.:2f~~--~~~~~~ z 1 X'I e -lO --. TRAVERSE 90' TO STRllE

Q"

0-20 -30'

- TUVE.SE 80' TO

----=,:----STRIU

Figure 1.33. Effect 01 skew traverse direction on response 01 dip-angle broadside array.

amplitude, whatever the method) between them is decreased. Of course, if tbe overlying slab is 01 limited lateral extent, it will also introduce an anomaly ol its own, as lor a horizontal sheet; such overburden anomalies are, unfortunate1y, quite commono


• lO' DI~ e lOe DI'

¡ 111

O~--------------------~~---------------------

...

15

(a)

OEPTH EXTENT íii

•a

6 UNITS 60

"w E

•

600

111 111 el:

W ..J

O

"OC Z

A.

l5

.~

.~~----~----~----~----~----~----------~----~~ -20 -I~ -10 O

X • AR8ITRAAY UNITS

~o (h)

\

Figure 7.34. Variations of AFMAG profiles w;th different parameters. (After Ward. 1967.) (a) Effect of dip (b) Effect of depth extent

Interpretation

391

DEPTH UI

• -

I UNITS

•

a::

D

3 10

...... ~

-20

(e)

Fisure 7.34. (Continued) (e) fffeel o( depth.

(e) Dip angle measurement; broadside (parallel fine). Geometry of the unit is seen in Figure 7.15.

The expressions for secondary-tield components are the same as for the tixed-transmitter system. The T-R coupling remains constant, however, whereas the transmitter-conductor coupling is obviously variable. Otherwise the dip-angle measurement is expressed as in Equation (7.34). With the same sigo convention as in Section 7.7.3b, the dip angle profile will again be asymmetric, but with sharper peaks and steeper tail slopes. A trio of broadside curves is shown in Figure 7.32 over sheets dipping 30, 60, and 90°. The effect of decreasing dip is most obvious on the hanging wall side, where the reduced peak is broader and tails off more gradually than the updip peak. This EM sys. tem resolves muItiple conductors much better than the fixed transmitter array. However, it is very sensi-

tive to off-normal traverse direction; deviations result in highly dislOrted profiles (Fig. 7.33). Otherwise it is similar to the fixed transmitter in regard to effects 01 depth, depth extent, and conductivity. (d) AFMAC and VLF resu(ts. With both these grouod methods, the results over sheet conductors are similar lO the fixed transmitter. We have the same secondary-field components, whereas the remote source provides a uDiform primary field over the eotire survey area. lo general the dip-angle curves are intermedia te between parallel-line and fixedtransmitter response, with rather better defined peaks than the latter and tail slopes more gradual than the former. There are, however, several specific differences in the AFMAG and VLF profiles with respecl to the controlled source units of Sections 7.7.3b, c. For

392

Electromagnetic methods Dip angle (degrees)

o

Modo' (!)Mode'

.-2"1'1 .-2"1'1 Travene60'lostrike

~~lor -, Figure 7.35. Effect of traverse direction on VLF profi/es over a semiinfinite vertical sheet.

dipping sheets of finite deptb extent tbe AFMAG and VLF curves become unbalanced, like the latter, but tbe larger dip-angle peak lies on tbe hanging wall side, tbat is, opposite to botb otber metbods. As tbe deptb extent inereases, however, the peaks become more nearly equal again and tbe ftanks inerease on botb sides. Witb constant deptb extent, tbe effect 01 increasing deptb to tbe top is to 10wer and spread the peaks, decrease tbe erossover slope, and lilt tbe flanks. The preceding (eatures are ilIustrated in Figure 7.34. The explanation for tbese deviations (rom controlled-source dip-angle response lies in tbe unilorm field from AFMAG and VLF, which makes tbe assumption ol long-line currents (§7.7.3a) approximately correet. Thus tbe secondary field from eurrent flow along tbe top ol tbe sheet predominates lor a shallow model, whereas tbe reverse fie1d lrom tbe bottom becomes more significant at deeper burlal. As mentioned in Section 7.4.2e, f, tbe VLF and AFMAG systems, which have little or no control over tbe primary field direction, lrequently do not permit measurement of the dip angle in the direction oC traverse. Altbough the profiles may be plotted as vectors, as shown in Figure 7.17e, tbe results are inevitably distorted when tbe primary tield is nearly parallel to conductor strike. This is a fundamental disadvantage of both metbods. Figure 7.35 shows two results ol skew traverses (70 0 and 60 0 to strike) aeross a vertical sheet. The crossover point is not shilted, but the asymmetry inereases as tbe angle between strike axis and profile decreases, which would give a lalse indication ol a dipping sheet.

(e) Shootback results. This system, described in Seetion 7.4.2d, was designed to overcome problems in measuring dip angles over rugged terrain. Protiles in Figure 7.16c show the response over vertical and dipping thin conductors. The first produces a sym· metrical curve with a central positive peak over tbe top and equal negative tails on eaeh flank. The dipping sheet enhances the hanging·wall negative while decreasing tbe otber ftank. (f) Measurement of phase components; horizontal loop. This system (§7.4.3e), witb coplanar horizontal receiver and transmitter eoils, measures the ratio ol vertical secondary to vertical primary magnetie fields at tbe receiver for the in-pbase and quadrature components, tbat is,

%in-Phase-[it.,{H:/Hf}} % quadrature -.1'", { H:/Hf}

(7.35)

Readings are plotted at tbe T-R midpoint. Horizontal-loop profiles over hall-planes dipping 90, 60, 30 and 0° are illustrated in Figure 7.36. Tbe vertieal-model profiles have the following general cbaraeteristics (see Fig. 7.36a): There is a single negative peak when the T-R spread straddles tbe conductor, two zeroes when eitber coi! is directly over it (zero eoupling), and two smaller positive peaks at approximately 0.7/, after whieh tbe flanks tail off to zero. The curves are entirely symmetrieal, that is, tbe receiver and transmitter and/or the direc· tion ol traverse could be reversed without affecting the shape. Tbe sizes of the maxima and hence the . steepness of the curves are an indieation of tbe deptb of conductor. Maximum deptb oC conductor tbat can

Interpretatían ~

393

, , ~,

.

I

I

,,

\

,

1

'-

,, , " " ....

H,'JH/ (%1

(i)

o ct>

o

ti - I.z/l-

..... -

1,

LI= I

p - 0, :/1 - , .. p -

o, ./1 - ¡

p -

o, 1/1_ I

Figure 7.36. fffect of vdrious pdrameters on horizontd/-Ioop profiles over dipping sheets, (a) fffec/ of depth of a semiinfinite ver/ical sheet.

i 1_

be detected is controlled by the coil separation, a1though the small power available in the portable transmitter is also a practical limitation, A rule of thumb lrequently used for the horizontal-loop method is that the maximum detectable depth is one-hall the coil separation, Tbe quadrature and in-phase profiles in Figure 7,36b are very similar and the former may be either much larger or smaller than the in-phase curve lor a very poor or good conductor, Tbe addition of the quadrature component clarifies greatly the ambiguity betweeo conductivity and depth ol burial, characteristic ol dip-angle measurements. Some horizontalloop f1eld sets use two or more frequencies as a further aid in estimating depth, With dip, the profile becomes asymmetric, although this is not very pronounced lor dip angles larger than 45°, Tbe in-phase peak negative response is increased as the dip angle decreases, the values being 57, 30 and 25$ lor angles ol 3D, 60, and 90°, respectively (Fig, 7,36c), At the same time, as the dip decreases, the negative peak is displaced toward the

hanging-wall side, as are the zero crossover poiots, while the positive peak on the same side is enhanced and the positive peak on tbe footwall decreased. Tbe result is an in-pbase curve that has a steeper slope on tbe downdip side, Tbe quadrature response is also asymmetric. The negative peak increases sligbtly as the dip angle decreases, the zero crossover points are shilted downdip, but there is little significant change in the positive peaks, Tbe negative peak, bowever, is shifted toward tbe footwall- just tbe opposite to tbe in-phase curve. Tbus tbe steep slope on tbe quadrature profiJe is on the updip side. Tbe direction and tbe approximate dip ol tbe conductor can be estimated lrom tbe characteristics ol tbe two curves. Tbe etrect ol a horizontal sheet, seeo in Figure 7.36c, is to split the in-phase profiJe into two equal Degative peaks, located in tbe interval -1 S xii S 1, wiili a positive maximum over the center oC the sheet. The magnitudes ol these peaks are greatly affected by the de¡th ol the sheet as well as its width. For instance, wheD :11- lo, the negative peaks go

394


o o o

Modo! profllo

O"""'', - lOS

Caleulale
l. P=

v' 2.

Q-

I

Modo' profl" O/lo"" - S

.2 i!

, .... _-- ... _0"" -

In-phI" componen.

_ -_ QUldra'u .. componen. 1_ T -R Sfparllion

./1- 1

Figure 7.36. (Continued) (b) Effect of conductivity of a semiinfinite vertical sheet.

lo 110%, while the positive is 75\{' (bUl still negative)¡ lor z/I- l, the Desalives are aboul 4% and the ceoler peak is 20% positive. For a narrower sheet (0.3/) the negative maxima are only 7%, while the ceo ter is 5% posi tive and practically Ilat. The quadrature profile shows three minor negative maxima, the outside pair being closer to the edge 01 the sheet than the corresponding in-phase maxima, and the center peak is also negative. AgaiÍl, this profile is largely inlluenced by the depth of the conductor, while the width has less effeet. The horizontal sheet could easily be mistaken lor a pair of vertical conductors if the in-phase profile were considered alone. The quadrature curve, however, is generally different. The depth extent of the conductor inlluences the horizontal-loop profiles only if it is small; if the depth extent is greater than 21, the profile is practically that of an infinite sheet. Depth lo the top affeets both component profiles in about the same

ratio, thal is, a depth iocrease of six reduces both peaks by roughly tbe same amount (Figure 7.44). Skew traverses have little effcct on HLEM profile shape unless the angle with strike is less thao 30°. Even then tbe profiles show little symmetrical distortion, although the negative peak decreases while the positive ftanks grow larger and broader. Cooductive overburden has somewhat the same effect 00 HLEM response as that described for the fixed-transmitter, dip-aogle system. (8) Measurements of phase components; Turam. This ground method. like VLF and AFMAG, is suitable Cor energizing tbe sheet model as a long rectangular current loop with flow along the top edge and retum at deptb. We obtain the in-phase vertical component in the lorm 01 a reduced ratio, because there are two receiver coils (§7.4.3b), whereas the quadrature can be found from the differeoce io phase aogle between them [Eq. (7.18)]. Tbus we are

r 395

Interpretation ln·phaSC' componenl _ - - Quadraturr componenl d = depth ellenl of conduclor in

Q) (2)

- widlh of conductor in (])

.~ !! -10

" E

1.,.

o

o

Q)

"#0 110)/1 -

I~

:/1 - l. dip - 60'. ti - oc :/1 - l. dip - 30'. d - oc

:/1 _

1. dip - o'. ti -

21

.. R

.T/I

( el Figure 1.36. (Continued) (e) fffee/ of dip and depth ex/ent.

measuring tbe total vertical fields at tbe two coils H:(x - 8x/2) and H:(x + 8x/2) (Fig. 7.37a), in the reduced ratio

Hf( x - 8x/2) + H:( x - 8x/2) } { Hf( x + 8x/2) + H:( x + 8x/2)

x{ Hf(x + 8X/2)} Hf(x - 8x/2) H{ + H() ( H{) 1 + HU H{ - ( H{ + H~ H{ - 1 + H2/ H{

R p

(7.36a) where R is tbe measured ratio, p is tbe normal ratio, and the difference in phase Al#> - 1#>1 - 'i>2 (see §7.7.3j lor details). \ f

Several Turam curves for model sheets oC essentially infinite conductivity are shown in Figure 7.37; these illustrate the effect 01 varying depth and conductivity. The vertical scale is amplitude ratio or phase difference whereas the horizontal scale is made dimensionless by dividíng the coil-cable distance by tbe conductor-cable separation. In Figure 7.37a it is apparent that the profile is sligbt1y asymmetric over tbe vertical half-plane (because of tbe transmitter cable location) unless tbe sheet is quite deep. The amplitude peak loca tes tbe tbin sheet quite accurately. Lateral extent of a tbick conductor may be established by repeating the traverse with tbe loop on the opposite side. For an increase in depth by the factor 2.5, Figure 7.37a indicates a decrease in tbe reduced ratio of about 55%. Because tbis is a model witb zero resistivity «11 - 00), the reduced ratio is the in-phase componen\. Figure 7.37b illustrates the effect oC changiog cooductivity for essentially the same vertical

0) In-phase nlio

zlc - 1

I ....phax

O ln-pIIue ruio ror 1 - \1'2. el - I {@ PIwe dill'_ ror 1- v'2. el - I O In-pIwe ralio 1 - l, Q - O·)S {@ PIwe dill'ercncc 1- 3, Q - ()O]5

... ,f'1\

,~

PIwc

ratio

I

I I

,

\

\

\ \

I I

. . /* -. ... ,

(,,)

"

-

ó

(b)

Surf_

1" ReceivcR 2

Figure 7.37. Effecr 01 depth dnd conduc tivify on Turam profiles over d sem;in finite vertical sheet. 0- wL/R, (Eq. (7.16a)), (Eq. (7.44b)), 'x/e - 0.1. (.J) E(fect of depth varidtions lor cr, ca. (b) Effed o, varying eonductivity; cr,/crz - 1.1, z/e - 0.1.

/l-

(1

+ 1/02)112

Interpretation

397

(0

o

o

~

Horizontal ,hee. Dip-lO° Dip-60'

______________ t ______________~

Figure 1.38. fffect of dip on Turam profiles over sheet of finite depth ex/ent. z/d z/c -

¡.

sheet. Here we ftnd that as the conductivity contrast is rcduccd to "1/"2 - 2.1, the in-phase component is increascd by about 24%, and the phase difference by about 37%. The effect of dip on Turam response is shown in Figure 7.38 for highly conductive sheets ol small depth extent. Curve symmetry is nol much aJfected until the dip angle is less than 45°, although the positive peak decreases steadily with increasing dip¡ a vertical sheet of the same dimension and depth produces a maximum ol 1.09 (compare this with the ball-plane in Fig. 7.37a). The negative peak is on the downdip side. wbereas the positive is sligbtly displaced toward the cable. When the sheet dips toward the cable, rather than away from it, the maxima are reduced, althougb the general sbape is similar. In faet there is a particular gcometry of thin dipping sheet and Turam cable lor which the uniform primary field is parallel to the conductor face, when the resultant induccd currents are practically zero, because they would have to ftow

j;

across the narrow dimensiono This situation can be demonstrated in model measurements and has also becn found in the field. The dip for tbis unfortunate location is known as the extirlctiorl arlgle; it also occurs in TDEM surveys that employ the Turam-type of fixcd-transmitter loop (§7.7.4c¡ also Gallagher, Ward, and Hohmann, 1985). For dip angles even shallower than tbis, the sheet still dipping toward the cable, the curves are inverted. In such cases it may be difficult to determine the attitude of the conductor. The sheet depth may be estimated from the width oC the profiJe at baH-peak vaJue. However, for the examples shown in Figure 7.38 and in Figure 7.37b, the depth estimates are too large by as much as 40%, so that better methods oC estimating depth should be used. The masking effect 01 conductive overburden 00 severa! electrica! survey metbods, including Turam, was mentioncd briefty in Section 7.7.3b. To aid in exposing conductive overburden effects, as well as

Electromagnetic methods Table 7.1. Tvram model data. Line 4 +

~.

transmitter loop 1,600 x 1,200 ft; freqvency 660 Hz.

Slalion readings Stalion (fl)

Rec'r eoils (fl)

I:~

Phase

FR

(6.)

NR

RR

200 250

1.77

0.25"

1.76

1.01

1.54

0.45

1.54

1.00

1.39

0.60

1.43

0.97

1.35

0.60

1.36

0.99

1.64

-0.25

1.31

1.25

1.39

1.45

1.27

1.10

1.26

1.50

1.25

1.01

1.24

1.65

1.22

1.02

1.23

1.80

1.21

1.02

300 350

400 450 500 550

600 650 700 750 800 850 900

950 1,000 1,050 1,100

discriminating between conductivity and conductor depth. Turam equipment is frequently operated at two frequencies. for example. 220 and 660 Hz. Before concluding this seclÍon. we shall describe the procedure required to CODvert Turam field data for subsequent analysis. As in Equation (7.35) we can separate the real and imaginary components in the practicaI siluation when the conductivity is finite. The Turam syslem. however. measures the phase difference between the two receiver coils. rather than the imaginary component. Thus the respective phase angles may be found from the ratio of the imaginary lo real parts of for eaeh receiver coil. where [see Eq. (7.18)]

H:

tan~ - J".

{H' + H' }/9t~ {W + H'} (7.36b)

As in the horizontal-loop system, the conductivity can be estimated from the maximum values of ratios and phase differences. The usual method of plotting Turam results is not convenient for this, bUl it is relatively easy to determine the real and imaginary components of the resultant field from these values by converting the phase angle to a quadralure component. This procedure is explained with the aid of Table 7.1, which shows sample data taken from a laboratory Turam survey on a model conductor. The firsl column gives the locatíon of the reci:iver slatíon (midway between the two coils); FR is the fteld ratio (HI + H:)/(Hl+1 + H!+I), shown at the beginning of this section and the measured phase

(degrees)

V

R-

1-

Veos.

Vsin.

O·

1.0

1.0

O

0.25

0.99

0.99

0.004

0.70

0.99

0.99

0.012

1.30

1.02

1.02

0.023

1.90

1.03

1.03

0.033

1.65

0.83

0.83

0.023

3.10

0.75

0.75

0.041

4.60

0.74

0.74

0.059

6.25

0.73

0.73

0.084

8.05

0.70

0.70

0.098

difference is A~ - +.. - +"+l.The normal ratio NR is HI/HI+1' or what would be measured over barren ground at the same two statiODS; this is calculated using Equation (7.1Oc) or (7.l2b). Dividing FR by NR, we gel the reduced ratio RR. In the next column I: A~ is the sum of the phase differences, assuming zero values at the stalÍon adjacent to the near side of the transmitter loop. Note that station readings, NR, and RR values are referred to the station point, whereas in the remaining fout columns the values are referred to the receiver coil nearer to the transmitter. This is because zero phase and unity total field are assumed lo exist al the poinl ol closesl approach to the transmitter (presumably the latter has been located a reasonable distance from any conductors in the vicinity). Total-field values V are calculated from the ratio Vw/RR"'l/l' assuming Vi to be unily at the first slation selUp. Thus V300 - V200/RR~, V400 V,oo/RR350' and so forth. Finally. these are converted to real (R) and imaginary (1) components in the last two columns by calculating R - V cos ~, I - V sin~. ~ being the corresponding I: A~ value Cor each V. Note that R is always positive whereas I may be positive or negative. By plotting the R and I curves, we can get additional estimates ol conductor depth - half the horizontal distance between maxima and mínima on elther curve. The current center of the upper part of the conductor is located directIy below the point of maximum slape al the R curve. Also the maximum

Interpretation

399

20' 10'

-10' Dip -20'

ans1.

1---------

± 30'

-20' ±30'

~s~

20' <;

lO'

(e)

-10'

-ID'r---~------------------------~------------14

Figure 7.39. Vi F profiles over two identieal semiinfinite vertical sheets as a (unetion of distanee between the sheets. (a) s a 2z. (b) s - 4z. (e) 5 - 16z.

I 1

i l

R and 1 values may be used with characteristic curves to determine the thickness conductivity product. Field example 7 in Section 7.8 provides phasecomponent data determined from this procedure. Clearly Turam interpretation requires much lowlevel calculation following data acquisition. The altemate spread described in Section 7.4.3b elimina les this work because the receiver coils are equidistant from the transmitter loop on each traverse. Unfortunately no published inCormation is presently available with regard to this configuration.

(h) Sheet conductors; miscellaneous considera-

t;on5. Two conductors. Using an extension oC lhe coupled-circuil analysis (§7.2.4b and §7.2.5a), Grant and West (1965: 532-6) have shown that the effect ol

two conduetors is not generally lhe sum oC eaeh one aeting alone, but involves mutual eoupling belween tbem. This means thal Equation (7.20b) becomes :: __ (

kC:~TCI ) ( ~; : ~~l)

_(kC~~TCl

)

x( Q~1 ++ QijQl) x { QIQ2(1

- QIQ2) - jQIQ2( QI + Ql)}

(1 + Q;)(1 + Qi) (7.37a) where QI = wL1/ RI

for conductor el' Q2-

400

Electromagnetic methods 60 ~

20

O -20

Di~

on,le

-~

-0--

10

*.

:---=+

I

JO

t"

20 10

O' -10

-20'

-JO 30'

20 10 O

,

-10

,:

-20 I 1 1 -24 -20 -16 -12

I

I

•

I

12

1 16

11/: I

I

20

24

FiBure 7.40. VLF profiles over multiple vertical-sheet conductors. (a) Five sheets spaced 000 sheet distant 10z from the midpoint of the five sheets, all at depth z. (b) Two sheets at depths of z and 3z, spaced 10z aparto (e) Three sheets at depth z and spaced Sz aparto

z apart plus

."L,./R 2 for conductor (2, and terma in k~,ca are neglected because the c:oupling between the conduetors is assumed to be relatively weak. Two limiting cases arise. If the conduetors are very far apart, k c,ca - O and

very close together. kc¡cz k czlt ' and

e,

-

-

..

1. k TC1

-

k TCz ' kc,,1t -

_( krckCIt ) { (Ql + Ql)l + j(Q. ; Q2)} k TR 1 + (Ql + Q2)

(7.37c)

which is tbe sum of tbe two conduetors separately, as one might apeet. Ou the otber band, if tbe two are

whieh is the response oC a single loop having response parameter Q. + Q2' The coupling between the two conduetors may be positive or Degalive. Model studies have shown tbese apressions to be quite good approximalions. MuJliple conduelon. Tbe various EM ground methods show different responses to multiple con-

Interpretatíon

ductors; clearly the differences are determined by the geometry of the particular system, as well as that of the conductors. The simplest dip-angle system to use as an iIIustration is VLF or AFMAG, in which the conductors are uniformly energized by the remote transmitter. Figures 7.39 and 7.40 sbow calculated profiJes over several vertical-sheet eonfigurations. Zero coupling is assumed between the conductors. When the spacing between the sheets is less than 2z, these curves will nOl be exact, because the mutual coupling would make the maximum tilt angles somewhat larger. From Figure 7.39 it can be seen that the proper crossovers are displaced to the ftan.ks of the curves, beyond the actuallocations of the sheets, unless their separation is less than twice the depth, in whicb case the profile indica tes a single thick conductor. The examples (a) and (b) of Figure 7.40 sbow that a conductor that is deeper or smaller (or oC lower conductivity, although this situation is not ilIustrated), than its neighbor will give a relatively weak response. Discrimination among multiple conductors is even more difficult with the fixed-transmitter dip-angle technique. Unless the transmitter is located Cairly well between two identical sheets, the more remote will hardly respond at all. In this case the two are not energized equally. Consequently it is more diCficult to resolve multiple conduetors with this type oC EM. The parallel-Iine dip-angle resolves adjacent conductors better than the fixed-transmitter unit, as might be expeeted. Furthermore the erossovers are in tbe right place. Even so, wben the separation is 1ess tban twiee the depth, the broadside traverse wil1 not distinguish belween two distinct sbeets, a single thick one, or a Hat sheet. The horizontal-loop EM is perbaps slightly better tban the broadside array in resolving two conductorso The in-phase profile shows two peaks at the proper location when the separation is twiee the depth or greater, whereas the quadrature component is almost the same. These curves are shown in Figure 7.41. Coupling between the sheets affects the quadratuce response particularly, so that the conductivity of two separate sheets would appear to be lower than when tbey are clase togetber. The resolving power of Turam over multiple conductors is probably not as good as with tbe horizontal-loop EM, because of the fixed transmitter, which wauld generally be located to one side. However, the fact tbat two receivers are used with fairly close spacing may heip the resolution somewhat. Discrimination between multiple and tbick conduclon varies with the different EM systems. From

401 Figure 7.41, the HLEM appears to have good resolution unless tbe width is greater than the T-R separation (see also Fig. 7.36c). It is possible to get a fair idea of conductor widtb with the horizontal-loop se!. Because the zero crossovers occur at x - ± 1/2 for a thin sheet, any excess, greater than /, in the separation between these zeros is an estimate of conductor widtb. Here again the horizontal-loop EM has a distinct advantage over dip-angle EM. As noted previously (§7.7.3g), the near-surface width of conductor may be estimated with the Turam unít by taking the sarne profile twice witb the transmitter cable on altemate sides. With dip-angle EM equipment it is difficult to distinguish between a wide conductor and lwo thin sheets unless, as we, have seen, tbe separation is appreciable. One method of determining conductor width witb the fixed-transmitter system is to offset tbe transmitter from the edges of the conductor 200 lt (60 m) or less and make several traverses normal to the conductor. As the reeeiver-transmitter separation increases, the crossoven shift toward the edge of tbe conductor remote from the transmitter. By repeating tbis measurement with the transmitter on either side oC the conductor, a fairly good outline oC its lateral extent is achieved. The broadside array is theoretically better tban the other methods Cor thick conductors, beeause the crossover at the center is reversed. Over separate tbin sheets the center crossover is in tbe normal sense. However, these crossovers are usually quite small and the difference between normal and reverse may be difficult to distinguish. (í) Sheet conductors - characteristic curves. General. The usual procedure in EM interpreta-

lion - comparison of field profiles with tbeoretical and mode1 results - requires a good-sized library ol tbe latter type 01 curves. A considerable advantage is achieved by combining the theoretical and model data into characteristic curves that emphasize certain features of the EM profiles, such as maximum tilt angle and crossover slope for dip-angle measurements, or in-phase and quadrature response for phase-component systems. Dip-angle characteristic curves. We have mentioned previously that the peak dip angle and tbe slope at the crossover are functions of botb deptb and conductivity. However, conductivity changes af· feet botb parameters about the same, that is, tbe ratio of slope to peak response is approximately independent of conductivity. Thus a simple charac· teristic, which works lairly weIl for steeply dipping conducton, may be prepared by plotting this ratio


402

-

In-ph ...

- - - QUidr.tur. fo •• 11 ftlures

.. - o·s/ z - 0·1/

/ -T-R sple;n, (d)

o,

Figure 741. Horizontal-loop EM profiles over various eonduetors great dep/h ex/en/o (a) Two /hin sheets with spdcing equal to the T-R spacing. (b) Two (hin shee/s wi/h spacing equal fo one-half /he T-R spacing. (e) Two thin sheets with spacing equal /0 one-qudrter the T-R spacing. (d) Conducting dike with width equal lo half the T-R spacing.

against the known depth, or z/I ratio, taken lrom model results. An example is shown in Figure 7.42a; fue slope near the zero crossover is plotted in the lorm ol a ratio, degrees/(x/I), against z/I. A more useful characteristic curve, which provides both dip and depth lor the semiinfinite sheet conductor, has been developed by Grant and West (1965, pp. 559-60) and is illustrated in Figure 7.42b. Rere the ratio of peak tilt-angle magnitudes on either side of the crossover is plotted against their total amplitudes. If the resultant point falls reasonably on this diagram. the dip angle may be interpolated and fue depth calculated from fue relation z - k/ sin a. This plot is developed for the fixed-transmitter set

and will give poor results if the sheet dimensions are less than the transmitter-receiver separation. Parameters lor characteristic curves. The response parameter Q. discussed in Section 7.2.5d and ilIustraled in Figure 7.10 for the simple electric circuit analogy, is a significant quantity in EM characteristic curves. Recalling the discussion ol scale models in Section 7.7.lb, the ratio ,,/12 /p - or what is the same thing, p."'Cl/ 2 - is dimensionless and invariant in passing from a field to a model system. Similarly the response parameter Q is dimensionless and has the same form, a product ol conductivity, permeabil¡ty, frequency, and area (or linear dimension squared); trus follows because L ex: ,,1, R ex: pi/A.

Interpretarían

403

o

+ Dip .~gl.

t

Brnadside protile

I

= T-R 'pacl"S

la)

I:tl I _ T -R 'p.ein.

(b)

Figure 142. Characteri~tic curvp.\ for semiinfinite dipping-sheet conductor. (a) Depth to the top of a steeply dipping sheet (rom the crossover slope and peak /ilt. Broadside array. (From Ward, 1%1) (b) Oep/h and dip using fixed-/ransmitter, dip-angle system, (From Grant and Wesr, 1%5.)

hence wL/R o: p,wI1A where A is the area, or produet of two significant dimensions, Employing a more sophisticated approach. electromagnetic theory gives the response parameters for several specific configurations. A few of tbese are:

Sphere Disk Thin sheet Half space

/LWl1a

2

p,wola /L

Wl1tc

"woe

2}

a - radius t = thickness

e - conductor-EM unit spacing

Note that the linear dimensions a, 1, and e appearing in \bese expressions are particularly signifi-

eant in determining the pattem and intensity ol secondary current flow in the conductor, Frequently there are several dimensional parameters of this type, in whicb case we are free to choose any two oC them. However, the efrect oC sorne oC these parameters may vary with the conductor-EM system geometry; this is evidently tme with moving source units. In drawing up characteristic curves for thin sheet conductors, for example, it is customary to use as parameters the thickness and whichever fixed dimension of the EM system controls the response. Thus we would insert the transmitter- receiver spacing in artificial source dip-angle (Fig. 7.43), the height aboye ground in airbome double-dipole systems (Fig. 7.81c), or the horizontal distanc:: between transmitter and conductor in Turam.


404

_::::::::::====== :/1 _ O.()l 11 OS

100

I!O'

~f1.

S--, . .

60'

_ _- - - - - - : / 1 . 0 · 1 2

40 ~_ _- - - -

:/1. 0·30

1- T-R spAdn. , _ - , ... - peak-la-peak IL,nplilude

Response parameter, ",.."'

1'"

100'

60' S""" - ,.... 40' 20'

___ - -

-

-

- - - - :/1- 0·30

dip90°

- - - dip60°

Response parameter. ",. ..,, (tI

Figure 7.43. Characteristic curves for semiinfinite sheet. (From Ward, 1967). (a) Fixed-transmitter di~ang/e system, vertical sheet. (b) Broadside array, dipping sheet.

As mentioned in Section 2.7.7, we should try to minimize the number ol variables in order to produce a reasonable number oC curves. Because we are

al liberty to employ one dimension as a scaling parameter, the number oC unknowns is reduced by 1. Tbis scaling unit may be either a length that has relatively little influence on the conductor response, or one that can be measured directly; Cor an example oC the latter, we could use the transmitter-receiver separation or the aircrart height. Dip-angle curoes. At least two types oC characteristic curves involving the response parameter have been developed Cmm model measurements in dipangle interpretation. In one of these, two source frequencies are required. The ratio oC peak highfrequency response (ODtl¡Opo&)HF is plottOO against

low-frequency peak response (BDtI¡Opo&)LF for various depth and dip angles. A large set of curves is required for diJferent dip angles, each set being drawn for constant depth and constant response parameter. TIte second type, Cor single frequency, consists oC plotting peak-to-peak (Opas - Olle') amplitude against response parameter for different depths, as illustratOO in Figure 7.43, for fixed-transmitter and broadside array_ The depth muSl be approximately known to use these curves. A complete catalogue again requires a characteristic curve for each dip angle. Presumably similar results could be developed Cor VLF. From the plots illustrated in Figure 7.43, it is possible to find p.watl, if we can obtain the deptb by other means_ We know w and I and can assume p. to

405

Interpretation

-20

~

= l! 11 -10

c5

" ~ lOS

(a)

-20

e

3 I!

11

=

-10

O'

(b)

X ~-20

!í

¡

c5 -10

r" \o~

Figure 7,44, Charaeteristie eurves for horizontal-loop system over a dipping sheet. p - 0l'..,tl, (Fram Strangway, 1966.) (a) Dip = 90°, (b) Dip - 60°, (e) Dip - 30·,

be che free-space value in most cases. Ir a reasonable estimate of che width I can be made, the approximate ronductivity may be determined. Phase-componenl curoes. Standard characteristic curve sets ror the thin sheet are illustrated in Figure 7,44 for che horizontal-loop EM. The ordinate and abscissa are, respectively, the quadrature and inphase response taken midway between the zero crossovers. Three sets are shown, lor dip angles of 90,60, and 30°. For the vertical sheet the responses are maximum values; this is not so for the dipping sheets, however, because oC the asymmetry ol the profiles. The depth and response parameter may be read off chese curves. If the conductor width can be estimated by other mean s, it is then possible to get some idea of the conductivity, There is some doubt, however, about the significanee in separating the conductivity from the conductor width in che product al. The chances ol a conductor being homogeneous over its en tire width

are extreme1y small. As a result, the values obtained for conductivity of massive sulfides are an average and generally fall in quite a narrow range - something like 0.1 to 10 S/m - which is a few orders of magnitude smaller than the conductivities usually assigned to the majority of sulfides in tables (§5.4.1). Possibly the conductivity-thlckness product is a more practical parameter and indeed it would give a rough estimate oC volume or tonnage equally well. Similar sets of curves are available for Turam, usiDg peak quadrature and in-phase response. One of these, for a thin sheet dipping 60° and ol 20 m depth. is shown in in Figure 7.45 for different values oC the parameter A - lOS latf and strike length ! (note that, although the transmitter-coil dimensions alfect the curve somewhat, they are fixed here). It should be mentioned that, although these universal plots are extremely useful for interpretation, they should not be used alone without comparison of the field profiles wich a standard catalogue of theo-


406

Figure 7.45. Characlerislic curves (or Turam syslem over dipping-sheet conductor of infinile depth extenl and variable strike leng/h t. Deplh z - 20 m, dip .,. - 60°. Tx loop 600 X 1,200 m, ;\. - 1O s/atf, " - 1'0 (mks uni/s). cnl.rged

H'I

~-----,

H' '.

f

I

I

\

\

Hi

I I

I

I

_>---_

H' .. ' " I

H'" \1 IL _____H' .!! ____ ...JI

Figure 7.46. Geometry of dipping-sheet model energized by VLF source.

retica1 and model curves as well. That is, because the cllaracteristic curves malee use of only a couple of critica1 points on the standard profiles, the field plots should fit the latter reasonably well before the former may be used with confidence.

the secondary field components in the form

H; - icx/2'11"(x 2 + Z2) - ic{x + dcos D) /2'11" { (x + deos D)2 + (z + dsin D)2}

H; - icz/2'11"( x2 + Z2) - ic{ z + d sin D) ü) FDEM systems; ac circuit analysis. In Sections 7.2.4b and 7.2.Sd we made use of ac circuit parameters to illustrate amplitude, phase, and conductor response for EM analysis, and in Section ?2.Sa several relations were given for mutual inductance between circular and linear wire models. The ac analysis is attractive because tbe models can have finite conductivities, aside from tbe simplifications compared to EM theory, Because tbe coupling between conductors and transmitter and receiver loops is genera11y complex, however, this approach is greatly oversimplified. It will not produce useful results when the conductor dimensions are mucll larger tban tbose of tbe transmitter, as with localsource dip-angle sets and Slingram, althougb it works reasonably well for uniform-field and long-wire systems like AFMAG, VLF, and Turam. We will consider tbe last two of tbese briefty for circuit analysis of the sheet conductor. In performing VLF surveys, the azimutb of the transmitter station should be as nearly as possible on strlke witb tbe sheet target. From Figure 7.46 we find

/2'11"{(x + dcosD)2 + (z + dsinD)2} where ic is the current in tbe conductor induced by the transmitter horizontal field H!, and d aod D are its deptb extent and dip. The transmitter field may be taleen as a constant. Because the dip angle B tan- 1{H;/(Hf + H!)} - tan- 1(H;/H!) we have, following some manipulation, taoB

-1 H;¡H; 1 -a/{1+K(1+a2 )} -(a + dcosD/z) /[K{(1+dsinD/z)2 +(a + dcosD/z)2} -(1 + d sin D/z)]

(7.38a)

where a - x/z and K - 2(z/ic )Hf. The dimensionless parameter K may be used 10 obtain depth estimates.

Interpretation

407

- - Oip - Q(J'. di' = 4. K = 1.13 - O i p - 135'. di: = 4. K - U3

and Fig. 7.37a] i

Hr =

p

2w(x - 8x/2) i c ( x - e - 8x/2)

H{ =

--~-----------~--~

2'IT{ (x - e - 8x/2)2 +

:2}

M) ip( x - e - 8x/2) ( {n 2w{ (x - e - 8x/2)2 + :2}

-

Hf = 2w( x + 8x/2)

M) ip( x - e + 8x/2) ( Hí = {3L 2w{(x - e + 8x/2)2 + z2}

(al

where M is the mutual inductance between transmitter and the long wire conductor [Eq. (7.21b)]. L is the conductor self·inductance [Eq. (7.22a), §7.2.5b]. and {3 = (1 + Q2)1/2. Then we have

lit

(!!.) (!!.)

=

Hr

{3L

Hí _ Hf

_Oip - 45'. di: - 4. K - 1.\3 --Oíp - 45'. di: - 10. K - 1.13 (bl

Figure 7.47. VLF pro files over dipping sheet obtained fmm ac circuit analysis. (a) Oip 90 and 135°. di z = 4. lb) Oip 45', d/z - 4 and 10.

j

VLF profiles usiog the relatioo in Equatioo (7.38a) are displayed in Figure 7.47; the pronounced effect of dip for two models of limited depth extent (d/z = 4), one vertical and tbe other dipping 135°, is shown by tbe change in the maximum dip angle by a factor of 2 as the dip changcs from 90 to 135°. Note that tbe maximum lies over the hanging wall. Comparing tbis profile witb the AFMAG profile in Fig· ure 7.34a, we see that the peak-to-peak ratio is larger for VLF (however, the depth extent is also targer for tbe AFMAG example so that the comparison is not entirely valid). Figure 7.47b demonstrates the effect of depth exlenl on VLF profiles. Two models, identical except Ibal d/z changes from 4 to 10, produce enlirely different curves; tbe peak·to·peak ratio is reduced from about 4 to 4/3 (see also Fig. 7.~4b for a similar AFMAG example). To work up Ihe ac circuil analysis for Turam, we return to Equation (7.36a) (§7.7.3g). For tbe in-phase component tbe various fields are given by [Eq. (7.lOc)

(x - 8x/2)( x - c - 8x/2}

fJL

:2

+ (x - e -8x/2)2

(x + 8x/2)(x - c + 8x/2) z2 + (x - c + 8x/2)2

Setting (M/fJL) = W. x/e = a. 8x/c'" 8a, :/e - y, and neglecting (8a)2, we gel

R = p [

[1 + 1+

1) -

W{ a( a 8a( a - t)} (a - 1)2 - 8a( a - 1) + y2 W{ a(

a- 1) + a-n }J 2

8a(

(a - 1) + 8a( a - 1) + y2

JI (7.39a)

This expression may be wrilten in a simpler form if we assume H; « Hf and 8x« x, 8a « a, SO Ihat

~

= 1_ (

~; )( d~;) _ 1 _ 2W~ 8x ( d:;)

and

This gives for tbe ratio R/p Ihe approximate expreso sion

R -

P

os

1 + Wa8a

{.,1_ (a _1)Z} .,2+{a-l)

2

(7.39b)

The real componenl may be obtained by multi· plying Equation (7.39a) or (7.39b) by Q2j(1 + Q2)

408

Electromagnetic methods 20"

Quadrature 10 (%)

O"

?~:=,H

.:_._.

-20'

_!Q!.Q_':'::::_~.•;_:b_W_:::~:_A_:::::::_rM_A_ _ _'\t-1OOO nm---'_. . _ . . ._%.3_'_t_._ .... :4fn7::~ (a)

IOOOOm

--r"'''''''~''''''''''''''' lb)

Figure 7.48. VLF profiles over vertical contacls between beds of different conduclivilies. (a) 1,000 11m bed between two half-spaces of 10,000 Qm; no overburden. lb) Same as (a) except overlain by 6 m of conductive overburden, p - 100 Qm.

(Eq. (7.16a»). For the imaginary component we return to Equation (7.36b) and find the respective pbase angles, using the same multiplier. Theo we have tan4l¡ -

{(M/L)Q(I- a - !Ba)(a + iBa)}/

[(1 + Q2) {yl + (1 - a - !Ba)2} + (M/L)Q2( 1 - a - !Ba)( a + !Ba)] tan+-z - {( M/L) Q( 1 -

a + iBa)( a - iBa)} /

[(1 + Q2) {y2 + (1 - a + iBa)2) +(M/L)Q2(1 - a + !Ba)( a - !Ba)] from which we gel (7.39c) Tbe expression for pbase angle is much simpler if we use the approximatioD in Equation (7.39b), wben we bave tan~ .. ~..

"'m {R/p } .."'m{ -R} p

1 + Sf.. { R/p }

Tbus, M

{-rl - (a 2 Y + (a -

f.1/I---(aBa){ L

I)Z} ( 1 ) l} Q (7.39d)

1)

Using Equatioo (7.39b), this can be written

ta.,. _

(1 _R)P (I+Q2)1/2 1 .. (1 _R)P ~ Q

(Q~3)

(7.3ge)

Tbe pro files oC Figure 7.37 were plotted from these relations. The VLF ground survey is attractive for mapping sbalJow geoJogical structure because of its speed, simplicity, and low. cost (Telford, Kin&, and Becker, 1977; Fiscber, Le Quang, and Müller, 1983). For example, the steeply dippiog contact or single-bed lault produces 8 cbaracteristic VLF sigoature when there is a conductivity contrast between the two sectiODS (see §7.8, Example 4, for a classic case). Although this COmmon struclure may be treated by ac circuit modeling, it is more illuminating to use 2·D MT relations for E polarization (§6.2.7), because the E and H fields from the VLF source

r

Interpretation

409

produce Ey (on strike) and Hz (on traverse) components, whereas a vertical component Hz results from the conductivity contrast. Equation (6.23b), the scalar diffusion equation io Eyo was derived from tbe 2-D relations Cor tbe VLF field in tbis orientation. These are

8H,J8z - 8Hz/8x

~

PLAN VI El

(i)

Strlh

h

lu,t •• '

---1:-t-t-+-~=--=-+--t-+--

I'/lOmE LIlE

loo,

CROSS-SECTtON

aEy

BEy/Bx - - jWJl.oHz 8Ey/8z = jW/loHz

COIDucrlVlrr- r"rcurss PIODUCr (1"

In the vicinity of the contact tbere is an Hz component which differs in phase from Hz. Thus the wave is elliptically polarized (§7.2.4<:). Witb the VLF instrument we measure dip angle 8 (inclination of major axis) and ellipticity e, or quadrature (ratio of major to minor axis). These parameters are c10sely related to tbe values of H,/ H" and z - ". Assuming H, « H" tbey are given approximately by tan8 =IH,/H"lc.os(
-1 H,/ Hz 1SlD(
-
(Ji)

(7.38b)

(a) Figure 7.48 shows profiles obtained over a wide conductive outcropping slab model sandwiched between two resistive sections. There is no pronounced crossover associated with these curves, but they have two distioctive features: botb dip angle and quadratUTe peak directIy over tbe contact, tbe Cormer positive, tbe quadrature a negative cusp, and both decay more rapidly to zero 00 tbe conductive side. As one would expect, the curves are reflected in the horizontal axis at tbe second contact. Figure 7.48b shows tbat tbe effect of an overlying bed oC conductive overburden is to decrease the dip readings and shrink tbe quadrature cusp.

7.7.4. Ground Systems¡ TDEM over Dipplng Sheet (a) Cenera ,. . Uotil tbe 19705, most practical TD interpretation analysis was done on Input data because it was tbe only ID equipment in general use (Becker, 1969¡ Morrlson, PhiJlips. and O'Brien, 1969; Palacky and West, 1973). At present tbere are at least six ground IDEM systems available. Compared to the diversity of FDEM ground units, however, there are no fundamental differences among tbem, except in transmitter waveform, loop(s) size, and portability. lnitially interpretation was obtained from scale-model measurements, but since the late 19705 computer modeling has been refined and has become increasingly popular (Annan, 1974; Dyck, Bloor, and

r

¡U,. lil1l'

21.61111 KI.hll

.\1

Transmltt8r Curren'

43.2111'

0.5,1.0, or 1.5 111 S

Figure 7.49. PEM(7) moving-source TDEM. (AfIe, Barrel and Hohmann, 1985.) (a) Geometry of rhin-plate and sphere models. (b) Wavefo,m fo, 70.8 ms pulse.

Vallée, 1981). The PLATE model developed by Dyck, 8100r, and Vallée is now widely used Cor botb ID and FDEM interpretation. The PLATE computer package measures tbe response of a dimensionally and inductively thin sheet conductor in free space, tbat is, tbe thickness t « (, d, where ( is strike length and d is deptb extent; at tbe same time I < 0.68, wbere B is tbe sldn deptb (§6.2.3). Eddy currents induced in tbe sheet by the primary field are simulated by a set oC so-called eigencurrents in the PLATE program, each baving a different circulation pattem on tbe sheet. Tbeir rate of decay increases with pattem complexity. Because


410

CHANNEL

10 m. PULSE CENTEA

PP

-.05 m.

20 m. PULSE

W.OTH CENTEA

.1 mi

·.1 m.

WIOTH

.2m.

GAIN F'ACTOA

-

I

. 1 !S

.1

.5

2

.5

.2

.e

5

.!S !S

.5

1.1

.e

1.85

4

.8

.4

1.8

.8

2.e8

IS

1.45

.7

2.9

J.4

5.75

e

2.4

1.2

4.e

2.4

5.18

7

4.0 es. 4

2.0 2.e

8.0 12.e

4.0 5.6

7.20 10.0

8

.2 .4

1.0 l. :ss;,

(c) Fi8ure 7.49. (Continued) (e) Channel data; PP denotes Hf.

the response ol each eigencurrent is independent oC tbe otbers, the solution becomes a summation suitable Cor the computer. It may be obtained by computing the magnetic field impulse response (§A.13) and convolving it witb tbe current waveCorm or its time derivative to obtain H' or aH' lato (b) PEM. The geometry oC tbe moving-source version oC this system, traversing a sphere (to be discussed in §7.7.5) and a dipping sheet is shown in Figure 7.49a, and the 10.8 ms waveform and channel data in Figure 7.49b (Bartel and Hohmann, 1985). In the PEM 1 configuration (see Table 7.3), oruy fJH;/fJt is measured usually, then normalized by dividing by tbe maximum value of aH! /a, and displayed as parts per thousand (Ppk) for each of the eigbt channeIs on an analog meter. Primary field is measured during the ramp turn-off. The effect ol dip is seen in Figure 7.50a Cor angles 010, 30, 60, and 90°. A positive peak precisely marks the conductor edge (Iocated below the zero distance) on the profiles oC Figures 7.50 and 7.52 00 the early channels, then driCts sligbtly inward 00 the sheet al Jater time; the latter is due to eddy current migration and decreases for steeper clip. There is a smaller negative side lobe off the conductor edge, which increases sligbtly with dip. Tbe corresponding negative lobe to the rigbl, considerably larger Ihan the other al 30°, decreases with dip. Consequently Ihe response indicates shallow dip but is not very sensitive to dips greater than 45 o . When the conductor depth is somewhat greater than the T- R separation there is insignificant response, as is evidenl in Figure 7.S0b, c for models dipping 90 and 300 • Ir the presence ol a sheet

conductor can be established at alI, the sligbt negative anomaly over the 30· sheet at z - 200 m migbt be interpreted as a shallow dip to the rigbt, because the rigbt-hand slope is more gradual. For the shallow dipping model, however, maximum detectable depth is li ttle more than 100m. PEM profiles over a 30· sheet oC variable conductance al are shown in Figure 7.5Od.. AlI channe)s respond to the 100 S model, the response increasing sligbtly from channel 1 lo 5, then decreasing. This minor peaking effect is caused by the gain factor in the receiver, shown in the rigbt-hand coIumn of the table in Figure 7.49c. When al - 10 S there is no significant response beyond channeI 6 and for 3 S beyond 3; Cor al S 1 S no measurabIe anomaIy is evident. Decreasing the strlke Iength 01 the model reduces late time response, much like the attenuation from a reduced conductance. Varying the depth extent gives similar results in addition to changing the horizontal extent of the profile for shallow dip. AlI oC the curves in Figure 7.50 are principal profiles over the center of a mode1 pIate 600 x 600 m. When the survey line passes over the end oC the plate or beyond it, response is greatly attenuated or zero (§7.7.3b). Tbe change in target response produced by conductive overburden is perhaps more difficult lO resolve lor IDEM than FDEM. Using a model HLEM unit, Lowrie and West (1965) found that an overlying conductive sheet, not in galvanic contact with a vertical sheet below it, made the latter appear more conductive and more deeply buried than it actually was, thus rotating the curves of Figure 7.44 dockwise about the origino The phase change, produced

Interpretation

."

411

10 3

10

10 3

2

10

2

30°

ppk lO'

lo'

o

O

-200

o

I 200

400

600

2

2

3

3

4

4

5

5

6

6

7

7

e

e

I 800

10 3

10 '

60°

ppk

lO'

I '-00

I 600

I

800

90°

O

2

2

3

,..

3

,..

6

6

7

7

8

8

(a)

.

r

200

lO'

O

"

O

10 3

10 1

•

I

-200 distonCf! (m)

figure 750 PfM(l) response /0 a dipping sheet as a fune/ion of dip. depth. and TCP. d = 600 m, T-R - 100 m. TCP - l1t - 30 5 (exeept in (d)). (After Bartel and Hohmann. 1985.) (a) Effeel of dip; z - 50 m.

t-

by the primary and secondary fields going and returning through tbe overburden, becomes a time lag in TO measurements. Its effects may be approximated by adding the separate responses of overburden and target in tbe frequency domain, then transforming the sum into tbe time dornain.

Using Nabighian's analogy (§7.2.6d) we may say tbat tbe srnoke ring tingers in the overburden layer, to diffuse downward at a later time. Thus tbe riog may be beyond the receiver coi! locatioD at a deJay time corresponding to, say, channel l. The response by tben is negative, producing a cancellation or

412

Electromagnetic methods 10'

Id'

50m lO'

75m

lO'

o

o

.

~------2

~=-------

~-----3

-;:.0------- 3

4

~------4

.:.:=-------

-------5 -------6

·:;.;.....-----5

-"-'"------ 1

--~~~~~--------1

~-----5

-----------8 1-1-+1----+-+-1-+----ll_. ·200

O

2

200

I

I

1

1

400

600

800

---------------------8 1

I

·200

distante

O

I

1

1

1

200

400

600

800

(m)

10'

10 2

10

100m

1

200m

ppk lO'

~----------------~, 2

3 4

5

-

6 1

8 (b)

------------------2

-------------------3 -------------------4 ---------------------5 --------------------6 ------------- 7

-----------------8

Figure 7.50. (Continued) (b) Effect of depth, dip - 51:)0.

reversal oC the target signal; thus thc latter may be detcctcd in the proper sense only in late channels whcn the overburden signal has decayed sufficiently. Figure 7.S1 shows the resultant effect OD the primary field and the target response bclow the overburden. Even ir the smoke ring has arrived in time lo produce a positive response in the receiver, al still

later times it may relum a negative signal as a result oC changes in overburdcn thickness and conductivity. Thus tbe profile may show positive and Degative fluctuations, unlike those in the previous figures. This is illustraled in Figure 7.S2b where the ovcrbur· den effect has been simulated by tracking the smokc riDg (Fig. 7.11) from surface down to the 300 sheet

f

Interpretation

413

10'

10

10'

2

10 '

SOm

ppk

lO'

lO'

O

O

I

I

-200

I O

I 200

I 400

I

600

75m

2

2

3

3

4

4

~

5

6

6

7

7

8

8

I 800

I

I O

I -200

I

200

I 400

I 600

I 800

distance (m) 10 1

lO·

ppk

10'

102

100m

lO'

lO'

O

O

200m

--------

---

2

3 4 ~

~

6

~

2

3 4 5 6

7

7

8

8

( e)

figure 7.50. (Continued) (e) 5ame as (b) exeept dip - 30·.

model. To emphasize the pro/He ehanges eaused by overburdeD, a curve set for no overburden is shOWD in Figure ':52a (e) EM37.

Model data for the EM37 ID system, obtained from the PLATE program, have been reponed by Gallagher, Ward, and Hohmann (1985). Fie!d procedure with EM37 is similar lo Turam; the large Tx loop is fixed and off the target and only the

1

1

smaIl Rx eoil moves (§7.4.4e). Two of the three magnetic components, H, and H" along traverse, were determined during the study, using a 30 Hz recurrence frequency (8 ms maximum window). For this frequency the window widths of the 20 channels ranged from 17 I'S at channel 1 to 1.56' ms for channel 20. Pertinent data for the channe! on-off times and with respect to switch-off are given in Table 7.2.

'1

'2

414

Electromagnetic methods 10'

1

10

1005

305

lO'

lO'

O .......-o:--JlIYt---

O

:::;;;:0-- 2 ----:=-- :5

2

:5

I 1 -200

4

-:::;;:-1fA1f-"~,L--7"-'---=---

5

--~~~~~~-~~~----5

6

--~~~r7~~~~~----6

7

-__=:-d----ft"""7,!C..-r--r--::::_--7

8

----~~~~~~~------8

+- -+----4 --+- -f - +- +--+----4 O

200

400

600

rl-+-+I-+--t--+i-+-+1 -1

800

- 200

O

200

400

4

I

I

600

800

distance (m) 10'

10 S

35

ppk 10 1

10 1

0~~-1~r---------~--~

O 2

--~~¡----7'~::::;:::----2

:5

--_....:::::.....~-r-=;::::oo---3

4

--------~==--------- 4

5

-------------5

6

----6

7

------------------ 7

8 (d)

----8

Figure 7.50. (Continued) (d) Vdriation wirh TCP; z - 50 m, dip - 30°_

The model promes Ihat follow, similar lo Ihose Cor PEM, are in terms of Ihe time derivative and plotted in nanovolts per square meter (nV1m2), converted Crom millivolt signal in Ihe receiver by using Ihe declive Rx coil area and Ihe gain. Except where noted otherwise in figure legends, plate dimensions are (- 800 m, d - 400 m, al'" 30 S, and deplh z - 100 m. On the horizontal scales, zero represents Ihe surCace point coincident wilh the center point oC

Ihe near side oC the Tx loop, whereas 300 líes over Ihe top edge oC the sheet, as shown in Figure 7.22a. Figure 7.53a shows profiles ol sheets dipping O, 30,90 and 150°. Dips less than 90° point away from Ihe Tx loop and vice versa. Loealion 01 the Tx loop creates an asymmetry which appears greater in lhe H, than the Hx curves. A verlical sheet produces symmetrical H" profiles which develop a minor negalive lail to the right as the dip angle decreases; tbis

Interpretatíon

asymmetry, as well as the peak-to-peak amplitude, is larger Cor dips in the opposite direction. The Hz curves, considered in the same sequence, are more asymmetric over the vertical sheet (compare with Turam c"rves in Fig. 7.37). As the dip decreases, so does the positive peak, whereas the negative peak ¡ncreases. When the dip is toward the Tx, the opposite is true, Ihe profiles becoming more symmetrical and the overall amplitude nearly doubling. rn the latter orientation the possibility exists oC vanisbing primary field coupling (extinction angle; §7.7.3g). Response is reduced or completely suppressed Cor sheet s oC limited depth extent and a sign reversal mayoccur. Dip direction may be indicated by the ratio of positive-to-negative peak amplitudes oC the Hz curves. When 9 < 90° the ratio is less than unity and vice versa. This estimalor does not appear to hold for the profiles where the positive peaks are larger throughout. For a horizontal sheet the negative Hz peak lies nearly over the center, whereas the edges are marked by the positive and negative Hx peaks. The top edge oI the sheet is roughly located by the positive peaks on the Hx profiles, although when 9 approaches 180 0 Ihis is not so, because both Hx peaks driCt toward the transmitter. Using the Hz curves, the top edge is more or less under the maximum slope for 0 0 < 9 < 135°; beyond tbis the same migration takes place. When plate dimensions are < 800 X 400 m these curves are modified, particularly Ior peak-to-peak ratios. The same is true when plate-Iransmitter geometry is changed. More models are required for complele analysis. It is also apparent that the profiles are displaced laterally, Crom early to late time, unless 45° < 9 < 135°, in which case interpretation may be refined by se\ecling particular profiles. To consolida te the data and simplify analysis, nomograms Cor dip estimates based on peak ratios are available (§7.7.4g). Figure 7.53b displays vertical-component profiles over a vertical plate at depths of 50, 100, and 200 m. The vertical scales are adjusted to give reasonable response for each curve seto Amplitude increases nearly exponenlially with increasing depth, producing a broader anomaly oC smaller amplitude. As in other geophysical methods, certain characteristics of the curves are used Ior depth estima te, such as change in slope, peak-to-peak distance, profile width at specific amplitude, and so on. One measure oC the latter which is used is the horizontal width on the updip (positive) part of the Hz curve (which is less susceptible lo dip and depth-extent variations) at two-thirds peak value. This estimate may also be made at early and late time without much error, unless the dip and depth are shallow.

415 Fr.e space

Hp

/

I

/' Below overburden

(a)

"x

(b)

dHJdl

(e)

Figure 7.51. Effeet of overburden (ob) on TDfM fields. (a) Primar." field at rarget. (6) Seeondar." field 03/ /arge/. (e) Reeeiver response from targe/.

Another estimate is obtained from the horizontal distance between positive and negative peales. It is not as reliable as the other because the apparent depth increases from early to late time due to current dilfusion into the plate. It is also less accurate for sheets of shallow dip and is alfected more by plate size and depth extent. The elfect oC variable conductance al is ilIustrated in Figure 7.53c for vertical sheets oC standard size and depth of 50 m. As mentioned earlier, there are practicallimits on al Ior the sheet to be classified as thin for all channel widths available in a particular TDEM unít. Apart Crom tbis and other plate dimensions that influence the response oC the system, the elfect oC variable conductivity is also significant. Because it is not possible usually to resol ve a and I separately (§7.7.3i), we must consider the al product (TCP) or conductance (siemens). The physical explanation of the elfects of variable conductivity and pI ate dimensions is that currents decay rapidly when al is sma1I, slowly when it is

(ti) No overbwden

lO'

_--2

---3 4

,;;=--

!5

:---- 6 __- - 7 ---==,,,IC-'~-:r-;1'~ : : ; . . ; . ; : - - - -

8 (e) o-tJurden madeI

i

i

-200

i

i

i

O

200

400

10Q·1II

I

600

800

dillonce (m)

50111 10000 Q'III

(") WIth overburd.,

O~----------------------~ 2

3 --4

5 1& 5¡-:::====I"-M-~¡:~~:::::::§~

S/~~~~~~~~~51~~=-_

6 7

-:7"~~~,........---8

FiBure 7.52. Approximate effect of eonductive overburden. t- d - 600 m, Z - 50 m, T-R - 100 m, lit - JO S, dip - JO·. Channel numbers are at the r¡Bht in (a) and (b), ehannel response at the lef/, (After Bartel and Hohmann, 19B5). (a) Response without overburden. (b) Response with overburden, (e) Overburden model.

Interpretation

large, whereas current diffusion from the perimeter toward the center oC the plate takes less time in a small plate than in a large one. Figure 7.53c shows the effect of varying at over a range of 10; the profiles show littIe response on the Rest 10 channels when the TCP is ~ 30 S and practically zero signal through channels 10 to 20 when it is 3 S. Depth extent is an important dimension because it aft'ects proper estimates of other parameters; however, it may be difficult to determine. Examples of variable depth extent are shown in Figure 7.53d, e lor vertical and horizontal field components, respectively, the first Cor 30° dip, the second for 90° dip. In both cases the protiles become sharper as depth extent decreases, the cbange in the H, component being the more obvious. Tbe signal decay rate is seen lo decrease inversely with depth extent but this is also true Cor conductance. Only at shallow dip angles (s 30°) is the estimate oC this parameter readily obtained. Decrease in stme length is not as significant as Cor depth extent. Although the relations with decay rate are like the latter, they are less pronounced. Generally a smalJer strike length merely reduces amplitudewithout much effect on the profiJe shapes. (d) SIROTfM. Two TDEM field configurations have beco considered in discussing PEM and EM37 interpretation. Tbe Australian SIROTEM equipment uses one field layout, adapted from the USSR MPP series, which is unique in the Westem World. Aside from variations in electrical and electronic detalls, mainly in the receiver, \here are differences as well as similarities among the popular TD systems. Tbese are summarized in Table 7.3. Four of these units resemble Turam FDEM and two are somewhat like the horizontal loop. Tbe novel SIROTEM(l) configuration has been identified by an astounding variety of names, inc1uding twin-, coincident-, single-, in-, and loop-loop, which all mean that it transmits and receives at the same station (the Russian equivalent transmits and receives on a single loop). We will use the names coincident-loop or SIROTEM(l). Tbe other more conventional arrangement is called SIROTEM(2), lwin-loop, or loop-loop. It is clear from the table Ibat PEM(2), EM37, EMP, and UTEM resemble one anotber, as do PEM(l) and SIROTEM(2). Only SIROTEM(l) appears to be different from all other systems. Several model examples of the coincident-loop system have been provided by Spies and Parker (1984). Tbey all involve tbe effect of current gathering and current channeling on TDEM response. Tbese terms are used interchangeably, altbougb channeling

417 Table 7.2. On and off rimes (e" r1 ) for fM37 channel windows.

t, Channel 1 2

3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

(ms)

0.080 0.097 0.121 0.158 0.195 0.224 0.316 0.393 0.492 0.634 0.790 0.962 1.221 1.58 1.95 2.44 3.16 3.93 4.92 6.34

0.097 0.121 0.158 0.195 0.224 0.316 0.393 0.492 0.634 0.790 0.962 1.221 1.58 1.95 2.44 3.16 3.93 4.92 6.34 7.90

is a restrietion of current ftow eaused by a resistive barrier, resembling de ourrent conduction. Gathering refers to a concentration of eddy currents or inductive ftow. Tbe distinction is c1arified in the following figures. Figure 7.54 shows large-loop (Turam-type) and coincident-loop profiJes over a semiinfinite horizontal conducting slab 60 m thic.k., simulating conductive overburden of 120m. In par! (a) the fixed loop lies on the overburden, in part (b) it is offset. 80th curve sets appear to reflect the edge boundary strongly; the first is a slight1y sharper version of Figure 7.54c, which was obtained over a 1-D sheet and inserted for comparison. That is, the lateral extent of tbe profiles is controlled by the smaller dimension of the Tx Joop rather than its fortuitous distance (- 550 m) from the overburden edge. When, as in Figure 7.54b, the Tx loop is located - 350 m off the sheet, the profiJes mark the edge quite precisely, resembling the EM37 examples in Figure 7.53a, or Z- and F-magnetic curves over faulted thin sections in Figure 3.23. Figure 7.54d displays coincident-loop profiles over tbe edge of the same overburden. Slopes are not as steep as in Figure 7. 54a, although they mark the boundary very well. Tbe curve shapes are also diCferent, lacking peaks and zero crossovers entirely. Large-loop and coincident-loop curves over a vertical sheet conductor are ShOWD in Figure 7.55. In Figure 7.55a the response is similar to that obtained over the edge of overburdeo, with steep crossover slopes, and the flanks fall away more rapidly than in

150-

"~19o-~

.

-.~ ""'!ll~§~r~~i •

."",.- i~~i ~:ll

lilE !

~:i)

.;W~

I~

6iK¡

....

·s

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oe

I

I

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-.~

•

?~:i

•

11.1

..

O"

30·

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;~

:':gJ

11il!•

::!l

:;~Jm f!='7~

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_~

::il

*=\Ir l

:~)

-..:1

I

;

~

dHzAlr

OJ

:

ow.a:::

:~] I

-111

•

;

m?

!

lit...... .... .. -.----T"-~~.

T

T----.---'

l1li

f?\ I

,

I

- ·111

I

I

I

I

~

I

lit

I

::01 !=~

".0)

I

111"""_ .e.1

1

i•

•

mil !

¡~.

~

_ .....-.

i

1?§0§ .... ...

T.~

H: HORIZONTAL COMPONENT

30·

~

d~~JiJ

# i••

G

lOO

.--111 • 111 .................

lÍo

H~ VERTICAL COMPONENT RESPONSE

• ..0

=ª

.""

•

-..

:

11 !

:;]I~~ -..

.•

150-

•

i

.sI 1 .il ~

gazA? ... ·.i·.~"-.IÍo~""'-_

,to,

_ . , . g~ lS

>'80

::8l

::i]

I§

1

~1

:~ll~~ -""-:-111

111.... ... _ ,e••

(a)

Figure 7.53. fM37 response over a plate model; eurves show aHzl al and aH.! at. t x d - 800 x 400 m {exeept in (d) and (e)], TCP - 30 S [exeept in (e)}. (Alter Gallagher, Waw, and Hoomann, 7985.) (a) fffeet 01 dip; z - ·700 m; /eft-hand half shows curves lor Hz, right-hand half lar Hr

419

Interpretation

z= so.

200 ..

::gl·~It1~~i§~ .o"'t.ll~~· .~ ~

••

00

." . ~~==:! 10

"::

o•

..tl~~~~~~::o.o.o. .~

'0

,

·411

I

lit

./10

I

I

I

/10 4to oCm)

I

I

111

I

I

111

I

I

IDIO

I

I

I

•• ./10

I

I

I

O

I

!

IGII 1110 "m)

I

1

•

IGII

t

t

IOGO

• loe

t

I

.2OCI

I

O

.... --+---+--*--+-~

I

loa

l.

'01

'DO

'OIO

• 1m)

(b) figure 7.53. (Conrinued) (b) V.lfidlion in

Figure 7.54. The coincident-loop profiles, however, are quite dilfereot io Figure 7.55b. From these examples it is clear that the coincident-loop TDEM system is superior lo the Turamtype fixed transmitter in discriminatiog between two dilferent model conductors. The vertical-sheet response in Figure 7.55a would be diffieult to distinguish from that obtained at any large-loop location over the sheet (Fig. 7.54a); on the other hand there is no ambiguity betweeo Figures 7.54d and 7.55b. Further examples of distinetive coincident-loop response are given in the Collowing figure. In Figure 7.56a, b the elfeet oC a gap or resistive discontinuity in eontinuous overburden 60 m tbiek is shown for lwo positions oC the Turam loop, whereas Figure 7.56c displays the SIROTEM(I) response; Figure 7.S7 shows a sel of eurves for the same unils over a vertical step tbat inereases overburden tbickness from 60 to 120 m. In both cases the coincident-loop response appears more realislie. AH the aforementioned anomalies are the result of current channeling, because the resistive underside oC the overburden model produces a lateral dilfusion oC eddy currents away Crom the source. Witb tbe vertical-sheet model in a homogeneous ground the currents are able to move downward as well, to concentrate in the conductive sheet. Field survey results from a fixed-loop system are ilIustrated in Figure 7.58. The seetion sbows a tbick overburden of 40 m with a step, from about 60 to 130 m leCt 10 rigbt, whicb was thougbt to continue to a deptb as a nearly vertical contact or shear. The latter feature is indicated by the dasbed lineo Two fixed-loop setups, one over the step, tbe otber 3S0 m lo tbe rigbt, produced tbe profiles sbown in the diagram. Those from loop A position are practically

aH,/ al with depth z; dip

90°.

-

305

.::.. ••

.••

'O~JI~~~: 1'"

°'8

;ro

J I

I

.,• . /10

I

I

I

I

I

I

I

J

I

I

I

I

I

rW/m'

..-'1tJ~~~~~ª::••

~

a(m)

00

( e)

figure 7.53. (Conrinued) (e) Variarion in eonduet.Jnee; z - 50 m, dip - 90°.

aHz/al

with

d-

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200.

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00

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av,.2

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-"'0

••

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100_

200.

,

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-

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- •• 0

(d)

"OO.

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l

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I

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.....,.. I

I

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,....'. '.

..

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I

,,,,,I ,, , 1..

'00

tl.,

...

l

110

I

(e)

Figure 7.53. (Continued) (d) Effecl of deplh exlent d on iJH./ iJt, z - 100 m, (- 800 m, dip - 30°. (e) Same as (d) except for H. and dip _ goo.

Table 7.3. Field layouls and dala retrieval for TDEM gfound systems. Model

FOEM equiv.

PEM (1)

Slingram

(2)

Turam

Tran5mitter Moving 6-15 m diam Fi~ed

100

x 100m

Receiver

Measurement

Moving, small Tx-Rx - 50-150 m Moving.5mall Tx-Rx - 50 - 350 m

H;. H;. 8 channels 0.1-12.8 ms' Same as aboye

H:,

EM37

Turam

Fixed 300 X 600 m

Moving.small b TK-Rx -10-1.500 m

H;, H;, 20 channels 0.089-7.1 ms'

EMP

Turam

Fi~ed

Moving.small b Tx·Rx-10-1.5OOm Moving. SOm Coincidenl Tx, Rx Moving, 25 m Tx-Rx - 100 m Moving. small Tx-Rx - 2,0.6 km

H;, H;.28channels 1-75 ms

SIROTEM (1) (2)

UTEM

None Slingram Turam

400 X 800 m Moving 50 m. sq. Moving 25 m diam Fixed. 1 x 2 km Fi~ed. 300 X 300 m

'Addilional base frequencies available for channel range (§7.4.4c, e. f). 'ti>K can be inside Tx loop.

H;.

H;. 32 channels

0.25 -150 ms Same as aboYe

H:, H;, H:, E~or 0.025 -13 ms. 10 channels'

421

Interpretation

(a)

TI : ; . i .. ! . (

..: '.

~oo,

OS

"!!

u.

(b)

1000111

T. LOO'

O

D

l'

E:t ",:$_t~;-,;"'''E~r.:i ... !.ff,,·;:g·~;:;·;. ,..;~...

10111

:.O -

Ila-III

Figure 7.54. Comparison of responses of Turam-type (TDEM) and SIRQTEM(l) over eonduetive overburden. Turam: TII loop 600 x 300 m in (a), (b), and (e). (After Spies and Parker, 1984.) (a) Tx on overburden - 550 m from edge. (b) Tx offset - 350 m (rom edge.

422

Electromagnetic methods (c)

'000

'-',0_

"~----~----~r----------------------t----~~----i

o·~--+-~--~-+~~--~-+--+--+--+-~r-~~~~--i -"~----~-----1-----------------------t------t-----i

~

....... ,...-11 A-.

:'i\'~'..: aa'f, Xt 1,

10OOOr-----------------------------------------------, '-.4 ....

1000~--~======~~======~--------------------~ .7

nV

100r----=====~~I.O~====~,,----------------__,

Arñt

1.5

10~--------------------~~~~~----------------~

l.'

-500

500

1000...

(d) Figure 7.54. (Continued) (e) Tx on 1-0 overburden. (d) SIROTEM(1) with 150 m diameter loop over overbvrden - 350 m from edge.

barren, whereas loop B gave a strong anomaly that resembles Figure 7.S7c. To explain the field data. the section was modeled using a conducting vertical sheet in contact with the overburden at the step. Three profile sets are seen in Figure 7.59, the first two for loop A and B positions and the last for a coincident-loop traverse. The fixed-loop models match the field profiles very well.

Figure 7.S9c shows an entirely different response, as one would expect; the overburden step is reftected in all four decay curves, whereas the vertical plate anomaly inereases at laler time. Drilling subsequentIy located a mineralized shear lone under the overburden at the step. Thus the Turam-type of TDEM field survey may give an incorrecl indication in situations like those

Interpretation

423 (a)

100

10r-----------------------~~

-IO~--------------------------~~~--------------------~

h O

LOOPO

" T

I

80 ..

IfT-138

f

IOO~---------------------------------------------~

1- 1.0""

IO~----------------------~~_f~----------------_1

.1~--------------~7'~~~~~~~~~~~~------__1 o~~~~~~~~~~~~~~~~~~~-.~~~

o

e

,

(b) Figure 7.55. Large-Ioop T)( and coincidenHoop responses over a vertical sheet. (After Spies iwd Parker, 1984.) (a) LarBe-loop h - 300 m from larget. (b) CoincidenHoop crossing sheet.

424


.

(11)

'

.. ~~

.-1.0 ..

L

•

(

,

Á

'Y

----- J

,

•,

./

, ·'0

.

., t--::: -, 00

------ - -

,

.L:..

~

,...

l.' l.'

~

,

--..N ~

J

\

......

./

-100

-

'ICIO

-

-

"-~

\. -tao

-lOO

o

'00

'00

-

MIO

lOO.

(6) '-1.0 ••

~

.....-

'

..

~

,

...

~

'0

~.

s.•

•

~

• -.• •

l'..

,

..· )

l\

V

l'

·'00 ·'IOO

.-

,---

-100

-tOO

-lOO

-400

-100

"'100

.. 100

o

...

:::--'00

MIO

-

lOO"

(e)

-

'DO

'0

-,DO

-.0o

.... ..

..

.............. , ~

---

.' o

~.~

00

-'00

..00

---'DO

J.J

l.' o

~

• 00

.00

.0•

.00

.-

Figure 7.56. Turam and coinciden/-loop responses /0 a discontinuity in eonduetive overburden. (After 5pies and Parker. 1984.) (a) Turam loop een/ered over /he break. break. (e) Coincident-/oop traverse over the bredk. (b) Turam loop offset to le't

o,

'·',0_.

..

'o

•••

I

l.'

(a)

~

,

lOO

~ .~

~

,

-.•,

"

-10

.. 100

.4DO

-lOO

100

/

~

:--

---

I

nV

Ami I

-.

..~ ........

l

I

O I

.,.-

-.-

•

-IDO

--

"-

100

...

'.0

1-

"-

--::. ...L

..... .....

t. I,ORt.

'

..

(b)

-..........

~

1.1

~ ........

l .•

¡...---

r ••

I

~

j

.10

-'" -'00

-000

-

100

\..

-

100

-

o

100

'"

...L

100

100

100

000

.-

,·',0 ••

¿

lOO

o /.

-.o I

1

-1

/ / ¿

J

-.00

-'00

. '00

••

. 100

(e)

/

/

o

..1.1.

/

~

1

l ••

7

",--

1

~

- I

00

o

I

o.

100

so.

'.0

Figure 1.57. Turam and eoincident-Ioop responses to a step in eonduetive overburden. (After Spies and Parker. 1984.) (a) Turam Tx over 60 m seetion. (b) Tx eentered over step. (e) Tx over 120 m section.

(

100_

426

flecrromagneric merhods

---1-1.0"'.

100

l.'

10

J.;'

~ .1

o

,

, -tOO

- 100

,

, o

100

400.

JOO

200

~r-'
.; .

"'

..

~'r-~--------~~--------~

.'.

1lO .. ':. '

: c

"

.

o',

..

,'

.. '

Figure 7.57. (Continued) (d) Coincident-loop Ir,¡verse over slep.

discussed, unless the Tx loop is relocated at least once and perhaps several times. This problem apparently does not arise with the coincident-loop system. The latter system, however. is not the ideal array Cor all structures, specifically the familiar thin conductive sheet witb steep dip. Consider the examples shown in Figure 7.60 from SIROTEM surveys in Australia. At each site both coincident- and twin-loop traverses were carried out. In Figure 7.60a the outcropping gossan containing pyrite at 320W produces a large aoomaly on a halC-dOlen early-time channels oC the twin-loop unít. Coincident-loop response in channels 10 to 14 in this vicinity is similar to Figure 7.55b. At the buried contact (- 100 m) between grapbitic siltstone and albitalite at 850W, the anomaly is clear on channels 2 to 13 of the coincident loop, but only on the tirst three of the twin loop. A better example is found in Figure 7.60b. Ore in the form oC a vertical sheet at about 120 m depth is well defined by twin-loop equipment on all su chaoneis, poorly on the coincident-loop profiles. Thus the coincident-Joop system gives poor definítion over steeply dipping sheets because oC the wide double hump in the response. With such structures it is preferable to employ the twin-loop survey. For tbin conductors of shallow dip, however, it appearS to be superior to other TDEM systems.

(e) UTfM.

The field layout and operation of tbis set is similar to the EM37, EMP, and PEM(2) units, because all employ a large Turam-type Tx loop usually located a Cew hundred meters off the target.

UTEM differs Crom the others in detail. particularly in regard to the continuous sawtooth transmitter waveCorm and in the capability of measuring the horizontal E field (generally Ey) in addition to three H components. Type curves Cor the sheet conductor, developed Crom the PLATE model, may be found in West. Macnae, and Lamontagne (1984). Field geomelry oC lhe system is seen in Figure 7.61a, together with a section showing sheets al various dip angles and the primary field vectors in their viciníty. This section indicates the location oC the extinction angle (§7.7.3g) around 150 to 165 0 and the effect oC sheet depth extent on the secondary response. UTEM field readings, as in other TDEM methods, are normalized for plotting by dividíng by the Hf field at each statíon. This procedure yields profiles that have the same general shape as those Cor EM37 (Fig. 7.53), but differ in relative amplitudes on the ftanks and peaks; Ibis is clear in comparing UTEM H. and H" profiles over a horizontal sheet (Fig. 7.61b) with the EM37 equivalents in Figure 7.53a. The Hz curves are quite syrnmetrical in both cases, but the positive overshoot, slightly larger in Figure 7.53a on the left, is c1early greater to the right in Figure 7.61b. Similarly the asymmetric shape for the H" profiles has the peak amplitudes reversed from leCt to right. This is due to the normalization of the UTEM plots (HP decreases with distance from the Tx loop). Profiles of H; over several model shapes are iIIustrated in Figure 7.62. Only early- and late-time response Cor each are shown, beca use changes over intermediate channels are smooth, as is apparent

427

Interpretarion

100 _cu....

---,.,

l.'

10

• .!

nV t

Am

r O

.

10W'

'.'w

• • • ,

-1

l.

• •

•••s.. LOOP A

nV,

~

Am

,

, O

10W

• IW'

o...... -10

tw

• OE

'

'I'E

1

•

-'-~

• • 4E

O

...

4.4

LOOP.

OE

tE

?,~

• lE .

'lE

~~' "-.J

Figure 7.58. Field traverses obtained with a fixed-Ioop system for two different transmitter-Ioop positions. The strong anomaly recorded wirh loop 8 disappeared when loop A was used. (After Spies and Parker, 1984.)

I• !

•

S,,

\

I

O

___ l.'

\ \

f

.

1.1

_

t.

O

l.'

_

" ~/O

O

_1.1

~ /-":

, l. \ \' 4~

•

o......

~

10

-1

• • • • • •

4W

100

O

...

4.4

1

,'

. ,

'00

10

f!.

• 6• 6

•

~

O

•

-

-

-'0

u

O

O

O

•••

u

IT

O

•

-.o•

l. I

l.'

~ f/.-

6

I

O

r

~

.

~

.A

V

::7) u

-tOO

11

•••

~ -100

.-

100

tOO

.00

O

-

...... lOO

'O

-

,

-"

~

'" A

A

~

~

\

A

~

·,, -.

•••

...

O

.:

~I

\

-10

-tOO

-'00

o

tOO

100

100

O

'-

.'. :' ..

'. (b)

.'-4.4.

".

'.' "

"

....... .. , .. ,'

· :

.

........ ,

;.

. '.. ..

Figure 7.59. Comparison of fixed-Ioop and coincident loop resu"s oller a model consisting of a semiinfin;te vertical-sheet conductor in contact with conducting oll~r burden at a step in the latter, (After Spies and Parker, 1984.) (a) Fixed-Ioop system with Tx loop located several hundred meters from the step. (b) As in (a) except that ,he Tx loop straddles the step.

'

Interpretation

429 B

B

, -.3 "'.

B

e

e

9

100

•• 1.1

DY. Ami

10

e

-------

e

e

e

~

B

o

•

A

. .

.1

o

-300

....(/.. .

"

~.:

...

-200

.. .

,'..

.

'

... '

. ,0~.::.:"".:.:>·:.::.·.::::>:-,.p'~3t,I\~.'"

:.¡,~

; '

.

o

-100

.... '.

100.

100

.-." . .

. .

.. : ',...

.............. .

',~

'. .. .

.

,'.

..'. .... ' .. 120 ... '.

.;

O,'.

.

SOO ...

.:,':'.': :. :.... :".:.:': ,-:-:.:.:.:.~,/.~.:~., . . :;... , : .',:. .

(e)

.

o

'"

. '. "

"T-4.45

~!lOO'" 5T,.IKE Figure 7.59. (Con/inued¡ (e) Coincident-Ioop traverse across ¡he step,

from previous examples, In all mode1s exeept (e) the transmitter loop (not shown) is offset left. The thin eonduetive sheet of steep dip in model (a) produces a lype of profile familiar in dip-angle FDEM. with nearly equal positive and negative peaks and a erossover, whieh, al early time, marks the top edge. In later time ehannels, amplitude deereases and the erossover slides downdip. A faír depth estimate is Cound at early time from half the horizontal distanee between peaks; this estimate deteriorates as the protile becomes broader with deeay time. Response rrom the horizontal sheet in model (b) is a symmetrieal curve with a low over the middle and positive ftanks near the edges. At later time the curve shrinks as the ftanks move inward. The exampie is similar to Figure 7.6lb. The vertical block conductor in (e) has the same general symmetry as (b), although the center response is stronger and the positive shoulders reduced. Depth may be roughly indieated at early time from the horizontal projeetion of the steep slopes Dear the block edge. In modet (a) eddy currents are coneentrated mainly on the steep sides, whereas in (e) they are on the top face of fue conductor. The dike in model (d) may support both eurrent pattems; fue top face

affeets mainly the early time, whereas response rrom the vertical sides comes on later (partieularly if the depth extent is appreeiable), henee the different shapes of the early- and late-time protiles of model (d). The 1-D shallow condueting layer in model (e) produces curves that are a sliee of those in Figure 7.54c, that ¡s, they are eontrolled by the Tx loop, not the model. Effects of eonductive overburden and current ehanneling are iIIustrated in Figure 7.63 with a vertical sheet-conductor model. When the overburden lies over the sheet in part (e), response is almost entirely from the overburden at early time, indieated by the curve labeled 8 on the left of parl (e), whieh is almost identieal to 8 in part (d) for overburden alone (reeall UTEM channels are numbered in reverse order from other TEM equipment). This is because the "smoke rings" have nol yet eseaped from the overburden. At later time. ehannels 6 through 1, they have penetrated to the vertical sheet. when the response becomes more oc less that of Figure 7.63a. If the vertical conductor makes galvanie eontaet with the overbucden, as in Figure 7.63b. the curves refteet the sheet through all channels, starting with

,.'

"l1li11" 100_

O··

C. .IOUI b,lo SI.U. , •

..'

. ....-.... e

;.

CIII_l 1ft

:: 1"

•

-.' •

;;

•e

1·1

" ti

II

.

e

;. I tMAlI[L

I

lOS.

...... , .......•. ,

-

I

O 1

,,

--... ., I

.••-. .,

- .,

ROM[m -4 • • 111 lIOPS 011( 00 ' ftIIIIS: ZSII .1$• SlACI"', ,"

e

•

'1

...

f' • !'It-

M".""

'."IIS

IISSA. SIIS..,acE " CMAlSn

lh ...

ti} (IIIMI'"

PItI!(

fl • SIAPtlte SIlISll. ) ,.•• ""'SlI."E SC""I CIllllUCINE

fk • &_IISln SCIISI IICCIIS • '''un,

Nf_' 1Il.'" 01 l1l5I,

fsr • lV.m I1II5CIYII( SCIl1' I

Figure 7.60. Comparison of coincident·/oop and separate Tl('Rx loop systems. (After 8uselli and O'Neill, 1971.) (a) Traverse over Ihe MI. Bu/ga minera/izatíon, New South Wales.

Interpretation

431 '00

..... lastD DI! Yln Il0l'' VAl.H

.,...,_._."._.

/ . _.

..

¡

......a

CtUnU .OS.

-

/-'~':\

'0

/-.-......../-~-

/'~~ ._.-:::::'-...

..

;;. "0

• ...• oc

2

::;::~~ • ~:~ ~'?f .. / • ... 1..\.

~ ;

O

SEOMlTn 164"

J 4 I

1

~ftD

", :

......" 0.°

..'

•

D'Z 40DW

1.00 E

00

eoOE IIntl

HOMlT"

... :lOO It

I!!J

~

-1

I!!l

Al, UCM

Z TUIIIS; IS •• u. STaCIII'" J. Z"

0" _

·ea~CUlOU5

$lUnDl!I I

r

OItSl"""TQ

.. '1

. , . Cll.CUlOU5

(b)

1L

o.,

SlLt\'DI!I

Figure 7.60. (Continued) (b) Traverse over a prospect in the Willyama Complex, South Australia. I

t

enhanced response at early time and decreasing later to levels about the same as those in (a) and (c) on the leCt. This signal behavior is caused by current channeling. These elfects are further c1arified in Figure 7.64, which shows the various data from Figure 7.63 in the form of decay curves over the complete channe!

range. The left-hand plot indicates the signal enhancement caused by current channeling, when overburden eddy currents pass immediately into the more conductive dike; the right-hand plot iIIustrates the blanlting or suppression oC the dike signa! when a resistive gap exists between the two. Both features take place at early time. When the same sheet is


432

, "'.,

LOOP F1ION r

l qJ II

"-1 1 I I "lO'-::f-' L L

,~

,

/~~~~~

,ID

/////

I~

"

"

/ / I

//////

................ a_lO" ______, . - / / / /

, , . . . . . . . . .-.._:e.-______.-,_______,.-/ /

SECT'lON v.E'W OF" PLATE CONDUC rORS PRNAR'Y MAGNEnC FlELO

ANO

GEOMErR'I FOil 90- CASE

505 PLArE

LOOP

(a)

Figure 7.61. UTEM profiles over a dippinl/"plate model. (After West. Milcnile. ilnd Lilmontagne. 1984.) (a) Geometry and dimensions of the model. and configuration of the primary field in the vicinity of the conduc/ive plate.

contained in conductive host rack, both of the preceding eft'ects are also evident, altbough at dift'erent times. Blanking again occurs at early time; gathenng takes place later after an elapsed time, which varies with hast rack conductivity. An example of electric-field response, measured over a vertical plate with a T" loop of 1 X 1 km, is plOfiles are inc1uded shown in Figure 7.65; the for comparison. Because tbe E-field solution is diCficult by numerical methods (§6.2.7), data were obtained by scale modcling. Tbe E, curves are not useful. Tbey do not locate the targct, which is well marked by the crossovcrs in the H, curves; they are also aaid lo be highly susceptible to conductive overburden.

H:

Resolving power of TDEM systems has not been reported to any extent in the Iilerature. Because four of the units Iisted in Table 7.3 are JiJee Turam in geometry, one (f) Resolution of multiple conductors.

would expect thcir discrimination to be much tbe same as that oC FDEM Turam. Nor do me Slingram-type sets appear lo be superior to their FDEM versions. Without any salid evidence, one may surmise that high resolution is not a great advantage of time-domain surveys. (8) Characteristic curves. Several oC these are available for rapid estimates of deptb. dip, and conductance oC sheet models. Gallagher, Ward, and Hohmann (1985) used the EM37 plOfiles oC a plate conductor 800 X 400 m, al variable dip and dcpth, to prepare early- and late-time nomograms. Tbese are based on the ratio oC small-to-Iarge profile peaks and are shown in Figure 7.66a. FlOm the dippingsheet curves of Figure 7.53a it is apparent tbat tbe ratios are less than unity for all dips except 90°. Tbe Caet that the small peak decays (aster than the larger one, producing early-time ratios larger than late-time, mues it necessary to plot two sets.

.,

•

•o

2

\O

...

o~

... l'

... .

. .. .

", "

.,

,-

'. ~ .': :. :. '.

.... : :.:.. "

..

i

-...

o

~ z C(

b,."

·0

...,

o

-

'0

•

." ~ ca. ~

I

I

~

•

i!

...en Q

434

Electromagnetic methods •~~~=1~;;;;::::::::: _LATEIIt (HANN[L -

---~~......".....--~,..~~-~I I

-----Pri........- - - _ EA",,"Y

...

...!::~==+~~------~:;::~

CHANNEL -

POORLY CONDuCTIV(

08.

D (a)

(b)

'rHIN DYKE

--1f~:::::::;~r-------4-LATEIIt

CHAHNEL

---ot----,,---I:=;:;:;---- tA"LY

(HANNEL

THIN H~IZONTAL FINITE CONDUCTOR (O.B. PATCH)

----~~~~~====~ -

---==::::::::~r-+-::;::::=-

D

(e)

BLOCK

CONDuCTOR

LATE" CHANNEL

EARLY CHANNEL

(d)

THICK OYKE W

">

O

I • liT

t.T ~200e¡.

•

LOOP

-=:...,

•

EXTENSlvE HORIZONTAL CONDUCTOR Figure 7.62. The form o( continuously norma/ized UTEM H: profi/es over some simple shapes. A/I conductors are in free space. (Afler West, Macnae, and Lamontagne, 1984.)

435

Interpretation

rI.

EA"LY

CHANNELS

LArE"

200

200

lOO

•

o

CitANNEL S

•

..", I

(d)

(e)

l~

(%1

1°°1 ,

~ \

-.

(a)

t

, ... 01 HU

"i" - -

1!l0",

Fi8ure 7.63. Model UTEM H: profiles over a vertical eonduetive sheet under a thin conductive overburden. (After West, Maenae, and Lamonta8ne, 1984.) (a) Effect of sheet alone. (b) Sheet in eonlael with the overburden. (e) Sheet not in eontact with overburden. (d) Overburden alone.

Because it is possible to determine tbe direction

lobes is the variable in this case, with dip and ratio

(> 90°, < 90°) and approximate dips from tbe orig-

oC depth lo T-R separation as vertical and horizontal

inal protiles, it is only necessary to enter tbe two boxes in Figure 7.66a along tbe same peak-ratio lines and obtain from tbe vertical and horizontal axes of each box tbe depth and dip values that agree best. A similar nomogram for PEM(1) data is given by Dartel and Hohmann (1985). It was noted in the discussion of dip (Fig. 7.50a) that the negative side Jobe over the conductor was larger than the negative lobe off tbe edge. Ratio of the areas oC these two

axes. The plot is shown in Figure 7.66b. Here an independent depth estimate is lirst found fmm the size oC the positive peak at the updip edge oC the sheet, seen in Figure 7.50b. When this peak is appreciable, which is so for z - 50, 75 m, and marginally so for z - 100 m, the horizontal scale ratio z/I S 1, that is, the depth is less than the coil separation. Having established these preliminary estimates, we proceed as Cor Figure 7.66a.

436


CURRENT GATHERING

BLANICNi EFFECT

EFFECT

'; '; '; ; ;-¡ :0.. --

.r--------,

# ir:

I

otOOIII

• 0'tlC[

..

a oe

1205

'-

.,1-1, S

" CXlNT.tCT

lit

II!

.- ......... -..................

• 0'tlC[ (lN..Y

%

.....

... Q

~

lit

~

lit

8

7

6

5

4

CHANNEL Fi8ure 7.64. Decay plots for Ihe H: anomalies o( Figure 7.63. (After West, Macnae, and Lamonta8ne, 1964.)

H'H~

20

t-1oI

·20

O

·40 O

Ey

100

500m

- t ... - 0

IKm ----1

E~ 1%1

• 0"'---Figure 7.65. Model UTEM magne/ic (Hz) and elec/ric (Ey) responses over a vertica/'plate conductor along the x axis. Tx loop - 1 X 1 km, conduclor - 1 X 0.5 km, Tx 450 m to (ight of plate, z - 110 m, TCP - 20 S. (After Wesl, Macnae, and Lamonlagne, 1964.)

Depth estimates may also be made with data from EM37 and similar systems, using the horizontal distance between peaks and horizontal width at two-thirds of the positive peak, as discussed earlier. A depth nomogram Crom the laller measurement is displayed in Figure 7.66c for sheets dipping 60 and

90°.

Two conductance nomograms are shown in Figure 7.67. Both are based on signal decay rate, which varies inversely (roughly) with al as discussed in Section 7.7.4<:. The pIot in Figure 7.67a uses response ralios in successive channe1s of the PEM(I) unít, whereas figure 7.67b is obtained from EM37 decay curves Cor specific al modeIs. Tbe response parameter, discussed in Section 7.7.3i in conneclion with frequency-domain characteristic curves, has an anaJog in time domain. For example, the thin sheet parameter in FD, JJ.watc, becomes pale/.,., where p. is normaJly p.o. e is a dimension - in this model the smaJler of strike length or depth extent- and .,. is a time constant. The lalter obviously depends on the eddy-current diffusion rate through the model and so is intimately related to the channel response at different times during tbe sigoal decay.

7.7.5. lhe Sphere Model in FO and lO Ground Systems (a) General. Tbe sphere and ellipsoid, simulating a model in the form of a conductive loop, are the only 3-D geometric shapes amenable to tbeoretical ana1ysiso The sphere has been solved for both FD and TD systems when the source fteld is either uníform or dipolar (Wait, 1951b, 1960b; Ward, 1967). The solulions are in terms of Legendre polynomials, as in the

Interpretation

437 lott-IIII. p.lk retl ..

300 r-rrTT'T"r-T"-r"r-""T----' ... t~ (11)

200

200

.05

./0

.10 lOO

./5

lOO

.tO

./5

.tO

50

90' 1S' 60' 45' 30' 15' O" 105' 120" 135" 150" 16S' 110' dip (a)

80

15

.. 10

• ..... •• ~

...

45

30 15

O O

2.5 ( b)

Figure 7.66. Charaeteristie eurves for a dipping-model plate. (Parts a, c: After Ga/lagher, Ward, and Hohmann, 1985; part b: After Bartel and Hohmann, 1985.) (a) Ear/y- and late- time peak ratio as a tune/ion of depth and dip, EM37; (b) Ratio of on-conductor side-Iobe afea to off-conductor side-Iobe area as a tune/ion of dip and depth, PEM(1).

result lor the sphere in resistivity (§8.3.5), but are considerably more complicated, particularly for the dipole field. !be two solutions are the same when the dipole is remote from the sphere. A brief discussion follows. (b) Frequency doma in. !be response parameter for tbe spbere is /1(,)(10 1 (§7.7.3i) and tbe response function is a more complex form of A + }B shown

in Figure 7.10. Wben /1 "" 1'0 tbe unifonn field re· sponse function is similar to that for a circular loop. Reasonable profiJes may be developed from tbe circuit analogy on tbis basis, mutual inductance being given by Equations (7.21c. d) lor tbe dipole and Equation (7.2lf) lor long-wire coupling. The dipole coupling is suitable for analysis 01 airbome as well as ground double-dipole results; the source and detector, being close togetber, are considered common

438


lOO . - - - - - , . . - - - - - - - - - - - - - ,

400 30

350

--.•., 500 :e .....•. m

10

-.........

--• :¡¡;

3

.......

•• 200

c c

150 IDO

0.3 50

o

50

200

100

300

d.,th .,,,,

0.1

(e) Time domain. Eddy-current diffusion in the sphere during transmitter off-time is different from that on the thin sheet because of the different geometry. Although the vortex curreot motion is toward the center in both models, the 3-D sphere causes these currents to coUapse from surface toward its center from early to late time; on the 2-D model they move inward from the edge, always in the plane 01

3 (a)

Figure 7.66. (Continued) (e) Two-thirds width versus depth for early and late times, dips 90 and S 60°.

and the sphere is remote lrom both. Thus the interpretation of FD response from 3-D tarsets roughly simulated by a sphere may be carried out directly, or by usinS the ac circuit modelo Two sets oí profiles over a spherical tarset at various depths are shown in Figure 7.68. The first is íor HLEM, the second lor the shootback method. In both examples dimensions are scaled to the T-R separation. Comparing the HLEM curves in Figure 7.68a with those of Figures 7.36c and 7.41 (and lacking the quadrature profiles in Fig. 7.68a), the sphere could be mistaken lor a horizontal sheet oí limited width, two vertical sheets 01 resolvable separation, or even a steeply dipping single sheet, al) oí rather shallow depth. This ambiguity applies to the shootback profiles 01 Figure 7.68b as well. The effect oí conductive overburden on the sphericaI model appears to be similar to that of the thin sheet (§7.7.3b and §7.7.4b).

'-----'-----'---"----~~

I

(e:)

ID

cOR~uctlvlty- thlc~n ...

30 ,roda,t ISI

lO~

mr-----------------------~ IDO

.....•

~

:

1e ~

-=• ! ¡ •

u

lIS

1.$11••

(b) O.DI

L-_~_...1_

_

_L_....J'__~-....L.-~......J

lIe. C.,I

Figure 7.67. Nomograms for estimating al producto (a) PEM(1) system, channel ratios versus TCP (numbers at ends of curves denote ehannels); model plate 600 X 600 m, Z - 50 m, dip - 30·, T-R - 100 m. (After Bartel and Hohmann, 1985.) (b) EM37 syslem, curves of response amplitude versus time for various values of TCP (or time eonstant); model plate 800 X 400 m, Z - 50 m, dip - 9(10. (After Ga/lagher, Ward, and Hohmann, 1985.)

--

o

..

_ _ - .. _.. ----. . ..

.. _-

__ . _.......

__

.. __ .. ---....:'...----------. ... _.. .. ..

~...,.. -.~.:

1.5

D .------------.. --"'- ··r·· ... .......... . ~.;"a.......... .. --.-- e_.------:... .

~-_ ~

."

O

,

-L5

....>-

'"z .... Z

o

,, , . / ,

...J

UJ

\

LL

w

>

....<1

., .I

...J W

ijj

Ir

!

.'

..

JI,

1

.~

-2.0

1

."_._.-.

UJ

-- _.

(

'.

\

I

~.\

,

J

\ h \ \I .,j' .\.

\",.,

~

(a) Figure 7.68. f?esponse lo d buríed sphere. (d) HlfM profi/es; 1- T-f?, deplh lo center of sphere is 1/8, 1/4,1/2.1, and 21 for curves A lo f, respective/y. (AfIe, BhdlldChdryd dnd Sinhd, 1965.)

_.-

'".... -------"T ....-, . .--\ ,\ .'. \

ID·

S.LIN'l 3N.L\1131:1

,IQ

-

...

I

I

• N

I \.

I

",'"

.............

.~,.,.",

.,.--

/

I

-.

" - . - ... _- .....

Q N

441

Interpretation

•

HiIh frequency

Late time

Intennediate time

Early time

•

•

•

Low rrequency

Figure 7.69. Time-domain eddy-current distribution in a spherical conductor. (a) Schematic comparing eddy-current diffusion in a sphere and a plate (After McNeill, 1980.)

tbe sheet. A schematic oC the eddy-current diffusion in the thin plate and sphere is illustrated in Figure 7.69a; also included is a pIot oC current distrlbution versus time in tbe spbere (Fig. 7.69b). The computer program SPHERE was developed by tbe same University oC Toranto group tbat produced the PLATE program (§7.7.4a). The SPHERE program was used to obtain Figure 7.70 which sbows tbe effect ol cooductivity on PEM response over a spbere. Over early to late time tbe positive peak deeays las ter tban the oegative tails, compared to the vertical plateo This permits discrlminatíon between thin and thick conductors.

7.7.6. layered Structure: EM Depth Sounding

I

~,

•,

(a) Introduction. The use oC EM metbods Cor deptb sounding was discussed briefty in Section 7.6. Until the early 1970s, this tecbnique was little used. mainly because oC the limited transmitter power and lrequency range available with most grauod equipment. Development ol titne-domain EM witb its potential lor greater depth ol penetration provided a stimulus lor this type oC survey. Multifrequency continuouswave systems have also beeo tested lor the same purpose. on a much smaller scale. lo both cases tbe practíce has been to maiotain fixed separatioo al transmitter and receiver as in magnetotellurlcs, ratber than resistivity sounding. It may be oecessary, bowever. to change T-R spacing several times when sounding over a oumber oC beds stacked to appreciable depth. Detailed accouots ol tbis application may be louod io Keller and Frischknecht (1966) and Patra and Mallick (1980), as well as a more theoretical treatmeot in KauCman and Keller (1983) .

(b) Frequency domain. The VLF EM16R unít provides a last and coovenieot shallow souoding measurement. As described in Sectioo 7.4.2C, with the setup oC Figure 7.18b we obtain values ol apparent resistivity p" and phase angle • (lag ol H. with respeet to E,) by adjusting tbe corresponding instrument dials lar mínimum signal. The expressions are

p"

-IE,/H.1

2

/",,,o -IZ.1

/",,,o)

2

(7.4Oa)

I

• - tan- Z. wbere E, and H. are tbe horizootal ortbogooal components ol dectrlc and magnetic fields írom the VLF transmitter. and Z. is tbe complex suríace impedance in the vicinity oC tbe measurlng statioo. Over bomogeneous ground p" is the actual resistivity and • - 45°. On a stratified ground. with severallayers differing in thickness and resistivity, P.. is a lunction ol these parameters (as in dc soundiog). al least to tbe depth ol penetration possible at VLF frequeocies. and the pbase angle geoerally will oot be 45°. In practice multiple-Iayer structure wiIl oot be resolved witb tbe EM16R sounding. lo tbe vicinity ol lateral discootiouities, the problem is even less tractable. For two beds, however. a solutioo may be fouod lrom master curves. In this case we bave three unknowns. PI' zl for the top bed. P2 Cor tbe basement and only two measured parameters Po and •• lor which the two-Iayer structure relatioos are

(7.4Ob)

442


"e.., .,.,

0'0001

~'~-----'-------r------'-------r-----~~~~--------,

0'001

0'001 0-01

-

t

0'10

~t~~~------~--------~

1 r'T

____ __ ________________ ~

;r~

~

0'10

0·10

~I'~--~--------~~------~----;r~------------------~

(b)

~~:------t.---~~~----~L---~~~--~~--~~------~ o 0·2 0·4 06 r 'i Figure 7.69. (Continued) (b) Radial distribution of current in a sphere for several values 01 (t/,,1.,). (After McNeill, 1980.)

where Ql is a correction factor of the form

QI - {PI + tanh(jal)I/l} /

{l + P. tanh(jal)I/l} (7.4Oc)

and

PI -

(p,/p¡)I/l, 111 - (lI)f1.o/pd/lz •.

1be master curves displayed in Figure 7.71 are plotted as a. versus P. for various values of Q. and •. It is sti11 necessary to assume a value for either PI or P2/p¡, based on all available information. If we setect P., the procedure is to compute IQ.I from

Equation (7.40b), locate ¡ts intersection with • to get 11. and P. on the master, and ealeulate z. from 11•• 1'2 from PI' When P. - (P2/pd/l is the "known" parame-tcr, we find its interseetion with • to obtain IQ.I, calcu1ate P. (from ¡ts relation with IQID, Zl from lit. and 1'2 from P•. In tbis case two solutions for 111 and Q. are possiblc because of the shape of the Q. curvcs. Confidence in the results from tbis exerase may be greatly enhanced by ineluding a portable de resistivity unít in the ficld lo measure PI at small spacing for several stations.

Interpretation

443

ro'

10'

10 2

10

1 S/",

2

3 5/",

1O'

O .......-o::--~r---:::oo---------J 2

-200

°

200

400

600

°

--~~~~~----------------

2

3

--~~~~~-------------- 3

4

--~~~~~,----------------4

5

--~~'-~~----------------5

6

----~~~~---------------6

7

-----===~---------------7

8

--------------------------8

800

-200

o

I 200

I 400

600

800

distance (m)

10'

lo'

10 2

10 5/",

ppk lO'

1O'

°

,

¡, , \

i

30 5/",

I

2

°

2

3

3

4

4

5

5

6

6

7

7

8

8

Figure 7.70. Response of PEM(1} syslem lo a buried sphere as a function of conductivity. Radiu5 of sphere - 50 m - depth fo lop, 1- 100 m. (Affer Bartel and Hohmann,

1985.)

Otber standard EM systems are suitable for variable frequeocy souoding (Wait, 19S5; Ward, 1967). These ioelude (a) double-dipole (horizontal and vertical coplanar, vertical coaxial, and perpendicular), (b) large transmitter loop with small receiver al ils center, (c) loog grounded wire or Turam-type loop with small receiver coi! located some distance from it. lo (a) the dipole condition prevails if the T-R separation is ~ S diameters oC either loop; (b) is

used more in time-domain sounding, sucb as witb the coincident-loop. TIte mathematical treatment for interpretation is well developed, being somewhat similar to both dc resistivity and MT sounding analysis, tbat is, the procedure for determining FDEM response over multilayer ground requires that we calculate a complex grouod impedance in terms oC the mutual coupling (impedance) between transmitter and receiver

444


lO"

10·'

10· /-¡

10'

(a)

(b)

1O••

+ .....1....."r"---+----1f----¡~......- _ t -....... 10"'

-,10'

FíBure 7.n. Master curves far two-Iayer VLF resistivity interpretatían. (After Mathieson aOO Crossley. 1982.) (a) Contaurs af • (solid) and IQ,I (dashed) as functians of a, and Ilr {Eq, (7.4O)J. (b) Enlarsement af the central portion af (a).

Interpretation

445

in free space (§7.2.S). This involves successive solulioos of the wave equatioo io two-layer struetures from the basemcnt up to surface; the solutions eontain integrals like lOOse appearing in resistivity sounding analysis [Eq. (8.47)]. The following examples for several EM systems over two layen sbould elarify tbe preceding general statement. The impedance ratio, related to the parameten of tbe beds, is given by an integral which varies with tbe type of FDEM.

\~««,<ºt'\4

(a) Horizontal coplanar loops:

•

\~,"""~,<, ~,~",,,\,Q,,, ,~,\,\"~<,<

e

.«,<'("'<"'"

e

b

d

(Z/Zo) .. -1 + B3(Tó + Tó') (7.41a) (b) Vertical coplanar loops:

(Z/Zo)" -1

+ B2(Ti + Ti')

(7.4lb)

i B2 {(Tí +

Tí')

-B(Tó + Tó'») (7.4le) (d) Perpendicular loops:

(e) Long-wire horizontal loop:

(Z/Zo). - 1 - B2( Tí +

12")

(7.4le)

where Zo and Z are the free-space T-R mutual eoupling and measured impedance, respeetively, B - R/B, tbe ratio of T-R spacing lo tbe slcio deptb 8 - (2pl/ 1A11' )1/2, and

Tó - fooo{A(D,>..) -A(oo,>..)p.lJo(>"B)d>" Tó' -

f" A(oo, >..)>..2Jo(>"B) d>"

1j.'-l°°{A(D,>..) -A(OO,>..)}>..2J1(>"B)d>" o

Tt" -

00

10

A(oo, >..».2J1(>"B) d>"

T'¡- fooo{A(D,>") -A(oo,>")}>..J1(>"B)d>"

12" -

00

10

8

1O

12

14

16

18

20

("'1'0(7 )I/ZR

(e) Vertical coaxialloops:

(Z/Zo). -1 +

4

A(oo, >")>..J1(AB) d>..

where D - 2z¡/B and Z¡ is tbe top bed thiekness. The terms A(D, A) and A(oo, A) are known as kernel or input functions. The funetioo A(oo, A) is related to homogeneous ground, iodieatiog that the

Figure 7.72. Mutual impedance ratios for systems (a) fa (e) in fquation (7.41) as a function of (wp.OIJ)1/1R. (Afte, Wait, 1955.)

integrals Tó', T¡", and 7;." describe secondary fields over this simple strueture and consequently may be solved analytieally. Iotegrals Tó , TI', and Tí are found by Dumerical integration in a variety of ways or by digital Blteriog (Koeloed, Ghosh, and Polman, 1972). Equations (7.4Ie) and (7.4Ie) may be writteo in terms 01 Equations (7.4la) and (7.41b):

(Z/Zo). -1 + H(Z/Zo)b - (Z/Zo) .. } (Z/Zo)," 2 - (Z/Zo)b so that we need only to determine the ratios for systems (a) and (b) to find solutions for (e) and (e). A set 01 curves showing (Z/Zo) versus (lA11'o)l/2R for systems (a) to (e) over homogcneous ground is ilJustrated in Figure 7.72. Note tbe similarity oC tbe vertiealloops (b) and (e), a1so tbe horizontal loop (a) and the long-wire transmitter in (e); tbe perpendicular loops ol (d) produce a completely different response because oC tbe minimum coupling. Numerous curves and tables for the two-Iayer eartb may be found in Frischk.necht (1967). Because Bve FDEM systems are eonsidered in terms oC four Corms of the coupling ratios (modulus, phase, real, and imaginary components) and Bve variables (<71'~' Zl' w, R), a great amouot oC data is presented, even for two beds, compared to de resistivity soundings. Several examples 01 two-tayer curves in Figure 7.73 illustrate soundings using systems (a), (b), (d), and (e) [Eqs. (7.41»). From top to bottom tbe first

446

Electromasnetic methods

;:

~ 0.5

Figure 7.73. Modulus and phase of mutual coupling ratio (Z¡ZoJ far systems (a), (b), (d), and (e) in Equations (7.41) over a two-Iayer earth. (After Frischl
447

Interpretatían

1.5

, \

lA. " , Ini.-.

III

",

,...

\ \

ItI

111

tUI

\

1.11-.:.:(1::,..'_-

\

, \

',,,miOOh'

......

1 )(iOO

ii r ---------4000

1000. (b)

(a)

-l-

a.

b b It. . .

.0 ., 2...

" ........

,--------- -----

,1,'-"', I I

I

O.,

I

-toO -40'

-", ...

-lO' ::

-IDO'

::

-120'

, ·.u. .~-7--7~-=:~.~10~1~2~14==1~' ,

O·

l· ....

-140'

::J: Z4 1I=z:l:O::::lZz-.J

I

(e)

I.'~-:-----------------' oe -1-

,.

, 6

-IOOUlUS -. _. 'USE

30.

"Aa ~olO

.11 500

/ ,

.............. _--.'500;-" ------------,~

_.. '~

, I

-40'

-to·

10 ..

·500.

-lO'

-lOO'

...""

-.. 4

-IZO'

.·JOo. ·soo.

(d )

-20'

·141'

.'I~O~~J,-~~.~IO~I~Z~I4:::::::1I1;=I;c.:::::O:zo==z....z=..&..z4.-JzillO.

O

I Figure 7.74. Mutual eoupling ratio (modulus and phase) for systems (a) and (d) of Equation (7.41) over multilayer earth. (After Patra and Mal/ick, 1980.) (a) Modulus and phase for systems (a) and (d) over three-Iayer type-A earth (§8.6.4b), geometrie sounding. (b) As in (a) exeept parametrie sounding. (e) Modulus and phase as funetlom of B for a three-Iayer type-H earth, system (a). (d) As in (e) exeept for a (ive-Iayer earth.

,,

,,

.-

Elecrromagneric merhods

448

.. -- -.. (t)

5001 10000 FIEOUUCl-

100000llz

F¡8ure 7.74. (Continued) (e) Ratio of moduli fo, systems (a) and (d) ove, one-, two-, three-, and four-Iaye' earlhs.

pair represeots a conductive top layer over resistive basement (~/Gt - 0.1), whereas tbe lower four portray a conductive basemeot (~al - 10.0). In each paired set the lelt-hand box 01 curves displays tbe absolute value or modulus 1Z/2'.o 1 01 tbe mutual coupling ratio and the rigbt-hand set shows the phase ol Z/7.o, a1l ploUed against B. Apart lram a general left-to-rigbt downward slope, wbich migbt be compared to a two-Iayer P. curve over a conduetive basement in dc soundings, these plots bear no resemblance to the latter; their decay merely represeots an increase in frequency and/ar T-R spacing on tbe horizontal axis. There are, however, certain similarities among them, for example, between systems (a) and (e) in both modu101 and phase, and between systems (d) modulus and (b) phase. It is elear a1so that the FDEM sounding is more sensitive lo a conductive than a resistive basement, as seen in comparing the upper two modulus and phase plots 01 system (a). 1bis is also the case 'lor the other systems. As in Chapters 6 and 8, curve matcbing may be . carried out successively on tbese master plots, provided tbe two-layer structure is actua1ly preseat or that additional beds are deep eoougb lo tie beyond the sounding rauge. Fie1d data are ploUed as .¡f versus Y, voltage induced in the receiver coiJ, on lag-Iog transparent paper with the same acale as the master, then moved about exactly as in MT and de resistivity practice (§6.2.8b and §8.6.3g). When a reasonable match is obtained we find a horizontalaxis value of .¡f on B, fram wbich we can ca1eulate

'1

al; an estimate 01 D/B gives and ~ is determined (rom tbe k value for tbe particular master set. It should be noled tbat the vertical scales, (Z/7.o) on tbe master and Y on the fteld plot, are relative ratber than identical. that is, Y - - jwp."zA1H Z/, whereas (Z/2'.o) - m"R3H/"lA1 / - H/H' [§7.2.S&, Eqs. (7.2lc, d)l. wbere m - 2 or 4, depending on the loop system; "1' "2' Al' A2 are the number 01 tums and areas of the transmitter and receiver loops, / the transmitter curreot, H' the primary fteld, and H the secondary field at the receiver in the presence 01 the earth. Thus Yex H, hence Yex Z a1so il / and R (- T-R spacing) are constant. If the phase angle is measured, the curve matching may be perlormed on plots similar lo Figure 7.73, the fte1d curve being semilogarithmie. Additional master curves have beeo prepared lor the same purpose, using the real and imaginary components of (Z/7.o) and parameters of tbe polarization eUipse (tilt angle, eUipticity modulus, and pbase). The latter, of course, require a dill'erent field mea· surement with tbe receiver coil. It is Dot possible to use partial curve matching on EM sounding data over multiple layers. Figure 7.74 displays several examples 01 response Irom three heds and one lram five beds. ID Figure 7.74a a theoretica1 geometric sounding (variable R and two values 01 f) over a three-Iayer type-A structure (PI < Pz < p,; §8.6.4b) lar systems (a) and (d) is plotted lor 100 and SOO Hz; the T-R spacing rauges lrom 100 lO 5.000 m. The curves would be difficuJt lo distinguish Irom two-Iayer or

449

Interpretatíon

-.ODULUS - --PIAIE

"

-ZO' &1.1

o

(J)

....

CI l:

N N

---- .. ...----.,L ,_ ....

a.

.-1.A .&

-100' -120'

o•• l=;;;;;;:=::::.t::::=-___"--____.J ....H'

.....1 PERfOD (5)

( ,,)

....

.....

I·'r------;::::::;:::=====::;-----, 0.1 ti .. , O' --.......... ""

... ... " ..

.... ... .. "'

:;: l.. 1.5 U :. 0t-~~--'----I

......-0.1

• lO'

-1-

'56~

ftX.'

-IZO'

m

-1'"

l: a.

CI

-zoo' -240'

2000

Figure 7.75. Modulus and phase 01 the mutual eoupling ratio in the Irequeney domain and time domain (small insert) for the horizontal eoplanar loop system [fq. (7.41a)). (Alter Patra and Ma/liek, 1980.) (a) Homogeneous earth. (b) Two-Iayer earth.

even homogeneous earth response. This is also true for the so-called parametric sounding in Figure 7.74b where tbe frequeocy is varied Crom 10 to lOS Hz. Figure 7.74c showing system (a) response over three-Iayer H-type beds (Pi> Pz < 1'3) is slightly more diagnostic, with a minimum around B - 6-8. However, tbe curves of Figure 7.74d for five layers show nothing of beds 3 and 4 and are practically identical to Figure 7.74c. By calculating the response of both (a) and (d) systems and plotting the ratio. it appears possible to estimate the number oC layers more successfully. Figure 7.74e illustrates this improved discrimination. Curves oC (Z/Zo)"/(Z/Zo),, - Z"/Z,, versus fre-

quency for one lo four beds are increasingJy complex, suggesting the performance of field surveys with two EM configurations. Thus. the forward or curve-matching approach 10 EM sounding interpretation is clearly more difficu1t than for dc resistivity sounding. Solution of tbe inverse problem, as in other geophysical analysis, is increasingly used instead. Methods are similar and involve digital filtering, Iinearization, and leastsquares minimization (§2.7.9). The transient, or pulsed, EM system was long considered attractive for sounding, initially because of its similarity to tbe (e)

Tíme-doma;n sounding.


450 seismic method. When suitable equipment became available about 1963, there still remained analytical difficulties. Then it was fouad that interpretation of the transient signal could be done by various transformatioos of frequency-domain response using Fourier series and Laplace and Fourier transforms (§7.2.6, §A.9, and §A.12). This analytical approach, however, has limitatioos when there are more than two layers; then it is necessary to use numerieal methods for the FDEM response, as mentioned in Section 7.7.6b (Koefoed, Ghosh, and Polman, 1972). To simplify the interpretation of TD sounding data it is desirable to eonvert the measured parameters froro the field survey [normalized magnetic and electric fields in a variety of forms (§7.7.4)] into Po' whieh is tben plotted. It is not possible to produce a unique definition of P., as in dc sounding, because of tbe numerous expressions for EM coupling (Kaufman and Keller, 1983; Spies and Eggers, 1986). The resulting P. curves, however, generally bear some resemblance to dc soundings whereas the original ro curves do not, as is apparent in Figure 7.75 where the ID curves, obtained by transformation from the FD (see the small inserts), are remarkably a1ike. lbey are also nearly identical to four- and five-layer curves (not shown). Conversion ol field data to resistivity curves is intimately related to the eddy-current dilfusion in the ground. For two layers, the current at early time is entirely confined to the upper bed, whereas at late time it has penetrated to the basement. Thus tbe sounding measures PI and Pz at the two limits. In between, the measurement is a combination of the two, dependíng on tbe thickness of the upper bed. Mathematically, at late time the dílfusion may be expressed as a relation between the measured parameter, say tbe vertical field component, time /, and tbe ground characteristics as lollows:

H, .. 2"MR 3("a )3/2/4wR 3 X 15w1/2/'/2

- ("M/30)( "a/Wl)3/2

7.7.7. Interpretation of Airborne EM Data

where R - T-R spacin&, and M is tbe transmitter dipole moment -lA. Because the receiver coil measures dH,/dl - H" we have

H, .. "M(

"a

)3/2/20w 3/2,5/2

(ignoring tbe minus sign). lbus the signa! decays as ,-5/2, whereas the apparent velocity of the dilfusing

current varies inversely with a. We may obtain the apparent resiStivity as a function of time from the preceding equations; because a - IIp -l/P., so

P.(t) .. (1'/wt)(I'M/20H,/)l/3

Data from ID systems, which record other parameters such as H" E" components, may be converted to Po in a similar fashion. Several sels of p" curves for two and three beds are shown in Figure 7.76. In all cases late-time response, which is most diagnostic of the strueture, is plotted, as (P,,/PI) versus (dlz l ), where d2,,(2t/""0(1)1/2 [the dilfusion distance given by Eq. (7.31)], and zl is the surCace bed thickness. Various values of R/zl are inc1uded in eaeh oC the three-Iayer curve sets in Figure 7.76c, d, e, f. lbe two-Iayer examples of Figures 7.76a, b, for resistive and conductive basements, respectively, re· semble the equivalents in dc sounding. The set oC three-Iayer H-type curves in Figure 7.76c are more charBcteristic of the bed sequence (PI - 16p2' P3 ... 00) than those for A-type in Figure 7.76d (PI 0.25Pl - O.0625p3)' which do not expose the intermedíate resístive bed. Curve shapes for the K- and Q-type layering in Figure 7.76e, f, bowever, are quite diagnostico Curve matehing is carried out by calcu1ating p,,(t) Crom values of li. (or whatever component has been measured) and plotting it agaiost tl/l on semitog scales identical to the master curves. Then the field curves are fitted to the lauer. Summarizing the EM sounding technique and comparíng it with dc resistivity, it is evident that both methods have a variety of standard lield systems and are capable of great penetration depth, although transient EM has the greatest potential depth. Resistivity equipment and analysis are cheaper, simpler, and probably superior to EM at present in providing detailed results. However, EM is more convenient in the field, requiring fewer setups and no long wires, and is less sensitive to surficial variations inc1uding lateral discontinuities. Finally tbe EM soundíng is insensitive to buried resistive beds, but both methods fail to resolve equivalent beds (§8.6.4C).

(7.42)

(a) Ceneral. Although fundamentally the same as in ground work, the objective in airbome EM surveys is more modest. Generally, the airbome results locate conductors, outllne their approximate extent, and perhaps provide enough information to estimate their characteristics. Ground followup is mandatory anyway, hence the airbome survey performs the function of rapid reconnaissance and elimination of barren ground. The preceding statement was true wben first written about 1970 but it is now unrealistic. Development of helicopter-bome systems, carrying automated EM and magnetie equipment and ftying slowly

100

.!:.L P,

50

25 11

e 4

Z

..!.

a,

Two layer curves.

!L>I .!...I P,

'2t

d

at

100

2

~------¡

.~-----,¡ ~

___ I

8

!LO!

(b)

Figure 1.76. Mdster curves of late-rime (P./p,) versus (d/z¡). {Parts (a) and (b): After MeNei/l, 1980; parts (e) to (f): After Kaufmann and Ke/fer, 1983.J (d) Tw~ldyer curves for resist;ve basement. (b) Sdme as (a) exeept for eonduetive basement.


452

--" •

Utl I l41 Z UI

______-4~~-----r----__

d

Z,

u

(e)

d

(d)

------+---------~-------.z. 11.

-t.

-~l.~------=:::=...

(e)

1/,.0.151 o.s ..JOl I IAI

({) Fi8ure 7.76. (Continued) (e) Three-Iayer curves far type-H strueture. (d) 5ame as (e) except for type Á. (e) 5.Jme as (e) exeept type K. (f) 5.Jme as (e) exeept type Q.

Interpretation

453

1"\

If

Tx 1.

'tr

......

..a. . , "

-. ~ i"""

ro....

T -¡

DDH

-001 JIlD ft

.....

-

"-

Sorf_

,-- i -~~

ft

T~/~'-r

.r~ p)'fThcMi.

"""'

0W'I'h1

uil

I\.Quottr.

1.00'

'==;;;2~==5)'4.FLIGHT LlNES

900'

--/-7'-/--+----- ":

-~'---+-----"

/ -/--7'----+-----',

_-/~::::g,:-=~J.~-=--=--=--=--=--=_"'_'_~ \.TRANSMITTING LOOP

700'

2.5-'r 1.25(b)

RATIO

PHASE

O

O

Figure 7.77. Examples al Turair responses. (a) Response over massive sulfide. (b) fffect al altitude over unknown conductor. FSFt - Field strength ratio, ., - Phase.

at Iow ground clearance with sopbisticated navigation aids, now make it possibIe to survey on 100 m line spacing. CoupIed. with the increasing cost ol ground work and difficulties with environmental agencies, tbis improvement may in time reduce surface expIoration in many areas to spotling drill sites, following surficial geoIogy and geocbemistry.

Large-scale reconnaissance airbome programs, however, still existo As a rule, tbis type ol AEM operation produces an excess of anomalies, because it detects without discrimination swamps, sbear zones, laults, and similar Iarge-scale features, as well as grapbitic and metallic conductors. Airbome EM sbould be, and almost always is, carried out in

454 conjunction witb airbome magnetics. Obviously tbe combination of two or more metbods generally produces more than tbe information obtained from each separately; in airbome work tbe enhancement is even greater, beca use of tbe abundance of anomalies and because tbe geological knowledge is Irequently limited in surveys of this type. Scale modeling is very useful as an interpretation aid in airbome work. Three-dimensional (spherical) and sheet models are usually employed. However, computer-controlled interpretation is increasingly applied, following tbe production of pro files and contour plots from tbe automated data. Heigbt of tbe aircraIt will normally replace T-R as tbe significant control dimensiono As a result, tbe response parameters for tbe sphere and sheet become (I'wa0 2 ) and (I'wath) where h is tbe aircraft height aboye tbe sheet. (b) Preliminary interpretatian. Because tbe c1assic asymmetric dip-angle curve is not recorded directly in airbome EM records (§7.5.4), tbe interpretation in various systems involves a consideration of peak amplitudes, widtb, and y-axis extent of a basically symmetric response. Consequently tbe initial step is to c1assify tbe anomaly as 3-D (limited x, y extent), 2-D (long, thin, appreciable dip), or I-D (large x, y extent). This rougb assessment may be made from tbe appearance of single profiles and correlation between adjacent ftight lines. Concurrently tbe interpreter notes the altitude and magnetic ftight records to see if tbe anomaly may have been increased or created by changing height and whetber tbere is any correlation between EM and magnetic profiles. This correlation is ex· tremely useful, because witb Cew exceptioDS most massive sulfides contain magnetic material, so that coincident or adjacent magnetic anomalies are particularly attractive. Having established the initial classification, quantitative interpretation will depend on the type of EM system used and tbe simplicity of tbe anomaly pattem. 1be detailed data recorded with phase-component and VLF airbome systems make it possible to produce shallow structure resistivity maps oC the survey area (Fraser, 1978; Seigel and Pitcher, 1978). These are a considerable aid in base·metal exploration to discriminate between bedrock conduetors and host rack or overburden structural anomalies. '!be contour map is even more useful Cor engineering applicatioDS, sucb as nonmetallic deposits, groundwater sources, thickness of soil cover, and permafrost. lbe mapping procedure is similar to that in Section 7.7.6c; an apparent resistivity is obtained from parameters of tbe coil system: receiver voltage V,


transmitter dipole moment M, and T-R separation. In this application, an additional variable, height aboYe ground oC tbe AEM system, is also present as an important item and a potential soucee oI error. Several computer programs have been devised to convert the data to p". In tbe following we consider briefly the Turair and VLF systems; the interpretation of phase-com. ponent and Input AEM data are discussed in more detail.

7.7.8. Turair This equipment, described in Section 7.5.3, consists ol a Turam transmitter witb a helicopter·bome re· ceiver measuring gradients of vertical and horizontal field components. Information with regard to field results is Iimited. Two examples are sbown in Figure 7.77, which empbasize the large exploration depth achieved with the ground transmitter. In Figure 7.77a, a 10 ft (3 m) section ol massive pyrite and pyrrhotite, 500 lt (150 m) below limestone, in the Manitoba Nickel Belt, produces strong response, indicating good conductor, accompanied by a cIear magnetic anomaly. Heigbt ol tbe aircraft is not given. Figure 7.77b illustrates the Turair flight pauem in tbe field and response lrom different altitudes ol an unknown structure, which appears to be less conductive tban in Figure 7.77a because of the larger phase difference. Whatever its physical cbaracter, tbis anomaly is still visible at 1,400 ft (450 m) aboye surface. lbe depth capability of this system appears suf· ficient almost to eliminate tbe need for ground fo1lowup, which was originally one of its advantages. Interpretation is like that in Turam ground surveys.

a

7.7.9. Airbome VLF Various airbome versions 01 tbe VLF receiver were described in Section 7.5.4. Because of tbe small weigbt and size, any of tbese units may be mounted easily on any carrier. lbus the VLF measurement is frequentIy combined with airbome magnetometer and phase-component or other EM systems for routine surveying; occasionally airbome radiometrics are included as well. Airbome VLF is not a carbon copy of tbe EMI6-EMI6R ground receiver (§7.4.2f, §7.5.4, and §7.7.6b), because it is impractical to measure tilt angle and more convenient to determine apparent resistivity from the wave-tilt W ratber tban from surface impedance Z,. 1be latter was defined previously [Eqs. (6.22) and (7.41)] in terms 01 p", invoIving tbe ratio 01 horizontal electric to horizontal mag-

455

Interpretat;on ANOMALY

-...

A

ANOMALY

8

200

E I

c:

~ lOO

.. ¡

I LEGEND

P

ORILL HOLES

O-m 1000 O-m

40

10

(a)

0-111

TIII

Gr... '

o

100

100'"

• Comout.d p. Figure 7.78. Results of .In f-phase survey for gravel near Wadena. Saskatchewan. (From Palacky and lagodits. /975.) (a) Pro file alon8 line 47 {see map in (b)) (or three frequencies plus interpretation of anomalies A and 8 based on P. values and results of OOH 1085. Be8 - Broadcast bando

netic field components. The wave titt is the ratio of horizontal to vertical electric fie1ds,

W .. EJE,

(7.43a)

Over homogeneous ground this can be wri tten

¡ - eirr/ 2, ¡1/2 ... ei "/.,

and elS .,,/4, so /12 = (±tI,2)(1 + j); see §A.7) and so for a layered earth we have [note that

(7.43c)

l ..

The Barringer E-phase VLF system measured only the quadrature component of W by phasing the receiver, to minimize the elrects of terrain irregularity and aircraft pitch and roll on the antennas. The in-phase component is much more sensitive to such disturbances. Simultaneous measurement oC VLF, LF (200 to 400 kHz), and broadcast band (550 to 1,500 kHz) Crequencies al the receiver was also a help in this regard, while providing responses from

dilferent depths. This was the tirsl AEM equipment in which all the operations were automated, from digital recording, data correction. and conversion, to plotting resistivity sections. An example of E-phase resistivity mapping is shown in Figure 7.78 for an area in Saskatchewan. Figure 7.78a shows three-Crequency protiles along line 47; the two anomalies and their interpretation (aided by tive drill-hole logs) located a gravel deposit. Figure 7.78b is the resistivity contour map, which outlines !he gravel and sand section where Pa is somewhat larger than average background. PresentIy available airborne VLF systems ¡nelude Scintrex SE-99, Sander EM-ll, and Herz'Totem-1A and 2A, all described in Section 7.5.4. The tirst two incorporate automatic leveling devices 10 correel undesirable aircraft movement. The Totem uníts, recording total-tield and vertical-quadrature components by means of three orthogonally mounted coils, require no other leveling controls. Furthermore, the total field is related to wave tilt and quadrature (§7.7.3j); thus !he Pa plOl migbl be computed from these parameters, aided by direct measurements of


456

0t::.::._ _ _...111111

(11)

Figure 7.78. (Continued) (b) map showing flight fines and contours of Pa fo, ',equency 368 kHz [LF in part (a)]; cross hatching indicates a gravef deposit focated by the survey.

P., sucb as EM16R or de resistivity ,(because the P" values are relative). CODtOUrs 01 total-field response from a Totem-2A survey Dear Utik Lake Manitoba, in tbe Precambrian greenstoDe belt, are illustrated by tbe CODtour map of Figure 7.79. CODduetors appear as long E-W strips; the superimposed circles are from a belicopter pbase-oomponent survey. Tbe Totem-2A UDit is equipped lO measure response frcim two VLF stations at once, which increases tbe possibility ol signal enhancement. As Doted .in SectiOD 7.4.2f, maximum coupting ol tbe VLF plane wave is achieved wheD the transmitter is on strike witb the conductor long axis. This advantage is DOt as great as it migbt seem because 01 tbe limited Dumber ol VLF statiODS and their global distnoution. Except ror North Cape, Australia, tbey are all located weU north ol the equator. In tbe WesterD Hemispbere the shutdown of Balboa Canal ZoDe has left the user with a compulsory prelerence 'lor E-W strike. Airbome VLF, like tbe ground metbod, is capable ol detecting conduetive structures with steeply

dipping boundaries. An example is shown in Figure 7.80a, obtained duriog a radiophase survey near Noranda, Quebee, where the Smoky Creek and Quesabe faults are marked by anomalies similar to Figure 7.48. Both tbis and an earlier airbome AFMAG survey outliDed many well-known faults in the area. Detailed EM16 ground folIowup (Telford, King, and Becker, 1977) located Smoky Creek lault very precisely, as seen in Figure 7.80b, tor the EM16 profile marked in Figure 7.80a. Altbougb there is no litbolagical CODtrast across the contact, both sides being granodiorite, an abrupt 15 m merease in conduetive overburden tbiekness was measured subsequently by shallow de sounding. This accounted lor the strong airbome and ground VLF anomalies.

1.1.10. Phase-Component AEM Altbougb tbese FDEM systems are DOt capable of reaching depths as ¡reat as Turair or Input, they produce more data and are more suitable lor de-

Interpretation

457

Figure 7.79. Toli/I-field VtF contours fmm i/ Totem-2A survey near Utik Li/ke, Mi/ni/obi/. Circles indicare conduc/ors loci/led by i/ helicopter phi/sl!"componenl 5 urvey. (Afler Herz, 1986.)

• t

J

J ..

tailed surveys, detection and resolution oC small-scale conductors, and mapping. We will consider the Tridem and Dighem versions oC this type of equipment, both introduced in the early 19705. Tridem carries two vertical coplanar coils approximately 18 m apart on the wing tips oC a De Haviland Olter aircraCt (Fig. 7.26a), operating at 520, 2,020, and 8,020 Hz to provide six channels ol simultaneous in-phase and quadrature data. The cutoff noise level is 50 ppm lor a 2 s time constant on a11 channels. Use oC these frequencies provides better discrirnination in depth and between thick and thin conductors. Otherwise, Tridem is much like earlier phase-component airbome equipment. The Dighem and Aerodat helicopter rigid-boom systems, described in Section 7.5.5, are multicoil as well as multiCrequency methods. The Cormer, illustrated in Figure 7.26d, shows the vertical transrnitter coil with ftight-line axis and three orthogonal recciver coils, two ol which are minimum-coupled, known as fishtail and whaletail Cor obvious reasons. Formerly single Crequency (900 Hz), there are two later models: Dighem 111 aperates two horizontal coplanar coil pairs at 900 and 7,200 Hz and one vertical coaxial pair from 385 to 7,200 Hz; Dighem

IV carries a 56,000 Hz frequency. The Aerodat boom contains two vertical coaxial pairs at 955 and 4,536 Hz and two horizontal coplanar pairs at 4,132 and 33,000 Hz. Coil separation is 7 m and noise level 1 to 2 ppm in both. An attractive feature oC phase-component AEM is its symmetry with respect to flight direction.. Data interpretation with these units is somewhat Iike the Slingram ground set, a1though the coils are mounted both horizontally and vertica\ly. The latter orientation is more sensitive to conductors of steep dip when the ratio oC z/I (Fig. 7.82) is large; with these AEM methods, particularly the helicopter system, such is the case. For example, the problem oC a sphere or serniinfinite vertical sheet lends itseU to an approximate solution using the lumped circuit analysis; for both models the loops are assumed to be superimposed. From the procedure used previously, we obtain lor the sphere:

9t4{ H;/H:} ., 0.8( a/h}'(I/h)' {1/11(1 + a2 )]} (7.44a)

-'m { H;/Hf} ... 9l1{ H;/H!) /Q (7.44b)

458


,---EMI6 FROf'ILE

, , - - AADIOFHASE PAOFILE

N

o,

QI

.,

,

•

(a) Fisure 7.80. Airborne VtF (radiophase) and detai/ed fM16 sround 5urvey, Smoky Creek fault area, near take Abitibi-Noranda, Quebec. (From Telford, KinS, and Becker, 1977.) (a) Map showins survey lines, fault traces, and profile loc:ations.

where a is the spbere radius, h the distance between centers of the dipole and sphere, 1- T-R, fJ(1 + 1/Q2)1/2, and a - x/h. For the vertical thin sheet, we have

H;/H! .. 2 X lO-'(h/f)(l/h)'{l/fJ(l

+ a 2)2) (7.44c)

wbere f is the effeetive conductor length energized along the top of the sheet and h is the distance from tbe dipole center lo tbe top of tbe sbeet. Profiles for tbese models are sbarper than tbose from AEM units witb large T-R separations. Depth may be rougbly estimated from the value of ClI/2 at half-maximum; for tbe sheet h - 0.8xl/2 whereas h - xl/2 for the sphere. Knowing the altitude of l1ight, one can get some idea of conductor geometry. From Equations (7.448, e) the spbere-model response decreases as h- 3, whereas the value for the thin sheet appears to be h- 2 (althougb the correet value is said to be h - 3.3 - and otber powers ranging

from - 2.6 up for equipment of this type). One might assume the 2-D geometry of the sheet should produce a slower falloff than the spbere, but tbe explanation is probably that the area of eddy-current induetion is quite limited and that the effeetive inductanee of the sheet a1so varies witb heigbt, possiblyas l/h. More satisfaetory interpretation aids in the form of charaeteristie curves are available for phase-component systems. Using a semiinfinite vertical-sheet model and considering only the maximum response, when the sensors are direetly over the top, we bave (Grant and West, 1965, p. 526), assuming x - CI - O,

H' - m .. {1/3 - (I/2h)2/ 5

+(1/2h t/7 - ... }/lh· 2h' wbere m.. - 4"/'HP/2 or -4,,/ 3HP, tbe transmitter dipole moment for coaxial and coplanar coils, re-

459

Interpretatíon

coaxial coils, but may be adapted Cor any maximum-coupled coil pair [e,g., §7.7.6b, systems (a), (b), and (e») and frequency, provided the coil separation is small compared to ftight height. The ftight heading is usually assumed normal to sheet strike; when it is oblique, the Dighem vertical null-eoupled eoil produces an anomaly. The angle may be determined from the relation

100

....Z

50

1&.1

u

a:

1&.1

a.

10

4

r---------------------------~~ where Rm and R. are the respective responses in the maximum-eoupled and vertical null-coupled channeIs. Tbis leads to an azimuth correetion

10 3

11

a,

t

(7.4Sc) 10 2

,

1

I I

DU,'U,v,T

¡

}

[ Ii ,

,I I

(1)

q;

...

1&.1

'.00

W INTE"'''l fED

IOtOON

.'.

srCTtON

2O t OON

Figure 7.80, (Continued) (b) Curves of (Hz/H.) and Po on the fM16 profile. plus interpreted section,

spectively (§7,2.3d). When h

::1> /

W/W .. (//h)3/ 24 ." or

this becomes

-(//h)3 /12 ." (7.45a)

lor the same configurations. Because Equation (7.45a)

-\

is derived for a model oC infinite conductivity, these relations must be separated empirically ioto in-phase and quadrature components R - M(I/h)3

Q - N(llh)3

(7.45b)

and then plotted as RIQ versus induction number (lloWIJth)1/2 (§7.7.3i), as shown in Figure 7.81a.

Because R/Q - M/N, we may now produce a response curve like that in Figure 7.10 for the M and N values oí the vertical sheet, using the induction number as the second coordinate; see Figure 7.81b. Finally, the characteristic curves, with in-phase and quadrature maximum response Cor varlous values oC at and h, appear in Figure 7.81c. These are for I

~

where HO is the signal normal to strike and H' the measured MC response at angle a. The Dighem horizontal NC coil indicates dipping conduetors, useful in distinguishing near-surface conductive beds of shallow dip. Response of the sheet target theoretically decreases as h - 3 only for infinite conductivity in a resistive host rock. In a reallstic situation, RIQ inereases with ftight altitude; from Figure 7.81c, at h - 100 ft, RIQ - 1.2; at 400 ft it is about 2.8. Effects of conduetive overburden and host rock (§7.7.4e) are also quite as significant in airbome as in ground surveys. AEM phase-component response over the spherical model has been well covered by Lodha and West (1976). Using the theoretical treatment available since the 1950s (e.g., Wait, 1960b), they computed the response íunction for a vertical coaxial-coi! pair, helicopter-mounted on board or in a towed boom. Characteristic curves, with plots of (llwlJa2) versus z/a for a range ol z//, are given in Figure 7.82 for a complete interpretation. In the diagram the rectangles mark the range oC calculating the parameters lor varlous vertical distanees to the sphere center. (Note that all dimensions are measured in units of /.) Empirically it has been Cound that over a wide range oí the parameters the hall-peak widths of the field profiles are related to z: O.58W1/ 2 S Z S 0.8W1/ 2 , and that W1/ 2 '" 10/. The method is to select the average value, z = 0.7Wj/2' and find the point for the in-phase and quadrature peaks on the figure. Tbis point will generally lie within the rectangle z/I - 7, from which zla, /A-wIJa 2 (hence " because z is assumed to be known) may be read directly. A second approximation may be obtained by changing zl/ to 8 or 6 and tben interpolating for a better result.


460

100~~~. ~ .

¡,. .

'.

e: luwalhl'" Figure 7.81. Response of a maximum-coupled coil ro a rhin vertical dike. (Afler Fraser. 1972.) (a) flatio of in-phase (fl) to quadrature (Q) components as a function of the indudion number 8 - (~",ath)1/1.

Characteristic response of a horizontal thin-sheet conductor is another useful interpretation model, particularly for resistivity mapping. The analytical procedure is similar to but simpler than that for the spbere (Grant and West, 1965). Figure 7.83 shows this set 01 curves for Tridem. In general form it is like that for the vertical sheet in Figure 7.81c. However, the solid curves are plotted for various values of /at, permitting a determination of at at all frequencies used in the Tridem system. The aforementioned model conductors may be analyzed by means 01 the computer programs PLATE and SPHERE (§7.7.4a and §7.7.5c) in both frequcncy and time domain.

7.7.11_ Resistivity Mapping Stagnation in base-metal prices and steady increase in exploration costs since 1978 bave reduced the use 01 airbome EM rrom a peak of 600,000 line-kilometen in 1979 to less than hall this figure in 1988. Activily in airbome magnetics and radiometrics, however, bas nol declined during the same period, the fint because ol its proven versatility and the secoDd as a resull ol shallow mapping applications.

The meSsage is c1ear enough: rather than detecting sulfide anomalies, airbome EM should be iocreasingly applied lo structural mapping. preferably in cambination with the other two techniques. Tbis trend is already cvident lo some extent. Development and interpretation oC resistivity maps from AEM surveys have been discussed in several reports (Fraser, 1978; Seigel and Pilcher, 1978; Geological Survey of Canada Paper 86-22, 1986). To prepare these, ftight data must be compared to zero or background-Ievel response. This is achieved by periodically increasing altitude to about 200 m at the end ol a ftigbl lineo Various layer models have been employed lor analysis in resistivity mapping. TIte recorded altitude of the system is a critical parameter in all cases, because the data are subject lo errors caused by irregular terrain and dense tree cover. Correet or not, the addition ol the altitude measurement to the other reoorded quantities, in-phase and quadrature response (preferably at severa! lrequencies for a layered section), is one parameter too many for UDique determination of the apparenl resistivity. The result is equivalent 10 simultaneous de resistivity profiling and sounding, that is, a strong probability of more

~

...

cb

m.

9

1m

<:)

~

.~

te

¿ ~

-"3 ~

~

CD

......

~

~

...r:

~

:el "-

'ti ~

..

.5 c

-

(3 I~

..:

'":s Q.;

~

~

--

..::.

,

2:• z :

N

•

.

~

o

.

]

....CI
~

--E

!l ,S '6

OO-

]

..

..c: ~

w

en :J:

~

z

'"

'S

'00

e~

~

~

~

1,s c:

13",..: a:l

"~

...

,!!l

N

(lIIdd) 3~nJ.naYno

Figure 7.82. Interpretation diagram for a vertical coaxial-coil AEM system over a spherical conductor of radius a for z/I- 5,6,7,8,9,10,12, and 14; 1- T-R, (After Lodha and West, 1976.)

"

(

.¡

Iban one solution, unless the ground is homogeneous and isotropic. For example. we may determine Po as a function of (i) bird altitud e and amplitude (R 2 + Q2 )1/ 2 , (ü) altitude and phase angle, lan-I(Q/R), or (ili) amplitude and phase. The first Iwo estimates will most likely be dilferent and neiIber supplies any depth information. Solutions (i) and (ili) are shown in Figures 7.84a, b. To avoid, or at least reduce, Ibis difficulty, it has been the custom to assume a fictitious highly resistive layer of variable depth overlying either a hallspace or two beds simulating overburden and bedrock. (Models with more layers are too complex for interpretation at present.) The tirst of these has been called the pseudo/ayer ha/f-space, the second a pseudo/ayer two-/ayer or three-fayer modef (Fraser, 1986; Paterson and Reford, 1986). This resistive top layer is a device to absorb the dilference between beight 01 the boom recorded by the altimeter and the sensor-source distance detennined from Figure 7.84b.

The two models are shown in Figure 7.84c and d, where Q is the altimeter reading and h the computed vertical height. A positive value of (h - a) may be the result of tree cover, permafrost, glaciated overburden, and the like; it could be negative over treeless surfaces with a conductive top, or z.ero if the open ground is homogeneous to a depth greater than the penetration of the AEM system. The ambiguity resulting when we attempt lo match a two-Iayer model with balf-space data from Figure 7.84a is illustrated in Figure 7.84e. The three-frequency AEM system produces three dilferent P values as expected, but none is c1early related to PI or P2. Qnly the hoOz.ontal coplanar pair al 4,020 Hz determines h reasonably well, but h is already known (because it equals the aircraft altitude approximately; see Fig. 7.84d). Thus, no useful information is provided concerning the overburden. . Tbe pseudolayer model of Figure 7.84c gives more reasonable results using the curves 01 Figure 7.84b, but only ir the field geometry is at least approxi-


464

" 0'1

-

IO'!----------+_

2

la: la:

TRIDEM RESPONSE HORIZONTAL THIN SHEET

~

,- FREOtJt:NCY 'HI) 1- CONOUCTANCE 'II1II01' h - HEIGHT ASOVE THlN SHEE T ' " I

IN PHASE (P. P. M.I Fisure 7.83. Chilracteristic curves fo, the r,idem system over a horizontal thin sheet. Solid-line curves are for constant (fat). dashed a'e for constant h.

mately a half-space. However, the assumption of three layers, Figure 7.84d, to match two bcds as in Figure 7.84e, is the most rcalistic model because it ineludes overburden in the four unknown parameterso Analysis may be done with atable lookup TOUline (De Moully and Becker, 1984; see also §7.7.12h), by comparing survcy data with standard models, or by an inversion technique describcd for FDEM (Paterson and Reford, 1986) in which the fit between the model data and the field data is optimized (§2.7.9). In lhe latter analysis scveral routines are necessary lo minimize the ambiguities in overdelermination. These inelude estimation of relative significance, error limits, and tolerancc of each parameter for acccptable model lit, plus maxirnization of stability and economy bccause of the large amount of data. The pracedure is knowo as singular value decomposilion (SVD) or eígenfunction analysis. The resistivity map can be a definite interpretation aid in base-metal survcys for distinguishlng bedrock from overburden conductors. An example is shown in Figure 7.85. The original ftight sheet in

Figure 7.85a locates anomalies with conductances marked 00 the ftight lines, along with the interpreter's assessment of their character. Resistivity contours superimposed in Figure 7.8Sb locate two low zones of 30 nm. which could be identified with more confidence as bedrock sources l>ecause thcy were not associated with drainage. The ground IP-resistivity survey results, displayed in Figure 7.8Sc, plus Jater drilling confirmed this interpretation by exposing graphite with disseminated pyrite.

7.7.12. Input AEM (a) General. Since about 1963, tbis unique airbome time-domain technique has been the oc bread and butterto reconnaissance EM system in base-metal exploration. Originally the interpretation procedure Was quite elementary, but improvemcnts in equipmenl- a 30% boost in transmitter power and more receiver channe1s- have greatly increased lhe signaJ.to-noise ratio and digital data acquisition and recording have provided higher quality dala. Increased power allowed a shorter time constant, which in tum pro-

'.

465

Interpretation 100

•

ao

101 fOO

ao

~

••

100

•

•• .... o

o

... ....J

••

e,

;:)

--'

..... .....

e o

o

a: ai

-I ~

~

• ...•••

le

•

CIC

el)

AMPLITUDE (ppm). [ INPHASE

2

+ QUADRATURE

2]'tZ

(a)

"'lit e

..

% IL

Z :;:,

!'" ~

~o

-'"• ..J

1...

i'

!• o

~

e

11:

'"~' f

.,

• AMPLlTUDE I ppml

I

[INPHASE·. QUADRATURE 1]

~

(b)

Figure 7.84. Interpreta/ion o( airborne resis/ivity data over a mu/ri/ayer hall spaee. [Parrs (a) and (b): Afler Fraser. 1978; parrs (c) and (d): After Fraser. 1986; part (e): After Palerson and Reford. 1986.J (a) Altilude o( bird verws amplilude for a maxinwm-coupled eoil over a homogeneous half-space; frequency 90Q Hz. (b) tan versus amplitude for maximum-coupled coil over Ihe pseudo/ayer half-space model in (c); frequeney 900 Hz,

466

f/eetromagnetie methods

h. MntOr- lOUfC8

altlm.ttr • a

dlstance

duced betler anomaly resolution and greater depth oC penetration. Development oC more sophisticated scale models and digital data processing have also improved the interpretation, as in other airbome systems. Consequently Input may now be employed Cor mapping, as we)) as detecting bedroclc conductors to considerable depth. (b) Vertical-sheet response. In a pioneering report on TD interpretation, Becker (1969) simulated the transient response oC the Input system to a thin conducting sheet. The procedure is carried out in the frequency domain; replacing the thin-sheet target with a loop conductor, L in series with R L (§7.2.4b, §7.2.5d), the loop response runction becomes

e( Col) - G( Q2 + iQ)/(l + Q2) (7.46a)

b!!!! PSEUDO 1

-

RE81STIVlTY

IHICISNESS

?

-

( e)

?

where Q - ",L/RL - "''1', '1' is the loop lime constant, and G is a multiplier relating to the transmittero, receiver-, and conductor-loop geometries. The conductor loop may be also simulated by the R-C network, shown in Figure 7.86, whose transCer Cunction is

c'( "') - G' Re/{ Re + l/j"'C)

- G'( ",2C 2R~ + j",CRd /( 1 + ",2C 2R~ ) (7.46b) also CR e - "''1''. For an exact simulation, we must have, at all Crequencies, c( "') - e'( "'), that is, G .. G', and '1' - 'T' or

L/RL - CR e

LAYER PSEUDO

1

2

-

RESISTlVITY

? ?

THICKNESS

1 1

(d) figure 7.84. (Continued) (e) Configuration of the Dighem system with horizontal cop/.mar eoi/ pair over pseudo/ayer half-spiJce modelo (d) As in (e) exeept pseudo/iJyer plus two-/iJyer model.

(7.46c)

Standard Input field equipment, coupled to the circuit oC Figure 7.86, may then be used as an equivalent analog model to simulate the transienl response under various geometric conditions. The preceding analog simulation, however, is not userul for conductor models other than the thin sheet. For different geometries, modeling is better done using a digital computer and convolution methods (§A.10, §A.13), provided the FD response is known. Becker, Gauvreau, and Collett (1972) used a scale model to simulate Input four-channel response over vertical dikes oC variable thickness and conductivilY, as well as horizontal sheets as overburden. The scaling relation in Equation (7.33a), which can be written (17",/17/) - (/¡/f",)(I//l",)2, was satisfied by taking 1m - 3/¡, /m - ///1560, and 17", - 8.1 X 10'(7/. As a result, aluminum, stainless steel, and graphite sheets (32 x 10 6 , 1.4 X 106 , and lO' S/m) correspond to field conductors ol 40, 1.7, and 0.12 S/m,

Interpretation

467 TWO- LAYER MODEL

8EST FITTING HALF-SPACE

~

~F

MODEL PARAMETERS

10", eI",' 20 ",S/III f G'.' 0.1 mS/m

O-!~I {" • 945 _!~[( .... 1 0(Pll'ft1

t, ' 0.7 f. ' 39.0 t. ' 14.0

13.1 209.3 63.6

Hz " • 5075 Hz

SYSTEM Pll'.RAMETERS

t,. 4020 Hz h(m!

.. 1mS/m I ~~

7.3 30.1 7.7

1.4

4.2

0.1 37.7

104.8

1.3

3.5

6'0

13.3

FITTED DATA

(e)

Figure 7.84. (Continued) (e) Comparison of actual /wo-Iaver and bes/-fitting half-spilc(, response.

}

respectively. Both minimum and maximum T-R coupling were tested, the first wi lh the receiver coil vertical, the second horizontal. It was found that sheets oC 60 cm strike length and 15 cm depth extenl, corresponding to 900 X 250 m field dimensions, were sufficientIy large 10 represent semiinfinite conductors, but unsuited as sheets oC low 01. Examples oC channe1 response for both couplings over the vertical sheet appear in Figure 7.87a. Amplitudes varie
overlay; the lOS ppm point is also marked on this vertical scale. The transparency is then moved over the curves, maintaining parallel axes, to obtain the best fit for the six data points. Conductivity and depth béJow the aircraft are then read off the upper auxiliary grid at tbe location oí the lOS ppm point, with respect to the slant and horizontal lines. An analogous nomogram for the conductive half-space is illustrated in Figure 7.88b. (e) Ribbon model. Profiles over a ribbon, or thin sheet conductor oC linite depth extent, show that amplitude varíes with deptb extent. but more for poor conductors than good ones. However. the channel ratios are practically unchanged, which is also true for limited strike length. Thus the conductivity estimates from the nomogram of Figure 7.88a are still valido 11 is not possible to distinguish depth extent Crom depth to the top without additional geological or geopbysical information. (d) Dipping half-plane. Figure 7.87b displays model Input Mark VI profiles over a vertical halfplane, at two altitudes and for three al values. Comparing tbese with the maximum-coupled fourchannel set in the upper part of Figure 7.87a, the six-channel Input c1early produces profiles with better definition, including a more obvious minor peak before (with respect to flight direction) the main anomaly. lnitially, from field survey data, the minor peak was assumed to be a minor conductor; however, because it could not be found from ground followup and because it was also present on model profiles, such as Figure 7.87b, the small peak was seen lO be an inherent feature of the Mark VI designo


468

EM onomol,

ol'd milo volv.

s

S?

--

COnduclor Olí.

Figure 7.85. Resistivily map as an .lid in dislinguishing bedrock from O\'C'fburden anomalies. (After Fraser. 1978.) (a) Airborne fM map showing conductor pallern similar lo thal for condUClive overburden.

Palacky and West (1973) have used the ratio oC major-to-minor peak amplitudes to estimate dips of the half-plane conductor. From model and fie1d data tbey found that the ratio was 10 for 90° dip, decreasiDg to about 1.5 lor 135° dip. When flying updip, IWO distinct peaks are observed, Ihe second over the

upper edge of Ihe sheet. Downdip. only one peak of much larger amplilude appears on Ihe profiJe plot. Dip estima tes may be made from Figure 7.89, which also ¡neludes an amplilude correction factor lor modifying the conductor deplh estímate. The procedure is to enter the righthand side of !he figure

Inrerprerarion

469

;.1

Resi.tlvity in ohlM-/Mllrl

Figure 7.85. (Conlinued) (b) Pseudo/al'er resislivity mJp of the areJ in (a) showing rwo bedrock conductors.

al tbe measured value of the major/minor peak ratio (2 in tbis case), proceed left 10 intersect Ihe slant line, then upward a distance 2 (using the lefthand scale), tben left to the leCtband vertical scale where we obtain the amplitude correction (- 1.4) for use in Figure 7.88a. Verticallines tbrougb the two inlersections with the slant line give tbe dip (120° and 65° bere).

(e) Conducrive overburden. Figure 7.90 shows the modification of six-channel response from a haH· plane mode1 of al - 27 S at 20 m depth due to conductive overburden. Background levels are in· creased in the first three channels and the overburden has a large, broad response, mainly confined to channe11 when its lateral extent is limited. Only the amplitudes are reduced over a vertical plane whereas

E1ectromagnetic methods

470

Resistivlty in ohm - meters Chargeability I resistivify

::> O· 5

1/4 mil.

400 m

(e)

Figure 7.85. (Continued) (e) Cround IP resistivity map 01 rhe same area showing two anomalies.

dipping sheets aIso suffer sbape distortion, wbieh inereases with the conduetance of both the target and its cover. A combination ol overourden and dip has changed the ehanneI 1 negative peak to a posi· tive trough over the two sheets dipping 36° and 144°. (f) Conducting sphere. This modeI gives an Input profiIe thát is perlectIy asymmetrie with a erossover

aboye the center, in contrast to tbe symmetric peak from 2·D sheet models (Mallick, 1972). Amplitude ol the secondary.field positive and negative peaks either side ol the erossover falIs off as 1/h 3 , h being the vertieal distance between tbe spbere center and the receiver, and inereases with tbe parameter fJ2 Jl.aa 2 , where a is the sphere radius. However, wben a goes to infinity, the tbeoretieal transient response vanishes; tbis surprising resuIt is related to the phase

471

Interpretation

AIIIP.

1·00 0·30

(/) 30{) w w

0·10 o ¡:: 0{)3 ~

~ 0·9

0·01 ~~~~_~I----~--~r-~

II'llUC TlON 02+

io

02+

I

G.F.· GEOMETRICAL

FACTOR

Figure 7.86. Equivdlence of e/eetronie and e/eetromagnetic tramfer functions. (After Becker. 1969.)

MAXIMUM COUPLEO SVSTEM

(11)

REAL TIME OElAV

-

CHANNEL

A

CHANNEL

B

CHANNEb

C

1800 I.lS

CHANNEL

O

2100 J,l.S

1500 I.IS 1650 I.lS

WR.T. PRI FIEL O ONSE T FLlGHT

+1000 AMPLlTUOE (IN PPM' O

OIRECTION ----t~.

O r-CONDUCTOR(REAl Tcp;rSO SI ,

~I----------~I-----------ff-----------+I----------~I

-0100

-200

200

0100

O

DISTANCE

-1000

IN

METERS

MINIMUM COUPLEO SISTEM

REAL TIME OElAV

CHANNEl A

1500 I.IS

CHANNEl

1650 J,l.S

9

CHANNEL C CHANNEL

O

__

,'VI/'--.-

1800

S

2100 J.4S

~~~~~---------- ~··--W-.R-.T-.-P-R-I.--FI~E~L-D-O-N-S-E--T Figure 1.81. Model Input response to a thin vertical sheet. (a) Four-chilnne/ response for maICimum- and minimum-coupled systems for vilrious viI/ues of the rea/- time de/ay. (Afler Becker. Ga~·reau. iJnd Col/ell. 1972.)


472 vto 10 S -300

•

o•

300

•

·300 ,

300

-300 ,

o

300

------, -

~OO

O

300m

.....~--.....-.....,...-

-- ...--

---HElti"l • 115m

.300

o

,

o

300

-,----_....,

-300

O

'500

m

--------

I

"IIU

1000'

".

"[Iti"' • 140m

FUGHT DlRECTDoI

(h) Figure 7.87. (Continued) (b) Six·channel response for two f1ight heights and several values of at; the top of the sheet i5 at zero height. (Afte, Palacky and West, 1973.)

difference belween primary and secondary fields, which decreases with increasing ¡P. (s) Mappins shal/ow structure. Input applications Cor outlining shallow geologieal struetures and esti· mating overburden parameters have appeared in the literature since about 1975. Response from a Cault containing conduetive serpentinite, near Lake Wa· nipigow in southeastern Manitoba, is sbown in Figure 7.91. Data Crom a mapping program carried out by the Geological Survey of Canada over conduetive overburden in the vicinity of Hawkesbury (near Ottawa) are displayed in Figure 7.92. The ll-channel verticalaxis Input receiver (Fig. 7.28e) was used for Ibis test. Typical response Crom one ftight line appears in Figure 7.92a. In the analysis, amplitudes and decay rates along the channel lines are averaged and en-

tered on a parameter interpretation chart seen in Figure 7.92b. (For large amounts oC data tbis obviously requires a computer.) The output is an esti· mate oC the TCP oC the overburden. Beeause the modeling routine assumes a threelayer structure as in Figure 7.84d, (§7.7.11), it is possible lo separate these paramelers only when the c1ay overburden is exposed al surface. In this event, its thickness and resistivity may be established independenlly. A comparison oC the interpreted airbome data with ground de resistivity is illustrated in Figure 7.92c. The 2 km spreads used for the ground survey resulted in less detail than thal of the Input profile. (h) Bathymetry. Input mapping of seawater depth in coastal regions has been described recently by Zollinger et al. (1987). Although lrequency-domain AEM is also a possibility lor this type of survey, the

Interpretation

473

OEPTH (ft)

E

E

10000

..-.

E a. a.

~

CI)

~ ~

-t"-rt--t1f+...UJ.: ---

~ ~ ..J

~ Z

g

2

10

20

100

0·1

ut (S)

(a) Figure 7.88. Nomograms for obtaining conductivlty and depth. (a) Nomogram givlng TCP and h for a vertical sheer. (After Palacky and West. 1973.)

maximum depth of penetration is not as great; both methods are doubtless suitable {or freshwater areas. Compared to mapping ground layers, the problem is greatly simplified, because the ground surface becomes sea level, overburden conductivity is constant (4 S/m) or practically so, and the only variable parameter is depth to the bottom, the lalter being generally highly resistive. Interpretation is performed with an automatic curve-fitting algorithm to determine the depth from the recorded EM and altitude

data. The algorithm is essentially a stored set oC models, judged to cover the maximum range 01 the survey data. Injected flight-path data points are compared with the stored models and the best fit is talten as the solution. Detaíls of this procedure, known as a table lookup routine (§7.7.11), are given in Zollinger et al. (1987). Two field examples are given, one line of 28 km over the E- W channel along the south shore of Cape Breton Island, Nova Scotia, the second heading

Electromagneric methods

474

§

mE 600= 5 10 • 1

-

~ w

30J

l:

l~

" T

Q.

10"Z

;

3

rJ.

•• 1

~' i~

~ a:

~ x

1041Z

Q.

e e

100

'I~.....

E

4

150~ &X)~

Id'

.I '

~ 10~

en

~

:1

3

10

w > 2 ~ 10 4 .J

w

a: 10

1 1 1

I.J

500 1000

FIO. 110

(b) Figure 7.88. (Continued) (b) palacky nomogram for interpreling conductivity and aircraft height (above the conductor) far a conductive half-spaee. (Afler De Moully and Becker, 1984.)

HALF PLANE AMp\,.ITUOE CORRECTrON FOR DIP

10

FLIGHT DIAECTION

•

1

~

6

~

~

~

3~

~ 3U

...

::1

15

~

~

::1

i

~ ca: 01

4!le

,•

.,.

I

, 1

tO"

DlP

lzoel~

A,e

Figure 7.89. Estimarjng djp of a half-plane 'rom the ratio o, majo,..to-mjnor peak amplitudes. The amplitude eorreclian (see left-hand vertical sea le) eorrects for the effeer of dip on amplirude. (After Palacky and West, 1973.)

Interpretation

475

Interpretation of AEM Mealurementl __ -1600

-

O

o

-1600

800 "

~~~_:J

-1200;;...=..._~_O .....~~......;I200:;.; tI

80011 -6-

, I

'-

-5-4-

-3."........ . ~ . -- __ .. __ -', ._.,- , . / -2------_._-- "

,

.

, ~ \ , :. \:

'-._. __ •• --, '.' ",-..

,

... ,'

.. -_.. -....

bCI~

5000 ppm

-1-

OVER8UftOEN

----- OS -12S

•

144·~

ti' : 27 S

Figure 7.90. Model profiles over dipping half'plane ((Jt - 27 S. dcpth lO top - 70 fl) under conductive overburden. Dashed fine indica tes shift o( anomafy peak (rom earlv lo late time. (Afler Palacky. 1975.)

'. , - 4... .... . . . ..... .. ........ '

~

~.. . ~"'...A-'--~

-.-.~.

~ ~

INPUT ANOMAl

"""~

FAUlT SERPENTlNE HORNBlENDE

.. <

t.

r

QUARTZ

DIORITE

Figure 7. 91. Slructural mapping with Inpul syslem; Lake Wanipigow area. Soulheaslem Manitoba. (Afler Dyck. Beder. and Col/etr. 1975.)

N500W for 19 km from coordinates 47°45'N, 64°39,S'W near New Brunswick, both on the Canadian east coast. The Cape Breton line was flown six times both east and west on the same track at altitudes of 170, 200, and 230 m above sea level. The line is centered al 45°35'N, 60 0 50'W and crosses the mouth of Lennox Passage near this location. Figure 7.93a shows altitude, normalized amplitude response, and

depth for W-E Hight al 230 m. Normalizing of the six·channel data was done by dividíng each channel by the geometric-mean amplitude oC channels 3 and 4, which were usuaIly the mosl stable. Sea-bottom conductivity was assumed to be 0.001 S/m. The bottom plot shows the interpreted depths to be witrun 2 m of the black dOls takcn from coastal charts, except for the deep break at Lennox Passage around 12 km. Results were poor here, indicating

>

.5

...o ;:)

~

..J

Q.

~

10

E

... ... ...O

;:)

200

..J <1

I~O

t

100 Al O

3

2

O

I DISTANCE (km)

I 10

1

1

20

30

1

I 60

1

40

50

FIDUCIAL

,J

lA 80

70

NUMBER

(a)

14

TCP

(SJ

30

~

10

..-_....

I.IJ O

~20

0'1"0.2"

~-"'---

....

-----------------28

----

~----------";;~1.0!5

..J Cl.

-

--- -

~

<[

I.IJ

_--------------0'1" 1.01 SI.)

C)

~

10

I.IJ

>

<[

Cí2"O I 00 00

I

0.1

02

03

0.4

0.5

I 0.6

DECAY TIME ,Id

I

I

I

0.7

OB

09

(ms)

lb)

Figure 7.92. Typical l'-channel vertical-axis receiver Input response over conductive overburden, Hawkesbury area near Otlawa. (Afler Dyck, Becker, and Collett, '1974.) (a) Response curves. (b) Nomogram for finding TCP and I in lerms of average amplilude and decay lime.

1.0

1.1

Field examples

477 DISTANCE {km¡

O

A O

F IDUCIAL

10

20

30

2

,

3

A'

NUMBER

40

60

50

70

80

O 111

G:

'"CI>-

10

...1

>CI ...1 U

-

~

o

-

OC RESISTIVITY INPUT

eL U f-

(e)

Figure 7.92. (Continued) (e) Comparison o( TCP va/ues (or the overburden obtained using (b) and by de resistivity 5urveys

depths oC 60 to 100 m; the chart depth was 43 m. Resolution below 40 m depth is thought lo be greatly reduced with the present system. Apart from this small area, the several ftights produced data within 2 mover most oC the lineo Results from the New Brunswick test are iIlusIrated in Figure 7.93b. Here Ihe bottom falls away sharply to the NW and is mainly shallower Ihan the first area over the rest of the lineo However, the agreement witb coastal chart values is quite good and persists over the ledge about 40 m deep between 26 and 28 km. Flight altitudes were a litlle higher (210 to 240 m) tban at Cape Breton, which wiped out channels 5 and 6, leaving four channels for interprelation. Sources of error considered troublesome in this type of sounding inelude atmospheric noise and eCfects oC bird motion on the receiver, as well as use of incorreet eonductivities for the mode\. Sea-water conductivity can vary because of ehanges in temperature and salinity. which are common in coastal waters. Changes in bottom conduetivity were Cound to be negligible except where a thin conductive layer covered a resistive bottom; this may account for the Lennox Passage anomaly.

7.8. FIELO EXAMPLES Because oC the great variety of EM field methods, the number oC case histories and problems is necessarily large. We have tried to provide examples oC aU oC the tecbniques commonly used at present.

It should be noted here tbat many oC the diagrams contain abbreviated names or acronyms Cor different types oC EM ground equipment. Thus, VLEM, VEM. and JEM reCer to vertical-loop units of various kinds, which employ a local transmitter (Cor the reader who is not familiar with the terms, it is necessary to specify a1so whether the transmitter is fixed or movable). As mentioned earlier, VLF reCers to very low-frequency sets (generally EM16), wruch use remote· transmitters. Likewise HLEM stands ror horizontal-loop (or Slingram or phase-component) EM equipment. l. An iJIustration oC the vertical-loop fixedtransmitter method is shown in Figure 7.94. This is the well-documented Mobrun sulfide body, 10 miles northeast of Noranda, Quebec. The deposit, whose section is shown in the diagram, contains about 4 million lonnes of massive pyrite. This is a elassical vertical-loop profile, obtained with the transmitter localed 400 ft lo the east. on the conductor strike axis. The large maximum dip angles on either side ol Ihe crossover are approximately equal, indicating a sleeply dipping good conductor at sballow depth. Although the crossover appears to be displaced about 25 lt north 01 the geometrieal center oC the section, this is not significant because the body is 100 ft wide. Depth estimates are not very satisfactory; using the curves of Figure 7.42b, the conductor appears lo outcrop. 2. Figure 7.95a is a good example 01 a verticalloop broadside or parallel-line EM survey, carried out over the Uchi Lake sulfide body, sorne 50 miles east of tbe Red Lake gold area in northwestem

HO--·

! •

",

~.:

e

~ lf" ~~~===~===~==:~=~ ,",,-~01IL

lOOI~ lO,

J Q

~

•ee

1

u

•

O

~

01

O

I { SYIII.

.. $PAN-

E

(

tMI--02) SPIIN- 063

• O." 123

~

O

Z

1'(111"-_ _ _ _ _ _ __

E

120

-

I I

~

•i

• •

•

•

O

1

I

40

,

•

I

.J

I

&0

OeP.... , _

c-t GuIwd CIIar '"

1

I O

1..... '

10

Il

14

ea .. 1r.1oft T_ L"'.

20

'11",1

22

24

l(,

le C[Q~II

(a)

Figure 7.93. &ithymetry survey off the Carudian eiJst coast using the Input system. (After Zollinger el al., 1987.) (a) Comparison of Input calculiJted depths iJnd coastiJl charts, offshore Nova Scotia.

. le

.

..

!

..

~

~

:

.. •.

~

~

..•..

• ..,. &.

U

•

..

.j

lO

X

,

u

i

t

.j

.j !

-..,N'" zll'lZ

•e .!E• '"

,~

..J ..J..J

E o

..

~

i

..

.

~

I

r·

I

•

• &. ~

o.

o'"

•

~

•

.~

'"t::

~

•

~

~ ::

::

~

o

...E

.1;;

:i:o

.

~

!

!

.E ......

'"

.~ ..J

..• oCl

.• .!:!'"

, ! • •. ~

:)

J

•

z'"

..'!. VI

'" E '"'"......
€.

~ <1.>

:::l

·s t::

8' ;;i

'" ~

:::l

...

.!!!l

....

480


o

200 ft

1..1.....,\,--1'

Disseminaled sulfides. densily 3.4S g/cm"

Figure 7.94. Vertical-loop f;lCed-transmitter profiles over Mobrun orebody. (Afte, Seigel, 1957.)

Ontario. 'lbe mineralization, consisting oC massive pyrite, chalcopyrite, and sphalerite, occurs in a como plex oC rhyolitic and dacitic racks in the form of Ienses striking, and probably plunging, northeast with nearly vertical dip. The lransmitter and recei.ver, separated by 400 ft, were moved along parallel lines crossing the stme axis; readings were taken every 25 fl. The strong croSSOver5 on lines 2E and 4E coincide with a sub· outcrop of one of these lenses. Strike length is indio cated by the small response on lines O and 6E. A second ore leos, about 100 fl, northeast, mainly rich in sphalerite, was not delected, probably because of poor conductivity. A single traverse on line 4E with a vertical·loop ftxed·transmitter unit is shown in Figure 7.9Sb. For reference the broadside prolHe is included. The dual·frequency ftxed traDSmitler (480, 1,800 Hz) was at station IS on line 2E. The similar response al both frequencies shows a highly conductive 7.one. The proftle asymmetry, which is surprisingly large, is probably due to the limited deptb extent of tbe lens, because it is mown to be approximately vertical. 3. The EMI6 (VLF) profiles shown in Figure 7.96a ar~ taken from a survey made on tbe Atlantic Nickel property near Sl. Stephen in southem New

Brunswick. The predominant geological feature in tbe area is a stock-Iilte ultrabasic intrusive in metamorphosed sediments. The sulfide mineraliution, consisting of pyrrhotite, chalcopyrite, and pentlandite, occurs close to contacts between tbe intrusive and the altered sediments. The VLF source was the transmitter at Cutler, Maine, located 110 km to the soutb. Huge dip angIes and steep crossovers on lines 160N and 162N are caused by a very good conductor, which outcrops on line 160N. On lines IS8N and IS6N the profiles indicate that the zone is either becoming wider or splilting in two, one leg continuing south, the other southwesl. On the northem lines the dip appears lo be steep and lo lhe west. A ditrerenl method of displaying VLF data is illustraled in Figure 7.96b. The profiles have becn converted to contours in such a way that proper crossovers are transCormed to positive peak readings, whereas reverse crossovers become negative values; in the pracess there is also a smootbing etrect tbat reduces the large geologic noise caused by tbe relatively high frequency of the transnútter (Cutler station operates al 24.0 kHz). The procedure for conversion is very simple. If '1' ... "4 are the dip angles obtained at stations

481

Field examples

.-.- ....... -. LOEL _ . - '

I

1

- IO'N ......

.......,

......... -

, - 10'5

,r ___ - IO'N

.- / \ I UE'''__~-~'--~______~'__~~~______~'__~~'______~

_ /'

I.

..-'

~

1I .

.u \

,.,.

/ .. "

.-.

- 10'5

/.{\1,\~,

- IO'N

~EL.-'__-_·-__·~l-_·_~ __ • __~'~~~\~':~\______~'__~~'______~

_.--.-.

,\

\\ JI

...... /

-

,'1

I

/ I

I

Conduclor IX'S

-IO'S

I

I

:.::: Orezone. 100 n level

,/

/ ,/

- 10'N

/ -1...-,-=. .,. - - - - 1 _·_-_-.··4,.y¡. .....,;-(-1--

L6E ... , __ '---O.,,,........-,.,;.'--_·_-_...L,

\' ~ ,>\, ( .-.-'

\ '

1.

I

,

35

25

15

•.1.

r"~ \ \,

o

IN

".",

- 10'S

,

,

2N

3N

(o)

Figure 7.95. fM survey. Uchi Lake. nor/hwes/ On/ario. (a) Dip-ang/e broadside pro(i/es. Frequency 1.000 Hz. / - 400 Ir. sta/ion in/erva/ 25 fr.

1, ... ,4, the contour value

Cz3

is

and is plotted midway belween stations 2 and 3. lbe sign of <;3 is positive in the vicinity of proper crossovers, negative lor slopes in the opposite direclion. lbe cootours in Figure 7.96b match the outline ol tbe ore zone very well. lbe smaller anomaly in the vicinity ol l09E, which is somewhat overshadowed on the profile display, is brought out more c\early in Ibis plol. Negative contours, which represent higher resistivity zones, have becn omitted here to c\arífy !he conductive areas. In resistivity mapping they would be inc\uded. 4. lbe VLF method has been used lor mapping shallow geologic structure, both on the ground and with the airbome version of the equipment. Contaets bctween beds of contrasting resistivity produce profiles that are quite different from the crOS50vers associated with the dipping-sheet conductor. lbis, ol

eourse, is due lO Ihe fact that the prolile over lhe contaet corresponds to only half that over the sheet (see Fig. 7.48). An EM16 survey, made over the Gloucester fault 50utheast of Ottawa, Ontarío, iIluslrales lhis type ol VLF response. Profiles and a Iypical geologic section are shown in Figure 7.97. The transmitter station was Cutler, Maine. This parl of lhe Ottawa valley regíon is a sedimentary area well suiled lo such a technique because ol the contrast belween lhe lowresistivity Carlsbad shales and the Nepean and March formations upthrust by Precambrian racks lo the west. The Gloucester fault is clearly displayed near the middle of Figure 7.978, with lhe steeper slope on the easl, over the low-resistivity beds. A seeond anomaly, parallel lo the Gloucesler fault and about 2,000 tt easl of it, from 21 + OOS to 65 + SOS, indicates a contaet with higher resistivity to lbe easl. Still furIher easl, from 32 + OOS lO 60 + SOS, there appears 10 be a lhird leature, whieh has higher resislivily on Ihe west. At 32 + OOS it is aboul 1,300 ft east ol lhe


482 B.l.

/

-'

B.rri ....r LE M, VLEM bro.dside, sopar.,ian 400 rt 1000 H.

/1.

\

//

.

~----~~--L---+4-----L--~~--UE

Clone VEM VLEM, fi.cd-lr.ns'r Trans'r .,2E. IS

~---~-_L--I--'d-----L..---""""-L4E

o SE

0------·.,

11r

NW

----- .. -........

lt

Massive sulfides

1\ -...t ! '.

,~,

.

'''', .. \ '

-200

\

~

• t I t

.1 II

(b)

•

o I

100 I

,

lOOrt

Figure 7.95. (Continued) (b) VLEM pro files iJnd ore section.

second conlact but, because of a more norther1y strike, thc separanon is 800 ft at 60 + SOS, producing a crossover type of response 00 that line, 5. Figure 7.98a shOW5 a pair ol AFMAG profiles over the Mattagami Lalte sulfide deposit al Watson LaIte, about 90 miles oorth of Amos, Quebec. The ore zone, shown in rough outlioe, cantains spbalenle, cbalcopyrite, and pyñle. and is associated with basic rocb that have intruded the regional volC8DÍcs and sedimeDts, A vertical secUOD througb line 4 + ooW is displayed in Figure 7.98b. Vedors drawn 00 the AFMAG profile give the azimuth direction of the fteld al various points ol the traverse.

Both the bigh- and Iow-lrequency anomalies are larger 00 line 1 + OOE than 00 4 + OOW, because tbe zooe pIuoges lo the west; tbe depth of caver is about 35 fl 00 tbe east line and at leasl 300 ft on 4 + OOW. The SIO Hz response is greatly affected by the iocreased depth at 4 + ooW. It is difflcu1l to gel much quantitative inforroalion concerning the ore zone from these profiles. Their general shape indicates dip to the south, a widening of the zone to the west, and a depth greater than the actual depth, particu1arly on line 1 + ooE. 6, Three HLEM profiles, from a property near Woburn, Quebec, are sbown in Figure 7.99. The

Field examples

483

(al

· . -.. ·-~ . ."'~;/". "t, ,, 4

I6<4N-

.\-

- N -

/62-

160-

-11-:1-11'

- Ih -

-lO·:1I

~n

• •

-~ ..

• • •

-

/11-

, ~

· . ." ~'"

."

156-

'J.

IS4-

-.~• -,-• -'•C':•-

1!2-

...

,

I

-

• •"1 -u•

1" ~ \11 - 1"

5ON-

. =.. -

I I /g5t/ ____-!I"'IO"'-E _ _ _ _ _-'-""'lE:;..,_-J

'--'-'-=-_ _ _ _ _-=-"-_ ____ 9SE /OOE

O

100 200

~

r,

A

Orrl('tnf'

!

Hud (nmr

....... - GrolOI,cal C('In'ael

( b)

Figure 7.96, Resu//s 01 VLf surve}'. Atlan/ic Nick,e/ propert}'. sourhern New Brunswick. Transmitler sta/ion: Cut/ero Maine (UO k Hz). (a) VLf profiles. (b) VLF contours.

mineralization consists oC severa! dipping sulfide lenses located in a shear zone near a contact between yolcanics and sediments. The sulfide content ranges Crom massive to disseminated, with considerable mineralization between the main zones. Qualitatively, all tbree profiles indica te a single sheet·like conductor oC shallow depth dipping west. In addition, it is probably a metallic conductor, because Ihe ratio or peak in-phase to peak quadrature is about 4 in each case. Quantitatively, we can use Ihe peak values with the characteristic curves or

Figure 7.44b, assuming Ihe dip lo be about 60°, to calculate sorne numerical resuIts. For a transmitterreceiver separation of I - 200 ft and frequency 1800 Hz, we find the data given in Table 7.4. Obviously more infonnation can be obtained from this type oí EM survey than any discussed so faro Although the 60° dip angle is only an estimate, it is c1ear that there is dip to the west and the resulls would not be much different if we had assumed 90 or 45°, since HLEM is not particularly sensitive lo dip. On the other hand, Ihere is no indication 01 the


484

. <+' ~

Line 50

o

'fS

1500

n

Horizontal seale ~ O 60~ Vertical _le~

+ OOS .~_ _~._ _ _~.:--_ _+-t___+.(,---:I..:.OOO:..:....:.n;"--b 1 _ _ _~If=-OE

10

20

JO

40

50

60E

Elevatlon (n)

~Carlsbad _:I~.- SIl. uncly SIl

~8 Eutview ~LI

~ SIl. Ss. La. 001

~Ls.001

~

Billinp

~~Iawa

~ Rocklill'e ~Sh

lITIprJI March Illlilllll SI. DoI

Nepean

r-;-l Pree&mbrian L.:...J 001. Ls. Gn. Qz

~Sh

s.

~StMartln

~OKrOrd

(b) Figure 7. 97. VU survey across the G/oucester Fault. eastern OnWio. (a) P/ot of the field data. (b) Geologica/ section. fine 50 + 005.

disseminated sections, except perhaps on line 4OS. A smaller separation (1- 100 ft) migbt possibly have detected these zones. 7. The Murray sulfide deposit, in Restigouche County, northem New Bnmswick, provides a good example of the Turam EM technique. This body, massive pyrite with sphalerite, galena, and chalcopyrite, occurs as a replacement in a chlorite schist along the axis ol a reverse drag fold in Ordovician sediments. Considerable leaching and weathering ol the near-surlace mineralization has produced a heavy gossan cover, varying in thickness from 50 to 200 ft,

which masks detection ol the main body by EM methods. Turam field-strength ratios, shown in con tour lorm in Figure 7.100a, correlate we)) with the outline oC tbe sulfide body at 200 tt depth. The phase-shift contours are said to be similar. This is only a small part of tbe wbole Turam survey. whicb covered an area about li miles E-W by! mile N-S: extensive rones ol graphitic schists also produced strong anomalies north and east of the sulñde body. Figures 7.100b, e show a profile across the sulñde area on line 136E, as well as a shorter one on line

485

Field examples - - ISO Hz - .-. 510 Hz ..., _ Appro •. oulline or orebody no. 1 j...--1í~_ _'"

'!l'.

Oip anll.

o

300 f1

I

I

(a)

Figure 7.98. AFMAC survey. Mattagami Lake Mines, Quebec. (From Paterson. 1966.) (a) Profiles along lines 4Wand 1E. (b) Cross sec/ion. fine 4W.

Une 365

2E

e

....' ¡.

=_;n.7J,I.¡¡ 1;

!

--'

u

I

i

1

u _ In.phase

1:;1

• - - QuadrllUre

.....--

?

Line 385

2E I

8E

14E

4_.=Z_~Z4 ~_:b

,1 •

Massive sulfldes

l1iij Disseminated sulfldes (J O',erburdcn

~ Line 40S 2E I

14E I

Figure 7.99. Horizontal-loop fM profiles. Woburn. Quebec.

486

flectromagnet;c methods Table 7.4. Re (max) 1m (max) Unes

(%)

36S 385 40S

z

(%)

-7 -11

-28 -38 -40

-9

al

Deplh 1'0"'011 (fl)

(S)

0.271 0.171 0.161

10 8.5 10

55 33 30

38 33 38

(a)

IOOfI 1

HO Une IlOE 1·10

1-0

(b)

Turam660 Hz

1·40

\

\

FR

,

\

O-tO

-40

\,

Une 1lOE

, \, \

R I

"~

,l'

.. --.__

I

140

-" ... _-100

O

~

100

I~m

ReaI.1Id im.JiIlUJ componenll

60

(R/I) ..... - H

1- 00

." ... 10

20

Figure 7.100. Turam survey over the Murray sulfide deposit, northern New Brunswic/r.. (Alter Fleming, 1961.) (a) Field-strength contours. (b) Craphite response.

Field examples

487 ..

FR

1·80

-

FR660 ti. Id rallo. 660 Hz

- - _. MO 1""'" ditfcrcnce. 660 Hz 1'60

20'

O- -
Lín. 1J6E

_. -

l.;llmp .. 220 Hz

comp .. 660 Hz

I

I :

Hz.

Im.~

_. - ' '660

1·20

re.,! comp .. 660

o- - -o 1220 inm~ 1·40 I

10'

R6M1

I

"' "

, "

' .....

-....~60

'- ........ I -40

0·80

-20'

20

,,,

"

"

.

............1 ...

• Massive sulfides + CuFeSz !! Massive sulfides

Sulfide

lOO I

400 ti ,

(e) Figure 7.100. (Conlinued) (e) 5ulfide response and interpreled seclion.

1SOE over the main grapru te zone - which is con tinuous for at least 1~ miles NW-SE. Both components in tbe first profile indicate a sballow dip to tbe north (see Fig. 7.38) whereas the grapbite; zone appears to have a mucb steeper dip in the same direction. In both examples the response is strong. On Une 136E tbere is, in addition, a minor anomaly 230 ft south of the main peak., wbich corresponds to the isolated 120 contour in Figure 7.100a. Apparently tbis is caused by the undulation in the top surface of the sulfides. Although the sulfide deposit is massive and appears homogeneous throughout the body, wruch is about 300 ft thick at 136E, the Turam anomaly

resembles that of a thin conductor. Possibly tbis is explained by the core logs of drill boles R3 and R20, which show a high concentration of cbalcopyrite in the first 15 ft of massive sulfides. The main bulk of the míneralization below tbis, mostly pyrite, appears to contribute little to tbe response. Massive pyrite is known to occur at times in a silicate matrix tbat isolates the sulfide particles from one anotber, reducing the conductivity greatly. Whetber such a situation exists here is not known. A very rough estimate oC the depth of these conductors (the estimated value is invariably larger than the actual depth to the top) can be obtained


488

LlIIII Z .00.

I

------+-------~-----

OOSSM ZOfIIE

10

4 ••

s--

,.,.. 10

t-----•.

•

• (a)

Figvre 7.101. Resvlts of PEM base-metal svrvey in Su/tanate of Oman using moving-eoi/ method and interpretation using a model plate. [Parts (a) and (b): After Crone. 1979: pilrts (e) and (d): After Barlel and Hohmann, 7985.] (a) Profile over Ghaylh showing: 50 m eoil spaeing.

lrom fue width ol the profile anomalies at hall maximum. For tbe larger sulfide response we get 85 and 115 lt lrom the field-ratio and phase curves, respectively, for the smaller peak about 140 ft. Because the actual depths are about 40 and 75 ft, a better result is obtained by usiog tbe hall widtb rather than tbe fun width. However, there is probably a widening of botb parts oC the profile because the anomalies are elose togetber. In tbe case of tbe grapbite zone the deptb estimate is about 150 ft. Real and imaginary components, derived from the Turam field curves, are also displayed in Figures

7.l00b, c for both zones. It is difficult to calculate tbe dcpth ol tbe sulfide from tbese curves because they do not bave well-defined minima, but for tbe grapbite zone tbe estimates are about 125 and 90 ft from tbe real and imaginary components, respectively. 111e al values are 65 S for tbe sulfide and 10 S lor the grapbite. 8. Several field examples of time-domain ground equipment follow. A large base-metal exploration program in tbe Sultanate ol Oman was initiated in 1973, ineludíng airbome magnetics, Input, and ground followup with tbe Crone PEM system, usiog

Field examples

489

200 100

.' .• o

10

100

~

40

30 20

..[TEIIS

10

COIL!

o

CI't ' 140'

·10 -lO

·30 ·40 • !lO

2

·100

J

• 5

• • 7

IS

IL

I

I

IN

I

MASSIVE PVRRHOTlTE ANO CHALCOPVRITE'

(b) Figure 7.101. (Continued) (b) Profi/e over Maydan deposit; eoil spacing 100 m.

the moving-coil method (Crone, 1979). In such arid areas, conductive surficial material produces background noise on all TD channe1s and the metallic anomaly may be further reduced by weathering to considerable depth. A saving feature of tbis weatherjng at depth is that it may produce for wide (> 10 m) conductors an oxidized sheath surrounding a thlnner core 01 bigh conductivity. 1bis pracess has occurred at the Maydan deposit, located in mountainous terrain, where the original 40 m wide massive sulfide body is weathered to a depth

01 10 m; as a result all eight channels in Figure 7.l01b are active. On tbe otber hand, in Figure 7.101a, wbicb displays the Ghayth showing, only channe1 1 is active because the zone was originally less than 3 m wide. The Maydan deposit bas becn modeled by Bartel and Hobmann (1985), using their standard 600 X 600 m pi ate. From the nomogram 01 Figure 7.67a they obtained estimate of TCP between 30 and 80 S and a steep north dip, deduced from the slight asymmctry oC the side 10bes plus geological and drilling infor-


490

,]

::l

,

(ppkl

I

(ppk)

1

lo'

o

o

10

i,

2

2

~

o ( e)

50

100

4

4

5

5

6

•

7

7

•

• -150

150

distanee

(m I

-lOO

-50

o

100

150

(d)

Fisure 7.101. (Continued) (e) Field datd over Mdyddn deposit; eoil SpdcinS 100 m. (d) Best-fit plate response to profile in (e); (- d - 600 m, Z - 20 m, dip - 80°, TCP

- 60S.

mation. Field profiles were then matched by PLATE program modeling to produce the best-fit curves; see Figure 7.l01c, d. 9, EM37 field results from the vicinity 01 the well-known Broken HiII ore deposit in New South Wales, Australia, arc displayed in Figures 7.102 to 7,104. This is the White Leads Ag-Pb-Zn prospect (Smith, 1985). Gravity, magoetics, ¡P, and mise-h-Ia masse surveys were carried out, as we)) as TDEM. Only the time-dornain rnethod was a success, after several attempts, when the double-dipole array spacing was reduced to 50 m. The pseudodepth plots and drill sections are shown in Figure 7.102a, where it is clear that the weathered zone oC about 20 m is more conductive than the arca containing massive sulfides. A plan oC the survey arca with two locations 01 the EM37 Tx loop and grid Iines is seen in Figure 7.102b. It also locates an earlier shalt and mapped "Iode horizon." The successful IP survey line (lOOS) is seen to cross sulfides, which dip about 7S o WNW. The first EM37 survey was perlormed with the Tx loop in position 1, lying over the lode horizon with its SE comer directly aboYe the sulfide zones. The resulting profiles, also on line lOOS (Fig. 7.102a), arc

barren lor both H, and Hx in Figure 7.103. When the loop was relocated in position 3 roughly parallel and adjacent to the favorable horizon, there is a weak response over tbe sulfldes and additional anomalies lurther west, as seen in Figure 7.104. Failure of the EM37 to detect the sulfide mineralization is doubtless caused by two lactors, the first being poor geometry ol the field layout. Second and more critical is the positive resistivity contrast between the sulfide zone and its surroundings, as is obvious in Figure 7.102a. 10. An early test 01 the UTEM system was made in 1977 at the Izok Lake base-metal deposit some 400 km north 01 Yellowknife NWT in northem Canada. This is a 12 X 106 tonne high grade massive Zn-Cu-Pb-Ag sulflde body that was used almost as a test area lor geophysical methods; EM was particularly suitable because 01 tbe lack 01 surlace cover and generally high resistivity. In this respect it is a complete contrast to the previous example. Figure 7.l0Sa shows tbe UTEM field layout and interpreted results in plan; a single proflle lor H, from line 12E in Figure 7.105b sharply marks the conductive section. Conductance and depth 01 this

491

Field examples

NORTH-WEST

SOUTH-UST Wlllle leedl lile" 1 130m Norlll) 160'" I

'''''' I

I

lOO'" I

lO"

Oal(OO)

• ~.

._a___ .

_1O~,______ ,o~f~¡~i

...,.

___~_~~I_'__~~__~~~

~~·.f

App.r.nt R.llltlYlt,

11:1

H·

••J.

~

(ohm-m)

lI:a

11:3 11:4

".

11:1

¡l.

11:1

_._.1-._

.i

_ _ _ ' " -_ _ - . i _ _ __ - ' - __

I

t

-'-. _ _ _ L-.

~t1

,., NI

r

¡-,

NI

NI

1.1

I¡o/

LOOP 3 --"",_

W.elll.,.d Zo".

-------------

so

100

i

..

":r IJO

S"

.-

•3 100

110

Figure 7.102. Resis/ivi/y ilnd IP resul/s plus drill sec/ion, line 100 S. White Leads prospect, Broken Hill, New Sou/h Willes. (AfIe' Smi/h, 1985.) (a) IP and resislivi/y pseudodep/h plols (dipole-dipole array, 50 m dipoles) wi/h drill sec/ion.

r

!t

492


TIANSMITTU lOOP

o,

eh)

Figure 7.102. (Continued) (b) Plan showing lode horizon, geophysical grid, and drill hole locations.

anomaly were interpreted as 500 S at about 300 ft (90 m).

Note: Fjeld examples for EMP and SIROTEM systems are DOt included here. The first is similar to EM37, tbe second is discussed in Section 7.7.4d, Figures 7.58 and 7.60. 11. Paterson (1967) has provided several good examples 01 tbe quadrature AEM system from surveys over the Canadian Shield. Typical profiles together with ground followup by varíous methods are illustrated in Figure 7.106. Figure 7.106a provides an estímate 01 the TCP from the airbome peak response ratio P in each example; jt is quite large: 4.5 S in Figure 7.106b, 2.6 S in (e), and 3.7 S in (d), suggesting good conduetors in all cases. In Figure 7.l06b tbe massive pyrite body is dceply buried, indieated by small quadrature response and 100 It (30 m) of overburden on tbe drill section. Tbe TCP is about 40 S. 80th ground magnetie and gravjty profiles appear to reftect the very massive pyrite. This is surprising in tbe case of the magnetie anomaly because pyrite is onIy weakIy magnetie, and tbe seetion 01 20!' magnetite al tbe bottom of tbe hole has DO apparcnt magnetie signature. Tbe vertical· loop profile is typical of a conductor with shallow dip to tbe left. This is also peculiar in view of tbe drill hole indination, which would not normally be downdip.

Tbe HLEM profile in Figure 7.106e, apparently plotted upside down from tbe usual orientation, sug· gests a dip to the left as well, altbough stecpcr tban in Figure 7.106b - whieh is reasonable. Ratio of realto-imaginary peales is only 1.5, indieating a poor conductor. Consulting tbe characteristic curves 01 Figure 7.44, we find the dcpth to be about 25 lt (7.5 m), with tbe TCP value 30 S, which agrees roughly with the airbome estimate of 20 S from Figure 7.106a. However, the validity of using tbe curves oC Figure 7.44 is questionable because the graphite zone appears to be at least 200 ft (60 m) wide. Correlation between airbome and ground data in Figure 7.l06d over shallow low-grade sulfides is again ratber poor. Tbe VLEM profile suggests a broad conductor (400 ft or 120 m), possibly witb shallow dip to tbe right. This is not in agreemcnt witb the gravity anomaly. Tbe magnetic profile seems to mark tbe sulfides located by drilling, although tbe huge negative peak on tbe right is not explained. Quadra. ture peak tatios here give TCP • 35 S. 12. Tbe Whistle Mine, located on the northeast rim of the Sudbury basin, nortbeastem Ontarío, js a favorite test site lor airbome e1ectromagnetie equipment. Tbe massive stecply dipping sulfides, mainly pyrrbotite, are botb conductive and magnetic. Figure 7.107 sbows an assortment of protiles from several

Field examples

493

•

projected sulfide positlon

~

I I ! I 8•• II~I~I~~lli*~~ 1. Y . . . . . · . . • I

:/i

r t'-,. " 1M

I

[,

.

~~~~~~~~~I~~~~~~~~I

,..

!J

il~

__

11·11

•

J /./

'"'

E$;

- - : : . ....... .u. / ....... -. ./ __

"-./

v·

I

I

:

1

I

l· . . . . ,

••

-,-----

/M~-:

..

_,12

JlI

..

•

¡

," ¡•

ez-ar:-u-ii--¡-¡--,-,,-.-r¡;JI~¡ ·rr:: I z ~

' ..¿

I l-1II

/'."", -

~I I I

I

I

--J.

-r

/ I ~1 ~. - / ~_/--- --~----~L-------------~ ~ )er Jl

--...

--~--.;. -

__

--

---;;.

,1

.J. a..

O~

-1M

¡"-¡-¡

__-

...

¡:; 1

¡rt:~

'---_--;=~--JI lJUIP

____~__~2~'_O________~'~~om (a)

Figure 7.103. EM37 profiles. line 1005, White Leads prospecto Broken HiII, New 50uth Wales. (After Smith, 1985.) (a) Vertical components.

airbome EM systems over this property. The upper tbree profiles in (a) inelude an airbome VLF (MePhar KEM), two-frequency quadrature (MePhar F400), and aeromagnetics, for a single traverse. Tbe next two io (b) show airbome AFMAG and a secood airbome EM response, from a quadrature system, on the same tligbt lineo The last set of three profiles in (e) is for a phase-eomponent helicopter system

(Aero-Newmont) with aeromagneties on the same line. The relative locations of tbese three traverses are not known. In Figure 7.107a the ratio of peak low-frequency (340 Hz) to peak high-frequency (1,070 Hz) response is about 0·78, giving a al prodUCl of 4 from Figure 7.106d. This is a moderately good conductor, lbe distinct erossover and field strength peak from the

494


projected sulfide position

I I

~

I I I I

'~ ••

IIII.II~I~~III~

..

I

I~

. .

I I

1'-

I

I

I~ I

...

•

I I I I I

¡::--\-

I

I I I I I

rs' I

t···

-s.

"••..a .,. •. •

-I.. 1

-•• 'O

¡:

\1-11

O

•Zc:

-SIl

¡:'. -21

~I

o

210

100 m

----~--~~--~--~' (h)

Fi8ure 7.103. (Continued) (b) Horizontal component.

VLF trace correlates precisely witb tbe quadrature

peaks and indicates tbat tbe conductor is very shallow. Tberc is in addition a large negative magnetic response to tbc soutb, whose nortb ftank corresponds exactly to tbe 'electrical anomaly. The AFMAG response in Figure 7.10Th shows a strong crossovcr witb stccp slope on botb frequcncíes. Prom tbese traces we may infer tbat tbe con-

ductor is near surface and has high conductivity, bccause tbe ratio of peak responses (+l50/~lO) ...... is approximately unity. The phase component system in Figure 7.107c produces a very strong in-phase peak of nearly 1,000 ppm. This is part1y due to me high conductivity and shallow deptb of me conductor, partly to tbe relatively low altitude which can be maintained by tbe

-c:

(.w 111U,

•

--

.~

;;

o

.'!

•

•

•

-

o

•

CP 'C

_1

_1

'C CP

Jl/.LI

U CII

lIIELl

In

'0 ... Q

--

€.. ..:

c:

'"c:

~

"

;;::

'3

o

:t:

J,

_1

Q

.~

• .;• '•" ~

8

--

-co

_1

!

&51

~

---~

.::!.

-

I

_1

~

~

E

'"~...

-

)151

.;:

_1

~

•::

!

~ ~

o

-S

::l

~ :t

~

--'i c:

<11

.oc

(.w I

--

c:

o

iñ

;;::

'3 In

-

'O GI ~.

.!!!.

..

o

,

•

..

~,

"U,

CI)

~

•

•

•.¡ • •~,

'" ,

_1

oQ

CP 'C

W.

•

--

_1

--

e '" ~

-

~

_J ,

~ ....'" .~

~

11

_1

--

Jl/.LI

~

lIIELl _1

E

lI!29l

N

'"

N ¡::¡

.~

5t ~

..S!

<.::

Q

e Q.

".....

&51

~

IiSI

.:!

l&I.tl

!

!I Jo

~

~-e -",

o

"c: ~8. !)

E

.2.0 e lO. \.¡

flectrom.gnetic methods

496 24[·

(o)

...

" ,

... ...

,

IZOK LAKE

- .. ,/ \

,•,

. ...

UTEM WtEf'f'IRETAT1ON

(h)

I

1001

O

,

-fIOO'

U T E M AREA IZO.LA.E LOOP IMCI LIME DCa: PLOT

i

i

i

I

Hr

I

FiBure 7.105. UTEM test oller Izolc Lalce deposit, North West Territories, Canada. (After Podo/slcy and Slanlcis, 1979.) (a) Map 01 interpreted mineralization. (b) Profile alon8

Une 12E.

,.

.:j

~p

O·

¡O"N

VUN

I

/'.

--.-.]

"

•"-

/

.......

~-=J~

1-6 mOa!

1·2

.,.. 0-4

~O

Owrburdcn

O-U 0-1

I

I

, < e .I .I•11 • '" •..••

, , I II I I

(41)

._....

I , I I 11 I .. ...

,_

.......

lron rom.üoa (20:Y. ......)

200 n

(b)

Figure 7.106. Comparison 01 airborne qwdrature EM and several ground methods over various conductt){S. (After Paterson, 1967.) (a) Curve of TCP versus P, the airborne peak, response ratio over vertical· sheet model; P - (400 Hz peak)/(2.](X) Hz peak). (b) Comparison with several methods over deep sulfieJes.

1° '-

Airbctne EM

E!:

2JOO Hz

0-6·

~

10

t.

~~

lO"S

/"\

~~·--~·~'-~~~~----~----1r0. -·/VLEM \ . "--." " \ //", lO"N

2000ft

l/

In-plwe

-30%

"LEM 2IJO.f\ spacina

Dip

f

400 N

MaplClics

-20

~ "' :... <'=, ".-

>

I

J

.-

\ -c:

-10

, "":-',.,....=;zc

o +10 +20%

=Q.vc.!!>u~n cOR,lomeralc

Sudacc

G~~~I

bloe" shale

(c)

Quartzitc

Sud..,.,

200ft

~

'5-10% sullides

Ovcrbwdcn;~\ ScdiJJlCl1Is

, /'W

_ > 10 % sullides ." '" Clcavqe

/!

200ft

(4)

Figure 7.106. (Continued) (e) Comparison with HLEM over shallow graphite dep05it. (d) Comparison with several methods over shallow sulfides.

Field examples

499 KEM fi.ld st,ength

:><::

/S Ss;? ;;;;;¿

KEM tilt angle ...... ,:os;;

'---Ss;;;:

2

?Ss

Ai'bo,ne VlF ?

...,25'"<

'
s

z;z;¿: ,.-

'S=2Z

MOlnetic coarse selle

Quad,ature

F·400 EM

1070 Hz 1

ID)

0·20 AFMAG

0·20

QUld,alure

E-:M==:!I!::~~:::"' _ _":::::==:=' [0.08

~

mile

{I>I

Figure 7.107. Comparison o( various airborne fM systems and aeromasnetics, Whistle Mine, Sudbury, Ontario. (a) Comparison oi VLF, quadrature fM, and aeromagnetics. (b) AFMAC and quadrature EM on the same /ine as (a). (From Ward, 1959b.)

..

helicopter. Using characteristic curves of the type shown in Figure 7.81c, the depth below the aircraft was lound to be 115 lt (35 m) and the af product 140 S. As in Figure 7.t07a. a large magnetic anomaly occurs with the EM anomaly. 13. Four examples from Input field surveys are illustrated in Figure 7.108. The first is taken from the

Manitoba Nickel Belt, northeast of Lake Winnipeg. This is an excellent test area lor AEM because the electrical conductors, occurring in Precambrian rocks, are quite deeply buried beneath Paleozoic sandstone and dolomite, which are in turo generally covered with unconsolidated overburden. Sulfide zones, with and witbout nickel, occur in ultrabasics

500

flectromasnetic methods >\I43ppm 1 Ll 1 I

1

+--T-+--+-II- t- r- . \- .

+-'<-+-+--1-++ -\

f-jiL....f-I",_f-,-J.+-+

I-Óul~pha~

+- \ \

\

1

III~ I ~ \ 11

_~

\.

componenl

1

. f-- ...... t-

'-l--

\ _..

\-\_1

. L

1"1''¡ -r--

AirborJIC puse

"1 296 ~m -1- - .. _-

/ ¡,'

\

- ++--1-+\--++

+- f- _¡. .•

I

\

.

I

Ir.'-f"/--/~~~~=t~=;

\

...

1'"

ll\l\ . \1 'VIl \ \ \

\

\

(e)

FiBure 7.107. (Contlnued) (e) Phase-component EM and aeromagnetie5. (From Ward. 1966.)

- r:.; : ehanllels I 2 -' : :"" 3 .... - - .... ,- - 4 r-- - - - 5 - - :- - .- 6 1:, : r"_-

.~

~:

~.... ¡.;;; f-: 1-" :"Ii 1....

~:::

DDH

Precambrian

(o) Figure 7.108. Input response over various eonduetors. (a) Manitoba Nieke/ Be/t, anomaly depth 115 m.

501

Field examples

....Icopt. MI< VI INPUT'

,

.. .,

" .

...

..

Ir

--I.!..",If------I¡

...

I ~ ••ctIon.

ANALOG PROFI.E

-<:;; I

~_.I

Sir., length -100m Depth Elet,",

- 400m

Depth

- SSm

Conductanc,

- 40'

110 1lOIII

.. • .. ·H .'1·.. •

'l'

Ita.

•, 55m

-

-

o

~ ·1

"-

•

I

tt

ti

l•

CONFUTER MODEl.LNJ

!:!I!!!! W~l Overburcleft

1I1S'

t::,,;:) cú:..._

50 100

Se.Ie-m,Ir,.

'l !tEtii

GEOLOGICAL

ptIrIIt.

_

Garnet phylllt.

O

8erlc:HI1I8I'tI ptIyM.

_

....IIve ......

l!m1 LIme'tone O

811c_ aerlc:He-IIIotIIecllloflt. ptIyM'

SECTION

(b) Figure 7.108. (Continued) (b) Goldstream sulfide body (Cu, Zn, Ag). In lower half of tap set af prafiles, salid line is eleva/ion, dotted line is aeromagnetics.


502 HorIzontal Axla

AeceIv8r CoII

Flxed Wlng MK VI INPUT-

-·ANALOG PROFLES

Fnght dlrectlon •

----

r--------,Strlke Length

' BOOm

Depth Extent

'.30Om

Oepth

,

10m

Concluctlnce

,

131

300 ppm

500m

,. North

I

I

Sec•.

South

South

...

.oCOMPUTEA ~ L-"

North

I!:J BI.llt. Il;.::.illntermedll.e tufl •

Cherl

a Mlnet'lIIzld tufl

O ChIorlll .uff. o

25

50 I

Scale-metrea

.,~ OEOLOOICAL SECTION

U@ F.I,lc "IIIIIIentl'., Tuffl

( e)

Figure 7.108. (Continued) (e) Detour Lake gold deposito

Field examples

503 Ch.

e 5 4 3

2

HeHcopter

1

MI(

VI INPUT e

._. 00 _125 ppm - ' ..• 120m ". ·150

•

10

.""lme'e,

n'

ANALOG PROFLE Strlk, L,ng'h Deplh Exl,"' Oeplh Conduclanct

- " -lO

Nonh-...I

t~:··

l

. t· ,. ,. " cMrreR lO

• 100m • 400m • Om • 50.

MODEU.ING

South-w ••1 ~

Met'n

1.00

...

Or. Zone

I!!!!I =,~ I'l!! ...- " -

Foolw..

•

Hangtngwd

:'::'"" -

o

lO lOO Ic_ _ n

GEOLOGICAL seCTlON .t

"Figure 7.108. (Continued) (d) Windy Craggy sulfide body (Cu).

and gneisses, and frequently exlend for kilomelers. There is also considerable grapbite witb tbe sulfides. lbe mineralization appears to be associated wilb a very large fault structure and is located in a bighly resistive host rock. Although the analog record is comparatively quiet in Figure 7.108a, there are discernible responses on all six channels from a targel - 380 ft (ll5 m) below surfaee, or - 800 rt (240 m)

-

.

below the Input reeeiver. This survey was performed with tbe fixed·wing Input system; the nexl Ibree examples were obtained with the helicopter version in wbich the boom is much closer to the Tx coil strung around the helieopter. Figures 7.108b, e display reverse protiles. on the same flight line, over two targets Ihat may be modo eled by tbin plates of gentle (b) and steep (e) dip.


504

Table 7.5.

5tation 42W 41 40 39 38 37 36 35 34

Une O 4>(2,400) 4>(600) (deg) (deg) -28 -35 -35 -30 -2 20 25 27 15

-22 -26 -30 -25 -2 15 20 18 10

.,,(e)

(deg)

5tation

-28 -36 -35 -30 -2 lS 25 27 20

43W 42 41

Reverse ftight profiles are an aid in interpreting dip, as is evident Crom matching oC the two views oC eacb model (see aIso §7.7.12d and Figure 7.S9). Figure 1.108b is the stratiform Goldstream sulfide body, north oC Revelstoke, Britisb Columbia. lt is contained in a thin layer dipping - 15 0 , sandwiched between metasedimentary beds at a depth oC - 50 m. Ore reserves are estimated at 3.2 X 106 tonne oC 4.5% Cu, 3.1 % Zn, and 12 g/tonne Ag. Response is strong on a1I channels. This example and the two following have becn computer-modeled using the PLATE program and the resultant profiles bere fit the analog data very well. (Model depth extenl, given as 400 m, is essentially the plale width.) Tbere is correlation with a SO nT magnetic anomaly displaced 200 m from the Input peaks, although neither the host rock nor the mineralization appear to oll'er significant magnetic contrasto Figure 1.108c displays data from the Detour Lake gold deposit. This target is of large extent and close to surface. It is readily modeled by a balf-plane dipping SO°. Tbe main gold concentration is in cherty tull'. which also contains sulfides (10 to 1S% pyrrhotite-pyrite, up lo 1% chalcopyrite). Tbese produce both the EM and magnetic anomalies; the lalter are much stronger than at Goldstream, as is evident from the scale change (l/lOO). Additional gold ia found in the adjacent basalta and talccarbonate rocks. Established gold reserves here are 30 X 106 tonne. although the grade is rather low. Magnetic correlation with the DÚneralization is excellent. In Figure 1.108d a buge, steeply dipping tabular pyrrhotite, pyrite, and chalcopyrite massive sulfide, which ell'ectively outcrops, has produced a strong Input response on all channels. 011' scale on the first two. This enormous deposit is estimated to contain 300 X 106 tonne 01 1.5% CUt with O.OS% Co. Again there is good correlation between EM and m&gnetics from the pyrrhotite. Extreme variations in altitude (60 m oYer - 200 m horizontal) are seen in the

40

39 38

37

Une 25 .,,(2,400) .,,(600) (deg) (deg) -15 -22 -24 -12 13 20 18

-13 -15

-20 -10 12 17 16

.,,(e)

(deg)

-13 -15 -20 -10 12 18 17

ftight profile. Tbese are the result 01 ground slope and atmospheric disturbance (the site is called Windy Craggy). Note that the comparatively rare vertical-axis receiver coil was used in this survey. Tbe change was made to reduce variations in the mínimum T-R coupling, which are greatly increased when the Rx coil is carried in the boom rather than the remote bird. The problem arises in obtaining continuous normalization of secondary field in terms oC primary (§7.7.4b, e). This ratio is highly sensitive to small changes from DÚnimum-coupling position. compared to using approximate coplanar geometry. Thus signal stability was mucb improved. Tbe profile shapes in Figure 7.l0Sd are quite dill'erent from usual Input response and may be compared to coincident-loop curves in Figure 7.SSb. Note: Tbere are numerous other AEM field examples not discussed bere. These inelude Turair. Figure 7.77; structural mapping. Figures 7.80a and 7.91; resistivity mapping, Figures 7.7S, 7.79. and 7.92; bedrock conductor location and resistivity mapping, Figure 7.8Sj bathymetry, Figure 7.93.

7.9. PROBLEMS 1. The VLEM readings in Table 7.S were obtained during a fixed-transmitter ground survey in northeast Brazil. Stations are SO m apart, the lines are 400 m ap8rt; the transmitter was located on line lS, midway between stations 38 and 39. +(2,400), +(600), and +(c) are dip angles measured. respectively, at 2,400 Hz, 600 Hz, and both frequencies simultaneously. Plot the profiles. Estimate the depth, clip, possible strike Iength. and location of this anomaly, as well as its TCP. Do you see any advantages in the dip-angle measurement at two distinct frequencíes? At two simultaneous frequencies?

Problems

505

2. Tbe data in Table 7.6 are taken from a verticalloop tixed-transmitter survey carried out in northern Quebec. Tbe transmitter was located at 7 + OOS on line 4W. Station spacing was 100 ft and the two lines are 800 ft apart. Transmitter frequency was 1,000 Hz. Make an interpretation, similar to that in problem 1, oC these results with the aid 01 the following additional information. " ... Geological mapping in the vicinity 01 the conductor shows that it lies in a band 01 ampbilobite intruded by gabbro sills··· tbis band, about 2,400 Ct wide, is bounded north and south by andesitic volcanic rocks ... outcrops of granite were located 2,600 Ct NW of the west end of the conducting zone ... Tbe axis oC the anomaly is parallel to the strike oC surrounding rocks ... Within the band a weak dissemination of chalcopyrite and pyrite has been observed in one outcrop." 3. Dip angles obtained with broadside VLEM equipment are given in Table 7.7. Four Crequencies (600, 1,000, 2,400, and 5,000 Hz) were used in this survey. Tbe receiver and transmitter were moved a10ng parallel picket lines maintaining a t1xed spacing of 400 Ct and readings were taken every lOO fl. Plot the protiles, preferably on two sheets by combining the 600 to 2,400 Hz and the 1,000 to 5,000 Hz dip angles, because these are the dual

Table 7.6. Une 8W

Line 0+ 00 Dip 5tation (deg)

Dip

5tation

(deg)

B.l. 15 2 3

3 3

2

2

12 11 14

4

3

13

4 5

4 3

4 5

6

5.5 10 13

6 7 8

12 15 9 10 -11 -15 -11 -11

7

7 + 50 8 9 10 11 12 13

B.l. lS

9 -8 - 22 - 24 -26 -25

9 10 11 12 13

-9

-8

frequencies on two dilferent EM units. Locate any potential conductors and estimate their depth, dip, and, if possible, the TCP. Discuss the advantages of using two frequencies in tbis type oC survey. Is there any point in employing four frequencies? Given a choice, how many or which oC these would be preferable? Any other frequencies? 4. Figure 7.109 shows a set oC VLF profiles, obtained with the EMI6 unit, taken from a survey

Table 7.7. Une 12N

Stn

600

1.000

2.400

5.000

600

1.000

2.400

(deg)

(deg)

(deg)

(deg)

(deg)

(deg)

(deg)

3 2

2

20W 19 18

0.5

17

6

16 15 14 13 12

-12

11

-14 -1

O O O

3 7 -16.5

8.5 -15

-18

-18

-7.5 O -1.5

-4 -1

-3

-2 4 -2

-1.5

O

O

9 8

O O O

-S -3

-8 -5

1

1

-2 1 1 1

2

O O O O

O

1 81.

3.5

O

1 1 1 1 1 5

1

O

2.5

S 4 3

4 8 -18.5 -22

-12 -2.5

-14

10 7 6

Une 4N

Une 8N

-4 6

-12 -10 -10 -4 2 1.5 2 -1

O O

o

7.5 2 2

-1.5 O

1

2

2 5

-s

-6

-10 -2.5

O O O O

-2

-1 1

3 2

O -1 1 O O

1

3 2 2

2

1

-2

2

1

2

2

-7 -1 1 1 1

1

2 15

-1 1 1 -1

-3.5 -2.5 O

2 3 2 3 1.5 O O

5.000 (deg)

2 3

3 11

-16 -14 -2.5

3 3 1.5 -8 -10 -4 3 O 1.5

600 (deg)

O 7

14 -11.5 -12 -4.5 -1.5

2.400 (deg)

O 5.5

O 8.5

1.000

-19.5 -18.5 -9.5

-235 -18 -12.5

-5

2 3 -2 -7 -4.5

-2

O 1

2 3

3

O

9.5 24.5

-19.5

O O 1

o

22

O

-2

5.000 (deg)

20 -13 -3 O 2

O O O O -1.5 O

5 3.5

(deg)

O -1

O 2 1 1

2 1 O 1.5 1 O

O -1.5 -1.5 -4.5 O

O O O O 1

O -2 -1 1

-1

3 1.5

1.5 3 2 2 3.5 2.5 O

506

Electromagnetic merhods

'7 '

4KN~ _______~____________-_I~K=-r'~~-~7p-.J_-.'~~~~~,~O~~f_~~~~~~O~-~'~-79~-~9~-~'~-~!~O~O~-~ 410 4 1 K K . & Ó ;t~__ .fi'4KN

(O./Oot

t ---'.,

- 20

~;';'? ?"'f

t

_u,.dip

qUldr.'"r.

O

~ -J-1-1-'-l-I1-IO-IO-'-~+-1

t.!

,...,--'

l

~~ ~ -

~~~_'f-....,c::;:=::~~~~~";;-~:';-;~.;:;-~K-;:"I~:.:.-~IO~-!I::":-~16~-:J'~:;-1~_:';'~O~~~~ 44N

N

O

0-1 O

-~-.'

O;·: - !'oI.'-i:I

!

•

,

l

.'

_:_~

40N

.......... ~-- ..... _4 -1

J

l

10 O 11

Figure 7.109. EM16 survey in eas/ern Nova Sco/;a.

in eastero Nova Scotia. TIte numerical values ol pereent dip angle are also shown for each station. The transmitter was Panama, roughly S30 0 W of the area. (This station no longer operates and its frequency, 24.0 kHz, is now transmitted from Cutler, Maine.) Real crossovers are in the sense of positive to negative going east, Cor example, near station 28E on line 28N. At first glanee there appears to be evidenee both of steeply dipping contacts and ftat-lying eonduetors here. TIte overburden varies between 8 and 20 Ct in thickness and is Irnown to have a resistivity of about 100 (lm in one zone to the southwest, although generally it is thought to be higher than this over most oC the area. Make what interpretation you can Crom the profiles. It is reco~mended that a con tour plot, as described in Seetion 7.8, example 3, be made from the dip readings Cor clarification. 5. TIte EM16 readings in Table 7.8 were taken during a survey in Nova Scotia, using the Panama transmitter. TIte topograpby here is quite rugged;

there is an inerease in elevation oC 250 ft betwecn line lON just east ol the base line and the westero portion oí line 6S. This is the spine oC a hill that has steep sides both east and west so that tbe terrain eontours resemble the bowl of an inverted spoon. TIte hill is thought to be sandstone and there is a contaet with limestone beds, whieh appear quite thin, on the east ftank. Stations are 100 ft apart, lines 400 ft. Real erossovers are positive to negative going east. Plot the profiles, contour tbe dip angles by tbe method oC example 3, Seetion 7.8. In making an interpretation of the' results, eonsider (a) overburden effects, (b) contaets between extensive beds oC contrasting resistivity, (e) topographic effeets, as well as the possibility oC metallic conduelors. 6. In making VLF measurements over irregular terrain it is Cound that the dip angle is affeeted by ground slope. This is because the secpndary field tends to be parallel to the ground surface whereas the primary field remains horizontal. A simple

Problems

507

Table 7.8. Une 10N Stn.

Dip

20W 19 18 17 16 15 14

-% 2 -12 13 9 5 7

13

S

12 11 10 9 8 7 6 5 4 3 2 1

8 10 23 15 1 -1

2 -2 -2 -6 -2 6 8 5 7 12 16 9 2

B.l.

lE 2 3 4

5 6

J5

ID

I

Dip

Quad.

Dip

Quad.

-% -7 2 -8 -3 1 1 2 3 3 O 3

14% 20 15 15 17 18 18 18 23

-3% -7 O -1 O 2 5 4 3 2 2 O O -3 1 O 5 3 O -1 -6 1 O -4 -2 2 4

20% 20 18 15 17 22 14 15 10 10 10 5 -3 -16 -25 -25 -15 -3 -12 3 8 11 19 11 9 7 12

3% 4 3 3 -3 -2

20% 18 20 17 10 5 5 -4 -3 -11 - 25 -38 -30 -27 -32 -20 1 18 24

-2% -2

25 14 6

-2

5

1 -3 -3 2 3 O -2 -3 -2 O O O -1 -2

1 -8 -12 -20 -20 O 6 O -10 3 15 15 11 11

/

/

/

/

Corrected wilh respect lo

~ A the tllt 01 the lIeld coll

I:i.

15

O Corrected with respect lo the everage value 01 the Iree-run test

20

25

50

Figure 7.110. ehart giving slope correction T in terms of s/ope. (From Baker and Myers. 1980.)

terrain eorreetion has been deve10ped by Baker and Myers (1980) from measuremenls in a tank mode!. Tbe correetion is direetly proportional to the s)ope ang)ej it is added going downhill and viee versa. ·Beeause e1evation ehanges between sueeessive field stations may readily be measured, it is convenient to consider the p)otting point to be

i

2 -2 -3 O O -2 O

-1 3

O -2 -2

-3 -2 5

-2 O O

1 -2

13

11 5 10 16 5 O 10

-2 -2

10% 8 10

Quad.

S -S

-4% 2 -2 4 2

-5

O

-10 -20 -25 -37 -29 -32

-33 -13 O

17 15 21 22 15

O

3 O -8 -2 3 13

2 O

-1 2 -2 O 4

7 -2 -1 -5 -3 -5 -3 6 O O 3 -1 -1 -2

halfway between. Then the corrected VLF dip angle is given by

SIOP8 (OOgr885)

l.

O

O

-2 -3 -2 -3 -3 -3 3 3 3 -2 -2 3 3 -3 -3 -5 3 2 2 -1 -5 -3

Dip

,¡;¡.

5 10

'.

Line 6S

Quad.

n .... IS

Line 2S

Dip

mW::I~:Al

-

Line 2N

Quad.

SO

ZU

Line6N

where 81 , 82 are the dip angles at stations 1 and 2 and T is the correction for s)ope, all in percent. The value oC T is read off the correction charl in Figure 7.110. Given that the topographic map of Figure 2.39 is for the same area as the VLF data in problem 5, lake off a lerrain correction. Does Ibis correclion make a significanl change in Ihe profiles and eontours p)otted from problem 51 Does il lead to a more definite interpretation of Ihe VLF survey? 7. The AFMAG profiles snown in Figure 7.111 are laken from a large-scale survey. Geologically Ihe area is Precambrian with numerous outcrops oC ultrabasic rocks in the eastem portion. and gneiss, generally covered by lbin overburden, to the west; the exposed rocks are extreme1y metamorphosed. Stations are 50 m aparl and the lines 200 m; Ihe AFMAG frequencies were 150 and 510 Hz. The predominant azimuth direclion for these


508

~'_'~-~I

LO ---;.~East

Figure 7.111. AFMACprofiles, northeasrern Brazil.

\

I

\ \

- - In-phase

\

\ \

\

- - - - Quadraturt

oI 85E

,

'--,

frequenc:y :z.4OO Hz T-R IpIIcin. 200 R

'

.

... , .... ,

I

, ,,, ,,

\

'

'. '

lOOR ,

HE

95E

90E

Figure 7.112. HLfM profiles, fastern Townships, Quebec.

signals was about N60 oW, although this was quite erratic, and the tilt angle lor minimum, particularly at the lower frequency, was often indeterminate over a considerable range. The effect 01 a high-voltage transmission line about 2 km to the east can be seen on the east end of several tines. Malee an interpretation of these profiles with regard to loeation, depth, and dip 01 potential conducton. 8. Figure 7.112 is a single HLEM profile from a survey made in the Eastem Townships ol Quebec. The main geo1ogica1 Ceatures consist ol Ordovician and Cambrian slate, calcareo\iS slate, greywacke, sandstone, and quartzite conglomerate; the general geological strike is slightly east oC north. The anomaly, shown here Cor line 8iN, has a strike length of at least 1,000 ft. Estimate its location, depth, dip, width, TCP, and conductivity. Js there evidence lor more than one con-

Table 7.9. IN·PH.

Quad.

(%)

(%)

4

2 O O

3 2

-1.5

1.5 O 1.0 O O O

SIn. 65 5

1 O

lN

O O O O

1.5 1.0

ductor? Witb the limited information available, can you suggest tbe source? What further work would you do to verify the suggestion, possessing very limited finances? 9. As a contrast to problem 8, consider the HLEM readings in Table 7.9 below, taken from a survey

Problems 4W

't::'!,_._ ~\7'''''''-,~,_

. __

509

J_ ... C.

I

c ... ..:_ ..

-In-pha ... - - - - Quadralure

In-phi'" and quadralure

Figure 7.113. HUM profiles, Chibougamau Area, Quebec.

!+--Iooon ________

~_,~

~

~ ______________ LmN I

- - - - - - - - - - ... - - L 16N

1--------L12N

¡--------UN

L-_I

}----,,---------LON Figure 7.114. Model Turam configurarion.


510 Table 7.10.

in Northem New Brunswick. The cable length (T-R separation) was 200 rt and the frequency 2,400 Hz. This traverse crosses a conductive zone that has a strike length of 1,100 ft. Is it possible to determine its properties from tbe horizontal-loop response? Would this response normaIly be considered significant? Would you recommend any further HLEM work or other geophysics on the basis oC these results? 10. The profiles shown in Figure 7.113 were obtained during a HLEM survey in the Chibougamau area oC Quebec. Geologícally the regíon is Precambrian, typicaI ol Northwestem Quebec, with metamorphosed, lolded volcanics and sediments, intruded by acidic and basic rocks. Transmitter frequency was 880 Hz and cable length (T-R spacing) 200 Ct. Make an interpretation oC tbese profiles, as complete as possible. 11. The Turam results gíven in Table 7.10 were obtained in a model survey over a sheet conductor in the laboratory. Figure 7.114 shows the .. field" layout. The rectangular transmitting loop is 2,000 X 1,000 ft and the field ratios and phase

SIn.

Firsl coil

(fl)

(ft)

Une 4N Station readings

Une 16N Station readings

Phase (A.,,)

Phase (A.,,)

FR

(deg)

FR

1.77

O

1.77

0.10

1.54

0.20

1.54

0.20

1.39

0.35

1.43

0.50

1.35

0.35

1.35

0.80

1.64

-0.50

1.30

1.0

1.39

1.20

1.30

-1.0

1.26

1.25

1.33

-4.25

1.24

1.40

1.27

-0.95

1.23

1.55

1.22

1.15

200 250 300 350 400

450 500 550

600 650 700 750

800 850 900 950 1000 1050

HLEM -In.ph ...

- - - Qu.d,•• u,.

A-RR b

c:...::.::::..,L.\., , , ,

I -10

.-_....I ...... --.,.

I

-

-'r

:1

I

,

..... - ...

I

,

'-'

I'---~

TUflm

T,am',

'\ \

\ \

\

_R'

2S I

SOm ,

10

,

2N

4 I

6 I

(deg)

K I

10 I

12N I

Figure 7.115. HUM and Turam profiles, northern Quebec.

Problems

511

readings are Cor lines 4N and 16N, at stations 250W to 1050W in 100 ft steps. The transmitter frequency is 1,000 Hz and the receiver coils are 100 ft apart. Calculate the NR, RR, E ~
Table 7.11.

SIn 3505 2505 1505 0505 OsON 150N 2s0N 350N 450N

FR

1.81 1.58 1.51 1.44 1.37 1.32 1.28

1.25 1.23

Phase

(~
NR

-0.75 -1.50 -2.00 -2.00 -1.50 -1.00 -0.50 0.00 0.00

I

Abitibi Ouest, Quebec. Because the overburden was thought to be thick and of low resistivity, it was hoped that Turam would have better possibilities of penetrating lo depth than other EM methods. The near leg of the transmitter rectangle, laid out E-W, was at station 6 + OOS and the dimensions of the rectangle were 1,200 X 1,000 fl. Transmitter frequency was 660 Hz and the receiver coíls were 100ft aparl.

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512


Complete the table Cor RR, E 4.", V, R, and 1 lable 7.12. columns, plot RR, 4», R, and 1 profi]es, and interpret (be results as completely as possible. HUM 14. Figure 7.116 shows Crone-shootback, Turam, Shoot· and horizontal-loop EM profiles over a sulfide back deposit in westem Ontario. Interpretation of 5tn. R I 2-1 VlEM shootback EM results is mainIy qualitative (ft) (%) (%) (deg) (deg) (§7.7.3e)¡ the ratio (4)>4I014>>1I00),,,u is somewhat diagnostic of the type of conductor as in AF7N O 2.5 O MAG and the quadrature AEM system. Use all 4 7 + 50 O O -0.5 -1 -1 -1 4 8 three plOfiles to assess the varlous parameters of -1 -O -2 8 + 50 3 this deposito -6.5 -3 -3 9 3 lS. The readings in Table 7.12 were obtained Crom a 9 + 50 -13.0 -10 -2 6.5 survey over a copper PlOspect near Val d'Or, 10N -14.5 -12 5 2 Quebec. Tbe respective EM set Crequencies were -12 -10 2.5 7 10 + 50 -1 l1N -2.5 O 6 HLEM: 2,000 Hz, shoot-back: 1,800 Hz, VLEM: 11 + 50 1.5 -2.5 4 S 1,800 Hz, and T-R separations 200, 300, and 300 4.5 -1.0 12N 1.0 2 ft. (In the VLEM setup the transmitter was 300 0.0 2.5 -0.5 12 + 50 2 ft cast and on the conductor axis, which had 13N 0.0 3.0 1 been previously located by reconnaissance EM.) Plot these profiles and extraet all the informadiagram. Make an interpretation oC these with tion you can from the data. regard to conductors present, their relative depth, 16. Figure 7.117 illustrates UTEM plOfiles from a depth extent, dip, geometry, and TCP. single traverse over a test site in Ontarlo. The host rocks are mainly gneiss in dipping contaet 17. Figure 7.118a shows test survey profiles consistwith crysta1line limestone near the east end, botb ing of Turam, IP gradient and pole-dipole arof high resistivity; overburden is generally thin. rays, and Crone PEM, over a sulfide ore zone in Sev"D oC the 10 UTEM channels are seen in the southwest Arriea. This was a difficult target for

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several reasons, inc\uding its relatively low conductivity with respect to the local country rocks. Data are shown lor the four methods over lour 400 m lines across strike, spaced 200 m aparto The sulfides lie along a synclinal axis striking N20W in a magnetite-quartzite host rock. The PEM unit used horizontal Tx-Rx dipoles separaled 75 m, whereas tbe Turam loop was 1,000 X 1,000 m operating at 400 Hz, witb a receiver coil pair whose spacing was 25 m. Dimensions of the IP array are given in the figure. Make an assessment of the ore lone, employing as much of the data as possible. to obtain the following information: conductor model and depth, deptb extent, cross section, 01 product; resistivity contrast with host rock; relative merits of the four surveys in tbis geological selting.

The two total-field magnetic profiles shoWD in Figure 7.118b were carried out on lines 118.50W and 115.25W. Given tbese additional data, can you add to or correct any of tbe conclusions reached from tbe interpretation of Figure 7.118a1 18. Quadrature airbome EM results over a test site in Ontario are iIIustrated in Figure 7.119. The location of VLEM and IP anomalies found in ground foIlowup are illustrated for Iones A and B in the upper diagram. This record is merely a small part oC tbe airborne survey. It is obvious, as mentioned belore, that airbome EM data do not suffer lrom a lack, but rather from a surplus, ol anomalies; tbere are 17 marked in Figure 7.119a. These are loosely graded as "definite," "probable," and "possible," based partly on the maximum response amplitude, partly on the ra-

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tio of low to high-frequency maxima. These values are given for one .. probable" zone F on tine Ew· From the ftight record s in Figure 7.1l9b, determine the low- and high-frequency response maxima and their ratios lor the remaining 16 anomalies. Do you agree with tbe c1assifications in Figure 7.119a1 Have they becn inftuenced by response on adjacent ftigbt lines, by altitude variations, by possible additional information

- airbome magnetics, terrain, geology, and so forth, not available here? What is the reason for the relative displacement oC airbome and ground anomalies (about 200 ft) in zones A and B1 Can you estímate other parameters of tbe conductive zones - depth. dip, width, strike extent, TCP - from the records? 19. Airbome EM data obtained witb the Aero-Newmont phase-component system are shown in Figure 7.120. This equipment is mounted on a

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Sikorsky S-SS helicopter. lbe coaxial transmitter and receiver coils are mOUDted tare and alt 18 m apart and the source lrequency is 400 Hz. In Figure 7.120a, note the sharp peak (160 ppm) on a broader anomaly ol smaller amplitude. How would you model thcse two coiDc:ident anomalies? &timate the depth and TCP ol each, usiDg appropriate characteristic curves lrom Section 7.7.10. What do you make 01 the response in Figure 7.12Ob? Try modeliDg it as in Figure 7.120a for similar parameters. Does the radiometric chanDel provide any useful informatioo7 Mate a similar interpretatioo lor the features in Figure 7.12Oc, with possibly extra aid from the magnetic record. 20. 1bree phase-component airborne EM profiJes, each trom 8 different area, are shown in Figure

7.121. Pertinent informatiOD with respect 10 each 01 thcse ftigbt records is: (8) Transmitter frequency, 400 Hz; T-R spac:ing, 60 ft; altitude, 140 It. (b) Transmitter frequency, 320 Hz; T-R spac:ing, 62 ft; altitude, 140 It. (c) Transmitter Irequency, 390 Hz; T-R spacing, 60 ft; altitude, 140 ft. Qne 01 these traverses was over 8 lake, one over a graphite zone. and one crossed a copper deposit of economic grade. By making as complete an interpretation as possible 'rom these profiles, can you loeate and identily the three sources7 Can you suggest any reason why the record is so noisy iD (c)? 2l. Figure 7.122 shows two Input airbome EM records, the first from Northem Manitoba, the second Northwestem Ontario. At least tour

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anomalies are evideot 00 tbese two pro files. Given tbat tbey are caused by graphite, conductive overburden, pyrite and ore-grade massive sulfides - pyrite, cbalcopyrite, spbalerite - at deptbs of 3, 7S, S, and 90 m (oot necessarily in the same order), can you sort out tbese anomalies? Are there any others iodicated? 22. Tbe airbome EM anomaly map from a Dighem II (900 Hz, three coi) pairs) survey, shown in Figure 7.123, was prepared on tbe basis that reasooable response from tbe coaxial coil pair could indicate bedrock metallic conductors. Cireles loeating tbese are marked witb tbe conduclance in siemens, determined from master curves for a vertical thin sheet. In some cases the interpreter, experienced at bis work, has applied a label "s?", showing tbat tbe profile shape and otber available information may suggest a surfi-

cial ratber tban a bedroek anomaly. He has also marked possible conductor axes with Iines between several circle sets. Noting tbe area topography, does this map seem realistic? Could the conductors represent a large-scale shallow structure instead? What additional data are necessary to develop the alternative interpretation? Assuming a crude pseudolayer modeJ with tbis limited information, con tour a map of shallow resistivity (or tbis purpose. Note that the .. s?" anomalies lie mainly on tbe peripheral area of Figure 7.123 and tbat tbeir ot values are small. Having completed tbis hypothetical map, make an interpretation. Are there indieations of any bedrock conductors remaining? 23. The airborne dala in Figure 7.124 were obtained in a test survey with tbe Dighem III system,


518

Figure 7.123. Airborne fM (Dighem 11) map of an area in the Appalachi.ms.

which uses two horizontal coplanar coiJ pairs at 900 and 7,200 Hz and ooe vertical coaxial pair (not shown), operating between 385 and 7,200 Hz, depending on the target and survey area. Tbe test anomaly js a wide graphite conductor oí irregular shape, somewhat resembling a tbick dike. It is overlain by 85 m of glacial sands

averaging 300 Om; host rock resistivity is probably greater than 3,000 Om. Usiog the curves of Figure 7.84a, b, attempt to reproduce the 900 and 7,200 Hz resistivity profiles shown in the lower part oí Figure 7.124. 24. Figure 7.125 displays profiles from the Input VI system recorded over four bedrock conductors

References

519 covered by conductive overburden of variable thickness. Malee as complete an interpretation of each as you can, wíth the aid of pertínent data from Section 7.7.12.

REFERENCES

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Figure 7. 124, Results of Dighem 111 survey over il wide dike-li!t.e grilphite conductor. fM curves are for two horizontal coplanar pairs of coils operil/ing al 900 and 7,200 Hz. Curves are: a/time/er, total-field magnetics, in-phase and quadrature componen/s, and apparent resistivity calculated using a pseudolayer half-space model.

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Abramowitz, M. and Stegun. I. A. 1972. Handbook oC Malhemalical Funclions. Na!. Bur. oC Standards. U. S. Gov'l Printing Office, Washington, D.e. 20402. Annan, A P. 1974. The equivalenl source method Cor electromagnetic source scattering analysis and its geophysical application, Ph.D. thesis, Memorial Univ., SI. Johns, Newíoundland . Annan, A. P., Waller, W. M. Strangway, D. W., Rossiter, J. R., Redman, J. D., and Walts, R. D. 1975. The electromagnetíc response oí a low-Ioss, 2-layer dielectric earth for horiwntal electric dipole excitation. G€'ophysics 40, 285-98. Arcone, S. A 1978. An investigatíon oC an airbome VLF resistivity survey conducted in northem Maine. Geophysics 43, 1399-417. Baker, H. A .. and Meyers, 1. e. 1980. A topographic correetíon for VLF-EM profiles hased on model studies. Geoexplora/ion 18, 135-49. Barringer, A R. 1962. A new approach to exploration - the INPUT airbome-electrical pulse prospecting system. Min. Congo Jour. 48,49-52. Barringer, A R. 1970. Regional reconnaissance lechniques applied 10 exploration. In Mining and Groundwater Geophysics, Eco71. Geo/. Report 16, L. W. Morley, ed. Ottawa: Geol. Surv. Canada, pp. 202-12. Barlel, D. and Hohmann, G. W. 1985. Interpretation of Crone pulse electromagnetic data. Geoplrysics 50, 1488-99. Beeker, A 1969. Simulation of time-domain airbome electromagnetic system response. Geoplr'ysies 34. 739-52. Becker, A 1979. Airbome electromagnetic melhods. In Ceoph.l'slcS and geochemislry in /he search for me/al/ie ores, Eron. Gto/. Reporl 31, P. J. Hood, ed. Ottawa: Geo!. Surv. Canada, pp. 33-44. Becker, A, and Cheng, G. 1988. Detection of repetitive electromagnelic signals. In Eleclromagnelic Me/hods in Applied Geophysies, M. N. Nabighian, ed. Ch. 7, Tulsa: Society of Exploration Geophysicists. Becker, A, Gauvreau, C., and Collelt, L. S. 1972. Scale model study of time-domain EM response oC tabular conductors. CIM Bull. 65, 90-5. Bhattacharya, P. K. and Sinha, A. K. 1965. Response oC a spherieal conductor to an oscillating magnetic dipole and its use in geophysical prospecting, Jour. Sei. a71d Eng. Res., Indian Inst. Tech., Kharag puro 9, pI. 1, 51-62. Buselli, G. 1980. Electrieal geophysics in Ihe USSR. Geophysics 45, 1551-62. Buselli, G .. and O'Neill, B. 1977. SIROTEM: A new portable instrument for multichanne1 transien! electromagnetic measurements. Bul/. A ustra/. Soco Expl. Geophys. 8, 82-7. Crone, D. 1979. Exploration for massive sulfides ín desert afeas using the ground pulse eleclromagnetie method. In Ceophysics cmd Geochemis/ry in the Search for Me/a//ic Ores, Econ. Ceo/. Report 31, P. 1. Hood, ed. Geo!. Surv. Canada. Ottawa: pp. 745-56.

c.,

520 De Moully, G. T., and Beclter, A. 1984. Automaled interpretation of airbome electromagnetic data. G~physics 49, 1301-12. Dolan, W. M. 1970. Geophysical detection 01 deeply buried sulfide bodies in weatbered regions. In Mining and Grollndwater G~physics. Econ. Geo/. Report 16, L. W. Morley, ed. Geo\. Surv. Canada, pp. 336-44. Duckwortb, K., and Bays, A. R. 1984. Modified mode 01 operation for the Turam elcctromagnctic exploration systcm with benefits lor deep exploration. Geophys. Prosp. 32, 317-35. Dyck, A. V., Becker, A., and Collctt, L. S. 1974. Surficial conductivity mapping with tbe airbome Input systcm. CIM BII/I. 62, 104-9. Dyck, A. V., Becker, A., and CoIICII, L. S. 1975. Input AEM results from Projeet Pioneer, Manitoba. Can. JOllr. Earth Sci. 12, 971-81. Dyck, A. V., Bloore, M., and Vallée, M. A. 1981. User manual for programs PLATE and SPHERE. Research in Applied Geophysics, 14, Toronto: Geophysics Lab., Dept. 01 Physics, Univ. 01 Toronto. Eve, A. S., and Keys, D. A. 1956. Applied Geophysics. Cambridge: Cambridge Univ. Press. Fischer, G., Le Quang, B. V., and MOller, l. 1983. Very-Iow frequcncy ground surveys, a powerlul 1001 lor the sludy 01 shallow Iwo-dimensional structures. Geophys. Prosp. 31, 977-91. Fleming, H. W. 1961. The Murray deposit, Restigouche Couniy. N. B., a geochemical-geopbysical discovery. 811/1. Can. Inst. Min. 54, 230-5. Fraser, D. C. 1972. A new multicoil elcctromagnetic prospecting systcm. Geophysics 37, 518-37. Fraser, D. C. 1978. Resistivity mapping witb an airborne muIticoil electromagnetic system. Geophysics 43, 144-72. Fraser, D. C. 1986. Dighem resistivity techniques in airborne electromagnetic mapping. In Airborne Resislillity Mapping, G.l. Palaay, ed., Geol. Surv. Canada paper 86-22, pp. 49-54. Friscbkneeht, F. C. 1967. Fields aboul an oscillaling magnelic dipole over a two-tayer earlh and application lo ground and airbome eleclromagnetic surveys. Colorado School 01 Mines Quarttrly 62, 1-326. Gallagher, P. R., Ward, S. H., and Hohmann, G. W. 1985. A model study of a !hin plale in free space for the EM37 transient eleclromagnetic system. Geophysics SO, 1002-19. Gamble, T. D., Goubau, W. M., and Clarke, 1. 1979. Magnetotellurics with a remo te reference. Geophysics 44,53-68. Geological Survey oC Canada 1986. Airborne resistivity mapping. Paper 86-22. E. J. Palaay, ed. Grant F. S., and West, G. F. 1965. Interpretation Theory in Applied Geophysics. New York: McGraw-Hill. Grover, F. W. 1962. Induclanu Calcularions. New York: Dover. Hawley, P. F. 1938. TransienlS in e1ectrical prospccting. Geophysics 3, 247-72. Herz, A. 1986. Airborne elcctromagnetic instrumenlS operating at VLF and higher frequencies. In A irbome Resistivity Mapping, G. 1. Palacky, ed. Geo\. Surv. Canada paper 86-22, pp. SS-62. Hohmann, G. W. 1971. Electromagnetic scanering by conductors in Ihe earth near a line source 01 current. Geophysics 36, 101-31. Hood, P. J. 1967. Mineral exploration lrends and developments. Can. Min.laur. 88 (appeared

Electromagnetic methods annually - in Feb. issue untill972, in lan. issue thereafter). Hood, P. 1. 1978. Sce Hood (1967). Hood, P. 1. 1979. Sce Hood (1967). Kauahikaua, 1. 1978. The electromagnctic fields about a horizontal electric wire source of arbitrary length. Geophysics 43. 1019-22. Kaulman, A. A., and Keller, G. V. 1983. Frequency and Transienr Soundings. Amsterdam: Elsevier. Keller, G. V., and Frischknecht, F. C. 1966. Eleclrical Methods in G~physical Prospecting. London: Pergamon. Kleinkopr, M. D., Balch, A. H., Frischknechl, F. c., Hovey, R., and Savitt, C. H. 1974. Exploration geophysics in the U.S.S.R .. G~physics 39,697-711. Koefoed, O., Ghosh, D. P., and Polman, G. 1. 1972. Computalion 01 type curves lor electromagnetic depth sounding with a horizontal transmitting coil by means 01 a digital linear filter. Geophys. Prosp. 20, 406-20. Koeloed, O., and Kegge, G. 1968. The electrical current patlem induced by an oscillating magnetic dipole in a semi-infinite thin plate of infinitesimal resistivity. Geophys. Prosp. 16, 144-58. Koefoed, O .. and Struyk, A. P. 1969. The eleclrical currenl panern induced by an oscillating magnetic dipole in a semi-infinite conducting thin plate. G~phys. Prosp. 17, 182-95. Labson, V. F., Becker, A., Morrison, H. P., and Conti, U. 1985. Geophysical exploration with audio lrequency magnetic fields. Geophysics SO, 656-64. Lawrence Berkeley Laboratory Research Review. Winter 1986. Compact generator passes earth-sounding test. 11, no. 4, p. 92. Lodha, G. S., and West, G. F. 1976. Practical airbome EM inlerpretation using a sphere mode\. Geophysics 41, 1157-69. Lowrie, W., and West, G. F. 1965. The elfect of a conducting overburden on eleclromagnetic prospecting measurements. Geophysics 30, 624-32. Macnae, J. C., Lamontagne. Y., and Wesl, G. F. 1984. Noise proccssing techniques lor time-domain eleclromagnetic systems. Geophysics 49, 934-48. Mallick, K. 1972. Conducting sphere in electromagnetic Input Held. Geophys. Prosp. 20, 293-303. Mason, M. 1927. Geophysical exploration lor ores. Tech_

Pllb. Amer. Inst. Min. Eng. no. 45.

Mathieson, C. c., and Crossley, D. 1. 1982. Intcrpretation of single lrequency VLF data. In Geophysical

Applications 01 Surface Wave Impedance Measllrements, L. S. Collett and O. G. lensen, eds. Geo!. Surv. Canada, Onawa, paper 81-15, Report IV, pp. 49-65. McCracken, K. 0., Oristaglio, M. L., and Hohmann, G. W. 1986. Minimization 01 noise in electromagnetic exploration systems. G~physics 49, 934-48. McNeill, 1. D. 1980. Applications olrransient electromagnetic ttchniques. Tech. Note TN-7, Geonics Ltd., Mississauga, Ontarlo. Morrison, H. P., Dolan, W. M., and Dey, A. 1976. Earth conductivity delermination employing a sin¡le superconducting coi\. Geophysics 41, 1184-1206. Morrison, H. F., Phillips, R. l., and O'Brien, D. P. 1969. Quanlitative interpretation 01 transient electromagnetic fields over a layered half-space. G~phys. Prosp. 11, 82-101. Nabighian, M. N. 1979. Quasi-static transient response 01 a conducting half-space - an approximale represcntation. Geophysics 44, 1700-05.

References

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Nabighian, M. N. and Oristaglio, M. L. 1984. On the approximalion of finile loop sources by lwodimensionalline sources. Geophysics 49, 1027-29. Orislaglio, M. L. 1982. Diffusion of eleclromagnetic fields into the earlb from a line source of current. Geophysics 47, 1585-92. Palacky, G. J. 1975. Interpretation of Input AEM measurements in areas of conductive overburden. Geophysics 40, 490-502. Palacky, G. J., and Jagodils, F. L. 1975. Computer dala processing and quantilative interpretation ol airbome resislivity surveys. Geophysics 40, 818-30. Palacky, G. J., and West, G. F. 1973. Qua"titati!'e int~rpretation o/ 'nput AEM measurements. Geophysics 38, 1145-58. Parry, J. R., and Ward, S. H. 1971. E1ectromagnetic scallerins from cylinders ol arbitrary cross-section in a conductive balf-space. Geophysics 36,67-100. Paterson, N. R. 1966. Mallagami Lake Mines - a discovery by geophysics. In Mining Geophysics, vol 1, pp. 185-96. Tulsa: Society of Exploration Geopbysicists. Paterson, N. R. 1967. Exploration for massive sulfides in tbe Canadian Shield. In Mining and Groundwaler Geophysics, Econ. Geol. Repon 26. L. W. Morley, ed. OUawa: Geol. Surv. Canada, pp. 275-89. Paterson. N. R. 1971. Airbome electromagnelic methods as applied lo search for sulfide deposils. ClM Bu/l. 74. 1-10. Paterson. N. R., and Reford, S. W. 1986. Inversion ol airbome electromagnetic data for overburden mapping and groundwater exploration. In Airborne Resistivity Mapping, G. 1. Palacky, ed., Geol. Surv. Canada paper 86-22, pp. 39-48. Patra, H. P., and Mallick. K. 1980. Geosounding Principies 1- Time-t'arying Geoe/ee/ric Soundings. Amsterdam: E1sevier. Pipes. L. A. and Harvill, L. R. 1970. Applied Mathema/ics for Engineers and Physicists. New York: McGraw-HiIl. Podolsky. G .• and Slankis, J. A. 1979. Izolt Lake deposit, North West Territories, Canada: a geophysical case history. In Geophysics and Geochemistry in the Search for Me/allic Ores, EcO/!. Geol. Report 31. P. J. Hood, ed. GeoI. Surv. Canada, pp. 641-52. Seisel. H. O. 1957. Discovery of Mobrun Copper Ltd. sulfide deposit, Noranda Mining District, Quebec. In Methods and Case Histories in Mining Geophysics. 6/h Commonwealth Mining and Met. Congress. Montreal: Mercury Press. Seigel, H. O .• and Pitcher, D. H. 1978. Mapping earth conductivities usins a muhifrequency airbome electromagnetic system. Geophysics 43, 563-75. Smith, R. J. 1985. Geophysics in Australian mineral exploration. Geophysics 50, 2637-65. Smythe, W. R. 1950. Static and D.ynamic Electricity. New York: McGraw-HiII. Spies, B. R., and Eggers, D. B. 1986. The use and misuse of apparent resistivily in electromagnetic measuremenlS. Geophysics 51, 1462-71. Spies, B. R., and Parker. D. 1984. Limitations of large loop transienl e1ectromagnetic surveys in conductive terrains_ Geophysics 49, 902-12.

P:

Statham. L. 1936. Electric earth transients in geophysical prospecting. Geophysics 1, 271- 7. Slrangway. D. W. 1966. Electromagnetic parameters of some sulfide ore bodies. In Mining Geophysics, vol. 1, pp. 227-42. Tulsa: Sociely of Exploration Geophysicists. Stratton. J. A. 1941. Electromagnetic Theory. New York: McGraw-Hill. Telford, W. M., King. W. F .. and Becker, A. 1977. VLF mapping of geological structure. Geol. Surv. Canada Paper 76-25. Wait. J. R. 1951a. Transient electromagnetic propagation in a conducting medium. Geophysics 16. 213-21. Wait. J. R. 1951b. A conducling sphere in a time varying magnetic field. Geophysics 16. 666-72. Wait.1. R. 1951c. The magnetic dipole over the horizontally stratified earth. Can. Jour. Res. 29, 577-92. Wait, J. R. 1955. Mutual electromagnelic coupling of loops over a homogeneous ground. Geophysics 20,630-7. Wait.1. R. 1960a. Propagation of electromagnetic pulses in a homogeneous conducting earth. App. Sci. Res. Seco B. 8, 215-53. Wait. J. R. 1960b. On the electromagnetic response of a conducting sphere lo a dipole field. Geophysics 25, 649-58. Wait, J. R. 1971. Transient excitation of the earth by a line source of curren\. Proc. IEEE Lett. 59,1287-8. Ward, S. H. 1959a. Unique determination of conductivity. susceplibility. size and depth in multifrequency electromagnetic exploration. Geophysics 24. 531-46. Ward, S. H.1959b. AFMAG- airbome and ground. Geophysics 24, 761-89. Ward, S. H. 1966. The search for massive sulfides. Introduction. In Mining Geophysics. vol. 1. pp. 117-29. Tulsa: Society of Exploration Geophysicists. Ward, S. H. 1967. E1ectromagnetic theory for geophysical applications. (Also) The elcclromagnelic method. In Mining Geophysics, vol. 2. pp. 10-196,224-372. Tulsa: Sociely of Exploration Geophysicists. Ward, S. H. and Hohmann. G. W. 1988. Electromagnelic theory for geophysical applications. In Electroma8net;c Methods in Applied Geophysics, vol. 1, chapo 4, M. N. Nabighian. ed. Tulsa: Society of Exploration Geophysicists. Weir, G. J. 1980. Transient EM ftelds about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space. Geoph.l·s. Jour., Roy Astro". Soco 61. 41-56. West. G. F .• Macnae, J. c., and Lamontagne, Y. 1984. A lime-domain eleclromagnetic syslem measuring the step response of the ground. GMphysics 49, 1010-26. Wieduwill, W. G. 1962. Interprelalion' techniques for a single frequency airbome electromagnetic device. Geophysics 27,493-506. Zietz, l., Eaton, G. P., Frischknecht, F. C .• Kane, M. F., and Moss. C. K. 1976. A Westem view of mining geophysics in Ihe USSR. Geophysics 41, 310-23. Zollinger. R., Morrison. H. F., Lazenby, P. G., and Becker, A. 1987. Airbome electromagnetic bathymetry. Geophysics 52, 1127-37.

Chapter 8

Resistivity Methods 8.1. 8.1. INTROOUCTION INTRODUCTION

All resistivity methods employ an artificial source of current, current. which is introduced into the ground through point electrodes or long line contacts; the latter arrangement is rarely used used nowadays, nowadays. The procedure is to measure potentials at other electrodes in the vicinity of the current flow. flow. Because the current is measured as well, well. it is possible lo to determine an elfective effective or apparent resistivity of the subsuñace. subsurface. In this regard the resistivity technique is superior, at least theoretical1y, theoretically, to al1 all the other other electrical methods, because quantitative results are are obtained by using a controlled source of specific specific dimensions, dimensions. Practica1ly, Practically, as in other geophysical methods, the maximum potentialities of resistivity are never realjzed, The chief drawback is its high sensitivity to ized. minor variations in conductivity near surface; in electronic parlance the noise level level is high, high. An analogous situation would exist in ground magnetic surveys if one were to employ aa magnetometer with sensitivity in the picotesla range, range. This limitation, added to the practical difficulty difficulty involved in dragging severa! several electrodes and long wires through rough wooded terraíD, terrain, has made the electromagnetic method more popular than resistivity in mineral exploration, exploration. Nor is resistivity particularly suilable suitable for oil prospecting, prospecting. However, it is by no means obsolete, because the rapid development of the induced polarization technique, which inc1udes includes resistivity data, guarantees its continued use, use. Furthermore the search for geothermal reservoirs normally involves resistivity surveying and it is also employed routinely in groundwater exploration, exploration. which is of increasing worldwide importance, and in civil engineering. civil engineering,

8.2. ARY THEORY 8.2. ELEMENT ELEMENTARY THEORY 8.2.1. 8.2.1. Potentials in Homogeneou5 Homogeneous Media Consider a continuous current flowing flowing in an isotropic homogeneous medium. (This analysis will also apply lo to ac il if the frequency is low enough that displace-

8A is an element ment currents are insignificant.) If 8A amperes per per of surface and J the current density in amperes square meters, then through 8A is then the current passing through J • BA. and the electric field E 8A. The current density J and are related related through Ohm's law:

J - aE

(8,1) (8.1)

where E is in volts per meter and a is the conductivity ol per meter meter (81m). (S/m), of the medium in siemens per 01 a scalar scalar potenpotenThe electric fleld field is the gradient of tial,

E- -VY -VV

(8,2) (8.2)

J - -avV

(8,3) (8.3)

Thus we have

From Equation (6,7), O, so (6.7), V •. J - 0,

. (avV) - 0O V '(avV)

(8,4) (8.4)

Using Equation (A.2l), we have

va'VV+av V-O va'VY+av 2 V - 0

(8.5)

lf term vanishes If a is constant throughout, the first term potential and we have Laplace's equation, that is, the potential is harmonic: (8.6) There that must There are two boundary conditions that hold at any contact between two regions of 01 different dilferent 6,2,4 we gave boundary bOUDdary conductivity. In Section 6.2.4 conditions for interfaces where a and and II " change abruptly, written abruptly. The fint first and and third third of these may be written in the form Ex¡ Ex" - E,,¡ E"3

and

alE•• - ~E'3 ~E,¡ alE••

(8,7a) (8.7a)

and normal, where the x and and z axes are tangential and being the tangenrespectively, lo to the interface, interface, E~ being

Elementary theory theory Elementary

523 523 Power Powcr

Umfcnn mcd.um medium Untrorm resistivitypp usistivlty

---- Current Current flow flow -

8.1. Buried poinl point 50urce source of currenl current in homogeneous ground. Figure 8.1.

tial component in medium 1, I, and so forth. In additia! tion, tion,

surface is is given by dV

1I -.. 4'1r,2¡ 0 - - = -4'1roA 4'1rr 2J =.. -4'1rr 20 dr

( 8.7b)

from Equations (8.3) and (8.9), so tbat that

Single Current Electrode at Depth 8.2.2. Single

A-

There are several field field configurations used in resistivThere will consider in tum. turn. In the first of tbese these ity that we will we have an electrode electrode of small dimensions buried buried in a we homogeneous isotropic medium. This corresponds to homogeneous the mise-a-la-masse method (see §8.5.4d) where the the single electrode is down a drill hole or otherwise single otherwise under the ground. ground. The Tbe current circuit circuit is completed completed through tbrough another electrode, electrode, usually at surface, but but in any any case far enough enough away that its influence is negligible. ble. From the symmetry of the system, the potential will will be a function function of rr only, onIy, where r, is the tbe distance distance from from the first electrode. Under these conditions Laplace's equation, in spherical spherical coordinates, coordina tes, simplifies to

Multiplying Multiplying by by r,22 and and integrating, we get dV A dr d, .. = r,22

(8.9)

integrating again, again, we have have

VV- -A/r+ -A/r+ B B

(8.10) (8.10)

where wbere AA and and BB are are constants. constants. Because Because VV .. = 0O when when r'" r'" 00, 00, we we get get B B -- O. O. In In addition, addition, the the current current flows flows radially radia!ly outward outward in in all all directions directions from from the tbe point point electrode. electrode. Thus Tbus the the total total current current crossing crossing aa spherical spherical

lp

4," 4'1r

hence,

V=(~)': V=(~)': 4'1r r

or

4'1rrV p - -¡ /-

(8.11)

Tbe equipotentials, which are are everywhere orthogThe onal to the current flow lines, will be be spherical suronal constan!. These These are illustrated in faces given by r = constant. Figure Figure 8.1.

Electrode at Surface 8.2.3. Single Current Electrode located If the point electrode delivering I1 amperes is located surface of of the homogeneous isotropic medium medium at the surface and if the air above aboye has zero zero conductivity, then then we and have the tbe single probe or or three-point system system used in in surface resistivity resistivity layouts. Again Again the the return returo current surface electrode is at at a great great distance. electrode of the the symmetry. Laplace's Laplace's equation equation in in Because of spherical coordinates is applicable, applicable, the the solution solution bebeby Equation (8.10) with with BB .. - O. O. The Tbe again by ing given again at the the surface surface requires requires that that E• E• .... boundary condition at av/ az ..= 0o at at z ..- 0O (because 0ail' 0air = 0). O). This This is is alal8V/8z ready fulfilled fulfilled because because 8V/8z" av/az - 8(-A/r)/iJz" a(-A/r)/iJzready -d/dr(A/r)(iJr/fJz) -- Az/r Az/r)3 .. - 0Oat al zz -- O. O. -d/dr(A/r)(iJr/fJz) In addition addition all all the the current current now now flows flows through through aa In or hemispherical surface surface in in the the lower lower medium, medium, or hemispherical

A= A=

lp lp

277

524 524

Res;stivity methods Resistivity Power Power

/"---,~ EqUipoltDliai. ...... - - - ' - - " EqUipoltDlial.

Figure medium. Figure 8.2. 8.2. Point source source of current at the surface surface of a homogeneous medium. Power

Figure Figure 8.3. Two current and two potential electrodes on the surface of homogeneous isotropic ground of resistivity p.

so that in tbis this case

v - ( ::

Thus, we have

H

or p _

2W;V

Here the equipotentials are hemispherical surfaces faces below ground as shown in Figure 8.2. 8.2.

8.2.4. 8.2.4. Two Current Electrodes at Surface When the distance between the two current electrodes is ftnite finite (Pig. (Fig. 8.3), the potential at any nearby nearby surface point will be affected by both both current electrodes. As before, the potential due to el C1 at PI PI is trocles.

Al v.--1 '1

Ip

A) - - where Al 2w 2w

Because the currents at the two electrocles electrodes are equal and opposite in direction, the potential due lo to <; <; at PI PI is

Ip .A A 2 - -2w -A1 2w - -,.(

VI V1

(8.12)

11) Ip ((.: - .:) + JIl JIi -_ -Ip 2w'1

'2

Fina1ly, Finally, by introducing a second potential elecdifference in potenpotentrocle trode at PI P2 we can measure the difference tial between p) wil1 be be PI and PI' P2 , which will

{(~ __.:) (~__ .:)} (8.13) .1V- Ip {(.: ':) _ (.: 2w 2w ' 1 ' 2 ','"

',r"

Such an arrangement corresponds to lo the fourlourelectrode spreads fleld spreads norma1ly normally used in resistivity field current-ftow 1ines ud work. In tbis lines and this conflguration configuration the current-flow equipotentials are dislorted distorted by the proximity of the <;. The equipotentials and and second current electrode <;. orthogonal current lines by plotting the lines obtained by relations

1 1 - - - constant R R1 RI2

R~

+ R~ - 2R)Rz cos9 - 4L 4L'1.2 2R 1R2cos9

are shown in Figure 8.4. The The distortion from spherispberical cal equipotentials is most most evident in the regions between the current electrodes.

flementary Elementary theory

525

Figure eurrenr on Figure 8.4. Equiporentia/s Equipotentia/s and eurrent current flow fines lines for rwo two point sources of current surfaee Vertical surface of homogeneous ground. (After Dobrin, Dobrin, 1960.) 1960.) (a) Plan Plan view. (b) Vertical seerion. section. (e) (c) Potenrial Potentut variarion variation at the surfaee surface along along a straight fine line through the point sourees. sources.

8.2.5. Current Distribution Figures 8.1, 8.1, 8.2, 8.2, and 8.4 8.4 iIlustrate, illustrate, in a general general way, tbe the ftow of current in homogeneous ground. Altbough though they they show that increasing the electrode spacing ing inereases increases the penetration, penetration. the quantitative distribution distribution in depth is not indicated. Consider the current current ftow in a homogeneous homogeneous medium between between two two point electrodes electrodes el C1 and <; in Figure 8.5. 8.S. The horipoint 'tOntal zontal current density at point P is

J" J" - (-I/p) (-l/p) 8V/8x

1/r2) - (-1/2,,) 8/8x(1/rl - 1/'1) =

(I/2,,){ xl'? x/r? - (x - L)/ri)

and ir if this point is on the vertical plane midway C1 and el' C2 , we have rl '1 - r'2 between el 2 - r, and

(8.14)

Figure 8.6 8.6 shows the variation in current density with depth across tbis this plane plane when the electrode separation is maintained constant. If, on the other other constant. If. hand, the electrode spacing is varied. varied, it is found that Ihat J" J" is a maximum when L = .¡2z. /2z. We can calculate Ihe ftowing the fraction of current flowing through a strip of this vertical plane, between depths 2 zl z2' Because Z2}. the ZI and z2' Because ,2 r - {(L/2)2 + y2 + Z2},

Resislivily melhods Resistivity methods

526 526 Power t+--------L-------~ ~--------------L--------------~

c,

¡.----X-------i~+IEE__----- L-x ---~ I,

l' ~

--,-+" I I I Figure Figure 8.5. 8.5. Determining the current density density in uniform ground below two surface electrodes.

1,,value of I. 0 ',,- valueof J, forz - O - 41/TrL 411TrL 2 (see eq. (11.14)) (11.14»

o·, 0,'

0·6 0·6

l' /

l' /

.- .- "

"'... -----

z consto canst.

I I

0·4 0·4

I

I

I

I I I

0·2

I

I I

I

I

I

o

0.4

0.8

1.2 1.2

1.6

2.0 2.0

L/z Liz

Figure Figure 8.6. Current density density versus versus depth (salid (solid line) line) and and electrode spacing spacing (dashed line).

CIl1TeDt current through an element element dy dz of the strip is

1

L

BI, 3/l B1, - J" J" dydz - 3/2 dydz 2tr {( L/2)2 + y2 y2 + z2 ))

tbe the lracnon fraction ol of total current tbrough through a long strip wide wide will will be

(z2 (Z2 - Z1)

1" 1"

1-¡ -

1'fez2 ¡oo

L fall 2t1' 2tl' '1 'I dz _ 00 all

(

(

dy L/2)2 + )'2 y2 + z2} z2} 3/l 3/2

2 2( 2 tZ 2z1 ) __ -~ (tantantan- t -2Zt) -2z -_ tantr L L

(8.lSa)

This fraction has a broad maximum maximum when LTaking a numerical numerical example, example, if ZI %1 - 180

2(ZIZ2)1/l, 2(%1%2)1/2.

300 300 m, the electrode spacing should be 420 m to get tbe the maximum horizontal current density in tbe however, is not very the slab. The concentranon, concentration, however, significant. significant. Otberwise, Equanon (8.1Sa) (8.1Sa) becomes Otherwise, if Z2 %2 -- 00, Equation

DI, m, Z2 %2 -

1" 2z1 1" 22 2%1 - - 1 - -tan- 1t 1 tr L

(8.1Sb) (USb)

Figure 8.7 8.7 shows shows tbe the electrode spacing necessary tbe current current into the to force a given given fraction of the tbis plot we see that, tbat, ground below a deptb depth Z1' %1' From this when L - 2z flows in the top 2%1' half the current flows 1, haJ! layer, hall half below it.

fffect Effect of inhomogeneou5 inhomogeneous ground

527

H) HI

10 10

L/l. LII.

Figure L. Figure 8. 8.7. 7. Fraction of current flowing beJow below depth Z, Z, for an electrode spacing L.

Because Because the variations in potential, measured at surface, surface, are proportional to the current ftow flow below, it is desirable to get as much current into the ground as possible. possible. For good penetration we must use large enough enough spacing that sufficient sufficient current reaches the larget target depth; if the latter latter is 100 m, about about one-third oC of the current will pass below this depth when the spacing is also 100 m. Compared to magnetotellurics, for for instance, tbis this places an inherent limitation limitation on the resistivity resistivity method. However the controlled control1ed power source source provides certain advantages.

8.3. EFFECT OF OF INHOMOGENEOUS GROUNO GROUND 8.3.1. Introduction So So far we we have considered current ftow flow and potential in and over homogeneous ground, a situation situation wbich which is extremely rare in the field field and which would be oC of no practical significance significance anyway. What we want to detect is the presence of anomalous anomalous conductivity in various forms, such as lumped (three-dimensional) bodies, dikes, faults, and vertical or horizontal contacts between beds. The resistivity method is most suitable for outlining horizontal beds and vertical contacts, less less useful on bodies of irregular shape.

8.3.2. Oistortion Distortion of Current Flow at a

J.,... I

Medium Medium (1) (I) P, PI

_J._-.J'1 _J._-+J _.:pJJ¡l

-.:p-

"

-_-:.LB.. -_-:. LB..__

Bound.ry Boundary

Figure al aa plane plilne boundFigure 8.8. 8.8. Distortion of currenl current flow at ary when p¡. when PI < Pl.

direction of this curtent current in medium (2) we recall the conditions given in Equation (8.7); using Ohm's Ohm's law to express these results in terms of the current density, we obtain J",PI = J",Pl J",P2

and

J., -

1"

Dividing these expressions, we have PI (

J",! J",I1,,) 1,,)

- Pl P2 ( JJ"./l.,) x , /l., )

or PI tan 91

-

P2 tan 92

so that ( 8.16) Thus the current lines are bent in crossing the boundary. If PI < Pl, bent toward toward the P2. they will be bent normal and vice versa.

Plan e Interface Plane 8.3.3. Olstortion Distortion of Potential at a

Consider two homogeneous media oC of resistivities PI Plane Interface and P2 separated by aplane a plane boundary as in Figure . 8.8. ir the current ftow 8.8. Suppose that a current oC of density J¡ ~ is flowing flowing in Clearly if flow is distorted in passing into another, the medium (1) in such a direction as to meet the bound- from a medium of one resistivity into possible to ary ary at an angle 81 to the normal. To determine the equipotentials also will be distorted. It is possible

Resistivity methods

528 528 Medíum{1I Medium {II p, P,

Imllt

Medíum{21 Medium(2J p, p,

e, C,

C',

Semi.transparenl mirror mirror (o) (0)

(h) lb)

Figure image. Figure 8.9. 8.9. Analogy between optical optical and elec/rical electrical ¡mages. images. (a) (a) Oplical Optical image. (b) flec/rical flectrical image. image.

Mcdíum{l, Medium (I) P, PI

Medíum (2) Medium p, p,

-t----.

e,' imaJe C,' imap

{,,¡ h')

- - Equipoltftlials -----Currrnl ---·-Currrni now now Unes lines

Planc Plane boundary

~~-+-+--;4~--+---+ imaae ~~-+-+--;4~--+---+e,' C,' imqt

(6) {hI

Figure between Figure 8.10. Distortion 01 of equipotentials equipotentials ami and current flow lines at a boundary between two P:z/Pr P:z/Pr 0.5. two media 01 of different resistivities. resistivities. (a) (a) Pz/ PI - 3, 3, lek - 0.5. 0.5. (b) Pz/ Pr - 1/J, kle - - 0.5.

... .... 529

Effect Effect of inhomogeneous Bround Braund

determine the potential field field mathematica1ly mathematically by solving Laplace's equation for the appropriate boundary conditions or by integrating it directly. Both methods require considerable mathematics. A much simpler approach employs electrical images, in analogy use of images is valid in with geometrical optics. lbe The use solving solving onIy only a 1imited limited number oC of potential problems, including the plane boundary and the sphere (see Bewley, 1963, Ch. S). Bewley,1963, lbe The analogy between the electrica1 electrical situation and optics is based on the faet fact that current density, like Jight light ray intensity, decreases with the inverse square of distanee distance from a point source in a medium oC of resistivity Pl' PI' separated from an adjacent adjacent medium 1'2 by aplane a plane boundary. In optics the analogous case case would be a point souree source of light in one medium separated from another by a semitransparent mirror, having reflection and transmission coeflicients coefficients k and 1 - k. lben Then the Jight light intensity at a point in the first medium is partly due to the point souree source and partly to its image in the second medium, the latter effect diminished diminished by reflection flection from the mirror. On the other hand, the intensity at a point in tbe the second medium is due only to the souree source in the fint, first, diminished by transmission through the the mirror (Fig. 8.9a). 8.9a). If we replace tbe the point source of light by a point souree source of current and the light intensity at a point by potential, the problem is now in the electrica1 electrical domain. main. From Figure 8.9b we see see that the potential at P in the fint first medium is

boundary underground or the measurement of 01 surface potentials across a vertical vertical contact.

8.3.4. 8.3.4. Surface Potential Due to Horizontal Beds If the current source and potential point are located located on surfaee, surface, abOYe above a horizontal boundary separating two media, the upper resistivity Pl' the lower 1'2, 1'2, the resistivity PI' analysis is more complicated. Because Because of the ground surfaee media, separated by two surface there are now three media, interfaces. As a result there is an infinite set of images aboye above and and below the current electrode, as illustrated in Figure 8.11. The The original image C{, at depth 2z below surface, is reflected reflected in the surface surface boundary to give an image C{' a distance 2z above aboYe Cl . This second image, reflected in the lower el' lower boundand so on. ary, produces a third Cl'" Cl '" at at a depth 4z, and lbe on the potenpotenThe effect of each successive image on reflection coefficient coeflicient tial al at P is reduced by the reflection lhe current source source and and between between the boundaries. For the its lirst tbe potential, is, as in first image below ground, the Equation (8.17),

V' -

IPl(~ +~) 2", '1

The effect of the second image at C{', C{', 2z above aboye ground, is

" X k ) IPI V -IPI -(-k y dQ

2'1l' 2'1!'

((8.17) 8.17) and in the second medium at P' it is

, 1"" I"" (

k)

1 -y- V -4" '3

"" - PI

Pl 1- k PI ",,-I+koorr k - - - ",,-l+k

""+,,.

where k k.d is the reflection coeflicient at the surface surfaee coefficient at boundary. Because PQd is essentially infinite Ibis this coeflicient efficient is unity, and from Equation (8.19),

(1

I

Ip (_+_ 2k) 12k ) V'+y,,=_l V'+V,,=-I 2'1!" 'l 2'1l" '1

( J.18)

Applying the boundary condition of Equation (8.7b), (8.7b), these potentials must be equal at the interface, '1 - '2 '2 - '3' lbus Thus we have face, when 'l

The potential due to the third third image Ct''', C¡''', 4z 4: below ground, will be further reduced, as will that that of its image 4z aboye above ground, hence

V'" Y'" + V

IV

(8.19)

!.

IPl

--

2"

(k- -x k+ '2

_ [PI (2kl) 2"

In Ibis this expression k is a ,eflection coejJicient coefficient whose whose value lies between ± 1, I, depending on the relative relative resistivities in the two media. Figure 8.10 shows the traees traces of equipotential surfaees faces plotted ploued from tbe the relations in Equations (8.17) and (8.18) (8.18) for k - ± A few current flow flow lines are also drawn. This situation corresponds to the practipractical case of resistivity logging with respect to aplane a plane

)

'1 'l

'2

lbe can thus be The resultant total total potential at P can expressed as an infinite series of oC the form V _ 1PI y .. [PI

{~ +

2",

2k + 2k '1'2

2

+ ... + 2k

m

+ ... }

r... ' ... (8.20)

530

Resistivity methods

ec...· ...· Figure Figure 8.11. 8,11. Images Images resulting resulting from two horizontal beds. beds.

l'

-

Toe,

Surface

Modium(1) P,

- --+

- E••

-oL--It---;::;;m-"--"'t-----x

). )'

Figure 8.12. 8.12. Buried conducting sphere in uniform field.

where

r. _

Z (2z)Z) l/Z { r + r1 - {r2 + (2z) Z}l/Z

rz - {r2 {rZ + (4Z)2) 1/l 1/2 Z 1/l 1/2 r", _ {r2 + (2mz)Z) r",{r Z+(2mz)} This series can be written in the compacl compact form

This series is convergent, convergent, because Ikl < 1, whereas the denominator increases TIte number number increases indefinitely. The of temlS terms necessary to get a reasonable answer depends mainly on the value of k and partly on the 01 r, the potential potentiaI differs dift'ers ratio zlr. For a fixed fixed vaIue value of from that ground. The latter that measured over uniform uniform ground. is given by the first term in the bracket of Equation (8.21) potential. The portion portion normalpotential. (8.21) and is caIled called lhe the normal poexpressed by tbe the infinite series is the disturbing potential. When k is positive and approximately unity, increased by a factor lactor the total potentiaI potential al at P may be increased ol2 of 2 or more.

8.3.5. 8.3.5. Potential Due to Buried Sphere (8.21)

A three-dimensíonal lor which the external extemaI three-dimensional body for Figure 8.12 potentiaI potential may be developed is the sphere. Figure sphericaI coordiiIIustrates illustrates this case, in which we use spherical

Effect Effect of inhomogeneous ground

531 Surface

-

--

EquipOI.nlial. Equipotenlial,

Figure 8.13. Equipotentia/s /ines lor Equipotentials ilnd and current flow lines for buried conductive sphere.

nates nates with with the sphere center as origin and the polar axis axis parallel parallel to the Xx axis. axis. Tbe The problem is to find find solutions oC of Laplace's equation for particular boundary ary conditions; conditions; for simplicity simplicity we assume assume the sphere lo to be in a uniform field field Eo parallel to the x axis. axis. This This is equivalent to haviog having the current electrode electrode at considerable distance from from tbe the sphere. sphere. Using Using spherical coordinates and applying applying the boundary boundary conditions of Equation (8.7), (8.7), we we can solve Laplace's equation in the form of a series series 01 of Legendre polynomials polynomials (§2.7.4), (§2.7.4), satisfying satisfying potential relations relations inside and outside the sphere. sphere. For r> a, we we get

(a)3}

(PI - Pz) VI - -Egrcos8 { 1 (PI + 2Pz) r

(8.22)

If tbe the potential is measured measured at tbe the ground surface, surface, the the sphere sphere will will have an image image tbat that will will double the second second termo term. In addition, if we we consider tbe the field field to be generated generated by a current source source el Cl at a distance R from rrom tbe the origin, origin, we we can write

VI

=-

/Pl{

(a)3} reos rcos 8(J

(PI-P2) /Pl{ (Pl-Pl) 1 - 2( 2) 2'1rR P2 rr 2"R PI + P2

--2

(8.23)

As As in Equation (8.21) we we have have two terms, terms, the first first being tbe normal potential, tbe beingthe the second the disturbing potential potential caused by tbe the sphere. sphere. Equipotential and current current ftow flow Iines lines are iIIustrated illustrated in tbe the section section shown in in Figure Figure 8.13. 8.13. Note that we we have have made two assumptions assumptions here Ibat that are not necessarily necessarily valid, valid, lirst first tbat that Ihe the external

or normal field Ihat there is field is uniform and second that no inleraction interaction between the sphere and its ¡mage. image. Both are strictJy strictly troe true only when the sphere is a great distance from both the current current source and surface, in which which case the anomaly eould could not be detected anyway. tbe sphere's way. However, However, if tbe the distance between the center and the surface is not less than tban 1.3.times 1.3. times the tbe radius, radius. tbe the approximation is reasonably good.

8.3.6. Effect Effect of Anisotropic Ground MoSI Most rock masses masses are anything but homogeneous and isotropic in tbe tbey are the electrical sense because they full full oC of fractures. fractures. In particular, particular, shales, slates, and CrequentJy frequently limestones and schists have a definite anisotropic character, especial1y tbe especially with respect to the bedding planes. planes. As an example of this type of anisotropy, consider a point source at the surface of a semiinfinite semünfinite medium in wbich tbe which the resistivity is uniform in the horizontal direction and has the value Ph; PA; in the tbe vertical difl'ervertical direction it is also constant and has a different magnitude Pu. Pu, Pu almost invariably being larger than Ph (§S.2.2c). Proceeding as in Section 8.2.3 with witb modifications to allow allow for the dilference difference between horizontal and vertical vertical directions, we we find find the equipotential surfaces to be ellipsoidal tbe z axis. axis. ellipsoidal and symmetrical about the Mathematica1ly Mathematically tbis this may be expressed by

01 anisotropy. where where )..7\ - (Pv/Ph)1/2 (Pv/Ph)I/2 is the coefficient of This relation is similar to Equation Equation (8.12) with witb

Resistivity methods

532

dI d8

Ellipsoidal Ellipsoidal

bowl bowl

z

FiBure res;stivities FiBure 8.14. Point current source atthe at the surface of anisotropic Bround ground hav;nB havinB resistivities in the horizontal and and vertical vertical directions, respective/y. respectively.

~ and and A,

2i/l replacing r to represent tbe yZ + A2z AZzZit2 the A/(x lZ + yl departure Irom from spherical symmetry. symmetry. lbe P, a distance rl The potential at a surface point P, from tbe the current electrode el' el , will will be Irom

(8.25) (8.25)

that is, is, the potential is equivalent to that for an isotropic medium of resistivity resistivity (PhP.)I/l. (PhPv)It2. lbus Thus it is not possible possible to detect this type 01 of anisotropy from field field measurements. measurements. From Equation (8.25) 8.14 it is obvi(8.25) and Figure 8.14 ous that tbe the resistivity resistivity measured over horizontal beds is larger tban than tbe the actual horizontal resistivity resistivity in tbe the beds, but smaller tban than tbe the vertical vertical resistivity. On tbe the otber other hand, if tbe the beds have a steep dip and tbe the measurement measurement is made witb with a spread perpendicular to strike, the apparent resistivity resistivity will will be smaller tban than the true resistivity resistivity normal to tbe the bedding, just tbe the opposite to tbe the result over horizontal layers; layers; this is moWD paradox al known as tbe the ....paradox of anisotropy" (Dhat(Bhattacharyya Sen, 1981). 1981). If tbe the array is para1lel parallel to taeharyya and Sen, tbe the strite strike al of the dipping beds, tbe the apparent resistivresistivity may be too large, depending on tbe the current-electrode separation. 8.3.7. 8.3.7. Effect of Topography As As mentioned earlier, resistivity resistivity measurements measurements are strongly strongly influenced influenced by local variations in surface conductivity, conductivity, caused by weatbering weathering and moisture content. Rugged Rugged topography will will have a similar eleflect, flow is concentrated or fect, because tbe the current ftow locused focused in valleys valleys and dispersed dispersed or diverged diverged beneath a hill. hill. lbe The equipotential sudaces surfaces are distorted as a result, result, producing fa1se false anomalies anomalies due to the topography alone. alone. Tbis This effect effect may distort or mask mask a real anomaly. anomaly. Fax Fox et al. (1980) (1980) made an analytical study of resistivity with a dipoleresistivity and IP response, response, obtained witb

2-0 terrain feafeadipole array (§8.5.3d) (§8.5.3d) over common 2-D tures; slopes, lbis approach was exslopes, ridges, valleys. valleys. This tended to tbree three dimensions by Holcombe and Jiracek (1984). finite-element nu(1984). In tbe the former report, the finite-element merical merical method was used for modeling, because itit offers matching irregular boundoffers more ftexibility flexibility for matching aries. lO each interior inlerior mesh, aries. Potentials are assigned to based on its boundary geometry and electrical properties, and recomputed by successive successive sweeps through tbrougb tbe tbe residuals become inthe whole section until the tbat at the tbe surface surlace of al significant1y significantly small. lbey They lound found that homogeneous homogeneous ground, resistivity is anomalously low on bilis valJeys and 3-D 3-0 depreshills and ridges, high in valleys sions. finite-element mesh sions. Figure 8.l5a illustrates the finite-element representing a 2-0 8.1Sb shows 2-D ridge, whereas Figure 8.l5b field produced produced by the the distortion ol of a unilorm uniform field ridge. ridge. The terrain effect incceases witb surface relief, rellef, increases with being insignificant for slopes of less than tban 10°. Furthermore the resistivity array tbe effect. eft'ect. array complicates the A double-dipole system straddling a hill produces current focusing higb, whereas a focusing and a cesistivity resistivity high, valley tbe opposite to valley results in a low resistivity, just the ahove. the results al aI. described above. of Fox et al. lbe 01 The response is a1so also sensitive to the direction of tbe tbe anomaly the measuring array; lar for 2-0 2-D structures the is smaller if the spread is parallel, rather ratber than normal, to strike. Analysis 01 type described above aboye of the type allows eartb by allows us to reduce the field field data to a nat earth removing or at least minimizing the terrain anomaly.

8.4. 8.4. EQUIPMENT FOR RESISTIVITY FIELD WORK WORK 8.4.1. 8.4.1. Power Sources lbe makiDg resistivity The necessary components for making lar measurements incIude include a power source, meters for measuring current and vollage comvoltage (which may be c0mbined in one meter to read resistance), electrodes, or low cable, and reels. eitber dc or reels. The power may be either frequency tban 60 Hz. Hz. frequency ac, preferably less than

Equipment for resistivity field work

533 533

(al
-

~ ..c~

CURRENT SOURCE ...,.c.VJ~ \ AT INFINITY "',.....: .-"""'!"_~

EQUlPOTENTIAL EQUIPOTENTIAL SURFACES SURFACES FLOW UNES CURRENT CURRENTFLOW LINES

~ ...

Ie---CURRENT---..j!.--- CURRENT DISPERSION ZONE FOCUSING ZONE (b) (bl

Figure 8.15. Effed Effect of a }-o }-D ridBe ridge on a uniform fie/d. field. (Afler (Af/er Fo]( Fo» el e/ al. 1980.) FiBure 1980.) (a) te terrain ridge. (b) Distortion Distonion of (a) Finite-element mesh used to calcula calculate terrsin effect effect of ridBe. uniform field by by ridBe. ridge.

'Ibe The power souree source is usually a motor generalor generator oC of several several hundred watts or a few few Icilowatts as in IP surveys. Equipment of this type, because 01 of its bulk and weight, weight, is only semiportable; it would not be moved each time the electrodes were shilted. shifted. When de is used, used,one or more storage batteries batteries or occasionally a set of B cells connected in series may be be employed, employed, although such sources are limiled limited lo to small-scale small-scale work, such as overburden or engineering

surveys. To avoid the eft'ects effects 01 of electrolytic polarization caused by unidireetional unidirectional current, the dc de polarity should should be be reversed periodica1ly, periodically. either by hand with a reversing reversing switch, or by a mechanical commutator, relay relay system, or vibrator. 'Ibe The rate 01 of commutation commutation may range from three three or lour four times a minute to 100 . times times per secando second. Altemating Alternating current is also also employed in place ol of commutated (eft'ectively (effectively square-wave) dc. A lowfrequency frequency sine-wave transistor oseillator oscillator with transformer output 01 of a few few watts makes a convenient

portable portable souree. source. Larger power power can be obtained from a motor-driven altemator. alternator. Each 01 of these devices obviously has advantages and limitations. 'Ibe pennits measurement measurement The de souree source permits desirable - but but it also of troe true de resistivity - which is desirable measures spontaneous potentials. This requires that that porous pots be be used as potential electrodes; the SP eft'ect souree is turned lumed on, effect must be noled noted before the source and then subtracted, either directly or by means of 01 a directly or compensating potentiaJ measured compensating voltage, from the potential when eurrent current is ftowing. ftowing. de eliminates elimina tes Tbe The use of ac or rapidly interrupted dc the SP eft'ect. effect. In addition, addition. narrow-band amplifiers tuned to the souree source frequency can be employed to inerease increase the signaJ-to-noise signal-to-noise ratio. However, the resistroe tivity measured wil1 will general1y generally be lower than the true de value. More serious, induetive coupling between inductive coupling wel1 as long current and adjaeent adjacent potential leads, as well ground, may leakage currents, partieularly particularly on wet ground. eft'ects increase with give give erratic readings. A1I All these effects the frequency (§9.4.4c). (§9.4.4c).

Resistivity methods Resistivity

534 534

I I

Power de or lF IF ae ac

1I

&\ .\ R \-

r-0Surraee Surface

c, Figure 8.16. Schemal;c Schematic of equipmenl equipment for measuring measuring resislivity. resistivity. Hand crank Handcrank ec paerator

Mec:hantcal rectifier c:oupled lo ,en. coupled10 IOn,

e, c. Figure Figure 8.17. Portable equipment for mei/suring measuring resislivity resistivity (schematic). (schematic).

8.4.2. 8.4.2. Meters Wjtb With dc or long-period commutated dc de sources, tbe the js measured witb current is with a dc de milliammeter, whose range should be from about 5 to 500 mA, mA, depending on tbe the electrode electrode spread, spread, type of ground, and power used. Potential is normally measured witb with a dc voltmeter of high input impedance (1 MU or ¡reater) greater) and range 10 mV to perhaps 20 V. When ac sources are used, used, ac meten meters are of course necessary. A typical resistivity set witb with voltage and current meters is illustrated schematically schematically in Figure 8.16. 8.16. In js maintained some resistivity equipment tbe the current is constant witb with a regulalOr, regulator, which eliminates tbe the current measurement. An instrument tbat that measures tbe the ratio or of potential to current (tbat (that is, resistance) - usually associated witb with tbe the trade name Megger - has been frequently employed for resistivity work. Originally

developed lor tbis device for testing testing cable insulation, this was easily modified lO to measure ground resistance. dc generator Power is developed by hand cranking a de or magneto; tbe the output is - 100 V and a dc current coi! witb one one side. The The output coil is connected in series with tben then is commutated on tbe the generator shaft and applied to tbe tbe rate rate of 01 reversal, the current electrodes, the being regulated by a governor. The The potential electrodes are connected to a second commutator, synsynchronized with tbe rectiftes the tbe ac pothe otber, other, which rectifies p0tential and applies it lo potenlial coil. The The latter to the potential is mounted witb coi! in such a way as to with the current coil V/l. make the needle deftection lo V deflection proportional to /1. This instrument is shown schematically in Figure 8.17. Several otber other all-in-one ail-in-one resistivity instruments are also available, available, employing a vibrator powered by dry cells or low-lrequency low-frequency transistor oscillator. Such devices, have low power power vices. like the Megger, necessarily have output. Furthermore, with some some electrode spreads. specads,

flectrode Electrode layout5 layouts and field procedure

535 535

tbe the combination 01 of power source and botb both meters in one one box may be a definite definite disadvantage. However, However, sucb such instruments are compact and completely portable. portable.

8.4.3. Electrodes and Wire Witb With ac power sources, sources, a1l all the electrodes may be steel, aluminum, or brass; stainless steel is probably best best Cor for combined strength and resistance to corrosion. sion. Metal electrodes should be at least ~ m long so tbey they can be driven into the ground several several centimeters ters Cor for good electrical electrical contact. In very dry surCaces surfaces this this contact may be improved by watering the elecelectrodes. If IC dc de power is used used the polenlial potential e1eclrodes electrodes should should be porous pots as in SP work. work. Connecting Connecting wires, wires, whicb which must be insulaled insulated and as lighl light as possible, possible, are wound on portable portable reels. reels. Plastic insulation insulation is more durable than rubber against abrasion sion and moisture; however, however, some plastics deteriorale rate in cold weather and animals seem to find find them very very tasty in any season. season.

8.5. ELECTRO DE LAYOUTS AND ELECTRODE AND FlEto FIELD PROCEDURE

where witb the tbe electrode where the parameter p has to do with geometry. By measuring ~V and 1I and knowing the electrode configuration, we obtain a resistivity p. Over bomogeneous lhis resistivity homogeneous isotropic ground ground this will will be constant Cor for any current and electrode arrangement. Ir the ground is inhomogeneous, however. however, and the If electrode spacing is varied, or the spacing remains fixed fixed while while the whole array is moved, then the ratio wiU, will, in general, change. This results in a different value oC of P p for each measurement. The magnitude is intimately related to the arrangement of oI electrodes. apparent This measured quantity is known as the apparent resiSlivi~y, lo some sorne resistioity; Po, Po' Although it is diagnostic, to extent, oC of the actual resistivity oI of a zone in the vicinity oC resistivof the electrode array, Ihe the apparent resistivity is definitely not an average value and only in the case oC of homogeneous grounds is it equal to the actual resistivity. resistivity. Cound in the Another term that is Crequently frequently found literature is the so-called surface resislivity. This is surface resistivity. e1ectrode spacthe value oC of Po obtained with small electrode ing. ing. Obviously it is equal to the true surface resistivity only when the ground is uniCorm uniform over a volume roughly oC of the dimensions oC of lhe the electrode separation. tion.

~\

,,, :¡l'

il

!

8.5.1. General An An enormous number of electrode spreads have been used used in resistivity resistivity al at various times; times; not more than a balC balf dOleo dozen have surVÍved survived to any extent. In principIe principle it is not necessary necessary to use a collinear array. Practically, cally, however, however, the electrodes are almost always always in line; line; otherwise otherwise interpretation oC of resuIts results becomes difficuIt difficult and the field field work is complicaled. complicated. One drawback in resistivity resistivity work is the practical difficulty of moving moving stakes with great lengths of wire attached, attached, a slow slow and expensive expensive task in relation lo to magnetics, EM, EM, and sorne some other electrical survey methods. Thus it is an advantage to use electrode spreads spreads that may require only one or two electrodes to to be moved, moved, and these these at close spacing where where possible. ble.

8.5.2. Apparent Resistivity Resistivity Before discussing discussing the various electrode spreads, it is necessary to consider what is actually measured by an an array oC of current and potential electrodes. We can rearrange rearrange tbe the terms in Equation (8.13) (8.13) to obtain 217'~V

p---

1

1

{(1/r1

217'~V) ... ( - ¡ - P

-

1/r2) - (l/r] - 1/r4)}

(8.26)

8.5.3. 8.5.3. Electrode Arrays (Spreads) (a) commonly used (a) Wenner array. array. The most commonly point-electrode systems are ilIuslrated 8.18. illustrated in Figure 8.18. The first first two examples, the Wenner and Schlumberger arrays, were formerly mosl develmost popular; since the development oC (§9.5.1) in IP of the pseudodepth section (§9.5.1) work, the double-dipole configuration has become equally so. In the Wenner spread (Fig. 8.18a) !he the electrodes r1 = r4 = = Qa are uniCormly uniformly spaced in a lineo line. Setting rl and r2 - r]r3 - 2a, in Equation (8.26), apparenl (8.26). !he the apparent resistivity becomes

Po -

217'a 2'ITQ !:J.V/l !:J.V/I

(8.27)

In spile spite oC of the simple geometry. this arrangement work, and has is often quite inconvenient Cor for field field work. oC view view sorne point of some disadvantages from a theoretical theoretical point as well. Ihe Wenner well. For depth exploration using the spread, the electrodes are expanded about a fixed fixed center, increasing the spacing aQ in steps. For lateral exploration or mapping, Ihe the spacing remains constant and all Cour four electrodes are moved along the line, then along another line, and so on. In mapping, the apparent resistivity for each array array position is plotted against Ihe the center oC of !he the spread.

I

j ¡l j

i

536 536

Resistivity methods

t-'T'T'--i

c.

p.

P,

C.

lo)

Jt----1~--------1'P,1V,,:j J;, '\~ ~, ~'=1 .~-----. k·--=;-----· l --------------..;c.'1

------LL - - - _:L.

u

c., C-

(b) lb)

t:

P, 1',

C. C,

C.

1'.

(t) (t)

£1.. . ------24. l1 24- -

c. c, c. c.

{'r 1:-*-

I)--------l'\... 1)

(d) Id)

Figure (e) PolePo/eFigure 8.18. E/eetrode Electrode arrays arrays in eommon common use. use. (a) Wenner. Wenner. (b) 5chlumberger. (c) dipole. (d) Doub/e-dipo/e. Double-dipole.

(b) Schlumberger (gradient) arfay. array. For the the Schlumberger array the current electrodes are spaced much lurtber further apart than the potential electrodes. Prom From Figures Figures 8.3 and 8.18b, 8.l8b, we find that

'I-(L-x)-I '2-(L+x)+1 ,,-(L-x)+1 '4-(L+x)-( Substituting these these values in Equatioo Equation (8.26), we get

2tr.1V [{ 1 1} I I } P·-r - (L-x)-'-(L+x)+1

{ 1

1]-1 ]-1

I

I

(8.28)

If the smallest current-potential c:urrent-potential electrode distance is always considerably greater thanthe than the distance between tween the two potential electrodes (by a factor 01 of 10 or more), then (L - x) ::. 31 and we have to the fint first ~proximatioo ~proximation 22

2)2

tr (L -- X2)1 X (( .1V) P. • U (L2 + Xl) x2)

T

n

Po ....

.. trL2 (( .1V) .1V) .. "L2 U 21 r I

(8.29a)

(8.29b) (8.29b)

Altemate Alternate symbols lor for !he the Schlumberger array are literalure; for lor example, A, lrequently frequently lound found in the literature; B, M, and N are used for B, lor C el' and P12 , I• C;, PI' and respectivelYi tMN. respectively; in this case L -lAB, 1- !MN. In vertical sounding (§8.S.4b) !he eleethe potential electrodes remain the current-electrode spacremain fixed while the ing is expanded symmetrica11y 01 symmetrically about the center of the spread. Por 01 L it lt may be be necessary For large values of lo I also in order to lo maintain a measurable to increase 1 TbiJ polcntial. potential. Equation (8.29a) applies in this case. This procedure is more convement convenient than the Wenner expanding spread because only ooly two electrodes e1ectrodes need move. ID elreet of ol shallow resistivity resistivity In additioD. addition, the effect variatioos flxed potential electrodes. e1ectrodes. variations is CODStant constant with with fixed Figures 8.42 and 8.44 illustrate vertical sounding results. Lateral profiling (§8.S.4c) may may be done done in two ways. With a very large fixed separation separatioo of ol the or more), the the potential pair current electrodes (300 m or flxed spacing, is moved between them, them, also with fixed subject lo to the limitation (L - x) ::. 3( [Eq. (8.29a»). Apparent resistivity is plotted against the midpoint ol of the potential electrodes.

-lAB.

and

- { (L-X)+I-(L+X)-I)

Tbis is. xx-O, This array is olten often used symmetrically, that is, - 0, in whieh which ease case

Eleetrode Electrode layouts and field proeedure procedure

1:

I¡!¡ 11 1.1

537

The otber other layout is similar to tbe the Wenner in tbat that tbe the electrode spaciDg spacing remains fixed fixed (L » () t) and tbe the wbole whole array is moved along tbe the line in suitable steps. Tbis This arrangement is less convenient tban than tbe the first because it requires tbat that all lour four electrodes be moved for each station. station. In lateral profiling with the Sch1umberger Schlumberger array (and with tbe the pole-dipole array; array; see next section) it is permissible to measure potential somewbat somewhat 011' the line between flxed flxed current electrodes, tbat that is, to map tbe the surface in two dimensions (because el C1 and <; are are far apart, tbe the current density is roughly uniform over a considerable lateral extent). (e) (c) Pole-dipole (three-point) array. array. One ol of tbe the current electrodes electrodes is fixed at a great distance from tbe the otber other tbree, three, all ol of wbich which can have various spacings. ings. !be The values in Equation (8.26) are now

so tbat that Po _ ti o

2'11'ab 2"ab ( 4V) b- a 1

(8.30a)

Wben When b - 2a tbis this becomes

4"a( 4;) 4;)

P Po.. -_ 4'11'a(

12

..o

1

ay) av) aa aa

( 8.30e) 8.3Oc)

Tbis This arrangement is equivaIent equivalent to a half-Schlumberger array. Equation (8.JOe) (8.3Oc) is similar to Equation Ba - 4" 4r, tbat that is, is. botb both electrode (8.34) witb with a - L, aa (8.34) configurations measure potential gradien!. gradient. Because tbe the electrode <; is remote, it is not necessary to have it in line witb with tbe the otber other tbree. three. lbis This permits lateral exploration on radiaI radial lines from a fixedposition both potential fixed position of C el'1• by moving one or botb electrodes, a particularly conveDÍent convenient method for resistivity mapping in the vicinity 01 of a conductor of Iimited limited exten!. extent. lbis This electrode arrangement is etreceffectively tively tbe the same as the laleral lateral spread spread used in well logging, logging, described in Section 11.2.3. lt It is also similar to lbe the mise-a-Ia-masse mise-d-Io-masse metbod method (§8.S.4d) (§8.S.4d) in wbich which tbe the electrode C1 is in contact witb with tbe the conducting zone.

el

(d) Double-dipole (dipole-dipole) system. system. !be The potential electrodes are c10sely spaced and and remote remote closely spaced from the aIso close the current eleclrodes, electrodes, which are also togetber. together. In this case, from Figure S.18d and Equation (8.26) we get

211t 211( r2- U (n-1) (n - l)

(8.JOb) (8.30b)

or double the ratio in the Wenner array (Eq. (8.27»). When the potential spacing is very small compared to the distance ol C1 of eitber either potential electrode from el (<; Bo/2, '3 (<; still at 00), we write rlr1 - a - 80/2. r3 - a + 8a/2, and tbe the apparent resistivity becomes Po .. 2'11'0 2"0 (

A furtber further variation on on the pole-dipole array is of the tbe potential electrodes. electrodes, obtained by moving one of aIso remote remote from say 1'2' to a distant point, which is also <;. as well. well, and and Equation <;. In Ibis this case, '3 r3 - b - 00 as (8.30a) is tbe tbe Wenner the same as Equation (8.27) for the half- Welllle, spread, hence tbis k.nown as the tbe half-Wellller this array is known array. one array. Although AlthOUgh it is only necessary to move one potential electrode, lo the tbe electrode, the long connecting wire to otber other is a disadvantage. In field field work tbe the loeation location of an electrode at infinity requires lbat liule influence on that it have very little instance, when using a the rest of the array. For instance. Wenner spread, spread. the remote remote electrode or electrodes must be at least 10 times the tbe spacing to reduce the etrect tbe Schlumberger system, effect to 10~ or less. Witb With the because tbe togetber, the potential electrodes are close together, the far current electrode need need only only be about three three times as far away as tbe tbe same the one nearby to get the resulto result. However, because the subsurface resistivity may vary laterally, tbese these spacing estimates can be much by a factor of too low and may have to be increased by lOor resistivity contrast. contras!. 10 or more, depending on the resistivity

r1 -- '. r. -'1

'] 11 » 1 r3 - U( n + 1) where II» Then, dropping the minus, minus, P 1) (4V/l Po.. -- 2'11'(11 - I)II(n + l)t4V/l

(S.31)

S or less, tbis tbe spread commonly When 11II is 5 this is the between used in IP work (§9.4.J). (§9.4.3). Inductive coupling between potential and tbis and current cables cables is reduced with this arrangement. When the dipoles are widely separated. separated, n» 1 and we have (S.32) tbis usually applied in resistivthis is tbe the approximation usually ¡ty aIso be placed p]aced broadity surveys. !be The dipo]es dipoles may also side, bisected by tbe lineo In this case, the traverse traverse line. 1/2 2) f/2 .. 2nt(1 2n( 1 + 1/2n 1/2112)

'2 '3 -- 2{ (II()2 + (1 r2 = ='3 2{(nt)2 t2}

..

and (8.J3) (8.33)

Res;stivity methods Resistivity

538

In a11 above e1ectrode electrode layouts the potential all the aboye and current electrodes may be intercbanged. interchanged. By By the principIe principle ol of reciprocity, reciprocity, the apparent resistivity resistivity sbould should be tbe the same in eitber either case. case. Tbe The switching switching ol of current and potential electrodes electrodes could be desirable, desirable, Cor for instance, in using high voltages voltages witb with large spreads in Schlumberger Schlumberger and, possibly, possibly, Wenner layouts.

8.5.4. 8.5.4. Resistivity Resistivity Field Field Procedures (a) Introduction. Regardless Regardless of the specific specific elecelectrode spread employed, employed, tbere there are really really only two basic procedures procedures in resistivity resistivity work. work. Tbe The particular procedure to be used used depends on whetber whether one is interested in resistivity resistivity variations with deptb depth or with lateral extent. extent. Tbe The first first is called vertical, electric, or verrical-electric vertical-electric (VES) sounding, the second second lateral or mapping. profiling profilingor mapping. (b) Vertical Vertical sounding. Because Because the lraction fraction ol of total current that flows flows at deptb depth varies with the currentelectrode electrode separation, as described described in §8.2.5, §8.2.5, the field field procedure procedure is to use a fixed fixed center with an expanding spread. spread. Although the pole-dipole pole-dipole array is not suited to tbis this technique, technique, any oC of the other tbree three configuraconfigurations may be used, the Schlumberger Sch1umberger having having the advantages advantages mentioned in Section Section 8.5.3b. 8.5.3b. Tbe The presence ence ol of horizontal or gentIy gently dipping beds of different resistivities is best detected by the expanding spread. Rence Hence the method is oseful useful in determining depth oC of overburden, depth, structure, and resistivity resistivity of flat-lying sedimentary beds and possibly possibly of the basement also iC if it is not too deep. It is frequently frequently necessary necessary to carry out tlús this expansion procedure at several several locations in an area, even even when when the main interest may be in lateral exploration, to establish proper electrode spacings spacings Cor for the lateral search. search. (e) (c) Lateral Lateral profiling. Tbis This method is particularly uselul useful in mineral exploration, where where the detection of isolated isolated bodies ol of anomaloos anomalous resistivity resistivity is required. required. Any of the electrode arrangements described in SecSection 8.5.3 8.5.3 may be used, used, tbe the selection selection depending mainly field situation. In Wenner, mainly on the field Schlumberger, and pole-dipole pole-dipole surveys surveys the apparent resistivity midpoint oC of tbe the potential resistivity is plotted at the midpoinl electrodes, electrodes, except where one of tbese these is effectively at infinity, infinity, as in tbe the modified modified three-probe system, system, when tbe the station is reckoned at tbe the near potential elecelectrode. trode. Por For tbe the double-dipole, double-dipole, tbe the station is at tbe the array midpoint. Wben electrodes are closely closely spaced When the potential electrodes with respect respect 10 to tbe the current spread, as in the Sch1umberger and possibly tbe the tbree-point three-point system, system, the measurement measurement is effectively ol of potential gradient

at the midpoint. Tbis This can be seen from Equation (8.29b) (8.29b) where, where, putting 21- !J.r, we can write

=

."L2

Po P"

II

(!J.V) Ar

(8.34)

If the currenl logether and recurrent eleclrodes electrodes are close together mote from tbe measuremenl is the potential pair, the measurement ol the field field or the tbe essentially that oC of the curvature curvature of second derivative. double-dipole spread in derivative. Por For the double-dipole Figure 8.18d, 8.18d, tbe the polential potential gradient at the midpoint ol P2 due lo !J.YíI!J.r, where !J.r is the Ibe PIP2 to el C1 only is !J.YiI!J.r, of PI spacing ol tbe of the potential potential electrodes. Similarly the potential gradient due to <; only is AVz/Ar. Then Tben tbe tbe limit the measured potential gradient becomes, in the as Ar - 0,

or, (8.35) (8.35) r. -- "r, r2 -- r - Ar, and r3 Also, witb with r11 -- '. Also, '3 -- r, +

!J.r, we obtain from Equation (8.13),

IpQ 1 Ip"(( !J.V-- -1- - - -1 + -1) 2'IT' r - !J.r !J.r 2'lT r r + !J.r r,

¡Po Ip" (!J.r)l (!J.r)2 .---." r ."

,33

using tbe Tbis the second approximation (Eq. (A.44». This gives gives

Lateral exploration by resistivity measurements is best suited 10 to detection ol of steeply dipping contacts and dikes oC tbat is, 2-D of contrasting resistivity, that 01 anomalies, extent for location of anomalies, and to a lesser extent anomalous 3-D conductors conductors such as could be roughly simutated simulated by tbe the spbere. sphere. (d) Mise-a-Ia-masse. Tbis tbe This is a variation on the three-point electrode system, used where wbere some part of tbe the conductive zone is already located and exposed, eitber Tbe near either as outcrop or in a drill hole. The current electrode is embedded in the tbe zone itself, itseU, the tbe Tbc otber other being a large distance away on surface. The

Interpretation

539

Figure 8.19. by a 8.19. Distortion Distortion of the equipotentials around the near near current electrode electrode by dipping conductor when using the mise-J-Ia-masse mise-s-le-mssse method.

pOlential potential electrodes are moved about, either either on surface face or in drin drill holes. The extent, dip, strike, and continuity of the zone will be better indicated by introducing tbe the current directly into it tban than by tbe the usual usual mapping techniques. The etrect effect oC of a dipping mineralized zone on the . equipotentials is shown in Figure 8.19. 8.19. Because the second second current electrode is at infinity, it is possible to map tbe the potentials in all directions around tbe the zone zone witbout without shifting tbe the current stakes.

8.6. INTERPRETA TlON INTERPRETATION 8.6.1. Introduction Tbe The mathematical analysis lor for quantitative interpretation ration 01 of resistivity results is most highly developed for for tbe the vertical sounding technique, rea50nably reasonably so lor of steep for lateral profiling over large-scale contacts 01 dip, dip, and least uselul useful Cor for tbe the detection 01 of 3-0 anomatieso ties. As in otber other geophysical metbods methods where quantitative tative interpretation is possible, tbe the assessment of results results should progress from rough preliminary estimates mates made in tbe the field field toward more sophisticated methods methods of interpretation, eventually based on the complete survey. Such a procedure keeps the field field work work up-to-date, controls tbe the day-by-day program, program, and and indicates where more intensive work is warranted, ranted, both in the field field survey and its inlerpretation. interpretation. Van Van Nostrand and Cook (1966) (1966) give a very extensive bibliography bibliography oC of resistivity interpretation techniques.

8.6.2. 8.6.2. Resistivity Modeling The use oC not as common in of models, although not resistivity as in EM, can be a useful aid in interpretation. Resistivity modeling is generally done in a water tank, Ihe liquid being being varied the resistivity of the liquid by the addition oC of salts such as NaCI or acids such of liquid, as H 2 S04' Sand may be used instead of provided reproducible contacts between the tbe model electrodes and the surface surface can be made. Various conducting or insulating in5ulating sheets, cylinders, and blocks are immersed in the tank to simulate Ihe the field field situation. The electrode spread is moved about lalerally mounl on the laterally in a convenient jig mount liquid medium, surface ol of tbe the tank; alternatively, in a liquid tbe past the tbe electrode the model anomaly may be moved past spread. Scaling is not a problem in resistivity model work resistivity is !J.VI' !J.VIl a: a: (§7.7.1b). (§7.7.1b). The usual relation in resistivity pll, than vary the pII, where I is scaled linearly. Rather than resistivily resistivity p, it is simpler to change ~V or l. I. However, somewhat could convesomewhat higher frequencies could niently be used in Ihe than in the field field without the model than introducing errors.

8.6.3. Vertical sounding; Two Horizontal Beds (a) Basic formula. The melhod oI images develmethod of oped in Section 8.3.4 is useful in dealing with soundprofiling ings on IWo two horizontal layers. layers. as well as profiling

Res;st;v;ty Resistivity methods

540

elementary 2-D struclures. structures. Its applicalion application lo to the over elemenlary former also provides sorne some simple ilIustrations illustrations 01 of lormer limiting cases 01 of the bed paramelers. parameters. IimitiDg the potential 01 of a single single Equation (8.21) relates the to the resistivity of the upper layer in terms electrode lo the e1ectrode electrode spacing, the depth to the interface, of the CODtrast between the two beds. beds. We and the resistivity contrast want this expression in the form of an apparent four-elecresistivity, which would be measured by a four-elec8.3 and trode system. Using the symbols of Figure 8.3 (8.19), (8.21), (8.21), and (8.26) Equation (8.13), Equations (8.19), us to write, write. for the measured potential differdifferenable U5 PI and P2 , ence between P1

+2

Ek"'{ (,f + 4m1 z

2 2

",-1

1/2

so that the apparent resistivity is

4k'"

ao CO

+ E

P" P. -- PI 1I [

+ 4D",) 4Dw )

- PI(l Pl(l

2

2) + 4 E k'" kIll

4k'" 4k'"

00

",-1

{4 + (2mz/ai) (2mz/ai}

",-1

XCL-n{l XCL-t>{l +(2~)2/(L_()2}1/2

(2~)' (2~)'/(L +I)'J." 1)') '" )]

() (1 + - (L + (j(. (8.37)

IPIU

- tr(L2 _

(L +

~

-(-- J

E {1+ (2mz) 2/(L ~ 00

2}1/2

() 2}1/2 kIll

- ( -t-- J"'~1 {I + (2mz)2/(L + t)2}1/2

]

- ( 1 + 41>.) -(1 4D.) 2f1'a 2tra w

1+

",-1

L -

IPI lPJ

[

km kIll

1/2

1/2

(2)

I( L +

00 X

00 - E

ao llD

L + 1t

L - 1t

2"

8.18a). Equation (8.37) is simplilied simplified to - 2a (Fig. 8.18a),

{I {1 + (2mz/a)2)

(8.38)

IP1 [( AV - -lPI AV -- - --

give

4k'"

]

(e) (e) Schlumberger spread. spread. When x-O, x - 0, '1 rl - '4 r4 L - 1, t, '2r2 - ')r3 - L + 1t (Fig. 8.18b), U8b), and and the potenpotential is

)

spread. Because rl - '4 r4 - a, a. '2 r2 - '] r3 (b) Wenner spread. Because'l

Ipl [00 lPl A V - - 1+ E 2tra ",-1 2f1'a

}

4k'"

ao co

(,l + 4m 2z 2 ) 1/2

4~2z2)1/2 }]

22 1/2

- ",-1 E + (2mz/a) 2 }1/2 ",-I {4 (4 (2mzla)

1

+ (,i +

{l {I + (2mz/a)

",-1

L:t> (. (, the terms terms inside inside the square brackets When t:» be simplified; simplilied; the potential difference then then bebecan be comes

where

Dw - f k"'[ {I D 1 1/2 {1 + (2mz/a)2)

2t[

P1 AV ... -l - 2 1

fl'L

w-

...-1 ",-1

- (4 +

(2~/a)2)

fl'L

1/2 1/2]]

P. - 2trAVp/1 2f1'AVp/l - 2trAV/I(I/a 2trAV/l(l/a - 1/2a - 1/2a + 1/0) l/o) - 2traAV/I 2f1'aAV/l

+2

"" E ",-1

IPJU .. - (21

From Prom Equation (8.26) we have

]

k'" 1/2 {1 + (2mz/L)2}

+ 2D.') •

where llD 00

D' ,

kIll k'"

3/2 E 3/2 ",-1 {I + (2mz/L)2) ",-I

1

Interpretation

541 541

The exact exact expression expression for for apparent resistivity resistivity is The PG

..

PI [1 +

0

(L;

(8.40a) (8.40a) k'"

00

xL.

{I + (2mz)2/(L -

",-I

-(

L~

X

- PI(I

The The apparent resistivity is is given given by by

t)2f /2

0

"'~I {I + (2mZ)2~:

where (1 + Ddd )) is the Ihe expression expression inside inside the the large large square square brackets above. aboye. If we make nn » I, 1, the the preceding result resull is simplisimplified Red and and we can can make make use use of oC Equation (8.21). DifDifferentiating Cerentiating twice. twice,

a2v L + 1)2fl2 ]

+ D.)

[DO

¡PI

Q

k'" km

L {1 + (2mz/r) 2} 3/2 ",-1

"r2 - _,3 1 "

(8.39a)

00

I:

+3

where

",-1

E

( L + '\ f'¡ km D _ (L k'" J ",-1 {1 + (2mz)2/(L • 1 {I (2mz}2/(L - t)2f/2 I

/

_(~f'¡ _(~'\

f

1/ - J ",-1

{1 + (2mz)2/(L (2mz)1/(L + t)2(2 {I

L.00... ",-1 ",-1

I +2 Pd"pl1+2L PG"PI

[

[

Pl(1 - PI(I

k'"

3

+ 2D;).

I

Po ,.. PI 1 [

(8.39b)

lbis result result can also be obtained by differentiating dilferentiating This Equation (8.21) with respeet respect lo to r, multiplying the result by 2 (because (because there are two current electrodes), electrodes). get P , and applying Equation (8.34) to gel Po' G (d) Oouble-dipole Double-dipole spread. spread. Because '1 q -- r4 - 2n/, 2nl. '2'" 2(n 2(n - 1)/, 1)(, '] '3 .. 2(n 2(n + 1)/ 1)1 (Fig. 8.18d), 8.18d). the exact expression for the pOlential potential is

IPJ IPI 2'IT(n -l)n(n + 1)/ 1)(

I: ",-1

L ",-1

PI(l - Pl(l

XL xL.

km k'"

xI: L [ 1}1}2))1/2 12 ",-1 [11 + (2mz)2/{2(n + 1)/}2 I

",-1

-2(n - l)(n X x

II> ...

L L.

",-1

+ 1) k'" km

{1 {I + (2mz/2nt)2}

] (8.40b)

(1 + 2f k"' km))

(8.41)

",-1

+n(n - 1) 1) ce 00

k"

(e) Discussion Oiscussion of theoretical rheorerical results. resulrs. Quantitatively we can see how the the apparent resistivity varies varíes from Equation (8.38) through (8.40) for lrom lor the different electrode spreads. When the tbe electrode spacing is very r-e: z, the series small, that is, r« series terms terms in all cases tend to zero, zero. so that we measure !he the resistivity in the This is the surface resistivity deupper formation. Tbis fined in Section 8.5.2. Rned the reftection reflection coefficient is less than Because tbe tban unity, when the e C- P electrode spacing is very wben very large coms, the deptb depth of of the bed, pared to z, bed, the tbe series expansions in all of the equations becomes the tbe same (beor 2): cause the denominators ... 1 or

Po ... ... PI PI

",-1 [1 [1 + (2mz)2/{2(n - 1)/}2r/2 I)I}2r/2

X

3/2

{1 + (2mz/, )2) 512

D,;) + D';)

X[1+n(n+1) x[1+n(n+1) k'"

{I + (2mz/r)2)

OIl

+3

]

{I (1 + (2mz/L}2} (2mz/L)2} 3/2 /2

... II>

k'"

00

km k'"

Approximately, we have

6V 6V _ _

and using using Equation (8.36),

-

1] 1/2

1. the summation term is an infinite Because k 2 < 1, geometric progression with the value 00

L. L

k'" -.. 1/(1 - k) k} - 1 1 km

",-1

(Pz - PI)/(P2 + PI)' we get P/I PG .- . Substituting k .. (Pz Thus at very large spacing, spacing. the apparent resistivPz. Tbus practically equal to tbe the resistivity in the lower ity is practicaJly lormation. formation.

Resistivity methods

542 542 C,

2t Cl

t=Lr=i SURFACE !i

P, Pl

PI

L,..

t

p¡ Pz

3OOr300

_

=

k = -0.5, P¡/PI PZ/PI = 1/3, 1/3. PI PI = 300 nm k =O,S,P¡/PI =0.5.Pl/pt =3,PI = 100nm

= : = 100 m

~

e

-e

200 a 200 ~

I ooILo_---l._L_...L........ ....l......~::!:[::r:::._..L.....J_ 100 10 60 200

_.JL::l::S.......__Ll..L._..L.....J_ 400

600 600 800 1000

2000 2000

L(m) LIm)

Figure 8.20. Po versus /wo horizontal beds fo, 8,20, Plo/s Plots of p, versus L over two for a Schlumberger expanding spread. Curves were calculated from fquation Equation (8.39b). (8.39b). spread. Curves

When the lower bed is an insulator, Pz P2 - 00 and k-l. k - 1. 111en Then the apparent resistivity increases indefinitely with electrode spacing, as is obvious from (8,41). Because Because all the current will will ftow flow in Equation (8.41). the upper hed, bed, it is possible to determine the value oC of P. when Pz P2 - 00 by calculating the electric field field at the midpoint ol of the current electrodes. Because Because their separation is much larger than the thickness ol of the upper bed, it is reasonable to assume a uniform current density from top lo to botlom. bottom. 111en Then the current from either electrode is Cound found by integrating over a cylindrical equipotential surface ol of radius r and height z. z, 111us, Thus, heigbt

1121'1

1- o o0 Jrdl 0~"1· Ird9 dz - 2ftrzJ 2"rzJ 6

From Equation (8.1) we we have in this this case (noting that the current is doubled because there are two current electrodes) E - 2P 2p11 p111"rz l J - Pll/ftrz For the Wenner array, We we get an apparent resistivity [Eq. (8.27)] [Eq. (8.27)] 2fta 2fTQ ~V

2ft'a 2fTa

~ - -- - -

•

11

1

/2.Edr - (-2ap¡- ) ln2 i"

1" 1 .

__l.39( 1.39( a;1) a;1)

2QPt ) z

(8.42a)

For the Schlumberger SchIumberger layout, using Equation (8.34) (8.34) with L - r, we get fTL2 sv LPt P,----• 1 ar z

(8.42b)

and Cor for tbe the double-dipole system, Equation (8.36) gives gives

(8.42c) where r is tbe oC the the curthe distance between between centers of rent and potential dipoles. In all tbree three spreads we have

p,,/ p.IPl P1

-

c( electrode spacing/ deptb to interface) interface) spacing!depth (8.42d)

where tbe witb the tbe type of of spread. the constant ec varíes varies with Thus il if we plot P,,/Pl p.lp1 versus alz, Liz, or rlz 111us a/z, L/z, r/z under these conditions, tbe straigbt line. the curve is a straight On tbe bed is a very very good the otber other band, hand, iC if tbe the lower bed conductor, 1'2 In this case P• .. P2 .. O 0 and k.. -1. In Pz P2 .. Olor 0 for large spacing. (f) Crude interpretation. Belore applying the tbe more interpretation, Before complicated metbods lo methods ol of interpretation it is useful to consider a lew Figure 8.20 shows a pair few rougb rough ideas. Figure ol witb contrasts of ol 3 of resistivity curves for two layers with and ~. 111e Cm The upper bed resistivity is 100 and 300 Om Cor on the tbe same for tbe the two cases (to put put tbe the two curves on ordinate scale), and the thickness is 100 m. 111e asymptotic to The curve lor for 1'2/ P21Pl PI - t is clearly asymptotic Pl and large spacing, P1 and 1'2 P2 at tbe the limits ol of small and and its point oC slepe is approximately at of maximum maximum slope 100 m. tbe depth and and the tbe m. 111us Thus we can estimate the resistivities 01 lor this simple example. of tbe the two beds for 111e The otber other curve gives tbe the upper layer resistivity at small spacing, but clear what what the value of ol but it is not not so clear P2 may be. If the spacing were increased increased to several kilometers, it would be asymptotic to 300 Om. am. The

Interpretation tmetpretetion

543 543 IO'r----,---,---¡------,----,----;--, IO'r----,---,----y-----,----,----.--,

IO'f----+----+---f---+--,Yf~~:::.......¡ IO'f----+-----t---+----j---75-"f-7""=:-l

10r-----+------t---+--~r;.o'I"7"''''''--+--,-----,~

1O.'t----+---f---+----\'I~c_t---+----I 1O-1r-----+----t---+----\'I~c-+---+----1

1O .• t-----+---j---+-+t~t----+~::-:-__i IO-'f----+----j---+--+t~t__---+~::-:-___i

al: 10-'

10-'

figure 8.21. and 8.21. Wenner Wenner spread - master curves for two horizontal beds. (From Kelfer Keller and frischknechr, frischknecht, 1966.) 1966.)

point point of inflexion is not at 100 rn m but at a larger spacing. Approxirnately Approximately tben, then, we can get sorne some idea of the unknown parameters PI and Pz Pz and z from the fie)d field curve, provided tbe the resistivity contrast is not too great and particularly if tbe the lower bed is the more conductive of the two. two. (8) (8) Curve Curve matching. A much more accurate and dependable dependable metbod method of interpretation in e)ectric electric sounding sounding invo)ves involves the cornparison comparison ol of field field profiles with characteristic curves. It is quite similar to tbe the interpretatioo interpretation Crom from master curves in magnetote)magnetotellurics, described in Section 6.2.8b. 6.2.8b. The master curves are prepared with dimensionless coordinates. Equations (8.38) (8.38) to (8.40) can be put in tbis this form by dividing Pd Pa by PI' PI' The ralios ratios P./PI Pa/PI are then p)otted plotted agaínst against a/z, L/z. Liz, or r/z. r/s, Ibat that is. is, tbe the electrode electrode spacing divided by tbe the deptb depth ol of tbe the upper bed lor for whatever electrode system is used. The The curves curves are on logarithmic paper, usually USUally six decades each way to provide a large range ol of both both ratios ratios on one sheet. Thus we are plotting (log Pda -log z). If we make PI logPI) agaínst against (log a - log lop). PI - 1 Om Om and z - 1 km. km, all tbe the characteristic curves are preserved in sbape. shape. The sets of curves are constructed structed either for various values oC of k between ±1 oc or for various ratios oC of Pl/ P21PI between O 0 and + oo. 00. A typical set oC of curves is shown in Figure 8.21. 8.21. The cbaracteristic characteristic curves are generally drawn drawn on a transparency. transparency. To match a lield field result it is only neces-

sary to slide tbe tbe field the master sheet around on the or less with witb profile until the latter coincides more or one oC of the master curves (or can be interpolated between adjacent master curves). The The respective respective cocoo ordinate axes must be kept parallel. The The point where Pd/PI sheet then then deterPalPI = a/z a/« = 1 on tbe the master sheet mines the values of PI and z on the field lield curve curve axes, axes. of k and while the actual curve curve tit fit gives the value of hence P2' (h) Interpretation byasymptotes. tbe event event that by asymptotes. In the the lower bed has very large resistivity we saw in twOoIayer curve Section 8.6.3e tbat that tbe the cbaracteristic characteristic two-layer becomes a straight line Cor for large electrode spacing. lo slope of oC 45° 45° In tbe the logaritbmic logarithmic plots tbis this liDe line has a slope Cor for aH all oC of the arrays arrays considered, because we have made PI PI and z unity. The master curves are not not necessary in this case. After plotting the field prolile log-)og paper, a profile on on log-log straígbt lit along straight edge is placed horizontally as a best fit !he The intersection the left-hand portion of the curve. The of tbis Next this straíght straight edge with the Pda axis gives PI' Next Ii.tted to the tbe !he the hypotenuse of a 45° triangle is fitted sloping part of the curve on the right-hand side of Cound on on !he the profile. The interface depth can can then be found the horizontal axis from the intersectioD oC the tbe triantrianintersection of gle and tbe This procedure the horizontal straight edge. This is iIIustrated illustrated in Figure 8.22. The asymptote metbod method may also be used even when tbe nOI been been large the maximum spacing has has not establish tbat enough to eslablish Iayer has has a very that the bOltom bottom layer

II

1

¡J1

544 544

Resistivity methods FleldcuM Field CUM

4S· 45' lrian,le Irian.1e

10 10 1', Io-S 11m 1', - 10-5 Om

Elc<:lrod. Electrode .pacing(m)

1000

.",lOn, ... SOn,

figure frischknecht Figure 8.22. fstimate of p¡ PI and z from the 45 450 asymptote. asymptote. (Afler (After Keller and Frischknecht 1966.) Electrode .pe.ina .plcing (m 1I Ekclrode 1000 10__..........__.....--I,OO--.......... 100 1000Irl..............................TI0 --.....--~1000

P.

(Um)

IOO't-------+-----"o__ +-------:~ OO'r------------t--------~~i---------~~

.....

10~1-----.....----I~O.....--------~~.....~=- --~ 10~1------~----_'7~:;__..,..::::r-___;~

10

Minimum deplh 10 lO hilhp I.~r hi.hpll~r ... 400m

Figure Figure 8.23. Asymplote Asymptote method method of estimaling estimating minimum depth.

high resistivity. resistivity. In this case the 45° triangle is placed lo to intersect the pOÍDt point of maximum spacing as, for example, in Figure 8.23. this case the depth esti8.23. In In this mate can on1y only be a mínimum. minimum.

8.6.4. Vertical Sounding; Sounding; Multiple Multiple Horizontal Beds (a) (a) Introduction. When there are more than two horizontal beds present, as is usually the case, the previously mentioned single overburden analysis is lirst ror relatively sma1l first used for small electrode spacing. This gives gives the depth and resistivity 01 of the upper layer. Next is is possible to estimate the mínimum minimum conductance of all layen aboye above the bottom by drawing

the 45° tine tbrough maximum through the point given for maximum electrode separation, as shown in Figure Figure 8.23. 8.23. The lbe ratio of spacíng Une will spacing to p" p" for any point on this line be a conductance representing all the rocks racks above aboye an an insulating layer; in Figure jt is js Figure 8.23, for example, it about 9 S. S. Ir If the rigbt-hand right-hand extreme of the field profile is itself a 45° line Une on the log-log log-Iog plot, the In this case the bottom layer is highly resistive. In actual, rather than minimum, conductance is js deterdetermined. (b) Crude interpretation. The lbe overall shape shape of of the middle portion of the profile will give us some idea o! between surface and and of the character of the beds between basement. Several sbapes iIIustrated in Figure Figure shapes are illustrated

Interpretatian Interpretation

545

TYPEH TYPER

TYPEX TYPE X

LogL Curve Curve (1) (I) (JI) (II) (m) (III) (IV)

Z,. P3 PI Z,. P3 »PI Z,. PI >PI

Z, Zz > Z,. Z, Z, > Z,. Z, > z, < Z,. Z,

P3 PI

Curve Curve

z, < Z,. Z,.

(1) (I) Z, (11) (II) Z2 Z, (111) (III) Z, (IV)

P3 >PI PI >P,

TYPEQ

LogL

LogL Z, > Z,. P3» PI (JI) (II) Z2 Z2 < Z,. P3 P3 > PI

Z,.

Z," Z," Z,.

TYPEA TYPE A

Curve Curve (1) (I)

P3 P3 «PI

> Z,. Zoo P3 P3 «PI P3 P3
Curve Curve

(1) (I)

Z,. PIP, < PI Z," Z,. Z,. p)PI <
Z, z, <

(11) (II) Zz"

Figure Figure 8.24. 8.24. Various Various types of sounding curves curves over multilayer structures structures of three three or more beds. beds.

8.24. Types H and K have a definile definite mínimum minimum and maximum, indicating a bed, or beds, ol of anomalously resistivity, respectively, respectively, at intermediate low or high resistivilY, depth. Types A and Q sbow show fairly uniform change in resistivity, the first first increasing, increasing, the second decreasing with depth. Obviously tbese these curves also may be combined. It is generally generally possible to tell lrom from tbe the shape 01 of the adjacent parts 01 of the profile which which layer corresponds to the maximum or minimum on the first two two curve types. types. Although, Although, in general, general, the cbaracteristic characteristic sounding curves ilIustrated illustrated in Figure 8.24 8.24 represent multiple Iayers. layers, in tbeir their crudest lorm form they may be be considered 10 10 be be lor for two beds over a basement. On this assumpliOD tion eacb each oC of the Cour four sets has particular properties Ibat that may may be roughly classified. For H- and K-type curves PI PI > 1'2 < 1'3 and PI PI < 1'2 > 1'3, respectively, respectively, aod we may be able lo andwe to draw some conclusions about Ibe the relative relative values of PI PI and P3 if the spread has beeD been extended sufficiently. Tbe The A- and Q-type curves correspond to PI PI < 1'2 < P3 and PI Pt > 1'2 > P3, respectively. Some Some idea oC of the relative bed thicknesses thicknesses may be be obtained Crom from the horizontal extent ol of the

maxima and mínima minima as well as the flanking portions in all cases. (e) paints. The Tbe (c) Use af of maximum and minimum points. coordinates of the extreme points in curves of oC types (Le., maximum or minimum H and K, Figure 8.24 (i.e., Pa be used with cerPa and electrode separation) may be tain characteristic layees employing characteristic curves for three layers a particular electrode spread. Figure 8.25 shows a set for the Sch1umberger p.(max)/p¡ Schlumberger array in which: (a) Pa(max)/PI is plotted against P2/PI lor ol Z2/z1 Z2/z1 for various values of and (b) the ratio L(max)/z¡ against z2/z1 zl/ZI L(max)/zl is plotted against for various values oC of P2/p¡, P2/PI' L(max) being the electrode spacing at which P p"a ís is a maximum or minimum. Because oC Pa(max)/Pl p,,(max)/p¡ and Because we know the value of L(max)/z¡ can be found L(max)/zi (presumably PI PI and ZI can leCt of ol the tbe from a two-Iayer two-layer curve match on the left profile), characterprofile), horizontal lines drawn across the characteristics in Figure 8.25a and b give two sets sels of possible lO the values oC of P2/PI and Z2/ZI' Z2/ZI' correspondíng corresponding to intersections. If we now plot these values of ol z2/zl zl/z¡ versus 1'2/PI' we get two curves which intersect at

Resistivity methods

546 546

100,...---------,---------..., loo.----------------r----------------~

,.(m"·)/" ,.(m"·)I"

loor---------,---------, 100,----------------,----------------,

LfIlWl.)lz,

~·~.I~-------~---~-----:'. ~~.I~--------------~I--------.~J.-,------~IO 10 (h)

Figure type-K Figure 8.25. 8.25. 5chlumberser 5chlumberser array array - characteristic curves curves for three layers layers with type-K curves p. (maIC.JIPr (malC.J/Pr 8.24). (After Kel/er Keller and Frischknecht, Frischknecht, 1966.) 1966.) (d) (d) Plots of Po curves (see (see Fig. Fig. 8.24). veTliUS zz/z, ratios. various P:z/Pr versus P:z/Pr for various various zz/z, retios. (b) Plots Plots of L(max.)/z, L(max.)/z., versus versus z}lz, z2/Z, for vsrious ratios. ratios.

one poinl point TIús lbis point represents the correct values ol of Zl and P2 for the layer in question as shown in 12 Figure 8.26. 8.26. (d) Partial curve matching. TIús This technique requires matching of small segments of the field field profile with theoretical curves lor for two or, if possible, three horizontal layers. Genera1ly Generally one would start start lrom from the lelt-hand left-hand (small spacing) side 01 of the profile and match successive successive segments toward the right (large spacing). spacing). When a portion of the fleld field curve is reason-

ably matched in this way, all a1l the layers in this segment are lumped together and assumed to have together and an elfective Z" This TIús lumped effective resistivity p~ p, and depth I" layer is used as a surface layer layer and and the next next portion 01 of the field field curve is interpreted in a similar way. It would be quite impractical to slide the field fleld curve on the master randomly in attempting to find flnd a 01 the curves. reasonable fit between the segments of The process requires that that we know where to locate the origin (lor (for example, where Po/PI - L/ziI - 1 on the master two- or three-Iayer three-layer curve) with respect to

547

Interpretatían Interpretation I OOr--·-------,...----------, OOr---·--------------r-----------------,

the lield lit to successive successive field curve to obtain the best fit lefl to porlions portions of tbe the latter as we progress from left right. This interim origin is known as the auxiliary point (Hummel. 1932; point or cross in the literature (Hummel, rJr, Zohdy. Bhattacharya Patra, Zohdy, 1965; and Patra, 1968). To .. ilIuslrate poinls, illustrate the signilicance significance of these auxiliary points, S.l and Equations consider a modificalion modification of Figure 5.1 (S.8) S.l so that Ihal it (5.8) and (S.9). (5.9). If we change Figure 5.1 represents a vertical stack resistivities of beds with resistivities lol_------~--+----I_--------------___l lol_---~-+--I_-------__j p¡, z¡, z2' z2" ...• ..• z" zn from top PI' P2 p",•...• ... , p" Pro and thicknesses zl' Inlenection li ... Ii... to bottom, and cross section 1 m 2,2. then v and 1 - v unique unique values of in Equations (S.8) lO the (5.8) and (S.9) (5.9) are proportional to p, p.,•• .I11' .I:I' thicknesses. thicknesses. (S.8) and (5.9) (S.9) we have in Analogous to Equations (5.8) the vertical direction a so-called transverse transverse unit resis.~.~

I

tance II...-----------,:':------,.---.....,J. I~I----------------~I~O--------~-------I~OO 10 100

n

T = p¡z¡ PIZI + P2z2 + ... + PnZ p"z"n =

P;l; E" P;z;

(8.43a)

i-I

Figure Figure 8.26. 8.26. Determining second'/ayer second-layer parameters using dala dala from figure Figure 8.25. 8.25. {After (After Kel/er Keller and and frischknecht. Frischknecht,

and in the horizontal direction direction a longitudinal unit

1966.} 1966.)

tI .-"1, I, ""

• "t. "Ir ."f.

".1,. ".1,.

,•

7" b-", b_

f,· ."

!,-I·",,,!. ,,-1'''11',. fA·

"S'''I,

/1:111, I.

II _ce::::::.1= " _=-=::1!~

z, z, (0) (a)

Figure pI). Figure 8.27. 8.27. Two-/ayer Two-layer Schlumberger master curves. curves. (a) Ascending type (PJ (/? > Pr).

Resistivity methods

548 548 )~,

&o,·n..,,, ".""'"

b_WR". ".WRTé·

,., ••,1111" ,., ••'1111',

".,./UI". ,.,., . b. '.;,.t! .".

" . '1tIH"

"-"""", 6:.H1NJt. &-H1NJt.

b·'·""

"·"""4

"....." (6) Fi8ure Figure 8.27. 8.27. (Contínued) (Continued) (b) Descendín8 Descending type type (p;¡ (P;z < p,). Pr).

conductanu conductanu S - ZI/PI Zl/Pl

given (8.25)] given by [compare with Eqs. (8.24) and (8.25)]

" Zj/P. + zzlPl zz/P2 + ... +z"/p,, - 1: z,/p, /-1

(8.43b) The vertical and horizontal resistivities resistivities are

p., - T/z~ P4 - z~/S (8.44a) Z~/S where z. - El'z,. I:1'z,. This column is indistinguishable lrom trom a single single isotropic layer witb with resistivity resistivity and thicltness thickness p", P'" (T/Sj/2. (T/Sjl2. Z~q - z~A - (TS'j/2 (TS'j12 [see [see Eq. (8.44b) (8.44b) below]. The quantities T and S are known as the Dar Dar Zarrouk paramelen parameten and have many interesting propmes erties (Maillet, (Maillet, 1947; 1947; Orellana. 1963). 1963). For example, example, the block can be considered anisotropic with an QlJtrage square resistivity p", Pm and pseudoanisotropy A

A .. (p.,/P4)1/2 (8.44b) Applying tbe tbe case of 01 two the preceding results to the beds, we change P. z~ to Zd in Equation P4 to P~2' Z. (8.44a) (8.44a) and get (8.45) (8.45) 'Ibis tbe parameters parameters ot 01 two This expression relating the individual beds to those of a single equivalent bed a1lows auxiliary charts to complement allows us to prepare auxiliary
549 549

Interpretation

L_-f---; !;ib:,..·...;;'!:.:",_ _ b ""

'--~-----+----~ ,_-1----+--""1 ~&~'_.~'~'---" •• "

___-+------i-----t h

• NJJ"

':--+-----1-----, PI

• '·1"1+

"VE,

."'.."', ".........., :::i"T-+-+-@--l----+---J!z .-~111p, . . ..:._-_,_,-""t-+-+-@-+---+---J!z ~Itlp, ~_n\l\l'

~

Im-

-6-$(1"", ==l:::-t--I--®-+-----l---J bPI·6-$11,,'1, fl- tJfllP,

-'~--ll---! rr-;----I----I r;--;----1----1 A • f1.JJJp, "~--II--.!

+ __

~t---L-_1<:!J'_;- _ _-1-_ _~ ~t---L-_1<:!J'_;-

b - (J1$fI" D1$f1p, b·

1--,t-~f>___I--.....jf_-__I1i 1--.,t-~f>___1--.....jf---1 Pz r--_ _-J J r

• (J·tllp, (J·tDDp,

;---t----I----I ., ~-t----f---I " • (J·/fZ" ,·/ft", t; •• f)/IIp, f>/II" )--1---+---1 ¡;

1--t-~~4--_+--_I ~ .1(/11...

_+ __-1 J':. J':' D'''", ()(JIDI" .''---1-_ '---1---+----1

'-¡--í~:,....--L-_..l.

__...J PI • "'110"

(al (a) Figure 8.28. Auxiliary-point charts (a) fa) far for H- and A-type saunding sounding curves.

ol of Sch1umberger Schlumberger two-Iayer two-layer master curves on the escale, e scale, shown shown in Figure 8.27, 8.27. are inc1uded included for ference. (Note !he the change in symbols: p ~ Po' Pal (ecence. B- 2L.) B·2L.) The procedure procedure Cor for matching successive successive left-toleft-to. t segments of a field sounding is as follows:

. The leCt·hand left-hand portion of the lield field sounding curve, curve. plotted on a transparency oC of identical log-Iog log-log scale, is fitted to as many points as possible on the

master. maintaining Ihe ues parallel. the respective axes This lit Ihe first tlrst cross or fit provides the location of the field sheet coincides auxiliary point where the field with PI = L = 1, Ihe the origin on !he the master. Hence we we obtain PI' ZI' whereas the best-fit segment gives gives (P2!P,) (P2!PI) or Pl. P2. [This segment may be extended beyond the fttted (Pl!p,) fitted portion along !he the (P2!PI) line with pencil for a check on the next step.] 2. Ihe appropri2. The sounding curve is transferred transferred to the ate auxiliary curve set where Ihe the cross is placed at

Resistivity methods

550

" . :0;-, " . !p. l,(O

-@-- -@-

--@-

ec

'J'¡

oJ "

~

'~."[ '~-"r

!z-'~I~~ ~.'~I~~

.,."",,

--;®- a-""', l .. o'mP, 4{;-- ".MP, ---- ---@ !J.0I·m" Cr fl.-'lHA {á):-- ".'lHA

"-,·m,, !J.."""" --~ "."""" " .fH.'~ o"' .',",, -@)-- ,.,.,m" ,., o,' ' --~

-- --

-- - -- ----

-

--

-u

-@J-~--

"-HII,,

(b)

Figure 8.28. 8.28. (Continued) (Continued) Auxiliary-point charts charts (b) for K- and Q-type sounding 50unding curves. curves. Figure

the tbe origin and the same (!i2/P.) (!Í2/P.) curve of oC the auxiliary auxiliary as that in step 1 is drawn in pencil on the sounding. 3. Replacing the sounding curve on the master and maintaining the (P2/P.> (Pl/p¡) line from step 2 on the master origin, a second master segment further Curther to the right rigbt is fitted to the sounding curve. curve. The second cross is marked over the master origin, giving Z,2 where Z,2 z.2 - Z. z. + Z2 and P,2 1I~2 is giving P~2 and Z,2 related to lO the other parameters by Equation (8.45), (8.45), that is,

P,. - P.PI and z,. z•• -- z. at al the first cross.)

(Clearly P,.

(1'3/1112) and and hence 1'3 from Irom the We also obtain (P3/PI2) fitted segment. retumed to to the auxiliary 4. The sounding curve is returned and step 2 is repeated. PIl' Z,3' z~3' as well as P" p" trom Irom 5. Repeat step 3 to get Pd' the third cross. and 5 until until the sounding sounding curve is 6. Repeat steps 4 and filted. completely fitted.

lA check on the (p" (P•• z,) values may be taken talcen at al [A relation in in step step 3. Also AIso the any juncture, using the relation found (Fig. 8.23) and and conductance may be found minimum conductance Cor the same purpose.] purpose.) employed for threeolayer master master curves are are available (Com(Como If three-layer Générale de Geophysique, Géophysique, 1955), itit is preferpreCero pagnie Generale il the field curve curve warrants warrants this. Ibis. The The able to use them if

Interpretation Interpretation

551 551

procedure is is similar similar to to the the steps steps 11 to to 6, 6, noting noting the the procedure following. Collowiog. The first first cross cross and and match match gives gives PI' Pl' P2' P2' ZI' Zl' Z,2 Z,2 7.7. Tbe (hence Z2)' Z2)' P,2' P,2' (heoce The second second cross, cross, equivalent equivalent to to the the third third in in step step 5, 5, 8.8. Tbe locates PP.3' Z.3' from from wbich which PJ PJ may may be be de deterterlocates 03' z03' mined by the the relation relation mined

Z3' Z,4' Z•• ' Z.' z•• and P4 P. are are a1S0 also oblained. obtained. %3' 9. The third third cross cross corresponds 10 to the the fifth, fifth, if ilit exists exists 9. the two-Iayer two-layer analysis, analysis, and so so on. on. in the

and and Jo 10 is is the the zero zero order order Bessel Bessel Cunction. function. This This expresexpression sion is is suitable suitable lor for solving solving any number oC of layers layers (see (see Keller EmKeller and and Frischknechl, Frischknecht, 1966; 1966; Zohdy, 1973). 1973). Eroploying ploying the the Schlumberger Schlurnberger array (which (which is is most most conconvenient venient for for vertical vertical sounding sounding and a1so also measures measures popoteotial tential gradient), gradient), we we may may write write the the resistivity relation in in the forro form (see (see Eq. (8.39b)] (8.39b)]

where where JI 11(( AL) AL) - - J1ri( AL) is the first first order Bessel Bessel ó(AL) fuoction. function. J1ó the lirst first derivative of 1Jo0 and we we have 0 isis the replaced replaced r by L, half the the current electrode separa- ,. tion. The product K(A)JI(AL) is known as the Slefanescu Stefanescu funclion. function. The solution of tbis this general expression may be obtained by expanding the integral as an inlinite infinite series series or by numerical integration, both methods being suitable lor for computer programming. These and other methods are described in the literature (Ghosh. Ryu, and Ward. 1973; 1973; Jo(Ghosh, 1971; 1971; lnman. Inman, Ryu. hanseo. hansen, 1975. 1975, 1977). 1977). Because an enormous number of theoretical models will will lit fit the field field data from an average soundiog 5% (which (wbich is quite sounding curve witbin within ± 5% within the data accuracy; see next section). section), some sorne optimization lechnique technique lor for determining the limits on the parameters providing Ihe necesthe curve match is necessary in practice. This addilional additional feature is included in the methods oC of Inman, Inman, Ryu, and Ward. and Ihal employs a program Johansen. An example that io Figure 8.29b. 8.29b. somewhat similar to those is shown in

should be noted noted that tbis this procedure procedure gives gives good good It should results ooly only if the bed lbicknesses thicknesses increase increase rapidly rapidly results with depth; in facI, fact, eacb each successive successive layer sbould should be with (z. > z<3' zo]' thicker tban than the total tbickness thickness aboye above it (z. tbicker etc.), Correction factors factors lor for Ihe the auxiliary auxiliary charts ele.). (Kunetz, 1966; 1966; KelJer Keller and Frischknechl, Frischknecht, 1966) 1966) rerethe etrecl effect ol of this this limitatioo limitation coosiderably. considerably. For duce the type-A curves curves require thal that z; - >'(ZI + Z2)' Z2)' example, Iype-A example, that is. is, the lumped layer is is tbicker thicker Ihan than the sum sum of Ihal (Pu / Ph )l/2 > l-see I-see the individuals individuals (because (because >. - (Pu/Ph)l¡2 the §8.3.6). For type-K curves curves the correctioo correction is still §8J.6). which increases increases nonlioearly nonlinearly greater by a factor 11II which grealer from 1 lo to 1.5 1.5 as >. increases increases from from 1 10 to 3. 3. from find that z; = (zl + Z2)/'1 Z2)/1I and With Q curves we fiod With P; -= P.II; varies from 1 to 1.25 1.25 p; Po'l; the correction factor varies Modifications lor for in the same sense as both zZ and p. Modifications H-type curves curves appear lo to be unnecessary. unnecessary. H-type An example of ol partial curve matching is shown in Figure 8.29a 8.29a from a groundwater sounding in Sri Lanka. Overall resistivity resistivity is unusually uniform and (f) Sounding interpretation errors. errors. Practically (f) high. bigh. Subsequent drilling produced a dry well. well. erra tic variations varialions in field field sounding sounding The crosses are marked on the sounding lor there are often erratic soundiog curve for measuremenls of PPGQ due to local resistivity changes both twotwo- and three-layer three-Iayer analysis. The curve is measurements surCace and poor poor electrode electrode contacts. conlacls. In addierratic erra tic beyond 20 m which wbich probably indicates noisy near surface and terrain lerrain effects etrecls will lead anisolropic ground ground and field readings. readings. In any case, resistivity resistivily increases with tion, anisotropic and PI' PI' both Z and to errors in estimating both depth. An expanding spread. in homogeneous ground, The technique of 01 partial curve matching, matcruog. although a1though verlical contact contact will give a rather crude compared to lo complete analysis of ol the parallel and adjacent to a vertical similar to lo that obtained over sounding curve by computing methods, methods. is quite useuse- profile that is somewhat similar layees. particularly particularly if if the the bed bed on on the the other otber ful fui in the field field to lo keep abreast abreasl of oC daily measurements measuremenls horizontal layers, 01 the contact contact has low resistivity resistivity (Fig. (Fig. 8.34c. 8.34c. and as a control for the more sophisticated sopbisticaled approach side of a11 depth-probing depth-probing operations operations the Ihe expand. expand§8.6.5d). In all later. out in in at al least leasl two two spread should be carried carried out ing spread sound preliminary preliminary procedure procedure in in any any case. case. (e) Complete curve curve matching. The expression for azimuths, aa sound oC pronounced pronounced topography lopography effect etrecl is is An example of surface surCace potential potential over two beds, Equation Equation (8.21), shown in in Figure Figure 8.30. 8.30. Apparent Apparent resistivities resistivities were were shown may may be be expressed expressed in in integral integral form form as as Crom an an expanding expanding Wenner Wenner system system over over oblained from obtained re1alively homogeneous homogeneous dolomite dolomite and and limestone. limestone. The The relatively v - (IPI/2'ITr){ . r) d>.} (IPI/ 2'ITr) {1 + 2r{''' K( >')Jo(>. >') Jopl.r) d>'} spread. however, however. is is parallel parallel to lo aa 100 100 ftft cliff, clitr, which wbich spread, Cor PG Pa versus versus produces aa linearly Iinearly increasing increasing curve curve for produces (8.46) (8.46) electrode electrode separation. separalion. The The bumps bumps in in curve curve A A are are probably the the result result of 01 local local variations variations in in surface surlace probably where resislivity near near the the cliff clitr edge. edge. Obviously Obviously this trus is is an an K(>') = = kk exp exp ((- 2>.z)/{1 2>.z)/{1 -- kk exp( exp( -- 2>'z)} 2>'z)} resistivity where K(>')

z; -

{'tJ

552 552

Resistivity methods 3

4

S 5 6

8S

10

20

30

40 SO 50 60

80 100 SO

300 200 P. (Om)

L -AB/2(m)

ISSnm,I.Sm ISS Om, 1.5 m

¡OJOm,7.5m 103 Om, 7.5 m

_

.. 400nm 400 Om

PARTIAL MATCH LAYERS 2 LAYERS

350nm,7m 350 Om, 7m (a) (Q)

300 P. (Om)

200

IS40m, 1.9 m 1540m,I.9m

800m, SOOm, 6.1 6.1 m

2330000m 233000 Om -

COMPUTERMATCH COMPUTER MATCH

1880m.0.9m ISS Om. 0.9m (b)

FINAL FINAL PARAMETERS ol STANDARD STANDARD DEVIATION DEVIATION LAYER THICKNESS &; &; RESISTIVITY RESISTIVITY LAYERTHICKNESS Sld. Sid. devn. devn. Zandp 1I 2 3 4 5S 6 7 8 9 10 11 II

1.9172 m ZI 1.9112 Z: 6.0628 Z, 5.1734 Z.9.5293 Z, .89508 PI 153.91 153.91 Om PI PI 79.962 p¡ P, 1353.0 p.61.104 6 1.104 P4 p,188.12 P, 188.12 P6 .233 29E+06 P6' 23329E+06

0.49198 14.597 423.76 1690.5 1\20.0 1120.0 3.2000 21.536 91\13. 91113. 13379. 0.1I483E+06 0.114S3E+06 0.59222E+08

(e) (c)

SPACING SPACING

08S. DATA DATA

CALCo CALC. DATA

~

!.SO m LSOm 2.00 3.00 4.00 6.00 8.00 10.00 12.00 16.00 20.00 25.00 30.00 40.00 50.00 60.00

1500m 140 130 122 lIS 115 120 130 135 160 185 185 185 220 230 250 290

148.6130m 148.613 Om 142.376 129.463 120.537 115.193 120.083 129.340 129.340 139.933 160.395 177.681 194.885 208.754 232.678 257.201 284.690 284.690

0.925 -1.697 0.413 1.199 -.168 -.069 0.508 -3.654 -.247 3.956 -5.343 5.112 -1.164 -2.880 1.831 1.831

(d)

Figure Figure 8.29. Examples of partial and complete curve matching of field soundings for groundwater, 5ri Sri Lanka. (a) (a) Partial Partial curve curve matching (two layers). layers). (b) Complete Complete curve matching. layers. (d) matching. (e) (c) Computer results results for complete curve ma/ching matching using six layers. Comparison from the data data in (e). (c). Comparison of observed Po and Po calculated fmm

extreme case, case. but but the curves would be similar if the clift' Cace were clift'face were a contact and the void filled filled with high resistivity rock. In the latter case the result could be resistivity rack. erroneously erroneously interpreted as a subsurlace subsurface layer of high resistivity. The eft'ect 01 of dipping beds is not serious in sounding operations unless unless the sounding array is normal to

strike and particularly ir spread crosses over an if the spread outcrop of the dipping bed. Parallel to strike strilte the z values point directly direct1y below the values will will be those of the point array, elecarray. and with a 1arge large enough separation of electrodes the response may hecome become similar to that in Figure 8.30. lo be 8.30. The doub1e-dipole double-dipole array is said to more sensitive lo to dipping heds beds than Schlumberger

553

Interpretation

100

OL-~--~~~~--~~~~--~~~-L--~80~-L--~100 20 40 60 100 80 $Cparalion (fl) (fl) Elc<:trod. separ.tion

e,y , PI." , p,t"

B~:.,' ,~l1Sn---Dolomite Ind limestone

Figure Figure 8.30. 8.30. Effect of topography on expanding Wenner Wenner spread. spread.

and Wenner configurations. Again. Again, to determine the dip dip it is is necessary necessary to measure Pa Po in two orthogonal directions. directions. Aside from from the preceding errors which which are related to the field field work, ambiguity in sounding interpretation may arise owing lo to two factors. factors. The first, first, mown known as principle 01 of equilJalence, equivalence, may be stated as as the principIe follows: follows: il it is impossible to distinguish between between two hlghIy highly resistive resistive beds of dilferent different z and p values values if the product zp zp is the same, or between two highly highly conductive beds ir if the ratio z/p is tbe the same. In Figure 8.31a offers a resisresis8.31a tbe the block of cross section ~A olfers tance to vertical current flow given by R - P2 zl/ flowgiven z2/~ A ; thus layers having an identica\ identical product zp are equivequivalent and we we cannot determine tbe the two parameters separately. In the conductive bed 01 of Figure 8.3Ib. 8.31b, the vertical current is deflected deflected almost normal to the vertical stack. P2h/z2/. Thus beds havstack, making R - P2h/Z2/. ing the same ratio p/z are equivalent so tbat that again p and z cannot be measured separately. For eilher either of Ihese these configurations the bed thickness witb ness and resistivity resistivity may vary within wide limits with respect lo il. However, However. these to layers layers above and below it. limits may be found by optimization methods as mentioned in Section 8.6.4e. 8.6.4e. Sorne equivalenee Some feeling feeling Cor for the wide limits of equivalence may be obtained from the examples of oC three-bed equivalenl equivalent curves displayed in Figure 8.32, parts (a) H, parts (c) (e) and (d) and (b) being for types A and H, ror Iypes lO the auxilfor types K and Q sections analogous to iary curves in Figure 8.28. 8.28. The dashed 45° slope lines represent equal S2/S1 ratios, whereas the P2/P¡ and limiling values of P2/PI solid-line curves are limiting ror equivalence equivalenee within witmn ± 5%. 5%. z.2/ZI for iJlustrate the application consider eonsider the hatched hatehed To i11ustrate 01 Figure 8.32b. 8.32b. An area in the H-type section of circ1e in the tbe shaded produced the circle approximate match produced al P2/PI Z'2/z1 - 3. The minimum square at P2/PI - 1/39, z.2/z1 limilS for ror the Ihe equivalence are at the and maximum limits 01 the square. Hence 1.6 < z.2/z1 Z.2/Z1 < 4.2, comers of

1m

= I S'lm

PI

S'lm PI = 1 Om

/-____~1l.5 ,.....!o.s m ...--:::

p¡=20S'lm 1m pz=200m

p¡ =400m =40S'lm Pz p¡ = 0O PJ

f

(a)

1m PI = IOOOm IOOS'lm 1m p¡=SS'lm 1m pz=50m p¡ = 00

= Pz

PI

= IOOOm

?Im

~.snm

= 2.5 Om

(b)

Figure 8.31. The equivalence principle principIe (schematic). (schemalic). (a) p, < P2 > PJ. PJ. P2z] P2z] -- constant. constan/o (b) p¡/z] = constant. constant. (b) p, > P2 < PJ. P2/z]

554

Resistivity Resistivity methods methods

,.·t ,.·r tt ::

, V " ,,' " ¡.,¡., v' " / /' ,,' " V " ." "" " " ." " / v' "" "" / " " ," 1; ", " "" 1"I" " , i-"', / ,," " "" " Ii ~ I.-' 11 """, ;'

i

;'

, ,,' " " "" ,"

t-

;'

li

;'

IfJ t- Do-t::: A~ A

"

"

"

..¡.,"""" 1/"" " ".0 L'

" " ¡/ ~" " v " /'V /;'

,

;'

/

,-

v"

/"1I~ V ~,l

lJ ,V

'~ l .L .J y ,~ I~ ld l/VV¡,v V jI' ,,'I'!"'¡'" "v ,," ..

........ -

r-

.~

/

l:"" ) l"- N!' N / ~~ r; :>~ .>l

,....-

/ V""" lL

rV

....,

// /

/,,/./.

I~ ~

1'. ~ J..

,,' /'

If ~ ,,:,a ,,:.a 1/

(b)

," "

¡...

Ie" t1I'

~, " L'

" 1/ !." ~' 1/ ,,'""" IL,,; V V' I."..... If·v ,,' " V

'",,'

~

~/

~p ~¿

"

~ F.=: ~

~~ ~V'

, ;

, " " "

~

"

,"

~

,

__ .... ",,'

" /

~

~

""

"

" ,,, , ..,¿.Y " .... , _ -.... 1.. ·..,. ..'

,..-: "~

""1'1~1 , ",,'" I-"~~ , V-~" ...

V V ~" ~'

-'

/

.......

Y

(a)

"\ t-F-f-"" V ~ r-

.L ~

"

~ " r;z ," ~ .... ~ , , /

t..:.. ~

I-'

~

~ /~ ~ ~ V;o V~ , /tÍ. ,." ~~2 ~ , /

~

~

~ ~"'-L' ,

¿u A'u ,,'"

~ .-~

'1. 'It

,

~" v"

~

;'

~

,,-,,'

I'

"

~

~ ...... ~ ~ -.

%

",,' Y.r.

~.

,/ lL

~ ~

..

" v¡,

.

;' /

/

,

•

,"'

" j

[,' 1,'

..

" " .t-, ...,

1".>0

~

Pfj r1f

C'

"

.J,." ~

~

,,' /'

14 \4

, ,,,' "" /

~

,.,-"/ ,-"

1./

"

Figure and Figure 8.32. Equivalent Equivalent curves. curves. Solid-line curves curves are Iimiring limiting values values of l' IA - P2/Pr and for equivalence; dashed dashed fines lines are are fines lines of equal 5¡/S, ~/S, in (a) (a) and (b), equal 1i/1f in (e) (c) and (d). (d). (a) (a) A·type A-type seetion, section, PJ - oo. 00. (b) H-type seetion, section, PJ - Pr.

P Z, p - Z2/ zz/z,

0.014 Pi < 0.038. 0.014 < poli Pd/Pi 0.038. lbus Thus the same same field field curve curve section section may be matched only within within ±45%. lbe The limits are still still wider in areas of the equivalent equivalent curves curves where where the z ratios are smaller smaller and/or P ratio estiestimates mates larger than this, this, as is c1ear clear from from the the open sections sections at the upper lelt. left. The suppression suppression principIe principle states that ir if a bed is is very thin compared lO to those those above above and below, below, its very thin

effect effect on tbe the sounding curve is insignificant unless its resistivity resistivity is extremely extremely high or low. low.

8.6.5. 8.6.5. Lateral Lateral Mapping; Vertical Contact (a) (a) General equations. AIso Also called lateral profilprofiling, this technique is of considerable importance in ing, mineral measuremineral prospecting. prospecting. It is also used for the measure-

Interpretation

555 555

,,

, ,,

,~

,

,

,~

r--..I' ~, r--.I' , , '." r-., r.., I~ , , ..~ " , ~ r-, ,~ " , I.,r--.... , r-'',""............ ,, "- ~

"-

,

'0

~

(e)

" '"

~ ~

, ....

~ 1\ r, :::> b.

,

~ ~

,,

~~ ~t-

,,

~ .... ~~

...

~ 1',

,

,,

-, •

~

,

"

,

%

,

..... ..........'".....'

~-( ~-(

, , ..... --~ -~ ~ t-.... 1"-" , , "-""" ~ '~ ,~ ~ r-~ ~ ""'," , 'D'" ,'" , , ... '~ ....; 'I)r-~\~ ,, " \\. ' .....: '. ,<:~ ,~ , ... '0, ~ "ft:~ ~~ ,r-"-. ' , J v.~fI. ~' " , ~r-, , fir-. 1', "

le Ie

~~ t>f , r ~

~ ... r~

,

,

""'-,

I--~ I"-~

.

~

~

I'~ ~~

",r-, ,

~-

, f-... r,r, '0 , r-, ~ ~ ,, 1'-, , .... " ¿ ,.....K "" .... '. ",

~

I'

, , , r:---- , ,, ')') [>k ~k I"'" y , r' ~ , ,

~

"

~

,

~ l~ ,, ~ r-,..... , ", ", , l'

""

~...

J

..

~ ..~

,.). -,.).

..

t,0'

~

\

f.,.

'

1

\

\

\

\

\

" \

, , \

1/IJ

\

\

\

\

\

.. lO''''''

II'' '

~, "~ Fe

~ ,\ ..,,

.,

.

. .......

,11 ' II !/

\

(d)

~,

l,.-

" '.

o.

Figure 8.32. (Continued) (e) PJ - 0. (c) K·type K-type seetion, section, PJ - PI. Pt. (d) Q-type seetion section PJ

ment ol of overburden depth in civil civil engineering work. work. The mineral exploration intepretation iDcludes includes location tion oC of vertical vertical contacts - faults, dikes, shear zones, zones, and steeply dipping veins veins-- and three-dimensional three-dimensional bodies bodies of anomalous conductivity, such as massive massive sultides. sulfides. In Section Section 8.3.3 8.3.3 the variation in potential crossing a plane interface was established for a single single current and a single single potential electrode system. system. Equation (8.17) gave gave the potential with both electrodes in the

same medium. (8.18) when they were on medium, Equation (8.18) opposite sides of the contact. Cor this Any 01 of the electrode arrays may be used for protiles differ considerably type oC of mapping, but the profiles from one to another. There is also a practical consideration: the traverse can be made faster and more move all the electrodes easily iC if it is not necessary to move for each station measurement. It turns turos out also al50 that the protiles welJ profiles are usually easier to understand as well in tbis this case. case.

Resistivity methods

556

the general case. case, with with spacing spacing '1' '1' '2' ']. ']' and For the we have have five five possible possible situatioDS, situations, depending on '. we electrode POSitioDS positions with with respect respect to the contact (Fig. (Fig. electrode 8.33): (i) AlI All electrodes electrodes OD OD left-hand side: side: (i)

(iv) PI on right-hand side: (iv) Cz. PP12 • PI VI _ 1fJ2 {( ~ _

2"

V ~;{(~ + 2S~,J -(~ + 2S-:'I-,J}

'1

~) '2

-k(': __+ l_)} '1

I -

V :;{(~ + 2S~',) -(~ + 2S-:'3-'.)}

2'1

21

'2 -

2 -

AV _

2"

'1'2

-

']'.

+k{(_l _2a - 1 ) 2a )}] -_(_1 ( 2a ~ '] -_2a - :'1 3 - ,J}] 2s - '1

2s -

2s - 2r] - '.

'3

(8.48a) (8.48a)

[(!:. _!:.) _(.: _.:) 2"

AV- [PI IpI

'1'2 '¡'2

')'. '3'.

'2

-( 2a ~ '3'3

-( 2s

-

~)}]

2'l 2'3

2a)})] +~. - 2S)})]

(8.48d)

(v) All e)ectrodes rigbt-hand electrodes OD on right. hand side:

Vt -

~~ { (~ - 2a:

~-

21

,J +

2~1 + ,J}

~ - ~~ {(~ - 28 ~ ~ )

+k{(_l _..!.) _.:) 2s-'1 2a-'1

~-

- {

[(.: _ . : ) _ (.: _ .:)

2"

-(

2s - 2'1 - '2

(il) Cz on rigbt-hand right-hand side (note that k changes changes (ü) right 01 of the vertical sign for a current electrode to the rigbt contact and that there is DO DO image image of Cz):

(ill) (ili)

-k{ - k { (~ - 2'1 + ~2 2a) 2s )

[PI [(.: _ .:) _ (.: _ .:)

(8.48b) (8.48b)

-(~ - 28+:,,+,J}

Cz. P2 P1 on right.hand rigbt-hand side: 1 k) 1 + k} + - -~;{(~ + 2s 2a~,J - l:k} 2", -

[PI {(

~-V¡-

'1

'1

'2

11- (1~ -

11'2 k IPz { V2z -- 2tr 2" ~ -

k)} 2'3 + '. - 2s

2a

Using UsÍDg Equation EquatioD (8.19) (8.19) to lo express 1'2 Pz in terms of 01 PI' and setting k" k· - (1 + k)/(1 k)/(l - k), we obtain obtain

_..!.) - k.("!' _..!.)

AV- [PI Ip¡ [(.: _.:) - k.(': _.:) 2", ')'. 2" ' 1 ' 2

'¡'2

','.

+k{{_l _.:) 2a-'1 2S-'1

p.lpl P,,/Pl - pIp' p/p'

1) +k {( -1- - '2

k.( ~ - -2-'3 -+-~.---2-S ) } ] +k.( -2-'3-+-~.---2-a)}]

+

Ir we ignore the tbe existence of of the tbe contact, CODtact, we can can If substitute for lor AVII AV/¡ in in Equation (8.26) and and get P._ P•. substitute Thisgives This gives

(8.48c)

where IIp' l/p' is the tbe quantity in in square square brackets brackets in in (8.48) and pp is the tbe quantity in in Equation Equation Equations (8.48) tbe particular electrode e1ectrode spacing (8.26) evaluated for the lor Equations Equations (8.48). (8.48). that holds for

Interpretation

557 C,imqe C,im.,e

(i) (i)

"

-e, <",

'\..: "...:

'. p. 1',

Medium (I)

"

(iii) J J; 7";

>, > J

.,.1

C,' c,'

•

1', 1'.

l· I·

1--.

'" Po

:tr1=±,l>;;;

j;;1, >>

c. c.'

Medium (2) Medium(2)

I

p,

c,

PI

p.

>, ;,;,;

Cit

.--1

'''7n"n"L'~''3 ,LJ"nl"",.., ,n, 1-. ,,'.

1',

c.

p.

,. '"

,., "en """.,,, ;:itt,,,,,,I,,,1, ",4",.,. e,' e,

c

I '

p,

1',

1',

e,

'"

Figure Figure 8.33. General resistivity spread over over a a vertical contacto contact.

ror tbe The expressions ror for Po for the Wenner and Sch1umberger Schlumberger arrays are cumbersome cumbersome in general. We shall consider certain special cases in tbe the folloMng following section. (b) Half-Wenner arrar. "'. -- oo. array. '1'"' 'I'"' a, '2'2 -'] -'3"'. 00. For tbe the preceding configurations, configurations, the results are:

(i)

P,,/PI ... ...

+ k( L - s)( L - f) ( ) (2s () f(2s - L + f) 8.5Oc

1 + {ka/(2s - a)} (8.49a) (v)

(8.SOe) (8.50e)

(iv)

Po/PI P,,/PI -

(8.49b,c)

(1 + k)

(

(8.49d)

ka)

II ka) -P -k- ( 1 - PI 2$+a 2s+a

(e) (c) Half-Schlumberger arrar. array. f, '2 '2 - '4 r.. .. f. L + t, - 00, L » t.

(i)

Po _ 1 PI

(8.SOb) (8.5Ob)

(8.SOd) (8.5Od)

Sameasin(i) Same as in (i)

P"

( iii)

Same as in (i)

(iv)

(ii),(ili) (ii),(iii)

(v)

(ii)

(8.4ge)

'1" L - t, f, '] '3 .. -

(8.S0a) (8.50a)

(d) Double-dipole arrar. lo array. (Potential electrodes to of current pair.) '1 'I - ''. right 01 .. - r " '2 - r , -- f, (, r, " -, + t, f, ,» r» t. f.

(i) AlI side: All rour four electrodes electrodes on left-band side:

(S.Sla) (8.5h)

558

'¡,·. .a--..,.". l

Resistivity methods

(a)

(a)

,. "

I"'Wa.... "..Wa....

_C.. 'p.••allao lID _C..

Slatlon _ midJlOinl'\

ta-.-a.a.

,..

1',

P,

C. C,

p.

«r», \\ orP.p. -~ ,1'-~-:,:I.I"",.~ /~

(6) (b)

Po

.... _ ...._

,.1'.¡;.:,:I.I..... /'i:.

c. Co

...___...... .......:..:; ••:.:-::.::.-:.::----.~. ,".... .:.-:;--:.:-::.::.-:.::-----~'

-,', ' ,I -

r

•,

'-J-L-t~ '-J-L-t'

Sehlumberaer.....

P.

-C... c... ao lID

Station _ mlclpolnl mJclpolnl of Slatlon oC

"'21'C. Station _ midpoint of 1','.

,.

p.p. ',1'.

C. C,

~p,'tP. L-;

C,

-----

Half.Sehlumberae r HalC.Sehlumberae

1','. p.'.

,-------a;--.. --.. --..,, r

M

(e)

~ 1',1'. Stalion Station - midpoinl midpoint oC of C.p. C,P.

,.

(d) (d)

P.

C .. P.al CloP. al lID ao

.. ......... ..........

~ C, C.

51allon p. Stllion - 1',

P, 1', (1) (I)

~--.Figure spreads. Figure 8.34. Profiles Profifes oVl?r a Vl?rtieal vertical eontact contact using different electrode spreads. (d) Spread with (a) Wenner spread (b) Sehlumberger Schlumberger spread. spread. (e) (c) Double-djpole Double-dipole spread. spread. (d) fixed e" movable p,. (e) 5chlumberger Schlumberger broadside brOiJdside spread spread

(ü) (ii) Dipole straddles straddles contact: Pa_ P"-l+k l +k

(8.51b) (8.SIb)

PI PI

(ili) (iii) All four on rigbt-hand right-hand side:

side, so that simuJtaneously. The that they a11 all cross it simultaneously. value of P"/PI p.JPt can be obtained in this case by substitution in Equation (8.48a) and and (8.48e). (8.48e). With the usual approximation (L » (), we have:

n,

Electrodes in medium (1) (I) :

2 (8.Slc) Profiles Profiles for these three electrode systems, plus some other other possible arrangements. are shown in Figure 8.34. 8.34. The profiles are characteristic of the array 8.34e, they all have discontiused. Except for Figure 8.34e, nuities in the vicinity ol of the contact, related to the e1ectrode electrode spacing. In Figure 8.34e 8.34e the electrodes are aligned parallel to tbe the contact and are moved broad-

:: • I

2

-3/2

+ k{ I + ( :) }

Electrodes in in medium medium (2): (2): Electrodes

p" PI -

[ k. 1

k {l + ( -

2-3/l]

2.1') } L

but it This profile is by far the best for interpretation but

~

I

Interpretation

559

V.rtical dik. dike

Figure Figure 8.35. Locations of current current images images near a vertical dike.

is is nol not very practical in the tield. field. ID In sorne some oC of the spreads the protile profile shape shape varies with the directioD direction ol of traversing, that is, it depends OD on which electrode crosses crosses the contact tirs!. first.

Pt : of PI: locations oC Medium (1): 1 k v, v, ... ... -[PI {{ -+--I

2'2'lT 17'

a

23 - a

8.6.6. The The Vertical Vertical Dike

el

ary

(k2)m

00 00

When a dike oí of anomalous resistivity and and tinite finite width is traversed, the protiles profiles are are eveD even more afi'ected affected by the electrode spaciDg spacing than in the case ol of tbe the vertical ror poteDtial vertical cODtact. contact. The expressions for potential are as in Section 8.6.5 plus tbe etrect effect oC of ODe one or two sets ol of images caused caused by reftectioDs reflections in the two bouDdaries. boundaries. Tbe not fUDdameDtally fundamentally difficult, but The development is Dol is is tedious. We will describe on1y only ODe one cODfiguratioD configuration in detail, that that in which we have one current electrode and and one poteDtial potential electrode, both initially in medium (1) (tig. (fig. 8.35). current source 1 I at el el has bas an image iD in the The CurreDt dike at (provided 3 < b), caused by reftectioD reflection iD in boundary M. Its strength is kl and and it is located (2$ - a) from PI' (2s Pt, the potential electrode. There is a secoDd second image 01 of CI reftected reflected iD in bouDdboundl , which is located iD ary N at ell, in medium (3) at a distance (2b + 23 - a) from PI' Pl' This iD in turo tum causes an image in medium (1) at el clll , (2b + a)vfrom PI' Pl' It is is reftected reflected iD in N to produce image e¡lV,, at (4b + 2s Pt. These reftections reflections are repeated in23 - a) from PI' definitely and N to give two infinite series, of definitely in M and which which oDly only the set oC of images iD in medium (3) have any effect effect on the potential iD in medium (1). WbeD When tbe the poteDtial potential electrode is iD in medium (2), !be does DothiDg, the image at nothing, but both the series iD in medium (1) and and (3) iDfluence influence the poteDtial. potential. Finally when PI P t is iD in medium (3), it is perturbed by and when all all the images iD in medium (1). As As a resuIt result we obtain tbe following potential expressions, for the ditrerent different

+A

E

el

el

(8.52a)

Medium (2):

+e

00

L

m-O

{k2)"'} 2mb + a

(8.52b)

Medium (3):

el

el

}

m_o2(m+ 1)b+23-a m_02(m+ l)b+23-a

(8.52c)

A, B, e, C, and D are constants that are evaluated by applyiDg condilioD of of Equation applying the bouDdary boundary condition (8.7b) turo out (8.Th) at tbe the boundaries M and N. They tum lo to be

A- -k(l- k 2 )

B--k{l+k) B--k(l+k)

e-l+k C-l+k

D - 1 - k2

el

By a similar analysis, we can obtain the potentials potcntials dike. when the current electrode is in the dike.


560

al of el' CI' the respective potentials are: Medium (1):

Medium (1):

IPI J!i' - -(1 + k) v.' 2"

l

k ", } E .... 02(m+l)b+25+a ",_02(m+l)b+2s+a 00

Z 2

(8.53a)

[a

Ip

1 + k { .. ( k ", )) 2" ( ) m~o ",~o 2mb + a

IpI _1 _

00 ..

2 ", kk1m

-» ...",~o -k ~o 2mb - (2s (25 + a)

}

(8.54b)

Medium (3):

IPlo{ 1

IPI(1 IPI(1 + k) V'¡ Vi - 2,,(1 - k) X -

(8.54a)

1m 2

Jr." -

2

Medium (2):

1

) .. ( k ", E ",-0 2mb + a

Medium (2):

E ",-o ... -0 2mb + a -k

k2)

2"

k2", kZm

00

X{

2

J!i" - ~(1 -

v." - -2". 2fT a 3

+k

00 00

21m ",

k

2 ", ",

-k ",~o 2mb _ (25 + a)

2 k Zm ",

{.. 2

k

00

+ k ",_02(m-l)b-(2s+a) E m.0 2(m-l)b-(25+a) }

(8.54c)

'::02(m+l)b+a From these relations one can obtain the value of Zm 2 k '"

} 00 +E ",_02(m+l)b-a .... 02(m+l)b-a

k 2 ",

00

-k { ... ...~02(m+l)b+2s±a k

1 2 ", ",

+ ...~ 2mb - (2s ± a) 00 00

}] }]

(8.53b)

Medium (3):

IPI 1", V,' V{ - -2 (1 f1

+ k)

{OO k {.o E 2 b

Z 2 ", '"

... -0 ",-0

m

+Q 21f1 2

-k

.. k ", E .... 0 2mb - (2s ",-0 (21 -

}}

a)

(8.53c)

In these equations the relative positions al of the potential and current e1ectrodes electrodes must be specified. specified. In Equation (8.53a) (8.53a) the potential electrode is a1ways always to tbe the ldt left al of tbe the current e1ectrode, electrode, whereas in Equation (8.53c) (8.53c) it is a1ways always 10 to the rigbt. right. In Equation (8.53b), (8.53b), however, however, it may be on eitber either side 01 of the current e1ectrode. electrode. Wh~ it is on tbe the lelt, left, one uses the upper signs lar for a in the denominators 01 of tbe the last bracket; when on the rigbt, right, the lower sigo. sign. Finally, when the current electrode is on the rigbt-hand right·hand side in medium (3), and PI PI is 10 to the lelt left

P. lar complete P. in terms oC of PI' in the usual way, for

profiles aeross across the dike. In addition, the expressions

can assuming a resistivity can be made more general by assuming P3 in medium (3). lbe a11 cases by differditrerThe formulas are modified in all entiating the potentials for a half-Schlumberger hall-Sch1umberger array and by using the second derivative derivative for lar the double dipole. Profiles obtained witb with ditrerent different spreads in traversing a thin dike are shown in Figure Figure 8.36. 8.36. On the whole the half-Sch1umberger half-Schlumberger curve reproduces the shape of the dike best, particularly for thin dikes. lbe The corresponding dipole profile has two peaks, the gap between being equal to the tbe dipole spacing. This double anomaly could be quite quite misleading. On the other hand, the half-Wenner spread over a thin dike half· Wenner spread of bigb al width high resistivity shows a "conductor" of greater than the actual TIte full-Wenner lull-Wenner system, actual dike. The however, a1thougb there are dishowever, gives better results, although continuities near the edges of the tbe dike, as illustrated iUustrated in Figure 8.36c. 8.36c. k in tbe the case of the single vertical contact, better proftles profiles would be obtained by moving the array broadside In fact, laet, the profiles are broadside to the structure. In considerably better over thin dikes when the traverse is made at an oblique angle, although althougb the anomalies will will be wider than the actual actual dike. Lateral exploration may also be applied applied to channeIs nels and filled filled sinks of anomalous resistivity when such features outcrop or lie very close clase to the surface. The profiles are similar to the dike, although a1though the lalter depth in the latter was assumed to have infinite depth previous discussions. °o

561

Interpretation Stalion of 1',1', 1',1', Station al at midpoinl midpoint of

r~~,~

C~t. ét. blr -

o

i

¡¡ "~'--r;, J

/ '

------

Station al of 1',1', 1',1', at midpoinl midpoint of

(6) (b)

blL-1

C,C,

Station al at midpoinl midpoint of Slation of C,C.

2rP._/P_' P'_/P_'_ _(Cl 2r __ - -...../Cl

r-"--r-"-,,-"-, 1r-"--r-"-,,-"-' c,

2

1', 1',

p,lp, p.lp,

1', 1',

C,

Slation at midpoint of C,P,

(d)

C•• Pt -

---~----P,

co

.....-a~

C,

b

",Ip, 1'211" - 5·67 5·67 k - 0·7 bla bill = l

p, P,

P,

Figure Figure 8.36. 8.36. Profiles Profiles over a thin dike using dif(erent different electrode spreads. spreads. (a) DoubleHdlf-Wenner dipole Half-Schlumberger spread. spread. (e) (e) Full-Wenner spread. spread. (d) Half-Wenner dipole spread. (b) Ha/f-Schlumberger spread. spread.

8_6.7. 8.6.7. Mapping Three-Olmenslonal Three-Dimensional Anomalies The resislivily resistivity melhod method is nol not particularly sensilive sensitive lo to 3-D anomalies anomalies for the same reason tbal that it is inelfecineffective tive over buried 2-D structures oC of finite finite widlh. width. This Iimitation limitation is well well iIIustratOO illustrated by reCerenee reference lo to tbe the buried spherc sphere considercd considered in Section 8.3.5. 8.3.5. Using a SchlumSchlumberger berger sprcad, spread, \he the apparent resistivity resistivity can be calcula loo by dilferentiating lated differentiating Equation (8.22) wilh with respect lo that lO Eo - PII, x - rcos(J, rcosfJ, and P,,to x [note \hat (1/l)(aV/ax)] and assuming tbat that the sphere is a very 0, we obtain very good conductor so that P2 - O, (8.55) where where x is the distance of the pOlenlial potential elcclrode electrode from from Ihe the surface point aboye above the origin and z the depth lo maxito \he the sphere center. When z - 2a the maxi-

mum contrast p" and PI is only 12$. Thus contrast between P" ties only 15 a sphere 30 m in diameter diameter whose 10p top lies IS m delecled. below surfaee nol be detected. surface probably would not A similar limitation exists when the \he body outcrops, for inslance, \he instance, a hemispherical sink. Unless the \he rim, the \he anomaly traverse passes very close to the wil1 will be missed. missed. These elfccts effects are illustrated in Figure 8.37. \he 8.37. Note \hat that when \he the survey line is over the center of \he O), the \he ratio ratio Pa/PI P,,/PI remains the bowl (d - 0), zero untiJ ol the sink, until \he the potential electrodes are out of S 2R. because &V - O 0 for a as It is not surprising \hat that numerical methods like Ihose those described in Seclions Sections 6.2.7, 6.2.8, and 9.5.3 have modeting as well have becn been developed for resistivity modeling (eoggon, (Coggon, 1971; Lee, 1975; Snyder, 1976; Dey and Morrison. inelude 2-D 2-0 and 3-D 1979). The models include Morrison, 1979). struclures tbe most strikslrikstructures of the usual types. Again, the ing fealure rcsults is the \he poor reo refeature of the rcsistivily resistivity results sponse ol of 3-D largets. targets. Unless they are shallow and the width aboul about the same as the depth, Ihe depth. the anomaly

562 562


1·0 1·0 0·9 P./P'0·8 P./" 0·8

0·7 0·6 O·S 0·5 0-4 0-4 O·) 0·3 0·2 0'1 D·' O l - - - -......--...l:---r--l.,----t1---.-+----!:----+--0~----~----~--~~~----~----~----~~----4----

C,.C,al C•• C,al ±a:> ±«> PI - Pa Pa moved alon, i Co) CD)

e, C,

Plan Plan

íe Ie P, P,

P,

e, C,

f' • • •

c, e, D/R 4

Elev. EI.v. 5

Figure Sch/umberger Figure 8.37. 8.37. Resistivily Resistivity profiles over three-dimensional conduclors. conductors. (a) Schlumberger array array over buried sphere. sphere. (b) Expanding Expanding Wenner array array over outcropping hemispherical conductor.

is weak. weak. Conductive overbutden overburden is also very very effective in masking masking such structutes. structures. Figure 8.38 8.38 demonstrates tbese these limitations witb with a display 01 of profiles profiles and pseudosections dosections (§9.5.1) (§9.5.1) over a vertical block witb with and witbout without overbutden overburden cover. cover.

8.6.8. 8.6.8. Measuring Overburden Depth and Resistivity Resistivity Obviously Obviously tbe the deptb depth ol of overburden can be found using using an expanding spread. However, However, if tbe the bedrock surface js irregular, many soundíngs surface is soundings will will be necesnecessary, Where sary, entailing considerable time and expense. expense.Where tbe the overburden has much lower resistivity resistivity tban than bedrock, which is the usual case, case, good results results may be obtained with three traverses, traverses, employing different different eleetrode electrode separations. Obviously Obviously one small small spread is necessary necessary to measute Pl' lbis This is achieved achieved witb with a separation that is less sure PI' tban than hall half the minimum overburden thickness; thickness; it should not be required at every profile station unless unless

Pl procedute has PI varies rapidly. The conventional procedure

been to complete tbe stations with a the profile at all stations second electrode spacing, which is somewhat larger than tbe lbis gives gives a the m8XÍmum maximum overburden overburden depth. This relation for z from Equation (8.42d): z - c(Pl/Po) (8.56) c(PI/PD) X (electrode spacing) (8.56) where LO, 0.5 and the spacing is js a, L, r where eC -- 1.38, 1.38, 1.0, lor and double-dipole for tbe the Wenner, Schlumberger, and arrays, respectively. obtained is respectively. However, the value obtained generalIy tbe correct correet value unless generally much larger than the p"D •- P'l' Pl. A the spacing is large enough to make P better estimate may be obtained by taking two readings 01 p" at two spreads m8XÍmum of P" spreads larger than maximum overburden deptb. obtained from depth. Then the z values obtained Equation (8.56) (8.56) are plotted against the correspondstraigbt line joining jojniog the tbe ing a, L, or r values; tbe the straight two points, when extended to the ordinate ordínate axis, gives gives the correet correct deptb. depth. Figure 8.39 clarifies this procedure on linear z versus a, L, or axes. Several additional or r axes.

Interpretation

563

lOO 100 90

i

S

80 .:. .:. 70 60 SO

-6 I

-4 I

oO

-2

2 I1

I

I

6

4

I

I

10110) :{~103101JOI 101 101 )02103IOJA~S I021031OJA~5 94 :{~103101..101 103 104 106 :{~. ~~~104

\~~~81t1lf\~~0 1~~~l::'~o ..r.JY,f~ S3 S8 54 S4 53 ~8 'eq00 -eq00 53 58 ... ~ 5.7 ...'J"~~6'')6 57 57 S.8.-S1

~ 61~M2OT1iT60 61~r-6~T60

65 65 66 66 70 70 71 71

-1 -1

0O

SURFACE

SURFACE O.-------~~~--~~~~~~-------L~~--~~~

D

(a)

30m 3 0m

4

I

l~

J

D

IOOOm 1000m

(b)

30m 3 0m

60

n-7 ------~ ------~

SO

40

30 20 10

-6 I

n

--------------_.... .....------_ ---------.. n -

n - I

----------------------------

=1 2 3 4

S

6 7 8 9 10

-4

o

-2 I

I

I

17 165165 17 17 16 15 16 1

-Vs::2Li6 24MM2

34 3434""31~¿8 27 28

fa

17 17

-6 I

o

-4 I

6 I

I

'20

26 34. 30

~~}k37:;3:Wr-40 484 § 48 48 43 48 43 SO S2 5l3S853S853S8 53 ti 62563 60

-i

f

6

I

I1

O

64 64 64

1

-1

O

1

SURFACE SURFACE

U¥M:-:-f (e)

D

3 0m

100Om

D

3 0m

Figure plols far Figure 8.38. 8.38. Resistivity finite-differenee finite-difference modeling; profiles and and pseudodeplh pseudodepth plots y of figure 9.&. 3-D block,. blocle,. the dipole-dipole arra array 9.&1. (Afler (After Oey Dey and and Morrison, Morrison, 1979.) (a) 3-D as (d) (a) and and strike length - 6 units. (b) 2-0 2-D block, infinite strilee strike length. (e) (c) and (d) same .IS (b) with conductive overburden overburden 0.5 units thiele, thick, p - 10 Qm. Om.

(d)

Resistivity methods

564 564

PI

Procedure Measure PI at al small spacing. Measure P. at al 2 larger larser spacings. spacings. Delermine (8.56). Determine Z. from Eq. (8.56). Exlrapolale Une to lo zero zero axis. Extrapolate line

30

(1) (I)

SURFACE

PI~~mm PI~~~ Pz P2 S~ s~ nm ;.r/. Z z

40

(11) (II)

SURFACE

Pl~;~ PI~;;;:~ P2·S00nm Pz - SOOnm

Figure small spread to Figure 8.39. 8.39. Graphical determination of overburden thickness using one one small get PI and two large large spreads spreads to get z. z.

¡;yL, j;yL, ..

300 3tlO

II1/

,"." ,

A.

, ~'\

~¥

:,

Prollle2........\ 'rollle 2........ \

»< ~ ,'" . ,t' ,,,,

..

I .... 1 / ... .-. :\ :.\ ....... 11..: I\..: ~........ :1 ......:1 .....-.. .........-~ ...... ~

~,

/ o

40

80 80

120 120

160 160

~

240 240 280 L(meten) L(melen)

Eal

Figure Figure 8.40. 8.40. Mapping vertical contacts with with the ha/f-Schlumberger half-Schlumberger a"ay, array, Kongsberg, Norway. (After Van Van Nostrand and Cook, 1966.)

points are included included in the plOl plot lo to indicale indicate wherc where the linc cxtrapolation straigbt straight line extrapolation begins to faíl. fail. Bccausc Because the rclation relation appcars appears to be linear, the usuallog-Iog usual log-log scale is nol not suitable. Altcrnativcly Alternatively the cxtrapolated extrapolated z valucs ues may be calculated from z, - nu nu + z~ wberc where $ is the separation, z. z, is obtained from Equation (8.56), and z~ is the interccpt intercept on the ordiDate. ordinate. If U bedrock rcsistivity resistivity is lower than that of the ovcrburden, overburden, it is ncccssary necessary lo to use usc expanding sprcads spreads lo to get quantitativc quantitative ValUC5 values lor for the dcpth, depth, althougb although the

electrode separation need not be as large as for Pz > PI' rclation between betwcen Pl' Wben When Pz < Pi, Pt. there there is no relation P. and z equivalenl can be equivalent to Equation (8.56), as can scen seen from Figures 8.21 and and 8.27b. Tbe lo find The cumulative-p. cumulative-p, plot plot was formerly used to sballow resistivities. rcsistivities. Aldcpth depth of ovcrburden overburden and shallow lor thougb though it bas has no sound theoretical theoretical basis, it works for rcquircs many constant soundings on thin heds beds but requires wbicb are small incrcments increments of electrode spacing, which Tbe data are plotted by compared lo to bed tbickness. thickness. The

Field examples

summing summing successive Po Po values values Cor for the ordinate, that is, is, if the readings were 100, 100, 200, 200, and 300 300 Om Om for spacings spacings of 10, 20, 20, and 30 m, one would would plot 100, 100, 300, lO, 20, 300, and 600 600 Om versus versus 10, 20, and 30 30 m. m. An attempt is then made to find find points where where straightline line segments segments (drawn through as many points as possible) change slope, slope, indicating depth to the interface. 8.7. FIElD FiElD EXAMPLES

t j

l'

In recent recent years most resistivity resistivity data related related to mineral eral exploration are ineluded included in the results of IP surveys; the resistivity resistivity method is not much used used as an independent technique in this application. application. It has, however, been employed employed to a considerable considerable extent in ground ground water search and for engineering engineering geologypreparation preparation of dam sites, sites, bighway highway routes, routes, building fouDdations, foundations, and so Corth. forth. Consequently the case histories histories and problems in this section inelude include several several examples examples not directly related to conventional prospecting. Further examples examples may be found in Chapter 9 of surveys surveys where where resistivity resistivity data were were obtained in conjunction with IP data. 1. Apparent resistivity resistivity profiles profiles obtained with a half-Schlumberger, or gradient, array traversing traversing ververtical tical contacts are shown shown in Figure 8.40. 8.40. The two profiles correspond to different different fixed fixed locations oC of the current electrode el' C1 • The potential electrodes, electrodes, which which are are close close together compared to their separation from from el' C1, are moved moved together, together, whereas whereas the second current electrode electrode is effectively at infinity to the easl. east. The contact with the low resistivity resistivity breccia is sharply defined in both profiles, profiles, wbich which are quite similar to tbe the theoretical theoretical resuIt result Cor for the vertical vertical contact shown shown in in Figure 8.34b. 8.34b. 2. 2. Resistivity Resistivity data obtained in conjunction with an lP IP survey survey are shown shown in Figure 8.41. 8.41. The area is tbe the Cavendish Cavendish Townsbip Township test site, site, 100 miles miles northcast east oC of Toronto. Unlortunately Unfortunately no detailed section section is available lor for the subsurface. subsurface. The rocks rocks are mainJy mainly metasedimentary with small small areas areas oC of acidic and basic igneous igneous types. types. The trend is Dortheast. northeast. Sulfides Sulfides are present throughout the area, at least least in trace amounts, and grapbite graphite occurs in a band oC of calcareous-siliceous rocks in the westem western part oC of the area. area. Figure Figure 8.4la 8.41a shows shows apparent resistivities resistivities plotted in profile profile Cor for four separations oC of the double-dipole electrode electrode system system (x '"' '"' 200 200 ft, ,.n ... 1, 2, 3, 3, 4) on line B; B; Figure 8.4lb 8.41b shows shows the usual pseudodepth plot employed in IP work (§9.5.1.) Clearly there is a low-resistivity zone, zone, continuous at depth from from 4W 4W to 18W, 18W, whicb which is capped by a higher-resistivity bowl near surface, surface, located between between lOW lOW and 14W. 14W. A variety variety of EM surveys surveys made on the Cavendish Cavendish test

565 site agree profiles, beagree with the shallow resistivity profiles, cause they outline two distinct zones rones trending NE, located at 8W 8W and lSW. 3. The search for groundwater groundwater normally requires resistivity resistivity surveys, surveys, both for regional mapping and for sounding. gravsounding. Frequently these are combined with gravity and seismic seismic refraction, the former during reconnaissance naissance and the latter to aid in identifying saturated beds containing fresh or salt water and to resolve resolve the equivalence ambiguity between z and p by unique determination of bed thickness. thickness. This problem is well well ilIustrated illustrated by a groundwater survey survey carried out in the central Sudan savannah 1981). belt near the White Nile (van Overmeeren, OvermeereD, 1981). Figure 8.42 (VES) 8.42 displays vertical electric sounding (YES) data from three locations west of the river and ineludes includes a schematic oC of two interpretations of the basement section, section, assuming either fresh or saline water. water. Both versions versions fit fit the sounding curves, although oruy However, only VES YES 13 suggests fresh water. However, the results from data from a from seismic seismic refraction plus data welI drilled earlier in the vicinity favored the shallower basement depths associated with salt water as shown in Figure 8.42d. 8.42d. 4. Resistivity component of mulResistivity is an important component tiple-method geophysical geophysical surveys for geothermal sources. sources. GeothermaI Geothermal targets are of two types: the more common hot-water systems characteristically oI chlorides and if the have high concentrations of aC subsurface temperatures are - 18D 180°C or higher they produce hot springs and deposit a sinter; the other type, low in chlotype, vapor-dominated geothermaIs, geothermals, is low rides and rich in sulfate ions or alternatively altematively in sodium bicarbonate. Tbe The Mud Volcano area in Yellowstone Park, a typical typical vapor-dominated system, was surveyed in the late 1960s 1960s using IP, SP, resistivity lateral mapping, and resistivity resistivity soundings (Zohdy, Anderson, and Muffter, PFE (§9.3.3a), (§9.3.3a), SP, Muffler, 1973). 1973). Tbree Three profiles of PFE and P. are shown in Figure 8.43 8.43 together with a 6.7 km wide geoelectric geoelectric section of the geothermal anomaly area. follows the YellowYellowarea. Tbe The profile line follows stone River slightly resistivity slightly SW of it. IP and resistivity profiles profiles were were carried out with a pole-dipole or halfSchlumberger Schlumberger array (Fig. 8.18) whose dimensions were m). The Tbe SP electrode were (a + b)/2 -'"' 1,000 1,000 ft (300 m), spacing was 400 400 ft (120 (120 m). m), The IP profile profile is not very significant except for a strong PFE response about 2,000 ft (600 m) wide at al the NW boundary of the geothermal area. The Tbe high IP background is attribuled attributed to widely distributed cIay clay with some pyrite, whereas the anomaly is probably caused by pyrite concentration at depth, because a second profile profile with spacing AB/2 - 600 ft (180 m) (not shown here) had a much reduced IP response in tbis this vicinity. vicinity.

.. -.'---'.

."".'.,...

-,'.

,

s&1

,

i !

.

,

\,

. __.<:.--'-- ---"-~.~.::::::--- '-. . ._ " '. . __,' 0_. '. .__

-.-1 --,,-2

_...:.~~.~.

--~--'It;: , .->C-=:,,,••, , '-.~'. '. "--"-_., -, \. .- .....-.__ ... ...... ._.~... ,,~' .-._\<: ~.--:" ............... , ".......' '.-.l._. ',_ . _- ,-",,-~.~------, ' ...... _-,

_.-. - 3 ··---.-4 "-'-.-4

~# ...

100f't

UneB I I 20W I I I I ~IJIIlPD I I 0-" I I I ~~~W~-----I~.~------~16~------~14~------~1~2------~IO~--i---~8~~~~~6~------~4~------~2W~------~O 4 16 14 II 2W o

.

( )

19W

17 11

n 11

15

Surface

IW

9

Appuq,t Appuq.t mistivity (Om)

n-I~ IO~

/;~'~Ar/~S ~\ ~M'~jlJ

._2~·300 J1''o//i~t( ~~tt:'/ ~ ~r ~I ~ ·

.

3800

5900 S900

•

S«Il S40I

•

2

n - 31-

• _ 4L.

14.200..f ~ ... .61

0

'..... ,

~

~

2S~

10.

\

5800 S800

•

•

(h)

Figure 8.41. Resistivity Resistivity results, results, Cavendish Township. Township, Ontario. (a) Resistivity profile using a double-dipole array with with n - 1.2, 1,2, 3, 4. 4. (b) (b) Pseudodepth plot using the data dat.! in (a). (a).

567 567

Field examples

10

)00 100

300 100

100

E

E

A8/2

10

~

10

AB/2

(m)

(a)

(m)

(b)

100 10 r-______~IO~-------IOrO------__.400

10 o0

o0

O 0

VES YES 13

8B

1I 1000 AB!2 (m) (e)

VES YES

O 0

!

1~8 t

t

...... ......iJ!!W~

~ter

250m 2Snm

30m 3nm

80

11 II

13

t

J5

t +

Nile

11.5 nm

...

preliminary interpretation

-S 160 -S
240 320

r:r',

O 0

!

"

Q

..

''I, 1,

I

iill

I

80

final inlerprelation interpretation

.c .c:

'Q. 'ó.

160 240 WI~ O

-:-,:I

10

~:-

I!

20

..

S

S

~~

I

30

E lE

~I

40km

(d)

Figure 8.42. 1981.) 8.42. Results Results af of vertical vertical electric soundings, Sudan. Sudan. (After van Overmeeren, 1981.) (a) 50unding (a) Sounding VES 6 and and two equivalent solutions. both for saline water. (b) (b) Sounding VES 8 and two equivalent solutions. (e) for (c) Sounding VES 13 13 and and equivalent solutions for fresh fresh water (A) and and saline water warer (8). (d) Preliminary and final final interpretation.

568 568

Resistivity methods

l1l

...

IJ.

::rUb>/"

,o.,

(a) la)

P, - P,

= 400 ft

> !

e; (b) (hI

(a (a

+ b)/2

a

1000 fl 100

10 (e) ld

16

NW

~

::c

t: Ul Q

(dI (dl

SE

0 200 400 600 800 1000 1200

r

I

o

t8 t

_

•

VES YES 2-6.5 2-6.S Station

2000M. Interpreted true resistivity (Om)

~~~ll!l!ITllWI:l ~ ~ ~ mr:ITll WI:! 8-12

18-35

40-60 4
75-130 150-200

f¡~·.:~M f!~·./:·3

500 > SOO

figure 8.43. Volcano, 8.43. IP, IP. SP, SP. and resistivity profiles with geoelectric section, section. Mud Volcano. and Muffler. Muffler, Ye/lowstone Yellowstone National Park Park geothermal zone. zone. (After (Afler Zohdy, Anderson, Anderson. and 1973.)

lbere There is a positive SP anomaly 01 of - 60 mV straddling tbe the target and persisting for some 2,500 ft (760 the SE side. lbis This anomaly is (760 m) beyond on the probably due to streaming or electrokinetic potential (§5.2.lb, but the SE segment is not ex(§5.2.1b, §6.1.1), but plained. The resistivity profile outlines the the geothermal area best with a well-defined well-defined low directly above. lbe The results oC of 16 vertical soundings were used to produce the geoelectric 8.43. geoelectric section in Figure 8.43. Soundings VES YES 1, I, 10, 14, and 16 (see Fig. Fig. 8.43d cor for locations) are displayed in Figure 8.44, 8.44, with the layer resistivities and tbicknesses thicknesses plotted along tbe the Schlumberger horizontal axes. axes. Interpretation oC of the sounding curves was done by two methods, one with partial master-curve matching and auxiliary-point

diagrams (VES otber using an auto(YES 10, 14) and the other matic technique for the complete complete curve (YES (VES 16). 80th VES 1, Both interpretations are shown for YES I, the first with a 6-bed model, the second with a 19-1ayer 19-1ayer computer model. 5. It is worthwhile to summarize some rough rules for suecess exploring for groundwater and success in exploring geothermal sources: (i) lbe The most important is to assemble as much geological information as possible, with particuparticular empbasis or drill emphasis on any 10gs logs from old wells or boles holes in the area. (ü) Cor geochemical geochemicaJ and (ii) Next is to do the same for geopbysical geophysical data.

Field examples

569 100

10

1000

400rlInTrrrr-~-rrrrrnr--rTlIT~--TlI 400 r-r--rrTTTrr--r.,...,.,..rrnr--.-TTTT"mT-"'-'

AB¡2(ft)

AB¡2 (r1)

( a)

(h) (hI

100

10

1000

1000

ec 100

10 10 100 100

10

AB¡2 AB/2

I

I

230 1 100 1 3' 13'

1400

(ft)

21 100 I1 30nm 30Um 600' 56 79 '100' ' 100'

(800)

100 290 AB¡2 (fI) AB/~ lfI)

3'

7'10' 19' 37'58'

(e) (c)

1115 I1

sonm 1115 SOUm 300' -700' 300'

9.5

((/) (d)

Figure 8.44. ... and 0 O 8.44. Soundings used to obtain geoelectric section in Figure 843. ... denote observed and calcufated used in in calculated values. values. (Note the alternative plotting plot/ing methods used (a) and see also Figs. Figs. 8.29 and and 8.42.) (After Zhody. Zhodv. Anderson. and Muffler. 1973.) and (b); see (a) VES 1 interpreted by partial curve matching (6-layer) (6-layer) and and complete curve curve matching (19-layer). H partial curve curve (19-layer). (b) VES 10. 10. partial curve matching (7-layer). (e) (c) VES 14. matching (6-layer). 16, complete curve matching (9-layer). (6·'ayer). (d) VES 16. Table 8.1. 8.1. Sounding data. data.

Well Well

R161 R162 Rl02 Rl02 R72 MH'10 MH'10

Min.p, Min.p. (Dm) (Dm)

55 55 14 25 25 20 20 60

Average

3S

R163 R164 R1ó6 Rl66

35 35 110 110 110

Average

85

Max.p, Ma •. p. mm)

Av. p. P, (Dm)

120 120 60 60 160 100 100 100 100

80 30 39 48 48 89

57

8.0 1.7 3.7 3.7

100 100 300 300 210 210 203 203

57 57 171 171 172 172 133 133

2.9 2.9 2.7 2.7 19 1.9 2.5 2.5

MaxjMin Max/Min

22 4.3 4.3

2.4 2.4

Depth (m)

Yield (min.) (gal/min)

2.5 2.5 3 30 16 10

Producer Producer

10 60 25 25

12 30 6 25 25

20

Dry Dry Dry Dry

---o ---0

Resistivity methods

570

(ili) (iii) Survey Survey procedures should be similar to those

described in field field examples 3 and 4. 4. (iv) (iv) On completion of resistivity protillng, profiling, it is desirable to select VES YES locations at resistivity resistivity lows taking into account (i) and (ü). (ii), (v) (v) Tbe The shape of the sounding curve is certainly significant. significant. The low-grade low-grade data from groundwater surveys surveys given given in Table 8.1 8.1 serve as an iIIusillustration of this. Tbe The data in Table 8.1 8.1 are from from various locations in Sri Lanka, whose whose geology geology is a continuation of the South India Decca platform, mainly Paleozoic Paleozoic and Precambrian with younger coastline sediments. Tbe The data in the table are not representative because the ratio of dry-to-producing wells wells drilled over the past five years (mainly less than SO m deep) is less than 10%. However, However, it seems seems clear from the aboye above and from from other groundwater results in West AIrica Africa that, for a successful successful well, well, the sounding curve should have a fairly fairly well well defined mínimum minimum at reasonable depth, although, if this minimum is less less than a few few ohmmeters, the chances are increased that any water will will be saline. saline. Although the same remarles remarks apply to geothermal exploration, the problem is more complexo complex. Depth of exploration is usually greater than that necessary necessary in groundwater search and more geophysical geophysical methods are required. The resolution of saline from fresh sources, sources, however, however, is not a factor.

8.8. PROBLEMS 1. In an investigation to determine the depth of a conducting layer ol of brine at Malagash, Nova Scotia, the readings in Table 8.2 were were tuen taken with a Megger Megger using an expanding Wenner spread. Tbe The surface layer was found to have a resistivity of 290m. 29 Om. Determine the depth and resistivity resistivity 01 of the brine layer.

rabie Table 8.2. Separalíon Separation (fl) (ft)

p. (Om) (Om) II.

40

28.5 27.1 27.1 25.3 23.5 21,7 21.7 19.8 19.8 16.0 163 14.5 12.9 12.9 11.3 9.9

bO eo

80 100 120 140

lbO 1bO 180 200 200 220

240

260 260 280 280

8.7 7.8

300 320 340

7.1 7.1 6.7 6.5

360 360 380 380

6.4

Table 83. fleClrode Electrode separatíon separation (fl) (ft)

Resislivíly Resistivity (Om)

5 10

15 20

25 30 35 40 45 50 SO

78,1 78.1 56.0 56.0

49.6 47.1 46.0 46.0 51.2 59.8 76.0 76.0 79.6 79.8 72.2 72.2

4OO..---------'it-------------.------,

~r-------------~------------------------------~

300~-#------j~_\----------------_1 300r1--~--------~--+----------------------------------i

p,l(lm, p.l(lmt 200r---~~--+--_r----------------__i 200r-----~~---r----_r--------------------------------_;

Fisure 8.45. 8.45, Resistivity mappins wilh with Wenner spread over Iimestone limestone and and sandstone ft. (After (Afte, Van section sepa,aled separated by vertical conldets. contscts. 5tdtion sution inte,val interval 100 fl, tt; a - 100 ft. Nostrand and Coo/t., Cook, 1966.) 1966,)

Problems

571

.. .

C, P, P, C, :l ~

Station

'cg }--"-"'--'-'---------------t----'o"\-------

"

2' 21--------------+--4-------

.a

~ ~1_--------_;__-+_1..,.rt_---\----_t\_

?> e:~ Et--------~\--I-----\----+-

E

c

a. 1 ~

CI.bc;"::7'''O',.......",_I--~.L-----------~_L...<

«

o

1000 1000

ISOO ISoo

2000 2000

2S00 2500

3000 3000

Figure Hilrdin Figure 8.46. 8.46. Resistivily Resistivity milpping mapping wilh with Wenner spreild spread over karsl karst lopography, topography, Hardin Counly, /IIinois. Sldtion Vdn NOSlrand County, Illinois. Station interval- 100 100 fl, tt, a - 100 fl. ft. (Afler (After Van Nostrand and Cook,

1966.) Table Table 8.4. Une Line 10 Station 26W 25 25 24 23 23 22 22 21 21 20 19 18 17 16 15 15 14 13 12 12 11 11 10 9 8 7 6 5 4

3 2 1 B.l. s.i.

p.(n - 1) (Om) 2,750 2.750 2,000 2.000 1,700 1.700 1,850 2,250 2,000 1,000 1.000 400 250 200 150 250 400

600 60CJ 900 1,000 150 150 550 4,100 3,600 3,6OCJ 2,800 1,000 1.000

+ OOS p.(n - 4) (Om)

1,450 700 450 250 200 150 150 200 150 150 100 20 150 150 350 200 50 20 25 100 350 700

lineO Line 0 p.(n-l) p.(n-1) (11m) (l'lm)

1,700 3,000 3,000 2,150 2.150 850 350 350 250 250 200 150 250 450 650 1,750 2,350 2.350 3,800 3,800 1,000 1.000 950 1,000 1.000 1,100 1.100 1,600 l,6OCJ 3,200

2. 2. lo In a resistivity resistivity survey survey performed lor highway highway construetion, construction, the readings in Table 8.3 8.3 were were ob· oblained tained with an expanding Wenner spread. Plot P. p. versus versus a. How many layen layers are indieated indicated by this of partial this curve? curve? Can you use the method ol curve jf so, curve matchiog matching for multiple Jayers layers and if so, do the results agree agree with those obtained by the

+ 00

Une 10 10 line

+ OON

p,,(n - 4) Po(n (11m) (l'lm)

p,,(n -1) Po(n (Om)

p,,(n - 4) Po(n (Om)

500 300 500 500 450 50 100 100 450 850 1,100 1.100 550 800 1,550 1.550 850 1,250 1.250 850 2,000 2.000 2,850 2,850 2,350

500 150 400 400 850 1,500 1,700 1,200 3,800 3.800 8,900 9,300 9,200 6,650 2,460 2,460 5,750 5.750 6,600 6,6OCJ 4,000 2,250 2,250 4,000 4.000 7,400 7,000 7,000 6,600

1,500 1,900 1.900 2,000 2,000 1,600 l,6OCJ 800 800 2,400 2.400 5,300 10,000 10.000 12,700 13,500 12,700 12,000 12.000 10,900 10.900 7,800 7,800 5,700 5,500 5,500 5,200 5,500 5.500 4,300 4,300 6,500 6.500 6,800

eumulative extrapolation cumulative p plot and from the extrapolation Find the depth of 01 described in Section 8.6,81 8.6.81 Find overburden by any or all 01 of these methods. 3. Figure 8.45 tuen with a Wenner 8.45 shows a profiJe profile taken of 100 Ct. ft. Station spread having a fixed fixed spacing oC intervals are 100 ft. seetion includes inc1udes Ct. The geologie geologic section sandstone and limes tone beds with practically praetieally limestone

Resistivity methods

572 Table Table 8.5. 8.5.

Table Table 8.6. 8.6. L (m)

1.5 1.5 2 3 4 6 8 10 12.5 12.5 15 20 20 25 25 30 40 40

50 50 60 80

Resistivity

1\ 1'.

EM16

(11m) (Om)

160

SIn. SIn.

1'.(10) 1\(10) (11m) (Om)

p'(30) Po (30) (nm) (Om)

Dip Dip

Quad.

(%)

(%)

-6 -5 -1 +1 0O -3 -4 0O 4 5 3 2 -1 -2 -2 -10 -19 -26 -27 -13 +3 +3 17 24 22 22 27 2B 28 13 7 3 2 1 -3 -4

6 4 4 4 3 1 1 0O -1 -2 -2 -3 -5 -2 -2 -3 -7 -7 -13 -15

96

70 70 54 54 40 40

33 33 27 27 20. 20 20 22 22 23 23 27 27 30 30 38 38 48 48 67 67

vertical contacts. Locate these beds and speculate on the souree source of the small positive anomaly al at 3,100 ft. 4. Tbe The profiJe profile 01 of Figure 8.46 was obtained in exacdy actly the same manner as thal that of problem problem 3; tbis this is an area of of karst karst topograpby topography io in Hardin County, IDioois. Dlinois. Tbe The timestone limestone contains numerous sinkboles holes and cbannels, channels, most of whicb which are filled filled with c1ay. clay. There are occasional occasional empty cavems caverns as well. Make a rougb rough interprelation interpretation of the oear-surface near-surface section from the resistivity profiJe profile by loeating locating the cJay-filled clay-fined sinks and/or cavems caverns in the timestone limestone host roek. rock. 5. Apparent resistivities in ohm-meters are given in TabJe Table 8.4 for portions 01 of three tines lines from an area area in eastem eastern Nova Scotia wbere where an IP survey was carried carried out. The The topography is generally ftat flat except for the west portion (line O 0 + 00 has an elevation cbange change of + 250 ft between stations 13 and and 20, tine line 10 + OON has a cbange change of + 100 ft between slations stations 15 and 20, tine line 10 + OOS has a cbange change 01 of + 75 ft between stations 21 21 and 26). 26). The rocks are known to be sedimentary io in the valley wbereas whereas the hins bills in the vicinity are mainly granitic. Lines are 1,000 ft apart and stations 100 ft. ft. The double-dipole spread (Fig. 9.8a) was used with dipole spacings oC of x-lOO x - 100 ft; resistivities are given for n - 1 and 4 onIy, only, Le., l.e., the distances between the inner electrodes were 100 and 400 fl, ft, respectiveIy. respectively. Ptot Plot these profiles and inlerpret interpret the results. 6. Tbe The readings readings in Table 8.S 8.S were obtained duriog during a Scblumberger VES YES program for rural groundwater supply. L - ABI2 AB/2 is ball half the current electrode spacing. Potential electrode spacing was

- 4SW 4SW -3 -2 -1 O 0 lNE 1NE 2 3 4 5 6 7 8 9 10 11 11 12 12 13 13 14

15 16 17 18 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28

135 135 135 135 160 177 lOS 105

75 75 80 80 87 87 90 100 150 300 300 460 460 250 250 204 204 103 103 90 60

225 225 180 220 220 210 210 190 172 150 168 130 137 168 165 165 245 245 355 355 270 270 242 242 190 197 178 86

30 32 32 33 33

68 67 102 60

30 30

47 48 4B 50

-13 -10 -12 -17 -19 -17 -17 -14 -14 -12 -7 -4 +1

increased three times al times during the sounding: at L - 8, 20, and 30 mi m; the resultant discontinu-

smootbing at al these ities bave been etiminated eliminated by smoothing have been points. Analyze the sounding using using partial partíal and complete curve matching with with auxiliary-point auxitiary-point curves plus two- and tbree-bed and by three-bed master curves and computer, whatever is available. available. Compare the results. 7. bas been been carried 7. Althougb Although resistivity profiling has out routinely lor for many years in groundwater exploration, it is a rather slow s]ow and expensive survey and the possibility of substituting a faster, laster, cbeaper cheaper technique is attractive. from part of of a The readings in Table 8.6 are from Scblumberger with two separations. Sehlumberger profile done with Tbe loeate an an intrusive ledge of The purpose was to locate basement roek section. At the rock in a sedimentary section. same time a VLF VLF profile was done with an

Problems

573 100 100 P. 80 (Um) 60 40

41W 41W

36W 36W

Dipole Dipole ,pacini 'paci., 10m

.. -1 ".1

Dipole

centen centeR 20m 20m

20 20

'~!

10m

.. -3 ".3

40m

10m

100 100

~

80

60 40

20 20

I

I

50m

20 20

-50m_

1~'::2W:=-:----!':----:'.:-----;=-----:=----t:;-----:t.-----~::;--' 1~~2W------4~1-------40~----~3~9------~3~8------~37~----~36~----~3~5W~~ 36 35W

39

41

37

38

Figure 8.41. 8.47. Apparenl Apparent resislivilies resistivities from IP survey. survey. norlheasl northeast Brazif. Brazil. 65 !

14--14--200 200 fl---lot rl--lot

1

!

Line 4

•" •_ 1 1- - 22---J:1/ ".2 • -2

31

o

4N I

!

+ OOW

~26

27

.-3 ".3

46

63

66 66

• _ 4 ".4

31

30

39 39 64 64

62

'1s'

70

51

74

7J

74

~

(a) ~ I

!

ffl 4N ,

O !

Lino 4 + OOW ••1 1--.

27 27

_-2---.• 2----

34

".)-----

::: ------~73 ".4-----Figure doubJeFigure 8.48. 8.48. Apparent resis/ivities resistivities (Po/2fT (Po/2fT Oft) from 11'10 two /P /P surveys using using a doubledipole array wi/h Dala from from with separa/ion separation 100 100 fl. ft. (a) (a) Dala Data from frequency-domain /P. /P. (b) Data time-domain IP. tP.

Resistivity methods

574

Figure Figure 8.49. Apparent·resistivity Apparent-resistivity contours ({Ut) (Oft) for a base·metal base-metal zone, eastern Nova Scotia. Scotia.

EM16 EM16 instrument (§7.4.2f; §7.8, §7.8, examples examples 3, 3, 4) which which measured measured dip and quadrature associated associated with the secondary vertical vertical EM field. These These data are aIso also given given in Table 8.6. 8.6. Stations are 10 m aparto apart. The resistivity resistivity columns columns are Cor for Schlumberger Schlumberger spreads with AB/2 - 10 m, MN/2 - 2 m, and with AB/2 - 30 m, MN/2 - 5 m, m, respectively. Plot the resistivity resistivity and EM16 EM16 profiles profiles on the same horizontal scales scales and compare them as to informainformation derived derived and correlation. correlation. Now plot the EM16 EM16 dip-angle dip-angle data using using the contouring relations given given in Section Section 7.8, 7.8, examexampie ple 3. 3. To maintain the proper polarity, the plotting is done from NE to SW SW (rigbt (right to left with respect respect to the other profiles). Also the vertical vertical scale scale should be chosen rougbly roughly the same length Pa scale to enhance the curve curve match. match. In as the Pa

considering the possible correlation correlation between the profiles, physiprofiles, why why should it exist? Is there any physical relation between the numbered vertical scale for the EM16 and the P p"a scale of oC the resistivity resistivity profile7 differprofile? Hence what is the fundamental difference remaining between the two types of survey with respect to acquired data7 The EM16 survey extended an additional 300 m SW and was perCormed resistivity formed by one man in 40 min; the resistivity profile Cor nearly 3 h. profile occupied Cour four men for 8. 8. The resistivity resistivity profiles shown in Figure 8.47 are taken from an IP survey. survey. The double-dipole spread was used with two dipole spacings: x 10 m for the top three profiles, proftles, 50 m for Cor the remaining four. Distances between the dipol~ centers are noted on the right-hand rigbt-hand column beside the proftles, profiles, corresponding corresponding to n - 1, I, 3, and 4 Cor m. for x-lO x - 10 m, and n - 1, I, 2, 3, 4 for x - SO m.

Problems

575

fH-_ _

.l,--\-_~-="'-_---if-_7_23_

) ' I64N

U6N

-

118

148N

200ft

Figure Figure 8.50. 8.50. Apparent·resistivity Apparent-resistivity contours contours (rlm), (rim), southern New Brunswick.

10000

A

B

1000

v~1.

~\ .r> \

\\

o

10km

(a) (a)

'''V

______-L________L-______ 10l...----.L-----l.----.....J 10000 10 100 10 100 1000 AB/2 (m) 10~

~

(b)

Figure 8.51. Example Example of "dry wedge" i/nd and related electric soundings for 8,oundwater. groundwater. (a) Vertical seclion. section. (b) Vertici/I Vertical sounding over the section.

Apparent resistivities resistivities are plotted on a log scale and vary from from a maximum maximum of about 700 700 Om (west (west end of profile profile lor for x-50 m, n - 3) lo to a minimum minimum of 7 Om (al (at 38W 38W on tbe the profile profile for xx-lO - 10 m, rn, n = 4). 4). Tbe The profiles profiles represenl represent successuccessively sively larger deplbs depths of penetration from top to bottom ol of tbe the figure. Tbe The overburden is considerably oxidized known to be thin, thin. about oxidized but is moWD 1-2 m. m. Wbal What interpretation can be made Irom from these these profiles? Would tbere there be any advantage in plotting expanding spreads, spreads. tbal that is, deptb depth sounding profiles, for fixed station locations? locations? 9. 9. Two deptb depth seclioDS sections oI of apparent resistivity resistivity are shown shown in Figure 8.48 8.48 Ior for an area in nortbero northern Quebec. Quebec. Botb Both employed employed tbe the same double-dipole

electrode system with x = 100 ft and n1,2,3,4. One was done with witb a time-domain, the otber sel. The Tbe traIraother with a Irequency-domain, frequency-domain. IP set. oI an old Qld mining operaverse verse is in the vicinity of tion in whicb lead, and some silver which zinc, copper, lead. were Ibe results obtained by were recovered. recovered. Compare the tbe tbe profiles profiles for the two methods by plotting the n - 1 to 4. tbe difference? difference? Are 4. Can you explain the Ihere fealures in these tbese there any obvious interesting features plots? The survey was done during winter because of swampy terrain. 10. 10. Figure 8.49 8.49 sbows shows apparent resistivity contours obtained from an IP survey in eastern eastero Nova Scotia. arrangement was doubleScotia. The electrode arrangement racks in dipole witb with x - 200 200 ft and n - 1. The rocks

Resistivity methods

576

o

-5 I

n - 1 "1 2 3 4 ~ 5 6

i e

-4 I

-3 I

-2 I

-1

I

oI

3

2

4

5

I

I

I

I

75 81 81 71 71 71 71 81 96 75 81 96 103 73 73 61 66 153 66 61 61 103 74 107 107 49 74 49 47 169 169 47 7S 75 110 110 75 4S 37 1'07 45 1'07 227 127 37 75 43 76 43 34 100 92 76 92 100 34 41 158 41 33 90 158 158 90 33 (a) (a)

O 0

AIR

AIR

-4

4

3

EARTH p= p = lOOnm

-5 -S

I

n - 1 "-

2 3

iE S

4 5 6

Q: ~

-4 II

-3 II

-2 I1

-1 -I II

4

3 1I

2 1

O 0 II

II

95 73 81 73 95 81 110 110 81 81 101 63 101 69 101 101 69 101 214 101 101 63 101 104 70 52 70 222 222 70 52 70 104 106 70 48 SS 55 161 161 287 181 181 SS 5S 48 70 106 71 SO 47 71 71 71 47 50 123 235 235 123 50 4S 47 109 188 45 188 109 47 45 (b) (bl

AlR AIR

-s -S -4 m..;¡;J&ih.-l a-.rJ&ih.-.l

-3

-2

-1

2

O

P2 P2 ·25 =25 nm

p¡-IOOnm i-:';;:::~:/

-S

I

.'

"~"'.

,"

-4

I 1

4

3

J~:Hii%fl&.:.;%k.J;.:::~:~:::::' . _ . lwp;:*l&.:.&::::;::J;.:::~:~:::::'

-3 I

-2 I

-I -1

I

::; ::;

O 0

2

I

3

II

II

........:: ::

..... ...•..

~. ~

4 II

97 97 98 84 84 97 97 98 2 101 101 102 100 81 81 83 100 102 101 81 81 3 102 104 100 80 85 85 80 100 104 102 4 103 87 86 80 lOS 103 lOS lOS 99 lOS 103 99 80 86

n " -1 -I

E S Q: ~

S 6

87 88 106 98 80 98 80 88 89

87

88 89

80 88

96 80

106

98

(e) (c)

Figure of Figure 8.52. 8.52. Effect Effect o( of terrain on dipole-dipole resistivity survey. survey. (a) (a) Pseudodepth plot ot At Oller llertieal Oller 2-0 2-D ridge. ridge. (b) Model results results for a 30· ridge. ridge. (e) (c) Resu/rs Results Oller Oller a buried llertical eonduetille conductive dike. dike.

References

~ ; r

i

!

I

I

t¡ ,i

the area are generally volcanics, voleanies, although in the seetion shown there are no outcrops; outerops; the oversection be anywhere more burden is not expected to be It deep and and usually is less than 15 ft. fI. than 25 ft geochemical anomaly (Cu, There is a large-scale geochemical Orainage is to Pb, Zn) associated with the area. Drainage the south whereas the glaciation direction is apdata make an proximately northeast. With these data interpretation of the zone. interpretation 11. The contours contours of of apparent apparent resistivity illustrated in 11. Figure 8.50 were developed from an IP survey in southem New Brunswick. Brunswick. The predominant predominant geosouthern logieal feature in this area is a stock-like basic logical introstive of 01 gabbro-norite gabbro-norite in an anticlinal antielinal strucstrocintrustive sI ate, quartzitic ture of metasediments - argillite, slate, gneiss. Note Note that the only lines mica schist, and gneiss. aetually surveyed are 148,156, 148,156, and 164N. Would actually eoverage sufficient sufficient to interpoyou consider this coverage contours of this type? Take off profiles protiles from late contours lines 156N and 160N and make an interpretation. 12. A problem encountered occasionally in ground12. ealled regions is called water search over large basin regions wedge." This is an area located above aboye a the "dry wedge." relative1y shallow section of inclined basement. relatively indieates, a well well that reaches reaehes the As the name indicates, impermeable basement above aboye the water level level in impermeable will be dry. overlying sediments will overlying The section shown in Figure 8.51a is a schematic of this situation from a groundwater Afriea. The dry wedge wedge is beprogram in West Africa. tween tween A and B. The two soundings shown in Figure 8.51b 8.51b were carried out in the area. lnterInterpret the geologie geologic section below eaeh each and determine roughIy roughly where where they were ]ocated located in Figure 8.51a. 8.51a. What prior inlormation information about the regíon region would would be neeessary necessary lo to eliminate this difficulty? 13. 13. The apparent-resistivity pseudodeptb pseudodepth plot displayed in Figure 8.52a 8.518 is from a dipole-dipole survey survey over the surface seetion section above it. This was a 2-0 ridge. 2·D feature that approximated a 300 ridge. The survey crew crew was supplied with a set 01 of model model cards for terrain corrections, of which which Figure 8.52b was the closest match. Correet Correct the data for topography and replot them. them. Compare the resolts results with the dike anomaly in Figure 8.52c. 8.52c. Oiscuss Discuss any obvious dilferenees differences between between your eorrected corrected plot and Figure 8.52c. 8.52c.

REFERENCES Bewlcy, Bewley, L. V. V. 1963. Two-Dimensional Two-Dimensional Fiellis Fields in in Eleclrieal Electrical EngineerinB. Enginuring. New New York: Dover. Bhauacharya, Bhallacharya, P. P. K., and Patra, H. P. P. 1968. Diree/ Direct Curren/ Current Elec/rieal Sounding. Amsterdam: E1sevier. Elsevier. ElectricalSounding.

577 Bhattacharyya, B. B., and and Sen, Sen, M. M. K. K. 1981. 1981. Depth Dcpth of of investigation investigalion of of colinear colinear electrode electrode arrays arrays over over homogeneous anisotropic anisotropic half-space half-space in in direct direct current currenl methods. melhods. Geophysics Geophysies 46, 46, 768-80. 768-80. Coggon, 1. H. 1971. 1971. Electromagnetic E1eclromagnelic and and electrical eleclrieal modeling modeling by by the Ihe finite finile element elemenl method. melhod. Geophysics Geophysies 36, 36. 132-55. 132-55. Compagnie Generale Générale de de Geophysique, Géophysique. 1955. 1955. Abaque Abaque de de sondage electrique. éleclrique. Geophys. Geophys. Prosp. Prosp. 3, 3. Supp. Supp. no. no. 3. 3. Dey, Dey. A, A.. and and Morrison, H. F. 1979. Resistivity Resislivily modeling for for arbitrarily struelures. arbilrarily shaped three-dimensional structures, Geophysics Geophysics 44. 44, 753-80. Dobrin. M. 1960. 1Tntroduction ntroduc/ion to lo Geophysical Prospecting. Prospec/ing. New York: McGraw-Hili. McGraw-HiII. Fox, Fox, R. C, c., Hohmann. G. G. W.• W., Killpack. T. T. 1.. J•• and Rijo. Rijo. L. 1980. Topographic Topographie effects effecls in in resistivity resistivily and induced polarization surveys. Geophysics 45, 45. 75-93. surveys. Geophysics Ghosh, Ghosh. D. D. P. 1971. The The application applicalion of of linear filter filler theory to lO the the direct interpretation inlerprelation of of geoelectric resistivity resistivily sounding measurements. Geophys. Geophys. Prosp. Prosp. 19,192-217. 19.192-217. Holcombe. H. T., T.. and and Jiracek, 1iracek. G. G. R. 1984. 1984. Threedimensional terrain lerrain corrections in in resistivity resistivily surveys. surveys. Geophysics 49, 49. 439-52. Hummel, Hummel. J. N. 1932. A theoretical study sludy of of apparent resistivity in surface potential potenlial methods. Trans. Trans. A.1.M.E. A.I.M,E. Geophys. Prosp. 97. 392-422. Inman. 1. J. R., Ryu, J.• J., and and Ward. Ward, S. H. 1973. Resistivity inversion. Geophysics Geophysia 38. 38. 1088-1108. Johansen, H. K. 1975. Interactive Interaclive computer-graphiccompuler-graphicdisplay-terminal system for for interpretation of of resistivity resislivily soundings. Geophys. Geophys. Prosp. Prosp. 23, 449-58. Johansen, H. K. 1977. A man/computer interpretation system syslem for resistivity resistivily soundings over a horizontally stratified Geophys. Prosp. Prosp. 25.667-91. 25,667-91. slratified earth. Geophys. Keller, Keller. G. V., V.• and and Frischknecht. F. C C. 1966. Electrical Elee/rietJl Methods Me/hods in Geophysical Geophysical Prospecting. Prospec/ing. London: Pergamon. Kunetz, PrincipIes of 01 Direct Direc/ Current Curren/ Resistivity ResislivÍ/y Kunelz. G. 1966. Principles Prospecting. Prospec/ing. Berlin-Nikolasee: Gebruder Borntracger. Borntraeger. An inlegral integral equation and Lee, T. 1975. An and its solution for for some some two- and three-dimensional problems in resistivity resistivily and and Geophys. Jour. Roy. polarization. Geophys. induced polarizalion. Roy. Astron. Soc. Soc:o 42,81-95. 42.81-95. Maillet, R. 1947. The The fundamenlal rundamental equations of Maillel, of electrical eleclrical prospecting. Geophysic:s Geophysics 12, 529-56. prospecling. E. 1963. Properties and drawing of Orellana, E. of the so-called Geophysics 28.99-110. Dar Zarrouk curves. Geophysics O. D. O. 1976. A method for Snyder. D. for modeling the the resistivity and IP response of of two-dimensional bodies. Geophysics Geophysles 41, 997-1015. 41. Nostrand, R. G .. and and Cook. K. L. 1966. Interpretation Inlerprelation Van Noslrand, of resistivity dala, data. U.S.G.S. Prof. Paper No. 499. of Overmeeren, R. A. 1981. A combination of van Overmeeren, of electrical resistivity, seismic seismic refraclion, refraction. and resiSlivity, and gravity measurements for groundwater exploration in Sudan. measuremenls Geophysics 46, 1304-13. Geophysics A A. A. R. 1965. The aUlÚliary auxiliary point method of of Zohdy, A. electrical sounding interprelation interpretation and and íts its relation to eJeetrical parameters. Geophysies Geophysics 30. 644-60. the Dar Zarrouk paramelerS. A R. 1973. Automatic inlerpretation interpretation of resistivily resistivity Zohdy, A. A. functions. sounding curves using modified Dar Zarrouk funclions. USGS-GO·74-017. PB-232703. U.S.G.S. Report USGS-GD-74-017. A R., Anderson. L. A., and Mumer, Muffler, L. J. P. Zohdy, A. A. 1973. Resistivity. self-potential and induced polarization surveys of a vapor-dominated geothermal system. Geophysics Geophysics 38, 38. 1130-44.

Chapter 9

Induced Polarization

9.1. INTRODUCTION

Because the equipment employed, although more elaborate, is similar to that used in resistivity, it is customary to measure apparent resistivity, in addietrect, at each station. However, intion to the IP effect, poIarization, being mainly electrochemical eIectrochemical in duced polarization, origin, has more in common with spontaneous polarization than bulk resistivity. In order to understand IP we will consider these origins in the next section. It is interesting to compare the growth of IP and EM techniques. At present it is possible to measure domain, and also to both in the time and frequency dornain, determine complex resistivity (amplitude and phase) with either rnethod, method, although the timetable for development is surprisingly different. ditrerent. For example, EM frequency-domain surveys (Turam, Slingram) of oC amplitude and phase have been carried out in Scandinavia since the mid-1920s (Hedstrom, 1940), although they did not receive much attention in the latero United States and Canada until sorne some 35 years later. Roughly another 10 years passed before the first time-domain EM equipment appeared (Newmont EMP, EMF, Input). On the other hand, hand. time- and frequency-domain IP were developed within a few years 01 of each other in the United States and Canada in the early 1950s, whereas the complex resistivity equipment was not available until two decades later.

Induced polarization (IP) is a relatively new techrnainly nique in geophysics, and has been employed mainly in base-metal exploration and to a minor extent in groundwater search. Although the Sch1umberger Schlumberger brothers, the great pioneers in geophysical exploration, had recognized the phenomenon of induced polarization some 60 years ago, during their original work in se]f-potential, self-potential, its popularity as a geophysical tool dates from the mid-1950s, following further development work from 1948 to 1953. One form of polarization, the overvoltage etrect, effect, has been familiar in the field of physical chemistry for an even longer time. polarlzation can be An illustration of induced polarization obtained with a standard four-electrode dc resistivity spread by interrupting the current abruptly. The voltage across the potential electrodes generally does uro instantaneously, but decays rather not drop to zero slowly, after an initiallarge initial large decrease from the original steady-state value. This decay time is of the order of seconds or even minutes. If the current is switched sud den initial inon again, the potential, after a sudden crease, builds up over a similar time interval lo to the dc amplitude. original de In one type of IP detector the decay voltage is measured as a function of time in various ways; this 9.2. SOURCES OF THE INDUCED method is known as time-domain ¡P. IP. Because the POLARIZATION POLARIZA TION EFFECTS buildup time is also finite, it is clear that the apparent resistivity (actually a complex impedance) must 9.2.1. General vary with frequency, decreasing as the latter increases. Thus the measurement of Pd at two or more The decay curve shown in Figure 9.1 represents a frequencies, retum to the original state following fol1owing the disturbance frequencies. generally below 10 Hz, constitutes an- return other method of detection. This is known as fre- due to applied current. During the time of the origiquency-domain ¡P. IP. nal current flow, ftow, presumably some sorne energy storage Superficially the decay and buildup time resem- took place in the material. Although this stored bles bIes the discharge .and ·and charge time of a capacitor energy theoretically could - and probably doesthrough a finite resistance. But the charge and decay exist in several forms, for lor example, mechanical, eleceJeccurves are logarithmic rather than exponential (as in trical, and chemical, laboratory studies of polarizaR-e circuit) and do not commence at the static tion in various rock types have establisbed the R-C established that the potentiallimits, potential limits, O 0 and ~ (Fig. 9.1). lar the most important. chemical energy is by far

Sources of the induced polarization effects

579

Transient decay in rock sample due to electrode polarization

E u

-...

c ... ~o

::I

V

Transient decay in R-C circuit

o

3

6

Figure 9.1. Comparison of IP and R-C decay curves.

This chemical cbemical energy storage is the tbe result of (a) ol ions in ftuids throughtbroughtbe mobility of variations in the out the rock structure and (b) variations between ionic and electronic conductivity where metallic mintbese effects is known erals are present. The first of these electro/ylic polarization and constias membrane or electrolytic tbe background or so-called normallP effect. effecI. It tutes the tbat do not contain metallic may occur in rocks that e/eclrode polarizaminerals. The second is known as electrode lion or overooltage. overoollage. It is generally larger in magnition tban the tbe background IP and depends on the tbe tude than ol metallic minerals in the tbe rock. The two presence of effects are indistinguishable by IP measurement. tbey appear to be independent independen t of ol the tbe Furthermore, they struclure in rocks and minerals, atomic or molecular structure buIk effect. that is, IP is a bulk

9.2.2. Membrane Polarization Electrolytic conduction is lhe the predominating factor §S.2.4), being tbe onIy in most rocks (§5.2.2 and §5.2.4), the only form of conduction when no minerals are present Crequency is low. Thus a rock structure must and the frequency be somewhat porous to permit current ftow when mineral s metallic minerals are absent. Most rock minerals have a net negative charge at tbe the interface between the rock surface and pore fluid. Consequently positive ions are attracted toward, negative repelled from, this interface; tbis this positive ion concentration may extend into tbe the fluid zone to a depth of about 10- 6 em. cm. If this tbis is the tbe order of widtb width of the tbe pore itself, itseU, wiIl accumulate at one end of the zone negative ions will wben a dc potential poten ti al is applied and leave the otber other when across it. As a result of this tbis polarized p01arized distribution, acrossit. later time, when the current flow is impeded. At a 1ater retum to their origiorigícurrent is switched off, the ions return

nal positions, taking a finite time to do so. This situation is illustrated in Figure 9.2. The membrane IP efrect effect is most pronounced in tbe c1ay minerals, in whicb the presence of clay which tbe the pores are particularly small. The magnitude of polarization, pOlarization, bowever, does not increase steadily witb however, with tbe the c1ay clay mineral concentration, but reaches a maximum and then decreases again. This is because because there must be altemate passages of ol larger cross section and very alternate cm) in tbe wbere ion short lengtb length (- 10- 3 em) the material where accumulation does not talce take place for appreciable time; otherwise botb both total current flow and polarization are reduced. Optimum concentration varies in oC clay, being low in montmorillonite different types of Sbales, with witb a high percentand higber higher in kaolinite. Shales, age 01 of clay minerals. have a relatively low polarization. The Tbe membrane effect also increases with the tbe tbe pore fluid. salinity of the As a result of these factors, membrane polarization is generally a maximum in a rock containing material s scattered tbrough ratber clay materials through the matrix in rather small (~ 10%) concentration and in which the elecsorne salinity. trolyte has some polarization include inelude Otber sources 01 Other of background pOlarization normal dielectric and electrokinetic effects, presence 01 condueting minerals mineral s in very small amounts, and of conducting possibly surface eonduction conduction on normally nonconducting material. Of these, the electrokinetic response due to variations in pore cross section affeetaffecting fluid flow is probably more significant than tban the tbese sources, however, is comparaothers. None of these ble in magnitude to membrane polarization. overal1 background polarization p01arization is about what The overall one would expect from a rock containing 1 to 2% conducting mineral minerals, s, but may vary from one-tenth to ten times this value. Because it cannot canoot be distinguished from electrode polarization, the background oC geological noise varying from provides a level of place to place.

9.2.3. Electrode Polarization This type, similar in principle principie to membrane polarizawben metallic material is present in the tion, exists when rock and the current flow is partly partIy electronic, electronic. partly e1ectrolytic. A chemical reaction occurs at the interelectrolytic. face between the mineral and solution. Consider tbe the two pore passages shown in the rock section in Figure 9.2c. In the upper one the current flow ftow is entirely electrolytic. In the lower, tbe the presence of a metallic mineral, having net surface cbarges charges of opposite sign on either face, results in an accumulatoo each. The e1ectrolyte adjacent to· tion of ions in the electrolyte action is that of electrolysis, when current flows and an electron exchange talces takes place between the metal

Induced polarization

580 Rock Rack .L L LIlIl «

•e

«

(<< ( , ~

<

(I tt I'

Eleclrolylc Eleclrolyte

o..... o.ooFo o.ooFO e • e •

O o

0O

e e • e • e ••

__ ,, ,,

•e

0O

e e ••

e• . •

0O

e e e e •••• •e

r:.-="!Y~;,»,;,~;;,; r:'-:-5Y~;'»';'~;;'; ,a, Rock ,a.¡ ~ Roc:k ~

(8)

a.y wilh Clay with •

Relativc charae Relative

+charae

O -charae o

.J-I« .J-I c ( ,' «

Roc:k Rock

_

0.. o..

c«,« " 1, « ", (, 1"'«" "

Elect~~e

• :ee •e

~o--:... ~o--:...

f$!IJ. • •

0..;:e O..;:¡

o~ O~ •e

•

~ -- ••

o;~¢;'";~j o;~Vr;~j , ) it~k' :' ,. ~

'L..f, tu _. _e 0 o-+ _. 0_e

(b)

FII ;I 1.,. ,.,. F

Clay partICles parllcles

-....

0-

Roc:k Rock Electrolyle Electrolyte

o0 .... -e

0+

o.... 0....

......

+

Rock Rack •e +charp +charae

o

......

(e) (c)

-c:harp -charp

Roc:k Rock

Electrolyte ElectrolylC o. 0.

+

o.0.-

Rock Roc:k

Figure 9.2. Membrane and electrode polarization effects. (a) Normal distribution of ;ons in a porous sandstone; (b) Membrane po/aflzation polaflzation in a porous parous sandstone due to an ions de voltage; va/tage; (c) fe) Electrolytic Eleetrolytic flow in upper pore, electrode e/ectrode polarization polarizaríon in lower /ower applied dc pore.

ud the tbe solution ions at the interface; in physical pbysica1 and chemistry this effect eJfect is known knOWD as ooervollage. ooervo/lage. Because tbe the velocity ve10city of current flow ftow in the tbe electbe pileup trolyte is much slower than in the metal, the 01 tbe extemal externa! voltage. When of ions is maintained by the the current is interrupted, the residual voltage decays diJfuse back to tbeir as the ions diffuse their original equilibrium state. tbat are e1ectronic Minerals that electronic conductors exhibit electrode polarization. 1bese These include almost all the sulfides (excepting pure sphalerite and possibly cinnabar and stibnite), some oxides such as magnetite, ilmenite, pyrolusite, and cassiterite, and unfortunately -grapbite. -graphite. The magnitude of this electrode polarization depends, penda, 01 of course, on the tbe extemal external current source and

also on a number 01 of characteristics of the medium. It varíes directly with the mineral concentration, but varies because it is a surface sudace phenomenon, it il should be larger when tbe the mineral is disseminated tban than when it tbe situation..is situation.. is Dot not as simple as is massive. Actually the tbis. lbe partic1e size me varies varíes lo this. The optimum particle to some extent ol the host rock rack and its resistivity. witb with tbe the porosity of Furthermore, so-called massive sulfides are generally not homogeneous, being interbedded witb with lower conductivity host rock. roclc. However, the tbe fact faet that disseminated mineraliza:tion gives good IP response is a most e1ectrica1 mast attractive feature, leature, because other electrical methods metbods do not nol work very well weU in these tbese circumstanees. stances. Considerable careful sample testing was done in tbe early days of IP (Collett, 1959). Unfortunately it the

Induced polarization measurements

is difficult to perform laboratory measurements at current density as low as those tbose encountered in field work. At low current density the overvoltage-current relation is known mown to be linear (Seigel, 1959a, b). Over a wider range, however, polarization varies inversely with current density, decreasing by a factor of 2 as the latter increases 1o-fold. 10-fold. Thus laboratory and field fteld results may not correspond, although the sampling work has provided additional useful information. For example, IP response decreases with increasing source frequency; this is true for ror membrane as well as electrode polarization, but the decrease is about 2 orders greater for the latter than for the former. Other definite relations depend on type and condition of rocks. For a particular fluid concentration tbe polarization decreases with increasing rock the porosity, because there is an increasing number of altemate paths for electrolytic conduction. Thus one alternate would expect a larger IP effect in a disseminated sulfide occurring in dense igneous rocks than in a (§9.3.7). Polarization also varies porous host rock (§9.3.1). with the fluid content of the rock; from sample experiments, it has been shown that a maximum occurs when about 75% of the pore space is filled with water. Further laboratory investigations may be found in Fraser, Keevil, and Ward (1964), Zonge (1972), and Katsube and Collett (1973).

9.2.4. Equivalent Electrical Eledrical Circuits It is attractive to replace the porous rock structure, with or without mineral and membrane zones, by an equivalent electrical circuito circuit. We have already seen in Section 9.1 that a simple R-C network will not explain the current flow and consequent IP effect. lbe The drcuit illustrated in Figure 9.3 provides a better effeetive analog for both types of polarization. The effective pore-fluid resistance is shown as Rl R1 and R Ro, o, the series section representing the solution resistance in tbe pore passages containing clay cIay or metallic metallie minerthe als (Zm)' whereas the parallel section R Roo simulates altemate zones that are purely resistive, with eleealternate electrolytic conduction. '!be The impedance Zm presumably represents a cIay shortage or excess of ions in tbe the vicinity of clay particles in the case of membrane polarization, or tbe metallic-ionic interface for electrode polarizathe tion. In early descriptions of the circuit, Zm was known as a Warburg impedance whose magnitude varied inversely as the square root of frequency (Marshall (Marsha11 and Madden, 1959). A more recent version, called the tbe Cole-Cole relaxation model (Cole and Cole, 1941; Pelton et al., 1978), has the frequency exponent ce in the range 0.25 to 0.35 (rather than 0.5) for most IP effects. However, lhe the range has

581 •.................. y ..../IIV"v "I' V V

....

",,,.., ~ ~~

zm

Figure 9.3. Equivalent electrical circuit to simulate the IP effect.

been extended upward to approximately 1.0 in dealíng with EM coupling (§9.4.4c) and occasionally as ing low as 0.1 (Fig. 9.16c) for certain minerals. The theoretical limits for ce are identical to those for Cor the chargeability (§9.3.2c), that This tbat is, zero to unity. 'Ibis circuit model, although still oversimplified, oversimplifted, provides an improved match of IP response parameters.

9.3. INDUCED POLARIZATION MEASUREMENTS

9.3.1. General As mentioned in Section 9.1, measurements of IP may be made either in the time or the frequency domain. '!be The former are known as pulse trans;enl transient measurements, the latter as frequency variations. In both cases, the voltage is measured as a function oC time or frequency. In a recent development either of (MIP), measure/P (M/P), (§9.3.5) known as magnetic IP ments are made of the magnetic field in either domain. The various units of measurement are deftned defined in the next two sections.

9.3.2. Time-Domain Measurements Miflivolts per volt (lP (fP percent). The simplest (a) Millivolts way to measure IP effect with time-dornain time-domain (T-D) V(t) equipment is to compare the residual voltage Vet) al a time t after the current is cut off with existing at the steady voltage ~ during the current-flow interval al (Fig. 9.4a). It is not possible to measure potential at the instant of cutoff because of large transients caused by breaking the current circuito circuit. On the other hand, V(t) must be measured rneasured before the residual has decayed to noise level. Because V( t) is much smaller than ~, the tbe ratio V(t)/~ is expressed as millivolts per volt, or as a percent. The time interval t may vary between 0.1 and 10 s.

Commercial IP sets generally measure potential integrated over a definite time interval of the transient decay, as shown in .Figure 9.4b. If this integration time is very short and (b) Decay-time integral.

Induced polarization polarizaríon

582

IItI) 1-

v.

(a)

v. (b) (6)

time-doma;n IP effect. (a) Comparison of V(t) V(I) Figure 9.4. Different measures of the time-domain V(I) over elc1 time interval. with Vc. ~. (b) Integral of V(t)

il the if the decay curve is sampled at several points, tbe values of the integral are efl'ectively effectively a measure 01 of the tbe difl'erent times, that is, V('I)' potential existing at different V( '1)' V(t V(t,,). This nis is an extension 01 Y(1 2 ), ••• , Vet,,). of the measurement in (a) from which one also obtains tbe the decay curve shape. (e) Chargeability. (c)

1bis This is defined as

M- -1

Yc ~

Y(t) dt f'i''1 V(t)

(9.1)

2

and is the most common1y commonly used quantity in timedomain IP measurement. When V( Y( t) and ~ have the tbe same units, the tbe chargeability M is in milliseconds.

9.3.3. Frequency-Domain Measurements Frequencyeffect. (a) Frequency effect.

lrequency-domain (F-D) In frequency-domain

al two or IP, one measures the apparent resistivity at lrequencies. The frequency effect is usually more frequencies.

defined as

perant frequency effect is given by tbe percent whereas the

PFE - 100( Pdc - Pac) P. c) / Pac P. c

(9.2b)

Ptlc' PIIC PIJC are apparent resistivities measured at where Pdc' dc de and very high frequency. As we have seen in Section 9.2.4 and Figure 9.3, Pdc is determined by tbe patb R Roo only, whereas PIIC PIJC depends on the altemate alternate path

R Roo shunted by R Rl1 and Z.... Z".. Hence Pac Pac < Pdc' In practice measurements are made at two or more frequencies in the range 0.1 to 10 Hz, or higher, Pdc being taken as the value obtained at the lowest frequency. Irequency. (b) Metal factor. We have mentioned tbat that tbe the IP effect varies with effective resistivity 01 of the tbe host rock, tbe type 01 eleetrolyte, temperature, pore size, that is, the of electrolyte, and so forth. lortb. The metal-factor metal-faClor parameter, originally suggested by Marshall and Madden (1959), correets corrects to some extent for this variation. It is a modification of the expression in Equation (9.2a):

MF - 2w - 2w

x 10'(Pdc - Pac)/PdcPIIC} ( 9.3a) x 10'FE/Pdc

frequent1y Because apparent resistivities were frequently (aetually in the form Pa/2" {Ht) given in ohm-feet (actually Cft) metal-factor Irequency domain IP equipment, metal·factor on frequency loot, rather uníts of mhos per foot, values originally had units than mhos per meter (now siemens per meter). Thus, (9.3a) is a more convenient form 01 of Equation (9.38) Pdt/2,,) MF - 10'FE/( Pdc/2,,) - 10'PFE/( Pdc/2,,) (9.3b)

9.3.4. Relative Phase Shift and Phase Components The relative phase shift (RP S) is the phase angle or time shift between the transmitter current and renis is a measurement of ol considerable ceiver voltage. This

Induced polarization measurements

583

significance in IP surveying, because there is a linear relation between phase and frequency effect in the form ~ =

k'FE

(9.4)

where ~ is the phase defined previously and k' is a constant for a particular sample or field situation, which appears to have an approximate range of - 0.3 to - 0.5 for different grades of mineralization (Scott 1971; see also Fig. 9.12b). carned out Measurements of RPS were originally carried on rock samples to identify IP signatures for particular minerals miDerals in the laboratory (Fraser, Keevil, and Ward, 1964; Zonge, 1972). The study was extended alter to field work (Lambert, 1974; Zonge shortly after and Wynn, 1975). The phase measurement led directly to a determination of sample or ground impedance, because the measurement of R, the real component of the impedance, and the phase ~ enables us to find the impedance using Equation (7.18).

9.3.5. Magnetic Induced Polarization (MIP) Measurements This method and another called magnetometric resislivity (MMR) appeared in the literature about the tivity same time (Seigel, 1974; Edwards, 1974). The latter dates back to a patent of Jakosky in 1933 (Edwards, Lee. Lee, and Nabighian, 1978). In this paper it is stated that MIP is related to MMR in the same sense that IP resembles the resistivity method, although the similarities appear closer doser than tban this. For Por this reason we will concentrate on MIP, with reference to reports on both methods. The MIP method utilizes a component of the magnetic, ratber rather than the electric, field due to galvanic current (Seigel and Howland-Rose, 1983). Two quantities are usually measured: The first, the normalized primary magnetic field, HN , is given by (9.5) H,. is the so-called steady-state sleady-state magnetic magnelic field where H" amplitude measured at a single transmitter frequency and H~ is the HI' value calcu]ated calculated for uniform ground at the same location; H HNN is expressed in percent. The second quantity is the magnetometric resistivity (MMR) (Edwards and Howell, 1976):

(H,. - H"o)/H"o H,.o)/H,.o MMR - (H"

(9.6)

H,.o is the predicted uniform-ground primary where H"o field at the midpoint between current electrodes. The preceding are frequency-domain parameters. ]n In the time domain we use chargeability M (§9.3.2c) averaged over preselected time intervals as in Figure Por the selected ith time interval we obtain M Mij 9.4b. For

I

V¡(t). During current on-time we from the voltage "1(1). HI' and calculate H N ; M; Mi is then normalmeasure H" ized by dividing by H N • The magnetic fields considT) ered here are very small, in the picotesla (10- 12 1) range and require a sensitive low-noise· fluxgate f1uxgate instrument (because components, not the total field, are measured).

9.3.6. Relation between Time- and Frequency-Domain IP Measurements In theory, because both frequency and time measurements represent the same phenomenon, their results ought to be the same; practically the conversion of time domain to frequency domain and vice versa is quite difficult. The square wave used in time-domain IP contains all frequencies, assuming that the fronts are infinitely steep. Seigel (1959a) defines the chargeability as M- { lim V(t) - lim V(t)}/ lim V(t) V(/)

,-0

'-+00 '-00

1-+00

By Laplace transform theory, it can be shown that Iim V( t) = Jpdc lim

'-00

and

lim V( t) = Jp""

1-0

bigh where P"" is the apparent resistivity at very high frequency and J is the current density. Consequently, using Equation (9.2a) and assuming that Pac = p,." Pac p.." we can write for the chargeability

M _ Pdc - PPoo _ 1 _ Pac oo _ Pdc Pdc

Pdc Pdc

1 FE = 1 - - - - - - ... FE 1 + FE 1 + FE

(9.7)

when FE < 1. tbis simple relation is not In practical situations this beca use an exact theoretical analysis of valid, partly because available (that ¡s, is, tbe the basic the IP effect is not avai]able premises of the two systems of measurements are only approximately valid), partly because the measurements are not made at dc and VHF in either IP system. Thus, in general, it is not possible to convert one result to the other (Fig. 9.11).

9.3.7. IP Response Examples Although the type and grade of mineralization are not fixed by the values of the IP response, the following tables may be of ol some sorne use in crude assessment of field results. Table 9.1lists 9.1 Iists the chargeability of a variety of minerals at 1% volume concentration. The duration of the square-wave current was 3 s and

polarizatíon Induced polarization

S84

Table 9.3. Chargeability of various materials.

Chargeabi/ity of minerals. Table 9.1. Chargeability

Mineral Pyrite Chalcocite Copper Graphite Chalcopyrite Bornite Galena Magnetite Malachite Hematite

Chargeability (ms) 13.4 13.2 12.3 11.2 9.4 6.3 3.7 2.2 0.2 0.0

Chargeability (ms)

Material

o

Ground water Alluvium Gravels Precambrian volcanics Precambrian gneisses Schists Sandstones Argillites Quartzites

1-4

3-9 8-20 6-30 5-20 3-12 3-10 5-12

rocles and minerals. Table 9.4. Metal factor of various rocks

Table 9.2. Chargeability of various minerals and rocks. rocles.

Material

Chargeability (ms)

20% sulfides 8 - 20% sulfides 2 - 8% sulfides 2Volcanic tuffs Sandstone, siltstone Dense volcanic rocks Shale Granite, grandodiorite limestone, dolomite

2,0CXl - 3,0CXl 1 ,0CXl - 2,0CXl 1,0CXl 500 -1 .0CXl ,OCXl 300-800 100-500 100-500 50-100 10-50 10-20

the decay was integrated over 1 s. These values measuremenls appear high with respect to usual field measurements because it is not customary to employ such a long timing cycle or to integrate the complete decay curve. tbey do illustrate tbe However, they the variation between different IP sources. Table 9.2 shows the response of a variety of mineralized and barren rocks. Here the tbe charging time is long (- 1 min) and tbe the decay curve is integrated over its entire duration (excluding (exc1uding tbe the initial transient and final noise). Table 9.3 shows further values of chargeability for various materials. The charging cbarging time was 3 s5 and the decay the integration time from 0.02 to 1 s of tbe curve. Table 9.4 lists typical metal factors for a variety metamorpbic rocks. of igneous and metamorphic Obviously because of tbe the considerable overlap in distinguisb hetween to distinguish between poorly values, it is not possible lo sueh as mineralized rocks and several barren types, such tuffs and clays.

9.4. IP FIELD FIELO OPERATIONS OPERATIONS 9.4.1. General As mentioned earlier, tbe the equipment and field procedure for induced polarization surveys are similar to

Metal factor (mhos/em) (mhos/cm)

Material

10,0CXl 1,000 -1 0,0CXl O,OCXl 3 - 3.0CXl 3,OCXl 30-1,500 100-1,000

Massive sulfides Fracture-filling sulfides Massive magnetite Porphyry copper Dissem. sulfides Shale-sulfides Clays Sandstone -1 - 2% sulfides Finely dissem. sulfides Tuffs Graphitic sandstone and limestone Gravels Alluvium Precambrian gneisses monzoniles, diorites Granites, monzonites, Various volcanics vo\canics Schists Basic rocks (barren) Granites (barren) Groundwater

3-300 1-300 2-200 10-100 1-100

4-60 0-200 0-200 10-100 0-60

0-80 10-60 1-10 1 O o

that used in resistivity exploration. lbis This usually results in a combined resistivity-IP survey; sometimes SP may be measured as well. The equipment is tbe commonly eommonly relatively elaborate and bulky. Of the used ground-exploration methods metbods (excluding (exc1uding seismic), míe), it is one of the most expensive, being roughly comparable to magnetotellurics and gravity in cost per month. The field work also is slow compared to magneties, EM, and SP. magnetics, ~

9.4.2. Field Equipment Transmitter. A block diagram of a conventional (a) Transmitter, wiU function in either time or IP transmitter, which win frequency mode, is illustrated in Figure 9.5. 9.S. It Jt consists of a motor generator whose output is converted de, to current-controlled (0.2 to 1%) high-voltage dc, followed by a switching system that produces square-wave output of various forms suitable for

IP field operations

585

A.C.

STEp·UP STEP-UP

GENERATOR

I

TRANSFORMER

................

SQUAREWAVE WAVE SCR BRIDGE ~ SQUARE CONSTANT ~ SCR SWITCHING CURRENT

...............

CONSTANT CURRENT

ANO POLARITY AND

PHASE CONTROL

WAVEFORM CONTROL

CURRENT SENSING REFERENCE MEASURING

FEEDBACK CURRENT AMPLlFIER AMPLIFIER

(a) (al

DUAL FREQUENCY

TIME DOMAIN

-

SQUARE WAVE WA VE

-

FREQUENCY DOMAIN (b)

Figure 9.5. IP transmitter for time- and frequency· frequency-domain domain measurements. measuremenfs. (After Sum5umner. 1976.) (a) Block diagram. (b) Typical waveforms.

either time- or frequency-domain operation, as shown in the diagram. Most units use a gasoline-driven ae ac generator, generally 110 or 208 V, 400 Hz (to reduce weight), the power varying from 1 to 10 kVA, occasionally more. Several portable T-D transmitters are also available in the 100 W range. These employ batterycharged capacitors to produce the high-voltage pulse Cor for shorter time periods and generally use signal stacking (§4.4.8). However, their range is limited, near-surfaee rocks particularly in areas of conductive near-surface and overburden. Large units are heavy, 70 to 350 kg. The timing cycle may be 1 to 10 s on and off for intermediale T-D and 0.1 to 10 Hz with various intermediate Oecasionally the frequencies for F-D equipment. Occasionally ranges are considerably greater. Outputs vary from 1 lo to 5 A and up to 5,000 V in the larger units. Use of solid-state (SeR) (SCR) switching has provided a great improvement in the control circuits so that a variety of output waveforms, sine- as well as square-wave,

may be produced. The sudden change to off-time during the T-D duty cycle cyc1e requires a dummy load in the output or an automatic cutout device to minimize generator surges. (b) Receiver; general. This hall half ol of the IP set measures the voltage at the potential electrodes. Formerly done with a simple voltmeter, it may now BOJh T-D and F-D involve a miniature computer. BOSh lor spurious SP and receivers require compensation for tellurie signals. On older instruments SP was bucked telluric out manually, manualIy, later Ialer automatically, using a potende offset at the receiver reeeiver input. tiometer control Cor for dc elirninaled by On some sorne F- D receivers the SP was eliminated tbe form ol of a high-pass filter, capacitive input in the whicb oC the telluric noise; of most of which also disposed ol however, the low-frequency low-Crequeney cutoff for the IP signals tbe telluric effect was about 0.3 Hz. In T-D receivers the may be reduced by averaging readings over several deeay cycles. decay

Induced Indueed polarization polarizatíon

586 4

INP

FJLTER FILTER SP BALANCE

ATTEN.

60Hz

FJLTER FILTER FILTER FJLTER CANCEL

~------,.-~ ~------,.-~

i

1

2

PROGRAMMER NETWORK

3 4

TRJGGER PROGRAMMER TRIGGER

TRANSMJTTER CYCLE TRANSMITTER --+---H-~.....---r+-:::::l;~I-----r+-:::::I;~I--- RECEIVER RECEJVER --+---H-~ INPUT

2:2:2:2:5 +:0:-:0

FJLTER CANCEL AND ANO DELAY· DELA Y • 0.4S FILTER 0.45 S. READ CYCLE (TxOFF)

-E

J.P. READ =0.65 S.

A.SP = 0.65 S.

RECEIVER RECEJVER OUTPUT REVERSING AT2

--Q-f----1H--t"-t----f-+-i'''--I- AFTER

II I

1 I 1 I

II

I 1 I II II 1 I I I I

I I I I

I I I

1 I I I II I1 I

I I I

I

I 1

II~ :~III : I I :I:I~~ I I I r""" II II~:::~.~.~~ I I 1: :I I

--01 --o~I------rlI I I II 1 I I I

I

I

I

I II I

I

JNTEGRATOR INTEGRATOR OUTPUT

I

(0) (a) Figure 9.6. Block diagrams of typical IP receivers. (a) Newmont T-D T-O receiver. (After Oolan Dolan dnd and Mclaughlin, 1967.)

(e) Time-domain receiver. reeeiver. Essentially an integrat(c) ing voltmeter with a range from dc de to very lowae, it measures decay voltage over a sefrequency ac, lected time interval following transmitter-current cutoff. This gives the chargeability M from Equation (9.1), ~ having been measured during current ontime. The integration time may typically be, as in the Newmont T-D r-D receiver (Fig. 9.6a), from 0.45 to 1.1 s, 5, during a 2 s on-off pulse. Obviously the charaeter character of the decay curve can be established by sampling and integrating the data in a series of windows to determine possible departure from logarithmic shape.

(d) Frequency-domain receiver. This also is a sensitive low-frequency voltmeter similar to the T-D version (Fig. 9.6b). Generally voltages at al two or altbough more frequencies are recorded separately, although sorne units measurements measuremenls may be made at two in some frequencies simultaneously; a McPhar instrument

achieves the latter by transmitting a dual frequency as shown in Figure 9.5 whereas a Scintrex model measures PFE between a fundamental and third oC a single square-wave transmission. The harmonic of Scintrex equipment also obtains the phase (RPS) between these components without the tbe requirements listed in Section 9.4.2f. (e) Magnetk Magnetic IP equipment. The onIy only addition to a standard IP instrument that is required for the MIP survey is a high-sensitivity vector magnetometer eleetrodes and receiver. lbe in place of the potential electrodes The magnetometer must have ftat fiat frequency response Crom de up to 1,000 Hz, resolution greater than 1 pT, from and noise level less than (1//)1/2 pT. levelless Magnetotelluric noise is a problem in MIP work; mainIy in equatorial regions this noise' (caused mainly by thunderstorms) is of relatively high frequency whereas at higher latitudes it becomes troublesome

587

IP (ield field operations WAVEFORMS

( Iv.

L c___r(

_...I..--_rL.JlIl~_--,-_JL..JU1~_ --~~~~--~~~~-

en. CH. I

23

CHI

2 3

WIRE OR RADIO LINK OR FROM TRANSMITTER TRANSMITIER

CHANNEL II MEASURES P" CHANNEL 2 MEASURES MI M. CHANNEL 3 MEASURES Mz ETC.

FILTER SECTlON SECTION

INPUT

__--J'

II II II1I111I I.. ~

I

I~-JW'\--""'--&---i I~-.JW'\--""--&---i

SP

I

1I II II r------, I1 11 II I

r-BUCKOUT

METER

--1

~ ~-----,'

CRYSTAL CLOCK

METER

I

: I1 I L _____ .J II r------l 1II L_...., I I I

I I

L _____ .-J

.

I

CASSETTE RECORDER

L_...,

I

"---..j

METER

_-~

I _ _ _ _ _ _ ..1I l....

(b)

F-O receiver. (After Sumner, 7976.) Figure 9.6. (Continued) (b) F-D

tbe 0 Oto irnproved by in the to 10 Hz range. The situation is improved (i) high-power higb-power IP transmitters to increase current density, (ü) (li) narrow-band filters, particularly in F-D surveys, (iii) (ili) digital stacking and averaging in either dornain, domain, and (iv) a refereDce reference magnetometer at a base station located some distance away from the survey tbe measuring measuriDg instrument, area, oriented parallel to the and transmitting its signal by wire or radio to be out-of-phase with witb the tbe recorded signals. mixed out-or-phase iD either The MIP technique may be performed in domaiD. The former allows meatime or frequency domain. surerneDt of broad-band response respoDse by recovery 01 surement of the noise the F-D system decay curve. In areas of high Doise tUters produces better signalwith Darrow-band narrow-band filters to-noise ratios but less IP information per measurement.

ffJ Spectral-phase Spectra/-phase equipment. Phase shift (RPS) and impedance were discussed in Section 9.3.4. There are several advantages gained from trus this measurerneasurement; (i) by obtaining amplitude and phase at a single frequency, one effects a saving saviDg in time over amplitude measured at two frequencies (although simultaneous transmission of dual frequencies is now available), (ü) (li) improved sigDal-to-noise signal-to-noise ratio

(Sumner, 1979), (iii) (ili) a means rneans of removing rernoving EM coupling effects (Wynn and Zonge, 1975; Pelton et al., 1978; see also §9.4.4c), and (iv) determination of ground impedance. The phase may be obtained from standard IP equipment in several ways: by a temporary T-R cable or radio link, by analysis of oC T-R data, or with dock reference. There are drawbacks with a precise clock oC these methods and they all a11 work better with each of sinusoidal rather than square waveforms. Recent computer-controlled systems, called spectral-phase /I P, measure amplitude and phase over a tra/-phase wide frequency band which mak.es it possible to ol the subsurface in obtain the electrical impedance of the field. The computer control of frequency, transvollage promitter current, and the linked receiver voltage R. and vides, after digitizing, response spectra of cfJ, R, X, as well as M (or FE) and PO' Po' Computer Cornputer analysis may then theD be used to distinguish EM coupling from normal IP response (§9.4.4c) in order to remove the former. Finally, plots of phase versus frequency using field data may be matched by computer iterative rnodels. A block diagram of oC a processes for various models. systern is shown in complex-resistivity IP (CRIP) system Figure 9.7.


588 , - ----computer -----Computer --I ,

I

...,_.

I'l'

I

-

I

I I

I I

I

I L_

I

Digital storage

-

Digital storage

f - . _ - >.-- -

Variable-frequency transmitter transmitler

TI e etype

I

Digital processor

I

i ¡i

~

I

I--_J

I

A/D converter con verter AID

I

Analog receiver

I I

.&.&.& .AAA .. ,.y

.. vv

Tape recorder

Output display

I I

Print output

I

A/D converter AID

I

I

t Analog receiver

jl

R Re·e·

I I I I I

1l

(Aiter Figure 9.7. Block diagram of complex-resistivity system with double-dipole array. (After Sumner, 1979.)

(8) Electrodes and cables. Current electrodes are usually metal stakes as in resistivity work. Sometimes it is necessary to use aluminum foil in shallow hoJes. tbe electrodes holes. It may also be necessary to wet the sufficientIy good contact with salt water to provide sufficiently lor the tbe desired high currents. Porous pots are often olten for used for the tbe potential electrodes because of the tbe low lrequencies. 1be frequencies. The current wires must be capable of withstanding witbstanding voltages of 5 to 10 kV.

9.4.3. Field Procedures Because the IP electrode system is identical to resistheoretica1ly one can use any of the field tivity, theoretically 8.S.3. In practice the tbe spreads described in Section 8.5.3. the pole-dipole in Schlumberger or gradient array, tbe which one current electrode is removed a great distbe double-dipole, with a rather ratber small tance, and the value 01 of n, PI, are the tbe three commonly used IP spreads, generally laid out across geologic or target strike. 1be The latter two configurations are illustrated iUustrated in Figure 9.8. Using the dimensions as shown dimensiODS shoWD and Equation (8.26), the tbe apparent resistivities for tbese these two spreads, over homogeneous ground, are Double dipole:

p,. - trn(n fTn(n + 1)(n P,. l)(n + 2)xAVjl 2)xAV/l

(9.8)

Pole dipole: P Paa --

2'11'''('' + 1) x AVjI AV/I

(9.9)

Values of " range from 1 to 10, although althougb 6 is usually tbe the upper limit. The electrode spacing may be as small as 3 m and as large as 300 m. To reduce tbe work of moving lhe the the current electrodes and parof ticularly the heavy transmitter unit, several pairs 01 current electrodes are often placed in suitable locations and wired to a fixed transmitter; tbe the latter is then switched from one to the other. of the Results are usually plotted at the midpoint 01 tbe midpoint of CtPd, C1P¡), spread (or in pole-dipole, the eitber current although occasionally the midpoint 01 of either or potential pair is taken as the station location. lor reTbe larger electrode spaciogs The spacings are mainly for althougb, as in resistivity, the connaissance although, tbe depth deptb of spaciog. penetration is controlled in part by the spacing. the same line is traversed several times Frequently tbe witb with different spacings, lor for example, x - 30 or 60 m and n - 1, 2, 3, 4, and so on; by so doing, one obtains a combination 01 of lateral profiling and vertical sounding. As mentioned previously, apparent resistivities are also obtained at each station. On older models tbe self-potential may also be recorded by noting the

IP field operations

589

tx, .l ,,,,_,~'" _,~ ,,,,.,". ,tXjn,,, :1:. ,Xj" ,,,, J:xj"" 1"

C,

C1

C

P,

'.

(o) (0)

7"'7""0,-,-~'~F"'; ~, . ,. . ". ,~:;. ,- ~-,. ; j t - - - - ."X

j

""'"r't.,..,. -,. .-,, ,"'1";; ; , " ; F."" i ;.» C,

,

t:i:·

:,:,:,

P,

(b)

Po/e-dipole. Figure 9.8. TypicallP spreads. (a) Double-dipole. (b) Pole-dipole.

bucking potential required before current is switched on. Field arrays for MIP, two examples examptes of which are shown in Figure 9.9, are considerably considerabty different from curreot elecconventional IP and resistivity. The current usua1ly oriented along strike and located trodes are usually tbe target. The arrangement in approximately over the Fig. 9.9a is Used for reconnaissance; el C1 and ~ are tyiog out fixed and joioed joined by a large U-shaped loop lying of the tbe area of interest. Magnetometer traverses are made 00 on lines orthogooal orthogonal to strike as shown, the horizontal component in this direction being measured at station intervals of 10 to 100 m, depending deptb. on target depth. Another Anotber MIP array is shown in Figure 9.9b. The current electrodes are aligned along strike as before witb larger separation, whereas the tbe cable lies but with tbem. Several orthogonal ortbogonal traverse directly between them. lines for lor the magnetometer are located off one end oC of tbe the current pairo pair. After surveying these, ~ is moved to q, the traverse lines are moved one spacing to el C. oC the rigbt, right, and measurements are repeated. Several of tbese displacements produce data for pseudodepth pseudodeptb Ithese 1plots as in conventional IP (§9.5.1). This type of array provides more lateral and deptb depth control tban than altbough signal strength strengtb is usually lower the first, although and more measurements are required.

Survey lines

Geologic strike ---...

------r --ril1-rl-- ------el C1

Besides SP, which is easily compensated, otber other sources 01 of background noise are telluric currents, capacitive and electromagnetic coupling, lrom barren rocks (§9.2.2). The and the IP effect from oC telluric noise has already been beeo men· menreduction of tioned.

III I I I IIII I I

2L

1

~L~

Transmitter

~---2L---~ ~-----2L------~

(0) (al

Survey lines

..

Geologic Geolo8ic strike Transmitter

•

9.4.4. Noise Sources

IIII I I I I I lit I I t M~gnet~meter M~8net~meter orientation orlentatlon I I I I I I eC z

2L

0 O

ez C

•

·f-f

I I I I M~8"et~meter M~ll"et~meter I I I t onentatlon I I I I

n I I fe~ I I I I I I

I I I I I I I I I

(b)

(Aftpr Seigel. 1983.) (a) Figure 9.9. Magnetic IP arrays. (After Horseshoe array for reconnaissance. reeonnaissance. ib) lb) Linear array for detai/ surveying. detail

(a) General.

(b) Capacitive coupling. eoup/ing. This may occur due to leakage currents between current electrodes and potential wires, or vice versa, or between current and

usualIy small potential wires. The capacitive effect is usually enough to be negligible, unless the insulation 01 of the wires is defective or the wires lie very close lO to electrodes other than their own. In IP well welJ logging, where the cables are side by side, it is necessary to use shielded wire. (e) Electromagnetic E/eetromagnetie coupling. eoup/ing. This effect is ex(c) tremely troublesome. It results from mutual induc-

590

pofar;zat;on Induced polarization

lance currenl and potential wires, both ditance between current rectlyand through the ground in their vicinity. The eft'ect can become quite large when long wire EM effect bigher frequencies are used. Double-dilayouts or higher pole and pole-dipole spreads are employed to reduee reduce coupling due to long wires and the frequencies are usually kept below 10 Hz. usualJy te approximately tbe It is possible lo to calcula calculate the EM coupling between two wires in the tbe presence of homogeneous ground (Millett, (MiDett, 1967). Resistivity variations in the tbe vertical plane also influence inftuence the EM effect eft'ect considerably. Coupling is genera11y generally in the sense of normal polarization when using tbe the double-dipole altbough it may be the tbe opposite, or negative, array, although witb with the gradient system. Madden and Cantwell (1967) give a rule-of-thumb for lor limiting either tbe the frequency or electrode spacing for Cor a particular array arcay eft'ect within background. lo to keep the EM coupling effect For double-dipole electrode spreads tbe the expression is 12 < 200 nx(l/p)l/2 nx(l/p)l

(9.10a)

lor F-D F·D measurements, where x is in meters and p for Por T-D T·D measurements tbe in ohm-meters. For the limit is (9.lOb) where

Table 9.5 shows tbe the maximum spreads permissible in F-D F·D measurement for lor double-dipole spreads lrequencies and ground resistivities. When at various frequencies pole-dipole po)e-dipo)e spreads are used, the situation is somewhat better (longer spreads can be used), whereas for lor the Schlumberger or gradient tbe gradienl array, the tbe maximum nx is reduced by 2. aIso be reduced in T-D IP EM coupling may also surveys by using the later laler (low-frequency) portion 01 of tbe decay curve lo altbougb sensitivity the to determine M, although will be reduced in the tbe process. The same improvement may be obtained with F-D units by measuring only on1y low frequencies Irequencies « 3 Hz, say) in sine-wave rather than square-wave form lorm if possible. ol spectral IP equipment, coupled Development of witb lor interpretainterpreta· with tbe the use of the Cole-Cole model for tion, has produced a possible empirica1 empirical metbod method lor for efl'ects from lrom normal IP reseparating EM coupling effects of the tbe equivalent Cole- Cole sponse. The impedance 01 circuit for the latter, latler, shown in Figure 9.3, may be written

o,

Z(e.t) - RO[1 - M{l-

1. c}] (9.11) 1 + (Je.t1')

Table 9.5. Maximum spredds for various frequencies res;st;vit;es. and ground resistivities. f (Hz)

50

p

nx (max)

(Om)

(m) 900 300 90 30

1,0CIJ 100 10 1 1,0CIJ 100 10 1 1,0CIJ 1.0CIJ 100 10 1

10

3

2,000

600 200 60 3,700 1,100 370 110

tbe complex compIex impedance (0), (O), 'T'T is the where Z(w) is the time constant (decay curve), R Roo is the resistive com(O), ce is tbe lrequency exponent, and M is ponent (0), the frequency tbe chargeability. the The ranges 01 of M and ec are restricted, the upper and lower limits being unity and zero, the first by definition (Seigel, 19S9b), 1959b), the second because Z(w) Z«(o) Crequency. Laboratory decreases monotonically with frequency. roeks indicate tbat fieId measurements on rocks that ec and field generally lies líes between 0.1 and 0.5 O.S and typically typica1ly is aboul 0.25, whereas .,l' and R Roo have a wide variation, about tbe first from about 10- 3 to 104 s. Note lbat that this the discussion relates to both membrane and electrode polarization. lor these parameters, paramelers, on the tbe EM coupling values for otber hand, appear considerably different, different. l'., being other very small « 10- 4 s) and e c large (0.9 to 1.0). Under tbese conditions the tbe phase spectra for lor typical porpor· these phyry copper mineralization and EM coupling are the phase versus well separated, as can be seen from tbe frequency plots pIots in Figure 9.10a. Values 01 of e c may be tbe slope 01 estimated lrom from the of the asymptotes on tbe the two curves, whereas tbe the time constants are roughly related lo tbe frequency lrequency maxima. Thus in situations to the tbe phase curve contains more than one maximaxi· where the peales at unusually high frequency, Irequency, the mum or peaks Cole-Cole model may be modified to account for sourees by including extra two (or more) distinct sources factors (called dispersion terms) tbe form the

or of

1_ [ or or

M'{l -_1 + (jW'T'Y' 1 }] (je.t'T')c' [ 1+

(~"T')< 1] (~"T')¿

which multiply the tbe right-hand rigbt-hand side 01 of Equation (9.11) (Pe1ton (Pelton et al., 1978; Major and Silic, 1981).

Interpretation

591

lOa

ta'

7

,

1

/

:s

II

2

I/

-• .~ 'U o0

II ; / II

10 1

;:;1

7

§I

5

01 (J, CJ1

.~

!

3

1&1 l&I

2

el) It)

I ~I ;:/ ;:1 {JI CJI ~I

ec

f

,o'

10 1

:5

'

~

2

I I

,o' 10'

I

INDUCTIVE TEST

I I

j

I I

~ s5

I

!

3

~

2

I

¡f

COUPLING No. I

.-3Om .-30m n- I l78ohm-m

Pe.OIlaPe.OIll-

7

,o·

10'

I 1 / 1 / 1 /

s5

2

'\

~/ ~I

7

:s

I

S 5

....

7

:55

I

3

, I

2

10°. 10

10'

100 '00'02 102

,(11 1(1'

,00 100

10Z2 10 10' FREQUENCY (Hz)

'O'

10 'O

,o' 10'

(b)

(o) (0)

Figure 9.10. Phase-angle spectra and their use in removing EM coupling effects. 1, x - 30 m. (After Pelton Pe/ton et al., 1978.) (a) Typical porphyry Double-dipole array: n = 1. coup/ing spectrum over homogeneous earth. (b) Observed data and spectrum and EM coupling curve (solid fine) line) obtained using two Cole - Cole dispersion terms; dashed fine line is EM coupling spectrum calculated using the ColeCo/e- Cole parameters; the dash-dot fine line is the difference between the two previous curves.

The curves in Figure 9.l0b 9.10b illustrate how the EM coupling may be removed. The eomplex complex resistivity measurements were made over relatively barren allubigh frequencies to vium and the spectra extended to high emphasize the inductive coupling component. Using two Cole-Cole dispersion terms the solid line was fitted to the data by an inversion process known as ridge regression (Inman, 1975: Petrick, Pelton, and pararneWard. 1977). Having acquired the various parameters for each term, the isolated coupling effect ror eaeh efreet (dashed Une) and IP response were calculated. Because there line) were no field data below 5 Hz, Hz. the IP response this is an extrapoJation extrapolation based partly on (a). The broad maximum around 0.1 Hz on the corrected curve is thought tbought to be caused by polarizable clays in the alluvium. Altbough Although this semianalytical tecbnique technique for remov· removing EM coupling is based on oversimplified modeling, it appears to be quite useful when spectral IP measurements are available witb frequeney with a wide frequency

band; it also has the advantage of using real field data.

INTERPRETA TlON 9.5. INTERPRETATION

9.5.1. Plotting Methods IP results are frequently displayed in simple profiles profiJes of chargeability, percent pereent frequen~y efreet, phase, pbase, and frequen~y effect, TIte various so forth, plotted against station location. The tbis fashion. fasbion. MIP parameters may also be shown in this exarnples are given in Figure 9.11. Several examples The profiles in Figure 9.11a show the same anomaly traversed with both time- and frequencydomain IP. There is little littte difference difrerence between the frequency-efrect frequency-effect and metal-factor plots, and the tbe chargeability profile is somewhat somewbat similar. However, lor tbe tbe the resistivity profiles are quite difrerent different for the two metbods. methods. Tbis This is probably due to the faet fact that the variable frequency IP used a double-dipole spread,

592

whereas the pulse system employed pole-dipole. These profiles are taken from line tine 29 + 00 on the contour con tour plot of Figure 9.Uc, 9.11c, which is a form of occasiona1ly used. From Frorn this illustration the display occasionally two methods appear to give similar results. Figure 9.llb 9.11b shows a variable-frequency profile over a massive sulfide covered by sorne some 80 ft of overburden (glacial till), which was a relatively good conductor. In the absence of this cover, the response Jt is also would presumably be very much larger. It worth noting that the larger dipole separation gave slightly better response. MIP data may be plotted in terms of H" the seeondary field due to polarization, in anomalous secondary such forms as H, - Hpll (1 is the primary ground current) multiplied by PFE, RPS, MMR (F-D sys· in-phase tems), or by M (T-D systems). Since the in·phase and quadrature components may be distinguished in F·D measurements, H, may also be converted to (cbange of in-phase in-pbase component witb AH" (change with fre· quency) and/or AH,. (quadrature). Three MIP profiles protiles of this type are displayed in Figure 9.11d. Tbese These were obtained over a zone of taiting disseminated sulfides covered by conductive tailing sands (- 10m) and salt-lake material in the Kalgoodie orlie area of Westem Western Australia. A vertical hole driJled drilled on the anomaJy anomaly peak encountered 47 m of tailing sands with overburden and weatbered weathered rock underlain by disseminated pyrite (~ 101) in black shaJes shales be· Tbe parameters plotted are relative phase pbase low 62 m. The magnetometrie resistivity (MMR), and the (RPS), magnetometric anomaJous normalized quadrature component of the anomalous secondary field, H,,/I. H'9/1. The TIte latter may be calculated from the measured phase angle and resistivity tbat in Figure 9.11b, (19.4.2f). This example, like that MJP to detect targets demonstrates the capability of MIP beneatb highly conductive eonduetive cover. beneath Figure 9.12 has been included to illustrate the pbase angle and frequency linear relation between phase effeet. The Tbe data, from northern northem New Brunswick, effect. were obtained over a shallow massive sulfide deposit diorite-rbyolite bost rock of high resistivity in a diorite-rhyolite (Scott, 1971). Almost perfect correlation between tbe profiles, phase and frequency effect is evident in the witb a slope of producing an excellent linear relation with IPFE in the lower diagram. In the course of oC - 0.37° 0.37°IPFE this trus study 10 sites with known moWD mineralization were oC these, 3 gave negative results owing to surveyed; of higb noise and conductivities beyond the tbe transmitter high capaclty. The average slope of the temaining remaining 7 was capacity. -0.38°11. II. ± 20%. However, it is not clear whetber whether slight1y for the slope should be constant or vary slightly mineraJs. different types of minerals. An alternative altemative display method, which has been used in plotting IP to illustrate the tbe effects of variable electrode spaclng, spacing, was originally developed by

polarizarion Induced polarization P.

(O fI/2..) ft/2.,) 110 (0

n

~~~--~~~~~L-~~---~~~n 9Ot-"""{---~~"""d~"--~"""'-~4000=

CD a>
70

-11-2 ._11 -- 3 • - - II

10 PFE

5tation at al mid.point miel-point Station

otC;1; Q) Doublc-dipolc Doublc-diPOIc

P. (O nIlf&') n{2.) 90 (0

@ ® CD Pulse transicnt trantient

- ~pl - 250 1'1 ~P. - I'll', • • • C"' _ P,P, p.",;;JOOñ ••• Cl '". P,',;;-wrr

Charpbility Char¡eability ,.,. l lO ..........., ,

~ (m~),' ..

"',

Slationalmldpolnt Slationatmidpolnt ot of C.p.

__• __ ..

l

••••./ ••••./

PoIe-dipolc C.-ao

O 0'--~""800~-A-""'1~600~"""2~400'="'''''''~]200'!=-''''''''''4000~ n 2400 800 1600 3200 4000ft (a) (0)

eo

MF

x- 1001'1

···11.2 .··,.-2 - , . .4 -4

50 40

-II

lO 30 lO 20 10

800

l600ft 16001't

Sulfide (II)

~

IIO-n conductive IIKial till

Figure 9.11. Display of IP results. (a) Comparison of time- and frequency-domain IP. ¡P. (b) FD IP over massive sulfides.

• ~

Manhall and Madden, Cantwell, and Hallof [see Marshall Madden (1959»). It is illustrated in Figure 9.13, for ShOWD in Figure 9.l1b. Values of oC tbe sulfide sulftde deposit shown the frequency effeet effect and apparent resistivity for each eaeh the points station are plotted on a vertical section at tbe Une of intersection of 45 0 lines drawn from the base line or surface, starting at the tbe midpoints of the tbe current and potential potentiaJ eleetrodes electrodes (double·dipole array). In this tbis way the tbe PFE values appear at points directly direct1y tbe center of the tbe electrode electrodc spread, at a vertical below the inercases with distance from the ground surface that increases

Interpretat;an Interpretation

593

4

U5

+ 00

LI .. _

~~

rrtqutn<:y effect cfreet frtquen<:y

+()()

1.29

+ 00

Shaded area.····aoomaJou$ arca,····aoomalou$ tone lone

Ch&rgeability (m~) .. -~. ~ Ch&r,eability

(c) (e)

20

-

< ......

.-..

-.

80

40

60

_30'

~ 40

~

,§ ...... ...... :J:" :x:"

100

~

~ 20 -

'"

~20 ~IO ~

0O

-10

0O

o.. 0..

CI/! crt:

0O

-20

-lO -10

-40

-20

I

3800E

I I

I

4000E

4200E 10m 20 -30

40

SO

o

70 80m

J

4400E

Talling sands Tailing

Overourden and rack weathered rock Tuffaceous greywacke mmor sulfides minor Shales and greywacke grey wacke with sulfides S 10%

(d)

Figure 9.17. (Continued) (Cantinued) (c) (e) Contours Cantaurs for far T-O T·O and F-O IP. ,P. (d) FO FD MIP profiles, prafiles, Kalgoorlie, Kalgaarlie, Western Austrdlia. Auslrdlia. (Afler (After Seigel and Howland-Rose, Hawland-Rase, 1983.) 7983.)

594

Induced polarization polarizatían ~ ~

t It

(0.1-1.0 Hz)

20 10 0O

4E

DOUBLE-DlPOLE ARRA y

..

.,; ..; -160 E El -140

.-.

'"rnllI:cw:11.ll.

'-'

~

~

iEif:

JI - 50ft - - n-l _ 11-4

-100 -80 -40 0O

3E (11)

__

O-=---r---.,---r---~--r---,O --~--~----~--~---r--~O -25

..... .-. ~

-2

d

-4

'-'

-75

13 ~

llI: cw:

~

Q P.l Pol

...J

~ <

-100

-6

-125

-8

-150 -ISO

P.l Pol

...

:; :a

~

'e

-175

~

iE

-200

SLOPE" -0.37 DEGREES/PFE

-225

-14 L.-_.J...._-I.._--I -14 L - _ - L - _ - - L oO 5 10 IS 20 25 30 15 % FREQUENCE EFFECT 0.1-1.0 Hz (b)

Re/alion between PFE and phase angle. (After (Afler Scott, Seott, 1971.) (a) PFE and Figure 9.12. Relation phase angle curves eurves over massive sulfides, northern New Brunswick. Brunswiclc. (b) Plot of PFE versus phase angle.

the n value for the spread. Similarly the P. values are lineo locatcd at mirror mUror image points above aboye the center line. located Fina1ly contours of equal PFE and apparent resistivFinally ity are drawn on these vertical sections; the result is a form ol of 2-D plot in vertical section. Clearly it is possible to display any of ol the tbe IP parameters in this tbis fashion fasmon provided the double-dibas been used for the tbe survey; data from pole array has bave also a1so been plotgradient and pole-dipole arrays have tcd in this way. Similar pseudodepth plots have been ted obtained from multiple T-R spacing HLEM, MT, where the telluric, and variable-frequency EM data, wbere logarithmic in frequency or period vertical scale is logaritbmic perlod for the last tbree three (16.3.2, examples 4 and 5), rather than tban linear with witb depth. The attractive feature of this that it tbis display is tbat gives some idea of the relative depths of anomalous conducting zones. The justification for such a plot is

that as the dipole separation is increased, the measured values are influenced by increasingly increasing1y deeper zones. (For multifrequency MT, telluric, and EM plots, deeper penetration is obtained at lower frequencies.) The resultant contours may be misleading, however, because tbey they appear to provide a vertical conductivit~. As pointed out in section of the ground conductivit~. Section 8.5.2, the tbe apparent resistivity is not in fact raet the actual resistivity in a volume 01 of ground below the electrode array, but depends on the geometry of the clectrodes as well as the surface resistivities. Conseelectrodes quently it should not be assumed that tbis this type of plot is a representation of the actual subsurface. Double-dipole pseudodepth plots, as is apparent from Figure 9.13 and several problems in Section 9.7, produce eontours sbape with 45° slope. contours of a tent shape This, nis, 01 of course, is a result of the plotting method. Pseudodepth plots developed from variable fre-

Interpretation

595

f0-I

M,

#f.'r

3

2

sS

4

7

6

::~~~-~--.-~:::/---:7--·::::::::-~----~::

Piol Plol value or PFE for electrodes IS shown PlOI value of PFE for electrodes II 11 2-3. 6-7. etc elc Plot

~ .

.~~~Ioo) .~~~Ioo) ..~ .~.'.' .3, .. ' .' . . . . . . .~ .•

' ..

.. .. .. . •• •• •• •• •• •. .• ••

o

I

200

~ '~' '~' ....... :: 'roo

'-

I

.•

¡ . i.

I

--. .

I

I

~75 ~75

./.

I

I

,

I,

I

I

200

PFE (b) lb)

Figure 9.73. Variable- frequency IP pseudodepth plots. (After (Afler Marshall and Madden. points. (b) Pseudodepth plot of the 1959.) (a) Graphical construction for locating data points, data of Figure 77b. Fi8ure 9. 11b.

quency soundings, on the tbe other otber hand, band, have bave a pole-like tbe appearance (see Figs. 6.29 and 6.3Oc) because the vinual1y below surface stadeptb points are located vinually depth tions.

9.5.2. General Generallnterpretation Interpretation fair1y recently recentIy IP interpretation was mainly Until fairly oC anomalies qualitative. Location and lateral extent of pseudodeptb plots by were marked on profiles and pseudodepth dark horizontal bars, solid for definite targets, stip. pled for probable or possible targets. The dimenwitb depth deptb and possibly dip, were genersions, along with p10ts. ally estimated from tbe the characteristics of the plots. The inherent advantages and weaknesses of resistiv¡ty (§8.l, §8.6.4f, §8.6.7) apply to IP as well. Among ity (§8.t, the former are good goad depth deptb estimate and depth deptb of penetration, whereas tbe the latter tatter include inelude ambiguity as lo to location, effects of ne~-surface ne~-surface variations, and slow field operations.

Highly conductive overburden overlying mineral conductors may hamper detection of the latter by IP altbough IP is as well as by EM and resistivity, although frequent1y more successful than the other methods in frequently such terrain. Similarly, water-filled shear zones are gene rally indistinguishable from mineral zones; howgenerally ever, in special circumstances, for example, if the electrolytic effect is not as pronounced 8:S the electrode polarization, it may be possiple to distinguish between the two with . witb IP. At one time it was thought that tbat massive sulfides sbould should have a lower IP response than disseminated mineralization; this is theoretical1y theoretically reasonable, as díscussed in Section 9.2.3. However, it is probable discussed tbat the opposite is true. This may be due to the halo that of disseminated mineralization that usually surrounds a massive zone. Another explanation is that truly homogeneous massive sulfide deposits do not exist; rather they are broken up into a great number of smaller conducting zones within a nonconducting,

596

poor1y condueting, or poorly conducting, matrix. Self-potential well 10gs logs generally indicate indieate this tbis internal subdivision for secseetbe descriptive log. tions designated massive in the The steeply dipping thin-sheet conductor, commonly used in EM modeling, is not a particularly good target for IP or resistivity surveys. The principal reason for this tbis is that the electrode spacings are norma11y too large to respond strongly to sueh normally such a structure. [In fact, an IP traverse made with small dipole separations of 8 and 15 m in one area prodireetly above aboye a sheet-like duced a strong response directly Althougb a disadvantage, this tbis is hardly a conductor.] Although fundamental weakness of IP, because the technique would not usually be employed (and should not be conductors of this nature. Hownecessary) to detect conduetors ever, it does account for the lack of response directly over some of these structures and in certain cases, an apparent1y apparently displaced IP anomaly on the flanks, the latter probably caused by the disseminated halo. As a result of recent developments, IP surveying inereasand interpretation techniques have become increasingly sophisticated. We may now use IP to measure eomplex impedance, possibly to determine various complex type of structure and forms of mineralization (veinmassive) , and potentially to distype, disseminated, massive), grapbite with broadcriminate between metals and graphite band spectral IP. Thus the method appears to have electrieal ground techniques tecbniques outstripped the other electrical and has become very popular in base-metal exploratioD ration (conceivably MIP migbt might become airborne, but tbis sti)) in the future). This popularity is certainly this is still not because it is eheap cheap or fast. Average monthly coverage varies enormously, depending on terrain faetors such sueh as surface conductivity, conduetivity, but and other factors 10 to 40 line miles (15 to 70 km) per month montb is common. The price per line-kilometer is thus about whicb is considerably eonsiderably higher than $500 to 800 (1988), which magnetics or EM. The popularity of IP is based on definite baseJow-grade metal discoveries, particularly of large low-grade bodies, made with its aid. A study of various field results rcsults indicates indieates that the IP and resistivity anomalies Jows) very often (generally IP highs and resistivity lows) occur together. One might migbt argue, argoe, therefore, that the expense of the IP survey was not warranted. It is quite unlikely, however, that resistivity alone would lbere enougb information to justify itself. There provide enough are also numerous case histories of IP successes in mineraJization, such sucb as porareas of disseminated mineralization, aIphyry coppers, where the resistivity rcsistivity anomaly is almost nonexistent (for example, see §7.8, example 9).

9.S.3. Theoretical and Model Work becn devel(a) Theoretical results. IP response has been analytica1ly for a few simple shapes like the oped analytically


sphere, ellipsoid, and 2-D features such as a vertical lbese contact and dike, as well as horizontal beds. These may be derived from resistivity formulas in simple cases (§8.3.5, §8.6.5, and §8.6.6) and for more commetbod (Coggon, plex shapes by the finite-element method 1971, 1973), somewhat similar to the analysis in Section 6.2.7. Figure 9.14 shows a set of theoretical oC these structures struetures using several eaeh of IP profiles over each arrays. In examples (a) to (e) the chargeability is determined from the relation (9.12) (Seigel 1959a). Numerical data for the models of Figure 9.14f to j are obtained from sets of equations for finite-element meshes in which the power dissipation due lO to ground current is minimized. In parts (a) to (e) the host rock is not polarizable, polarizabJe, that is, MI M1 - 0, O, otber five parts, (I) (l) to (j), PFE - 1% whereas in the other in the host rock. Note that most horizontal scales in Figure 9.14 have no units. For pseudodepth plots and sometimes for profiles, units are generally equal to tbe the potential-electrode spacing. IP response is not always positive. Negative apparent IP may oceur occur in the vicinity of 2-D and 3-D polarizable bodies (Bertin, 1968; Dieter, Paterson, and Grant, 1969; Coggon, 1971; Sumner, 1976). This is a geometrical effect related to the dipolar dipoJar field and the position of the measuring electrodes (Figs. 9.14a, b, c, e, 9.21c, and 9.25). Certain 1-D structures also produce negative IP response [see model (d) in the text]. following lext]. We may summarize the salient features of these models as follows: (e): For contrasts (pt/P2) greater Models (a) to (c): than those shown, the response does not change [tbis applies also to models (e) to (i»). appreciably [this For an ellipsoid dipping less than 90°, the profile is not signifieantly significantly different from those in parts (b) (e). and (c). Model (d): IP over two horizontal beds is quite eonventional, but not necessarily so when there are conventional, more than two. For example, K- and Q-type struc(PI < P2 > Pl P3 respectively; PJ and PI Pt > P2 > PJ tures (Pt see §8.6.4b) produce a negative JP response for the first layer which masks the effeets effects of substrata, often causing an incorrect interpretation. Data must be analyzed with care with tbis this possibility in mind to avoid errors in interpretation (Nabigbian (Nabighian and Elliot, 1976). This, of course, assumes that the upper layer(s), unlike Figure 9.14a, b, c, e, d, are polarizable. Model (e): The lbe curves were obtained for the model shown below them by the method melhod of images (§8.3.3), hence the sharp breaks in the flat ftat portion. Otherwise the profiles would resemble gravity profiles for a semiinfinite horizontal slab (Fig. 2.30).

Chargcability II al 0.12 M

...

9 9

0.08 0.04

~ ~ ~

Pole-dipole array Depth ==- 2 Radius ... - 1I k,.. k - -0.3

a ... 4 a-4

C ~a a/2~.c,

Sphere

I

Km»»»I» KJ»»»»I» d P~ PI PI P2

TMzM, TMzM,

0.08

Ibl fbi

a - 8 a/d ~a/d

M

-6-5-4-3-2-1 0O I

Ii

1.2

(el lei

0.8

3

4

5

Itt' ..

n=-3

"

n=4 n-4 n=5 n=6

:

,:if ..

0.4

,,=

-

:,f

-.

PI/PZ

=5

~"; .................... •,/.,1.••.•.-

I

Double dipole

..

.

.~ ~

Om

f ~ 'E z

20

P .. 500 Om PFE =- 1 PFE,.. 1

~

l\ ;i ':" .'7 'z' '.'" .) .1 .f , " '.; , .;.,

=7

8 ]2 16 20 24 28 32 36 40

t6l t6l

n

= 4

n

=

=

., ; .'..

, ,,

3 .'

"

(il til

5·f ... ..

,

.......

.' ~

.1

..-.

7-! .,

.;

.,

.

. 7

Double dipole

o_ .~ __ _ _ _ _ _---=:;Surface Surface Om

=

n = 8

• }. .J

n=8

= 500 Urn Um (D, CD, 100 PI lOO Om (D. P~ = 100 CD. 500

n

n

I .¡ !. ..

.' Surface

n

o.Jt

.. .;; ..

n=2

~

n

(hI thl

P2 Pz

I ,r • l." l~ ., .9 I I n=2 /." . l.~ . t • . ,i' , ,,?;';,'.;. i, ' .6 '~9.f.• !' i !' ,. , ..; .., n=3 t gl . ;. . . . ,'7.7 ..; •. , $ .77 .,, ., . .f . n=4 ,.-_•. "'l.:\.~;'\.j-' I .jo • ~ ., i i '' ., . t " 7 n =5 II ~.' 7 . '¡' '6 ... .·..., .~·"·6 .' ·1 r n=6

Double dipole P2 = PI apo m 0.8 m=-0.8 P. ilpz P. ilP2 0.6 Idl fdl

i

n=7

n=3 n=4 II n = 5 n=6 n=7

1.0

i

Surface

Double-dipole array \I\1 Depth = 2 n ... - 1 l O, 3.1) nn=2 ~ Semiaxes (2, O. = 2 k = - -0.3

k

I

0=

~ ~

M

0 o 1 1 2 2 3 3 4 4 55 6 6

6

i i i i ,, i i

J' :

..

PI

j

n -= 1 n-2

CIC~

0.4 0.2 oO

2

1 234

PI PI

0.04

0.02

I

i i I I i

I,

II

lel tel

x/d 0.02 0.08

I

Double dipole

OL

0.04

I

fl"/ 1111 1

25 Om PFE ,.. 20

cCl'C 5 l .e2 at +15 PI - P2 = 0.5 4 33 PFE t%l (%1 Itjl ji 2 l 1 Gradient

oO

-11 -1L--~6~~--4~-_~2~~O~~2L-~4~~6 I

I

-6

I

-4

P P

I

I

I

I

-2

= 500 0 m = PFE 500 Om = 1 PFE= 1

0

I

I

I

2

~ ~ 250 25 Om m

I

4

I

f

6

Surface Surface = 20 PFE PFE = 20

"

models, (a) Sphere. (b) and (c) (e) Ellipsoid. (d) Two beds, Figure 9.14. IP response trom from various theoretical models. beds. (e) Vertical contact. (f) and (g) Vertical dil
Indueed polarization po/arization Induced

598

Models (f) to (j): Double-dipole and pole-dipole arrays show sbow appreciable response over the steeply dipping dikes whereas wbereas the gradient spread (not illuswben the tbe dip is appreciatrated) is quite insensitive; when ble, the tbe respective amplitudes are also in the tbe preceding sequence. All three respond quite strongly to a horizontal slab. However, the gradient system is more tban the tbe other otber two arrays, as is clear sensitive lO to dip than from Figure 9.14j. Conduetive overburden masks conductive conduetive strucslrueConductive tbe current is tbe bedrock because much mueh 01 of the tures in the short-cireuited. The buried anomalies, when they are short-circuited. tban they tbey actually are, detected at all, appear deeper than lor all three arrays. Lateral ehanges as in EM, for changes in overburden tbickness thickness and resistivity are best delected tected by the gradient spread, which whicb also aIso discriminates between multiple buried targets more successfully tban than tbe the other two systems. TIte The double-dipole, however, is considerably superior to the gradient array for lor deptb depth resolution. As mentioned previously tbe the double-dipole array is affected least by EM coupling and the tbe gradient array most. Ana/oBY between M and total-field total-fie/d magnetic (b) Analogy anomaly. Quick (1974) points out an interesting anaIogy between ¡P witb the tbe analogy IP chargeability obtained with gradient array over a 2-D dipping polarizable prism and the tbe total-field magnetic anomaly due to the tbe same tbe magnetic equator and striking target located at the tbe gradient layout provides a uníE-W. Because the unilorm electrie otberwise homogeneous form electric field in tbe the otherwise tbe prism is horizontally polarized and the ground, the tbe magnetic field. This response is equivalent to the estímate ol permits a fast approximate estimate of dip and depth tbe prism, because of the ese xl/2 - 2d esc

t

M - 2dsect

or

~ - tan- 1 (M/Xl/2) (M/xl/z)

d - ( x 1/2 sin () /2 - (N cos () /2 luIl widtb where Xl/2 is the full width at half-maximum amplitbe horizontal distance between profile maxtude, N the deptb to the tbe top ol tbe imum and minimum, d is depth of the tbe dip. Examples prism, M is chargeability, and ( the tbe sphere and horizontal cylinder are also disof the cussed. Clearly tbe the host material must be barren ¡P. lor for IP. (c) (e) Interpretation of spectral speetra/ IP data. Because ol of the recent development ol of the tbe complex equipment, stiIl in a development stage. TIte interpretation is still The main tbrust, tbe previous section, has thrust, mentioned in the

IMAG

~

~REAL

~------------------------~~ 1.0 IMAG

TYPE

B

TYPE

eC

IMAG

~

\t-_________________________ ~

~.~AL

~.REAL

1.0

Figure 9.15. Idealized spectral spectrallP IP response for three rhree types of host rock. (After Zonge and Wynn. 1975.)

identily and discriminate between IP rebeen to identify sponse characteristic of the tbe host rock and various types ol ilS of mineralization; it has bas already proved its usefulness in reducing the tbe EM coupling effect etrect (§9.4.4c). Zonge and Wynn (1975), among others (§9.3.4), attempted lO to classify background rock rack signatures by plOllaboratory and field measurements. Results are plotted as real and quadrature components (R, Q) over a four-decade frequency lrequency range on a conventional lorms Three idealized forms Argand diagram (see Fig. A.S). lbree of response are shown in Figure 9.15. In types A and eC the tbe quadrature component componenl varies varíes inversely and directly, respectively, witb with frequency whereas it il is tbe spectrum for lor type B. Type .If A is constant over the said lo to be characteristic of strongly altered rocks, grapbitic mineralization, and some clays, sulfide and graphitic whereas e C usually represents wealdy weakly altered strata, chloritized fresh volcanic roeks, rocks, Jjmestone, and alluwitb vium; type B is intermediate and is associated with otber mixed moderate alteration, low pyrite, and other mineralizatioD. 1ms c1assification, however, is mineralization. This simple classification, tbe authors show by no means all-embracing and the several nonconforming examples in which whicb the R-Q relation gyrates wildly instead of being roughly linear. Other Otber authorities autborities have criticized the general hypothesis on various grounds. ditrerent lypes types of Distinctive IP signatures for different bave been considered in a number of mineralization have studies (§9.3.4). From spectral IP laboratory mea-

.. Interpretation In terpretatíon

599 103

7 ~§~~~:;::=~~03

--_

3

-----

103

.... 5

... ~9 _ - - - 11\,-""", ", ~ '" ...,2,;---"",,,..." .-'-;;; ........... ", " , ' m -_ 0.5 0.5 ..... ...... """"~ _--_

"

~

'" . .,2,;---__

,.-,/ "/," ." """,... .".-~-

Q

¡:

""" / ", " m - 0.3 .~", .",..';1'''' ----",,/ ",,/ m - 0.1

:i c.

","'"

:E

<

.......... ..........

"' .....

............

-------....

"

"'-,

",..------..............., ,,,... " ,,~

"

",

3 2

Zeit' Z(w)) =R+ =Ru(t -- m( 1I + e~Il/T)(·)] (~WT)(·)]

R Rnn - 1.0

T -

C - 0.25

0.01

7

5

3

3

2

2

1022 .10 lA 1A' .: .!:l

~

--<--

a

5

§

3

w U.I el)

2

7

w ~

fI:J

2E

c. l:l.o lO'1 10

-< :x:

el)

00(

00(

101

102

ec

al at ~ al at

.

3 2

--'" III

7 .S! .§ 'O 5-g 5 .!:I

MAGNETlTE MAGNETITE

7

7

S 5

5

3 2

3

R..[t zZ- R..(t

R Rnn =- 25. m ni -- 1.0

.,. =- 6.3 ti.3 x .,.

2

'-:----L~_'_.:~....&.:-_ _'_:__'_:_-'~...... 1 100 10- 3 '-:---L~-'-.::--""""":-_-'-:-_'-:--'~--' 00 1I00- 2 10- 1 10° 1I 01 1I0' 01 1I00 3 105 FREQUENCY (Hz)

- m( 1I + c'ill/r)< /íwr)< )]

10° 2 10-

=0

1O-~. IO-~. C -

100 110 0 1 1I00 2 1I003 FREQUENCY (Hz)

(Q) (a)

0.53

1IO· o·

1I 0' o'

(b)

loJ c=----r--.,---r----..,---r--r--.. I~~~---r--~~---r--~~ 7

5

NICKEL-PYRRHOTITE NICKEL·PYRRHOTITE

3

2

-;- 102 1A' .: c .S! .!! 7

'O '0

~

·s's

w U.I

el) fI:J

~ g., l:l.o

5 3 2

Z-RII[I-m( Z=RII[I-m( 3 2

lI.. ,.)1 (.)1

(}wT) 1I + (Jwd

100. =0.65

Rn - 100. m Rn T

0.65

= 1 X IOS.C = 0.16

IloO~~-~--~--~~~~--~ 00 L.....:---I.~-&-_.J---I~--L._--L----I 10- 2 10- 1

100

101

102

10 3

104 1Q4

1()5

FREQUENCY (Hz) (c) (e)

Pe/ton et al Figure 9.16. IP signatures for different types of minerals. (After Pelton a/.•.• 1978.) (a) re/afion model mode/ for Amplitude (solid line) dnd and phase (dashed) curves for a Cole- Cole relation Roo - 1.0. T - 0.01. c e - 0.25. (b) Mdgnetite Magnetite signature. southern various values of m; R (e) Nickel·pyrrhotite, Niekel-pyrrhotite, Sudbury, Ontario. Utah. (c)

surements on various mineral samples it was found tbat the phase pbase spectrum peaked at ditrerent that different frequencies for certain minerals, being much mucb lower for grapbite tban Altbough this tbis distinction graphite than most sulfides. Although tbe possibilities was not nearly as clear in field tests, the have been pursued with witb more advanced equipment

and with the aid of the Cole-Cole model for interpretation. Several examples oC of this tbis work, taken from Crom Pelton et al. lbeoretical aI. (1978), are shown in Figure 9.16. Theoretical plots of oC amplitude and phase for the Cole-Cole relaxation model for various values ol of M are shown

Induced polarization l()l r---'---r--r--,--~-r---, I~r-~--~--r-~--~--r--' 7

I()l .-----t---r--r--oy----,r-----'T"--, I~~~--~--~--~-'~-T--~ 7

PORPHYRY COPPER

5

MASSIVE SULFIDES

5

3

2 .- 1& IOZ

I!Ii!

a~'s.

7

"O

5

....--

3

w

2

.11

en

i

101 7

5 3 2

Z-Ro[l-m.(l- 1+ (;wrl)
Z-Ro[l-m(l- 1+(~lAJT)t)] +(~IAJT)t)] I

R Roo - 15.7. m - 0.911

e -- 0.306 r - 3.08 X lOIO- z•, C

T, -

m. •- 0.63 Ro - 251, TI - 6.4, m, 1, C - 0.34 el ;. 0.32. 0.32, rz - 0.88 x 1010-'. z

c. ;.

100 '----I-_-'-_.&.---I_--L._"""----' I~~~--~--~~--~--~~ 10- 2 10- 1 100 tOZ l()l 1()4 lOS I~ 101 t& I~

FREQUENCY (Hz) (d)

GRAPHITE

m.(l- 1++ (;lAJrl)t,)] (;lAJr )t,)] ml(l-

Z - RO[I Ro[1 --

1

l

[I[1 - mZ(1 UIW.,z)tJ)] mz(1 - 11++ (¡l/Al"Z)")]

RoRo -- 3250, mi - 0.794 MI -

." - 4.17 ".

mz - 0.686, T2 3 mz 2

1~0-2

-

X

103.C. - 0.218

2.52

X

10- 6', e C z - 0.349

l()l IOZ l()l lO' 102 I~ FREQUENCY (Hz)

10-' 100

lOS

(f)

fe) Massive sulfides, Fisure 9.16. (Continued) (d) Porphyry copper, New Mexico. (e) Timmins, Ontario. (f) Craphite, Labelle, Quebec.

Obvious1y the phase curves are in Figure 9.16a. Obviously more diagnostic. diagnostico Changes in M merely move both of curves vertically. If we wc vary R Ro, c, and T, we sets 01 seta o, e, find that (i) changing R Roo shilts shifts the amplitude amplitudc curves the phase curves, (ii) (il) vertically but has no effcct cffcct on thc increasing e c makes the phase set more sharply peaked the slopes 01 of the amplitude curves, and and increases thc (üi) ,If controls the horizontal positions of ol both sets (iii)

of curves and consequently is the most significant parameter in source determination. The remaining diagrams in Figure 9.16 contain Thc profiles from field surveys. Note that the frequency lrequency Irom 0.01 Hz to 60 kHz. 'Ibe band extends from The UDUSUunusually high frequencies required very small electrode minim;zc EM coupling effects, effccta, spreads (- 1 m) to minimize and tbis this in turn necessitated extremely shallow lartar-

Interpretarían Interpretation

601 2000

20

Pole-dipolc .rray Pole-dipole array

,, ", '\\/P. ,~, ,~"

\

,, ,,

"" \

IMAI\I Fauh Faull ~De\'onian ~Devonian ~ Old Red Sandslone Sandslonc

r--1 Carboniferous L.-..J L-...J dolomilic limestone 1-2

o

200 ft

0,25-0'5 0,5-1 0·25-0'5 r.Cu

Figure 9.17. Time-domain IP over Gortdrum copper-silver copper-si/ver body. (From Seiger. Seigef. 1967.)

gets. Consequently the sites selected were mainly in opeo iUusopen pit mines. Only the phase spectra are illusbeeo trated and best-fit Cole-Cole models have been matched to the data in all cases. ioelude a The examples in Figure 9.16b to f include porphyry copper, massive sulfides, magnetite, (e) grapbite. Profiles (b) and (c) nickel-pyrrhotite, and graphite. were carried out to discriminate between two commoo sources in nickel sulfide areas. Although Altbough the mon magnetite was of ol - 76% concentration, coocentration, the phase al high bigh frequency and requires a very curve peaks at small time constant to match the model. This is ol continuity between betweeo very probably due to lack of small mineral grains, because T values were larger at other sites with conventionally massive magnetite. The profile in Figure 9.16c indicates closely connected pyrrhotite mineralization of higher bigher conductivily ity with a very low-frequency phase maximum requiring a large T. The phase curve for the porphyry copper deposit 9.16d is not as simple as the previous in Figure 9.l6d examples. Sulfide concentration was high (- 17%) and the mineralization was of vein type rather than highly bighly disseminated as in true porphyries. Fitting tbis curve required two Cole-Cole factors as shown this and the primary time constant 'rTIt was much larger (to fit the tbe low-frequency peak at al 0.1 Hz) than tban at al other porphyry sites surveyed. Figure 9.16e from a volcanogenic massive sulfide is similar to spectra obtained from disseminated Tl-value, although the sulfides, requiring a small 'rl-value,

chargeability is higher. The curves from Fig. 9.16b, e and from several porphyry siles sites are similar in lbis this respect, suggesting that electrical continuity in massive sulfides is relatively poor. Figure 9.16f shows phase spectra from a graphite deposit. Even in small concentrations graphite and pyrrhotite seem to be excellent conductors. The Tbe curve lrequency decreases; if there is a rises steadily as the frequency TI is several peak it occurs further to the left. Thus TI orders larger than in the other examples (except for the nickeliferous pyrrhotite). The possibilities in using IP equipment of tbis this type to obtain a whole body of additional information in base-metal search seem promising. Certain reservations. however, remain concerning the blanket use of the Cole-Cole model; also the complex surveying equipment requires some expertise in operation, and the long" time constant" involved in carrying out measurements down to frequencies of 0.001 inereases the cost. The use of T-D instead of F-D Hz increases techniques is potentially attractive with respect to tbe the latter drawbaek drawback (Johnson, (Jobnson, 1984). Spectral IP application in petroleum exploration has recently been considered. Resistivity and IP oH and gas fields. anomalies have been detected over oil The response is thought to be the result of geochemical alteration of overlying rock structures caused by transport of H 2 S and CH 4 upward to shallower levels from the reservoir. In the USSR IP surveys have beeo been employed for this purpose since about 1978.

602

polarizatíon Induced polarization .... x ___ "X ___ x-+ ....x x--.

~ 8@l n0rx "

Double-dipole array x-2oor. x-2oon

Slalion Station

,./2" p./2" (ohm-feel)

0

2S

53 - - S3

45 4S

-

23

22

,

8,I

lOW IOW I

-

28 24 6,

43

9

45

2E

52

lOW IOW

8

o

~i).. ~~~10~1O 6

4

41-" - 2

26--",.,1 2 6 - - " ,., 1

1

6E I

IP anomaly MF (mhoslftl

12}~1 41 2~5 26 52 6~7 13 34 6~7 11 5 ~ 11 II 27. 260 2 S II 21

89-"" 4

63--,,-3

27

26

22

2W ,I

4,I

86

60

26

38

- - 26

69

2W

o

2E

19--,,-1

9

IS-,,-2

8--,,·3

" 4

!-I-,,_4 1-1-" - 4

6E

200

Figure 9.18. Frequency-domain IP results for massive sulfides overlain by thick conductive overburden.

FIELO EXAMPLES 9.6. FIELD Several examples 01 of IP field results have already been given in Figures 9.11, 9.12, and 9.16. Three lurther illustrations i1Justrations are described in the following lollowing further paragraphs. 1. Figure 9.17 is a profile 01 of apparent resistivity and chargeability obtained during a time-domain IP survey on the Gortdrum copper-silver copper-Silver orebody in lreland. Ireland. lbis This is a low-grade deposit, averaging on1y only 0.750%. 1.2% by volume 01 of copper and 0.75 oz. 01 of silver per ton, that is, 1ess less than 2% metallic conducting minerals. With this type of mineralization, the conductivity is often enhanced by the presence of pyrite or pyrrhotite bul but this is not nol the case here. However, the chargeability anoma1y loanomaly is very strong and well 10caled. The P Paa profile shows a large resistivity concated. trast between the dolomitic limestone and sandstone direct1y over the fault; laolt; there is no with a minimum directly of the sulfide Iones zones containing chalcocite, indication oC bornite, and chalcopyrite. The pole-dipole spread was used in this work, with spacing as shown in the diagram. 2. Pseudodepth plots from the results of oC a double-dipole traverse using frequency-domain IP are shown in Figure 9.18. This is in the Timmins area of northem Ontario where the glacial overbur-

den is frequently 100 to 200 ft thick. and, being of elrectively masks the response of conlow resistivity, effectively dipo1e spacing It dipole ductors lying beneath it. Using 200 ft fl, a good and separations of 200, 400, 600, and 800 ft, IP response was obtained. The shape of the metalal depth. The factor contours indicates a source at resistivity section shows low resistivity continuing lo to depth with a westward dip, as well as the effect elrect of dri11ing inthe conductive overburden. Subsequent drilling tersected massive sulfide mineralization over 100 fl ft wide at a depth of 240 Ct. ft. It is not surprising that EM methods failed lo to detect this zone. 3. Figure 9.19 displays curves oC of M and Pd for Cor a traverse over the Lomex porphyryr copper deposit in British Columbia. 1ms This is a lype type of mineralization for which the IP technique is particularly effective, because no other electrical method would be capable 01 of detecting the main body, although there might be ftanlts. Moreover, it is unminor indications on the flanks. likely that the gravity would produce any response. lbe Cl elecThe resistivity profiles for 400 and 800 ft trode separations might be interpreted as showing a reflection of mild reftection ol the mineralization, were it not nOl for ror faet that the apparent the fact apparenl resistivity increases ineceases with depth. 'Ibis This tells us that the overburden, which is 200 Ct ft thick on the east, has a higher conductivity than mne below be10w it. On the other hand, chargeabilthe ore zone ¡ty ity response inereases increases with e1ectrode electrode separation and

603

Field examples 15

Char,ubility Charlubility

!:

10

, "...... , ' ,-.-' -' ,,'

s

+0--ie

PI Pole·dipole P~ C spread spread ~ o

(ms)

/'

,,------ ...... ,

SI.lion Sialion

\

,

\ \

t.,.'

\\

,"II'

, . ....... ........""':':- .... \\

\

........

Resistivity (Om) mm) .-0-800fl .-0-800fl - - - Q.., 0'" 400fl ······0-200fl ······0-200ft

,,

,._-'" "..... ,---'"

300

,.

'...... 200

,"'~'II\, ,"'~'II\ ,

... .,,,

,

'

..

,-_J..' '\'''. II 11

.

"

" ." .,. ....../'# ••••• l'#

,'tJI'.' ,'tf1I'.' ,I

:'

/-.~ /--~

,

I

\.,'

I()() 100

I

I

,

,

B

,

Overburden

8ethsiSida ~ 8ethslSida

L.!-J ~

Granodiontc GrlSnodiorllc

~l Skeena ~ quarll quarl1 diorile

2

~I Mineralized Mincróllized

~

Skecna quarl!. diorile diorilc Skeena quam pyrite. pyrile. bornile. bornilc. chalc:opyrile ehalcopyrile

Seige/, 1967.) Figure 9.19. Time-domain IP results over porphyry-copper deposito deposit. (After Seigel,

Table 9.6.

n-l n-1

n-3

n - 2

Potential dipole

p./2."

MF

p./2." Pa/ 2."

MF

p./2."

105-95 95-8S 95-85 85-75 75-65 65-55 55-45 45-35 35-25 25-15

180 210 270 315 480 330 1,091 1,200

28 31 42 39 40 88 46 31

1CJO 275 280 80 220 1,120 1,130 1,510

24 36 35 172 17 41 29 27

280 270 2CJO 72 70 675 1,751 1,830 1,710 1.710

MF 27

33 60

219 175 99 61 31 28

604

\

Induced polarization polar;zat;on

.....III

20

,"- ....

800

P.~

.E

,

:s:0

,

,,,,, ,

~

.c

'\

, ,,

~ IS

e.o :0

'\

10

"--. ....

S 200

o

, I

,

U

I

I

I

,

I

' .....'

400 n

200

Figure 9.20. fP chdrgedbifity ch,¡rge,¡bility and apparent resistivity, Northwest Territories, Canada. Ca nada. (After Seigel, 1967.) (o) (0)

45

0O ,

!

-H

)00 3-0

H

--loS --20'

400 4-0 H

4-4 404 H

H

~

S-o SOO

4N !

H Sol H

,,-2 ".2 ".] ".3

1-2 Jo2

H 4-6

4-9

H 5-1

2-3

H

11-1 11·1

0·] 0·3

O'S

H

,,-4 ".4 4N !

S·I '·1

P

(6)

-3-7

22 16

23 II 22

17

24 28

17

45 ,

S3 41 24 26

H

38

".2 ".2

11

JO

43 18 0O ,

,,-1 ".1

H

"

27

".] ".3

,,-4

".4 4N ,

J6

.

(c) Ce)

-0'9

]oS JoS

H 4-6

- - J.2

3

H

]oS JoS

,.,

4·9

S

2·7 4·0

SoS

H

O-oS O-OS

H

-0·27

1·6 ',6

0·29

-0'] -0·3

-0,6

1·7 J.2 Jo2

0,) 0·3

-0·7

,I

~ ".3

,,-4 ".4

-O·J 0O

" • I

" - I 0')'0'3'-

1I 100

1i

200ft

Figure 9.21. Time- and frequency-domain IP fP pseudodepth plots. Double-dipole array, )(. ft. (a) Percent (requency frequency effect. (b) Metal factor (mhos per (001). foot). (c) )( - 100 (t. (e) Chargeability abifity (milliseconds).

tbe lateral extent and depth deptb of oC the tbe zone determines the quite well.

9.7. PROBLEMS 1. The results in Table 9.6 were obtained using frequency-domain IP in a survey over suspected sulfide mineralization in northern nortbem New doubIe-dipoIe array was used Brunswick. The double-dipole

witb dipole separations of 100 Ct 1,2.3. with ft and n - 1,2,3. O-fl. Resistivity values are in the fonn P Po/2" o /2'f1 O-ft. 1be witb stations every The grid line is rougbly roughly N-S with 100 ft. In all cases the potential dipoIe dipole was soutb south oC of tbe the current dipole. p,J2f1 Prepare pseudodepth pIots plots for P o /2" and MF; draw contours and interpret the results. 2. A time-domain IP profile profi1e of chargeability and This apparent resistivity is shown in Figure 9.20. 'Ibis is from Crom the Pine Point sedimentary area arca of the

ProtJlems

605 Pole-dipole IIrrlly luray

0=400 a=400 Ii ti

16/2 ,£,2 0/2 0/2 012

;!; Pjc.. ~ ~ ;t; Pi 00-+ C/I C;I e, Sin P, p. C,

N

1

o interva/: 2 ms. Figure 9.22. Time-domain IP tP survey, southern New Brunswick. Contour interval:

methCanadian Northwest Territories, where IP meth· sueeessfully employed to locate ods have been successfully large lead-zinc deposits. The host rocks are carbonates and the background IP is generally low and uniform. uniformo With no additional information, tey to answer the following questions. try (a) What type 01 of electrode array was used? (b) Was the eleetrode electrode separation relatively large or small? (e) Is the anomaly eaused (c) caused by electrode or membrane polarization? (d) Is the anomalous souree source deep, shallow, wide, of great depth deptb extent? (e) Would you recommend further geopbysical geophysical work, and if so, wbat? what? (f) Would you drill this anomaly, and if so, where? where7 nortbwest3. In the course of sulfide exploration in northwestem Quebec, both botb frequency- and time-domain ern teehniques were employed. Figure 9.21 shows IP techniques pseudodepth plots for PFE, metal factor, and chargeability cbargeability from a particular line traverse; as tbe double-dipole array was used in both noted, the cases, with 100 ft separation. Compare the results obtained with the tbe two methods metbods and make tbe whatever interpretation you can from all the data. What is the significance of the negative chargeability values?

4. Figure 9.22 shows chargeability contours from a time-domain IP survey carried out on a basemetal property in southem southern New Brunswick. During previous drilling, massive sulfide mineralization, striking N-S, had been found in the Une lO5E, about tbe vicinity of line the middle of tbe the map; the zone was not very veey wide. Take off an E- W profile across the sheet around 156N. From tbis this profile and tbe the contours, make whatever interpretation you can of tbe the data. Can you explain why the known mineral zone was not detected by IP? tbe metal-factor contours in Figure 9.23 5. Data for the were obtained from a survey in Nova Scotia, using tbe x - 100 ft the double-dipole array with x-lOO and n = 1. Make an interpretation of tbe the area based on tbese these results. Can you match this map witb with the one from problem 10 in Chapter 8 and il so is the tbe additional information an aid to the tbe if interpretation? 6. A frequency-domain frequeney-domain survey, similar to that in I, carried out over two lines on a propproblem 1, erty in Brazil, produced the tbe results in Table 9.7. The dipole separation was 50 m, with n ... 1, I, 2, 3, 4. Lines are E- W and separated by 400 m, with witb stations SO m apart; the current dipole was a11 cases. Resistivities are in ohmto the west in all meters.

o0

-

200

4000

Figure 9.23. Meta/- factor contours, double-dipole array: x - 100 ft, n - 1.

Table 9.7.

Current dipole lineO Line 0 44W-43W 43W-42W 42W-41W 41W-4OW 4QW-39W 4OW-39W 39W-38W 38W-37W 37W-36W Line Une 25 4OW-39W 39W-38W 38W-37W 37W-36W 36W-35W

n-1 p.

PFE

MF

228 248 220 76 30 36 114 190

1.6 1.7 1.2 2.5 11 3.7 1.5 0.2

13 13 10 62 7fIJ 195 25 2

150

1.7 4.5 7.4 0.2 1.3

24 100 390 5 10

86

36 260 240

n-3

n-2

PFE

MF

390 520 128 34 17 38 217 305

1.8 1.5 3.0 13.5 11.5 3.5 1.5 0.7

9 5 45 750 1,330 175

120 52 71 305 355

4.5 8.5 8.0 1.3 0.5

PFE

637 217 44 22 19 59 275 410

1.6 4.5 14.5 11.5 9.8 4.0 2.2 1.0

72

59

315

88

9.0 8.7 8.5 1.4 0.5

13

4

215 8 2.5

61 380 460

n-4

MF

5 40

630 1,rm 980

130 15 5 290 190 265 7 2

PFE

MF

250 71 29 29 34 65 340 650

4.8 14.5 11.5 9.5 8.4 4.2 1.5 1.2

37 390 740 630 470 124 8 3.5

105

8.0 8.5 8.3 1.3 0.5

150 200 230 5.5

ao eo

69 450 670

1

I

Problems

607

22W ,

20 ,

I

16 ,

II 11

I

I!

14 ,

I8,

10

12

I

I

I

2W ,

4,

6 I

I

0O ,

'creenl Percenl frequency rrequeney ell'eel ell'ecl x.IOOft x.lOOn

0O t I

Melli Melll flclor faclor

".1 1·9 "70)()2OO 4-8 z.s H'~3 12' 125 34ClO ".I-----~ 2-6 1-9.,70 30200 83 4-1 34CJO ,., 2) 0;8 tI2.70tU~0("16!00· ~ ~.' 3;4 H·..., ".2 2:1' 0;1'I2,70'U~0()16!00' 4:' I Ip·61.30·~· IPI6l1)()1~' I? 0-7 321 328 5330 2440 8450 84SO 24 2-2 5800 9600 3100 4-) ,,-3 14 0·' H B5 S8IlO ".. ".4 ' 0:' 0-7 .. 1~7' 1~7 t 7¥, 7~ •'22!'O' 22!"'· ~'~70' 8~0(" ~70· 19 1.9 • 71 • 7~ n~ 'tl~· ~IO· m . 13400' 8010'

2i W,---..."a-2iftW 1,0

I

I

I

•

_... 100 ft .... 1001'1

I

2W ,

4I

6I

O 0,I

'erunl 'ereenl frequency frequenc)' effeel effecl x-lOOn x-200ft

"=1---"=1-----

II

4·J

48

, '-.:/

4:5 4:S

I I

3;5 /1.4 _ _ _ 23 11.4

\)

14

4-5 4·S

4;8

3;S

+-_'''--- /Ir _ _ .r ...

~"'~ i1 ~

.

~2W ,

.

.

il is

20

14 ,

16

12

•, 8

10 ,

I

•..

6

o0,

2W ,

II

I

I

I

MCII&! faclor fllclor Meu&l .-200 1'1

"s~--"s~---

".J-

II.J-

115 715

11 II

II-I ".1

011

1-1 1·1

160 SIlO

.. -4---

SS/! SS6

17

22

4-S 4'5

1-3 1·3

730 no

950

NR

... 410

17

1-4 1·4

H

340

1240

41000

26000

0-6 0·6

3200 211200

102

357 3S7

196

o4JS 4JS

140

4-S )~

1860

92

... 4 - - - 106

10300

41S 415

1;1

Pseudadepth plats far frequency-damain Dntaría. plots for frequency-domain IP. western Ontario. Figure 9.24. Pseudodepth

o0

6S II

...

,,\1 --Pcrcenl ,,·2 Percenl frequency clrecl efreel ".4 6S !

,,·2

".)

o4N 4N

II

.~~., .~ ~o,

8

0-1 0-1

0·1

0·1 0-1

(i:' ,-o o.,o, r.'o

.,~., .. ~o, 0·1 0-1

~Ol ~Ol

~ @j'

0·1 0-1 O-I~O-I O'I~O'I

--,0o

I

I

0-2 0·2

9

·0

02

,

4N

n1..l 1 1Melal n-l' n-2 fllClor faClor 11 .. 3~ (mhosfll lmhosftl " ".4 6S

.

o4N 4N , I

I!

,,-1-,,-1--

Chilraeablilly ChilrJCablllly .... " .. 2 (ms) ,,"') ,,-4 ,,-4

01-.

o-s ~I-~ O'S ~I'~

'O-S~-J...; 0-4 'O·S~·J..,; 0'4

04

~'·;!~O.6 ~1'2~O'6 1.2: '-2: IVO-~9 IVO-~9 ~ 2-7 2·7

;!7 27

.....1'1\ /41. .....1'1\ AI.

o0,I

2001'1 200ft

o0

dauble-dipale array, x-lOO Figure 9.25. Time- and (requency-damain frequency-domain IP. double-dipole x - 100 (t, ft, Abitibi West, Quebec.

12 1;1 1:1

....

ge 98 ,

96 9,6

,

91

•

•

•

99

...•...

-.. .•• oo.. ..'.

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e

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101

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PHASE ANGLE ANGlE AT 0.1 HZ OEGREES DEGREES

•

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RESISTMTY (OHM-METERS) AT 0.1 HZ

• •

, -. . . .

,

APPARENT METAl. "TAl. FACTOR (0.1 TO 1.0 HZ)

APPARENT

-

lOS 104 lOSE lOS , , , • • -i -I "-4 /~ -1 "::'ya __ .• ~" ~..•• ......~\:.~~.~.~ ~\:.~~'~ . ....~"'.'. ~'.,. p ..::.Y•.•.•.• .•--.• ......... P -~~~~~. -.,~~~ .&.~~~.". '.' ".• , ~. (~~ ." .,....... .~ • .•,(kY-' ,'~ ...«•. ' .~ . -:;;; ·a. '. '. .• ~-;. ~ ·.4 , 9·.. -. .,. .1• • 1. a • ~''14 .~. .,.

95£ 95E ,

1I II

_0-.

-

~

......... _

--.---.----, -'-0

lONE ZONE C Figure 9.26. Results of an F-D f.O survey in southern New Brunswick, using a double-dipole array: aTTay: x-50 ft, n - 7, 2. 2, 3, 4. (After Scott 5cott, 7977.)

---

, References

609

Table 9.8.

7.

8.

9.

10.

Freq (Hz)

Phase (mrad)

0.01 0.0316 0.1 0.316 1.0 3.16 4.79 19.0 62.5 175 350 1.660 5.500 17.000

340 330 330 335 344 346 355 344 344 321 300 270 230 195

cal calculation of a few points in Figure 9.16a. [Hint: Eq. (A.46c) is useful here.] 11. The broad-band IP readings in Table 9.8 were obtained from a survey over mineralization conbotb sulfides and graphite. taining both oC phase pbase Plot these values on a log-log scale of versus frequency and attempt to match tbem them with a best-fit Cole-Cole model of two terms. Assume plausible values for tbe tbe the parameters, the two M and ec values being approximately the same and tbe the time constants widely different.

REFERENCES

Sorne aspects of oC induced polarization (time Bertin, J. 1968. Some domain). Geophys. Prosp. 16, 401-26. Coggon, J. H. 1971. Electromagnetic and electric modelling Coggon. Make pseudodepth plots of Po' Pa , PFE, and MF, by the finite element method. Geophysics 36, 132-55. tbe results. and interpret the Coggon, J. H. 1973. A comparison of al IP electrode arrays. Coggon. 38, 737-61. Pseudodepth plots for frequency effeet effect and metal Geophysics 38. Cole, R. H. 1941. Dispersion and absorption factor, on a base-metal prospect in westem western On- Cole, K. S., and Cole. Chem. in dielectrics. 1 Alternating current fields. J. Chern. tario are shown in Figure 9.24. Two spacings 01 of Phys. 9, 341. Pltys. double-dipole array were employed - 1()() lOO and Collett. L. S. 19S9. oC overvoltage. 1959. Laboratory investigation of Con tour the 200 ft - as noted on the diagram. Contour OvenJoltage Research Researeh and Geophysical Geophysieal Applications, App/ications, In Overvoltage J. R. Wait. ed., pp. 50-70. London: Pergamon. metal-factor data and compare the results with R .• and Grant. F. S. 1969. IP and the PFE contours. Can you see any particular Dieter. K.. Paterson. N. R.• bocHes. resistivity type curves for three-dimensional bodies. advantages in using two spreads? Is one more 34, 615-32. Geophysics 34. this particular job than the other? suitable for tbis otber? Dolan, W. M., M .• and McLaughlin. G. H. 1967. Considerations concerning measurement standards and design 01 of Interpret the data. pulsed IP equipment. In Proc. Symp. on lnduced Induced Figure 9.25 shows frequency- and time-domain E/eetrical Polarization, Po/arization, pp. 2-31. Berkeley: Univ. Calif. Callf. Electrical eontours lor an area in the contours in pseudodepth for Press. regíon of Quebec. As noted in the Edwards, R. N. 1974. The magnetometric resistivity method Abitibi West region diagram, the double-dipole array had a separaand its application to the mapping of a fault. Can. J. Earth Ear,h Sc. Se. 11. 1136-56. lion oC 100 Ct ft with witb " - 1, 2, 3, 4. The Tbe IP results tion of Edwards, R. N., and Howell, E. C. 1976. Field tests 01 of are obviously not very promising, particularly in Geophysies magnetometric resistivity (MMR) method. Geophysics lhe the frequency domain. There ¡s, is, however, a 41, 1170-83. bere of ol economic eeonomic grade. Can Edwards, R. N., Lee. H., base-metal orebody here H.• and Nabighian, M. N. 1978. On deptb, you make any estimate of its location, depth, the theory 01 of magnetometric resistivity (MMR) Geophysies 43. 43, 1176-1203. methods. Geophysics and width from the IP survey? Can you explain Fraser, D. c.. c., Keevil, N. B.• B.• and Ward, Ward. S. H. 1964. Fraser. KeeviJ. the poor response? Conductivily spectra oC racks from the Craigmont ore Conductivity of rocks Figure 9.26 shows pseudodepth plots from a environment. Geophysics 29. 832-47. detailed frequency-domain IP survey performed Hedstrom. H. 1940. Phase measurements in electrical electricaJ prospecting. Trans. A.l.M.E. 138. 456-72. al a base-metal property properly in southern southem New at TIte short (50 ft - 15 m) double- Inman. J. R. 1975. Resistivity inversion with ridge Brunswick. The regression. Geophysics 40, 40. 798-817. tbat Inman, J. R., dipole array was used because it was known that R.• Ryu. 1.. and Ward, S. H. 1973. Resistivity the mineralization occurred in several thin shalinversion. Geophysics 38,1088-1108. 10w low zones eontained contained in silicified wall rocks of Johansen, H. K. 1975. Interactive computer-graphicdisplay-terminal system Cor for interpretation 01 of resistivity ol profiles high resistivity. Take off a couple of soundings. Geophys. Prosp. 23,449-58. from each of the Po' Pa , PFE, and phase sections to . Johansen, Johansen. H. K. 1977. A man/computer interpretation check this. tbis. Compare these results with problem system for ror resistivity sounding over a horizontally 4, particularly with regard to electrode spacing. stratified earth. Geophys. Prosp. 25, 667-91. polarizadon Using the Cole-Cole model of Figure 9.3, deter- Johnson, 1. M. 1984. Spectral induced polarization time·domain parameters as determined through time-domain mine the real and imaginary components of oC 49, 1993-2003. measurements. Geophysics 49. impedance Z from tbe the mathematical matbematical expression Katsube. Katsube, T. 1.. l. and Co))ett. Colleu. L. S. 1973. Measuring techniques oC tbis of this circuit in Equation (9.11), hence obtain Cor pennittivity and high 105s. for rocks with high permittivity loss. ~. Check your result by numerithe phase angle 4'. Geophysics 38. 92-105.

, 610 Lambert, R. 1974. Etude des parametres afl'ectant atl'ectant ~Jectrique de certains certaios metaux et el mineraux. mioeraux. I'impedance ~Iectrique Pb.D. thesis, McGill Univ., Montreal. Ph.D. Major, J., and Silic, J. 1981. Restrictions on the use of Cale-Cole dispersian Cole-Cole dispersion models io in complex resistivity GftJphysics 46, 916-31. interpretatioo. interpretation. GftJphy,lc, Marshall, D. J., and Madden, T. R. 1959. Induced MarshalJ, polarization: A study sludy of its causes. GftJphy,ic, 24, 790-816. Elcetromagnetic coupling of collinear Millett, F. B., Jr. 1967. Electromagnetic dipoles on a uniform half-space. lo In M;ning Mining Geophysics, Geophy,;c" 11, pp. 401-19. Tulsa: Society of Exploration ExpJoration vol. II, Geophysicists. Nabighian, M. N., and Elliot, C. L. 1976. Negative induced polarization Geophysics 41, polarizatioD effects elfcets from layered Jayered media. Geophys;" 1236-55. Hallolf, P. G., O., Sill, SilI, W. R., and Pelton, W. H., Ward, S. H., Halloff, discriminalíon and Nelson, P. H. 1978. Mineral discrimination removal of inductive coupling with multifrequency polarization. Geophy'i" Geophysics 43, 588-609. induced polarizalion. Petrick, W. R., Pelton, W. H., and Ward, S. H.1977. Ridge inversion applied lo to crustal resistivity regression inversíon sounding data from South Africa. Geophysics 42, 995-1005. Intcrpretation of gradient array Quick, D. H. 1974. Interpretation chargeability anomalies. Geophys. Prosp. 22, 736-46. Seott, W. J. 1971. Phase angJe rneasurements in the IP Scott, angle measurements method of oC geophysical prospectiog. prospecting. Ph.D. thesis, McGiJJ Univ., Montreal. Montrea!. McGill 01 induced polarization Scigcl, H. O. 1959.. A theory of Seigel, elfects tor step-function step-functioo excitation. In Overvoltage effects for

Induced polarization Research Researeh and Geophysical Applications, J. R. Wait, ed., pp. 4-21. London: Londoo: Pergamon. Seigel, H. O. 1959b. Mathematical Malhematical formulalion rormulation and type curves for induced polarization. GeophysicJ 24, 547-65. Seigel, H. O. 1967. The induced polarization method. In Mining and groundwater geophysics, L. W. Morley, ed., &on. GeoJ. Oeo!. Report No. 26, Geol. Oco!. Surv. Canada, pp. 123-37. Seigel, H. O. 1974. The magnetic induced polarization (MIP) method. Geophysics 39, 321-39. O., and Howland·Rose, Howland-Rose, A. W. 1983. The magnetic magoetic Seigel, H. 0., induced polarization Deve/opmenll in poJarization method. In Developments GftJphysica/ Exploration Explora/ion Methods-", Methods-4. A. A. Fitch, ed., GftJphysical pp. 65-100. London and New York: Applied Science Publishers. PrincipIes of ollnduced Polarizalion /or Sumner, J. S. 1976. Principles Induced Polarization for Exploralion. Amsterdam: Elsevier. GftJphysical Exploration. Sumner, J. S. 1979. The induced polarization exploration melhod. seareh method. In Geophysics and geochemis/ry geochemistry in tht search lor for metal/le metallic ores, P. J. I. Hood, ed., Econ. Geol. Report 31, Geol. Geo!. Surv. Canada, pp. 123-33. C., and Zonge, K. L. 1975. EM coupling, its Wynn, J. C.• intrinsic value, its removal, and the cultural coupling problem. Geophysics 40, 831-50. Zonge, K. L. 1972. Electrical parameters of rocks as applied Atizona, to geophysics. Ph.D. dissertation, Univ. of Arizona, Ano Arbor.) Tucson. (Microfllm at Univ. Michigan, Ann Zonge, K. L., and Wynn, J. C. 1975. Recent advances and compJex resistivity measurements. applications in complex Geophysics 40, 851-64.

Chapter 10

Radioactivity M ethod 10.1. INTRODUCTlON The geophysical techniques described in previous chapters have depended on variations in the mechanical, chemical, electrical, or magnetic properties of rocks and minerals. Since about 1945 another property of certaín elements has become oC considerable economic importance. This property is known as radioactivity . The original discovery was made by Becquerel in 1896, shortly alter R~ntgen had announced in 1895 tbe discovery oC X-rays. Becquerel Cound tbat minerals contaíning uranium, as well as salts oC uranium, emitted radiations that passed tbrougb material opaque to ordinary ligbt, affected pbotographic emulsions in a manner similar to X-rays, and would ionize a gas. The discovery oC other radioactive elements soon followed. Mme. Curie, investigating minerals of uranium, extracted two new elements, polonium and radium, which were much more active than uranium. About the same time Schmidt discovered tbat tborium was radioactive and Debieme found tbe new radioactive element actinium. Altbougb at least 20 naturally occurring elements are now known lo be radioactive, only uranium (U), tborium (Th), and an isotape ol potassium (K) are of importance in exploration. One other, rubidium, is use fui in determining ages of rocks, but tbe rest are either so rare or so weakly radioactive, or both, as to be of no significance in applied geophysics. A complete Iist, witb characteristic radiations and otber pertinent data, is given in Table 10.1. The two elements, uranium and tborium, are important today as a source of fuel lor tbe generation of heat and power in nuclear reactors. Large areas in all parts of the world have been surveyed on the ground and particularly by aír in the search for uranium, using special detectors, which will be discussed later. Surface work in radioactivity expluration is relatively a minor effort (see Table 1.2 for 1987 figures.) Airbome radiometric prospecting is still comparatively cheap and efficient from tbe point ol view ol

detecting gamma rays (y rays) because the intensity of a 1 MeV beam is reduced by only 50% at 100 m above surface. Considerable aírbome work was done in tbe late 1950s using scintillation meters witb large crystals. The results were not very useful owing to tbe lack 01 discrimination in total-count measurements (§10.3.4). Wben tbe demand for uranium lell off, the technique was almost abandoned. A revival of interest in uranium in the early 1970s, plus the avaílability of greatly improved y-ray spectrometers (§10.3.4), made tbe method more attractive. A large-scale airbome radiometric program was initiated by tbe Geological Survey 01 Canada (GSC); this provided a stimulus for ground followup by private interests in various parts of Canada (Darnley, Cameron, and Richardson, 1975; Bristow et al., 1977). The radioactive metbod is relatively unimportant in comparison with otber geopbysical techniques. It was first used in tbe late thirties for stratigraphic correlation in oi! well logging (§l1.l.2). Radioactivity prospecting became quite popular in tbe period 1945-57, fell off witb tbe decrease in demand for uranium, and was revived agaín in tbe late sixties and early seventies. This sporadic progress, however, has not affected well-Iogging applications of tbe metbod, wbere several radiometric techniques have become standard. These will be discussed in Chapter 11.

10.2. PRINCIPLES OF RADlOACTIVITY 10.2.1. Constituents of the Nucleus (a) Introduction. A1thougb much of the original work on emanalions from radioactive subslances was do~e by Rutberford and others nearly 80 years ago, tbeu source - the nucleus of the atom - was nol well understood al the time. We shall now consider this source and its elementary parts.

The atom, which is tbe fundamental part of all the elements, consists of a dense, small (b) Atoms.

Radioactivity method

612

------RadIo

I

Inft.red .__ ..... •__ 1 Microwa"~r.,.

X-tay • . __ ..J>'_ __

-o., ,, ____"___

Ullrav'lOlel

-"--

1• 1,

i'.~)')

10' •

10"", 1 in Hz ,\ in meten

JI. - (' =- .l

)( 10111 mIs

Figure 10.1. The electrom.1gnetic spectrum showins rel.1tive frequency (w.1velensth)

bands.

(- 10- 13 cm in radius), positively cbarged oucleus surrounded by oegatively charged electroos, io number equal to tbe nuclear cbarge. Tbe arrangement is quite analogous to a solar system, with planets moving about a central SUD. Because tbere are never more tban 92 e1ectrons and because the atomic radü are 01 the order 10- 1 cm, DIOst of tbe atom, like tbe solar system, is empty.

(f) Alpha partícles. Actually tbese are tbe equivalent of a helium nucleus, 2p + 2n; the Dame was . attacbed in tbe pioneer days of radioactivity, before tbe oBture of tbe particle was understood. It has a charge + 2, mass 4.00389, and is frequently a tigbtly bound entity within nuelei heavier tban helium. It may be ejected from the nueleus during a disintegration.

(e) Protons. Tbe nucleus is composed 01 tigbtly packed protoP/S and neutron.s. The proton, carryiog unít positive cbarge, has a mass 1.00812 on the pbysical scale (O - 16.0000 ... ), the actual mass being 1.7 X 10- 24 g. 1be number of protons in a nucleus determines the elernent itseU. Por example, the first e1ement in the Periodic Table, hydrogen, has 1 proton, oxygen has 8, cadmium 48, and so 00, up to uranium, witb 92 protons.

(8) Eleetrons. Tbe outer atomic constituent, tbe electron, has a charge - 1 (actual charge on tbe electron and proton is 1.60 X 10- 19 q and mass about 1/1,840 01 tbe proton. Altbougb tbe electron does not exist as a separate eotity in tbe nucleus, it is ejected in certain nuclear disintegrations when a neutroo splits into a proton and an electron. tbe proton remaining in tbe nueleus. nis transmutation results in a gaín of + 1 unít of charge and practically uro mass change, tbat is to say, tbe e1ement moves up one place in the Periodic Table. EJectrons ejected from the nueleus were origina1ly called beta ({J) particles or rays.

(d) Neutrons. Tbe otber nuclear particle, tbe neutron, has uro cbarge and a sligbtly greater mass tban tbe proton (1.00893). Tbe only element lackiog neutrons is common hydrogen. As we proceed througb the Periodic Table, tbe ratio 9f the number of neutrons to the oumber of protons increases from 1 to - 1.5. Tbus helium has 2 neutrons and 2 protons, whereas tborium contains 142 neutrons and 90 protons.

Mast elements are composed 01 a mixture 01 nuclei having different numbers 01 neutrons, tbe number of protons, 01 coune, being the same. These are called isolopes, tbat is, forms of tbe same element having diJferent atomic weigbts. (Practically aIl tbe mass of an element is CODtaíned in tbe oucleus, hence is determined by tbe number 01 protons and neutrons called tbe atomic weight). For instance, bydrogen is a mixture 01 two isotopes: 1H1 , whicb is a single proton (99.985% abundance), ud 1H2, one proton and one neutron, familiarly known as deuterium (0.015% abundance). Titanium has 5 isotopes, (in has 10, tungsten 5, lead 4, and so on. (e) Isotopes.

During nuelear disintegrations, pure electromagnetic radiation representing excess energy is frequently emitted from tbe excited nucleus. The early name assigned, gamma ray (y ray) is quite appropriate in thls case (a and {J rays are really discrete partieles). Gamma rays differ from X-rays only in name, a1tbough usually the Iatter term is used for radiation of lower energy. The relative location 01 y rays in tbe electromagnetic spectrum is illustrated in Figure 10.1. (h) Gamma radiatíon.

10.2.2. Nuclear Dlsintegrations While carrying on pioneer work in nuclear physics, Sir Emest Rutherford investigated tbe radiations from naturally occurring radioactive elernents and showed tbat tbey consisted 01 tbe three distinct types mentioned aboye: a, {J, and y rays. Eacb of tbese rays produces three different effects in varying

PrincipIes of radioadivity

613

Table 10.1. Naturally occurring radioactive isoropes. Abundance Elemenl POlassium Calcium Vanadium Rubidium Indium lanthanum Cerium Neodymium Samarium Samarium Samarium Gadolinium Lulecium Halnium Rhenium Platinum Platinum lead Thorium* Uranium* Uranium*

Isolope

(%)

K40 48 Ca 20 50 V 23 t:f'7 37 R115 In 49 138 57 la Ce'42 58 Nd'44 60 147

0.012 0.18 0.24 27.8 95.72 0.089 11.1 23.8 14.97 11.2 13.8 0.2 2.6 0.16 62.9 0.013 0.78

19

6~~'48 6~m'49

6~G~152

64

,1f>

71 lu

n HI'74 7§Re1B7 78 Pt1'lO PI192 78 p¡,204 82 Ttrl2 9O U235 92 238 9ZU

1.48 100 0.72 99.3

Hall-lile (yr) 1.3 > 2 6 4.7 6 1.1

x x x x x x

109 1016 10'5 1010 10'4 1011

Type 01 radiation

Energy (MeV)

13,1< cap 13 p,1< cap 13 13 13,1< cap

1.46 0.12 0.71,1.59 0.27 0.60 0.54, 0.81, 1.43 1.5 1.8 2.32 2.14 1.84 2.24 0.088,0.20,0.31 2.5 S 0.008 3.11

a a a a a a p,y a

5 x 10'5 1011 1.2 x 1013 - 4 x 10" 1.1 x 10" 3 x 1010 2 x 10'5 7 x 1010 6 X 1011 - 10'5

13

a a a a,p,y a,p,y a,p,y

1.39 X 1010 7.1 X 108 4.5 X 109

2.& 0.03 - 2.62 0.02-0.9 0.4- 2.5

*[ach 01 Ihese undergoes a long series 01 disintegralions yielding lead isolopes 208, 207, 206, respeclively. During Ihese disinlegrations numerous y rays are emitted, in addilion lo Ihe a- and 13 parlicles.

degrees, namely: l. They affect photographic emulsions in much the same way as Iigbt and X-rays. 2. They iome gas, maklng it electrically conducting. 3. They produce scintillations or phospborescence in certain minerals and chemical compounds. AII tbree elfect5 have been used in geopbysica1 prospecting by tbe radioactivity metbod. The three .. rays" cbaracteristic oC natural nuclear disintegrations have very dilferent penetrating powers. Thus, a rays are easily stopped by a sheet oC paper, fl rays by a few millimeters oC aluminum, whereas y radiation requires several centirneters oC lead. Their equivalent range in overburden or rack is tbus practica1ly zero for tbe first two and not more than SO to 7S cm oC rock Cor y rays. In Cact, this range is a complicated function of tbe energy and character of tbe particles or radiation and of the density or atomic nurnber of tbe rnedium througb which tbey pass. It is clear tbat tbe range varies with initial energy and tbe rale oC dissipation of energy. The latter is a complex process of scattering, collision, and absorption involving tbe atoms 01 (he host material and resulting in iomation along the patb. Charged particles (a, fJ) iome strong1y, uncbarged electrornagnetic radiations (y rays, Xrays) do noto Maximum energy in natural nuclear disintegrations is generally less tban 3 MeV [1 MeV - 106

e1ectron-volts (eV), tbe energy acquired by a partic1e of unit charge, falling tbrougb a potential 01 lO6 V.] Even in air, tbe range 01 3 MeVa and fl particles is only a few centimeters and melers, respectively. On the otber band, y rays 01 Ibis energy will travel a lew bundred meters in airo In addition to a, fl, and 'Y emissions, tbere is one otber type of nuclear lransmutation, called K capture (see Table 10.1 and Fig. 10.2), which occurs in several ol the natural radioelements. In this process, an electron from tbe innermost K orbit enters tbe nucleus, whicb tben emits y rays; as a result oC the electron capture the atomic number decreases by one and a dilferent element is created. TIte equations representing transitions oI elernent X lo Y by a- and fl-ray emission and eleclron capture are pxp+N .... P_2 yP + II - 4

P

X P + II

pXP+"

....

p+1

YP+II

+ e- .... p-1YP+II

+2He4

+ e-

(aemission) (fJ emission)

(K capture)

In this nornenclature, the number oI protons in elernents X, Y, and He is the lower left subscript, whereas the number oI protons plus neutrons (atomic weigbt) is given by the upper rigbt superscript. Because the X, Y, and He symbols define the number of protons uniquely, this notation has recently been changed by entering tbe nuclear mass (p + n) al the

614

Radioactivity method ..,...,..,....,,.;:r~..,,...,'"T'"r

Oround sta,e

_ _---,,.c...___ ExCited stale 10·9%

Ground

slale

""""".,....-;""",,-r-n"7'"

FiBure 10.2. EnerBy-level diaBram far radiaactive potassium.

upper lelt and deleting tbe f.roton number altogetber. Tbus )7Rl>,17 beeomcs 8 Rb.

10.2.3. Radloactive Decay Processes In 1902 Rutberlord and Soddy announced the tbeory of radioaetive transformation, in whieh they

stated that when an elernent emitted a or fJ rays, it was transmuted into a new element, the rate oC disintegration being a characteristic of each radioactive nucleus. Tbey showed that the rate oC change was proportional to the number of atoms present and was not aft"ected by physical or chemical processes in tbe surroundings. Tbus, Cor any type of radioactive atom, we have tbe relation

dN/dt - -'AN where N is tbe number oC atoms present at time t and 'A is a decay constant that is characteristic of each element. Tberefore,

where No is tbe number ol atoms at an arbitrary time t - O. If T1/l is tbe time required lor hall oC the nuclei to disintegrate, we have

N/No -1- ,- ATl l2 or A - (1n2)/T1/2 - O.693/T1/2 (10.2)

Hall-lile values of radioactive nuclei vary enormously, from 211pO .. 10- 7 S to 204Pb .. 1019 y. Obviously a short half-life goes with a vigorous rate oC disintegration, wbereas the lead isotope 204 is, lor a1I practical purposes, stabIe - the disintegration rate is three or Cour nuc1ei per week per gramo As mentioned earlier, on1y three radioactive eIements, U, Tb, and K are ol practical significance in prospecting. Tbe potassium is mainly a nuisance when searehing for the other two; although the 40K isotope is, apparently, no more plentilul than U or Tb, the widespread occurrence oC potassium-rich rocks and particuIarly the association of tbese with U and lb, Cor exampIe. in pegmatites, creates a problem somewhat analogous to tbat oC graphite versus metal suIfides in electrical prospeeting. As shown by Table 10.2 and Figure 10.3, tbere are three radioaetive series lor uranium and thorium, starting witb 9011i'32, 92U23S (the so-called actinium series), and 92U238. AlI decay eventualIy to stabIe isotopes of lead, witb 10, lS, and 17 intermediate radioaetive stages, respeetiveIy. It is useful to caleulate the number oC daughter atoms present al any time, given the number No oC the parent at time t - O. Tben the number of parent atoms lelt at a later time t will be NI - Noe- At ', where 'Al is its decay constant. But the rate oC decay oC tbe parent atoms, dN1/dt - -A1N1, is just the rate of produetion of the daughter. At the same time tbe daughter atoms are disintegrating at arate A2 N2 , where N2 is the number present at time t and Al is tbe decay constant. Hence the rate of accumulation of tbe daughter atoms is tbe difference between produetion and decay, or

--""'""""7-,"'"

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fU!

'1!

~

J ;; e

i

O

•

r

rd

0811

@

g

.8H6 e

•

:1

!;

"'114

•

~ .... :t 1

b~~1

.

rd

U!J'

Thonuln

@

110

•

~ •

...oa.

11'

@

•

.\~,.'~

mi

~

sen"-,,,

Jfrj •

10001I0Ium)

•

UUI series

senes

•

n

,

1:!6

,

no

l.'" I

I

,

UH

I

1~1

I

I

I~b

1.10

1J.f

..L.

..L....I..-:-!:'::-"'-1.......I-:-7:~

I.IX

141

114

128

ll2

\' tnuo).t"",T 01' I'h:uunns'

Figure /0.3. Ur¡¡nium dnd thorium rddiodctive series. 5chemdtic showing decd)' processes.

136

140

144


616 Table 10.2. Natural radioactive series o( thorium and uranium.

HalHile

Isolope

Decay conslanl (s -1)

Thorium series gol¡r32 Ra228 88 AC 228 89 ¡r28 gol Ra 2H 88 n2 20 86 R 94 Pd'f' 82PtJZ12 8'112 83 1 8. pol12 11 208 81 PtJZ08 82

1.4 X 1010 yr 6.7 yr 6.1 hr 1.91 yr 3.64 day 51 s 0.16 s 10.6 hr 60.6 min 0.3 X 10- 6 S 3.1 min Stable

1.58 X 10-'18 3.3 x 10- 9 3.1 X lO-O 1.15 X 10- 8 2.2 X 10- 6 1.3 X 10- 2 4.3 1.8 X 10- 5 1.9xl0- o 2.3 X 106 3.7 x 10- 3

Actinium Series U 235 92 ¡r1'1 gol Pa231 91 AC 227 89 ¡r27 goT Fr n ) 87 223 Ra 88 86 Rr!'9 85 Atl19 8. po215 At 115 85 '215 8)01 8'111 83 1 8. Ptl" ptf" 82 207 TI 81 ¡f07 82 P

7.1 X 10B yr 25.6 hr 3.4 X 10' yr 21.6 yr 18.2 day 22 min 11.7 day 45 54 S 1.8 X 10- 3 S 10- 4 5 8min 2.15 min 0.525 36 min 4.8min Stable

3.1 X 10 -17 7.4 X 10- 6 6.5 X 10 -13 10- 9 4.35 X 10- 7 5.2xlO- 4 6.76 X 10- 7 0.17 1.28 X 10- 2 3.8 X 10 2 6.9 X 103 1.44 X 10- 3 5.35 X 10- 3 1.32 3.2 X 10-· 2.4 X 10- 3

4.51 X 109 yr 24.1 day 6.7 hr 2.48 X lOS yr 8 X lO· yr 1622 yr 3.82 day 3.05 min 1.35 s 0.03 s 19.7 min 1.64 X 10- 4 s 26.8 min 21 yr S day 138.4 day 1.3 min 4.2 min Stable

4.9 X 10-'18 3.3 X 10- 7 2.84 X 10- S 8.9 X 10- 1• 2.75 X 10-10 1.35 X 10- 11 2.07 X 10- 6 3.8 X 10- 3 0.51 23.1 5.85 X 10-' 4.2 X 103 4.3 X 10-' 1.05 X 10- 9 1.58 X 10- 6 5.7 X 10- 8 8.85 X 10- 3 2.75 X 10- 3

Uranium Series 238 92U¡rH goT pa 234 91 23. U 92 ¡r30 gol Ra 226 88 n2 22 86 R e. Pa118 85 Atl18 86 R"ns 0'21. 83 1 Po214 84 plfl 82 '

Ptf1O

82 8'210 83 1

e. pa21O

8111210 TI 206 81 P¡fD6 82

Radialion

a,SfO,y

{l,y {l,y a, y a,y a,y

a {l, Y {l,a,y a {l,y

a, SF*, y {l,y a,y

(l,a, y a,y

{l,a,y a,y a,y

y-ray energies (MeV)

0.059 0.03 0.06-0.97 0.085-0.214 0.24,0.29 0.54

No. 01 y-rays

> 10 5

0.11 -0.41 0.04- 2.2

> 10

0.28- 2.62

S

0.07-0.38 0.08- 0.31 0.29-0.36 0.09-0.19 0.05 - 0.33 0.05 -0.31 0.03 -0.45 0.27,0.4

5

10

> 10 > 10 9

> 10 4 > 10

a,p a,p a

{l a,p,y a,y p,y

0.35 0.56,0.88 0.065-0.83 0.89

a, SF*,y p,y P,y a,SF*,y a,y a,y a,y

0.048 0.03-0.09 0.044- 1.85 0.053,0.118 0.068-0.25 0.19-0.64 0.51

{l,y

4

3

> lO 7 4

a./l a a

p,a,y

0.61 0.45 - 2.43

> 10

a

p, y {l,y

P

a,y

P. y

0.05 -0.35 0.047

> 10

0.79 0.3,0.78,1.1

{l

SF* - spontaneous fission.

We can solve tbis equation by assuming

Ae- A" + 8e- A2 ', with the condilion that, when N2

-

N1 t -

O,

O. The result is

N2

-

Al No (e-A" - e-A2') A2 - Al

(10.4a)

This caJculation can be camed on lor successive members 01 the series, The number 01 8toms 01 the n th product produced after time t is given by

Nn

-

ele-Al' + Cle- A2 ' + '" + c"e- A.,

(lO.4b)

Principies of radioactivity

617

Table 10.3. Em;ss;on of y rays by U and Th series and by K. Uranium series Energy (MeV)

(Photjs g)

%U

x 103 x 103 X 103 X 103 X 103

36 31 17 12 4

9.4 8.0 4.3 3.2 1.1

0.2 -0.5 0.5 -1.0 1.0-1.5 1.5 - 2.0 2.0- 2.5 2.5 - 3.0 Tolal

2.6 X 10'

POlassium

Thorium series (Photjs g)

%Th

x 103 X 103 X 103 X 103

34 47

1.5 X 103

13 100

3.9 55 0.4 0.3

100

(Photjs g)

%K

3.4

100

3.4

100

3 3

1.2Xl0·

tban the radium. From Equations (10.1) and (10.4a) we can gel the ratio oC the number oC atoms 01 parent to daughter at any time

wbere

>. 1

N - 2 _

NI

~-

(>-1 - >'2)( >'3 - >-2) ... (>'" - >'2)

.. KNo/8 2

>-

>'2

or

>. 1 {1 _ >'2 - >'1

e(A,-A,),.. }

>-1

e(h, -A,)'.. = _

(lO.4c)

where

e(A,-I\,),}.

When equilibrium has been reached, tbe rates oC decay oC parent and daughter are the same, that is, N2 /N1 .. >-1/>'2' Thus we have _1 =

- KNo/6"

{l _

>-2 - >-1

>'2 hence, (10.6a)

and

10.2.4. Radioactive Equilibrium From Equation (10.3) it fo)]ows that when a radioactive series is in equilibrium, we have

That is to say, at equilibrium the number of daughter atoms disintegrating per second is the same as the number being created by disintegrations oC the paren!.

The state oC radioactive equilibrium merits further explanation. Consider radium and radon, the successive intermediate products in the mU series (see 88Ra223 and 86RJl219, Table 10.2 and Fig. 10.3). Here the daughter product decays about lOS times raster than its paren!. If we start with a sample oC pure radium, we find that its decay rate is practically constant ror the first day or two, because the halC-lile is about 12 days. During the same interval the supply oC radon atoms is building up at the same rate, although the radon is decaying considerably Caster

For Ibis example Ihe value oC t.q is about 1 min, aCter wbich the two will be in equilibrium, as long as the radium holds out. In the case oC a series with n products, the time to reach equilibrium can be Cound Crom Equation (lO.4b). It is

{1

N" - - K -+ ~ 81

e(ht -A,)I..

~

e(A,-I\,)leq

+--~

e(h,-A.)'.. }

+ ... +

6"

>-1

- - (10.6b)

>."

where K and B were defined in Equation (10.4c). Por thorium tbis time interval is less than 100 yr and Cor the two uranium chains, oC tbe order 10 6 yr. Measuremenl oC series products. in wbich tbe equilibrium situation is significant, will be discussed later; under these conditions it is possible to determine the amount oC a parent product in a sample by measuring the amount oC one oC the succeeding members. Table 10.2 and Figure 10.3 show the three radioactive series in detail, with the principal radiation accompanying each disintegration. There is in addition a wide spectrum ol y rays accompanying both IX

618


Table 10.4. Radioactive minera/s. POlassium

Mineral

(i) (ii) (iii) (iv) (i)

Orthoclase and microline feldspars [KAISiPIIJ Muscovite [H 2 KAI(Si04 hJ Alunite [K2AI6(OH),~O.1 Sylvite, carnallite [KCI, MgCI 2 • &HPJ Main consliluenls in acid igneous rocks and pegmatites (ii) Same (iii) Alleration in acid volcanics (iv) Saline deposils in sediments

Occurrence

Thorium

Mineral Occurrence

Uranium

Mineral Occurrence

(i) (ii) (iii) (i) (ii) (iii)

Monazite [Th02 + rare earth phosphateJ Thorianite [(Th, U)Ü:2 ) Thorile, uranolhorite [ThSiO. + UJ Granites, pegmatites, gneiss Granites, pegmalites, placers Same

(i) (ii) (iii) (i) (ii) (¡¡i)

Uraninite [oxide of U, Pb, Ra + Th, rare earlhs) Carnotite [Kp.2Uq,.Vps.2H 20) Gummile (uraninile alterations) Granites, pegmatites, and with vein deposits of Ag, Pb, Cu, etc. Sandstones Associated with uraninite

Table 10.5. Background radioact;v;ty in rocks and waters.

Rock Homblende Granite Basalls Olivine Ultramafics Marble Quartzite Sandstone Slates Oolomites Chalk Chondrites Iron meleor.

( X 10- 12 )

K (ppm)

Th (ppm)

1.2 0.7-4.8 0.5 0.33

35,000 9,000

15

Ci/S

10

U (ppm)

2

4 0.&

0.2

0.05

0.08 0.015

0.02 0.04

1.9 5.0 2-4 3-8

8

Water (radium)

CVg ( X 10- 12 )

Saratoga, NY Bath, England Carlsbad, Czech. SI Lawrence River Valdemorillo, Spain Aix-les·Bains, France Manitou, CO Hot Springs. AR Atlantic Ocean Indian Ocean

0.01-0.1 0.14 0.04-0.1 0.00025 0.02 0.002 0.003 0.0009 0.014 - 0.034 0.007

0.4 850

aud fl emission, some of which are included in the table; also, Table 10.3 gives y-ray emissions in UDits 01 photons per seoond per gram for various energy windows. Tbe thorium series has an isolated 'f ray lrom 208 n al 2.62 MeV; the uranium series do not produce such distinctive radiations, althougb the 1.76 MeV 'f ray from U4 Bi is reasonably so.

10.2.5. Unlts Tbe unít used lor measuring the activity 01 aradioactive specimen is the curlt (Ci) named for the discoverer of radium, Mme. Curie. It is the activity, that results in 3.7 x 1()1o disintegrations per 5eCOnd, this being the number ol ex particles emitted by 1 g of pure radium, 2l6Ra, in 1 s.

&cause 'f rays are similar in nature to X-rays, the StreDgth or intensity 01 gamma radiation (as weD as ex and fl particles) is also measured in the X-ray unit, caDed the rOtntgtn. 'Ibis is the quantity 01 radiation that will produce ooe e1ectrostatic UDit 01 charge (2.08 x lO' ion pairs) per cubic centimeter in air at O°C and 760 Torr (NTP). SubUDits are the millir5entgen (mR) and micror5entgen ("R). This is the UDit uled in defining maximum dosage permissible to humana exposed to radioactivity, about 300 mR/week. Some field ÍDStrumeDts indicate radioactivity as counts per minute, generally marked on the scale 01 a microammeter in an integrating circuit that adda up pulses to measure total intensity. None 01 tbese UDits takes into account the energy of the radiation.

PrincipIes of radioactivity

10.2.6. Radioactivity of Rocks and Minerals Sorne oC the common radioactive minerals 01 Th and U are lisled in Table 10.4. The polassium minerals, as mentioned previously, are very wídespread. Large deposits oC monazite are Cound in Brazil, India, and South Africa. Thorite and uraninite (pitchblende) occur particularly in Canada (Great Dear Lake, northem Saskatchewan; Blind River, Ontarlo), in Zaire, Central Europe (Saxony and Czechoslovakia), Malagasy, and so Iorth. Trace quantities oI radioaclive material are found in al1 rocks. Along with minute amounts oC cosmic radiation always present in the air, these trace amounts produce a continuous background reading, wbich may vary Irom place lo place by as much as a factor oC 5. Table 10.5 gives the activity and¡or trace amounts oI radioactivily oC a number oC typical roeks, as well as the amounl oC radium in waters. In general the aclivity in sedimentary rocks and metamorphosed sediments is bigher than lhat in igneous and other metamorpbic types. with the exception oC potassium-rich granites.

10.2.7. Age Determination Using Radioisotopes Determining the age oC rocks is oCten an important Cactor in deve10ping an overall geologieal picture of an area and thus is indirectly retevant to applied geophysics. lsotope ratios that are useCul for geotogieal age dating inelude the natural disintegratioD reactioDs I7Sr¡87Rb, ~Ar¡~K, I<16Sm ¡147 Nd, 14C¡1lC, varlous Pb¡U and Pb¡Th ratios, and others. For the decay pracess 87Rb .... 87Sr + 11, taking the initial number oC 87 R b atoms as No and assumíng that no 87Sr atoms were present initially. Equation (10.1) shows that the numbers 01 rubidium and slrontium atoms now present, NRb and NSr , are

NRb'" Nooe -A. so that

Tbus, knowing the decay constant A, the time t can be determined by measuring (he ratio oC 87Sr to 87Rb. Because the halC-liIe is 4.9 X lotO years, the Sr¡Rb method is userut in determining the age oI Precambrian rocks. An advantage ol the Sr¡Rb method is that alt products are solids and therefore unlikely to have been lost. Minerals suitable ror analysis inelude mica, feldspar, granite, and gneiss.

619 The halC-life oC 40 K is about 1.4 X 109 years; thus the K¡Ar method is useCul in determining ages Crom about 50 thousand years to about 3.5 billion years. The reaction is complicated because 40K disintegrates in two ways: (i) capture oC an eleetron from the innermost shell (K capture): ~K + e .... ~Ar; (ü) beta emission: ~K .... ~Ca + {J. Each reaction has its characteristic decay constant. so that the ratio of the rates of deeay is constant; therefore the e,ustence oC tbe dual decay modes does not interfere with the use oC ~K for dating. However. ~Ca a1so occurs naturally and tbis makes the seeond mode uDsuitable Cor dating. Using the tirst mode. the ~Ar can be obtained by melting tbe specimen. An a1ternative method is to place the sample in the neutron flux of a nuclear reactor where stabte 39K (which has a fixed abundance ratio retative to ~K) undergoes the reaetion 39 K + e .... 39Ar; the age can then be determined from the ratio ~Ar¡39Ar. tbis ratio being found by mass spectrographie analysis. This method yields high accuracy because mass spectrograpbic ratios can be determined to better than 0.01 %. Argon diffuses rapidly aboye 300°C, hence ~K measurements determine tbe age since tbe temperature of the rock dropped below about 200°C, ~Ar is also present in the atmosphere and this sometimes results in contamination; 40Ar (presumably coming from trapped magma tic gases) is sometimes a contaminant in ocean-floor basalts. Minerals suitable for analysis by the ~K mcthod include mica, hornblende. and ptagioclase fcldspars. Several isotope rations can be measured for the disintegration series l38 U ..... 206Pb, 2J5U .... 107 Pb. and 23lTh ..... 208Pb. Having several dilferent ratios to measure permits contirmation oC determinations. Ratios sometimes measured inelude 207 Pb/U, 206 Pb¡U, 208 Pb ¡Th. 207 Pb¡ 206 Pb (sinee Ihe ratio of 235 U ¡2J8U is fixed). Zireon is especiaIly suitable for such anatyses. 14C has a half-life of 5,730 years and disintegratcs according to the equation 14C .... 14N, 14 N then disintegrating to give stabte 12 C finally. The reaction is used to date events during the last 30,000 years or so. The 14C is produced in the upper atmosphere by cosmic-ray bombardment oC 14N. The carbon subse· quently becomes incorporated in plants. animals, or othcr materials; the ratio of 14C to llC (or other carbon isotopes) gives tbe time elapsed since tbe plant or animal was alive. The 180 to 160 ratio in ocean waters changes during cool continental glacial periods and bcnce the 18 0 to 16 0 ratio is an indicator of paleo-temperatures. Altbough not useful for age determinations, tbe ratio of oxygen isotopes is a useCul toot in the study of depositional temperature changes that are associated with the low-stand sea-Ievel patterns sometimes seen in seismic data.

620

Radioactivity merhod

Geiger tubc Anod.

Thin window

+ (a)

LOI pul .. height

UnlilCd f1hlf1"rlicmal

Ion-chambo. region

Proportlollill rC'gíu" rfgion

Cont. i.1i"'·h.u¡!...•

,,, ,

/'I-particle lb)

~------------------~~--~--~~---~-------

Anode yohage. '.

Figure 10.4. Geiger-Müller counter. (a) Simplified counter circuit. (b) Geiger-tube characteristics as a function of anode voltage.

The foregoing age determinations all assume that the system is c1osed, that is, DO daughter isotopes were present at the beginning and Done escaped lrom the system up to the time 01 measurement. If some daugbter isotopes were lost in some manuer, for example. by rebeating aboye a critical temperature which resulted in the loss of the daugbter isotopes, the radioisotope clock is "reset" and the abundance ratios give the time elapsed since the loss occurred. Zircon 5eems to be especially resistant to resetting so that analysis 01 :zircons from granite overgtown rims using an ion microprobe gives ages differeDt from those 01 zircons in the core (which presumabJy carne from the original source oC the granite). Thus, it is possible at times to date processes as wen as rock samplcs.

plus tbe pulse-height analyzer or "(-ray spectrometer, which is an exteDsion of tbe scintillation meter. Both tbese detectors also were used very early in the course of radioactivity study. In their present prospecting form they are adaptations of laboratory instruments developed in the period 1944-50. The heart of the radioactive detector is a device tbat will respond efficiently to (J and 'Y radiation (a particles have such short ranges that they need not be considered generally). As noted previously, natural (J rays also have a short range, even in air; hence a (J detector is elfective only within a few meters oC the source. ConsequentIy gamma-radiation detection is most desirable.

10.3.2. Geiger - Müller Counter 10.3. INSTRUMENTS 10.3.1. Introdudion Various devices havc bcen used Cor thc detection ol radioactivity. One of the earlicst was the ionization chamber. At present tbere a~ two principal instroments, tbe Geiger counter .and the scintillation meter,

This is a very simple device that responds primarily to (J radiation. Consequently it can be used only in ground travcrsing. A diagram showing the essential parts is given in Figure 10.4a. Like the ionization chamber, the detector is a tbin-walled cylindrical tube, often with a very tbin (s; 0.025 mm) mica window in the end, to permit the passage of (J particles.

Instruments

621 H.T. ~upply

I

v /l.

6

Photomulliplier tube

Figure 10.5. Scintillation-meter schematic.

The tube contains an axial anode wire with a coaxial cathode cylinder and is filled to a pressure of about 0.1 atm with an inert gas, such as argon, plus a trace of alcohol, methane, water vapor, or a combination of these. This gas mixture produces a quenching action. A dry cell or other low-current source supplies several hundred volts across the diode, as shown in the diagram. Radiation entering the tube ionizes gas atoms and the positive ions and electrons are accelerated by the high voltage to tbe catbode and anode, respectively. These charges also ionize other gas atoms en route. The ionization is cumulative and the original ray produces a discharge pulse across the anode resistor, which is amplified in the transistor stage to produce a click in the headphones. Figure 10.4a also sbows a simple integrating circuit in series with the headset. Successive pulses charge up tbe condenser which then leaks off slowly tbrough the high resistance R, in series with the microammeter. The meter registers a current proportional to the integral of the charge entering the condenser. The purpose of the quenching agent is to suppress secondary electron emission Crom the cathode, caused by positive ion bombardment. This effect tends to prolong the discharge. Fast quenching of tbe discharge allows tbe tube to retum quickly to the nonconducting state and hence respond to succeeding rays entering the chamber shortly after the first. Although even in a good tube the c1ean-up time is still appreciable, it can be reduced to less than 100 p.s with a suitable quenching gas mixture. The electronic section of Figure 1O.4a is oversimplified. Normally the Geiger tube pulse drives a

multivibrator círcuit which shapes the pulses as well as amplifying them. Figure 10.4b shows the characteristics of the Geiger tube as a function oC anode voltage. Normally the voltage is kept within the plateau (ionchamber) region of the curve, where pulse beigllt is independent of tbe voItage, thus reducing the effect of variations in battery voltage. The prospecting Geiger counter has the virtue of being simple and cheap. However, it has little else lo recommend it. It must be held close to the outcrop to detect P rays (because it is an extremely inefficient detector of y rays, which are weak ionizers and tend to pass rigllt through the tube without being registered). Lead fins have been mounted on the oulside oI the tube to degrade and convert the y rays to f3 rays; however, this has not improved the efficiency enough to make the instrument competitive with the scintillation meter. Thus the Geiger counter remains a tool oI limited application.

10.3.3. Scintillation Meter (a) General. The counting of scintillations produced by radiation bombardment of a zinc sulfide screen was one of the earliest methods of detection. Other materials that have been used for this purpose inelude anthracene, stilbene, and scheelile. One of the best scintillation detectors is made by growing natural crystals of sodium iodide (NaI), treated with thallium (11). The Na! is transparent to its own ftuorescent emission and al1 faces but one are coated with light reftecting material. If the crystal is large enough, its conversioo efficiency for natural « 3

622

MeV) y rays is practically 100%. A portable device of tbis type became possible following the development of the photomultiplier tube. (b) Gamma-ray interaetions. As mentioned brie~y in Section 10.2.2, the dissipation of energy as radlation passes through matter is a complex process. To explain the operation of the scintillation m~ter, i~ is necessary to discuss the sequence of events In wbich the radiation is absorbed. The interaction of y radiation with matter takes place by the folJowing processes (see also §11.8.1c). (i) The photoelectric effect, in wbich the y ray loses alI of its energy to a bound atomic electron, part of the energy being used to overc?me its ?in~ ing to the atom, the remainder appeanng as kinetlc energy of the electron. Tbis elfect predominates at low energy (S; 200 keV) although it also varies great1y with the atomic number oC the absorbing material. (ü) Compton scattering by atomic electrons, in wbich the y ray is deflected in its path. When tbe y-ray energy is much larger than the electron binding energy (wbich varies from - lO' eV for innermost K electrons of heavy elements to a few electron volts in Iight elements), the scattering takes place as though the e1ectrons were unbound and at rest. Tbis is the dominant interaction at intermediate energies (100 keV to 2 MeV), and the elfect of atomic number is not so pronounced. (iii) Pair production, in wbicb the y ray is annibilated near a nucleus or electron wbile creating an electron-positron (positive electron) pairo The energy required far tbis pracess must be ¡reater than the rest energy (energy equivalent to the mass) of the pair; any excess appears as kinetic energy of the electron and positron. Because the electron rest energy is 0.51 MeV, pair production cannot take place unless the y-ray energy originally was larger than 1.02 MeV. Hence it is essentially a bigh-energy phenomenon. OC these three modes of interaction, the first is most desirable for y-ray spectroscopy (see next section), because the original radiation is converted to a light photon, giving up all its energy in the process. For the ordinary scintillation meter, bowever, the only requirement is tbat tbe input y rays be eventually converted to light, regardless of the mode of absorption.

A schematic of the scintillation meter is shown in Figure 10.5. Ught generated in the NaI crystal by y conversion falls on the semitransparent pbotocathode oC tbe photomultiplier tube, causing e1ectron emission. The crystal and multiplier tube are mounted as a single (e) Descr;ption of scintillation meter.

Radioaetivity method

unít in a Iigbt-tigbt cylindrical can, the crystal face being in contact with the photocathode end. The electrons emitted from the photocathode are accelerated toward the tirst electrode, DI' operating at - 150 V positive with respect to the grounded catbode. The intermediate electrodes, DI to DIO' called dynodes and usual1y - 10 in number, provide electron multiplication by secondary emission from surfaces coated with low work-function material, for example, Cs)Sb, tbe chain being so mounted tbat the electrons must proceed from Dl to D1 , and so forth, then tinally to the anode. With a gaín factor of - 4 per stage, the total current amplification is roughly 10 6 • TIús produces a current pulse of about 0.5 /lA through the anode resistor, RII' and tbe resulting_ voltage pulse oí sorne 20 mV is amplitied and integrated as in the Geiger counter circuit. The great advantage of tbis instrument is in the efficiency of y-ray detection. lt will also detec~ fJ rays. The price is about 10 times tbat ol a Gelger counter and the size and weight are somewhat ¡reater than tbe Geiger. It can be used in completely portable form (frequently witb detachable crystal-multipli~r head Cor entering a confined space), or as a seIDIportable unít in a car or aircrart. The airbome instrument is much more elabora te. Portable sets usually bave crystals 40 to 75 mm diameter, 25 to 75 mm tbick, with a multiplier photocatbode to match the diameter. The earlier aírbome versions used several crystals about 100 mm tbick and 200 to 250 mm diameter, with a group of photomultipliers (three t~ seven) on each crystal; tbis was necessary to m8XImize tbe light collection, because the photocathode diameter was limited. Such an arrangement required manipulation of many gaín adjustments to optimize the overall resolution. More recently arrays oC four to six prismatie erystals 400 mm long and 100 X 100 mm cross section with a single multiplier mounted on one end ol eaeh have resulted in a compact paekaged-Mab geometry and red~eed th~ equaliza. lÍon time. Airbome uníts are eqwpped Wlth analog and digital readouts. Further improvements in scintillation meter detection may result from using (i) relatively huge organic plastics as scintillators, (ü) germanium solid-state detectors, (ili) combination NaI-CsI crystals, and (iv) silicon-diode "one-shot" photomulti· plier tubes.

10.3.4. Gamma-Ray Spectrometer A logical extension oC the scintillometer is a sj¿,ec. trometer that separates characteristic y rays oC K, U, and Th lor identiftcation of tbe source. Sueh instruments are widely used in airbome surveys and a couple of portable uníts are also available.

Instruments

623 lOO

so

¡.. 3 in. dl.m., ] in. Ihick

--r-'" \ '""'- -----

(%)

~

~

\

20

lO -

pe~/IOtal I

'\(\

/\

Theorelical ¡/ak/IOlal no muUiple proce• ..,

Peak

iOiiT

/1-- -

Peak/lolal l" in. di.m., I in. lhick

"-

'" ~

S

r-...

"po

I!!!' 0Pft

d ... ", _

+ de +

01 .. ,.

Photoeleclric cross~set'tion

tJc - Compton

G',., -

-

"""

............

'--t--

cro5s-sec:tion

Pair production cross-section

2

! 1 O

2oo

I

600

looO

1400

EnerlY CkeV)

Figure 10.6. y-ray absorption efficiency in Nal crystals.

Speclromelers 01 this lype, known as pulse-height analyzers or "kick sorters," have been used for y-ray analysis in nuclear physics laboratories for some 40 years. They malee use oC the CaCl thal lhe inlensily ol the light pulse, and hence the amplitude 01 the voltage pulse lrom the multiplier, is proportional lo the original y-ray energy. Actually tbis is only partially true, due lo the complex process ol y-ray absorption, and further explanation is necessary. When the y-ray loses all of ils initial energy at once by photoconversion, the preeeding statement is entirely correet. Even if it is firsl degraded by scatlering and/or pair produclion, resulting eventually in pholoelectrons of lower energy, these will still add up lo a pulse of the same amplitude, provided lhe y ray does nol escape from the crystal, that is, it is completely absorbed. This is lrue because all the processes occur essentially sim,ultaneously (because y rays, being eleclromagnetic radiation, travel with the velocity 01 light). However, ir the beam of y rays entering the crystal were monochromatic, 01 energy E, and some rays escape wilh lower energy e, there is a contribution to the pulse-height spectrum corresponding lo E - e.

Figure 10.6 illustrates the efficiency of Na! crystals in converting the y rays into pulses of maximum amplitude by multiple processes. A theoretical curve e shows the ratio 01 cross section (effectively absorption) by photoconversion onIy, to total eross section, thal is, all three conversion processes, for comparison. For energies between 1.5 MeV and 100 keV (below which the photoelectric effeet predominates) the larger crystal is on average 35% more efficient, whereas the smaller loses an increasingIy larger fraction of y rays by scattering out of the crystal. To obtain l()()% efficiency in convertíog the y rays, it would be necessary to mount the radioactive source, as a minute grain, inside the crystal, and in fact this is done in laboratory installations. In these circumstances - and provided the crystal is large enough - aH the y rays would be absorbed in' the crystal and lhe original y-ray spectrum of the source would be quite faithfully reproduced as a pulse-vohage spectrum in the analyzer. In a field measurement, however, the situation is more complicated. Some y rays lose energy by scattering in escaping from tbe source and also during passage through the

624


Relali•• counl rale

I~----~----~----~----~----~~--~. o Figure 10.7. .,-ray spectra of K, U, and Th samples and granite-gneiss outcrop.

&ir to the crystal. lbis, coupled with the faet that the U and Tb series emit numerous 1 rays over a wide energy range, results in a comp1ex pu1se-height spectrum, as shown in Figure 10.7. All four curves have characteristic peaks and, in additioD, an increasing continuum at low energies. due to Compton seattering. The pure potassium sample produces a relatively simple curve, having oo1y the oIOK peak at 1.46 MeV. lborium is characterized by the strong 2.62 MeV lbe uranium spectrum is most compeak of plex, although the peak at 1.76 MeV is reasonably distinctive. Potassium and thorium are clearly evident in the granite gneiss, as weU as a smaller Craction of uranium. A prospecting 1-ray spectrograph, theo, should be capable of isolating the K, U, and lb peaks at 1.46, 1.76, and 2.62 MeV. This is accomplished by replacing the integrator-counter circuit in the scintil!ation meter with three electronic circuits 10 select the appropriate pulse beights that correspond to the preceding y-ray energies. Considering channel 2 in

lOen.

Figure 10.8a, the detail diagram at the upper right of tbe figure shows that tbe mannel is actual1y two parallel mannels. Tbe discriminator 2A is biased so tbat it gives an output pulse only for 1 rays with energy greater than 1.36 MeV, wbereas discriminator 2B responds oo1y to 1 rays with energy in excess oC 1.56 MeV. lbus neither diseriminator registers 1 rays wbose energies are less than 1.36 MeV, whereas for values greater than 1.56 MeV the anticoincidence circuit adds the two outputs out of phase to give zero output as weU. Tbe other two channels operate in the same manner for 1.76 and 2.26 MeV. Generally the channeJ centers and widths are adjustable. Oearly the window musl be wide enough 10 accommodate the finite width of the peaks in Figure 10.7, bUl not so wide that the flanlts of adjacent peaks may be accepted as

weU. The pulses are counted and integrated separately and, in the airbome instrument, applied lo a threechannel recorder. Because the radioactive sources

625

Instruments

,------------, FROM AMPLlFIER I DISCRIMINATOR 2A

r-1

Nal CRYSTAl(S)

DISCRIMINATOR 2B

I I I I

I I

H.T. POWER PULSE SHAPER 2A

PULSE SHAPER 2B

I I I

I MULTIPLlER TUBE (5)

-

I

L.T. POWER

CHANNEL CONTROLS

I I I

I

I

l I

CHANNEL 1 0.4-2.82 MeV

TOTALCOUNT

I

I

I I I

I

CHANNEL 2 1.36-1.56 MeV

I

¡

1

I

POTASSIUM INTEGRATOR

I 1

CHANNEL3 1.66-1.86 MeV

I I I

SHAPER DISCRIMINA TOR INTEGRATOR

I I

I

I I

I

.~.

íF=:..o·I=';'=;;:'¡:I

ANTICOINCIDENCE

I

PREAMP (S)

MAIN AMPLlFIER ANO ATIENUATOR

I

I I 1

~ _ _ _ \-T.? RECORDER _ _ _ _

CHANNEL4 2.42-2.82 MeV

:,

I

I I I -.J

\ DETAlL OF CHANNEL 2

~ f-.f= I

j--1----J

I

I

4 CHANNEL RECORDER

(o) Figure 10.8. Four-channel y-ray spectrometer. (a) Block diagram.

often contain bolh U and Th and eveo K as well, and beeause the count level may be considerably higher ror one channel than the others (as in Fig. 10.7, where the count rate oC the Th sample al 1.46 MeV, eveo io the absence o{ a peak, is more than 100 limes larger than the potassium peak), some means oC subtracting a predelermined fraction oC the higher couot rate, known as spectral stripping, is generally incorporated near the output end of the spectrometer, as shown by the subtract lines in Figure 10.8a. An early model oC tbis type of inslrument designed for airborne work is illustrated in Figure 10.8b. 11 employed twelve 9 X 4 in. (23 x 10 cm) crystals; the correet position of the channels was monitored with a es slandard y source (661 keV). Note that this instrument has four channels (Fig.

10.8a), channel 1 being Cor total counl over the whole energy band from 0.4 to 2.8 MeV. The block diagram in Figure 10.9 shows a more recent computer-controlled airbome syslem. Spectrometers with 256 and 512 channels have also been used in airborne surveys. An inherent problem with the pulse-height anaIyzer is the elrect oC pulse shape, vollage drift, temperature changes, and so fortb, on the instrument sensitivity and accuracy. Further improvements in instrumenlalion have resulted from usíng analogto-digital (A/D) conversion and by incorporating a minicomputer to provide on-line dala correction and ultimately interpretation during tbe survey. [For these and other developments in instrumentation, see Bristow (1979).) A glance at Figures 10.8 and 10.9,

627

Instruments NaviRation data

~

Upward-viewing detector

I

Shleld Detector array

I

~

9-track mlanetic tape uní!

AID con verter

conditioning

Minicomputer

~cs

~

A/D converter

l CRT spectrum display

I I Keyboard entry terminal

l Multichannel record"r

Figure 10.9. Modern y-ray spectrometer. (After Bristow, 1979.)

the second displaying a block diagram of an up-todate airbome installation, shows c\early that the present-day model is considerably more eomplex and sophisticated than the earlier one, employing as it does analog-to-digital conversion, a minieomputer, and eonsequent additional electronies, as well as an upward-view detector, shielded from ground radiation. lo monitor atmospheric radiation. lbe computer is particularly attraetive for storing useful control data to correct ror background effect of atmospherie radon, whieh is erratic and oCten large.

10.3.5. Mlscellaneous Instruments Some portable seintillation meters have simple circuit modifications that permit rough diserimination between K, U, and lb, as well as measurement of total y-ray count. A switch provides two bias levels on the pulse amplifier, equivalent to about 2.5 and 1.6 MeV, so that one can, in effect, introduce wide windows, one at a time, for lb and U + lb. Calibration of this type of equipment is discussed in Sectioo 10.3.6. An instrument known as the emanometer, or radon sniffer, has been used to me asure the radon content of waters, oils, and soils. Because radon is a noble gas, it does not form chemical compounds. lt moves freely through pore spaces, joints, and faults Cor distances up to several hundred meters. It will also dissolve in ground water and so move about in the subsurfaee. Air samples are obtained from the soil by drilliog a shallow hole (0.5 to 1 m) and pumping air from the hole through filters and a dryer into an ionization

chamber or thin ZnS scintillator. Water samples are degassed and the gas-air mixture goes to the detecting ehamber. In one mode1 the 4.8 MeVa partic\es of 222 Rn are eouoted, rather than the 0.51 MeV y rayo If the radon is in equilibrium with the other decay produets in the vicinity, the amount of parent produet may be determined from Equation (10.5),

Nw- N,,,A,,,/Aw ... 2 X 1O- 6 N,,,/5

X

10- 18

... 4 X 10IlN,n assuming the radon originated from 238 U . The numerieal factor would be about 4 X 1015 for radon gas from mU or 232lb. lbese have very short hallIives, however; hence it is mueh more Iikely that 222 Rn is the isotope detected. If tbe series is not iD equilibrium, for example, some member or members are redueed or missing beeause of weathering, and so forth, the eount would be reduced and the preeeding relation would not hold. Two otber integrating-type radon detectors, whieh colleet and measure a radiation over much longer periods than the sniffer, have been in Iimited use siDce about 1978. The first, known as the Traek Eteh, consists of a eellulose nitrate film (sensitive to a partic\es) taped on the inside bottom 01 a plastic cupo lbe inverted cup is placed in a soil hole for about tbree weeks, accumulating a radiation inside from soil gas (the cup wall is thiek enough to exclude penetration from outside). The film is retrieved, chemieally etehed to expose the a traeks, and the


628 amount oC radiation is Cound Crom the track density viewed under a microscope. The Alpha Cup, similar to the Track Etch in principIe, uses a silicon semiconductor in place oC the film. This detector is connected to an electronic unit outside the cup and the whole is buried Cor three days. ACter digging up the device, the a counts stored io the eleetronic memory are transferred to a reader. A later modification called Alpha Card appears to have better countiog geometry, which reduces the burial period to 12 hr. This reduction in ¡ntegrating times compared to Track Etch is said to be possible because of higher colleetioo efficiency. The alpha devices also have an advantage, beeause there is no need to flush out the collector (required Cor cleaning out the sniffer) or change the detector after each station. Because the radon diffusion process is complex and sensitive to several external Cactors, such as temperature, pressure, and climale, generally, ooe might expeet that the long integration time would produce more reliable results. However, there is little available evidence to establish a definite superiority oC one instrument over the others (Warren, 1977; Wollenburg, 1977; Telford, 1983). A varlety oC other instruments bas beeo developed for radioactivity measurements in geophysics. Several are adaptations oC nuclear physics laboratory equipment Cor assaying. Others, such as the bery/lium detector, used Cor ground prospecting, and the density logger, contaio their own radioactive sources to initiate artificial radioactive processes in nearby rock. Sorne 01 these are discussed in Sections 11.8.3 and 11.8.4.

caused by terrain relieC may be reduced by providing an extra energy window (3 to 6 MeV). Clearly these background sources are larger and have higher intensily than laboratory standards, even though the count rate in the uranium window is the main concem Cor good calibration oC the instrumento Two empíricallechniques bave been used to measure uranium background. The simplest is lo fly over a lake, where the measured activity will be the total Crom K, U, and 111, but several orders lower than from the ground surface. An altemative is air sampling with filters, using an upward-view detector as in Figure 10.9; although nol as reliable, this may be a necessity where reasonably sized bodies 01 water are not available. For a satisCactory and complete spectrometer calibration, however, it is neeessary to employ concrete structures oC appropriate size as secondary standards Cor sta tic calibration of ground, airborne, and borehole instruments, plus larger ground strips lor test ftights oC airbome systems. 111e Geological Survey oC Canada has five concrete slabs (- 7.S X 7.S m, O.S m thick) at Uplands Airporl near Ottawa. These contain varying Cractions of radioactive material (Cor example 2.2% K, 3 ppm eU, 26 ppm eTh; see §10.5 Cor definition of eU and eTh) and are suitable for calibration oC ground and airbome equipment. At the same locatioo nine concrete test columns with standard size boreholes are available for calibrating logging instruments. Ground strips lor fligbt tests are also installed near Ottawa. Similar installations exist in the United States and several other countries.

10.4. FIELO OPERATIONS 10.3.6. Calibration of Instruments The ca1ibration of instruments Cor reasonably quantitative measurements in radioactivity is a straigbtforward procedure in laboratory work, more complicated lor field operations. For example, the scintillation meter described in Section 10.3.3c, may be adjusted to determine the relative amounts of uranium and thorium by means oC a standard Th source and successive adjustments oC the bias potentiometer control. When an instrument like the Courchannel spectrometer is used in the field, bowever, a small standard source is quite unsuitable for overall ca1ibration. Some of the difficu1ties encountered in stabilizing and calibratiog multichannel speetrometers, particularly lar airbome work, were mentioned briefly io Sections 10.3.3c and 10.3.4. Measures designed lo resolve these difficulties inc\uded the stripping process and an upward view detector to correet Cor atmospberic radon background (see Fig. 10.9). An additional effect Crom cosmic-ray variations

Ground prospecting is readily carried out with any of the instruments described in Sections 10.3.2 to 10.3.5. The Geiger counter is used only Cor Coot traversesi the scintillometer and y ray speetrometer, especially the former, may also be used in vehic1es. Radiometric surveys are comparatively cheap, whether airborne or on the ground (see §10.1); in surCace work tbis is partIy beeause the line cutting is oCten unneeessary and measurements are simple and rapid. No particular expertise is required Cor this work. It is sufficient to note the count rate (counts/s, mr/br) of the instrument and compare it with a background reading. Ratios > 3 : 1 over background would generally be of interest. The background itself may vary considerably from place to place, depending on depth ol soil cover and potassium content ol the local rocks. Sorne notice must be taken oC the geometry oC outcropping formatioos in this regard, because the instrument response is influenced by source-detector separation

629

IntNpretiltion

and tbe source dimensions. This is particularly true of tbe Geiger counter. Obviously tbe source-detector geometry will have a significant elfect on tbe readings; compared to tbe usual position of the instrument over a Hat surface (2". geometry), a wide ledge backed by a vertical walI (311") or a steep road cut (- 411") wiIl increase response by 50 to 100%. Background variation in different rocks has already been referred to in Table 10.5. In the early days of radioactive prospecting, erratic inereases in background oceurred oceasionally as a result of atomie tests; tbis is no problem nowadays. Two good reports on y-ray spectrometrie methods for uranium - airbome, ground, and well-Iogging - may be found in Grasty (1979) and Killeen (1979). Airbome radiometric reconnaissance has frequently been accompanied by aeromagnetics and occasionally EM. This stage is generally followed by detailed ground radiometrie eoverage of favorable areas, possibly witb geochemieal sampling, auxilary geophysical metbods, and finally trenching an.d drilling plus y-ray logging. When the surve~ area.lS small or difficult for ground access, a detruled rurborne helieopter survey may be warranted to reduce tbe ground foIlowup. Airbome radioactivity surveys have been carried out for minerals otber tban uranium and thorium, such as titanium and zirconium-bearing heavy minerais, including tantaIum, niobium, and tbe rare eartbs. In this conneetion carbonatites (such as at Oka and other locations in tbe province oC Quebec) are an intriguing target for y- ray spectrometer exploration because tbey have a very low ratio oC uranium to tborium. This distinctive signature applies to kimberlites as we\1; hence tbe metbod is useCul in prospecting Cor diamonds. Limited auempts have been made to use tbe radioactivity metbod in oil exploration. Surveys in known oil fie1ds sometimes indicated a radioaetive low direct1y over tbe oil-bearing structure with a halo sligbtIy aboye tbe background surrounding it. Actually this pattem was reported about 1928 from crude ground surveys in Texas fields. The source of radioactivity appears to be radon gas, which moves upward tbrougb fractures in tbe perimeter rock to escape al surfaee; the suggestion has been made that tbe tigbt cap rock over the oH pool is reIative1y impervious to tbis migration. Otber indirect applications tbat may be worthwhile are in relation to pbosphorites, whose host rocks often are anomalous in uranium content, and even for sulfides. Also, radiometrics occasionally have been used as an aid to geological mapping; a case history using airbome data is illustrated in Section 10.6, example l. These indirect applications oC radioactivity will be discussed Curtber in Seetion 10.5.

10.5. INTERPRETATION In spite of great improvement~ in instrumen~atio~, lhe interpretation of radiometne survey data 1S sllIl mainly qualitative. This is partIy due to the extremely small depth of penetration possible with the metbod. It is also the result of tbe inherently complex OBture of tbe y-ray spectra. Spectrometer profiles taken in a helicopter are illustrated in Figure 10. lOa. Altitude in both cases was 150 m. The ]ow air speed possible witb the helicopter (40 km/hr) is a decided advantage both Cor amplitude oí response and discrimination of anomalies. This was an early test oC the four-channeI spectrometer. Its superiority over instruments providing only total-count data is clearly demonstrated in Figure 10.lOb where the strong U anomaly. marked by tbe arrows is lost in the total-couot (1OtegraI) profile beeause K and Th responses are low over tbe Same 5 km stretch oI tbe profile. Botb airbome and ground spectrometer data may be plotted as profiles or contoured as s~own in various diagrams of Sections 10.6 and 10.7, ID terms of U, Th, K, and total counts per second, ratios of U : Th, U : K, or in relation to sorne arbitrary background. Uranium and thorium amplitudes may also be given as eU and eTh; that is, equivalent uran~um and thorium. These designations arose because 10 y-ray spectrornetry tbe elements aclually measured in the 1.76 and 2.62 MeV channels are mBi and 208n, respectively, rather than their U and Th parents. Th.e distinction obviously is unnecessary Cor K because 11 is rneasured directly in tbe 1.46 MeV channel. Sorne attempts have been made to obtain quantitative results in airbome work. By correlation oí detailed ground data witb airbome surveys over tbe same area, it is possible lo get an approximate tit between the airbome profiles and upward continuation oC the ground data, using an empirical expression Cor tbe y-ray attenuation in air (Soonawala, 1968). This correlation is reasonably valid because of tbe bigb attenuation in solid material; tbat is, the source must outcrop to be detected in eitber survey. Characteristic curves for elementary shapes are then drawn up for the airbome interpretation in other areas. Three elementary geometries are considered: 1. A finite or elementary circular source. 2. Aa infinite plane source (outcrop) of great lateral extent. 3. The line source, having infinite exposed Iengtb along one axis, considered to be the strike dircetion. CIearly tbe finite source is tbe most usual geometry encountered in the fie1d, because either of the


630 epm

Eltiot Lalte &fea

D _ Di.ba...

ISOO

A - Archean

UM - Upper Missis..'; 1000 MM - Middle Missi....; LM - Lowcr Missis..,i

D

B.neroft ...a

T.....;n c1earance - SOO n

(a)

J

(km)

(b)

Figure 1a 1a Airbome y-ray spedrometer profiles. fa) Total-count profiles in the flliot Lake and Sanaoft afeas, Ontar;o. (b) Four-channel fesults, Uranium City afea, Saskatchewan. (After Damley, 1970.)

•

631

Interpretatíon

3200

A

-F"lld ---ModQl

I!~\\\\ II

:: I

'\

2400

\\

«

lo

1600 ::

\.

Ü Q

\

I

\

I

\

\

\

\ \ \ \ \

\

-

\

~

5m

13+505

135

12·505

Overburden 1-1.5 m Figure 10.11. Radon profile and model resu/ts. Northern 5askatchewan. (F(om 500nawala, 1976.)

others will generally be covered with overburden at various places. Practically, the elementary source need not be circular, but its largest dimension should not greatly exceed the altitude oC the aircraft. 10e characteristic curves enable us to determine a parameter involving the product oC surface area and source intensitYi tbese quantities (as iD gravity, EM, and other situations) cannot be resolved individually. Measurement oC the K, U, and 10 y-ray peaks in tbe 1.46, 1.76, and 2.62 MeV energy windows, together with U : K and U : Th ratios plus total count (using a four-channel spectrorneter) is only a tirst approxirnation to a quantitative determination oC relative ground abundance oC the three elernents. The numerous background variables, sorne of which have been mentioned already, inelude source-detector geornetry, sampling rates, aircra!t altitude, ra-

dioactive equilibrium, Compton scattering, and cosmic and atmospheric radon background. Crossley and Reid (1982) used a matrix equation (see §A.2) to solve Cor tbe abundances

where fE is an (m XI) matrix oC the abundances, the (n xl) matrix r¡ gives the counts in tbe n channels, and .fII is an (n X m) matrix of the calibration constants. For three-channel equipment the elernents a,} are stripping constants (see §10.3.4 and problem 4) Cor K, U, and Th. To improve the accuracy, we must use more than tbree channels. Crossley and Reid (1982) used data from 63 channels in the range 0.78-2.98 MeV (n 63) to solve Cor K, U, Th, and cosmic background

632

Radioactivity method Porphyrilic biolilo ,ranilo

O.bbro

rB Gnetss and

schi,'

Sed. and volc. rocks

t=·=:=l Radioaclivily contour!ll

(2;

O

counts/s Ooololio

.-

_con,.cl ..... , ..... 2

O

4

miles

Figure 70.72. Airborne radiometrics as an aid to ge%gica/ mapping, Concord Quadrartg/e, North Carolina. (After Bates, 1966.)

abundances (m - 4)j because n> m, they used a least-squares solution (§A.8). The results indicated that a lull-spectrum multichannel matrix solution was desirable, particularly additionaJ U and Th windows al 1.12 and 0.94 MeV, respectivcly, well below the usual 1.76 and 2.62 MeV windows. They also lound that the cosmic background varied appreciably over periods 01 a lew secondsj this might be significant in calibrating equipment by Oying over Iakes (although their assumed cosmic data might inc1ude other background elrects not taken into ac()()unt, that is, m > 4). Ana1ytic work involving diffusion and ()()nvection ol radon through overburden has led to numerica1 methods lor modeling various geometries such as 2-D and 3-D blocks under overburden (Soonawala, 1976; Soonawala and Tclford, 1980). lbc trealmenl is similar lo thal used in EM and MT analysis. Figure 10.11 shows an cxample in which a thin zonc

of 0.14% U, 0.5 m wide, surrounded by a 0.03% halo, all under 1 m ovcrburden, was used to match a ficld profilcj thc anomaly had been partly ()()nfirmed by previous drilling. Use ol the radioactivity method in exploration for petroleum and natural gas was mentioned brieOy in Section 10.4, where thc anomaly and its possible mechanism were described. An early reference to tbis lechnique is given by Silla (1959), who analyzed radiometric contours from an airbome test survey over the Redwater oíl tield near Edmonton, Alberta The area was ftown mee, tirst in 1951 with a scintillometer measuring total counl, and again in 1957 using a total-count y-ray instrument that also recorded energies aboYe 1.5 MeV, thus eliminating the elrect of oIOK (see problem 5). Recent applications of this method are reported in Weart and Heimbcrg (1981). They measured total y-ray ()()unt in a large ionization chamber from a

Interpretatían

633

O...lin.

soo---.. . . 1405

1325

I

124S

I

o

200

108S

1165

I

I

I

400H

4O~

RE

128S

1205

112S

(b)

Figure 10.13. Uranium exploration using ground magneties and radiometries. (a) Ma8netie contours (nT). (b) Radioactiviry contours (roral y-ray flux in counrs/s).

vehic1e or on foot where aeeess was diffieult. Surveys were earried out in six sta tes (United States) generally before, in sorne cases after, drilliog. Of sorne 1,000 wells drilled, about 750 are reported lo have beeo correctly predicted, either as producers or dry, by their location witb respect to the radiometric survey data; tbis compares favorably with domestie drilling statisties Cor oil and gas. Curry (1984) gives somewhat similar results Cor about 500 wells in the Powder River Basin area of Wyoming. Limited tests with ground radon detectors lor shallow structural mapping have been reported. King (1978) measured 222Rn on the San Andreas faul! in California Soonawala (1976) obtained feeble radon anomalies across fault planes in tbe Eldorado area, northwestem Canada, about the magnitude expected from dilrusion theory; the fault response, however, was contaminated by mining aetivity, because there are several major orebodies nearby. Abdoh-Reza

(1984) measured distinctive anomalies over Caults in the vicinity oC IIe Bizard, west oC Montreal. The c1arity oC response here, eompared to that obtained by SoonawaIa, is probably the result of much lower background radiation in tbis area. Airbome radiometrics have occasionally becn used as an aid in geologicaI mapping; a ease bistory is discussed in the next section. An attractive color map for tbis purpose was recently reported by lhe U.S. Geologieal Survey (Duval, 1983). A eomposite color image con tour map is produced by combining any Ibree K, U, Th parameters, or their ratios. Anomalous areas may be shown either as dark zones, known as direCI image displays, or bright sections, cal1ed inverse images. This type oC reproduction at both ends ol the visible spectrum is said to olrer more complete sensitivity to the eye for interpretation. Judging by an example of the color maps from an area in southeast Texas, the technique might have

634


12.000

, I I

10.000

I

I I I

I

, I I I

I

I

I

I :

¡ I

I

I I

I I

I

I I

I

.'

I

I

I

1

I I I

I

I

i ! l

I I

II

e

1

I I

I I

II I I I I I

1"-Radiomeuics I I I

I I I

• 4 +OOE

Arailliles

and

qUlrtZiles

-100

g

1 -200

Figure 10.14. Radioacrivity and magnetic profiles plus geologic section, line 132 uranium survey.

limited application in mapping and qualitative interpretation of surface geology.

10.6. FIELO EXAMPLES 1. Figure 10.12 illustrates the application of airbome radioactivity to geologic mapping. The arca shown is the Concord quadrangle 01 Nortb Carolina, where the U.S. Geological Survey carried out an airbome radiometric survey as an aid to detailed mapping of complex geology. Six Na! crystals, 10 cm diameter, S cm thick, and six pholOmultiplier tubes connected in parallel were used for the detector. Particular care was takeo lO correet tbe data lor variations in aireraft alatude. The compilaaon oC geologic and radioactivity inlormation in Figure 10.12 represcots a progressive refinemeot 01 data; tbat is, the original geologic inCormation was changed as a result oC additional geologic mapping, wbich was to a considerable ex-

+ 005,

tent guided by the radioactivity results. For example, tbe radiometric survey outlined a granite stock, northeast 01 the town 01 Concord, whose borders could not be well defined by field geology; it also located the smaller granite body in tbe ·nortbwest part of the lOwn. The granitic zone in the soutbeast comer oC tbe figure is marked by bigh radioactivity, whereas that on tbe soutbwest is not. A porphyritic biotite granite in the northem part oC the quadrangle shows medium to bigb radioactivity, but in the vicinity oC the gabbro mass in tbe nortbwest comer tbe response is lower. The anomalous bigb along the east border coincides witb a considerable injeetion 01 granite into tbe surrounding gneiss and sebist. FinaDy, the large gabbro-syenite mass in the center oC tbe quadrangle is fairly well outlined by !he radioactivity contours, because tbe syenite zones on the east and west flanks show higber response than eitber the gneiss-scbist surroundings or tbe enclosed gabbro.

635

Field examples

o

Q5

1.0

1.5

lO krft

2I • Figure 10.15. Airbome survey fOl porassium used to loca te associated Zn mineralization. (Mter Gnoje/t. and Priehystal, 1985.) (a) «k eontours. contour interval 0.5%: • mar/t. two dril/holes.

The variation in radioactivity response over different granitic zones is not definitely explained, although it is suggested that there may be different types of granite within the quadrangle. No mention is made 01 the depth of overburden; slight variations in the thicmess or type of cover could account for the lows in the northwest and southwest comers. Neither the airbome radiometrics nor the geologic mapping could have produced this inter-

pretation independently. It is the product of a combination of the two, plus some aeromagnetic data. Furtbermore, the airbome survey, as mentioned previously, was useful in selecting areas for further detailed mapping, thus saving time and money. 2. An example of the direct method ol radioactivily prospecting is shown in Figure 10.13 and 10.14 taken from an extensive survey for uranium in

636

Radioactivity method Th

tj"m I

e

ir./.

u

,

e

11 5

K

4

J

2

e Th I K (!)ptn lper cent 1

1 11

5 4 ]

2 1

J'I;:~~~::::::~~::::

e

4

__________

~'

D

tel'. Cprtl )

TOTAL (

~l'-'"

~

I

e

o (b)

o

a

n

n

,

0.1

0.2

0.3

0.4

e

0.5 km

Figvre 10.15. (Continued) (b) Th, U. K, ThIK. and total·coun/ profiles on line CD [see part (a) for loca/ion).

Labrador. Following large-scale reconnaissance with airbome radiometrics and magnetics, a set of targets was seleeted for detailed ground followup. lbe latter operation proceeded in two steps. First, the airbomc radioactivity anomalies were located and assessed rougbJyj then the more promising of tbese were examined in detail by scintillometer and magnetometer (in some cases ground EM was also employed, because there were sulfides associated with tbe radioaetive minerals). Stations were 10 to 25 ft apart aJong cut lines spaced 100 ft aparto Figure 10.l3 shows the radioactivity and magnetie contours for a small area of the ground survey.

Strong anomalies oC both types are coincident on Ll32S at 2E. These were indicated by the airbome survey, the location being almost exaetly the same as the ground anomaly. At L1l2S, 6E, howcver. there is no abnormal radioactivity associated with the high magnetics. Magnetic and radiometric profiJes on L132S (the latter being obtained by using the uranium channcl on the scintillometer), together with a vertical gcologie section obtained from drilling, are displayed in Figure 10.14. The host rocks are argillites, quartzites, and amphibolites. The mineralization, consisting of magnetite and pitchblende with sorne chalcopyrite, sphalerite, and pyrrhotite, occurs in bands of ferruginous quartzites whieh a1temate with diorite dikes. lbe overburden at the collars of the two drill holes is . about 2 m thick and the huge magnetic and y-ray peaks occur directly over exposed mjneralization. Although the U:,o. mineralization is probably oC economic grade, the volume is small. The maximum depth extent js 40 m, whereas addjtional drilling showed the zone width and strike length to be no greater than 3 m and 75 m, respectively. Although the contotirs oC Figure 1O.13a and b indicate the small lateral extent of the showing, this evidence is not conc1usive in itself Cor two reasons: first, a meter oC overburden would be sufficient to mask the presence oC uraniumj second, the association oC Fe304 and U:,O. mineralization does not prevail throughout the area, as proved by drilling in the vicinity oC the magnetic anomaly near 6E on L112S. 3. Gnojek and Prichystal (1985) report the deteclion oC zine mineralization in northem Moravia by potassium anomalies from airbome y-ray spectroseopy. Hydrochemical and self-potential anomalíes accompanied by tectonic considerations had shown that sulfides might be present in the area. lbe airbome survey was carrled out with a four-channel spectrometer and a magnetometer in a helícopter at 80 m ground clearance with 250 m line spacing. Two distinct o4OK anomalies of ~ 5% were deteeted, accompanied by variable U and very low Th. The anomalies were verified by ground Collowup using radiometrics, a variety of electrical methods, and geochemistry. Despite the presence of basjc rocks, there were no magnetic anomalies. The 40K data provided locations for drilling, which encountered ZnS at 150 and 75 m depths in two holes. Figure 1O.15a displays contours oC 40K over the area and the borehole locations, and Figure lO.15b shows varlous concentrations from a profile aloog líoe CD. lbe latter again illustrates the superiority 01 separate K, U, and lb measurements over total count. Unless this example is an isolated case, tbe use oC radometric surveys for base-metal and other mineral targets may be useful, particularly in areas where

Problems

637

Table 10.6. lines Station

1 2 3 4

5 512 6

11 12 14 17 19 16

7

17

8 8 12 9 10 11 12

16 15 14 13

12

2

3

4

5

6

7

8

11 12 14 15 18 30 25 23 17

11 11 12 15 18 21 24

14 15 17 17 22

15 17 17 17 16

47

36 22 18 15

27 30 47 66 260 46 33 14

'18 24 38

22 18 15 12

11 12 14 15 17 22 28 34 46 200 200 35 26 17

12 15 17 24 34

30

12 12 14 15 18 24 23 28 36 70 1.200 50 22 18

25

normal techniques are ruled out by bigh e1ectrical noise.

10.7. PROBLEMS 1. Scintillometer readings were talten al station inlervals oC 8 m on a set of parallel lines 8 m aparl

over an area in Saskatchewan during the course of a uranium exploration programo The readings, in counts per minute, are given in Table 10.6. Plot and contour tbese readings; estimate the strike and width of the anomalous zone. Are there indicatioDs of tbe depth ol overburden and variations ol the overburden thickness in tbese values? 2. A 2.5 kg rock sample was tested for radioactivity witb a scintillometer, both being enclosed in a large sbielded container. Tbe average count rate was 540 cpm. Tbe background count in the container was 35 cpm. Assuming the overall efficiency ol the scintillometer to be 30%, and either tbat the radioactivity is approximately equally distributed belween uranium, thorium, and potassium or !hat tbere is no potassium in the tock and tbe U : Th ratio (§1O.5) is about 0.5, determine the content of each element in the sample for tbe two cases (see Table 10.2, §10.2.4). 3. Scintillometer and vertical-component magnetic contours, talten from a detailed ground survey lor uranium in northero Canada are shown in Figure 10.16. An excerpt lrom tbe geological report on the region says: "Geologically tbese areas are quite featureless and consist of pim: quartzites with dark bands ol mafic minerals, tbe latter coinciding witb the radioactivity and magnetic anomalies at a number ol places."

47

66 310 35 26 17

60

40

25 17 13

Make an interpretation ol tbis small section using the limited data available and keeping in mind possible coincidences of magnetic and fadiometric anomalies, variations in deptb ol overburden, presence oC granitic rock ~K radioactivity), and so forth. As an aid to interpretation, it is suggested that the two contoured maps be overlaid and also Ihat a few protiles be taken off each map. 4. As mentioned in Section 10.3.4, the present type of 'Y-ray spectrometer has three channe1s at 1.46, 1.76, and 2.62 MeV to isolate K, U, and Th peaks. respectively. Consequently it is possible to deter· mine the individual amounts of potassium, uranium, and thorium contained in a rock sample when the spectrometer has been calibrated by using standard samples of known composition. We obtain the relative content of the lhree elements in terms of the count rates of lhe instm· ment as outlined in lhe following tex!. None ol the 'Y rays lrom uranium or potassium has sufficient energy lo be recorded in the thorium (2.62 MeV) channel; hence

where T is the thorium content in parts per million, ~ is the 2.62 MeV channel count rate less background. and k l is the constanl lor the thorium channel. The 1.76 MeV uranium channel records 'Y radiation for uranium and thorium bul none from potassium. Hence we have

638


o

o

40

OON

1 +OON

'--[--3000---

lb)

Figure 10.16. Radioactivity and magnetic contours, Northern Canada. (a) Wide-window y-ray flux (countsjs), background 60 countsjs. (b) Vertical-component of the magnetic field (gammas).

where U is the uranium content in parts per million, k 2 is the constant for the uranium channel, U. is the 1.76 MeV channel count rate less background, and S1 is the stripping constant ror thorium y rays in the uranium channel (see next paragraph). Fina1ly, in the 1.46 MeV potassium channel we may have counts from uranium and thorium as well as potassium. The potassium content, K" (expressed as a percentage because it is generally much larger than the amounts of U and Th), is given by

Table 10.7. Spectrometer readings (cpm) Slation (ft)

O

100 170 200 210 230 300 400

425 SOO

where k] is the constant lor the potassium channel, K. is the 1.46 MeV channel count rate les! background, and Sz, S¡ are the stripping constants lor U and Th y rays in the K channel. Because the y-ray spectrum of an element is in-

Te

Uc

Kc

13 8 22 25 18 10 15 15 12 8

28 27 34 36 30 24 27 30 20 21

195 243 265 218 135 223 193 197 242 233

variant, the stripping constant is merely the fixed ratio 01 the count rates ror U or Th at the appropriate energy levels; thus, S1 is the ratio ol the count rates lor Th in two channels centered at 1.76 and 2.62 MeV¡ hence multiplying the observed count rate for the 2.62 MeV channel by SI

;JU~e(~ y)~l~

\ \lL

ns

T5l

(bl

(al R~~

R~O

R~I

------. ~ - - Cllntour mlcn,¡¡1 ! ..I;andatd d~t.lllon,

o rrom

R!2 J males

R21

R!O

I~ rne-.an

Figure 10.17. Aeroradiomerric sUTVey, Redwater Ojlfield, Alberta. (a) Ared flown edSr- west, winter of /957; contours are total-count for energies above 1.5 MeV. (b) Area flown east- west aurumn oi 195·/; contours are for tordl counr only.


640

:'1

," ,

,, II

I I

I I

I

,:~R.diO'CliviIY

I

I I I I I

,,, , I

3 +OOW

2

+ooW

1 +oow

B.L.

2

1+ ooE

+ OOE

figure 10. 78. Rad;ometric and magnetic profiles Irom a survey lor base-metals plus uranium.

oé:==-_1.00 l\

(a)

_eU

K

x--x en 150

60- •• -6 K

~

í

.

• """ ,• •,

,"" I I

(:.

I

.. 100

I

1 ::¡

..

6

I

I

• I

•

I •

6

I

r, .

~•

• I

~

f

~

0- •• -.0

eU/en

eU. eTh-estimated concentf.,ions ofU. lb

•

f U " • t ,

• ••

oL-__~~~~~~~~~~~~~~~~~~~~~~~~~o 11 + ooN 11 + 50H 12 + ooH _______ loon

c:===~50

(b)

Line I09W

Figure 10..19. Results 01 radiometric sUNey over pegmatite, Portneuf, Quebec. (a) /sorad contours; contour inteNal 7.000 counts/mín. (b) Radíometric profiles 01 eU, eTh, K, and eU/eTh ratio lor line 109W.

Probfems

641

IEDIMIITAIY IIDClS

O

cTtrt.., .. _..... _" .."

aF-3

c........ S¡..,..

(a)

•

le.rDUS IIDCIS

10 km

H.fl' ..... ., .... e

flfh.".o-ttr.,,·._,.kt _ _

'_,Itt

"'....oIltt

CIMltt ........,..••

-

lZ:::J ~

mm ~

Figure 10.20. Airborne radiometric and magnetic surveys over granite zone. Morocco. (a) Detailed ge%gy of the afea.

yields the thorium count rate that would be observed at the same instant in the 1.76 MeV chanDel. Tbeoretically only ODe thorium, two uranium, and three potassium standard samples are required to fumish the dala lO solve the three equatiODs and determine the three cODstants, k 1, k 2 • k]. In practice it is best lo use as many

standards as possible because of instrumental and sampliog errors. Tbe readiogs in Table 10.7 were obtaiDed witb a y-ray spectrometer in a traverse perpendicular to foliation across a granite-gneiss outcrop Dear SI. Columban, Quebec. Given tbat k 1 - 0.6, k 2 - 0.13, k3 - 0.020, S¡ - 1.0, ~ - 1.5, and Sa - 1.7, determine tbe


642 JSI

Figure 10.20. (Continued) (b) Tota/-field magnetic map; contour interval (ive gammas.

lb, U, and K content at each station and plot profiles lor each elernent as well as a profile ol the lb: U ratio. lbe formation appears lO be homogeneous, that is, completely granitized, except for remnants ol sedimentary rocks at 35 and 215 ft. Do the profiles bear this out over the whole 500 ft traverse or any part of it? On the assumption that higb Th : U ratios would be more characteristic of sediments than of the granite-gneiss intrusive, does the lb : U profile provide any additional information? Is the sampling density adequate lor a petrogenic study of the roen? 5. Figure 10.17 shows radiometric cootours from an airbome test survey of Redwater oil field oear Edmontoo, Alberta. Figure 10.17a shows total count lor y-ray eoergies aboye 1.5 MeV, Figure

1O.17b, total couot only. The rocles of the area are mainly shales and sandstones, with some conglomerate, black quartzite, and argillaceous sandstone in the SW and SE comers 01 the survey area. Green shale forms a caprock over the oil pool.

The airbome data have been analyzed by Sildca (1959), who made corrections lor variations io the radioactivity 01 the different soils in the area Tbe arithmetic mean and standard deviatioo were cal· culated lor the area. Tbe difference betweeo each observed value and the arithmetic mean was divided by the standard deviation and the result plotted as the statioo value; thus, the cootour interval is a multiple of the standard deviatioo. Sildca also measured the distribution 01 radon emission 00 the ground. In the course 01 this

643

Problems

Figure 10.20. (Continued) (e) Total-eount map; eontour interval 50 eounts/s.

work, be found tbat tbe type of soil, for example, sands, sandy loams, loams, and so forth, as well as tbe soil parent material, controlled the regional patlern of radioactivity to a considerable extent. Details may be found in the original work. The airborne radiometric data from 1951 (Fig. 10.17b) were corrected only for the soil type. The contours of 1957 (Fig. 1O.17a) were corrected Cor soiJ parent material as well. This was done to sbow the significance oC botb factors. Sikka sta tes tbat tbe two maps would be similar if the complete corrections were made in both cases. On the hypothesis that radioactivity lows reflect the re1atively impervious caprock over tbe oH pool, try to outline its boundaries on each map. (Note: The survey covered only about 65% oC the total area oí tbe oilfield.) Can you spot muskeg

and swamps from anomalous high radioactivity? Apart from a possible halo of bigh radioactivity around the oilfield, are there any structures, such as faults. indicated by linear bigh-Iow contraslS striking in a preferred direction? 6. The profiles in Figure 10.18 are talcen from a detailed survey for base metals and uranium. Station readings were made every 10 fl. The magnetic-radiometric correlation is similar to that oC Figure 10.14. although the geology is different and Ibis anomaly has a strike length of 1.600 ft. Locate the radioactive source, the boundaries oC the magnetic anomaly. and the dip oC the mineralized section. What is the likely source of the magnetic mineralization? 7. Sorne results from a radiometric survey over a pegmatite in Portneuf County, about 35 miles

644

west oC the city oC Quebec, are shown in Figure 10.19. This feature outcrops contioually lor a distance oC about 1,100 n. As can be seen in Figure 10.19a the strike is rough1y N200W over most of the length, the main width varying between 30 and 80 ft; there are oarrower pegmatitic bands 00 the flanks. lbe host rocks are gneisses with sorne hombleode. lbe uranium, thorium, and potassium conteot oC the racks, shown io the pro/Hes of Figure 10.19b, were determined with a multichannel y-ray spectrometer by a method similar to that described io problem 4. Locate the maio pegmatite section and any additional pegmatite bands with the aid ol these data Are these sections oC shallow or steep dip? Can you determine the direction of dip? Does the uranium mineralization appear to be oC economic grade? Compare the U: lb ratios with the actual uranium and thorium concentrations at varíous places along the profile. Do large ratios correlate with high uranium content? 8. lbe maps in Figure 10.20b and c are taken Crom a large-scale airbome magnetic and radiometric survey in Morocco, carried out in 1972. Geology oC thls 30 X 30 km granitie zooe is iIIustrated io Figure 1O.20a. Flight lines were NW-SE, with 1 km spacing aliSO m grouod c1earance. Data compilation was by computer, corrected for altitude; radiometric background was obtained beCore and after eaeh f1ight by means of a short pass al 600 m, whereas a fixed magnetic grouod slatioo provided a similar check Cor the magnetic data. Qnly total couot radioactivity is shown here, although lb, K, lb/K, and U couots were also available from the three-channel spectrometer. Malee a sufliciently detailed tracing oC the total eouot and magnetic contours for overtays 00 the original maps oC Figure 10.20. Assess the correlation and eomplementary information obtained by the airbome data with respeet to the geologie map; do the same for the two survey methods. 15 there evidenee oC much overburden in the area? From the limited lists of racks and minerals in Tables 10.4 and 10.5, can you suggest any further anomalies that might appear 00 the lb and K maps? Why was the U channel not reproduced?

REFERENCES Abdoh, A. B., 1984. Field geophysical studies io the PierrefoiJds-ne Bizard region, Montreal. M.Sc. tbesis, McGiD Uoiv., Mootreal. Bales. R. O. 1966. Airbome radioactivity surveys, an aid to geologic mapping. lo Mining Geophysics, Vol. 1, pp. 67-76. Tulsa: Sociely oC Exploratioo Geophysicists.

Radíoactivíty method BriSIOW, Q. 1979. Oamma-ray speclromelric methods in uranium exploration - airbome inslrumenlation. In Geophysics and geochemistry in the search lor m~tal/ic ores, P. J. Hood, ed., &on. Geol. Repon 31, Geol. Surv. Canada, pp. 135-46. Bristow, Q., Carson, J. M., Damley, A. O., Holroyd, M. T., and Richardson, K. A. 1977. Speciflcations for federal-provincial uranium reconnaissance program 1976-1980 airbome radioaclivily surveys. Oeol. Surv. Canada Open File No. 335. Crossley, D. J., and Reid, A. B. 1982. Inversion of gammaray data Cor elemenl abuodances. Geophysics 47, 117-26. Curry, W. H., 111 1984. Evalualions oC surCace gamma radiation surveys for petroleum exploration in the Deep Powder River Basin, Wyoming, In Unconv~ntional Methods in Exploratioll lor Petroleum and Natural Gas Il/, M. J. Davidson and B. M. OOlllieb, eds. pp. 25-40. DalIas: Southem Methodisl Universily Press. Damley, A. O. 1970. Airbome gamma-ray spectroscopy. Can. Inst. Min. Bull. 63, no. 694, 145-54. Damley, A. O., Cameroo, E. W., and Richardson, K. A. 1975. The federal-provincial uranium recoonaissance programo In Uranium Ifxplora//on '75. Geo!. Surv. Canada Paper 75-26, pp. 49-63. Duval, J. S. 1983. Composile color images of aerial gammaray speclromelric data. Geophysics 48, 722-35. Onojek, l.. and Prichystal, A. 1985. A new zinc mioeralizatioo detected by airbome garnma-ray speclromelry in northem Moravia (Czecboslovakia). Geoexplor. 23,491-502. Grasty, R. L. 1979. Gamma-ray spectrometric methods in uranium exploralion - Iheory and operating procedures. In Geophysics and geochemistry in rhe search lor metal/ic ores, P. J. Hood, ed., Beon. Geol. Report 31, Geol. Surv. Canada, pp. 147-61. Killeen, P. O. 1979. Oamma-ray speclrometric melhods - application and inlerprelatioo. In Gtophysics and geochemistry in ,he search lor me/allíe ores, P. J. Hood, ed., EcOD. Oeol. Repon 31, Oeol. Surv. Canada, pp. 163-229. King, C. Y. 1978. Radon emanatioo on San Andreas fault. Na/ure 271, 516-19. Sikka, D. A. 1959. A radiomelric survey oC Redwater oilfield, A1berla, Canada. Ph.D. Ihesis. McOill Univ., Montreal. Soonawala, N. M. 1968. Correlation of ground and airbome radiomelrics. M.Sc. lhesis, McGiII Univ., Monlreal. Soonawala, N. M. 1976. Dilfusion of radon 222 in overburden and its application to uranium exploration. Ph.D. Ihesis, McOill Univ. Monlreal. Soonawala, N. M., and Telford, W. M. 1980. Movemenl oC radon in overburden. Geophysics 45, 1297-1315. TelCord, W. M. 1983. Radon mapping in the search Cor uranium. In Dtv~/opments in Geoph,rslcal Exploratio" Methods- 4, A. A. Filch, ed., pp. 155-94. New York: Applied Science Publishers. Warren, R. K. 1977. Recenl advances io uranium exploration wilh electronic a1pha cups. Geophysics 42, 982-9. Wearl, R. C., and Heimberg, 0.1981. Exploratioo radiometrics postsurvey drilling results. In Unconllentional Methods in Explora/ion lor Petroleum and Na/ural Gas l/, B. M. Gottlieb, ed., pp. 116-23. DalIas: Soulhem Melhodist Universily Press. Wollenberg, H. A. 1977. Radiometric methods. In Nuclear Me/hods in Mineral Exploration, J. Morse, ed., Ch. 2. pp. 5-36. Amsterdam: E1sevier.

Chapter 11

Geophysical Well Logging 11.1. INTRODUCTlON 11.1.1. Uses of Well Logging Well loggiog involves measuring the physical pro~er tíes of surrounding rocks with a sensor located m a borehole. The record of tbe measurements as a function of depth is called a welllog. Geophysical well logging has become a standard operation in petroleum exploration. Identification of geological formations and Connation ftuids, correlation between holes, and evaluation of the productive capabilities of reservoir formations are usually the principal objectives. Except for the natural y-ray log, wbich is used routinely io uranium exploration, well logging is sti11 not used extensively in the search lor metallic minerals. Sorne argue that the complete recovery of cores in diarnond drilling eliminates the need for logging holes because the inlonnation is laid out in the core box. It is unCortunate that tbis attitude still prevails because well logging is cheap compared to drilling and would be valuable in correlation and identification of mineral-associated anomalies, particularly when core is lost or difficult to identify. Geophysical well-Iogging methods inelude mechanical methods, passive and a number oC active electrical methods (ioc1uding self-potential, resistivity, inductioo, induced polarization), several nuclear methods (natural y-ray detection and observations from induced nuclear reactions), acoustic logging, and measurement of magnetic and thermal properti es. Tbe emphasis in what follows wi11 be on 10gging for petroleum (Pickett, 1970) because tbis is the major applicatioo.

11.1.2. History of Well Logging The 6rst borehole log, roo 00 September S, 1927 by the Schlumberger brothers in the PecheJbron oH field in France (Segesman. 1980 and Snyder and Fleming, 1985, upon whom tbis bistory is mainly based), measured formation resistivity. The first log (called

electric coring) in the United Sta tes was in 1929

when Doll noted spontaneous potentials (SP) and that negalive SP was associated with permeable formations. Beginning about 1932, two 10gs were usually run, resistivity and SP. Around tbis time Schlumberger also began using differeot electrode configurations and spacings to reduce distortions. About 1936 photograpbic recordiog oC measurements replaced manual reading of meters and tabulating of data. The first efforts to measure dip in a borehole carne in 1933, using an array oC electrodes, and the first uses of a recording thermometer and teleclinometer (to measure borehole deviation and direction) were also about tbis time. lo 1941, Arehie developed empírical equations relatíng resistivity measurements to porosity and water saturation and in 1945, Guyod published a discussion oC well-log interpretation. In 1949, Wyllie related electrochemical SP effects lo differences between the resistivities of mud filtrate and formation water and to chemicaJ activities. The induction log, developed in 1949, allowed the measurement oC eIectrical resistivity (actually its reciprocal, conductivity) without requiring fresh water mud; it was an outgrowth of World War 11 research. A number of other electrical logs, such as microresistivity and focused logs, were developed in the 19505. Natural y-ray logging, introduced about 1939. permitted distinguisbing shales. fro~ .other formations by their bigher natural radloactlVlty. A oeutron log was described in 1941; it utilized a downhole neutron source and measured the y rays emitted upon the capture of the neutrons, a response depending mainly on a formation's hyd~ogen content.. Logs depending on other nuclear reactlons followed 10 ~he 1950s. Gamma-gamma (density) 10gs for determlOing density began about 1957. The first continuously recording dipmeter io 1950 utilized a three-arm mechanical scratcher ror correlating irregularities in the borehole wall. The measurement of seismic velocity in boreholes was first done in the 1930s aod continuous velocity logging began about 1953. However, sonie logging

646 did not become used widely until Wyllie's time-average equation related seismic velocity to porosity (Wyllie, Gregory, and Gardner, 1958). Although digital tape recording oC log data becarne available about 1961, wel1-10g processing did not progress much until the 1970s. Downhole digitizing of measurements, multiplexing of different measurements, and telemetering the data to the surface have increased greatly the number of measurements that are feasible. Processing made it practical to combine the readings of different logs so that the plotted values give the needed inCorrnation more direct1y.

11.1.3. General Aspects of Well Logging Well bores are generally drilled by circulating a fresh-water suspension (drilling mud) down through the drill pipe and back to the surface through the annular region between the drill pipe and the rock. Occassionally salt-water mud, oil, or air is the circulating medium. The circulating drilling fluid removes rock cuttings from tbe bottom of the borehole. The Huids in a rock's pore spaces (interstitial ftu;ds) are normally under a pressure about that of a column of water extending to the surface. Their pressure is rough1y in balance with that oC tbe borehole fluid. If the borehole pressure were less, the pressure dift'erential would tend to expel tbe interstitial fluids into tbe borehole. Sufficient solids are added to the mud to malee the pressure of the fluid column approximately equal to tbat of tbe formation fluids. Mud densities range between 1.1 and 2.0 gjcrDJ. Exact balance is rarely achieved, however, and the usual tendency is for tbe mud to be under sligbtly greater pressure. This causes tbe borehole fluid (mud ji/trate) to enter porous formations and push the indigenous Huid back from the borehole, a pracess called invas;on. In tbe invasion process the mud solids plaster tbe borehole wall to form a mud cake whereas the fluid portion (mud tiltrate) coters tbe formation interstices. The mud cake quickly becomes sufficiently thick (up to 2 to 3 cm) to prevent Curther entry oC borehole fluid into the Cormation. However, tbe mechanical aspects of drilling abrade the mud sheatb, which is then repeatedly renewed by additional tiltrate invasion. Boreholes are ordinarily cased with steel pipe ( casing) several times during drilling to provide permanent protection against collapse of the borehole, loss of borehole fluid into .. thief" formations, or formation fluid entering the borehole. This is necessary because different formations have different interstitial fluid pressures relative to the borehole fluid

Ceophysical welllogging

pressure, so that the borehole fluid density cannot be adjusted to be appropriate for all of them. Open-ho/e logs are usually run just before the setting of casing. Consequendy, most welllogs consist oC portions run at different times. Sorne logs (cased-hole logs) measure through casing and cemento The cable used to lower and raise the sonde in the borehole usually contains seven conductors. It is wrapped (armored) witha steel mesh to prevent abrasion. Ordinarily the well tool (the part containing the sensors being called the sonde) is lowered to the bottorn of the borehole and logging is done as the sonde is pulled up the holeo Depths are determined more reliably corning out of the hole than ir measured going into the hole because the sonde may not sink at a constant rateo Borehole diameters are usually 6 to 10 in. (15 to 25 cm), occasionally up to 16 in. (40 cm), in petroleum exploration·and 1 to 4 in. (2.5 to 10 cm) in mineral exploration. Boreholes are often not uniform (Fig. 11.1a) eitber along their axis or in cross section, tending to be sligbt1y egg-shaped (Fig. 11.1b). Some forrnations, especially shales, absorb fresh water from the borehole, soften, and then slougb off material to make enlarged portions called caves. Usually a sonde rests against the side of the borehole. Some logs employ an eccentering arm to press tbe sonde against the borehole wall and some employ a centra/izer to keep it in the center of the borehole. Sondes have to be built to withstand the very higb pressures (1,000 to 1,500 atm or 100 to 150 MPa) and temperatures (100 to 250°C) in a deep borehole. Sonde deptb is deterrnined by an odometer counting the revolutions of a measuring wbeel over which the cable passes. Deptbs are usually referred to the kel1y bushing (KB) on the drilling rig ftoor. In addition, magnetic marks located every 100 ft (30 m) along tbe cable are sensed to check the odometer readings. The sonde is lowered to the bottom of the hole and then slowly raised until the sonde begins to move. The cable depth is then compared with the drill depth record; a cable stretch correction usually has to be made. Occasionally during logging the sonde may stick temporarily and then jerk free, producing a yo-yo motion. Usually several sensors are recorded on each log run and a y-ray record is made on every logging run to correlate between recorded depths on different runs. Portions logged on previous rons are usually repeated on a subsequent ron as a cbeck. A mernorizer in the recording cab corrects tbe depth differences between sensors located at different places on long sondes (which may be up to 30 m in length). Bottom-hole temperature is obtained by a maxirnum-reading thermometer attached to the sonde.

.

647

Introduction

!

l.. BIt llze

(o)

Eft"'~1 by drltlltent rubbl

Clre" drtlled by tM bit

(b) Figure 11.1. Borehole shape. (a) Conceptual vertical slice through el borehole showing caving elnd mud buildup on permeable formations. (From Tittman, 1986.) (b) Egg-shaped cross section of borehole showing most probable location of a sonde equipped with an "eccentering" armo

11.1.4. Rock Property Measurements The objeetive of welllogging is to me asure in situ the properties of the undisturbed rocks and the ftuids that they contain. However, tbe aet of drilling a hole disturbs tbem. Appreciation of the ínvasioD process is essential to ínterpreting well ]ogs because the rock region that exerts tbe greatest effeet on log readings is tbe portion nearest tbe logging sonde, tbe portion altered most by tbe drilling process. The relative eontribution of formations at various distances from tbe logging t001s varies with different sensor configurations (Fig. 11.2). Tbe effective depth 01 penetration (invesligalion), a qualitative term, is tbe distance from tbe borehole that contains the

material whose properties domínate the measurements (Roy and Dhar, 1971; Moran, 1972). Deep penetration implies that the dominant contribution is from formations that have not been disturbed by invasion. At the other extreme, very shallow penetralíon implies that the properties of the mud cake or of the borehole mud domínate the measurements, dependíng on whether the logging too1 is pressed against tbe boreho]e wall or is eentered in the borehole. Intermedia te penetration implies domínation by tbe area invaded by mud filtrate in porous formations. Eleetric ]og measurements using different eleetrode arrangements may give different results because the mud and filtrate are usually more resistive than tbe indigenous formation wbose water is usual1y highly satine and conductive. Well logging for petroleum usually has the primary objective of identifying potential reservoir rocks, determining their porosity and permeability, and determíning the nature and proportions of tbe ftuids present. Porosity is the fractional portion oC rock volume occupied by pore space, often expressed as a percentage. Reservoir rocks usual1y have from 10 to 30% porosity altbough roeks 01 lesser porosity can also be hydrocarbon reservoirs. The product of porosity, area, and average thiekness of a reservoir gives the volume of ftuids tbat the reservoir contains. Porosity can be determined lrom resistivity, aeoustic velocity (sonie), density, and neutron 10gs. Each may be subject to distortions and hence better determinations can be made from combinations 01 logs tban from individual logs. In most reservoirs hydrocarbons fill on1y part of the pore space, tbat fraetion being tbe hydrocarbon saturalion. Where water is tbe only other fluid present (the usual situalion), the water saturation plus tbe hydrocarbon saturation equals 1. The water saturalion is calcu1ated from the Archie equations (11.1), (11.2), and (11.3) and porosity measurements, and it oflen provides the distinguishing trail of formations that are capable of cornmercial hydrocarbon production. Besides porosity, an equally important property is tbe degree to which the pores are interconnecled, that is, the permeability. Permeability is usually measured in darcys; a darcy is the permeability lhal will allow a ftow of one milliliter per second 01 fluid of one centipoise viseosity through one square centimeter under a pressure gradient of one atmospbere per centimeter. Commercial reservoirs generally have permeabiJities ranging from a darcy to a few millidarcys. Permeability is estimated from 10gs using empirical ru]es but only with order of magnitude accuracy. The SP curve is usually a reasonably good indicator of permeability.


648 lOO

w

'" 5 8!w a:

u.

o

w

50

~w U

a: w Q.

o

Figure 11.2. Percent of response attributable to rocks within different distances from the borehole for infinite homogeneous medium. (After 5chlumberger, 1972).

Formation identification and correlation between wells is often as important as tbe determination of porosity and estimation of permeability. Particular formations may yield distinctive pattems making it possible to correlate not only major litbologic breaks but many points witbin formations tbemselves. Faults and unconformities often can be located fairly precisely by noting a missing section (or repeated section, in tbe case of reverse faults) in one well compared witb otbers nearby. Stratigraphic details often can be worked out from log-shape patterns. As logs from more wells in an area become available, the amount of detail that can be extracted increases.

11.2. RESISTlVITV METHODS 11.2.1. Introduction to Resistivity Logglng The physica1 properties oC roeks and minerals measured in electrical well logging are principally electrical resistivity and seU-potential (SP). The inducedpolarization etrect has not yet developed as a routine logging technique in petroleum application (see how-

ever §11.6). In most petroleum exploration logging, several logs are re-:"Irded on tbe same logging run (Fig. 11.3). Resistivity and SP logs are generally recorded as adjacent curves. Because most electrical measurements can be made onIy wbere tbe bole has not beco cased, logs are commonly run over different parts of

tbe borehole al ditrerent times. Also, because the primary objective of logging usually is to evaluate the productive potential oC reservoir sands, logging is often done soon after sands are drilled, before drilling deeper; otberwise the sands may change tbeir log characteristics as a result of standing open to drilling fluid with the consequent invasion of mud filtrate. Resistivities of various rocks and minerals are given in Tables 5.1 to 5.4 (§S.4.1). Sedimentary minerals normally encountered in oil wells are generally poor conductors, having resistivities in the range 103 to 1010 nm. Tbe minerals common in sedimentary rocks (silicates, oxides, and carbonates) are practically al1 nonconductors. However, most sedimentary rocks contain water in wbicb various salts are dissolved; in solution these disassociate ioto catiODS (Na+, Ca++, Mg++, and so on) and anions (0-, 80¡-, and so on). 11le movement of ions in the interstitial fluid provides the formation's conductivity. Metamorpbic and ignecus racks may contain minerals (usual1y disseminated), such as pyrite, chalcopyrite, graphite, magnetite, galena, and so on, which contribute to their conductivity. As in sediments, bowever, interstitial water is often the controlling factor on resistivity. Three equations used in petroleum work relate tbe resistivities of rocks and interstitial Huids, porosity, and tbe fraction of water filling tbe pore spaces. These are modifications oC the empírical formula of

649

Resistivity methods :;¡l

...¡

...¡

::E

llI:

!il

o

~

¡¿

'" '"

1., 00

~

~

...'" ...9 :J:

On clble sheath well aboYe sonde'

-<

-< llI: oz

'-"B

~

~

9

B

N-M-

Nt~-I....,r176" 447 cm M

-ll:

r-:-¡r32"

B - ,-

SP-M

(a)

81 cm

16" 41 cm

,;-'-'16"

I A-A-A- ~,......--

ELECTRODE USE

Two-electrode (normal) arrangement. (b) Three'electrode (Iatpral) arrangemeflt; the upper B electrode is on the cable sheath well above the sonde.

SONDE

Figure 11.3. Showing how eleclrodes on a sonde can be used lo record differenl electrical logs. A and B ilre curren' eleclrodes, M ilnd N are polenlial eleclrodes. (Afler Labo, 1987.)

Archie (1942) [see Eq. (S.7)]. The first expresses the bulk water-wet resistivity oí a rock sample, Po, and the resistivity oC the water contained in its pores, Pw, in terms of a formatíon resistivi~v factor F:

F - Po/Pw

(11.1)

(In formation evaluatioD the symbol R is usually used for resistivity; however, we sha11 use P to be consistent with Chapters S to 9.) Values oC Po can be determined Crom resistivity logs, those oC Pw Crom prior experience in the area, Cormation water samples, SP logs, or resistivity log crossplots (Schlumberger, 1987, pp. 28-31). Archie showed that the formation Cactor is a function oC the porosity and, to a les ser degree, oC the permeability oC the sample. His second re1ation is F-lj4/"

(11.2a)

where ~ is the porosity oí the material and m is a cementatíon factor whose value lies between 1.3 and 2.5. An altemative form 01 tbis expression, called the Humble formula, applicable to many granular rocks, is (U.2b) Another form, the Shell formula, is used lor lowporosity carbonates:

F ...

(I

1/~(l·87+0.019/.)

figure 11.4. Electrode configur,Hions afld lag curves; Pr, P:z indicate resiMive beds. P is Ihe power so urce, I is the ammeter, V i5 the voltmeter, .~ is the spacing (a)

(ll.2c)

If the rock pores are not completely filled with water but contain gas and/or oH aIso, the effective resistivity is larger than Po. The third empirical equation oC Archie accounts Cor partial water saturation oC the rock. If S.. is the Craction oC the pore volume fil\ed with water. Sw

= ( Po/p, ) 11"

(11.3)

where P, is the true resistivity oC the sample. derived by applying corrections for logging tool dimensions and configuration, borehole diameter. mud resistivity, and so on, to the measured (or apparent) resistivity Po' and n is the saturation exponent that lies between l.5 and 3.0; it is usually assumed to be 2 where there is no evidence to the contrary. Determination of Sw under a variety oC circumstances is discussed by Schlumberger (1987. pp. 9S-125),

11.2.2. Normal Resistivity logging The basic methods oC resistivi ty logging are similar to those used in surCace resistivity prospecting. A low-frequency alternating current is applied between current electrodes and the potential is measured between two or more potential electrodes. The record is then a pIot of potential variation (or its equivalent. apparent resistivity) versus depth. Figure 1l.4a shows a normal electrode configuration. One current electrode (A) and one potential electrode (M) on the logging sonde are c10sely spaced

Ceophysical welllagging

650

downhole [16 in. (0.4 m) apart for lhe short normal, 64 in. (1.6 m) for the long normal) and the other two electrodes (B, N) are either fixed near the top of the hole or a long distance away in the borehole. From Equation (8.26) and Figure 8.3, we get Cor the apparent resistivity P" in bomogeneous ground,

Cable _ _ _ _

P" - (4tr~V/I)(1/AM -l/BM -l/AN + l/BN)-1 (11.4) [Tbe factor is 4fT bere rather than 2fT as in Equation (8.26) because this equation bolds in the interior of the medium rather than at the surface of a semiinfinite medium.] Because the distance AM is much smaller than any of the other three dimensions, this becomes

P,," (4dV/I)(AM)

(11.5)

Tbe measured apparent resistivity depends mainly on the resistivities of the beds in the vicínity of A and M. Measurements will a1so be affected by the mud in the borehole and by the penetration oC the drilling fluid into formations. Tbe resistivity log of Figure 11.4a is symmetrical with respect to beds wbere the resistivity differs from that aboYe and below. Tbe interfaces are marked sharply (but not necessarily at their true loeations), particu1ar1y in the sbort-normal curve. High resistivity beds appear thinner than their actual thickness whereas conductive beds appear thicker. Tbe effective penetration into tbe formatioDS is about twice tbe electrode spacing and varies inversely as tbe hole diameter. The definition and sharpness of normal logs decreases witb an increase in the hole diameter and witb a decrease in mud resistivity. The effects of adjacent beds and tbe invasion of porous zones by drilling fluid are a1so significant. Tbese effects used to be reduced by tbe use of correction charts called depanure curves, but today corrections are generally made by computer a1gorithms. Tbe short-normal spread is sometimes suitable for measuring tbe resistivity of porous zones flushed by mud tiltrate (flushed zone) and hence for determining formation porosity. It is most useful in geological correlation between wells, because tbe interfaces between be
Sprin¡

Figure 17.5. Micr%g wa/l-resistivityarrangement.

11.2.3. lateral Arrangement A tbree-electrode sonde yields a la/eral curoe, iIlustrated in Figure ll.4b. Tbe downhole potential electrodes are usually separated by 32 in. (81 cm) with tbeir center 18 ft 8 in. (5.7 m) from the near current electrode; this latter distance is cal1ed the spacing. Tbey measure a resistivity oC the form

Po - (4".~V/I)(AM)(AN)/(MN) (11.6) where (AM), (AN), and (MN) are distances between the respective electrodes. Tbe most striking feature of lateral curves is their asymmetry; in Figure 1l.4b this is particularly apparent at the upper and lower boundaries of the thick bed. If the current and potential electrodes are interchanged. the asymmetry is reversed. Lateral curves are distorted by borehole effects similar to those described in the preceding section, as well as by the electrode geometry. Tbe depth of investigation is large and is often talten as approximately equal to the spacíng. For homogeneous beds ol thickness greater than about 12 m, tbe lateral curve measures formation resistivity P, unaffected by the invaded zone. A combination oC lateral and normal logs permits approximate determination of Pi and "', as well as the extent of fluid invasion. Despite its deep investigation, the long lateral (now obsolete) was of little use except in thick beds.

11.2.4. Microlog The microlog (wall resis/ivity log) is used as a detector 01 mud cake and for measuring mud resistivity. Mud cake is a qualitative indication that formatioDS

Resistivity methods

651

•

CB _ Curren!

conlrol box

" (a)

(e)

(h)

(d)

Figure 11.6. Focused current /ogS. (Courtesy Sch/umberger.) (a) Cuard /og (Later%g-3). (b) later%g-7. (e) Dua//ater%g showing how deep and shallow penetra/ion modes o( operation can be aehieved by reversing /he po/ari/y o( the A; e/ee/rodes. (d) Micro/a/er%g wi/h schema/ic curren/ flow /ines. The shdding in (e) and cr05s-hdtehing in (d) indica/e /he current eoncen/ra/ion.

are permeable because mud cake forms only on formations that are invaded. However, it may not form in a carbonate seetion with vugular or fracture porosity. The mierolog is iIIustrated in Figure 11.5. The button-size eleetrodes are imbedded in an insulating pad that is pressed against the borehole wall by means oC an expansion device which is also used to measure hole diameter. Because the electrodes are against the wall, the effecls oC hole diameter, mud resistivity, and adjacent beds are negligible. Because the e1ectrodes are very c\osely spaced (1.5 and 2 in., that is, 38 and 51 mm, apart), very lhin beds can be sharply detined, but tbe depth oC penetration is small, less than 10 cm_ Differences between resistivities measured with

different electrodes is called separation, which depends on tbe thickness oC the mud cake. The mierolog al80 measures mud resistivity when tbe electrode is not pressed against the borehole wall.

11.2.5. Focused-Current Logs The normal and lateral resistivity de vices are too large to measure thin beds. whereas the microlog is influenced by mud cake, and all are ineffective with saline muds. The possibility of using a sharply focused current was realized in the guard log or Later%g-3. iIIustrated in Figure 11.6a (0011. 1951; Moran and Chemali, 1979; Jackson. 1981).

652 To measure resistivity, p" witb a vertical resolution oC a Cew centimeters and in tbe vicinity of thin beds and conductive muds, tbe current is focused into a horizontal disk that penetrates the formation laterally instead of fiowing up the walls. The focusing is achieved by maintaining electrodes G at tbe same potential as the A, M electrode. Depth of penetration, taken as the distance at which tbe current begins to defocus appreciably, is approximately three times tbe length of the guards. Thus a long guard produces great penetration, but the lower guard prevents logging to the bottom of tbe hole. The system known as Laterolog-7 (Fig. 1l.6b) achieves a focused current sheet about 80 cm thick by maintaining the G electrodes at the same potential. Deptb of penetration is about 3 m if the spacing between A, M and the nearest guard point is 1.2 m. This arrangement gives essentially the same results as the guard log except tbat measurements can be made c10ser to the bottom oí the hole. 90th shallow (LLs) and deep (LLd) measurements are made by a dUIJI larerolog sonde (Fig. 1l.6c); the figure is split to ilIustrate tbe two modes of operation. By reversing the polarity oC the Al electrodes, tbe focused current bends back after a short distance, producing a focused beam with shallow penetration. The focusing principIe is used with very small electrode spacing in the micro/arer%g, or rrumper /og. illustrated in Figure 1l.6d (Dol1, 1953). The e1ectrodes are mounted Iike the microlog on a rubber pad that is pressed against the borehole wall. The electrodes are concentric rings 9/16 in. (1.4 cm) apart. Electrodes Ml and M2 are maintained at the same potential so that an essentially constant beam of current is produced. The depth of penetration is about 8 cm. This device is used to measure the resistivity of the fiushed zone; it also calipers tbe hole diameter.

11.2.6. Induction Log The induction log involves tbe same principie as FDEM prospecting. It is effective witb high-resistivity oil-based muds, in an air-filled borehole, and in fresh muds. A schematic diagram is shown in Figure 11.7. A simplified explanation is tbat tbe EM fie1d produced by a transmitter coi] (witb time factor eiOl') induces circular eddy currents in conductive formations; their time dependence is the time derivative of eiw" that is, jllJe iw ,. These eddy currents in turn induce secondary vollages in the receiver coi! proportional to - (JlIJle'w, where a is the conductivity. The transmitter coi! also induces directly into the receiver coil a voltage whose time dependence is 90°

Geophys;cal welllogg;ng

1 ~ ¡:::~

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(

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~sonde

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I

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\

,

I

I

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--

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I

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,

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,

,

,

L

:::\~:dYturrenl loop' in rormltions

f-

Oseilla'o,

_ _ T,anomine, .oil

~

Figure 11.7. Induct;on log schematic. The tool itself ;s made of nonconducting material.

out-of-phase (in quadrature) with the secondary currenl. Most of this mutual-inductance voltage can be compensated (bucked out). or a phase-sensitive discriminator can be used, so that the secondary voltage can be detected by itseU. The induced secondary voltage is the sum 01 all the eddy-current loops s(r, z) weighted by geometri. cal lactors to allow for their radial distance from the borehole g( r) and distance above or below the sonde g(z); this can be expressed approximately as

v ...

f f 8( r) g( z) dr dz

K

(11.7)

Graphs of 8(r) and 8(z) are shown in Figure 11.8; the radial dependence is greatest at a radius of about LI2 where L is the distance between transmitter and receiver coils, and g(z) is nearly constant over the range Izl LI < 0.5 but falls off rapidly beyond them. However, the conductivity of formations has such a broad range tbat a highly conductive bed weU beyond the tool may still have a significant effecl. Less conductive nearby beds have litt]e effect. The current in an additional coil midway between transmitter and receiver coils can be adjusted so that the secondary voltage in tbe rccciver coi! cancels out some of the contribution from the very shallow rone, producing the effect shown dashed in Figure 11.8a. Awilliary coils are also used to focus the effective

Resistivity methods

653

Curve without

~enter

coil (r)

Curve with auxiliary transmitting coi! midway between t.ansmitte. (TI and receiv •• IRI; coillurns .atio TI r

=

8

rlL

(a)

l

r

O~---------------+

lb)

Figure 11.8. Geometric facto,s fo, induction sondes without (salid curves) and with (dashed curves) auxiliary coOs (T', T", R', R" J. (Afte' Do/l. 1949.) (a) Radial factor g(r). (b) Depth factor g(z).

deptb. The induction-Iog signal is proportiooal to the conductivity oC tbe Cormations. The dual induction log records separate responses tbat peak at ditrerent distances into the formation, a deep (40 iD.) ioduction log (ILO) and an intermediate (27 in.) induction log (ILM). The inductioo logging tool usually also ioeludes a sballow focused log (16 in.) so tbat it measures tbe resistivity at tbree distances. The tbree measuremeots witb ditrerent

depths of penetration can be interpreted to iodicate the invasion oC filtrate, implying permeability. Ground currents generated by atmospheric etrects cause no problem because oC the high Crequency (20 kHz) oC the transmitter. Altbough interCaces oC low. resistivity beds are sharply marked. the log is automatically corrected for adjacent bed effects and it provides an accurate measure oC the conductivity for formations more than 10 cm thick. Anomalous read·


654 ings may result from a low-resistivity ring ealled an annulus whieh is sometimes produced in oil-bearing lonnations by the"invasion process; beeause 01 their greater mobility, hydrocarbons are displaced farther beyond the invaded zone than formation water, resulting in a high proportion 01 conductive formation water in a ring around the borebole. Sueh an annulus may move with time. A phasor induction log separately measures the quadrature and in-phase signals. The additional information allows a better correetion lor sltin elreets and improves the thin-bed response. The sonde can be operated at lO, 20, and 40 kHz, which give dilrerent elrective penetrations. Measurements at 10 kHz also bave less skin elrect [Eq. (6.17)) and those at 40 kHz give more reliable readings in high-resistivity fonnations. (Correction is automatically made for the skin elreet with standard induction logs operating at 20 kHz.)

N

A

----1'1 M

(41)

11.2.7. Resistivity Logging In Mineral Search Resistivity logging has not been used extensively in mineral areas except in connection with IP logging. Because the strueture in mineral areas is usually complex, the interpretation may be only qualitative. Electric logging should lacate high-conductivity zones and help in identifying and correlating them. The resistivity tool5, employed main1y in experimental work, are single-point resistance, normal, and poledipole (similar to the lateral) arrays. These have been used for estimating borehole fluid and resistivities of the host rock (Glenn and Nelson, 1979). Glenn and Nelson also used a combination of resistivity and IP logs to discriminate between disseminated and veintype sulfide mineralization and to estimate mineral content. Directional resistivity and mise-d-Ia-masse (sometimes called applied potential) conligurations are illustrated in Figure 11.9 (Roy, 1984). Tbe lirst is designed to locate the azimuth of conductors with respeet to the borebole, whereas the second is capable of tracing interconnecting anomalies (Mansinha and Mwenifumbo, 1983) and outlining their geometry (§8.5.4d). It is necessary to calcu1ate the geometric factor for each location of the moving eleetrodes. Tbe expression for P. is given in terms of flV/1 and a geometrlc factor whose general form for dowohole eleetrodes is

k-

4"./[ {1/r1 + l/r{} - {1/r2 + l/r-1} - {l/r, + Ir;} + {l/r. + l/rJ}] (11.8)

where r1 - AM, r2 - BM, r, - AN,

r. -

BN, and

L---t'IM

(6) Figure 11.9. Resistivity 108 configurations for orebody definition. (After Roy, 1984.) (a) Directional resistivity method; the azimuthal direction of AS is chiJnged ~. between measurements. (b) Mise-A-/iJ-miJsse method with the A electrode embedded in conductive orebody iJnd potentiiJ' meiJsured in nearby boreholes.

the r' values are tbe corresponding distances to the images ol A, B, M, N reflected in the air-earth interface. That is, an eleetrode located at + z below ground produces an image at - z above ground (see also §8.3.3 and §8.3.4). For electrodes on the surface the r' terms are zero and k is merely twice the p factor in Equation (8.26). For downbole arrays the k factor is approximately constant.

11.3. SELF-POTENTlAL (SP) LOGGING 11.3.1. Sources

o.

SP

Tbe principal sources ol SP (shale potential, liquidjunction potential, streaming potential, and mineralization potential) have been described in Sections 5.2.1 and 6.1.1.

Self-potentiaf (SP) fogging

-

655

Na'

Shale

Shale

I

wen

Na+Na+Na+Na+

tL-irlmFmfrñ:fv771

CI-

(

N.

SandSlone

CICI-' CIN. ' CI-

Equivalent~ battery ~~

IN;;

Equivalent, battery SandSlone

I

Invaded lORe (b)

(al

Figure 11.10. The self-polenlial effeel in a sand- shale ser/ion. (Cour/esy Srhlum. berger, Ltd.) (a) Liquid-june/ion (diffusion) po/en/ial. (b) Shale (Ners/) porenria!.

In oil-welI logging the pOlentials involve principally the boundaries of the shale units, espedally shale-sand interfaces, and the principal effect is the electrochemical (shale plus liquid-junclion) potential, wbich is normally less than 75 mV. Shales are permeable to Na+ cations but nol to CI- anions; as a result a shale potential is set up when Na+ ions pass from satine formation water in sands into adjacent shale beds, tben into the fresh water of the mudo In addition, a liquid-Junction potential develops al the interface belween lhe fresh-mud filtrate in the invaded zone and satine formation water beyond the invaded zone; as a result of the grealer mobility oí CI- anions over Na+ cations, there is a net flow of CI- into the invaded zone. These effects are illustrated in Figure 11.10. Equation (5.4) can be modified by repladng the ratio of concentrations with the resistivity ratio to give

Ec - -70.7{ (T + 273)/298} ln(

Pm¡lp.,) (11.9)

where E, is in millivolts, T is the Celsius temperature, Pm¡ is tbe mud-filtrate resistivity, and Pw is the resistivity ol the original formation water. The shale potential contributes 59.1 and the liquid-junction potential11.6 to the factor 70.7 in Equation (11.9). A streaming potemial arises because of differences in pressure between fluids in tbe well and those in the surrounding formations. Equation (5.1) can be cxpressed in tbe form

(11.10) where Ek is in millivolts, Pmc and t me are the resistivity and thickness of the mud-cake, respectively, f is a filter-loss factor, and Il P is the pressure difference bctween the borehole mud and the adjacent formation fluid.

The streaming potential usually is much smaller than the electrochemical potential, hence Ee in Equation (11.9) represents approximately the total SP anomaly in oil-well logging (Wyllie. 1949). In mineral-zone logging a mineralization potential is usually dominan t. In zones involving sulfides, grapbite, and/or magnetite, the mineralizatioD POtential between the minerals and surrounding rock may be as much as 700 10 800 mV. Because tbis is generally much larger than the shale, liquid-junction, and streaming potentials. they can be ignored. The principal uses of SP logs are in (1) identifying permeable zones, (2) correlation, (3) providing a measure oC Cormation water resistivity p." and (4) providing a measure oC the amount oí dispersed shale in the formation pore spaces.

11.3.2. Instrumentation Equipment for SP logging is fundamentally very simple. A recording potentiometer or dc voltmeter with bigh input impedance is connected across two nonpolarizable electrodes, short lead cylinders. The poten ti al recorded is generally between a moving downhole electrode and a fixed electrode at the surface or in the borehole near the surface. In mineral logging the potential gradienl between lwo downhole electrodes at a fixed small spacing is occasionally measured. Errors may be caused by armor leakage, bimetalism, current leakage causing electrode polarization, or faulty design, especially when SP is run with a single-point resistance log (Keys and MacCarey, 1971; Roy, 1984). The first arises Crom cables with an external metal sheath in contact with the borehole fluid, which produces spurious potentials varying with cable depth. The second is the result oI a voltaic cell between the probe casing (usually stainless steel) and the insulated lead electrode. Current leakage

656

Geophysical welllogging SP (mV)

o

80

100 -

200

-=

300 -

Depth (m) (a)

(b)

Figure 11.11. SP log comparison. (Data courtesy Atomic Energy Canada, ud., Chalk River, Ont.) (a) Result of a careful/y designed survey. (b) Commercial log in the same borehole.

caused by large telluric transients or current injection through the SP electrode in single-point resistance loging may change the electrode polarization. Faulty instrument design usually means that tbe input impedance is too low. Errors tend to be more severe in mineral logging where resistivity is higher than in sediments. Errors can be reduced by using a cable with isolatOO extemal jacket, by isolating the instrument ground lrom the reference electrode, by insulating the SP circuit from the single-point resistance circuit, and by maintaining a high input resistBDce. Figure 11.11 compares an SP 108 produced in a carefully designOO survey with a commercial log. lbe former shows mucb larger differences and more

complexity, the latter is nearly a greatIy smootboo mirror image of the SP log lo the Ielt with a level shift around 540 m.

11.3.3. Uses of SP Curves in Oil-Well Logging The main uses of SP logging are locating boundaries between shales and porous beds such as sandstones, determining the cleanJiness of sands, correlating between wells, and determining formation water resistivity. lbe sbape of the SP curve is often characteristic of particular depositional conditions and

Se/f-porential (SP) logging

657

I

I

I I

:.rSand line I I

I

. i

(dI

(b)

(e)

Figure 11.12. Ch.uae/erislie SP curves for a sand- shale seelion. (AflE'r Pirson. 1970) (a) Curves for /hiek beds. (b) Curves for /hin beds. (e) Charaelerislie curves for various forma/ions; Ihe dis/anee be/weE'n Ihe dashed lines is Ihe stalie SP.

well-to-well correlation can be used to indicate thinning, pinching-out, and dip oC Cormations. Equation (11.9) is used to determine Pw, Pon, being Cound by measurements on samples oC mudo Having Pw, we can determine F in Equation (11.1) because we can measure Po from a resistivity log. F is an important quantity in calculating water and hydrocarbon saturations. If a thick shale is adjacent to a tbick, c1ean, permeable sand, tbe maximum potential dilrerence across tbe sand-shale boundary develops between two points in the well located some distance from the actual interface. The SP values at these respective points indicate tbe sha/e-base-line va/ue and the sond-/ine vo/ue. The dilrerence is called the stotic SP (SSP). The static SP depends on the dilrerence in salinity between tbe mud and tbe formation water. If the formation water should change salinity, as might be the case between formations aboye and be10w an unconformi ty, the shale base line will shift. If the formation water should be fresher than tbe mud, the SP phenomena will be inverted and produce a rel'erse SP, sands being positive with respect to tbe shale base line rather tban negative. When a sand is not c1ean but contains appreciable disseminated c1ay or shale, tbe full static SP may not develop and the SP value is called tbe pseudostotic SP (PSP).

Typical SP curves for thick beds are shown in Figure 11.12a. The interface between shales and porous beds can be located by tbe inftection point on the SP curve. In thin beds, as illustrated in Figure 1l.12b, the maximum negative SP may be considerably less tban tbe ideal static value. Figure 1l.12c shows an SP log through several dilrerent formations. Note the elrect of tbe thin bedding in the laminated shale-sand, the asymmetric curves for colloidal shale-sand and rhyolite, tbe positive anomaly for a reducing bed, and tbe large anomaly associated with disseminated pyrite (FeS). A1though borehole and formation factors influence the SP curve, as wíth resistivity logs, most of tbese can be corrected. The elrects of hole diameter, adjacent beds, and bed thickness can be eliminated by corrections from standard charts. The density and resistivity of the mud alrect the curve greatly. Spurious elrects due to streaming potentials depend on tbe mud density and can be removed by use oC a correction chart based on Equation (11.10). The ratio of mud resistivity to formation-water resistivity, Pm,/Pw. is tbe main factor controlling the curve shape. The temperature is corrected Cor in Equation (11.9). The elreet of penetration ol mud filtrate into porous zones is complicated. Generally the SP defteetion decreases with depth oC invasion. but ocea-

Geophysical we/llogging

658

1001'1

1001'1

200

200

lOO

400 500

o/e Sulfides

JOO

10% 50-80% 30-80% 20%

(a)

«lO Mlnor FeS

500

20% FeS

(c)

(b)

Figure 11.13. Charaeteristie SP curves in mineral zones. (a), (b) Logs through sulfide zones. (e) Log near a massive pyrite zone not intereepted in the borehole .

. Shale base lino

Sand

Increasins

lino

depth

)o

Figure 11.14. Charaeteristic SP curves for transgressive and regressive sands.

sionally the reverse is true. TIte poten ti al may ehange witb time as a result of invasion of zones containing water; tbe faet tbat the curve is not reproducible on successive logging runs may be diagnostie of this situation. Polarization of eleetrodes, as in surface SP surveys (§6.l.2), aft'eets SP measurement but usually the electrodes can be restored to equilibrium by leaving tbem in tbe mud lor a time. Tellurie eurrents, proximity to power Iines, local eleetrical operations, large-scale electrolytic corrosion in the vicinity, and cathodic-protection devices affect SP readings.

11.3.4. Uses of SP Curves in Mineral Logging Potentials may be considerably larger in the presence ol sulfides (Becker and Telford, 1965) and graphite than for sedimentary beds; consequently borehole effects are insignificant as long as tbe hole is filled with water. TItree examples ol SP logs run in 2 in. diamond-dri11 holes are shown in Figure 11.13. From the first two curves tbere appears lo be no correlation between tbe deftection and the mineral content ol the anomalous zones, The largest negative potentials occur al the interface belween barren rock and disseminated mineralization, but this is nol loo significant because "massive sulfides" are usually inho-

mogeneous, being composed ol many thin sections ol high concentration intersperscd with disseminated or barren zones. Two other effects in these log5 are worlh noting. In tbe second curve there is a base-line drilt with depth, which is not due lo temperature. In the third example the broad positive anomaly is caused by a massive pyrite zone near the hole but not intersected by it. TIte current flow in the barren host rock is lrom depth to surface. By having both electrodes downhole at 5mall fixed spacing (15 cm), one can measure the potential gradient. The resultant curve shows sharp deftections at the edges ol mineral zones. Except for this feature, the regular electrode arrangement provides more information.

11.3.5. Geological Interpretation 01 SP In addition lo its use in identilying shales (and especially, distinguishing shales from sands in a clastic sequence) and for correlating corresponding points from well lo well, other stratigraphic interpretation can sometimes be inferred from the SP curve. In a somewhat simplistic way, the SP value is read as the degree ol shaliness (or the relative abundance of clay minerals) and as the inverse 01 the "energy" in the original depositional environment. For example,

The dipmeter

659 No.•

N-+

-3800 -3900 4000

-4100

-4200 -4300 ~

-4400

!

4500 -4600

-4700

SP

P

""I~o--------20 miln----------;~...

-4900

Figure 11.15. WelJ-/og corre/alion. The convenlion for plo//ing welllogs ;s /o show an SP or y-ray log to the left of the borehole and a resistivity log to the righ/, (After Pirson, 1970.)

proximity to a shoreline where there is wave action represents .. high energy," with the consequent removal 01 clay minerals. Rence an SP curve that gradually increases in shaliness as we approacb the surfaee indicates a receding sboreline and hence a transgressive sea. Conversely, increase in sbaliness witb depth is interpreted as a regressive sea. This concept is used to develop .. theoretical" SP curve shapes sucb as in Figure 11.14. This concept can be expanded to many other types 01 sedimentation pattems (see Fig. 11.18). Correct recognition of such pattems, however, is often not very clear in practice. Figure 11.15 sbows sbort portions oC SP and resistivity logs in four wells located approximately in a N-S line. Tbe correlation oC corresponding points on tbese curves is clear despite minor differences. The resistivity curve in tbe vicinity ol tbe point A is characteristic oC a marker bed that can be correlated over a Cairly wide regíon. Obviously the formations dip south about 400 ft in 20 miles; this is a gentle slope of ~ o. The SP curve deftection to tbe left in regíon B indicates sand in a predominantly sbale environment. The shortened distanee between marker

A and the top of this sand in well no. 1 indicates missing section - a normal lault with about 150 Ct oC throw. The lower portion of sand B indicates a regressive pattem as far as well no. 3. Sand B is not secn in well no. 4; correlations oC points below the sand compared with those aboye indicate that the sand bas not merely been faulted out bUI ralber that shale was being deposited al the localion oC well no. 4 while sand was being deposited in the other three wells. Rence a sand-shale facies boundary must lie between wells no. 3 and no. 4. Such a pinchout, ol course, represents a poten ti al oH field.

11.4. THE O!PMETER In some cases formation dip can be estimated by correlation between holes where no structure interYenes, bul often the determination is difficult or impossible. Early dipmeters employed EM response and later SP. TIte modem dipmeter (Fig. 11.16a) employs four microresistivity pads in the same plane, pressed against the borebole wall at 90° intervals. TIte upper

".,

~;,

I.Jp ....._ ~~ '·':r .... 5"; ••,,,,,

''''''''al'Zr, .

'\'''.',,-

15/)0",,,

"'" .... """

-

"",

111

Bor-.hole

Resislivity

Relative bca'in, anlle---.... ..

Hale Caliper 2 Drift 4" - - 20" Caliper 1 4" _ _ 20"

(21

o

Dips

Correlations

N W"*-E

Aesislivity Increases

20

S

40

•

6080

Curves 1 2 3 4

1

(3l

(4)

(5)

Eloclrock pad as.. mbly (conltoU.d parallolo,ram sysrem wilh adJuslablo pad p'rssure)

Corrdation cur_

r

2

(a)

J

4

(b)

Figure 11.16. The dipmeter. (a) 5chematic ot diplog tool. (Courtesy Dresser Industries.) (b) Portion of a four-arm processed dipmeter /og showing deviation of the hole, caliper /og, smoothed resistillity, tadpole plor of dips. roselles (each showing directions of all dips within a 10 ft. inteNal), and output of the tour microresistivity pads with compute,..drawn correlations. (Courtesy 5chlumberger Ltd.)

The dipmeter

661 Qeolo,ic fUlura Uniform monodinal dip

The ,yst.m.lic elemenl io Ihe r.,ional dip

A,ymmelrical ~ anlicline ~

Normal fauh with roll ovef

R.>."al 01 dip, a. a.is

11

No~mal rault ~.-:-. w.lh dr.. .. '., .r·

. ,,:

Off.. t in dip al f..uh:

anomalouo dip. near fauh

..,.". ,

~';.I "."~ ....~$:.

"""""mi [J-. ~

R.ve".' 01 dip diree.ion ir ovc-rturn ¡"volved

...

Sall dome.

Dips ine,n •• wilh d.plh dips wi.hin sall rtW and trrltic

Oouae zonr

Shoa, zone Compr.... d ZOM

Unconlo,mitits

C,o.. -bodd.d ~dimenl'

~;:;::;:;::

11 ,

Otlt.~. ... ..

itquenre . .~.~.,,: _"" .. ~

.-

',;

•

.....

• '!'II>

Se .. or dip' dcc,.. 'e wilh deplh

Chan.e in dip bol"een lopsel and ro'e... bod.: ror.sel dip, dccrca,. wllh deplh. bOllom-s.1 d.p. 101"

.~.

"I·-~·~·"-, 1 -

" J''.

..

.

Ab,upt sh.ft in dominanl dip and dip dircclion

. .1.;; ... '.1

Ine,e ... in dip ov., , •• r duo lo d,.p.n.: .. ,alic d.po wilh.n rt.r

-.'

Figure 11.17. Idealized dipmeter pal/erns indicaling structllral and .sIratigrdphic fedtures. (After Pirson. 1970.)

part of the 16 ft (4.9 m) long sonde contains an inclinometer to record lhe drill-hole drifl angle and bearing and a magnelomeler to determine the azimuth oC the reference pad. Two hole-caliper logs at right angles are also recorded. The log recorded in the field shows the azimuth oC the no. 1 eleclrode, the relative bearing oC hole driCt. the deviation oC the hole Crom the vertical, the resistivity curves from the tour pads, and the caliper logs. A portion oC such a log is shown in Figure 11.l6b.

Formalion boundaries are defined by the microresistivity curves and the dip and strike are determined from the slight differences in depth oC the boundaries and the orientation dala. Rough interpretation based on major features oC the raw plots can be made Cairly easily. The correlation oC many c10sely spaced points, however, requires processing. The resull is usually a .. tadpole plot" such as shown in Figure 1l.l6b where the resull oC each correlation is shown as a small circ1e indicatiog the dip angle, with a short ray

-...

30°

0°

.-

60°

90°

....

\.,

Dips in direction of ~.... seclimenttransport, SE

~....

Distribulary MouthBar

~:;:.

. - Struclural dip

-;:..

t rT

Dips toward ctlannel axis ~ and normal 10 channel strike

....

.....

Reworkad

Distribulary Channel

I

Oips IDWard shale-oul

and normal 10 llrik. DI bar

:::.

Beach Ridge

,

Dips IDWard shal&-Oul

~

'"0,

.......

,:'" : _

StruClural clip

,

Randomdips

.....

~

or Mouth Bar Sand

90°

~ and normal ID slrika DI Beach Ridge

Dips in direction 01 curren! lIow

/Tr

60°

::::.

Braakpoinl Bar

o-

Distributary Channel

30°

0°

Dips loward pinchoUI and normal ID real SIra

~ Strucluraldip

Seour Channel overlying Oistribulary MOUlh Bar A Scour Channel usuaOy has limitad areal extent

Real

I

_.-. . . . 4o-

";:.

Panern resulls Irom compaction; dips loward reef canler

Dips in direction 01 secliment transport

o-

Crevassa Splay

Dips in directlon 01 currenl ftow

.:::= __ StruClural di¡) Channel-like sand lormad by COmp8Cllon 01 underlying muda during sand deposiIion: Ihis type of salid also depositad in other environmenla

Btank zone wilhin real

~

I

-;..

i

DiPS toward channel axis and normal lo strika DI

OOlilicSar

-

~ ::

..........-......

...

:: _

~

. - Slructuraldip

~~ .... ~

convex downward sand I ~ A downward decreasing .... ... resistivity gradienl will ... be presenl beIow sand

.......

,

Dips towald pinchoul and normal 10 strike 01 bar

~o:::'

Beachrock

-

....t: .... .... FigUfE' I l. la Strdtigr~ic pdllems in SP (ex y-rdY) and diptnf'Il" d.J/d. (From GiI'f'dlh, 1CJ87.)

.

Slruclural dlp

==

....

1:::

Parallel cross-beds dip _ald

Electromagnetic wave propagation method

emerging from the circle indicating the down-dip direction, north being upward, east to the right, and so forth. The variation oC dip with depth ohen indicates geological structure. as shown in Figure 11.17. The dip dislortions resulting from Cault movement may not extend very far Crom the fault plane. Various types oC sedimentation pattems sorne times may be distinguished when many detailed correlations exist (Fig. 11.18).

11.5. ELECTROMAGNETIC WAVE PROPAGATION METHOD Althougb the induction log discussed in Section 11.2.6 is an electromagnetic method, this term is usually reserved for other devices. The phase velocity of an eleclromagnelic wave al gigahertz frequency V is given by (Freedman and Vogiatzis, 1979; Pascal, 1983)

where po is the magnetic permeability, t is the dielectric permi ttivi ty, a is the absorption coefficient, f is the Crequency, and T is the time to travel a unit distance equal to interval transit time. Both the attenuation and the interval transit time can be measured. Because the dielectric perrnittivity of water is much larger than that oí oH or rock (by a íactor oC 10 to 40), water dominates measurements with an electromagnetie log. The large contrast between the dielectrie permittivity oC water-saturated sediments and rock salt malees it possible to map a salt dome from a borehole in the dome. Nickel et al. (1983) report a survey oC tbis type using a pulse system operating at 20 and 40 MHz in a salt-dome borehole. With closely spaeed Tx and Rx antennas they obtained good reflections Crom lones oí anhydrite, clay, and basalt embedded in the highly resistive salt at distances oC several hundred metc:rs. They also measured absorption in these struetures by moving the receiver to a second borehole. The results were eompared with sonic log data from the same location. By analogy with the time-average equation (Eq. (11.l4b») used in sonic log interpretation, we write for the porosity seen by the electromagnetic waves o/!EM'

(11.l2) where T.In and T... are the interval transit times Cor the rock matrix and Cor the water in the pore spaees.

663

Because the total porosity .¡. can be obtained from neutron and density 10gs, we can solve Cor the water saturation S.. : ( 11.13) The eJectromagnetic propagation log at 1.1 GHz detines interfaces sharply but has Jimited penetration and thus yields mainly the water saturalion oC Ihe invaded lone. In conjunction with density and neutron logs, it also locates hydrocarbons. identities the hydrocarbon type, indicates mobile oil. and provides residual oil values. The EM propagation log at 10 to 50 MHz ordinarily has a penetration oC about 1 m and is userul where the salinity is small. Moditications oí EM suríace-prospecting units (§7.4.2 and §7.4.3) have been employed to a minor extent in mineral-hole logging. Usually the aim is to locate mineralized (bigh-conductivity) lones nearby, rather than lo evaluate the Corrnations intersected by the drill hoJe (Wortbington. Kuckes. and Oristaglio, 1981). An example is shown schematically in Figure 11.19a. The transmitting coil is a conventional verti· cal loop, set up near the hole and pointing toward it: connected in series with tbis loop is a small vertical verniercoil, wbich can be rotated about its vertical axis. The sonde lowered into the hole consists oC a small receiver coil wound on a high-perrneability core, amplitier. and battery. The received signal can be nulled by rotating the vernier transmitting coil and the azimuth angle is plotted against sonde depth. The measurement is repeated during the uphole passage, this time with the transmitter coil and vernier rotated 90°. The maximum azimuth angles oC the two curves. when plotted as vector components paralle\ to the planes oC the transmitter coils produce a resultant vector that points loward the conductor; the depth can be obtained from the curves. The amplitudes oC the maximum azimuth angles are roughly indicative oC the horizontal distance and/or the eonductivity oí the zone, and the distance be· tween null points oC the curve gives an indication oí the vertical extent. The range oC investigation is about 100 m. A somewhat different drillhole EM log is ilIustrated in Figure 11.19b. The transmitter loop is a large square oC one to íour tums laid out on the surCace. The vertical depth oC penetration desired and the type of objective determine the required loop size; loop sides are usually 125 m or longer. A receiver coil with preamplifier is lowered into the hole, the gain being adjusted to maintain constant meter reading: gain is then plotted against depth. Alternately. two coils 15 m apart are connected in opposition to produce a difference signal. as with the Turam method. The transmitter square with the hole

664

Geophysical welllogging -20· -10·

O

Remote conductor Conductor

Main field

(b)

(a)

Frequency (Hz)

35 1053159452835 35 1053159452835 100

--t--t--+-+iH-iSOOi---H--4-H-H--

\

,

)~

_.....L..L..J-+.L.,-~L..J

L....l-J

-S· O S·

1400 L-.J...,...a.,.-IJI-L--IL..

Depth (ft)

Phase shift

Field stre"8th ratio

Id Fisure 11.19. EM logsinS. (a) Loss for two orthosonal directions of the vertical transmitter loop. (b) LOS$ for a horizontal transmitfer loop and one (solid line) or two (dashed line) receivers in rhe hole. (e) Multifrequency loss. (After Seisel, 1979.)

665

Elastie-wave (acoustie) methods Depth

O

r--.__~__

Phase 60' 120' r-~~~~1.2 O 32o I I I r

(m)

;t

UJ

180'

¡

oc

-

r-

r-~r-~----~----~340

;,,;

17.8M

~--~------~~--~360

~ Iz~';; ~

~¿

IL--,"C ~

o/ r----t----/-~-9----~ 400

Y

,

UJ

": N

I

Figure 11.20. Amplit~de and phase plots of VLF log past a conductor. f i5 Ihe electric and M 15 the magnetlc reading. each at 17.8 and 21.4 kHz.

located at one comer ís rotated 90 0 for a successive logging run so tbat a rough estímate oC conductor ~~utb can be made. The interpretation is qualIlatJve. A recently developed EM log uses a large transmiuer loop laid out on tbe ground to one side of tbe borehole. A moving detector coil coaxial wítb tbe hole compares tbe axial H-field amplitude and pbase at five frequencies witb tbose obtained from a similar near-surface coil. Logs from a drill bole near tbe Gertrude sulfide deposit west of Sudbury, Ontarlo, are displayed in Figure 1l.19c. The EM16 VLF receiver (§7.4.2f) has been adapted for borehole logging (Rey. 1984). The downbole unít has magnetic and electrica1 sensors tbat detect in.phase and quadrature components of tbe axial magnetic field and electrical potential. A sur· face reference magnetic sensor is oriented for maxi· mum coupling witb tbe distant VLF transmitter and provides reference data for tbe downhole magnetic readings; tbe downhole potentials are measured witb respect to surface potentials nearby (analogous to SP - see §11.3.2). The log (Pig. 11.20) sbows tbe amplio tudes and phases oC tbe VLF magnetic and electrical vectors measured witb respect to tbe surface values. Botb vectors are determined at two frequencies: 17.8 and 24.1 kHz. The effeets of two conductors are quite cIearly seen.

11.6. INDUCED POLARlZATION LOGGING IP can be measured simultaneously witb resistivity, either in the frequeney or time domain, to determine tbe frequency elreet, pbase shift, cbargeability. and complex resistivity (Wagg and Seigel, 1963). The Kenneeott IP-resistivity logging tool gives continuous measurement oC IP amplitude and pbase as well as resistivity to depths of 1.500 m. Glenn and Nelson (1979) suggest a relation between IP and sulfide pereentages. For disseminated porphyry-type minero alization, tbe resistivity is independent of sulfide coneentration wbereas tbe phase shift is proportional to tbe sulfide surface area exposed to pore ftuid. In vein-type mineralization, the phase is independent oC sulfide content and the resistivity decreases inversely as the square oC the sulfide percentage.

11.7. ELASTIC-WAVE (ACOUSTIC) METHODS 11.7.1. Elastic Waves In Boreholes Elastic (seismic) wave trave! was discussed in Chapler 4. The sonic lag Iransmitter generales several wave modes (PailIet and White, 1982; Scbmitt and Bouchon. 1985). which are subsequenlly picked up

Geophysical well logging

666 MUD ARRIVAlS

COMPRESSIONAL (P) ARRIVALS

1

SHEAR (5) ARRIVAlS

BOUNDARY (TUBE) ARRIVAlS (a)

\

Tube (b)

Figure 11.21. Waveforms recorded in a borehole. (a) Waveform showing formation arrivals (P and S waves), mud arriva/s, and boundary (tube·wave) arrivals. (Courtesy Schlumberger.) (b) Waveforms ¡rom eighl broad-band receivers spaced al intervals o( 6 in. (15 cm). (Afler Morris, tittle, and Lellon, 1984.)

by tbe receivers (Fig. 11.21). The first energy lo arrive is almost aIways a refracted P wave (headwave mode) in tbe rack wall. It has impinged on tbe borehole waIl al tbe critica1 angle 9, - sin- 1(V¡/V,), where V¡ is tbe seismic (acoustic) velocity of a P wave in tbe borehole fluid and V, tbal in tbe formalion (Fig. 11.22). The sonic log records tbe transit time (reciprocal ol velocity) ol this wave. Some ol tbe headwave energy "pee1s ofl'" at various places along its travelpatb, reflects al tbe sonde or opposite borehole wall, and rejoins tbe headwave; tbis adds lail to the headwave, which tbus develops a "ringy" appearance. The acoustic wave striking tbe borehole wall at the angle 9s - sin- 1(Ji/JoS), where JoS is the S-wave

ve10city in the formation, generates a converted S wave (also a hcadwave mode) whenever Vs is larger than Ji. The S-headwave deve)ops a ringy character by tbe same mechanism as tbe P-headwave. It is usually the second arrivaI and stronger tban tbe P-headwave. Much of tbe energy reflects at tbe borehole waIls to reverberate in the boreho)e fluid. Energy striking tbe borehole waIls at angles larger tban is totaIly reftected and bounces back and forth in the borehole as a trapped dispersive wave (guidtd WQ"e; see §4.11.3). This energy constitutes a mud WQve (whose onsel may nol be recognizable). MOSl of tbe reverberatory energy striking the borehole waIls al angles between 9, and 9s is aIso reflected, except lor small

's

t

667

f/astic-wave (acoustic) methods

(b)

(a) Receiver

1

Transmitter

2'

1

I

1

Figure 11.22. Propagation palhs for P, 5, mud, and lube waves. (From tabo, 1987.)

portioDs wruch are lost by beiDg cODverted to relracted S waves; t1ús leaky-mode lransmission is also part of the reverberatory trapped wave. The trapped mode is often the strongest in terms ol energy deDsity and sometimes obscures the S-wave arrival, especially in soft formadons. A tube wave, also called a Stoneley wave, travels as a surface wave on the borehole wall (see Sherilf and Geldart, 1982, pp. SI-52). This wave is only mildly dispersive and thus shows as a reasonably sharp arrival, The shear modulus can be calculated from the Stoneley-wave velocity. The Stoneley wave is often very strong and oC re1atively low frequency conten!. AH oC Ihe waves Iravel as P waves in the borehole fluid, and hence the lerms aeowtic and sonie; however, the major interest is usually in the seismic wave in the adjacent rock Cormations. Although it was introduced to determine seisrnic velocity as an aid in seismic prospecting, determining porosity. which correlates with seisrnic velocily. soon became lhe major application oC t1ús log. Sonie logs continue to be used for seismic velocity measurement and reHection (synthedc seismogram; see §4.10.2) analysis. Seisrnic detectors located iD boreholes are also used lor determining surface-to-depth traveltimes for velocity surveys (§4.5.5) and for vertical seismic profiJiog (VSP) sludies (§4.11.4).

i

Figure 11.23. Sonie /ogging sonde. (a) Boreho/e-compensated sonde. (b) The sonde in a boreho/e. liertie.¡/ S/i15 are openings lo tr.¡nsmillers .¡nd reeeivers; horizonI.¡I slils prevenl signal Ira~-el in lile sonde i/self.

11.7.2. Sonie Log Early cODtinuous velocity loggers consisted of a single reeeiver a Cew meters away from a transmitter that emi tted pulses oC aeoustic energy. The traveJtime of the tirst arrival was measured to determine the P-wave velocily in Ihe adjacent rock. The design oC the logging sonde prevents energy travel through the sonde from transmitter to reeeiver. The traveltime is determined by the time when the receiver output exceeds a threshold that is sel rugher than the noise but lower than the tirst cyc1e of energy. If the threshold should be too high. triggering may not oceur unlil a later eyc1e. producing an error in measurement. called cye/e skip. Cyc1e skipping is more likely when the signal has been attenuated by unconsolidated formations, fractures. gas in the pare spaces, aerated mudo or caved seclions. Errors of lhis kind can usually be recognized and eliminaled. However, with single transmitter-receiver sondes, errors aIso resulted when the axis oC the sonde was nOI

668

Ceophysical we/llo8gin9

(e) figure 11.23. (Continued) (e) Long-spaeed sonde in the twa positians far barehole compensa/ion.

Table 11.1. fluid and matrix velacities. 5 waves

P waves

Material Water (20% sall lo pure) Salt Shale Iron casing Unconsolidated sands Sandstone Anhydrite limeslone Dolomite

V, or Vm (mis)

1,400 -1 ,600 4,570 4,875 5,334

5.180 5.490- 5,940 6,100 6,400- 7.010 7.010- 7,925

41 (I's/m)

V, ar Vm

4/

(mis)

(I's/m)

714- 625 219 205 187 193 182-168 164 156-143 143-126

[870]'

[1,150]'

3,550 3,030 3,400 4,000

282 330 294 250

'AllhoUBh water does nol carry 5 waves, use 01 this value in the time-average equations yields Bood resullS.

paralleJ to the borehoJe wall, from eularged borehole, from mud buiJdup, 8Dd from inadequate penetration beyond the altered invaded zane. Erron in transit-time measurements occur beeause of hole-size ehanges (eaving) or tilt of the sonde in the borehole. These effects opposite the transmitter are largely eliminated by measuring the difference in the traveltimes to two receiven at difrerent distauces, Likewise, the use oC two transmitten allows eliminating variable effects opposite the receiven. The borehole-compensated sonie-Iogging

sonde, iIIustrated in Figure 11.23a, employs two transmitters (whieh emit short 20 kHz pulses alternately about every SO ms) and four receiven. About five measurements are averaged for eaeh value recorded and the sonde is usually moved at about IS em/s, so that it moves about 3 em during a measurement cycle. Centralizen keep the sonde in the eenter of the borehole. The borehole-compensated sonde jusI described does not a1ways eorreetly measure the velocity in tbe formalion. Penetration may DOt extend beyoDd the

f/astic-wave (acoustie) methods

669 8

7

6

Velocity (km/s) 5 4

3

H'-'-- Limestone

.ff!'--- Cemented sandslone

Figure 11.24. Porosity versus in!erval !ransit time. The eurved lines are empirical, the straight lines give values (rom the time-average equarion. (After 5ehlumberger. 1986.)

invaded zone, and shales al the borehole wall may have been allered so as lo have lower velocily Ihan Ihose farlher away from the borehole wall. Use of a long-spaced sonde, shown in Figure 1l.23c, remedies Ihese defects. Because the sonde moves, the transmitlers are subsequently opposite Ihe portion of the borehole that the receivers previously oceupied (Fig. ll.2Je); trus permits averaging appropriate values to compensate lor changes in borehole diarneter and other abnormalities. The sonie log displays the time interval lor the sonie wave to Iravel one foot, usually expressed in mieroseconds per foot. Porosity usually is determined from the empiriea! time-average equation developed by Wyllie, Gregory, and Gardner (1958): /:1/ .. l/V,

O.AII

., It IN"

(......)

.,(... /It)

•

100

'O

.

1--+--1 o~ H"--_.............- - I

= (.¡./Ij) + (1 - '¡')/Vm (11.14a)

or

ItIC IOIIIC LOG

CALI""" MOLI

Figure 11.25. Portion

o( d

sonie log. (From 5chlumberger,

1987)

where Ilt is the formation transit time (or slowness), V, is Ihe formation velocity, Ij - 1/M¡ is the velociIy in the fluid wruch fills Ihe pore spaces, V,"1//ltm is the velocity in the rack matrix, and .¡. is the porosity. Velocities used in trus caleulation, given in Table 11.1, involve ranges from wruch the velocity Ihal gives Ihe best porosily va!ues is seleeted. Figure 11.24 indicates the dependence ol matrix velocity on porosity and provides a way of getting better porosily values lrom Equation (11.14).

For many formations, especially consolidated sandstones, the inlerval time in sands does nol depend markedly on whether mud fi!trate, lormation water, or sill fills Ihe pore spaces. Consequent1y the porosily ca!culaled Cor shaly sands is too large. Where a sand is filled with oi! or gas, especially with high porosity sandstones, the aClual porosity is oflen 70 10 90% of Ihe calculated porosity. In unconsolidated sands, porosities are sometimes eorrected by dividing by 1/I00th 01 the transit times (in microseconds per


670

Figure 11.26. Microseismogram lag used ro indicare cemenr bonding. (Courtesy Welex.) (a) The fjrst arr;val ;s a 5trong signal rran5mitted rhrough the casing befare cementing. (b) After bonding Ihe casing lo Ihe formation with cemen/, Ihe firsl drrival is energy which travels through the formarion.

Coot) oC adjacent shales (when the shale transit time > 100 "s/ft). The transit-time oC shale normally

increases rather stcadily with deptb, cxcept whcre the shale is overpressured (§4.2.8a); a break in lhe shale transit-timc curve provides an indication of an abnormal pressure situation. In carbonates the velocity is mainly determined by the primary porosity and yugular and fractme secondary porosity has relatively little effect. Correction is also accomplished from cross·plots with values determined from densily and/or neulron logs (§11.10.2) and in other ways.

The sonic log is automatically integrated to give the total travcltime; this is shown on logs as ticks at intcrvals oC 1 ms (track 2 in Fig. 11.25). However, small systematic errors lend to accumulale in integralion. Traveltimes from check ShOlS (from a source al lhe surface to a geophone in lhe well) can be used lo remove accumulated errors.

11.7.3. Amplitude and Full-Waveform Lags Whereas the sonic log measures only the traveltime oC tbe first arrival P wave, the amplitudes and

Elastie-wave (acoustie) methods

671 Slowness (pslft) ~40~________~____________~____________~________~24-,O

2900 r

I

Mud41 Measurement

Section

Sonic Logglng Receiver Section

1 3.5ft

Eight Wideband Ceramlc Receiv8Is

8ft

TwoCeramlc ReceiYers

Sonic LoggIng Sonde

2ft

_tI-- •••

TwoCeramlc Transml1ters

Fi8ure 11.27. Array sonie sonde with two transmitters and 70 reeeivers. An example of the output of rhe upper 8 reeeivers is shown in Fi8ure 17.27 (From Sehlumber8er, 1987.)

traveItimes of the various arrivals also convey information. The amplitude of arrivals is plotted in an acoustic amplitude 10&. The entire acoustic wavetrain is recorded on the microsei5mogram and variable density 10&5. Such a log is shown in Figure 11.26. These logs may use only a single transmitter and receiver separated by a greater distance than for sonic loggín&. Logs of this type are also made of the S-wave arríval. An array sonde (shown in Figure 11.27) multiplexes (§4.5.3f) and transmits to the surface for computer analysis the measurements from a number of receivers. lt yields the same measurements as the borehole-compensated and long-spaced sondes, plus additional ones. 1t determines the traveltime slopes, and hence the transit times, by searching for semblance maxima (§4.7.13) of P-, S-, and Stoneley-wave

Fi8ure 11.28. t08 of p., S·. and Stoneley-wave transit times. (From 5ehlumberger, 7987.)

arrivals among the full-waveform Signal5 recorded by eigbt wideband receivers (Fig. 1l.21b). These are displayed as shown in Figure 11.28. The mud transit time is atso measured on fluid drawn through the upper part of the sonde. The S-wave transit time plotted against P-wave transit time helps identify lithologies, as discussed in Section 4.11.5. S-wave arrivals have appreciably higher amplitude than Pwave arrívals, so S~wave transit times can also be detccted by setting the picking threshold bigh enough tbat the S-wave tríggers the time counting. However, where the S-wave velocity is low, mud- and Stoneley-wave arrivals may override the S-wave arrívals. Amplitudes are especially u5eful in determining the quality of the cement-to-casing and cement-toformation bonding. Where the casing is not well cemented to the formation, the first-arrival headwave in the casing is especially strong, but when it is well cemented, tbe energy passes on throu&h into the formation. Figure 11.26 shows a cernent-bond log, a microseismogram log used lo indicate the quality ol cementing. Hi&h-velocity Cormations (.1t < 57 "s/ft) can be logged bebind casing when they are well cemenled to the casing. Sonic log5 are used for fracture detection. Fractures cause a decrease in seismic amplitude, often by

Geophysical welllogging

672

Il'"' ' ' . . ,.

(a 1

-

N

E

...

S

W

. ~

.. it.:.,"

---• '.• _ ..I • •-~

~

• ••

...... ..".

!

~.

!

= ~

~

N

~

_.

1..-:-

S

11 lE .',

5"

f

~

• •

.

,. ¡i

!!

:: e

a:I

•"

O

......

lE ;'.~

I I ,.

~,

N

...fIi,;~"" ..

E

S

(h)

W

N

,• ". ...

.

-&.~

iiiii-. (e)

Figure 11.29. Fracture detection. (a) Fracture finder log showing low S-wave/P-wave amplitudes in a fraetured zone. (After tabo. 1987.) (b) Fracture seen by a borehole televiewer. (Courtesy Cearhart Industries.) (e) Formatíon mieroscanner showing fractures. The m;eroseanner uses a number of eleetrodes on each of (our pads pressed aga;nst the borehole walls to give four swaths of c10sely spaced electric log responses. The sonde was twisting somewhat during this log run. (Courtesy Schlumberger,J

a factor of 10. However, thín beds, thin shale streaks, and healed fractures often give much the same resp(>ose. Fractures dipping up lo 70" also may cause a 20 to 30% lowering of P-wave amplitude and a 60 lo 80% lowering ol S-wave amplitude (Labo, 1987). The fracture-finder log measures the peak amplitude witbin a gate that ineludes botb P- and S-wave arrivals (Fig. 11.29a). Fractures also tend to show on fu1l-waveform logs. Off-centering of the sonde in the borehole may also reduce amplitude due to waves from different azimuths not arriving simultaneously.

An amplitude decrease where 41 is constant may indicate fracturing.

11.7.4. Borehole Televiewer An ultrasonic transmitter-receiver is rotated in the borehole as tbe sonde is raised. The ultrasonic beam, whicb does not penetrate into the lormation, traces a helix on tbe borehole wall. The receiver records the amplitude 01 the refleClion from the borehole wall the borehole wall (Fig. 11.30). TIte display is as

ir

Nuclear methods

673

----. -- --.

__

o

-- _--1

\

I

,1 PI[lOlLr(UhC

I

TRA"II!lOvC(ll~

(a) Figure 11.30. The borehole televiewer. (From Zeman('k f'I al.• ·'970.) (a) Schematic v;('w of the sonde; the magnetometer g;'·es the sonde orienta/ion.

... \

V

were cul longitudinally and then laid out Hat (Zemanek el al., 1970). Tbe result is used to study Cractures (see Fig. 11.29b).

11.8. NUCLEAR METHODS 11.8.1. Nuclear Processes (a) Introduetion. As discussed in Chapler 10. sorne atomíc nuc1ei emit natural radíations and others can be induced to do so by bombardment. The nuclear radiations are in the f.orm oC a, 11, or y rays. Natural and induced y radiation and neulrons possess appreciable penelrating power and are used in radioaclivity logging. Well-Iogging instroments that measure radioaclivity of nearby formations may be considered under three headings: (i) those that detect y radiation resulting from natural radioaclivity, (ii) those Ihat employ artificial y rays, and (iii) those that use neutron sources lo induce nuclear processes. Instromenls employing 1'-ray detectors are calibrated by measuring the detector response at various distances from a standard 1'-ray source. Slow-neutron devices are calibrated by surrounding them with a standard volume of hydrogen-bearing material.

(b) Natural radioaetivity. Natural radioactivity results from Ihe presence of small amounts of U, Th, and 4O K; it is usually lowest in basic igneous rocks, intermediate in melamorphic rocks, and highest in sorne sedimenlary rocks. especially shales. Although the y radiation from either the U or Th series is much higher intensily than tl:at of 40K (see Table 10.3, §10.2.4), 40 K is lar more common and the total background radiation is a\tributable more-or-less equally to the three elements. Gamma-ray emissions ol U. Th. and K are shown in Figure 11.31. The energy spectra of U and Th are broad and relatively comf¡lex, wilh characterislic y rays: 1.76 MeV from U ( 14Bi) and 2.62 MeV from Th 08 TI). The y ray from 40K is monoenergetic al 1.46 MeV. Radiation oC differenl energies can be distinguished by using a 1'-ray spectrometer (§1O.3.4) sensitive only lo narrow bands.

e

(e) Interaction of y rays. An energelic y ray may interact with the surrounding malerial by Ihree distincl processes (see also §1O.3.3b): (i) it may Iransfer its entire energy to a single atomic eleclron (photoeleetrie eonversion), (ii) il may lose a Craclion al a time lo several e\eclrons in successive collisions


674 1.46

Potassium

Thorlum Series

2.62

Uranium·Radium Series

3 Gamma Ray Energy (MeV)

Figure 11.31. Cdmma-ray spectra of potassium dnd the thorium and uranium series. (From Sch/umberger. 1987.)

Table 11.2. Absorption of yrays in various materia/s. Half-value layer (cm) Water

Sandstone. CaCÜ]

Iron

tead

5 10 23

2 5 10

0.7 1.5 3.0

0.1 1.0 1.5

Energy (MeV)

N

E

S

w

N

(b)

Figure 11.30. (Continued) (b) Portion of (rdctures.

d

log showing

(Compton scotteri,,!), or (ili) the 'Y ray may disappear iD the ereatioD oC an electron-positron pair (pair production). The probability of each pracess occurriDg depends OD thc encrgy of thc phOtOD. Thc photoelectric clrcct occurs mainly at low eDergies « 0.2 McV), whereas pair prodUCtiOD can talcc placc only iC thc y-ray CDCrgy is sufficient to creatc two particles of 0.51 McV eaeh (that is, > 1.02 MeV). The three processes are all related to the dcnsity of clectrons iD the medium, that is, to the atomic Dumber Z. Photoconversion is proportioDal to Z', Compton scatteriDg to Z, and pair production to Z2. Thc attenuation of a 'Y ray is thus dctermined by the material through whieh jt passes. MOSl logging sources do not emit y rays oC sufficient energy lo cause pair production. Table 11.2 shows the penetrating power of 'Y rays iD various media. The attenuatioD js mcasurcd in terms oC the material thickncss, whieh rcduces the

0.2 1.0 5.0

inlensity lo sorne fraction of the original. The relalion js exponenlial, as for electromagnetic waves generally:

(11.15) where /l js the absorptjon coefficient. When l/lo .,. 1/2. the thickness oC tbe halC-value layer is xl/2 ., (1/I')ln 2 - 0.69/1'. The average energy oC natural 'Y rays is abaut 1 MeV and lheir range in sediments is roughly 30 cm. About halC ~ 'Y rays detected in a borehole originale within 15 cm oC the borehole walls. CasiDg reduces the inlensity by aboul 30%. (d) Interaction of neutrons. Thc interaction oC neutrons witb surrounding matter is also diagnostic oC the medium. Fast neutrons (kinetic energy > 0.1 MeV) are slowed down by elastic and inelastic collisions with nuclei. Inelastic collisions resolt in the nuclcus (in addition lo aequiring kinetic energy) beiDg leCt iD an excited state; it subscqucntly emils a eharacteristic 'Y rayo E1astic collisions resolt iD a

Nuclear methods

675

Table 11.3. Neutron"Cilpture and inelastic"scattering cross sections with characteristic y ra~'S emitted.

Cross section (barns) Element

Inelast. seatt'

Hydrogen Beryllium Boron Carbon Oxygen Sodium Magnesium Aluminum Silicon Sulfur Chlorine Potassium Calcium Manganese Iron Cobalt Nickel Copper Zinc Molybdenum Silver Cadmium Tin Tungsten Gold Mercury lead Uranium

OA 0.25 0.5 0.7 0.7 0.7 0.8 08 1.0 1.0 1.2 1.4

1.4 1.5 1,5 2.0 2.0 19 1.6 2.5 2.5 2.5 1.8

Capture 0.33 0.01 755 0.003 00002 0.53 0.27 023 0.16 0.52 34 2.1 OA3 13.3 2.6 3.7 4.6 3.8 1.1 2.7 6.3 2.500 0.63 19 99 360 0.7 7.7

Characteristie y rays (MeV)

2.2 6.8 1.3,4.9 3.6.3.9 2.8.3.9 2.8,7.7 2.7.4.g 3.0.5.4 2.0.6.1,6.6 4,4.7.7 1,9,6.4 1.8. 5.3. 7.2 5.5.6,2 8.5 7.9

1.0- 7.0

4.8 4.0-7.0 3.8 6.7.7.4 1.0.3.0

'Average value over the energy range 1 to 14 MeV.

partition oC cncrgy and the rate at which a neutron loses cnergy varies inversely with the mass of the target nucleus. When a neutron has been slowed to a velocity compatible with the temperature of the environment (kinetic energy < 0.025 eV), it is called a rhermal neutron and can be captured by a nearby nucleus, which then emits a characteristic y rayo The probability oC neulron capture depends on the capture cross section, a quantity that is measured in barns (1 b - 10- 24 crrh Table 11.3 gives neutron capture cross sections and sorne of the characteristic y rays emitted on capture.

11.8.2. Gamma-ray logging (a) The gamma-ray log. The y"ray sonde consists of a detector and an amplifier. Early y-ray logging used either an ioruzation chamber or a Geiger counler, but these have been replaced by the more efficient scintillation counter. The last two detectors are described in Section 10.3. A scintillation counter is only - 20 cm in length so Ihat resolution is good. Several measurement units have been employed, such as microroentgens per hour (IlR/hr), counts per

minute, and micrograms oC Ra"equivalent per ton (Ilg oC Ra-eq/ton). but y·ray logs are now calibrated in API units (American Petroleum Instilute unilS. which are differenl from APl neutron units; §11.8.4b). The difference between the high- and lowradioactivity sections oC cement in the API calibration pit al the University oC Houston is defined as 200 API units, Average shales have values around 100 API units. In sediments the y-ray 10g (Wahl, 1983) reftects mainly shale content because the radioactive elements tend to concentrate in clays and shales. Vol· canic ash, granite wash, formation waters that contain radioactive salts. potash, and uranium ores may cause y-ray anomalies. The y-ray log responding to shale and clay is generally correlatable with the SP log. It now oCten replaces the SP log in general logging. especially where the SP is nol diagnostico as in very resistive formations where there is little diC· rerence between the salinities oC the mud and Cormation water, or with oil-based muds. in empty holes, and in cased holes. Figure 11.32 shows a schematic y-ray log. Statistical varialions, significant al low counting rales. are


676 Gamma..,.

+

wall as wilh the y-ray log. TIte spectra of potassium,' uranium, and thorium are smeared out (as shown in Fig. 11.33). Measurements in four or tlve windows permit solving for concenlralions of K. U. and TIt. A portion of a y-ray speclrometer log is shown in Figure 11.34. This log is used to identify and evaluate radioactive minerals. It can a1so be used lo identify e1ay Iypes.

11.8.3. Density Log EfI'eclor lo";n, 1110

r••• +

Umeslone

Figure 11.32. A y·ray lag.

smoothcd out by integralion over a time interval of several seconds. If the hole is logged too quick1y, the smoothing efl'ecl causes barren zones lo be apparentIy shiftcd iD the direction 01 the logging, as iIluslrated iD Figure 11.32, and thin beds lo be missed. TIte logging speed is determined by the measurement time interval se]ecled. It generally defines beds tbicker than 1 m. TIte interface between adjacent barren and radioactive bcds is loeatcd fairly accurately at hall the maximum deftection when the bcds are thicker lban 1 m. For thinner beds the bed cenler is taken as the peak deftection. Because the y-ray log generally defines formation iDterfaces sharply iD both open and cased holes, it is often ron with other ]ogs and production tools so lbat one can correlate the cascd and apen-hole logs and relate other logs to spccific formations with greatcr certainty. TIte y-ray lag is used quantitatively to iDdicate shale percentage and to grade uranium deposits. It is the only logging tool used routinely in the mineral iDdustry.

(b) Natural gamma-ray spectroscopy. TIte natural gamma-ray spectroscopy tool (§10.3.4) measures the energy level oC y-rays and permits determiDing the CODccntrations of K., U, and TIt in roeks. TIte NaI scintillation detector is held agaiDst the borehole

(a) Density log. TIte density lag. or gamma-gamma lag. is used lo delermine porosity. Figure 11.35 is a schematic diagram of a density-Iogging sonde; the sonde is pressed against the borehole wall. TIte bottom of the sonde usually contains 137CS. a coneentrated source of 0.662 MeV y rays; early sondes used a 6OCO souree. A scintillation meter is ... 60 cm above the source. Both source and detector are surrounded by lead shielding except for wiDdows faciDg the wall. so tbat only y rays that have traveled through the adjacent formation reach the detector. TIte spring force that presses the sonde against the borehole wall is considerable and the skid has a plow-shaped leading edge so Ihat it cuts tbrough 50ft mud eakes. TIte sonde oecasionally sticks and then jerks free. TIte y rays from the source interact with the elements in the rock mainly by Compton scaltering, to a lesser extent by photoconversion (the sonde design exc1udes the portion of the spectrum afl'ectcd by photoelectric absorption). The detected y-ray intensity is an exponential function oC the roek density. TIte maximum depth 01 investigation is about 15 cm, with most oí the signal coming from the tlrst 8 cm. Modern devices measure separately the Compton scattering and photoelectric absorption elfects, the former depending mainly on formalion density, the latter on lithology. TIte instrument is calibrated for source intensity and de lector sensilivity by clamping an aluminum, manganese. or sullur bloek to it. Corrections for borehole size are small for hole diameters under 10 in. (25 cm) but amount to - 0.03 g/caf for large holes. It may be used in empty holes as well as those filled with mudo Logging througb casing is gencrally poor (accuracy ... ±0.05 gjcm1). A hole caliper log is an auxiliary output. Because the tool is short, adjacent beds or thin bcds have little distorting elfects. The logging speed must be adjusted iD relalion to the instrument time constant to avoid distortion ol the curves and 1055 01 sensitivity. Because count rate is high, fairly fast logging (2,000 m!hr) is permitted. The compensated density-logging sonde employs two detectors at difl'erent distances from the source. TIte shorter spacing is more afl'ectcd by mud buildup

Nuclear methods

677 dN dE

Energy (MeV)

r-:W ';";71"""-~W~2::--""'-~W~3::--"'T'"-:W::-:-:-4--r----:W=5--""'ISchlumberger Figure 11.33. Camma-ray spectra using aNal crystal detector and energr window.s for examining portions of (he spectra. (From Schlumberger.I987.)

and the ditrerence between the readings Crom the two detectors is used to correct Cor the thickness and density of the mud cake. Compton scauering cross sections per electron are nearly ¡ndependent of tbe atom containing tbe e1ectrons, and so the density log responds to the density oC electrons (Table 11.4). Mosl atoms have nearly two electrons per atomic-weight unit; hydrogen is an exception and a few other elements also depart slightly from this ratio. lOe densi ty log is usually caJibrated Cor fresh-waler saturated limestone, but it also gives quite accurately the bulk density in sandslone and dolomite. Corrections are needed lo give tbe bulk density in sall, gypsum, anhydrite, coal, and gas, ror wbich the ratio of electron densily lo atomic weight deparls Crom that for limeslone (Z/A ... 0.5). Porosity <1> can be detennined from the bulk density Pb by the exact relation

( 11.16)

.'

'1

II

where PI and P"," are the densilies oC the formalion fluid and tbe rock malrix. Density values are too low (up lo 0.08 g/cnr) ror formalions Ibat conlain gas (because the pore Huid is assumed to be brine). lOe matrix density of most clay minerals is c10se enough lo that of quartz thal no difficulty is encounlered in calculating the porosily of shaly sands. Disseminated shale oflen has a lower density than inlerbedded shale. Density logs are used lo predict overpressure (Fig. 11.36) because shale density begins to decrease 100 m or so aboye bigh-pressure sands. The bulk porosily determined with Ibis log includes secondary porosily and porosily lbat is not interconnected. Ir interpreled witb other porosity-sensitive logs (§11.l0.2), sorne of tbese complicating factors can be

sorted out.

(b) lithodensity log. The litbodensity logging sonde employs a beryllium window that passes lowenergy y rays. By comparing counts at very low energies with Ihose al higher energies (Fig. 11.37), this log measures a photoelectric absorption index (Tittman. 1986, pp. 33-6) which is related to lithology of the Cormation.

11.8.4. Neutron Logging (a) Neutron reactions, sources, and detectors. High-energy neutrons from a source in the sonde bombard the Cormations and lose energy mainly in el as tic collisions wilh nuc\ei. The energy loss per collision is greater when the neutron and the nuc\eus with wbich it colJides have comparable masses. Hence, the rate of energy loss (moderation) for fasl neutrons is almost proportional to the density oC protons (whieh have nearly the same mass as neutrons). Consequently, the response is primarily lO hydrogen eonlent, and neutron logs locate porous 2.Ones and determine the amoun! oC Iiquid-filJed porosity, The amount oC hydrogen per unit volume is caJled the hydrogen indexo ACter neutrons have been slowed to thermal energies, they may gaín or lose energy in collisions because their energy is comparable to Ihat of the colliding particle. Eventually they are captured by nuclei. which then emit capture y rays. Where thermal neutrons or capture y rays are measured. the nature and abundance oC the capturing nucleus have a perturbing etrect. Several neutron sources have been used ror the neutron log. These inelude combinations oC berylHum with an a-particle souree sueh as radium, polonium, plutonium, or americium. Most log5 today use

Ceophysical we/llogging

678

been used to produce neutrons by the reactions IH2 +IH2 ..... ¡He) +Olll} IH1 +I H3 ->2 He" +onl

(11.18)

The firSI reaction produces 2.3 MeV neulrons. the second 14.3 MeV neutrons. These neulron sources are monoenergelic and the so urce can be sbut off. Either tbe capture 'Y rays or the neutrons tbemselves may be counted. In porous Cormations saturated with water or oil, the neutrons lose energy rapidly so that the counting flux is high and most oC the response is within 20 cm or so oC the borehole. In low-porosity Cormations the neutrons penetrate Cartber, producing low counting flux, and tbe response range is oC tbe order of 60 cm. Several types of detectors are used. Sorne use a proportional counter shielded by a sheet oC cadmium that absorbs thermal neutrons, so that only neutrons with energy aboye sorne threshold are detected.

Figure 11.34. A natural y"ray spectrometry lag. (From Schlvmberger, 1987.)

an americium-beryllium source with a 460 yr halfIife. Tbe reaction is

(11.17) A 16 curie source produces about 4 X 107 neutronsjs. Charged-partide accelerators have also

(b) Neutron log (hydrogen index /og). The neutron log indicates porosity by determining the amount 01 hydrogen and hence the amount 01 fluid filling the pore spaces. The first neutron 10gs were nondirectional and their detectors responded lo both thermal neutrons and high-energy 'Y rays resulling Irom the neutron capture; however, these 10gs needed correction Cor salinity, mudcake, hole size, and casing. Best resolution was obtained when the hole was small, so that fewer neutrons were lost in the mud column. Sometimes the source-detector spacing was increased Cor operation in large diameter holes. The sidewall neutron /og is a sidewall device (like the density logging sonde); it was used in empty (but not cased) hotes, but it is now obsolete. It employed a proportional counter so shielded that it measured only epithermal neutrons (energy .. 0.4 eV), whose energy is greater than that oC the thermal neutrons invotved with capture. Hence it was not perturbed by neutron absorbers, such as ch10rine and boron, and was not sensitive to hole size. However, the count rate oC epithermal neutrons was smalt so the detectors had to be close to the source and consequendy depth of penetration was smalt and invasion effects large. . The compensated neutro" log measures thermal neutrons. It employs two detectors spaced at different distances from the source, which makes it possible to correct for the effects oC mud cake and hole roughness (rugosity). It has greater depth of penetralion than the sidewall toot and can be ron in either cased or uncased holes but not in empty hotes. Jt is sensitive to shales, which often contain small amounts of boron and other etements with high capture cross section.

Nuclear methods

679 Density 2·22-4 H2·HO

SandSlone

Figure 11.35. Oensity lag schemiltic i1nd typicilllag. Table 11.4. Camman elements encountered in

hydrocarbon exploration.

H

e N

o Na Mg Al Si el K ea

Z

A

l/A

1 6 7 8 11

1.007 12.011 14.006 15.999 22.989 24.312 26.981 28.085 35.453 39.098 40.08

0.9921 0.4995 0.4998 0.5(0) 0.4785 0.4934 0.4818 0.4984 0.4794 0.4859 0.4990

12 13 14 17 19

20

The dual porosity neutron log employs two detectors lO measure tbermal neutrons and two detectors to measure epithermal neulrons, oeulrons of both energy e1asses being measured at different distances from the source (Fig. 11.38). The additional measuremeots permil correctioos for shale content and saJinity, and also yield improved gas detection in shaly reservoirs. Neutroo logs are usually plotted either io API oeutron units or in "limestone porosity," which assumes tbat the matnx is limestone. API neutron units are based on measurement io a standard neu-

tron pi! where 19%-porosity water-filled limestone is defined as 1,000 API neutron units. Correction is made for mud weight, temperature. hole-size varia· tions, and saJinity. The salinity is usually taJeen as !hat of the formation water excepl for invaded zones, where il is assumed lo be Iha! of the mudo A plot of a portion of a dual-porosity neutron log is shown io Figure 11.39. Neutron logs are affected by all protons, ineluding those in bound water associated with shales or water ol crystallization, such as contained in gypsumo Consequently, shales and gypsum have distorting effects. Because neutron 10gs are affected by Iithology, !he best porosity values are obtained from !he combined interpretation of neutron logs with other porosity-sensitive 10gs, especially with density logs (§11.10.2); this is particularly useful with a density 10g to indicate gas in the pore spaces. (e) Pulsed- neutron logging. Pulsed-neutron log5, which inelude the thermal-decay-time-Iog and neutron-lifelime log, record the rale of decay of thermal neutrons. Chlorine, the most common element with high capture cross section (Table 11.3), is fouod in most formatioos and is the principal absorber of thermal neutrons. Consequently pulsed-neutron 10gs mainly determine the amounl oC chlorine, that is, Ihe amount of saJine water presen!. They thus accom-


680 Gamma Ray ~u

....

Bulk Densily ~

2.8

(Low Z) (Med

Z)-4~.1

Region 01 Photoelectric Effect (1/ and Z Information)

(High Z) -b14-+-'_~

Region Of Compton ScaHering (Q Information Only)

cpslkeV

1.4U"

Figure 11.37. Camma-ray energy speclrum showing Ihe two windows in which measuremenls are made. The counts in the high-energy window H depend on densi/y only. whereas /hose in the low-energy windows depend on both densi/y and a/omic number Z al the capturing atom. (From Snyder and Fleming. 1985.)

Thermal Detectors

1

1•

Source )16 Curie AmBe Epithermal

Detectors

Figure 11.36. Densily log. wilh overpressured shale below 5,490 fl. (From Schlumberger, 1987.)

1

Figure 11.38. Schema/ic of dual-porosity neutron-Iogging sonde. (From Schlumberger, 1987.)

681

Gravity, magnetic, and (hermal methods

i' __________ 1JI ir.S Caliper HoIe 0iIm. in.

~

Del18ily Porosily % Li..-one MaI'¡x

"2

Gamma Ray

-15

O

Neutron Porosity %

API UnH.

u.n.tone Malrix

150

O

15

30

4~

___

ªº- ____t.L ___ º____-_l 5

'? f

Ji,,,

,, ,I, ,,• •,

,I \, ,,,, , ,,, , ,I

~

-.;;;;

~

(~ ~

I

,, ,

I

slowed to thermal energies and caplured. whereupon capture y rays are emitted. Tbe y rays arriving during a fixed time interval after the burst .are detected a short distance away Crom the source. Measurements are made over two or more time intervals (Fig. 1l.40) to determine tbe die-away time; tbis permits correcting Cor background effects and determining the rate oC thermal-neutron capture. Absorption by the borehole fluid and casing primarily afrects readings made soon after the burst; absorption effects can be largely eliminated by delaying the first measuring intervalo The gamma-ray spectrometT}' log involves a 256channel spectral analysis oí either elastic scattering or capture y rays in two modes oC operation. It gives water saturation ¡ndependent oí salinity and provides the data for determining the ralios of various elements. such as C/O and Si/Ca, by measuring their capture y rays. This tool can also be used in analysis for coal, Cu, Fe, and U.

~

I I

.~

I

I

\

I

,,•

,.

--

"'- ... ,

I I I I I

/

"

1!

~-, _........-_ ..:

-......

--"-.•

.....

¿: -

.'

Figurf! 11.39. Portian of a dual-porosity nf!utron lag. (From Schlumberger, 1987.)

plish essentially the same purpose as resistivity logs and can generally be correlated witb tbem. Their advantage over resistivity logs is tbat tbey can be used in cased holes. A neutron generator emits a burst of high-energy neutrons, as in Equation (11.18). Tbese are rapidly

11.9. GRAVITV, MAGNETIC, ANO THERMAl METHODS 11.9.1. Gravity and Magnetic Field logging Borehole gravity measurements were discussed in Section 2.3.4b. Borehole magnetic measurements (Silva and Hohmann, 1981) can be made with fluxgate or proton-precession instruments (§3.4.2 and §3.4.3). Vertical-gradieot measurements can also be made in boreholes.

11.9.2. Susceptibility lag Borehole instrumentation is similar to the field susceptibility meter (§3.3.8a). The solenoid is wound 00

~

JI

!l '"

,<

r

~

..

.;',

u '¡; ~

§ ~

..E

~

~/

'1>"'Jt

:;" ,.'

~I'"

~

t.?

,.'.

~L:Jl~Jl4 I S I

6

~~2J141

Gates

Figure ". 40. Pulsing and gating parameters for pulspd neutron lag. A burst of nputrolls occurs f!very 800 IH. (From Sn)'der and Fleming. 1985.)

Geophysical wel/ logging

682

1 kW

Envelope

PoIarizing Pulse

(nol lo seale) 2.2.kHz Signal

I Polarization -2 seconds

\

Ringing

Figure 11.41. Nuclear-magnetic-resonance signal decay. Signals from resonances other than those of the free fluid decay befare measurement begins. The signal decay is exponential so that the free-fluid index (,) can be found by exlriJpolaling the log of the decay back lo zero time. (After Pinnington, 1981.)

a core of low-reluclance malerial and connecled lo one arm of a Wheatslone bridge. If the bridge is balanced in a barren environmenl, the presence of formations of anomalous susceptibility or conductivjly unbalances jI, because the susceptibitity etrecl changes the resetance and produces a quadrature voltage whereas the conductjvity produces an inphase voltage. lbe etrects can be separated by phase detectors and logs of susceptibility and conductivity displayed separately. lbe susceptibitity lag is nol affected by mud resistivity and can be ron in dry holes. lbe conductivity lag compares favorably with resistivity logs for p" > 2 Om. Depth of penetration is about equal lo the coil length. Anomalous susceptibility may indicate the presence of magnetic materials, such as magnetite, ilmenite, and pyrrhotite. Good correspondence be· tween SP and susceptibility 10gs jndicate that porous zones have been enriched by ground-water deposi. tion al magnetic minerals. 11.9.3. Nuclear Magnetic-Resonance Log

lbe proton.precession magnetometer was discussed in Section 3.4.3 as a device lo delermine the magnetic field strength, which is proportional to the measured Larmor lrequency. [Eq. (3.30a)). When, in the measuremeot cycle, the impressed field is removed, the protons with aligned spins gradually get misaligned (and the protoo signal decays) as the protons are affected by somewhat random local magoetic fieJds. lbe time required for the proton reso-

nance signal to decay following the removal 01 an impressed field js a measure 01 the environment of the protons. The nuclear magnetic-resonance log measures the decay rale lo determine this environment. An impressed field at a large angle lo the Earth's field is applied for about 2 s to orient the prolon spins, and then the impressed field is cut otro lbe signal due lo the residual orlented spjns (Fig. 11.41) precessing about the Earth's field is measured beginning - 2S ms later (to a1low transients to die out). lbe signal decay is affected by the protons in the borehole fluid, protons in moveable lormation fluids, and protoos bound to the lattice. lbe borehole fluid signal decays very rapidly because the drllling mud contains fioely divided magnetite and the contribution of the borehole fluid is over before the measurement perlod begins. Protons in solids or bound to surfaces also have very short decay times. lbus the only significant contrlbutioo during the measurement perlod is that due to the protons in fluids that are free to move in the rack's pore spaces. lbe amplitude of the decaying signal is thus a measure ol the amount of fluid (hydrogen) that is free to move. lbe measurement yields a free-fluid index (FFI), a measure 01 the porosity occupied by Cree fluids ~. The rate 01 signal decay furlber indica tes the type of fluid (water or hydrocarbons). Combining these measurements with data from other 10gs permits estimates 01 the Irreducible water saturation (trapped water which is not free to ftow), the permeability, and the residual oil saturation (the oil that can not be

Well-/og interpretation

683

flushed out by invading fluids) in the invaded zone (Tittman, 1986).

¡

30

X'~I/

20

,,0.,' ~ ~,

'VI'
~

?.,/

,.o
.~

v

1-<:>.(

o

~I.

y)~7r-

11.9.4. Thermal Logging Measurement ol temperature has been employed mainly to determine large-seale terrestrial heat flow, but it can also be used to locate thermal anomalies eaused by ftuid ftow, abnormal radioactivily, and oxidation regioos. Various types of thermometers have been used, ineluding resistance thermometers and thermisters.

0\.

<:> ' / ._--

-

h"

--\7<' ,y J

~>P~~
)( 11.10. WEU-LOG INTERPRETATlON -10

11.10.1. General Interpretation ol welI logs for mineral objectives is usually qualitative, that is, locating and eorrelating anomalous zones. Interpretation for oH objectives, on the other band, is bigh1y developed. A variely ol methods is employed and an enormous amount of data is accumuIated. Oddly enough, geophysicists playa miDor role iD oil well-Iog iDterpretatioD. Tbe logging cODtractor usual1y carries out routine iDterpretatioD, whereas detailed assessmeDt is left to a special1y trained oil-company geologist who has all the pertiDeDt data (iDcludiDg elassified data) at bis disposal. Detailed log interpretatioD for the evaluatiOD of porous and permeable formations for potential production is beyond the scope of this book. Inspection of conveDtional electric logs (SP, normal, lateral, microlog, iDduction) ofteD can locate, correlate, and ideDtify formatioDs of iDterest. WheD this iDformatioD is combined with data obtained from additionallogs (caliper, acoustic, radioactivity), the iDterpretatioD begios to be diagnostic and quantitative. FiDally, iD favorable situations, quantitative estimates of porosity, ftuid conteDt, water: oH ratio, and so OD can be made. The results are cODtrolled by the combinatioD of logs available and borehole and drilliDg factors.

f-<:\. -20

~/ --~~

~~1"

r

o

. 10

~ (neutron

20

30

101)

Figure 11.42. Porosily cross-plot. (Courtesy Schlumberger

Ud.) PorosUy ('Yo)

Figure 11.43. Moveable oil plot. (Courlesy Schlumberger

11.10.2. Combining Measurements from Several Logs Each log is affected by a number of parameters (Hoyle, 1986) of Ihe rocks and boreholeconditions, and differeDt kiDds of logs depend on the same parameters. By USiDg combinatioDs of logs, the iDterpreter hopes to separate these effects. As an example, consider the measurement of porosity. Resistivity, sonic, density, and neutron )og measurements all depend on both the porosity and Ihe Iilhology, but iD different ways. Cross-plots involve plottiDg resuIts lrom different kinds 01 mea-

Ud.)

surements asainst each olher. Figure 11.42 shows plots oC the porosity calculated from density and from neutron logs. These caIculations, in limestone porosity units, presumably give correet porosity values ir the Iithology is Iimestone (the limes tone curve on tbis graph is linear with 45° slope). However, if the lithology is not Iimestone. the porosity is in error, but by different amounts depending on the nature of the Iithology; thus the location of a plotted point on tbis graph gives both the Iithology and the correet porosity. For mixed lithologies. interpolation be-

684

tween the curves gives tbe porosity and tbe average litbology, altbough tbe lauer usually involves sorne ambiguity. Hopefully tbis can be further reduced by cross-plotting different log combinations. Tbe fact that tbe porosity determined rrom difIerent logs is different is used in a moveable-oil plot (Fig. 11.43). Total porosity (~,) is calculated from a sonic log (§11.7.2), apparent water-filled porosity (1/>,.) from a deep-investigation resistivity log such as a laterolog (§11.2.3), and flushed zone porosity (~%O) from a shallow resistivity log such as a microlaterolog (§11.2.S). Tbe difference between tbe latter two curves is interpreted as "moveable bydrocarbons" and tbe difference between the first two as .. residual bydrocarbons." Tbe concept oC cross-plotting two sets ol measurements to separate tbe effects oC two Cactors can be genera1ized to separate more tban two factors. Extended analysis generally requires a computer witb lookup tables of empirical relationsbips. Several analysis programs are now available. Tbe Saraband* sand-shale program utilizes five cross-plots and tbe Coriband· complex Iitbology program utilizes many more. Tbe "wild-card" in most analyses is cIay content. Ions in tbe layer ol water surrounding cIay minerals contribute to tbe rack conduetivity, requiring modifieation of relations, sueh as tbe Arebie equations, wbieh assume tbal tbe Cormation water is tbe only conductor present. A dual-water model allows Cor botb tbe bound water and the formation water. It forms tbe basis for several eomputer-analysis programs (Volan·, Cyberlook·, and Global·).

11.11. FIELD EXAMPLES Although tbe detailed interpretation of well-Iog data is beyond tbe scope of tbis book, a Cew simple examples may indicate tbe possibilities. Tbese are taken mainly from Pickett (1970). Tbe variety of mineral s encountered in tbese examples iIlustrates tbe versatility of logging techniques, especially combinations ol logs.

11.11.1. Analysis of an Oi! Sand Figure 11.44 shows SP, resistivity, and aeousticvelocity 10gs Cor a Miocene sand section containing gas and oiJ. Tbe SP log has a distinct break oC 100 mV from positive to nesative at 9,270 ft, indicating shale aboYe and sand below tbis (compare witb F~g. 11.12). Having found tbe mud filtrate resistivity by otber means, we can use Bquation (11.9) to get p..; it is about 0.06 Om. Using a combination of tbe lateral and normal curves witb departure charts to correet Tradename oC Schlumberger, LId.


for borebole, invasion, and tbin-bed effecIs, we obtain the formation resistivity P" It is about 300m from 9,272 lo 9,308 Ct and 0.6 Om between 9,308 and 9,3S0 ft. Finally, by means oC Equation (11.3), the water saturation S.., i5 Cound to be about 15% between 9,272 and 9,308 Ct and 100% below 9,308 CI. Significant qualitative inCormation may also be derived from tbese log5. Separation of tbe two microlog curves (note that tbe electrode spacing is different) indicates sections tbat are more permeable. Tbe resistivity logs suggest wbich oC tbese contain gas and oil (because oC tbe resultant bigh resistivity). In tbis ratber simple example using only Cour logs, we can estimate a possible 15 ft oC gas-hearlng sand and 15 Ct of oil-bearing sand, botb having an average porosity oC 30% [calculated from the sonic . log and Eq. (1l.14b)] and a water saturalion of about 15%.

11.11.2. Ana!ysis of Carbonate Section Tbe section in Figure 11.45 consists of dolomitic sands, evaporites, carbonates, and sbaly carbonates. Gamma-ray, sonie, SP, and induction logs are shown at tbe leCI. Tbe break in the SP curve is less definite tban in tbe previous example so tbat an estimate oC p.. would be unreliable. TIte induction log gives a reasonable value lor P, in tbe sands, but not Cor tbe bigher-resistivity carbonates. Tbe porosity estimate Crom tbe acoustic log was questionable because tbe values oC V¡ and V," for Equation (11.14) were not well established. Tbus an evaluation of the carbonates was not possible witb lbis log combination. Neutron and focused resistivity logs were added to aid in determining .p and Pr in the carbonates. In botb these devices tbe relative response between different zones was reliable bul tbe absolute calibration was noto Sand porosities obtained from tbe acoustic log were used to calibrate the ncutron-Iog response and tbe carbonate porosities were then determined. A similar calibration oC tbe Laterolog-7, using the induction-Iog response in sands, permitted estimates oC P, in the carbonates. Values of p.. were obtained by measurements on cores. Tbis interpretalion does not seem as satisfactory as in the previous example; more logs would be required Cor a more reliable evaluation.

11.11.3. Coal Identification Coal may be idenlified by bigh resistivity, low density, and low acoustic velocity. Electric logs were used as early as 1931 for tbis purpose. Figure 11.46 shows a section containing bituminous coal beds from a well in Colorado. Tbe logging program included density, sonic, induction, 16 in. normal, y-ray

685

Field examples

SP

+

A

Nonnals

lateral

B

e

o

Mlcrolol

sonlC

I( . - , f - - - - - - - ~_.

9250

\ f'

-~

-

~__

--

L I

l

- --

r

(""

1,

.. S·¡·;-;····

~b

lOmV,..

-

9300

-

_~-:

___111

A' .......

~

'~

"'- - -_\... ...

í{

(

- - - '., -,

~

!l:

~

\

>-i

1-

r-'"

"

...

~.

1. ~

~:'

{

--

c~

>.-'

I

9350

.... ~"

"

1

f

Depl h II (rll 1;1

-

(

_--- --- .. "

.--,- "

r-

,

01

(ft/ms) 8 9 10 JI

(

Figure 71.44. Log suite in Miocene sand section containing oil and gas. Ful/ .Kale for the 16 in. normal (salid curve) is 10 Ilm. for rhe amplified 16 in. normal (.mlid h,Khured) ;s 100 !1m. for rhe 64 in. normal (dashed) IS 10 IJm. for the amplified 60l in. normal (crosses) is 1,(100 IJm. for the 18 fr 8 in. lateral (solid) is 10 Ilm, for the amplified 18 ft 8 in. lateral (dashed) is 100 Slm. and for the microlog inverse (solid) and for the micronormal (dashed) is ·,0 Slm. Induction log 10 100 11m

SP

Neutron log

LatrroJol

O_ _ 2oooUm 0·····20.000 !1m

\

Figure 11.45. Log suite in Minnelusa oil·bearing sand section. Zones A. B. and contain oil.

(not shown), and SP logs. The first three correlate particularly welJ with coal seams. Generally the ÁI values from the sonic log are larger for coal than in the adjacent shale beds. although the contrast depends on the coal grade and depth. both ol which alfect the compaction. For example. lignite produces a larger ÁI excursion than anthracite, but increasing depth oC burial will reduce the variation. The same factors atrect the resistivity log. because higher grade coal and deeper beds con· tain less moisture and consequentIy have higher resistivity. The density 10g is probably the most reli-

e

able. because coal density is considerably lower than that oC the adjacent beds, ranging Cmm a maximum oC 1.8 for anthracite to less than 1.0 g/cJtr Cor Iignite. The SP curve occasionally is anomalous op· posite a coal seam.

11.11.4. Evaporites Caliper. y-ray, and density curves through a section oC interbedded shale. halite, and anhydrite are dis· played in Figure 11.47. HaUte and anhydrite are nonradioactive evaporites. The y-ray log would be

686

Geophysical well logging Formation density 150

Figure 11.46. Identification T;xier and Alger. 1970.)

),-,.y CAPI unil.)

o,

IOmV

- +

100

coal beds by density. sanie. and resistivity logs. (From

Deplh

m

O

Induction-cleelricalloa

Sonic (PHC/ft) 100

Bulk density CI/cm') .~

loS

.1

Cali¡ler bole diameter (in.)

~-\ --------.\"!~ .... f".~

j:::~ ~ I ~~ f'

t::

ts P¡r ~~

~~

...r-

~~

r·

~ ~~~ t:: ¡=i:

l.'

':

L", I·~

t

~

~ ~ ~ ~.'

~ ~ ~~~

c::

-~

!

~

~

~

~

rl

~~

-

~:

~,.

~

---

~:.

~. ~,

~

oc

11

~ r· b, ~ Anhydrile

I

.if.

-L.

~

_Halite

R='-.:.:] Shale

Figvre 11.47. Identification o( evaporites by density. r'rar, and caliper logs. (From Tixier and Alger. 1970.)

687

Field examples Rrlalhe i'-ray

or-'J~,_nl_tn_"-,-IY~~

Re,i,liviIY

Malnelie

O (kllm) 12

susceptibility

Magnelile ( ~'.)

o

10 20 30

Ca"ns

~

lOO f-7"'-----~

Chtrl and sla1t

2001---:>~-~

f---I

,. ~

Silicale ,Iale

300 1-+-------1 Magnetite

che"

Magnelite chen

Figure 11.48, Gamma-ray. susceptibility, and resistivity 1085 in chert and slate beds.

more useful for potash, sylvite, and similar varieties containing potassium. The y-ray log identilies tbe shale beds because of their higher radioactivity. The caliper log shows hole en1argement in tbe salt and shale zones. Anhydrite, witb a density of nearIy 3 g/cm', is c1earIy identified by tbe density log, whereas the interca1ated shale is indicated by coincident higbs and lows in the y-ray and density curves.

11.11.5. Sulfur Sulfur, which occurs mainly in limestone, may be identified by the density or acoustic log because of its low density and low velocity (large Al). The neutron log is also useful in sulCur detection. Occasionally the neutron log is replaced by a resistivity device for porosity determination. In Cormations containing only limestone, sulfur, and water, two of these logs may suffice to provide a quantitative evaluation as well as identification. Where other rock mineral s are also present, it may be necessary to employ all three logs.

11.11.6. Slate and Chert Figure 11.48 shows resistivity, y-ray, and magneticsusceptibility 10gB through a section of slate and chert beds. The y-ray log clearly shows the slate because oC its K content and the susceptibility curves show the chert because it is enriched with magnetite.

11.11.7. Mineral Exploration The Lac Dufault orebody northwest oC Noranda, Quebec, is a classic example oC the use oC geophysical well logging in mining exploration where no other technique is Ceasible. Massive sulfides, pyrite, pyrrhotite, chalcopyrite, and sphalerite are Cound in gentIy dipping contacts between rhyolite and andesite at depths greater than 1,000 Ct. Although the lateral extent oC these ore zones is small, the high grade oC chalcopyrite and sphalerite makes an aUractive mining operation, provided they can be located. However, a deep-hole diamond drilling program on 200 ft centers is eXlreme1y costly. Salt (1966) described a logging sludy that was carried out in 1962 using vertical-loop EM, horizonlal-loop EM (Iarge Turam-type transmitter loop), induced-polarization, and resistivily methods. The problem was to establish the existence oC a nearby mineralized zone by logging a hole Ibat missed it. It was found that any one of Ihese melhods would detect an orebody roughly 400 x 400 ft in horizontal extent and 150 fl thick using a vertical drilI hole within 125 ft of the edge of the orebody. However, it was difficult to determine the direction of Ihe orebody wilh respect to the hole and lo distinguish between massive sulfides and other conductors oC unknown character. A plan oC the orebody and diamond-drill-hole (DDH) locations can be seen in Figure 11.49a.


688

NIIOe eNI39

eNI62 eNI63

eNISI e NIl3

eNI70

eNI~ eNI42 eNI28 eNI38 NI25e

eNI24 eNI26

NUle

eNI37 eNI27

eNI~NI32

eNI40 eNI41

NI0ge

e

eNIS2

eNI54 eNI65

eNI64

~

Shan 200

O

!

200 n

!

N 10. .

!

(a)

OOH

DOH

NI35

Nm

3

lO

30

300

1000

.-".. -_.- ....... '. ' .......

10,000 JO,OOO

3000

.- -- .... -"

,"

.... . '

•••••• Apparent resistivity

-

,am'

Metal factor

Figure 11.49. Combined IP- electrical survey to laca te orebody at depth, Lac Dufault, Quebec. (From Salt, 1966.) (a) Plan of orebody and diamond-drill holes. (b) IP logs in DDH N125 and N735.

Field examples

689

o --- EaS! positive (curren! ftow E-W)

Nonh positive (current ftow N-S)

-

1000

.,, , ,.

1200

I

,I

... -. -."

_ 1400

-200

o PotenliallmVI (,.\

Figure 11.49. (Conrinued) (e) log of potential in DDH N13s.

Two logs from this study are shown in Figure 1l.49b and c. Figure 1l.49b shows metal factor and apparent resistivity measured with a frequencydomain IP unit. Large cable-coupling effects made it necessary to place the current and poten ti al e1ecIrodes in separate drill holes (N125 and N135); with one current electrode at a distant poinl on the surface. a second currenl e\ectrode was lowered down one hole and the two potential electrodes down the other al the same time. In Figure 1l.49b the anomaly around 400 ft is not explained, but a definite peak at 1,100 tt corresponds to the massive sulfides east of Ihe electrodes. Both the MF and p. peaks decrease slowly to 1,300 fl, indicating thal the sulfides tie mainly below 1,100 fl. The response al 1,400 ft is caused by disseminated sulfides below the main ore zone. The second log. Figure 1l.49c. is essentially the vertical potential distribution produced by currenl ftow from two orthogonal pairs of current e1ectrodes (connected altemalely) al tbe surface. One potential eleclrode is fixed near the top of DDH N135 and the other is lowered in the hole, while direcI currenl ftows from north 10 soutb between surface e\ectrodes 2,000 ft apart slraddling the holeo Then the moveable

potential electrode is raised, with current ftow E- W between similarly spaced current electrodes. In botb curves the potentiaJ increases steadily downhole to about 850 fl. The E-W potentiaJ curve remains relatively constant between 850 and 1.050 ft and then faJIs off at greater depths. This effect is not apparent in the N-S curve, allhough Ihe posilive gradient is not so pronounced below 850 fl. Prom the differences belween tbe two curves and the ~irec tion of currenl ftow. one concludes thal a conductor is located east oC drill hole N135 and has a depth exlent no greater than 200 fl. Neither lag is conclusive by ilseIC. nor were the other techniques used in the survey. However, the reduction of drilling costs by aJlowing increased hole spacing would be significant and the possible control of future drilling programs by immediate logging is attractive.

11.11.8. Borehole Methods in the USSR Borehole geophysics apparently is essentially routine in the USSR (Zielz et al., 1976; Buselli. 1980). Well logging is carried out during detailed surveys with all types of mineralization; this is said to reduce by 50%


690 Table 11.5. Well-Iogging techniques used in U55R. Borehole logging method

Purposes for which used

Various nuclear IOg5 Gamma, gamma-spectro5copy Gamma-gamma Three-component magnetics and magnetic 5usceptibility IP, resistivity Three-component EM

Qualitative, quantitative mineral valuation locate U, Th, K, evaluate formations Determine density. porosity, clay content Dip, strike measurements, evaluate formations, locate and trace missed beds Structure, continuity, sulfide evaluation Outline structures, locate missed conductors Determine depth extent 01 sulfide bodies

SP I

.,.

=0

c:¡! c:¡! u

~

;¡; c:

~,..

.., . N

u

I

:a~

j

I

.!

'c

- .. .§--

.!!

ce

8

"ª

Ó

"1

'"

d~

c: ..

d:Ó

¡;¡ d:

I.!I u'C

·S

~

08

!a

•

00

I

.~

'ó

..

i!

l:

.!:i

.~

!

.!I

.~

'€

l: Figure 11.50. Po/arization curves for a copper- nickel and pyrrhotite ore bodies. Cvrrent I is in amperes and contact po/entia! r/> is in volts.

tbe drilling required to evaluate an orebody. Table

11.S lists metbods and applications; tbe last four metbods in this table are used between holes and for mise-a-Ia-mosse applications as well as in single holes. AD acoustic shadow techDique uses an exploding wire source in one bole and receivers in another a few hUDdred meters distant. It is designed to outline faults, fractures, and anomalous beds. A radiowave shadow technique using frequencies in tbe range 1 SO kHz to 40 MHz is used to locate conductors in hole-to-bole measurements. A piezeoelectric metbod detects seismic and electrie signals from a small explosive charge; it is used to trace quartz veins, spbalerite, and cassiterite mineralizatiOD between adjacent holes up to 120 m apart. A CODtact metbod 01 polarization (somewhat analogous to mise-a-/a-nwsse, see §8.S.4d) uses one

current electrode downhole in contact wilh mineralization and tbe other on tbe surface; voltage measurements are made on a surface grid as current is increased from O to - 2S0 A. The breaks in a curve (Fig. 11.S0) represent diagnostic contact potentials of various minerals; tbese are identified by extending the linear segments back to the .¡, axis. The maximum current required lO produce complete polarization curves indicates whether the mineralization is economic.

11.12. PROBlEMS 1. In the example in Section 11.11.7, is it possible to concJude from tbe IP log that the conductor is

691

Problems

definitely located east of drill holes N125 and N135 or merely Ihat it is either easl or west? A direct-current source was used with the surface eleclrodes for lhe resislivily log in hole N135. By skelching the currenl lines and equipolentials. allempl lo reproduce the curves in Figure 1l.49c. How would you change either curve ir the elecIrode polarization were reversed? Sketch Ihe E- W pOlential curve if Ihe drill holes were easl oI Ihe orebody. What difference would it make ir ac were used? 2. The IP log shown in Figure 11.51 was obtained in a base-metal survey in northweslern Quebec. The mineralization consists of pyrile (up lo 20%) and chalcopyrite (maximum 2.6% Cu) in a hosl rock of tuffs and agglomerates. One currenl and one potential eleclrode were lowered in the hole with

Figure ·/1.5/. IP lag in northwes/ Quebec

T I

Mon""l~trod.

I

\

80 1---+--1-4·-1

'-

---

$=.

90 1---1---+-+--1

o::::

o:

1I01---I----'l"__..--I

1201---+--A---I ~

i

r

1401---+--+1

~

1501----I---4J ~

1601----1---+1,--1

1101----1----11---1

-UOmV -100 -50

,.,

o

,00 lb,

200

]00

400 m'"

l"

Figure 11.52. Experimental logs in base· me tal afea. (a) SP lag. (b) focused electrode sonde. (e) Monoeleetrode sunter using current-return elcctrode 80 to l/O It deep in adjacent hole.


692

+100

so

o

Millivolts

Millivoltl

~LO.~'~='~'~~'~~'~~'~ O -100-lOO-300-~-SOO

Millivoltl

figure 11.53. SP'logs in base-metal zones.

a fixed separation oC 2 ft; the second currenl and potenlial electrodes were located on the surface at a considerable distance from the drin collar. Identify tbe mineral zones and if possible distinguish between chalcopyrite and pyrite sections. 3. Sorne results from an experimental logging study in base-metal areas are shown in Figure 11.52. The minera1ization here occurs in two steeply dipping zones, one containing pyrite and chalcopyrite, the other mainly pyrite. The diamonddrill hole from which the logs were obtained was inclined approximately 60°. The SP log is conventional with one fixed electrode in the hole jusI below the water level (and below the casing). The focused-electrode sonde, similar to Figure 11.6a, was made from 1 in. diameter lead-antimony pipe with PVC spacers, with 2 ft guard eleelrodes, 3 in. measuring electrode, and 2.5 in. spacers. Current return was lhrough tbe uphole fixed SP eleelrode. The currenl source was a small 60 Hz motor generalor. The monoelectrode curve in Figure 11.52 measured the currenl between lhe eocused-eleetrode system and a seeond hole (previously logged and found to be essentially barren) in an atlempl to establish minera1ization continuity. The eleelrode in the second hole (an aluminum rod) was long enough lo slraddle tbe main mineral inlersections; specifically, it exlended from 80 lo 110 el. The lwo holes were about 100 fl apart. Identify tbe minera1ization zone or zones. Is there any

indication of laleral eXlenl? Caleulate the effeelive resistivity at a few points on lhe focused resistivity eurve from the formula of Dakhnov (1962),

Lm)( V) (L~ - 1)1/2

P. - 2 rr ( L, 7 Lm

log(

L: - 1)

is the length of the facused electrode, where L, is the ratio of lenglh to diameter of the eleelrode assembly, V is lhe potential ol lhe focused electrode (110 V). and 1 is lhe currenl in the facused eleetrode. 4. SP logs al a base-metal property in northweslern Quebee are shown in Figure 11.53. The host rocks are andesites, diorites, and rhyolites, Ihe overburden is sand and c1ay. The minera1ization consists oC pyrite. pyrrhotite. sphalerite, chalcopyrile. ando in places, bands or magnelite. An earlier surface SP survey showed no anomaly. What is your explanation for the barren surfaee SP? Given the additional inrOrmalion Ihat massive sulfides were Cound Crom 25 lo 31 ft and Crom 65 lo 89 ft in a Courth hole nearby, would you change your explanation? Can you aecount ror the pronounced positive excursion in holes V77 and V86 between surface and 200 ft? Make as complete as interpretation as you can. 5. Use oC airborne and ground radiometrics for gold exploration has been reported in Soviet journals since 1970; these indicate a strong association

Problems

693

: •:¡ ~

I _ "-20%

""lIe

m

OU-cb etockwo,k

(Ir)

I

j

_ "-at' ""lIe

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(b) Figure 17.54. Gamma-ra)' spectra llogs in four bOff'holes in Ihe Larder Lake gold camp, norther n Ontario. (a) L08s in boreholes 8L-80-25, (b) 8L-80-4 0

694


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, ....,..

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(d) Figure 11.54. (Continued) (e) BL·80·31. (d) BL·80-30. (From Mwenifumbo, Urbancic, and Killeen, 1983.)

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Figure 11.55. Logs ¡rom three holes in the Pascalis gold drea m~ar Val d'Or in norther n Quebec. For the (ir5t hole, gold and copper assays are shown; for the second hale, SOld assays ,ue shown. (a) Logs in boreholes 83 - 22.


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lb) Figure 11.55. (Continued) (b) 83-102.

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697

Problems

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between gold mineralization and potassium a1teration rones. Mwenifumbo, Urbancic, and Killeen (1983) applied y-ray spectrallogging in tbe Larder Lalte gold camp in nortbem Ontario. lbey used a Geological Survey 01 Canada logging unit described in Conaway, Bristow, and Killeen (1980). Results from lour boreholes are displayed in Figure 11.54 which include total count (TC), stripped K, U, and lb (K I , U., and lb.) (§10.7, problem 4), gold assay (Au), and core logs sbowing pyrite mineralization. lbe geology consists of flow-type pyritized and silicified rones lying in a1lered volcanic flows and tuffs. Gold correlation with pyrite mineralization is very good. Wbat can you say about gold association witb 4O K7 lbe ratios Th/K, U/K, and U(lb are used as halo indicators around mineral deposits; do tbey correlate witb gold? What logging tecbniques are suited for detecting tbe pyrite zones? Sorne elementary statistical analysis should be usefu!. 6. Pyrite, after quartz, is tbe most abundant mineral associated witb gold; a more general statement would link gold occurrences with a variety of sulfide mineralization. Examples are shown in Figure 11.55 rrom the Pascalis gold deposit near Val d'Or in northem Quebec (Roy, 1984). Three drill holes were logged witb SP, IP, resistivity, and VLF EM tools. lbe SP is conventional witb one electrode downhole, tbe other at surface. IP and resistivity, measured simultaneously, are identical eitber in the normal or pole-dipole configuration. Two spacings are available for each; Cor tbe normal, AM - 0.4 or 0.8 m, MN .. 7.5 or 2.2 m, respectively, whereas for tbe pole-dipole, AM "" MN - 7.5 or 15 m. lbe VLF log measures two phase components of tbe downhole signal, witb a maximum-coupled magnetic sensor al the surface lor phase and amplitude reference. The VLF frequencies used were 17.8 kHz (NAA Cutler) and 21.4 kHz (NSS Annapolis). Figure 11.55 shows an uninteresting SP log, strong IP, and resistivity response at the two normal spacings, much less so for tbe pole-dipole. Figure 11.55a also shows gold and copper assays over the 180 m deptb extent of DDH 83-22 and Figure 1l.55b shows on1y gold. The VLF amplitude and phase variations have been norma1ized. Corre1ate tbese logs witb gold and copper as completely as possible.

REFERENCES Archie, O. E. 1942. Thc eleclrieal resistivily log as an aid in dctermining some reservoir characteristics. Trans. A.l.M.E. 146. 54-64. Becker, A., and Te1lord, W. M. 1965. Spontaneous polarization sludies. Geophys. Prosp. 13, p3-88.

Geophysica/ well/ogging Buselli. O. 1980. Eleclrical geophysics in the U.S.S.R. Geophysics 45, 1551-62. Conaway, 1. O., Bristow, Q., and Killeeo, P. O. 1980. Oplimization oC garnma-ray logging lechniques Cor uranium. Geophysics 45. 292-311. Dakhnov, V. N. 1962. OeophysieaJ welllogging. Quar/er~1' of Col. S,-hool of Mines 51. Doll, H. G. 1949. Inlroduction lo induetion Iogging and applications to logging oC wells drilled wilh oil-based mudo Trans. A.l.M.E. 186.148-62. DoII. H. O. 1951. The laterolog. a new rcsistivily Jogging method with electrodes using an automatic focusing system. Trans. A.I.M.E. 192.305-16. Doll. H. 0.1953. The microlaterolog. Trans. A.I.M.E. 198, 11-32. Freedman. R .• and Vogiatzis. K. P. 1919. Theory oC microwave dielectric constanl logging using Ihe eleetromagnelie wave propagation method. Geoph,l'sics 44,969-86. Oilreath. J. A. 1981. Dipmeter inlerpretation rules. In The Techn;ca/ Review. Houston: Schlumberger Educalional Services. Olenn. W. E.. and Nelson, P. H. 1919. Borehole logging techniques applied 10 base-metal ore dcposilS. In Geophysics and geochemisrry in /he sean:h for me/a/lie ores, P. J. Hood. ed .• Econ. Oeol. Repon 31, Oeol. Surv. Canada, pp. 273-94. Hoyle, J. B. 1986. Compuler techniques Cor the zoning and correlation oC well-10gs. Geophys. Prosp. 34, 648-64. Jackson, P. D. 1981. Focused electrical resislivily arrays: Sorne theorelical and practical experimenls. Geoph)'s. Prosp. 29, 601-26. Keys, W. S., and MacCarey, L. M. 1911. Applications ol borehole geophysics to waler resourccs investigations. In Teehniques of Water Resources lnves/igation, Book 2, Ch. El. Washington: U.S. Geo\. Surv. Labo, 1. 1987. A Prac/ica/ lntrodac/ion 10 Boreho/e Grophysics. Tulsa: Society oC Exploration Oeopbysicists. Mansinha, L., and Mwenilumbo, C. J. 1983. A mise-a-Iamasse study ol tbe Cavendish geophysical test site. Geophysic$ 48, 1252-7. Moran, 1. H. 1972. Discussion on radius ol investigation in dc resistivily well logging. Geoph.l'sics 31, 542-3. Moran, 1 H., and Chemali, R. E. 1979. More on the Laterolog device. Geoph)'s. Prosp. 27,902-3. Morris, C. F., Little, T. M., and Letton, W. 1984. Soc. Pelr. Eng. 591h Ann. Fall Tech. Conf.• paper SPE 1328S. Mwenifumbo, C. 1, Urbancic, T. l., and Killeen, P. O. 1983. Preliminary sludies on gamma-ray speetral logging in exploralion lor gold. In Carrent ,.,s,a1'ch, Pa,., A, Oeol. Surv. Can. Paper 83-1A, pp. 391-1. Nickel, H., Sender. R., Thierbach, R., and Weicharl, H. 1983. Exploring Ihe interior ol salt domes lrom boreho1es. Geoph)'s. Prosp. 31, 131-48. Paillet, F. L., and White. J. E. 1982. Acoustie modes or propagation in !he borehole and their relationship lo rock properties. Geophysics 47, 1215-28. Pascal, H. 1983. Further diseussion or attenuation and dispersion oC eleelromagnelic wave propagation in ftuid-saturaled rocks and applications to dieJectrie conslanl well logging. Geoph}'sics 48, 1313-80. Pickett, G. R. 1910. Applicalions ror boreho1e geophysics in geophysieal exploration. Geophysics 35, 81-92. Pinninglon, D., ed. 1981. Well Eva/uatiOll Conferenc" Abu Dhabi. Ridgefield (CT): Schlumberger. Pirson, S. J. 1970. Gr%gic Well Log Ana/ysis. Houston: Oulf Publishing.

References Roy. A .• and Dhar. R. L. 1971. Radius of investigation in dc resistivity well loging. Geophysics 36. 754-60. Roy. J. 1984. E1eclrical melhods in mineral wellloging. Pb.D. tbesis. McGill Univ.• Monlreal. SalI. D. 1. 1966. TesIs ol drill-hole methods oC geophysical prospecting on tbe properly oC Lac DufauIt Mines LId .• Dulresnoy Twp .• Quebec. In Mining Geophysics. vol. l. pp. 206-26. Tulsa: Sociely ol Exploration GeophysicislS. Schlumbergcr 1972. Log Interpreta/ion 1- PrincipIes. Houslon: Schlumberger LId. Schlumberger 1986. Log IlIIerpreta/ion Char/s. Houslon: Sch!umberger Educational Services. Schlumberger 1987. Log Interpretation Principies"; Applications. Houslon: Schlumberger EducBlional Services. Schmill. D. P .• and Bouchon. M. 1985. Full-wave acouslic loging: Synlhclic microseismograms and frequencywavenumber analysis. Geophysics 50. 1756- 78. Segesman, F. F. 1980. Hislory of geophysical exploration: Wellloging melhod. Geophysics 45. 1667-84. Seige!. H. O. 1979. An overview of mining geophysics. In Geophysics ami geochemistry in /he seard! for me/a/lie ores. P. 1. Hood. ed.• Econ. Geo!. Report 31, Geo!. Surv. Canada, pp. 7-24. Sheriff, R. E.. and Geldarl. L. P. 1982. Exploration Seism%g)!. vol. 1. Cambridge: Cambridge University

Press. Silva. 1. B. C .• and Hohmann. G. W. 1981. Inlerprelation 01 Ihree-component boreho!e magnetometer dala. Geophysies 46. 1721-31.

699 Snyder. D. D .• and Fleming. D. B. 1985. Well!ogging-a 25 year perspective. Geopltysics 50. 2504-29. . Tittman. J. 1986. Geopltysical Well Logging. New York: Academic Press. Tixier. M. P .• and Alger. R. P. 1970. Log evalualion of non-melallic deposits. Geoplt)'sics 35. 124-42. Wagg. D. M .• and Seigel. H. O. 1963. IP in drill holes. Can. Mining Jour. 84. 54-9. Wahl. J. S. 1983. Gamma-ray logging. Geophysics 48. 1536-50. Worthinglon. M. H .• Kuckes. A.. and Orislaglio. M. 1981. A borehole induction procedure for invesligating eleclrical conductivity slructure within Ihe broad vicini Iy oC a hole. Geopltysics 46. 65- 7. Wyllie. M. R. J. 1949. A quantitative analysis oC the eleclrochemical component oC the SP curve. Trans. A.J.M.E. 186. 17-26. Wyllie. M. R. J .. Gregory. A. R., and Gardner. G. H. F. 1958. An experimenlal investigation of factors affecling elastic wave velocilies in porous media. Geophysics 23. 459-93. Zeitz. 1.. Ealon. G. P .• Frischknechl. F. C .. Kane. M. F .. and Moss. C. K. 1976. A Weslem view oC mining geophysics in Ihe USSR. Geophysics 41. 310-23. Zemanek. J .• Caldwell. R. L .• Glenn. E. E .. Holcomb. S. V .• Norlon, L. J., and Slrauss. A. J. D. 1970. The borehole leleviewer - a new logging concepl for fraclure localion and olher lypeS of borehole invesligation. J ollr. Perro Tech. 21. 762-74.

Chapter 12

Integrated Geophysical Problems 12.1. INTRODUCTION Tbe application oC several disciplines - geology, geochemistry, geophysics - constitutes an integrated exploration programo In a more restricted sense we may consider tbe integrated geophysics program as tbe use oC several geophysical techniques in tbe same area. Tbe Cact tbat this type oC operation is so commonplace is because tbe exploration geophysicist, by a suítable selection of, say, lour metbods, may obtain much more tban four times the information he would get Crom any one oC them alone. Before elaborating on this topic it is necessary to point out again the paramount importance oC geotogy in exploration work. Every geologica1 Ceature, Crom tectonic blocks oC subcontinental size to tbe smallest rock fracture, may provide a clue in the search Cor economic minerals. Thus geologic information exerts a most significant inlluence on the whole exploration program, the choice of area, geophysica1 techniques, and, above all, the interpretation of results. Without this control the geophysicist figuratively is working in tbe dark. Tbe subject oC integrated geophysical surveys has received considerable attention in the technicalliterature since about 1960. In petroleum exploration the combination oC gravity and magnetic reconnaissance, plus seismic Cor both reconnaissance and delail (and, oC course, varíous well-Iogging techniques during lhe course oC drilling) is well established. The besl combination lor an integrated mineral exploration prog"ram is nol so definite because oC the great varíety oí targets and deteclion methods available. Base-metal search is a case in point. If the area is large enough and tbe money available, the program normally would 5tart with a combined airbome magnetic and EM survey. On a more modest scale, the work might proceed from a study oC acquired airbome data or from a reconnaissance geochemical survey. In either case the ground Collowup would

include magnetics, one or more EM techniques, and possibly gravity. IP may replace EM or follow it, particularly where the mineralization appears to be diffuse or low grade. There are, of course, additional possibilities, Cor example, SP, tellurics, and magnetotellurics. In any event, the base-metal program, compared lo tbe standard sequence in oil search, appears eitber pleasantly flexible or somewhat fuzzy, depending on tbe altitude and experience oC tbe exploration manager. There is anotber significanl factor affecting exploration work in general and multiple geophysical surveys in particular, wbich is nol sufficiently stressed. This is the time element. In an ideal situation the survey work would be carried out in a weJI-ordered sequence, proceeding from reconnaissance to detail and extracting all possible information from eacb survey beCore starting the next one. Practically tbis orderly, controlled procedure is impossible. Frequently there is pressure from the competition and from the equipment suppliers and contractors (several surveys must be done simultaneously, or in the wrong sequence, or one survey canoot be made until it is too late to be of much use). Time is money as well; tbe financial source may elect to Slart drilling or lO abandon the operation entirely (Ior reasons wbich could be quite valid) before the survey is complete. Finally it is wise to keep in mind that tbe exploration program should lead to elimination as well as acquisition oC prospects. An overabundance of anomalies is, in tbe end, almost as unattractive as Done at al\. The reader who has studied the field examples and problems in the varíous chapters with anything more tban casual interest doubtless will have deduced tbal many oC tbem are nol ;colated examples oC a single geophysical method applied to a particular area. This is indeed tbe case and in the present chapter we wil1 assemble some oC tbese lo make

Examples and problems

701 10N

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Figure 12.1. Magnetics, /P, and Turam results, Loul'icourt ilreil, Quebec. (a) Magnetic dnd IP pro files. L16 W. and vertical section (b) Turilm results; loop locatC'd ill O + OON,

integrated surveys for further consideration. AnaJyses of the examples and problems given here should be made on tbe basis of severaJ factors, inc1uding the followiDg. How much additionaJ informatioD is provided by me combinatioD of techniques? Is this information positive or negative. definile or indefinite in quality? Is the proceduraJ sequence reasonable (magnetics with EM, followed by gravity, or whatever) ando if not, why was it done in tbis way and how would you modify it? Are me number and seIection of methods necessary and sufficient to make a decision either lo waIk away from the prospect or deveIop it further?

Are any of the methods used in a particular exampIe superfluous? WouId the money be better spent on drilling?

12.2. EXAMPLES ANO PROBLEMS 1. Compare the gravity interpretation of problem 17, Section 2.9, with the anaJysis oC the magnetic featurc

near St. Bruno, Quebec, described in tield example 1, Section 3.8.2. PresumabIy the same structure produces both anomalies. Are the results satisfactory and if noto is it possibIe to make reasonable adjustments of cerlain parameters to obtain better agreement? 2. The large gravity anomaJy oC tield example 1 (PortIand Creek Pond), Section 2.8, occurs witbiD

Integrated geophysical problems

702

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Figure 12.2. Tota/·(ield ground-magnetic pro(i/es, Uchi Lake, northwestem Ontario.

the area ShOWD in Figure 3.42, probtem 13, Section 3.9. (It is difficult to locate it precisely because the aeromagnetic section is Crom a much targer map: certain topographic features, such as shorelines in Figure 2.36a, which were not reproduced in Figure 3.42, do nol coincide. Furthermore it is surprising thal there is no mention in tbe gravity work report oC the 200 m scarp descnbed in probtem 13; such rugged topography would eertainly require a terrain correction.) UnCortunately ground magnetics were nol carried out during the gravity survey. In spite oC these discrepancies, the positive gravity feature appears to correlate with a zone of low magnetics striking SW- NE. Take off a SE-NW profile through the magnetic low and attempt to match it with the aid of the dolomite section oC Figure 2.36c, using Equation (3.59b). Alternatively, because the inclination is about 15°, one might approximate F by Z and employ Equation (3.44a). The height of the aircraft was 300 m and one would expect the susceptibitity contrast between the dolomite and adjacent sedimentary rocks to be small ud negative. 3. The aeromagnetic contours in Figure 3.43, problem lS,.Section 3.9, are from the same area (St. Lawrenee Lowlands) as the gravity profile oC Figure 2.38, field example 3, Seclion 2.8. The north end of the gravity profile terminates approximately at the eross on the north direction arrow shown in Figure 3.43. Take off a N-S total-fteld profile from this

Table 12.1. Survey lechnique

Section

Problem or field example

Figure

GravilY Magnetic Seismic EM16 Resislivily IP

2.9 3.9 4,12 7,8 8.8 9.7

prob.1& prob.7 prob.21 field ex. 3 prob.11 prob.4

2.44 3.3& 4.122 7,9{, 8.50 9.22

point for about 10 miles south and compare it with the gravity profile. If the geologic section of Figure 2.38 is correct (there is considerable evidence to show that it is), the magnetic profile, like the gravity, should be a refteclion of the Precambrian step. because the sedimentary beds have very low and uniCorm susceptibitities. Henee it should be possible to obtaio a fair match to the magnetic profile, using a form of Equation (3.59b), Sectioo 3.6.1. (or altematively §3.6.9), given that the inctinalioo and declination in the area are about 1So ud 22°W. respectively, and tbat tbe aireraft altitude was 300 m. If this interpretatioD is oot satisfactory, can you establish some definite limits 00 the depth of tbe magoelic souree? (See also §3.1.11) Would such a depth be salisfactory lor the gravity profile? Are the gravity and magnetic results compatible at all?

703


la' 100

102

104

108

106

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-20

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Figure 12.3. Resu/ts of differenl e/eetriea/ surveys, At/an/ie Nieke/ Proper/r, sou/hern New Brunswiek. (a) SP profiles. (b) HUM profi/es; frequeney 876 Hz, coil separa/ion 200 fr. (e) TelJuric con/our map; frequeney 8 Hz, eleelrode spacing 100 fl.


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Figure 12.4. Te/lurie profi/e and ce%cie seetion, Mobrun Sulfide Deposit, norlhwestern Quebec. For theoretiea/ mode/, P.ul - 1 Gm, A-r - 70 Om, and PhoSl - 7,000 Qm.

4. The magnetic and IP profiles of Figure 12.1a and the Turamoprofiles oC Figure 12.1b are from the Louvicourt copper deposit near Val d'Or, Quebec. Line 16W passes almost direcdy over the main copper mineralization, shown io vertical section below 15N. This ZODe has an oval cross sectiOD - 300 ft by 100 lt and is enclosed in a stccply dippiog bed 01 disscminated pyrite (- 20$) - 160 ft tbíck. The pyrite extends lor more than a mile alODg strike, which is paralle1 to the bcddiog oC acid tuffs and agglomcrates. Consider these profiles individuaJiy:

(ü) Turam - the original discovery hole was driUcd on the streogth oC the weak Turam aoomaly at 15N. Would you CODsider tbís a good bet lar drilliog? (üi) IP - this profile was obtained after drilling, using the thrce-electrode array with 200 Ct separation. Chargeability aod resistivity are botb strongly aoomalous over the ore zane. Js the former response due to pyrite, chalcopyrite, or both? Would you mate a similar interpretatioD lor the resistivity low?

(i) Magnetic - note the strong negalive anomaly caused by the drill-hole casing. Can you explaín the lack 01 magnetic sigoature associated with the ore zone?

The gravity profile ol field example 2, Section 2.8, along with Figure 2.37 aod the EM data given in problem 15, Section 7.9, are also from line 16W. In addition, the IP aod resistivity logs shown in Figure

Examples and problems L66SE

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O ' , 100 fl N•• r sid••• 7SW _ Loop 1600 x 1400ft

-.

...... ,

~_.-

.. ~

, ,

,

-,

•

0·8

L72SE

.

Phase 10 0

1

,

,

,.

• R•• io 1.2

L69SE

1

0

Frequency: 660 Hz

L72SE

L69SE

,

•

-

.Q:._.~.

L72SE

L66SE

L69SE "'

I

-10·

-,

"0

Frequency: 220 Hz

L72SE -,

r

'4NE 5SW'

,

,

,

O

r

1-

'y'dCI

T

-,

4NE

Transmilter cable_o, SNE (ncar Loop 1200 x 1000 ft (o)

,

,

Real _.' • Quadralllre

4NE

R,Q

L69SE

,

........ 1. ••• 1• • • ~.'

.......

10%

.

o

L71SE

,;¡;¡-..•.. """........

•

4NE (b)

o

Keewalin acidics

m:a Mineraliulion: pyr.

~

Rhyolile porphyry

••• Gcolo,ic con'.CI

35·~

(e)

Figure 12.5. Ceophysieal resulls and geo/ogie seclion. Barraule. northwestern Quebec. (a) Turam profiles; frequencies 660 Hz (upper three profiles) and 220 Hz (Iower three profiles). (b) HUM profiles; frequeney 1.000 Hz. T·R spacing 300 fl. (e) Assumed ge%gic section.

11.51 (see probtem 2, §11.12) were taken in a hote thal intersected the ore zone, The geotogicallog gave the followiDg information. 0-25 fl: overburden, 25-175ft: barren tuff, agglomerate. 175-240 ft: pyrite mineralizatioD, 20% average. 240-300 ft: coppcr mineralization, 2.6%, pyrite - 5%. 300-330 ft: pyrite - 5%. 330-345 Ct: pyrite - 5%, coppcr 1.3%. 345-435 ft: pyrite 10-15%. 435-480 ft: barren.

Although we have a greal variety oC geophysical results Cor this retativety small copper orebody, seven 01 the eight sUlVeys were perlormed' after drilling, to determine which 01 the methods were best suited lor such a target. Assess tbe geophysical data and consider the results on the basis 01 tbe lactors Iisled in SectiOD 12.1. 5. Figure 12.2 shows a set of total-field groundmagnetic profiles lrom tbe Uchi Lake sulfide deposit in Dorthwestem Ontarío. Other geophysical results from this ZODe have a1ready becn displayed in Figure 7.95 (see fietd example 2 in §7.8), a1so Figures 7.116 and 7.122 of problems 14 and 21, Section 7.9.


'\',1"'r.::,-

'~~.J- _/$0. D~-1

" }

(~. (

-,-- ,,'. ''\ '\ ~;~ __

1

, ,

'- ---..

'. Oo.

.,. toO"

~-::-

.'

']

- ___ o

:¿' / " ~\~ \1 \.

1&1

l!iI

:

:\ ', ,

If

lN--~~~~--+_~~--_r--_i

8

,

, J~"" •I

-. --. -", -------- --

·250·'.:

I

l1Jj

L,'.-" , ,

't

•

,

6N·----r---~--~--~--~--_,

,i I

• -" u.I

~

(a)

(b)

O !

~

IN I

4,

6 I

800R

400

!

I

12

8

I

I

,

14N

-Rell

oO-- Iml.inlry (e)

Figure 12.6. Magnetic and electrical data, Murray sul(ide deposit, New Brunswic/t.. (a) Magnetic contours; contour interval 25y. (b) SP contours; con tour interval 100 mV. (e) HLfM profile; frequency 440 Hz, T-R spacing 300 ti.

The original reconnaissance work was done by air, including the Input and nuc1ear-precession airborne magnetic profiles shown in Figure 7J 22, The line spacing was 1 mite at an altitude of 380 ft. Although the Input anoma1y is weak, it stands out c1early against a low background and persists through at least three channels, Favorable geology, involving siliceous volcanic racks surrounded by extensive granites, made it attractive to investigate this anomaly in detail with ground geophysics. The first ground followup inc1uded the vertical-loop broadside method, which located the conductor outlined in Figure 7.95a, and the magnetic profile ol Figure 12.2, which indicated a possible weak anomaly associated with it. Thc sulfide structures are described in field exampIe 2, Section 7.8. Initial drilling g le good grades of copper (3-8%), zinc (9-12%), and sitver (2-4 mi ton). The wne near IN between SE and 7E (see Fig. 7.9Sa), is mainly sphalerite with very little iron minerallzation, and is probably a poor target lor EM and magnetics. The horizontal-loop, Turam, and shootback EM profiles shown in Figure 7.116 were obtained in test surveys performed alter the preliminary drilling. In this regard the procedure and sequence ol events are similar to the previous example at Louvicourt, be-

cause the discovery was made on the basis ol only part ol the geophysics. As in example 4, the problem should be assessed by considering al) the results, to establish a necessary and sufficieot exploration procedure, il, in lact, one exists. 6. Numerous geophysical techniques have beco tested over the Atlantic Nickel base-metal property in southern New Brunswick. Examples already included in the text are listed in Table 12.1. In addition, the SP log of Figure 6.7a, SeCtiOD 6.1.4, was made in a diamond-drill hole near line IS6N. Self-potential, horizontal-loop EM, tel1uric, and further IP results lrom the same arca are shown in Figure 12.3a lo d. Although the gravity data plus earlier magnetic and vertical-loop EM surveys were used directly lo establish the ore :tone OD this property, much oC tbe subsequent geophysics was done lor test purposes, or to find possible extension 01 the mineralization. As a result there is an enormous amount ol inlormation here. In general, one can see that the gravity and EM anomalies are very strong and relatively simple, tbe magnetics are complex, whereas the original IP and the tel1urlc data are poor. However. the IP and resistivity sections in Figure 12.3, obtained by using unusualty smalt electrode spacing, shoYo' extremely small anomalies. What are the reasons lor the

707


lal

~

~

..

:g

""I! 9

i

.~ 0·01

.

1

'"

eh)

Figure 12.7. fM and telluric resu/ts, Bartouille, northwestern Quebec (a) VLF·fM/6 profile. (b) Telluric profi/e, e/ectrode spacing 25 ft.

di~an8/e

tremendous difrerence between the results in the two IP surveys? Make as complete an interpretation as you can. 7. Gravily data ol Figure 2.40, problem 10, Seclion 2.9, and magnetic contours in Figure 3.34 of probJem 2, Section 3.9, are from the Mobrun sultide deposit, which is also i11uslraled in example 1, Section 7.8, Figure 7.94. The dip angle and gravity protiles in Figures 7.94 and 2.40 are on the line marked N-S in Figure 2.40; the appropriate magnetic protiJe may be oblained on a line joining the Iwo crosses in Figure 3.34. A measured telluric profile is shown in Figure 12.4, accompanied by a rough vertical geologic seclion. This was a N-S traverse about 60 m west ol the dotted line in Figure 3.34. Thus the sections of Figures 7.94 and 12.4 should be much the same. The mild magnetic low indicates that the sulfides are nonmagnetic, but otherwise Ibis survey is oI little significance. High background noise from nearby power lines afrected the telluric measurements somewbat. The telluric profile is interesting because it reflects a much lower resistivity north of tbe ore zone tban soutb of il. This large efrect partially masks tbe anomaly directly over the sulfides. It may be due to a considerable resistivity contrast between rbyolite and tbe volcanics to the north. However, tbe steep slope ncar 400N looks very much like an overburden

anomaly, as indicated in Ibe tbeoretical pro file obtained by numerieal modeling. Would you expect to see lrus anomaly in the vertical-loop profile? 8. Figures 12.5a and b show Iwo-frequency Turam and horizontal-loop EM profiles over zones of pyrite mineralization in Carpentier Township, ncar Barraute in nortbwestem Quebec. Magnetic and IP data from tbis area are lound in Figure 3.28 of example 1, Section 3.8.1, and in Figure 9.21 ol problem 3, Section 9.7. The magnetie results have been discussed in sorne detail in Section 3.8.1, where it was concluded thal the large magnetic anomalies eould only be eaused by magnetite or pyrrhotite zones near surlace. IP and EM responses, on the otber band, are uniformly negative, wbieb should eliminate the possibility or pyrrhotite. The geologic section shown in Figure 12.Sc is based mainly on information from diamond-drill bole T - 1 (see Fig. 3.28) and to a lesser degree on the magnetic anomalies. Drilling results establish lhe depth of overburden to be 82 ft at tbe collar and tbe presence of two zones of 35% pyrite al - 300 and - 450 ft depth. There is sorne doubt of the bedrock surface outline shown in Figure 12.Sc in view of tbe seismic results on line 75SE, mentioned in cxample 1, Seetion 3.8.1. Howevcr, even ir tbis surfaee is correet, it is difficult to understand the lack of hori-


700

2S ~

S

50

"

100 ~

S

50 100

-

S

50 100 1 5E

1 6E

I

7E

lE

I

(b)

9E

lOE

IIE

12E

Figure 12.8. Magnetic and electrical results. Woburn, Quebec. (a) Vertical component (magnetic field) profiles. (b) IP and apparent'resistivity pseudodepth plots.

zontal-loop EM aod Turam response, especially tbe latter, because shallow resistivity values iD tbe area would not normal1y be low enougb to mask tbe presence of tbe SO fl wide pyrite zones at a deptb oC 80 to 100 ft. One is forced to concIude eitber tbat tbe pyrite zones do not continue lo bedrock surface or tbat tbe pyrite is not a good conductor. Try to make ao iDterpretation oC tbese results tbat is consistent witb tbe magnetic aod electricaJ data. 9. Tbe Murray sulfide deposit in Restigouche County, nortbem New Brunswick, was used as ao iIlustration oC tbe Turam metbod in example 7, Section 7.8, Figure 7.100. Addilional geopbysical results. are displayed iD Figure 12.6 Cor magnetics, selfpotentiaJ, aod horizontal-loop EM. Altbougb tbere is no magnelic reftection oC tbe sulfide mineraIization (for a description, see §7.8), tbe SP and HLEM anomaJies are very strong, possibly as a result of tbe gossan cover. In particular tbe borizontal-loop profile iDdicates a wide conductor dipping nortb, witb tbe Degalive maxima falling belween tbe Turam peaks. Make an estimate of tbe gcometry and conductivity of tbe zone from borizontal-loop characteristic curves. Take off a SP profiJe from line 136E and iDterpret tbe SP results. 10. Tbe VLF dip-angIe and telluric profiles of Figure 12.7 were obtaiDed from tbe same road lra-

verse tbat supplied the following data: Self-potential, example l(SP), Section 6.3.1, Figure 6.25. Magnetotellurics, problem 9, Section 6.4, Figure 6.37. 'Ibis massive sulfide sbowing, in Bartouille Town&hip, near Senneterre in nortbwest Quebec, is described iD tbe SP example. There is good correlatíon bere betwccn tbe various geopbysical methods, altbougb it is by no means exact. 80tb SP and EM16 profiles iDdicate tbe strongesl anomaly lo be a tbin conduclor dipping nortb, located al 40N (SP) and 70N (EM16). (The laUer is measured from tbe zero crossovcr, which may be sligbtly downdip.) 80tb show a second conductor in tbe swampy area al 180S, altbougb it cannot be located witb any precision iD tbe EM16 profile. There is a tbird smaller SP anomaly al llON. Magnetíc anomalies are similarly sharp. The smaller positive is al 25N, whereas tbe mam peak is at 125N. A delinite magnetic low at lSOS correlates witb tbe swamp zone. These are nol shown here. The telluric and MT profiles of Figure 6.37 reftect a wide conductive zone extending al least 200 fl nortb and soutb oC statíon O; tbe MT profile also bas a sligbl dip near 200S. When Figure 6.37 is com-

fxamples and problems

709

Magnelie.

-130Hz .- - 4751iz

......

,,~-

" '''',,~------------~--- ~-~---_.-----------.---

T- R soparalion 200 n

1

in-phase response - - - quadrature response

Hotizonlal loop EM

+ "

.....

_--~".

... 600 Hz

Surrace

, , 100 , , 200n ,

o -

~ 10% sulfides

Figure 12.9. Ceophysicill results and geologic sec/ion, Une

e

Ca\'endish Township,

On/ario.

pared with Figure 12.7b, there is c1early a lack oC discrimination in the Cormer. This is caused by the larger electrode spacing, 100 fl. rather than 25 Cl as in Figure 12.7b. With tbe 25 ft spacing the wide conductor is resolved into lwo peaks. tbe main one being at llON and the 5econd al 100S. There is also a minor low al 350S, coinciding with a magnetic anomaly. The telluric low at 10005. wbicb was equally strong with 100 tt electrode spacing, has no correlation with tbe magnetics. 11. Induced polarization, resistivity, and magnetic data, shown in Figure 12.8, are taken Crom the same area discussed in (i) field example 6, Cor horizontalloop EM, Section 7.8, Figure 7,99, (ü) lhe telluric profiJes oC problem 6, Seclion 6.4, Figure 6.34, (ili) drill-bole IOg5 in problem 3, Section 1l.12, Figure 11.52. The zones oC mineralization, wbich are mainly pyrite, are shown in Figure 7.99. There is, in addilion, a section oC chlorile scbist containing lraces of

pyrite between 7 + OOE and 7 + 50E. A11 zones dip about 70 0 west. Considering line 385, lhe three-frequency telluric protiles in Figure 6.34 have two peaks, at 8 + 30E and 9 + 30E, wbich correlate very well with the two sulfide zones. The bigh-trequeney response is most pronounced, whereas the 8 Hz profile indica tes lhat tbe better conductor is at 8 + 30E. The horizontalloop EM profile, on lhe otber hand, reftects only the massive sulfides. Neither sulfide zone appears lo have any magnetic contrast on line 38S, altbough there is a small tail on tbe west ftank of lhe magnetic peak al 7 + 75E, wbich falls between the chlorite bed and lhe massive sulfide. The IP lraverse was made with a double-dipole array, with x - 25 ft and n - 1. ... ,7. The small 5pacing was used purposely in an attempt to discriminate between the conductors. Clearly tbis was only part1y successful, because the frequency-effect con-

/ntegrated geophysical problems

710

AFMAG

IlOHz --- 47S Hz

"

(%)

20~ o ,,!

...... '------ ... -.,. ,..------_.- .--

2400 Hz I

(" .. _... ~,.7

-20

'Pe

t

--,-.

•

a'.... ~

#>n

T -R separltion 200 n in-phl" r.spon.. -- - quadraluro rnponse

Horizontal 1001' EM

(%'l-':--J--' 1

.... __".. --'

600 Hz ~_

. H. . -

J"> ,

-20

m m

8iOlil. gn.in

Hornblende In.iss

m o-

Gnnile gneiss

-

~

o 1

,

100 I

,

2000 I

2% sullides \0% sulfides

Figure 12.10. Ceophysical resul/s and geologic sec/ion, line D, Cavendish Township. On/ario.

tours show a single wide zone froro 7 + 75E to 10 + 50E. Apparent-resistivity and metal-factor results are better in tbis regard, with the stronger response over the better conductor, but only lor n - 6 and 7, the largest dipole separations. On lines 36S and 4OS, the HLEM peaks again occur over the massive sulfide rone, wbereas the telluric profiles (whicb, it should be nOled, were made with 50 ft electrode separation) locate both zones. In addition, the strongest response in al) three lines is at 145 Hz. However, this is not particularly significant, because the average resistivity is sufficiently higb to make the skin depth at 145 Hz considerably greater than the depth extent of the conductive zones. This is a relatively straigbtforward example of nonmagnetic sulfide conductors lying at sballow deptb. The magnetic data are, at best, merely an

indicator oí mildly anomalous susceptíbility contrasl on tbe flanks of lbe sulfides. A11 the electrical techDiques responded lO the anomalous zones in some fashion. The horizontal-loop survey located only the better conductor, indicated jts dip, and provided an estímale of depth and conductivity-tbickness prodUcl; these plOfiles also sbow that the zone js tbin. As mentioned in the discussjon of field example 6 (§ 7.8); it migbt have becn possible to detect the two zones by usjng 100 ft spacing between the transmilter and receiver. The telluric measurement resolved the lWO conductors wjtb 50 íl electrode spreads, bUl failed to do so when tbe separation was 100 ft; there js little evidence of dip on lines 38S and 4OS, whereas the plOfile on 36S suggests a dip lo the east. Finally, tbe IP survey successfully established the presence 01 two conductors by employing extremely small dipole spreads. Had the conventionallOO fl separation been

Examples and problems Table 12.2. Problem

Section

4

6.4 7.9 7.9 9.7

3 18 7

Method

Figure

Correlation 01 lines

SP Vl Broadside AEM Quadrature IP Freq. domain

6.33

Une 12N is line C. BN is O line 12N is line C. BN is O

7.119 9.24

Data obtained on line C

Table 12.3.

Conductor

",

z

Frequency (Hz)

zlf

(ft)

p...,,,rf

(5)

(ft)

600 2400

0.1 0.05

40 20

45 60

140 55

70 100

7

600 2400

0.2 0.1

80 40

3

10 4

< 10

1

Zone A Zone 8

4

I

"

(5/m)

2

Table 12.4. Cavendish fine C data Location Method Magnetic

SP Vl Broad. AFMAG HL IP Drilling

Zone A 16W 16W 16 + SS 16 + 50 16 + 55 15 - 15 + 50 16 + 30( cone.) 15 + 60 -16 + 40 (disseminaled)

Dip Zone 8

A

8

Deplh (ft) A

B

1001 9W E W 1001 9-11W W W 9-9+65 W W 120 ~ 100 ? E 1 W W 20-40 40-80 9 9-11 E W < 100 < 100 .. 20 9 + 30 E W .. 20 9 + 1S -9 + 4S

used, it is practically certain that tbis resolution would nol have been achieved. 12. Vertical geologic sections obtained by drilling lhe Cavendish Township area in central Ontarlo are displayed io Figures 12.9 and 12.10. Lines C and D are 400 ft apart. This bas been a favorite sile for testing geopbysical equipment since 1967, when a case bistory was prepared by McPbar Geopbysics for tbe Canadian Centennial Conference 00 Miniog and Groundwater Geophysics. Practically all the electrical techniques, plus magnetics, have been used here. Magnetic, AFMAG, and horizontal-loop EM profiles are also shown in tbe same diagrams. Other examples from Cavendish already incorporated in thls book are listed in Table 12.2. A shallow drilling program, carried out by tbe Geological Survey of Canada, produced the sectioos of Figures 12.9 and 12.10. The rocks are Grenville mafic gneisses, crystalline limestooes, and granite gneiss, which generally dip steeply to the eas!. Pyrrbotite is associated witb calcite and pyrite with quartz in calcareous-silicate sulfide a1teratíon zOnes

Depth ex!. (fl) A

B

Width (ft) A

B

", (5)

A

B

5

4001 > 125 > 125

70-100 S 10 55 -140 4-10 1501 1001 10 0.3 80

30

and there is a general background content of 0.1 % sulfides in the rocks of tbe area. Botb zones A and B strike approximately N30 0 E for more tban 1,600 ft, the B zooe appareotly splitting into two or tbree zones, over a greater widtb, to tbe soutb. The sulfides. a1most entirely pyrrhotite and pyrite, occur io widtbs up to 80 ft at coocentratíons of 1 or 2%. Within tbese zones tbere are narrower sections or 10% and bigber grade; for example, in zooe A, tbe 10 ft wide section on line e extends 100 ft north and south, whereas within zone B there appears to be a similar, bUI much narrower, scction that is - 1,000 ft long. The mineralization occurs as stringers tbal are mainly parallel to tbe foliation, althougb zone B appears to dip west. Neither tbe depth nor the depth extent of tbese zones has been established by the drilling to date. However, they seem to be no more tban 25 ft deep and probably subcrop al bedrock surface in many places. The depth exlent is at least 125 fl. With sucb a wealth oC geophysical data available here, it sbould be possible to make a fairly complete

In tegrated geophysical problems

712 TN

t ENO OF ROAO TRAVERSE

DOHI -4S·

(a)

S6OcOr-----ir-------------------------------------------------, M• total field .".tics

(b) Figure 12.11. Ceophysical data from a base-metal prosped in eastern Nova Seotia. Data in (b) are from ground surveys, data in (e) lo (1) are Irom helicopler ajrborne surveys, f1ight fines (light sofid fines plotted at map posilions) are E- W at nominal 200 m spaeing. (a) Map 01 area and road traverse. (b) Total·field magnetics, SP, EM16, and three- frequency tel/urja (rom road traverse.

713


o

r-

8

""

".-0----""

_____ -2

J

I

/

./

181280

o

500

L..I_---"1'--_--'

O

N-S. E-W Flight lines I intersectio~ Con tour inlerval ± I <;(

Con tour interval 250 nT

(dI

(e)

Figure 12.11. (Conlinued) (e) contours.

TOla/-fie/d milgnetie contours. (d)

interpretation oC these zones_ Considering line C. tbe magnetic profile shows a good peak at 16W and a much stronger one at 9W, correlating well with lone A. centered at 16W and reasonably well with lhe main section oC B at about 9 + 25W. There is no! much indication of lhe dips oC these beds, although tbe peak al 16W has a sligbtly steeper slope on tbe west flank and Ihe larger anomaly al 9W decreases more rapidly to the east, suggesting east and west dips, respeclive1y. The two peaks, oC course, are a reftection oC lhe pyrrhoti te lhat apparently is in greater concenlralion and/or doser lo tbe surface al lone B. Deptb estímates from the width at half-maximum indicate about lOO ft in both cases, bUI lhese are obviously unreliable because bolh lones are probably wider than the depth lo the topo U we take a SP profiJe from line 12N in Figure 6.33, Section 6.4, we find good correlalion belween Ihe negative peak oC 373 mV and rone A. The

Totil/-fic/d VlF

broader mínimum from gW lO llW. however, indicates a second SP source al 11 W. whlch is not apparent from lhe geologic section. The asymmetry of lhe SP anomalies suggests a general steep dip lo tbe west. Clearly no valid depth estimates can be made from thls profiJe. On plotting the broadside vertical-loop profiles for 12N (line C) from Ihe data in probJem 3, Section 7.9, we find tbat zone A produces a good anomalyat all four frequencies. The crossovers Jie between 16 + 50 and 16 + 60W, and the asymmetry oC the 1.000 and 5,000 Hz profiles indicates a westward dip. Employing tbe characteristic curve oC Figure 7.42a, Section 7.7.3í (admíttedly thls is a very crude approacb, because tbe marked asymmetry oC the profiJes does not imply a steeply dipping sheet). we fiad thal zll == 0.3, or z 120 ft. This value appears lo be mucb too large. Further evidence Ihal it is unreliable is provided when we attempt to estímate the

=


714 , ........,

o

"

~

f-- ~-.;---"

,/', ..........

1.10.-

-

"""'--'IiII

~---

¡...------

~/

.,..; _..............

-

=-.-.~

\

.

--

l'"

--

.",., ... --....::.•

~

~o,-.'_~

-

_o

."..--,

"

""",."'-'

-.,..

-.0- "'._

-,,.-~-

_._-- '-

,,-.....

~--

.... _.---

~

' ......

~ 1, ~, _--~~~.~-_ .~

_ _-r

\

i

....

- ::~ -20

.........' - .

.~\

o~o

I

--'

Di:

O (ppm)

:!\ .... _ - - - -812iO -

o

Horizontal seale: I

500 I

-=-"

,-

~

-

1000 (ft) I

>DDHOLES el

_-_-

'.

'........... .~ 1 - ....

....

e2

1/

~,

7

-

....

~:\

.-or

-.....

- -

_---

8

00o __

-....;;

-.-

DDHOLES~\

....

-

.--- ....

81280

". . . . __ .... .,..-- .... -....

~---...,.'-:---

.",

r,

... ................

or-

o'""
....._-.,/.-....I"~

._0

...-..,,----.....

o

./-', ~

........,.... ......-

~-._."" _-------

or-

I

,,)

E·W, N·S

J interseetion FlIght IInes I

_.... ---

----...........

O

Horizontal sea le: I

SOO I

1000 1ft)

~

--

;::~ 80

O (ppm)

812801

1

I

(fl

Figure 12.11. (Continued) (e) 935 Hz coaxial pair in·phase ( - ) ; 34 kHz cap/anar pair i""phase (•.•.•) and quadrature (•.. ) on line 81210. (f) 4,600 Hz coaxial pair ( - ) ; 4,175 Hz coplanarpair (.•• ) (both in·phase) on line 81280.

response parameter from Figure 7A3b, Scction 7.7Ji. The peak·to-peak response is much too large, at both frcquencies, for a conductor 120 ft deep. Using tbe same curves lor zone B, we find that z .. 100, 120, and 340 It, for frequencies of 5,000, 2,400, and 1,000 Hz respectively. (There is no re· sponse at 600 Hz.) From Figure 7A3b, we tben obtain values of tll .. 5 at 5,000 and 2,400 Hz; tbe deptb z correspondíng 10 1,000 Hz is again loo large lo fi t tbe curves. The AFMAG profiles in Figure 12.9 show a good crossover approximately al 16 + 50W, corresponding lo zone A, while tbe asymmelry indicates an castward clip. There is little more tban a suggeslion 01 zone B on tbese profiles. It should be noted tbat in botb tbe vertical-loop and AFMAG metbods (and in tbe borizontal·loop results as well), tbe high. frequency response is lhe larger, which lens us that tbe conduclors are shallow. Figure 12.9 also sbows a very strong response lor tbe borizontal·loop EM, ccnlcred al 16 + 50W over

~one A and a relatively weak anomaly at 9W for tone B. llis Iype of EM equipment is not particu· larly sensitive to clip; one might guess tbat the profiles indicate a general dip to tbe west. Employing tbe characteristic curves of Figure 7.44b, Section 7.7Ji, we can estimate tbe parameters in Table 12.3. The values ror t are obtained from tbe profiles in Figure 12.9, being the excess of tbe borizontal dis· tance between zero crossovcrs over tbe lransmitterreceivcr separation. Finally, the IP data ror line e (Fig. 9.24, §9.7) present a somewhat different picture. The top of tone A is located at least 100 ft east of its actual position. Botb frequency-effect and metal factor contours suggest it 10 be a conduclor of ralber limiled deptb extenl dipping east. Zone B, on tbe otber band, appears to be located in about tbe right place; it aIso appears lo dip west and to increase in conduclivity at deptb. In tbe pseudodeptb plots for x - 200 ft tbere is an indication that Ihe zones come togetber al n - 3 (supposedly - 400 ft). Altbough the freo

715


•

6 CHANNElS

(lit !5

()

@

CHAN NEL!

4 CHANNELS

4 CHANNELS WITH MAGNETIC CORRELATlON

(a)

t!

o

w .....

EM I'IlSI'ONSI!

.-.a_ . _ , "1O_tL_1'I' YAUa 10'"'''' ...

DI'

PHAllOII_aTUM' COI. H COICIUCTMn' 'ner;ICNQ, _ / COICIUC1aI Ala

O ..._

DI' 1M. COIJII.EI)

I? _ I .....ACI!~ , 'OSI&. FICTllIOUII - . ,

MAGNl!TIC CORAIElATION

r

~

DNCT eOlllllLATICIN DI'

*"r

........

~---'---f Localfon o( Dlghem elecll'OlllGgnetlc anomalles,

".:'~~

m~

J.I ! r '~ ~

--'

(h) Figure 12.12. Geophysiealground surveys over anomi/liesloeated b)' i/irborne Input i/nd Dighem surveys. (a) Mi/p showing loei/tions of Input i/nomalies. (b) Map showing loea/ions o( Dighem anomalies. (e) to (e) VLEM, HUM, dnd IP profiles over anomaly A along the N-S lines tBOOW, LO + 00, LBOOE which straddle the reetang/e mar/t.ed NEW INSCO in (a).

Integrated geophys;cal problems

716

.os

YIIlTlCAI. I.OOP 1111

T. AT 400.,

MOIIIIZONTAI. LOOP 1111. 'OOMa, T'1l .'OO"~'.

.1.

...

.............. • •••'

'NDUCID POI.A'UZATlON • • ,OO't., •• ,

.,p,. ...... -

"'l .. '·· (c)

.., ""

eoQMI-

'400

T

..:

MO'"IO.TAL LOO' 111 'UOU."C,. 100MI T.a •• 00ft

=

.

"a-'

___;:.::::: as ~.,.

i

;-,!

...._.. . lu •••• '.~NA'I_ 'U •• _.

·tO .10

'0· ••• ~. O

-

", ....

--.__._.-

'00

PeA_

O

'o,

•,

.

•

.

(d)

••

o

,

•

I

~.,;. 1001

' •• OU'"C" 100M,

tO

t·

'0

o • '0

; ·±%L....~ ..

.. -c?

m

....

f

......

;a0

'

"OIt'ZOllT&~

,lO

LO., , .

l. P... 'C _

ou.o •• "u.r •..•

' ... ·,OOft

...

....__ ... -_........_............-..................

.'0

·'0 lOO •

;!;...

IDO

I 100 I -ZOO • 00

". ..ouero

'OLAtlIZA"O" •• '00"_ ... I

., ......... - .

~

"

....

~_

...

- -....... - .......-..... .......

.... ......

".""., , ....

Figure 12.12. (Continued)

'.,-

..

,

'00

'O

(a)

•

•

•

-

II

'.

.

....

B-HORIZOH SOIL GEOCHEMlSTIIV

Ur

GAAVIT y

Glt

g

.ut:::¡-I_~_'>"""",=====-,,-L_~_~_~~

2000.,

MAGNETICS

~L~~~~==~~~ HORIZONTAL LOOP EM 2G.

~U=JUIII

1400HI , 200FI

-,-,

(%):;f-..o.-.....------J<:t:""-.........-......~.....~.~~;:;,..':'o;.~;::-.r..?.=::::'~~"""~;';:'--~~--,; •.

(b) Fi8ure 12.13. Geophysica I and geochemical 8round surveys over Di8hem anomaly discovered during airborne surveys in Figure 12.12. (a) ¡\lap showin8 location 01 Di8hem anoma/y 8. (b) ro (d) Geochemica/ and 8eophysica/ profi/es a/ong fines O + OOf. 2 + OOf. and 4 + DOf. respective/y,

na

In tegrated geophysical problems

'" RISPONSI •• 100'. "., ,PI -.-

r.=

4000

(1

MG. . TICS

20

'1

ID

.....

_ _ _ .,.

HORIZONTAL LOOP 1111 '<100M•• 200,.

~I'\N""

10

10 ~O

40

8P~21

-lO

SIL' I'OTINTIAL I

-100 -1110 -200

Figure 12.13. (Continued) (e) Same as (b) (or line 2 + OOE

quency-effect values continue to n - 4, main1y below zone B, the metal-factor anomaly appears to pinch out at this dcpth. ludging (rom the evidence presented by the shaIlow drilling program, Ibis site is not a particularly good target lor IP. However, a limited amollOt of deep drilling (say, 750 It holes) would be very interestíng, both to determine the dcpth extent of the two zones and to check the IP indication that they are joined at dcpth. lbe inlormation obtained Irom the various surveys on line e is summarized in Table 12.4. We may conclude that all these methods locate the zones reasonably well, with the exception 01 the IP and possibly SP. lbe dip of zone B is estabtished to be steep and to the west. whereas there is considerable doubt about the attitude 01 zone A. OnIy the horizontal-loop technique gives reasonable dcpth estimates; the SP and vertical-loop data, qualitatively al least, suggest that both zones are shallow and that B may tie somewhat deeper than A, although the magnetic profile does not necessarily bear this out.

Dcpth extent cannot properly be determined by any 01 these methods. whereas the width is roughly indicated on1y by the horizontal loop. Final1y, conductivity or conductivity-width producto as estimated by horizontal loop and partia11y by vertica1100p. tells us that zone A is a better conductor than zone B (probably because 01 the width 01 the 10%-sulfide section), but that neither zone is a very good conductor. It is suggested that the interested reader carry out a similar interpretation 01 Line D, 13. lbe profiles in Figure 12.l1b were obtained lrom a bush-road traverse (Pig. 12.11a) in eastem Nova Scotía during base-metal reconnaissance work. !bere is a strong electric and magnetic anomaly in the westem part of the traverse. Interpret the lour sets ol proftles as completely as you can, estimating dcpth, geometry. and character ol the anomaly source. Is there evidence ol conductivc overburden varying in thickness? Consider as weU the sharp teUuríc response arollOd station 31, where the road has


•

•

-

I

719 '2

,.

••

GEOCHEMIITAY

(p:,.~ .-_'ION __

_ e........ c. _. ~

. a.. -

D

.~'--~~-~

==~~

Po,

._100

(Om) ._

tIO 1)0

10

'"

MSPONIE • -1OOF1.n.'

••••""L __ /.. . . ........./\ c.._. . . , ._.-....... .::~~~~~~~. .:a~\~-:'~~__~~~ o 11 i 10

'. "-/'/

=

' " .•••

1:

"r

I .. .... .. .. -

oL-----~~--~~~~~~~~~~~:~~

I

• •

__~____~__~~O t

f MAOHETICS ~ tOO:L__~c==~========~======~==========~=z~==== ~ 2000

__ ______

--

HOIIIZOttTAt. LOOP EM 2400HI. 2001"

._u_····

IEl' POTENTIAl

(dl Figure 12.13. (Cantinued) (d) same as (b) far line 4

tumed north. Given that the VLF station was NAA Cutler, almost due west of the area, could the EM16 profiles be significant in this vicinity? Later, a detaíled helicopter survey was carried out in this region, producing multifrequency EM, VLF, and total·field magnetic data, which are displayed in Figure 12.llc to f over a larger portion oI the same area. Try to locate the ground traverse from the aírbome data and make use of any additional inlormation derived from tbe combination (see §7.5.4, §7.5.5, §7.7.9, and §7.7.l0). The following detaíl will clarify the aírbome data for correlation and further interpretation. The magnetomeler is an optically pumped Cs type taking 5 samples/s: noise level is 0.1 nT. The Herz Totem 2A VLF unit measures total field and quadrature components Cor two stalions. EM equipment consists oC two vertical coaxial-coil paírs (935 and 4,600 Hz) and Iwo horizontal coplanar-coil paírs (4,175 and 34,000 Hz). Coils are separated - 7 m in the boom mounting, which is camed - 30 m aboye ground level.

+ OOf

Lines were flown both N-S and E-W at nominal 200 m spacing. Clearly, E-W line 81260 was out 01 position by about 100 m most 01 the way between the E-W limits on Figure 12.l1c lo f; this figure is within the contraet limit over 1 km. Quadralure data for 935, 4,600, and 4,175 Hz are not included here because they provide no additional information. The same is true Cor the dala on the N-S flight lines which are barren. This faet is significant. 14. The discovery in 1972 of Iwo small eeonomic base· metal deposits near Rouyn, northwestem Quebec, was the direet result of a large-scale aírbome Input (and subsequently other) EM surveys in the region. Both are located on the nortb slope of rbyolite, dacite, and andesite flows bounding the Dufault and Flavrian granodiorite intrusives of the area, about 30 km northwest of Rouyn. Only a limited ground followup with magnetics, VLEM, and HLEM was necessary to outline both mineral wnes, alIhough other geophysical techniques were camed out later. Preliminary drilling at the larger property in late 1972 encountered ore-grade sulfides, while the


720 Table 12.5. Survey

Section

Problem

Figure

Gravity Tellurics VlEM

2.9 6.4 7.9

4,12 7 1

6.35

AFMAG Resistivity IP

7.9 8.8 9.7

7 8 6

5tations

Unes surveyed

53W-24W 55W-23W 42W-34W, 43W-37W 52W-0 42W-35W 44W-36W, 4OW-35W

0,25 O,2S 0,25 6(N), 4, 2,0 O 0,25

7.111 8.47

t---'----'----'--"Ul:::k:JlCldII___---L--......L--1...--' LION

I¡W

2W

o

Anomaly } !mIZ Possible IP

I¡E

2E ~

'n-phuc

_ • • Quadralu",

}

6E

SI'Inpam

Figure 12.14. Slingram and IP results, northern New Brunswick. EM frequency 876 Hz, T-R separarion 200 fl.

___ __

;r~ ~~ ~~~lS~~=~-~~~-~-;--~-~~~~~---B.=L=.==~¿~rx~_~_~::I::~~~3N~;L~6~+OOW ...... -..... -... _~

-5

-Real

Real ud quadralu",

- - - - Quadralu",

(i'J

5~sI

o -S

-

JS I

I

15 ____B.L. .Jn !.us __ IN J

JN I

LI¡ +OOW

Figure 12.15. HLEM profiles, Abitibi West, Quebec. Frequency 1,000 Hz, T-R separarion

300 ft.

olher wu brought in wilh a disc:overy hole in January 1973. The original Input EM map of tbe area is displayed iD Figure 12.i2a, sbowing strong response froin the larger deposit, marked A. Fligbt-line spacing varied between 300 and 1,000 ft (100 and 300 m), 'with the bird at about 300 ft. In Figure 12.l2b, Digbem results at 100 m spacing and ISO ft (4S m) altitude, are illustrated lor the same area. No men-

rabie 12.6. Type of survey Magnetic Turam Resistivity IP

Section 3.9

Problem

Figure

S

7.9 8.8

13

9.7

8

9

8.48 9.25


721

2-S~

~~. 2-O1-_----~~ Bouguer gravily

-,-::...0! L--'--=;;-'-L--'--'-.L---.L.L:7.;:-1---L--L--L~:;-'---L--L....L.-=:-'---'---'-...L..*..J~'--'--'--'-!::--'

-_ "·.0' -

t:

~

__

__

20W

I

"W

'OW

SW

B.L.

SE

VlF-EMI6 Pan.m. ".Iion

Tollurics

, Hz 8 Hz .•-•. _.. 145 Hz -.-

Figure 12.16. Magnetic, gravity, VlF, and tel/uric pro files, eastern Nova Scotia.

Table 12.7. Type 01 Survey

Seclion

Problem

Figure

Type 01 display

2.9 2.9 3.9 7.9

7

1S 11 S

2.39 2.43 3.40a

Terrain conlours Bouguer gravity contours Terrain and magnelic contours Profiles

Topographic Gravity Magnetic EM16

Table 12.8. Type 01 survey Magnetic Telluric Resislivity

Section

Problem

Figure

Type 01 display

3.9 6.4 8.8

11 S S

3.40b

Terrain and magnetic contours Single profile Three profiles

tion is made ol the conduetors along the Magusi River or those south oC anomaly A, whieh appears to strike E- W lor - 2,000 lt (600 m). Ground profiles from three N-S lines over the Dighem anomaly appear in Figures 12.12e, d, e. A1though two of tbe Input eonduetors show magnetic correlation. this was weak as can be seen from the Dighem data. Consequently no ground magnetie measurements were made. The IP survey was earried out later to determine possible lateral and depth extensions of tbe mineral zone.

By selecting a suitable model, make use ol al) data in Figure 12.12 to estimate the depth and deptb extent, dip, strike )engtb, thickness, and al produet oC the conductor. Is tbe lack of a magnetic signature significant witb regard lo mineralization? Are there evidenees of conductive overburden oC variable thickness? lS. The smaller sulfide deposit near Rouyn noted in problem 14 was not detected duriog the Input survey. However, the Dighem operation located it at B on line 66 in Figure 12.13a, where it obviously has

722


.

.

...

....... .

OUI~16~24U~H4~"qU"~«H72"~«M

SEISMIC REFRACTION 6 EMISR OVERBUROEN-SEOROCK SURVEY

¡ H

....---SEISMIC .. EMI6"""MLES -[Mil" OHLY

01:: 1 ===::d'poo ".

r4N~

· 14N

2ON~

""H-+-+-~-+--SHO"T IAULINE

JIN

ZN

·

IN

- IN

4NtIL

MAIN IAULINIE

t--+--1r--t--+-t--t---t-+--+--1r--t--+-+-+--t-+--+-_-

· IL

41

•

1St-

S

ZS

'" zos

• Jt i

· o

ZOE

40[

lOE

lO[

Figure 12.17. Groundwater survey, northeastern Ontario. (a) Survey grid system.

a limited strike length (- 200 m). Again there is no referenee to conduetors aJong Magusi River to the north. Three sets of N-S ground profiles are shown in Figures 12.l3b, e, d. They inelude B-horizon soH geoehemistry, gravity, magnetics, and HLEM on all tbree lines, along with FD IP and SP in Figures 12.13e, d. The sharp magnetie peak: oC 5,000 nT on line 2 + OOE does not appear to comlate witb the gravity profiles; the latter are somewhat anomaJous on aJl three lines, whereas the magnetie feature extends barely 200 Ct (60 m) aJong stme. Carry out an interpretation similar to that for anomaly A in problem 14, estimating the same parameters, but with emphasis on the gravity and magnetie data Attempt to explain the differenees between gravity and magnetie models in terms ol the probable mineralization, as· well as the geometry. Why was anomaly B not deteeted during the Input survey? Mak:e an estimate 01 tonnage and type of mineralization for botb tbese properties. 16. The problems Iisted in Table 12.5 are all Crom tbe same survey area in northeastem Brazil. As noted in problem 12, Section 2.9, the base line Cor Ibis survey, which is at station O, strlkes 20° east, making an angle oC 110° with the Iraverse Iines,

which are due E-W. Thus it is necessary to shift the AFMAG Iines in Figure 7.111; that is to say, Iines 2, 4, and 6 (lines are 200 m apart measured on the base line) should be moved 68, 137, and 205 m respeetively, east 01 line O. 17. The gravity and SP data, problem 11, Seetion 2.9, and problem 2, Seetion 6.4, Figure 6.31, are on the same grid. To these have been added tbe Slingram (horizontal-loop EM) and spot IP results ShOWD in Figure 12.14. 18. Figure 12.15 displays horizontal-loop EM profiles on two Iines tak:en from a survey in northwestem Quebee. Further geophysieaJ results, a11 from line 4 + OOW, are given in Table 12.6. 19. The profiles in Figure 12.16 are a compilation for a single traverse line from a survey carried out in eastem Nova Scotia Other problems dealing witb Ibis area are listed in TabIe 12.7. The contour map of Figure 3.41a may be located with respeet to the other survey data by noting tbat the upper left-hand comer ol the margin is statían 22W, line 12N. As 3D aid to the assessment of Ibis area, it should be explained that the original geophysical reconnaissance was a followup ol a geochemieal anomaly with EM16, SP, and magnetics. Tbe first two methods loeated a weak anomaJy just


723

MAY9, '77 LIS ION-2S SHOT S-N

'~ ~ ~l~'

I

• _/ \ 1-

~ I

1, 1'-1-'''''

..,l

J

¡...

"'1' r-

rt, 1'1'-1-

..

y,

,\

~ It

I

-:2

:&l~

I~

f

~~ ~

¡v'\

(b)

"

,

"

' ....\

\

\

\

(e) Figure 12.17. (Continued) (b) Typieal reversed refraetion profiles, line 16f. (e) Retraetion time- distanee plot, line 16f.

l'

fntegrated geophysical problems

724

N

IEDROCIC CONTOU'" 'ROM SEIIMIC RE'RACTlON

0["" Ino. IUIt'ACI.CIOIfTOUIt INTlItVAL

1

10".

1M

•

•

'01

lO.

1. .

N

t

EMI." SURYrv CONTOURS OF' S[CONO lEO OVE"IURDEN RESISTIYITY IIATCIIIO ANO ,MAOIO lEeTION. INDICAn AIIOIItALCIUI LOW 1IIIIITIVlTY.COIITOUIII or,. IN l11li

., lO

rol

toe

101

101

(t) FiBure 12.17. (Con/inued) (d) Bedrocfr. con/ours from se;smic refrac/ion. (e) EM16 survey con/ours.

Examples and problems lOOOm N

1100

725 1200

1300

1400

1600

1500

1700 m S

SOm 100m

ec:

150m

ti

= I

1.7

•

50 lOO

•

~ al

...

Lo.

150

50

" - I

E

3

100

-

¡;; Lo.

::E

4

•

S

•

150

u

885

-x: a: ... ~.., :jz

1170

..,Iii

415

w:,¡.;

... a: ~Q

... ..1

5000

..1-

u.lLl.

a:

Figure 12.18. Resistivity. (P. and telluric pseudodepth plots. northern Chile.

west oC the base line between lines Oand 8N. FoIlowing the layout oC a small grid. HLEM and limited gravity surveys produeed promising results. The survey area then began to grow. 20. The data contained in Table 12.8 originated in the same area in eastem Nova Scotia. 21. A contraet survey lo map bedrock lopography and eharaeter oC overburden was carried out al a mining site in northeastem Ontarlo to determine Ihe presenee oC groundwater and leikage paths into a nearby open pit. The site lies witbin the regional eonduetive c1ay belt extending across tbis part oC

Ontarlo and Quebee; frequently underlain by sandgravel beds immediately above bedrock. The area surveyed was about 4.000 X 9.000 CI (- 1.200 x 2.750 m), over a praetieally lIat surface; the NW comer was swampy. Seismie refraclion and EM16R surveys were earried out on N-S grid lines spaced 400 ft (120 m). Ihe seismic lines generally 800 fl (240 m) apart, EM16R on all 23 Unes; 10.000 fl (- 3,000 m) of E-W base lines were done wilh both lechniques. The grid is shown in Figure 12.17a. Time limitations made it impossible lo employ resislivity sounding profiles.

726

Because of high attenuatioD in the clay, it was necessary to fire three or more sticks of Tovex high explosive to obtain reasonable bedrock retums at 100 ft (30 m) geophone intervals using a 12-channel seismic unit, and this ruled out measurement of velocity variations in the overburden with smaller spreads (because suñace motion was 100 violent lo give useable tirst breaks). Reverse profiles generally overlapped 400 ft to provide reasonable coverage. Figures 12.17b, c show a typical pair of reversed protiles on line 16E plus tbe time-distance pIols lor the same lineo Determine the velocities and deptbs along the protiles by analysis of Figure 12.17c, assuming a constant velocity throughout the clay and sandgravel overburden, and hence plot tbe bedrock topography. Is there evidence that this assumption is incorrect? Check your result from the contours in Figure 12.17d. Locate possible faults. From a few conventional soundings carried out to measure tbe resistivity of tbe clay and sand-gravel beds, tbe near-surface value ol resistivity was lound to be about 200m, inereasing with the spread length. Results of tbe EM16R survey, shown in contoured form in Figure 12.17e, verified this over much of tbe grid where tbe phase angle was less tban 45 0 and p" frequently increased. In tbe NW portion, however, > 45 0 and p" < 200m at many stations, indicating a more conductive second layer. This is illustrated by tbe shaded arcas. Do tbese zones refteet tbe sand-gravel, the bedrock, or some other possibility? Consider the skin depth in this connection, as well as the fael tha! EM16R measurements are ineapabIe 01 resolving more than two beds.

+

Integrated geophysicaf probfem5

22. Figure 12.18 shows a set of pseudodeptb plots from frequency-domain IP and four-Irequency tellurie protiles over a poryphyry eopper prospect in northem Chile. The IP seetioDS were obtained from a conventional double-dipole array expansion (sce Figs. 9.88, and 9.13) witb x - SO m. Tellurie depths were estimaled from an assumed ground resistivity of 100 Om and by calculating skin depth for each of the four measured frequencies: 145, 32, 8, and 1 Hz. Of course, tbe skin deptbs, whieh are approximately 41S, 88S, 1,770, and 5,000 m, are mueh larger than tbe penetration of tbe double-dipole array, which ranges from SO to 1SO m. The tellurics are plotted on a compressed log scale of about tbe same dimensions as the IP and p" sections. The telluric survey was performed some months alter the IP and there were difficulties in establishing tbe precise station locations ol the latter, although botb traversed tbe same N-S lineo Telluric measurements were made al 30 m electrode spacing. Because of tbe regional aridity, !he IP work (ol whieh this example is only a part), took three wceks. Tbe same eoverage with telluries was done in two days. It is clear that !he three pseudodepth plots from the IP survey have general similarities, becoming inereasingIy anomalous with inereasing n. The p" response, bowever, is weak eompared lo the IP sections, particuJarly the metal factor. What is the probable reason for this? Make a transparency 01 the tellurie data and attempl a tit on eaeh of the other plots. Whieh scems best? Which parameter is aetua1ly measured in a telJurie survey? Is the skin depth a realistie figure?

Appendix A

M athematical Background A.l. DETERMINANTS A determinant is a square array ol nurnbers or syrnbols, ca1led elements, with a rule for finding the value of the array. Determinants are denoted in several ways, for example,

- - 2. Determinants are usually evaluated using the first row or column. but the rule is better iIIustrated by expanding the following determinant using the second colurnn:

det( a) - laul au a21

°22

a10 a2.

a n2

ann

a12

""

a nl

+(_I)J+2(6)lj

the elernent alj being in the ¡th row and ¡th colurnn. Tbe determinant obtained by deleting the i th row and ¡th colurnn is the minor, Mlj , of the elernent a/ j . Tbe quantity, (-l)l+jM;j' is the cofac· lar of a/ j , Al]' One rule Cor finding the value oC det( a) can be stated thus (Pipes and Harvill, 1978, pp. 85-6): ¿aijA/] - ¿aljA lj - det(a) j

~ aljA kj '¡

+(_1)2+2(_8)1~ ~I

(A.l)

- -2( -57) - 8( -43) - 6(11) - 392. Tbe same result is obtained regardless ol which row or column is used. If we expand the preceding determinant using the third row and coCactors oC the first row, we obtain

(_1)3+1(9)1-:

I

O

Ea/JAu: ... O I

*k ¡ *k i

(A.2)

Tbis equation states that the value oC det(a) can be found by surnrning the products of each element of any row (or any column) and its cofactor. However, if we sum products oC any row (or any colurnn) by the cofactors oC a different row (coturnn), the sum is zero. We iIIustrate Equation (A.2) by finding the value ol the determinant

li

~I

Using the first row, the value is (2 X 5 - 4 X 3) - 2; using the first coturnn, we have (2 X 5 - 3 X 4)

~I

~1+(_1)3+2(6)1~ ~I

+(-1)3+3(5)1~

-:1=0

Tbis iIlustrates the second result in Equation (A.2). The solution of a set of sirnultaneous linear equations can be expressed in terms ol determinants using Cramér' s rule (Pipes and Harvill, 1970, p. 101). Given a set of n equations in the n unknowns Xl' X2'···' X n ,

1

aux + a'2x2 + ... +al.x. = a21 x I + a22 x 2 + ':" +a2n x • =

kl} kt

(Aja)

a.lx, + a.2 x 2 + ... +an.x n - k n the solution is Xi =

det(a)/det(a)

(A.3b)

Mathematical background

728 where det(a) is the determinant ol the coefficients and det(a) is det(a) with the jth column replaced by the column (k¡, k 2 , ••• , k,,). As an exampIe, we solve the equations

Q,.

+ 2xl + 7x] 3x¡ - 8xl + 8x] 9xI + 6Xl + 5x]

4x¡

-

- 4

- -15

- 11

The value of del( a) is found to be 392. Then,

2 -8 6

-4 det( al) -

-15 11

- -4

oC 91.

7 8 5

-8

11 1 2 71+ 5 -8

6

1

-664

~I

so that XI - 664/392 - 1.69. The values of Xl and are found by substituting the k column for the second and third columns of det( a).

X,

A.2. MATRICES A matrix is a rectangular array of numbers or symbols (elements) plus rules lor their manipulation. Matrices are represented in several ways; Cor exampie. a matrix oC order (m X ,,) may be written

(A.4a)

Matrices ol the same order (m X ,,) can be added (or subtracted) by adding (subtracting) corresponding elements; thus, if ~,91, "1 are matrices ol the same order, then "1- ~ ± 91 has elements el) - a l ¡ ± b/j" To lorm the product ~91, the orders ol "" and 91 must be (m X p) and (p X "), the product r¡ being 01 order (m X ,,). Tbe elements el¡ are given by the lormula

(A.4b) that is, el ¡ is the sum of the products, elernent by elernent,ol the ith row of ~ and the jth column ol 91. ID general, ~91.,. 91"". To illustrate.

lIi

-4 S (2 X 3)

-

~

-!II

-6 31

6 S 2

2

-8

1

-3 -7

9 3

O 2

(3 X 4)

9 -49 33 3 (2 X 4)

-:11

Tbe elernent CI3 is, lor example, 2 X (- 8) + (- 4) X 9 + 1 X 3 - -49. The lra1t!1pOSe 01 a matm, ""T, is the matrix "" with rows and columns intercbanged. A matrix 01 order (PI X 1) is a eolum" matrix, for example, the k colurnn in Equation (A.Ja). A matrix of order (1 X PI) is a row matrix. A Plull matrix • has uros for a11 elernents; thus, if .JII- 91, then "" - 91-' and eacb elernent of .JII equals the corresponding elernent An (PI X n) rnatm is a square matrix and has a determinant, det( a), whose elernents are those of the matrix; elernents a ll forro the principal diagoPlal oC the matm. A square rnatm in which a11 elements off the principal diagonal are zero but at least one of the diagonal elements is not zero is a diagonal matrix. The identity (unit) matrix is a diagonal matrix with elements QI; - l. A symmetric matrix is a square matm with al ¡ - a¡l; if al) - -a¡I' the matm is

skew symmetric. If each element of a square rnatrix is replaced by its cofactor in det(a) of the rnatm and the result transposed, we get the adjoint of "", adj "". The reciprocal oC "" is

.sr I

-

(l/det( a)} adj ""

(A.Sa)

[provided that det(a) ~ O]; this fottows (rorn Equation (A.2) because on using Equation (A.4b) to find the elements of the product """,,-1, aIl off-diagonal terms are zero whereas a11 diagonal terros equal det(a). The equivalent of division by a square matrix is multiptication by .sr l. If "" is not square, we rnake it square by Cormíng the product ""T.JII, which is always square. Thus, the solutions oC the matm equations ..K - "".#' and !JII- 9191, where "" and 91 are, respectively, square and nonsquare are

Matrices can be used to solve equations. EquatiOD (A.3a) in matrix form is (A.6a) where "" is a square matm ol tbe coefficients. ~ is a columo matrix 01 the unlmowns and Jf" is a column matrix ol the k. 's. Tbe solution is

x.,

(A.6b) Equatiog the (PI X 1) columo matm on the lelt with the producto whicb is also a (n X 1) column matm, we get the n values ol XI'

729

Vector analysis

-8

8

()

>~

L B

~,

-+-,

~I

~

8

A

(b)

(a)

(e)

LJ B

•

Id)

z y

Q

-- -----,..p /

/

//

k

/

M

/

/

//

n

(g)

Figure A, 1. Various operalions on veclors. (a) Two vec/ors lo be added or sub/racled. (b) Addition and sub/raelion of veclors in (a). (e) Summing several vec/ors. (d) Resolving A into eomponents paral/el /0 and perpendicular lo B. (e) Resolving A in/o eomponents parallel lo and perpendicular lo aplane. (f) Resolving A ;nlO rectangular components. (g) /IIuslrating Ihe producls A • B and A x B.

A.3. VECTOR ANALVSIS A.3.1. Baslc Theory AlI measurable quantities can be divided into two classes: (i) sea/ars, which have magnitude onIy, hence can be completely specitied by a single number, for example, temperature and density, and (ü) vectors , which have both magnitude and direction so that they are specified by giving a number (magnitude) and a direction, lor example, lorce and velocity. Vectors will be denoted by boldface letters.

A vector can be represented by an arrow whose length is proportionaJ to the magnitude and whose direction is that oC the vector. To add two vectors, A and B (Fig. A.la), we move one of them as in Figure A.lb, and the sum is the vector from the initiaJ to the finaJ point. The vector - B is B reversed in direction, so we subtract B from A by adding - B to A (Fig. A.1b). SeveraJ vectors can be added together as in Figure A.1e. CaJculations involving vectors are olten facilitated by resolving them into components. Any vector can be regarded as the sum of severaJ arbitrary

730

Mathematical back.ground

vectors; for example, in Figure Alc the sum (A + 8 + C + D) can be a given vector with arbitrary components A, B, C, and D. Sometimes we resolve a vector into components paralJel to and perpendicular to another vector (Fig. Ald) or lo aplane (Fig. A.le). More oCIen we use components parallel lo the axes ol a coordinate system¡ Cor example, in Figure A.U we talce vectors oC unít length, 1, j, and k, along !he x, y, and z axes, and the components oC A are !he scalar quantities a.. , ay, a,. TIten A - a.. i

+ ayj + a,k

-

l

ay/A = cos tl2

-

m

I·I-j·j-k·k-l i·j-j·k-k·i-O

A' B .. ( a) + ayl + a,k) . (b.. i + byl + b,k)

'" ( aJA

+ ayby + a,b,)

(A.IO) From Ihe definition, we sce that A x B - - B X A, a1so (for a right·handed set of orthogonal coordinate axes) IXj-k

a,/A - costl, - n

jxk-i

kX¡-j

IX!-jXj-kxk-O

where 91 , 92 , and 93 are !he angles between A and the three axes. (l, m, n) are the direetion eosines oC A. and A is the magnitude 01 A. Because A2 - a; + + on dividing by A 2 , we have

A X 8 - (a.. i + ayj + a.k) - (a"b. - a.by )!

a: a;.

+( a.. by

(A.8)

X

- a"b.. ) k

j

A - 2i + 3j - 4k B .. 4i-j-Sk C - 2i - 3J + 3k

then

A - 8 + C" (2 - 4 + 2)1 + (3 + 1 - 3)j +(-4+S+3)k

-J

+ 4k

A.3.2. Vector Produds Products involving vectors are oC three basic types. A vector can be multiplied by a scalar lo give a new vector changed only in magnitude; this property is used to write a vector A in the lorm Aa1 where A -1A1- magnitude of A and al is a unít vector parallel to A. TIte other two basic products involve two vectors and are written A • 8 and A x 8. The first, called the dot product or scalar product, ís equal to the scalar quantity (AB cos 9) where 9 is the acute angle betwccn A and 8 (Fig. A.1g); it is aIso equaJ to the magnitude of one oC the vectors times the component ol the other paralJeI to the first. The second producto A X B. called the cross product or vector produet. is defined. as the vector (A B sin 9)0. where n is a unít vector perpendicular to the plane containing A and B and in the direction oC advance

(b.. ! + byj + b,k)

+ (a,b.. - a.. b,)J (A.na)

k (A.llb)

We can add and sublract vectors by adding and subtracting components: if

(A.9)

(A.7)

Also, from Figure A.1f, we gel a.. / A .. cos tl 1

ol a right-handed screw rotated from A lo B (Fig. AIg). TIte definition ol the dot producI shows that A • B - B • A, a1so

Figure A.lg shows that

lA

X BI

- Harea oC parallelogram MN PQ)

This means that aplane area can be considered as a vector with direction along the normal to tbe planeo Therefore we can resolve areas into components; in particular. an infinitesimal area ds can be wriUen ds" (dydz)i

+ (dzd.x)j + (d.xdy)k (A.12)

Vector products may involve more than two vectorso Because (8 • C) is a scalar, it can only enter into a triple product in tbe form (8 • C)A. On the olher hand. (8 X C) is a vector, so we can have the products A' (B X C) and A X (B X C). From Equations (A.9) and (A.llb) we find tbat A • (B X C) - B • (C X A) - C • (A X 8)

(A.13a) - - A • (C X B) - - B • (A X C)

- -C'(BXA) Q..

_ b" e"

(A.13b)

aya,

by ey

b, e,

(A.13c)

Vedor analysís

731

Thus, interchanging dot and cross does not change the value, but changing the cyclic order changes the signo The triple product A X (8 X C) can be expanded twice using Equation (A.llb), the result being A X (8 X e) - (A • C)8 - (A' 8)C (A.14) Although any number of vectors can be multiplied together, products of more than three are rareo

The expression {(a/8x)i + (a/8y)j + (8/8z)k} is known as a vector opera/or; it is represented by the symbol V (pronounced del). When we apply it lo a scalar Cunction (x, y, z), we get V or grad . It can also be applied to a vector function oC position, A(x, y, z), by taking either the dot or the cross product. In the first case we get

V • A - {( 8/8x)i + (8/8y)j + (8/8z)k)

• ( A..,i + Ayj + A,k) - (8A x /Bx) + (BAy/8y) + (BAJ8z)

A.3.3. The Vector Operator V If Ij»(x, y, z) is the value ol a scalar function at P(x, y, z), then the value at a nearby point Q(x + dx, y + dy, z + dz) is Ij» + d~ where

d4» - (a4»/ax) dx + (a4»/ay) dy + (84)>/az) dz (A.lS) Writing dr for the vector displacement from P to Q, we have

dr - dx i + dy j + dz k

(A.19a)

- divergence of A( x, y. z)

(A.l9b)

= divA(x, y, z)

(A.l9c)

In the second case, Equation (A.llb) gives

8/8x

V XA -

Ax

j

k

8/8y Ay

8/8z

(A.20a)

A,

== (8A,/8y - 8Ay/8z)i

and Equation (A.lS) can be written as

+ (8A x /8z - 8A./8x)j

+( 8Ay/8x - aA,J8y)k (A.20b)

(A.l6) =

where

v4» - (al/»/ax)i + (a4J/ay)j + (a4J/8z)k (A.17a)

- gradie,,/ oC 1/»( x, y, z)

(A.l7b)

- grad 4J

(A.l7c)

DividiDg both sides of Equations (A.lS) and (A.16) by dr gives

curiA

(A.20e)

The operator V involves differentiation, and when i I is applied to the product A, being a scalar function. we get two terms involving differentiation oC 1/» and A separately. ThereCore, V • (4)>A) - VI/» • A + V • A

(A.21)

V X (cf>A) - VI/» X A + 4»V X A (A.22) Treating V as a troe vector, we would have

d4»/dr - (V~) • {( dx/dr)1 + (dy/dr)j

+ (dz/dr)k} (A.l8a) - (V4J) ·(ti + mj + "k) (A.18b) - (VI/») • r1

(A.18c)

r1 being a unit vector along PQ with direction cosines (t, m, ,,). Because (V4J)' r1 is the derivative of 4»(x, y, z) at P as we go in the direclion r1, it is called the direc/ional derivative. The vector VI/» is fixed at a given point but (V4») • r. varies as the direction r1 is varied. When r1 is parallel lo V4J, the product will have its maximum value because /1'11 - 1 and cos 9 is a maximum Cor 8 - O. Therefore V4» is a vector in the direction oC, and equal to, the maximum rate of increase oC 4»(x, y, z).

v •V

-

v2

_ 8 2/8x 2 + 8 2/8y2 + 8 2/8z 2 - Laplocion

V X VI/» - O

(A.23)

V • (V X A) 2

V X (V X A) - v(V • A) - v A

=O

(A.24)

(A.2S)

Equalions (A.21) to (A.25) can be verified by substiluting the definition oC V. [Note that Equalion (A.25) is valid only in rectangular cartesian coordinates.) A.3.4. Vector Theorems

The divergence oC a vector has a geometrical interpretation Ibat is oCten very useful. Let A(x, y, z) be


732

written IsA· ds, I lA • ds, IsA. ds, or l/A. ds, is the limit of the sum over Ihe surface S oC prodUCIs of elemenls oC the surface ds and the components oC A normal to the surCace, A.: iC the surface js closed, A. js positive when it is in the direction oC the outwarddrawn normal. A IJolume integral, fv~(x, y, z) dIJ, f I I~(x, y, z) dxdydz, and so on, is the limit of the sum oC producIs oC elemenls oC volume dv and !he values of a scalar Cunction ~(x, y, z) al !he centers . oC du. Gauss 's theorem, a1so known as !he diuergence theorem, Slales !hat (A.27) where the surface S encloses Ihe volume V. To prove !he theorem, we evaluale the firsl term oC Ihe volume integral, (8A x /ax) dxdydz, along a strip parallel to the x axis with cross section dy dz and extending from P.(xl' y, z) lo P2(X2' y. z) (Fig. A.2b). Because y and z are fixed along !he strip, the result is (b)

fv( aa; dX) dy dz

Figure A.2. Vector theorems. (a) Signi(icance of divA. (b) Der¡vation of G.auss's theorem.

a vector equal lo the velocity times density oC a fluid. Relerring to Figure A.2a, the quantity oC fluid entering the e1emenl 01 volume ( dx dy dz) a10ng the x axis per unit time is (A" dydz) whereas that leaving the opposjte Cace per unít time is {A,,+(aA,,/ax)dx} dy dz. Sublracting, the net outward ftow is (iA,,/ax)dxdydz. Adding terms Cor the outward flow a10ng the y and z axes and djviding by the volume dxdydz, we tind that the net loss per unít volume per unít time is

v .A-

divA

-(aA../ax) - -( ap/at)

+ (aAy/ay) + (aA./bz) (A.26)

- {AAx2'y,Z) -A..{x¡,y,z)} dydz

-A x ds-"Ipz +Ax ds-xl", because dydz equals ds-x [Eq. (A.12») at P2 (X2' y, z) and -ds-x al P1(x¡, y, z) (note lhat !he outwarddrawn normal is along !he negative x axis here). Letting y and z vary, !he right-hand side becomes the integral ISA., ds" over the surCace S. Adding tbe integrals along the y and z axcs, we obtain Equation (A.27). Gauss's theorem has an important corollary known as Green's theorem. Wc let A in EquatioD (A.27) be the vector wVu, u and w being scalar Cunetions of POSitiOD, u(x, y, z), and w(x, y, z). Replacing A in Equation (A.21) with V u and ~ wi!h w, we sec that

v ·(wvu) where p js the density 01 the fluid. lbe lollowing theorems involve line, surCace, and volume inlegrals. lbese are discussed in any advanced calculus text, Cor example, Wiley (1966, pp. 559-67), and so we shall give here onIy a very terse dcscription. A líne integral is written in various ways: IlA • di, leA· di, kA • di, lA· di, e denoting a spccitic curve and I a closed curve; the line integral js the limit 01 the sum a10ng the curve 01 products 01 the elcment 01 the curve di and the component 01 A at di and parallel to il. A surface integral, usually

WV

2

u + (vw) ·(vu)

Equation (A.27) now becomes

J.v {wv

2

u + (v w) ·(v u)} dv -

J.(wv u ). ds S

Interchanging u and w and subtracting the two results gives Green's tbeorem:

Curvifinear coordina tes

733 z

y

Qd"

M

,ir

o

N

x (b)

(a)

(c)

Figure A. 3. Derivarlon of Srokes's theorem. (a) fvaluating a fine integral around a rectangle. (b) fvafuaring a line integral around an arbitrary closed planar curve C. (e) Resolving a surfaee integral over aplane triangle into eomponents.

Stokes 's theorem relates the line integral of a vector A along a closed curve C to the surface integral oC curl A over any open surCace that terminates on C. We establish the theorem first Cor the infinitesimal plane area dx dy in Figure A.3a, We talce Ax and Ay as the values of the components at M(x, y). Then the line integral around the rectangle is the sum oí the line integrals along the sides MN, NP, PQ, and QM. Thus,

JA· di - Ax dx + (A,. + (BAy/Bx) dx} dy -{A x + (BAx/By) dy} dx-Aydy - (BAy/Bx - aAx/By) dxdy - (z componentof V X A)(drt

)

(A.29a)

Next we generalize Equation (A.29a) for aplane surCace oC arbilrary shape (Fig. A.3b). We approximate the area inside C by a large rectangle, then add smaller and smaller rectangles untiJ, in the limit, their sum equals the area inside C. The line integral around the perimeters oC tbe first Iwo rectangles in Figure A.3b is along PQRFGHESP (because EF is traversed twice in opposite directions), and in the limi! the path ol the line integral will be Ihe curve C and Equation (A.29a) will become

Because Equation (A.29b) holds lor a plane figure ol any shape, il holds ror aplane lriangle. Any 3-D surrace oí arbitrary shape can be approximated as closely as desired by an infinite number oC plane triangles. In Figure A.3c, tl. PQR oI area ds can be resolved into components (Eq. (A.12») tl.QRO, tl.RPO, and tl.PQO with areas drx ' dr., and drt . The right-hand side oC Equation (A.29bf then becomes three surface integrals over these lriangles with integrands (V X A)x ds x ' (V X A), ds y , and (V X A)t drz • When we sum the contributions for all of the triangles making up S, the line integrals along

interior paths canee" in pairs leaving only the line integral along C; Ihe surface integrals over the triang1es can be replaced by integrals over the component triangles perpendicular lo the axes, which are then summed at each point and reconstituted into (V x A) • ds Cor each e1ement oC area ds. The result is Stokes's theorem:

{ A· dI -

le

1.s(V X A) • ds

(A.29c)

The positive direetion of traversing curve C is the one in which the area is on the leC!. lf we integrate Equation (A.16) a10ng any curve e joining PI and PI we get

(A.30)

Obviously this result is independent of the patb followed. Ir e is closed, 4>2 - c/ll and the integral varushes. On the otber band, ir eurl A vanishes at a11 points, the left-hand side oC Equation (A.29c) vanishes; therefore A must be Ihe gradient oC a scalar. Thus, il curl A - O everywhere,

A - Vc/I

(A.3l)

In trus case A is said to be irrotational, or the fieId ol A is eonservative.

A.4. CURVILlNEAR COORDINATES Often we require the functions div, grad, curl, and the Laplacian in cylindrical, spherical. or otber coordinates. The first two systems, ilIustrated in Figure A.4a, b are related to rectangular cartesian coordi-


734 z 1,

(a)

(e)

figure A.4. Curvilínear coordinares. (a) Cylindrical coordinares. (b) Spherical coordi. nates. (e) div A in curvilínear coordina tes.

nates as follows:

Sphe,ica/

Cylindrica/ x - pcos+ y-psin+

y - , sin I sín+

z-z

1"

x - ,sínlCOS+)

(A.32)

rcosl

In cylindrica1 coordinates we can draw unít vectors i ,i., ir in tbe directions of íncreasing p, +, 1, re-

s"pectivelYi for spherical coordinates the uDÍt vectors are Ir' 1" l •. In botb cases, the three unit vectors are orthogonal. If we write Xl' X2' X, for a set of orthogona/ curvilinear coordinates in general, the coordinate sur· faces XI constant are curved; for example, in spherical coordinates, r constant is a spherical surface, I constant is a CODe, and + constant is aplane. When tbe coordinate x, increases by dx a point moves a " of all tbe x/'s distance h, (/xl where h/ is a function in general. In cylindrical coordinates, hr - 1 - h, and h. - r; in spherica1 coordinates, h. - 1, h, - r, and h. - , sin 9 (because as + changes, r and 9 being fixed, a point moves on a circ1e of radius

r sin 9. hence a change d+ movcs tbe point a distance (rsid) d+). The gradicnt in curvilinear coordina tes is ohtained by rcplacing ax, ay, az in Equation (A.I7) by h1 aXI' h 2 ax2• h , aX3; the result is

vI/! ;. (al/!¡h l aXl)11 + (al/!¡h 2 aX2)12

+ (al/!¡h, éJx,)i,

(A.33)

To find div A, we use the same concept tbat wc used to gel Equation (A.26). Referring to Figure A.4c, the inward flow along thc Xl axis is A1(h 2 dX l h3 dx,) - (hlh3AI) dXl dx , . Subtracting this from the outward ftow [(hlh3Al) + {a¡éJxl (h l h3A1 )} dxtl dx'J, (/x" adding terms for the Xl and X, axes, tben dividing by tbe volume (hlhlh] dx¡ dxz dx,) gives V • A - (1¡ht h2 h])

X {éJ¡aXt(h2h3Al)

+ a¡éJx 2(h,h 1A 2 )

+ éJ¡éJx,( h1h 2 A3)}

(A.34)

735

Taylor's series; Maclaurin's series

To gel tbe Laplacian, we find V 2 - V • V. ApplyiDg Equation (A.34) lo Equation (A,33), we get tbe result

Curl A in spherieal coordina tes is given by Equation (A.36): V X A - (l/r siDO) { B/BO(sinOA.) - BA,/B. }I,

V%,¡, - (l/h1 h 2 h,)[ 8/8xl {( h2 h 3 /h 1 ) 8'¡'/8xd + 8/ 8x l{ (h,h 1 /h 2 ) 8'¡'/ 8xl} +8/Bx,{(h1 h z/h , ) B'¡'/Bx,}]

(A.3S)

We get tbe expression for curl iD tbe same way that we derived Equation (A,29a). Because the dimensions 01 lace MN PQ in Figure A.4c are infinitesimal, we start with the components Al and A, at M, tben apply Equation (A.29a) for aplane area. This gives

I

(v

+ (l/r sinO) { BAr/B. -sin08( rA.)/8r

Ji,

+(l/r){ éJ(rA,)/Br - BAr/BO}i. (A.38)

A.5. TAYLOR'S SERIES; MACLAURIN'S SERIES Taylor's series is discussed in most advaneed cale ulus texts, for example, Wiley (1966). One form 01 the series is

X A}¡hldx2h,dx]

+ {A,h, + 8/8xl( A,h,} dX2} dx] - {A2hl + a/ax,(A1h z ) dx,} dXl

- A 2 h 1 dXl

- A]h] dx,

h2 f(x + h) - f(x) + hf'(x) + -/,,(x)

2!

+ ... +

- { 8/Bxl( A,h,} - 8/Bx,( A 2h 2 )} dX2 dXl (V X Ah

-

h"-1 (n-l)!

f"-I(X) + R(n (A.39)

(l/h 2 h3 ){ éJ/ 8x 2(A , h , ) - 8/8x,( A 2 h 2 )}

When tbe otber two components are found iD the same way, the result can be written:

h 1 i1

h,l, 8/ax] h,A,

V X A - (l/h 1h 2 h , ) 8/Bx1 h1A 1

(A.36) Equations (A.33) to (A.36) can be used to obtain grad, div, curl, and the Laplacian in cylindrical and spherical coordina tes by iDserting the appropriate values of h¡; for example, the Laplacian in spberical coordinates is, from Equation (A.3S),

where f'(x), /,,(x), ... , r-1(x) are derivatives of order 1,2, ... , (n - 1), respeetiveJy, ~ - kh, O < k < 1, and R«() is tbe rema;nder after n temu. Tbe series is valid for al1 values of h provided the n derivatives exist. Also, R(E) "" (h" /n!)f"(~) and approacbes zero as n approacbes infinity. Taylor's series enables us to find the change in [(x) when x inereases by h in terms of h and the derivatives of [(x). The larger h is, the more terms that we must talce to get an aeeurate value of f(x + h). When h is smal1, often tbe first two or tbree terms are sufficient. A special ease of Taylor's series, eaJled Maclaurin's series, is obtained by interchanging x and h in Equation (A.39), tben setting h equaJ to zero. This gives Mac1aurin's series:

X2

f(x) - [(O)

+ xf'(O) + -/,,(0) 2!

x'

+ -/,,(0) + ... 3!

- ( -12 ){ - 8 ( r 28'¡') r ar 8r

(1)

B ( sinOB'¡') + - - -sinO

80

80

(A.40)

where all derivatives are evaJuated at x =- O. As an example, we caJculate tbe series eorresponding to sin x. Beeause the derivatives oC sin x are either ± sin x or ± eos x and these equal O, ± 1 at x - O, tbe series is sin x

x'

=x- -

3!

xS

+-

S!

- ...

(A.4la)


736 In the same way, we get for cos x Xl

cosx -1 - -

2!

X.

+-

41

- ...

(A.41b)

A.6. BINOMIAL EXPANSION If we set n equal to 2, 3, 4, and so on, we can show that the general binomial expansion of (a

+ b)"

Relzl

is

Real Axis

(a + b)"

Figure A.S. Plotting complex quantities in the complex plane.

When n is a positive integer, the series ends with r - n, but otherwise the series is infinite. The infinite series is valid provided lal > Ib~ (Pipes and Harvill, 1970, p. 843). We are interested mainly in using Equation (A.42) to lind approximate values, so we divide through by a" and lben set X - bla so lbat Ixl < 1. Discarding the factor a", the series becomes

" n(n-l) (1 + x) - 1 + nx + 2! x2 + n(n - 1)(n - 2) 31

x, + ...

(A.43)

1

(l=Fx)- -1±x+xl ±x'+·..

(4 - 7j) + (6 + 4J) - (18 - 12j) - ( - 8 + 9j) Multiplication of complex numbers follows the usual rules ol algebra, keeping in mind that j2 - -1, j' - -j, /' - +1, and so on; thus,

(8 - 9j)( -4 - 6j) - -32 + 36j - 48j + S4j2 - - 86 - 12j

Note tbat the series converges (has a ftnite sum) lor aJJ values ol n (Pipes and Harvi)), 1970, p. 843). The series for n - -1, - 2 are especiaJJy uselu1: .

complex numbers are similar to 2-0 vectors, real and imaginary parts corresponding to components. Complex numbers are added (or subtracted) by adding (subtracting) separately the real and imaginary parts; thus,

(A.44a)

(1 =F x)-2 -1 ± 2x + 3x2 ± 4x' + ... (A.44b)

A.7. COMPLEX NUMBERS Because we cannot calcu1ate lbe square root 01 a negalive number, a quanlity such as 01 -7 is said to be imagina'}'. Writing j - .¡( -1) (i is also used), imaginary numbers can be written jy (or yj),y being real; thus, .¡ -7 - )/7. The sum 01 a real number and an imaginary number is a complex nuntber, lor example, 3 - Sj. The conjugate complex 01 z - (x + jy) is ¡ - (x - Jy). A complex quantity I(z) can be represented geometrically in the complex plane; tbis is merely the xy plane with lbe real part, Re{f(z)}, ol a complex quantity plotted on the x axis, the imaginary part, !m(f(z)}, on the y axis (Fig. A.S). Plotted thus,

Multiplicalion by j rotates z and its real and imaginary components through 90° counterclockwise (Fig. A.S). Multiplication of z by z gives (x 2 + y2); the square root ol tbis quantity is the magnitude 01 z, Irl; thus Irl is the length of the line representing z in Figure A.S. Oivision is done by multiplying the numerator and denominator by the conjugate complex of lbe denoDlÍnator (called rationalization 01 the denominator), lben dividing; lor example,

(7 - 2j) (-9+5j)

-

(7 - 2j)( -9 - Sj) (-9 + Sj)( -9 - Sj) -(73 + 17j) (9 2 + 52)

-

-(73 + l7j)

106

A complex quantity is zero only wben its real and imaginary parts are zero. It follows lbat two complex quantities are equal only wben tbeir real parts are equal and their imaginary parts are also equal.

Method of least squares

737

The base of the 5ystem of naturallogarithms, e, is defined by the infinite series, valid for al1 values of x, X

x,

X2

e" - 1 + - + - + - + ... 1! 2! 3!

(A 45a) .

Selting x-O, we get a series from which the value of e can be ealculated. Replaeing x with ±jx, we get \he following series:

(In finding the fourtb root ol z, insertion ol 2T'lT gives four dislinet rools; tbese repeat when r> 3.)

A.8. METHOD OF LEAST SQUARES Assume Ihal we me asure a quantity y for various values of x and end up wilh a set of values (yj' x¡); oflen we wish lo express y as a Cunclion of x in the form

e+J" -1 + jx - (x2/2!) - j(x'/3!) + ... (A.45b)

e- j "

-

1 - jx - (x2 /2!) + j( xl/3!) + '" (A.45c)

Comparing these series wilh Equations (A.41), we find lhat cos x -

Hel" + e-

j

")

}

sin x - (l/2j)( el" - e-P') (cosx + jsinx) - ei". } (cosx-jsinx) -e-'"

(A.46a)

(A.46b)

Replacing x by nx, we get De Moivre's theorem: ( cos nx

± j sin nx)

- e ± Ju

-

(eos x

± j sin x) " (A.46c)

When z - x + jy, we define 8 by the relation (Fig. A.S) 8 - tan-ley/x) ... tan-l[.I'm{z}/!R~{z}] (A.47a)

In principIe, we could solve for the (m + 1) unknowns al if we had (m + 1) seis ol values (Yj. XI)' but usually we bave 1'1 sets. n > (m + 1). so the conslants a j are "overdelerrnined." In this case we look for Ihe "besl-fit" solution; the usual criterion for best lit is tbat the sums of the squares of lhe "errors" be a mínimum, an error being the difference belween a measured value of y, and the value calculaled from Equation (A.48) for the corresponding value x, and lhe best-fit values of a j • Squares ol the errors are used to avoid cancellation of positive and Desalive errors. The sum of the errors squared is E-

Le? ¡

- L{y¡ -

(a o + al x¡ + a2xl + ...

(A.49) To gel the mínimum ol E, we vary Ihe (m benee for each a j,

where 8 is the phase of z. Also,

íJE/íJa, - O z -lzl(cos8 + jsin8) -lzieJl

Equalion (A.46b) again, we obtain (A.47c)

L {y¡ -

(ao + a1x¡ + a2xl

so Ihat ~x'j + a1 L.. ~ x,+l + alL.. ~ x,+l aOL.. , ¡ I

i

The polar form of z is convenient ror multiplieation, division, and finding powers and roots; for example. ir Zl -lzlleJl, and z2 -lz2IeJl,. tben

(l zll11 z20 eJ("

+'2)

zl - IZ11SeJ SI, zV4 - IZ11l/4ej (1¡ +2",)/.

+ .. ,

+a",I:Xr+ m ... Ly,xf I

(A.SO)

I

where r - 0,1,2, ... , m (note that for r - O, E,x? n and L,y¡X? - E/y,). Tbis set of (m + 1) equations can be solved for the (m + 1) a¡'s.

Zl z2 - IZ1I1z1Ie}(1¡ +'2) ztlZl -

+ 1) a/s;

I

(A.47b)

using Equation (A.46b); this is known as lhe polar form of z. Cbanging tbe sign of j sin 8 and using

+a",x;,,)}l

I

r - 0,1.2.3

For a more detailed discussion, including the matrix solution oC Equation (A. 50), see Sheriff and Geldart (1983, §1O.1.5).


738

1..9. FOURIER SERIES ANO TRANSFORMS

where the coefficients are given by equations such as

1..9.1. Fourier Series

bm "

A periodie funetion 1(1), which repeats itself exactly after each interval T, can (with few exeeptions) be represented by a Fourier series of the form

-

(4/~:r,.) XfT/2 fT/2 g(x,y)cosmw.,xsinnw,ydxdy -T/2 -T12

(A.S2b)

g( t) - ao + al cos "'0' + a2 cos 2~t + .,. +a" cos n~1 + .,. +bl +

sin~t

bz sin2~t + '" +b" sin n "'01 + .. , (A.Sta)

where ~ = 2"'''0 - 2"'IT is the fundamental angular frequency and t is the independent variable (often time or distance). TIte frequency n~ is the nth harmonic oC the Cundamental ~, and so expressing a funCtiOD as a Fourier series is called harmonic analysir (the same name is applied to transCorming a funetion into its Fourier transform; see §A.9.2). TIte integral over the interval T 01 the produet 01 any two cosines, two sines, or sine and cosine in Equation (A.SIa) is zero ex:cept lor the integrals oC cos 2 n~t and sin2 n~I, and these both equal T12. Thus, to find the values oC a" and b" we multiply both sides of Equation (A.Sta) by cos n~t lo gel a", then by sin n~1 to get b•. Integration over the interval T resulls in

a" - (2IT)

b" -

T/2

f-T/2g(t)cosn"'otdt

(2IT) fT/2 g( t ) sin n~ldt

(A.Stb)

Equation (AS2a) defines a Fourier surlace that can be fitted to a two-dimensional set 01 data, for example, gravity readings over an area, by finding the four sets oC coefficients using double surns equivalenl to lhe integral in Equation (A.S2b).

1..9.2. Fourier Integra'; Fourier Transforms Equation (A46a) can be used to wrile Equations (A.Sl) as +110

g( 1) -

E a"e}lIwor

-110

a" - (liT) fTI2 g( t) e-¡""o' dI -T/2

n-O,

± 1, ± 2, ... , ± 00

(A.S3)

Combining the two relations gives

g(l) -

+110

T/2

-110

-T/2

E (1IT)eJ""o'!

g(/)e-¡·"o' dI

If we let T approach infinity, g( 1) repeats itself at longer and longer intervals; in the limit when T - 00, g( 1) does not repeat, hence is aperiodic. The preceding expression then becornes the Fourier integral:

-T/2

g(/) - (l/2fT)!_:e¡"'{fOllOg(t)e-JW'dt} dw In practice Fourier series are used to analyze a set cf observations, such as gravity readings along a

(A.S4)

profile; the integrals become sums, the length 01 the profile is T (note that this means that we are assuming that the readings wiU be repeated exaetly ir the profile is extended), and the relative values 01 a", b" [more accurately, (o: + b;)l/2) are interpreted as mUfPiitudes oC the nth harmonic. Fourier series can be developed Cor more than one dimensiono TIte 2-D form is

(see Wiley, 1966, §6.7, lor more details). If we evaluate the integral within the braces, we get a Cunction ol w; then the integral with respeet to fA) gives us g(t) again (except for the factor 1/2".). The Fourier integral is easier to apply ir we break Equation (A.S4) down into two operations:

G(w) 110 110

g(x,y) -

-110

E E(a",,, cosmw"xcos nw,y

- Fourier Iranslorm ol g( t) llO g(t) -(l/2fT)f G(w)e¡"'dw

o o

+b"," cos mw"x sin nw,Y

(A.SSa)

-110

- inverse Fourier transform of G( w) (A.SSb)

+c",.. sin mw"xcos nw,Y

+ d",,, sin mw"x sin nw,y)

fIlO g(t)e-¡W' di

(A.S2a)

When I is time, application 01 Equation (A.SSa)

739

Fourier series and transforms

transforms g(t) from che time domain into tbe frequency domain whereas Equation (A55b) does the reverse. (The terms time domain and frequency domain are often used even when t and 101 are not time and frequency.) The distinction between transform and inverse transform is arbitrary and is due to our greater familiarity witb the time domain. The Fourier transform has several advantages in data processing. Equations (AS5) show tbat g(t) can be transformed into the frequency domain, tben back to tbe time domain unchanged, tbat is, tbeoretically chere is no error involved [in practice tbe integrals must be calcutated numerically and so errors (1oss of information) exist, but tbese can be made as srnall as we wish]. A rnajor advantage is that we can do part of the processing in one dornain and parl in tbe otber, laking advantage of tbe fact tbat sorne processes can be executed more economically in one dornain tban in the otber. The functions g(/) and G(w) [G(JI) is sometimes used, 101 being replaced by 2"-JI in the exponentials in Eqs. (A.55), dw/2fT becoming dJl] are referred to as a transform pairo The relation between them can be expressed as g(l) ... G(w). In general, G(w) is complex and can be written in the form [Eq. (A.47b)]

G( (01) - A( (01) e l.(")

(A.56)

Shift theorems: g(t - k) ... e-j""G(w)

(A.58a)

e-Jk'g(l) ... G(w + k)

(A.58b)

Sca/ing theorem: g(k/) ... (l/lk¡)G(w/k)

(A.59)

Symmelry theorem: G(t) .... 2'ITg( -(01)

(A.60)

Derivalive rheorems: d" (1) g

dt"

.... (jw)"G(w)

" d"G(w) (-jt) g(t).... dw"

(A.6la) (A.6lb)

Integral theorem:

f'

g(/) di'" (l/jw)G(w)

(A.62)

-00

A(w) is tbe frequency speclrum and +(w) is the phase speclrum of g(I). Like tbe Fourier series, Fourier transforms can be used witb functions of several dimensions. In two dimensions, we have G(IC", lC y } -

¡"'" ¡"'" g(x, y)e-j(··H',y) dxdy, - "'" - "'"

(A.57a)

g(x, y) - (1/2,,-)2 X

loo loo G( IC -00

-00

A"

IC) e /(-.+-,) dlCJI: dlCY Y (A.57b)

where IC" - 2fT/A" and IC" ca 2fr/>'" (compare with w - 2"-/T). Calcu1ation ol Fourier transforms of continuous functioDs is often quite difficult; however, in practice we use digital functions main1y (§A.9.3) and their transforms are easy to calculate. Calculation of both types is greatly lacilitated by using several tbeorems regardiDg Fourier translorms¡ we list che most important of these in Equations (A. 58) to (A.62) and give brief explanations of tbeir applications. Otber theorems plus proo!s can be found in Sheriff and Geldart (1983, pp. 164-6).

When we add a constant to the independent variable, functions of the variable are shirted atong tbe horizontal axis; for example, che curve y(x - 3)2 is the curve y - X2 shifted tbree uníts to the right¡ y'" (x + 3)2 is y - xl moved to tbe teft tbree units. Equation (A.58a) states that sbifting g(l) k uníts to the right multiplies the transform by exp( -jwk); shifting G(w) k uníts to the left multiplies g( t) by exp( - jkt). Also, ir we know G( w), we can write down the transform of e-¡k'g(l) by inspection. Equation (A. 59) permits us to replace t with, for example, -7t/8, without having to recalculate the transformo Equation (A.60) is useful in obtainíng new transforrns; if we know a transform pair, g(t) and G( w), we get a new transform pair by replacing w in G(w) witb 1 and.t in 8(1) with -101. The derivative tbeorerns are probably the most important tbeorerns. Equation (A.61a) enables us to replace transforms of derivatives of g(t) with (jw)ft times tbe transform ol g(l)¡ tbis is very useful in flnding new transrorms and in replacing differeDtial equations with algebraic equations (§A.13). Equation (A61b) is useful in getting transforms of ,"g(,). Equation (A.62), although used infrequently, is nevo erthdess important; note that for causal functions (§A9.3), tbe lower limit of the integral is zero.

740


A.9.3. Digital Functions; z Transforms A continuous function g(t) has a definite value for a11 values of t (disregarding discootinuities, iofinite and multiple values), whereas a digital function, which we write as g" has values only at discrete values 01 t; lor example, a seismíc trace (§4.1.3) may be sampled at intervals ~ • 0.002 s so that g, is known on1y at the diserete times 0.000, 0.002, 0.004,. .. s, or we mígbt measure gravity values aloog a line at intervals of 100 m so that gx is known only at points 100 m aparto (Wbenever convenient. we talce ~ - 1, that is, we talce it as the unit so that I - n or x • n inslead ol n~.) The unil impulse or Dirac delta, B(I) or B" is by definition zero lor all values of t except I == O where B(,) (or B,) equals + 1 (for a more rigorous delinition, see Papoulis, 1962, Appendix 1). The product g(t) 8(1) • g(O), the value of g(l) at 1'" O. The shilted impulse B(t - n) or B,_n is zero except at t • n. A comb is an infinite series 01 unit impulses spaced at intervals ~; thus,

L

(a)

I ~f(l) ~~ O

(b)

I ~ ¿-'It&: ~ f(tl

o

T

(e)

Figure A,6. lIIustrating f(t) • g(t). (a) Two funclions, 1ft) and g(t). (b) 8(1) reflected in the vertical axis. (e) g(l) refleeled and displaced T unils lo Ihe righl.

ao

comb(t) -

o

B(I - n)

-ao

n-O,

± 1, ± 2, ± 3, ... , ± 00

Multiplying g(l) by comb(t) gives g,:

8,·

ao

LS(I)B(t-n) -00

often need values of G(z) for a large range of z values (lhal is, t.o) values); if we adopt the straigbtforward approach, the calculations are extremely laborious. However, the method known as lhe lasl FOUl'ier Iranslorm (FF1) reduces the labor by a factor of 103 or more when n > 103 [Sheriff and Geldart, 1983, §10.6.4].

Nonnally the digital functions that we encounter are

causal, that is, they are zero for negalive values of t; in this case the first tenn is 80. If we subslitute 8(1) for g(l) in Equations (A.55a) and (A.58a), we find that

8(t) .... e-}wII,_o· 8( t - n) .... e-j"OJA

+1}

A.10. CONVOLUTION The convolution al two functions, I(r) and g(t), often written 1(1). g(I), is defined by the integral

(A.63)

Accordingly, the transfonn ol S, is

(A.64) where , . e-jt.I4. The rigbt-hand side ol Equation (A.64) is G(I), the I translorm of g,. Obviously, calcu1ation ol I transfonns is trivial, lor example, for a causal function ,,- 0.56, - 1.24, - 2.45,0.67, 3.78, tbe I transfonn is 0.56 - l.24z - 2.45z 2 + 0.67z' + 3.78z·. In data processing, PI in Equation (A.64) may be severaI hundred or thousand; at the same lime we

The curve g( - t) is g(t) reftected in the vertical axis (Fig. A.6a, b) and g(T - t) js g(-I) moved T units to the rigbt (Fig. A.6c). Thus, geometrically, Equalion (A.65a) means that we reftect g(I), move it T units to the right, and then sum the products of the corresponding ordinates. The result depends on the displacement T, hence the argument T on the ldt side of Equation (A.6Sa). For causal functions of length m and n, it is obvious that O ~ T ~ (m + n). Also, we get the same result jf we reflect and displace 1(1) jnstead of g(I), thal js, (A.66)

Laplace transforms

741

lbe convolution theorem states that

therefore

cf>/. ( T)

~

To prove the theorem, we write

convolution of f( t) with g( - t) (A.7ta)

cf>,,( 1") ... convolution of f( - t) with g( t) fCr) - g( 1")

(A.7tb)

.... { : {f_:f( r)g( T - r) dt} e- J'" dT

using Equation (A.SSa) with T in place of r [because f( T) - g( T) is a function of TJ. Interchanging the order of integration and writing s - T - t and ds dT (because t is fixed in this integration), we obtain

f( 1") - g( T)

. . f"./( I){

f_:

g( s) e- j .,(8+t) ds} dr

The cross-co"elation theorem states that (A.72a) The prooC follows directIy from the proof of the convolution theorem 00 changiog the sigo of t in the argument oC g( T - t) in the lirst step oC the prooC. The digital forms oC Equations (A.70a) and (A.72a) are

.... f'.1J f(t)e-JOI'dtf'.1J g(s)e-j."ds -00

-00

.... F(w)G(w)

where - m < k < n or - n < k < m.

For digital functions. Equations (A.65a), (A.66), and (A.67a) are f •• g. - Lfkg.-k - Lgkf.-k k

where

(A.67b)

A.11.2. Autocorrelation

where the sums in Equation (A.65b) are over the appropriate values of k (O ~ k ~ (m + n )]. In two dimensions the convolution of f(x, y) and g(x, y) becomes (Sherift' and Ge1dart, 1983, §1O.3.9)

f( T. a) • g( 1". a) -00

e+j..tl. and F(z) - F( z).

(A.65b)

k

f.-g ..... F(z)G(z)

- ¡OO ¡OO

z-

(A.72b)

If f( t) is the same as g( t). the cross-correlation becomes the autocorrelation. Replacing f(t) with g(l) in the preceding sectioo, we get the followiog results.
loo g( t) g( t + T) dt .... IG( w)l2

(A.73)

00

f(x, y)g( T

_

x, a - y) dxdy

(A.74)

-00

(A.68) A.12. LAPLACE TRANSFORMS

and the convolution tbeorem states that

A.12.1. Basic Theory A.11. CORRELATION A.11.1. Cross-Correlation The cross-correlation of f(t) and g(t),

¡OO f( t) g( t + T) dt

(A.70a)

-00

Ir we find the coovolution of f(t) aod g( - t), we change g(T - t) in Equation (A.65a) to g(T + t);

Laplace transrorms are c10sely related to Fourier transforms (Sherift' and Geldart, 1983. pp. 172-4). The commonly used Laplace transform is one-sided, that is, the transform integral has the lower limit t = O, so that all fuoctioos are io effect causal. The transforrn pair g(t) .... G(s) is delioed by the relations

G(s) -l°Og(t)e-" dt o (O +j'"

(A.75a)

g(l) - (1/2'ITj) J_ . G(s)e" ds (A.75b) a-JIM

742


where s - (J + jw, (J is positive and large enough that Iim,_ .. g(l)e-'" - O (in practice almost all functions satisfy this requirement). Generally G(s) is more easily calculated than G(w), but the inverse transformation of Equation (A.75b) involves integration in the complex plane, wbich is usually difficult. Fortunately, many extensive tables of Laplace transforms are readíly available (for example, Pipes and Harvill, 1970, Appendix A), so we get transform pairs from tables, just as in the case of integrals. Most theorems for Fomer transforms have counterparts for Laplace transforms. The most useful are listed in the following equations (proofs can be found in Sheriff and Geldart, 1983, pp. 173-4): Shift Iheorems: g(l - a) ++ e-"'G(s)

(A.76a)

+ a)

(A.76b)

g(al) ++ (1/a)G($/a)

(A.77)

e-II'g(l) ++ G(s Scaling rheorem:

Derivalive theorems:

Many transCorms can be Cound by using the theorems, for example, the transform of sin al can be found by differentiating cos al; te'" can be found by applying Equation (A.76b) to the lransCorm oC r" with n - 1; I sin al can be found using (A.78b). Two useful "spedal" functions are the unít impulse, 8(1), introduced in Section A.9.3, and the unil srep ¡unclion, "(1), defined as I ~ 1~

14(1) - O

- +1

O}

(A.79)

O

The step function is discontinuous at I - O; it is often used to "wipe out" a function for I < O; thus, t~O

cosatu(l) - O

- cos al

I ~

O

The transCorms oC 8(1) and 14(1) are easily found Crom Equation (A.75a):

8(/) - +1

u(t)

-l/s

(A.SO)

d"g(I)/dt" .... s"G(s) - s"-lg (O +)

- s"-2gl(0 +) - s"-'g2(O +) - ... - g"-I(O +) (A.78a) (-I)"g(l) ++ d"G(s)/ds"

A.12.2. Calculatlon 01 Laplace Trans10rms Many transforms are easily found using Equation

.1/( .1 2 + a 2 ) sin al .... a/(s2 + al)

cos al

++

t" ++ "!js,,+1

le'" .... 1/(s _ a)2

t sin al'" 2as/(s2 + a2)2

The error fundion. erf( x), is defined as

(A.78b)

The notation g(O + ) and g'(O + } denotes g(l} and d'g(I)/dt' evaluated at 1-0 where I approaches zero from the positive side (this allows Cor discontinuities at 1-0). Pourier transforms are convenient for studying the frequency and phase characteristics of a function whereas the Laplace transform is more useful in studying the analytical properties of the transform (as in filter design). 80th are useful in solving dífferential equations with constant coefficients, the choice dependíng mainly on the type of boundary condítions.

(A.7Sa); for example,

A.12.3. Transforms 01 the Error Functlon and its Derlvatives

(A.81) We also use erfc(x) - 1 - erf(x} wbich is the complemenraTy error ¡unclion. Prom the definítion, erf(O) - O, erf( + 00) - 1. The error function is tabulated in many handbooks (for example, Gradshteyn and Ryzhik, 1965). Derivatives or erre x) can be obtained Crom Equa. tion (A.SI). Thus, erf(x) - d/dx{erf(x)} - (2/,,1/2) e-,,2 (A.82a) on using Leibnitz' rule (Wiley, 1966, p. 274; Kaplan, 1952, p. 218). If x is replaced by (a/2t 1/2) [Eq. (7.31)] and we write erf(a/2tl/2 ) for the derivative of erf(a¡U/2) with respeet to 1, then on setting y - (a/211/2 ), we find erf'( a/2t1/2) - d/dy{ eñ( y)} dy/dt _ (2/,,1/2) e-YZ( -a/4t 3/2) _ ( - a/2,"I/2t 3/2) e- a2/4' (A.82b)

743

Linear systems

We can expand erC(x) in a power series, one Corm being (Pipes and Harvill, 1970, p. 493) erf( x) - (2/".1/2){ x - x l /3 x 1!

+ x S/5

x 2!

Stegun (1972) and Erdélyi (1954) respectively, extend tbis series: e-«·,/2/S3/2 ...

2(1/1I')1/2 e -«'/4'

-

aerfc( a/2t1 / 2 ) (A.85c)

- ...

+( _1)n x 2 n+1/(2n + 1) x n! + ... }

e- ....I/Z /S2

...

(A.83)

t( 1

+ a 2 /2t) erfc( a/2t l / 2 )

_ (21/".1/2)( a/2t1/ 2 )

e-«'/4,

(A.85d)

The Laplace transCorm of erfc(a/2tl/2 ) is listed in most tables (Pipes and Harvill, 1970, p. 778):

A.13. LINEAR SYSTEMS bence erf( a/2tl /2) u(t) ... (1 - e-·"I/1)/s (A.84b) on using Equation (A.SO) [U(I) is usually omitted in tables). Altbough a is a constant in Equation (A.84), we can tix t and vary a; tben

iJ/iJa - iJ/iJy( iJy/iJa) - (1/2t 1/ 2 ) a/ay Writing Equation (A.84b) in tbe Corm oC Equation (A.75) and differentiating witb respect to a under tbe integral sign, we obtain

fo'( 1/211/ 2 ) erf'( a/2tl / 2 ) e-SI dt _ d/dex{ (1 - e-

cul

/1)/s} == e-cul/Z /SI/2

The term syslem, as used here, refers to a set oC objects and/or concepts such Ihat an input signal applied to lhe system results in an outpUI signal. We concero ourselves solely wilh lhe reIation between lhe inpul and oulput signals, and not with lhe inner workings of the system. A syslem is linear if lhe outpul h(l) is proporlional lo the inpul signal of g(t). If we were lo study tbe inner workings oC the system, we couId, in principIe, describe the relation belween h(t) and g(l) by a linear ditrerential equation with constanl coefficients. Because the order oC the equation is rarely more than 2, we take as a typical equation d 2 h(l)

dt 2

dh(l)

+ QI-;¡¡- + a2 h ( t) - g( 1) (A.86)

Taking Fourier transforms and using Equation (A.6la), we get

Comparing witb Equation (A.75) we see that

so

H(w)

Using Equation (A.82a), Equation (A.85a) becomes

= F(w)G(w)

where

F(w) Differentiating again witb respect 10 ex, we get

or, on using Equation (A.82a),

Equations (A.85) and (A.84) comprise a series oC translorm pairs with descending powers oC s. The following two pairs, found in Abramowitz and

2

{

(jw) + (jwatl + a2

} -1

(A.87a) F( w) being the transfer fune/ion. If we know F( w), we can tind H( w) for any input G (w). If we apply a unit impulse 8(1) to tbe input, then G(w) - 1 from Equation (A.63) and the transform oC F( w) gives the output, Ihat is,

F( w) ... f( t) - unil impulse response Thus, application ol a unit impulse al tbe inpuI oC a

744


linear system gives us the data to calculate the output for any other input Equation (A.87a) can be written in terms of Laplace transforms, the onIy difference being that use of Equation (A.78a) adds terms in h(O + ), h'(O + ), and h"(O + ) to G(s) [which replaces G(w) in Eq. (A87a)]; however, the usual assumption is that the system is ¡n¡tially relaxed, meaning that h(O + ) - O - h'(O + ) - h"(O +), so that Equation (A.87a) becomes H(s) - F(s)G(s)

}

where

(A.8Th) F(s) -

(Sl + als + a1r

1

REFERENCES Abramowitt, M. and Stegun, l. A. 1972. Handbook 01 Math~mot¡cal FlUlclions. Nat. Bur. of Standards. Washington: U.S. Gov', Prinliog Officc. Erdl!lyi, A. (ed.) 1954. Tab/~s 01 lnl~gral Transforrns, uol. l. New York: Mc:Graw-Hill. Gradshteyn. l. S. and Ryzhik, 1. M. 1965. Tabl~s ol'nt'8rals, S~ri~$, and Products. New York: Ac:ademic:. Kaplan, W. 1952. AdVQnc~d Calculus. Rc:ading, MA: Addisoo-Wesley. Papoulis, A. 1962. The Fourier Inlegral and lIS Applications. New York: McGraw-HiIl. Pipes, L. A., and Harvill, L. R. 1970. Applied Malhemalics lor Engineers and Physicisls. New York: McGraw-HiII. Sherilf, R. E., and Geldarl. L. P. 1983. Explorarion Seismology, Vol. 2. Nc:w York: Cambridge University

Press. Wiley, Jr., C. R. 1966. AdlJanced En8ineerin8 Mathematics. New York: Mc:Graw-HiII.

APPLIED GEOPHYSICS Telford Geldart

SECONO EOITION

Sheriff

This is the completely revised and updated version of the popular and highly regarded textbook, Applied Geophysics. It describes the physical methods involved in exploration for hydrocarbons and minerals. which include gravity, magnetic,seismic, electrical, electromagnetic, radioactivity, and well-Iogging methods. AII aspects of these methods are described, including basic theory, field equipment, techniques of data acquisition, data processing and interpretation, with the objective of locating commercial deposits of minerals oil, and gas and determining their extent. In the fourteen years or so since the first edition of Applied Geophysics, many changes have taken place in this field, mainly as the result of new techniques, better instrumentation, and increased use of computers in the field and in the interpretation of data. The authors describe these changes in considerable detail,including improved methods of solving the inverse problem, specialized seismic methods, magnetotellurics as a practical exploration method, time-domain electromagnetic methods, increased use of gamma-ray spectrometers, and improved well-Iogging methods and interpretation. As before, the intent is to be practical, and thus many field examples and problems are given, In this edition the authors have adopted SI (Systeme Internationale) units to a considerable extent, but other units are also used where SI units are still not in common use in exploration geophysics. The authors assume that the reader has at least a general background in geology, physics, and mathematics. While many of the derivations require more than an elementary knowledge of mathematics. readers may skip these if they are interested only in the results. An appendix gives a concise explanation of the more advanced mathematics used in the book. This is the most complete book available on the subject. It is suitable as a text for an undergraduate geophysics course for geologists, geophysicists, and engineers, as well as for more advanced study at the graduate level. Its comprehensiveness makes it eminently suitable as a reference work for professional geologists, geophysicists, and mining and civil engineers. Reviewer praise for the first edition of Applied Geophysics

" It is an excellent text book ... it will serve well as a reference for practicing geophysicists and for other earth scientists who become closely involved with geophysical prospecting. I believe that it will be necessary for almost every practicing exploration geophysicist to have a copy available to him. The book is well produced:' G. V. Keller, EOS: Transactions. American Geophysical Union "This book provides a thorough and comprehensive treatment of the various geophysical measurements used in the search for hydrocarbons and other minerals. An obvious effort has been made to describe pertinent geologic concepts in ways that make understanding easier for physicists, mathematicians, and electrical engineers!' Mahlon M. 8all, American Association of Petroleum Geologists Bulletin "This particular volume is an excellent complete treatment of applied geophysics, useful both as a comprehensive textbook and as a basic reference. The knowledgeable economic geologist can be well prepared for a variety of important applications of geophysical methods. A total compilation in exploration geophysics." John A. Sumner, Economic Geology

ISBN O- 52 1 - 3393 8 - 3

JU121 3J383

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126380767-Applied-Geophysics-by-W-M-Telford-L-P-Geldart-R-E-Sheriff

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