1_Basic_Concepts.pdf

Chapter 1

Basic Concepts Introduction A principle that is emphasized throughout this book is that the physics of any multicomponent seismic technology cannot be understood unless that technology is viewed in terms of the particle-displacement vectors associated with the various modes of a seismic wavefield. This material therefore begins with a discussion of seismic vector-wavefield behavior to set the stage for subsequent chapters. Several approaches can be used to explain why each wave mode of nine-component (9C) and three-component (3C) seismic data that propagates through subsurface geology provides a different amount and type of rock /fluid information about the geology that the wave modes illuminate. Some approaches appeal to people who have limited interest in mathematics. Other options need to be structured for people who have an appreciation of the mathematics of wavefield reflectivity. Another argument that can be used focuses on the fundamental differences in P-wave and S-wave radiation patterns and the distinctions in target illuminations associated with 9C and 3C seismic sources. We will consider all of those paths of logic. A principle that will be stressed is that each mode of a multicomponent seismic wavefield senses a different earth fabric along its propagation path because its particle-displacement vector is oriented in a different direction than are the particle-displacement vectors of its comp compani anion on modes. modes. Alth Althoug ough h esti estimati mations ons of of earth earth fab fabric ric obta obtained ined fro from m variou variouss mod modes es of a mu multi ltico comp mpon onen entt se seism ismic ic wav wavefie efield ld can di difffe fer, r, eac each h es estim timate ate sti still ll can be co corr rrect ect be becau cause se each wave mode deforms a unit volume of rock in a different direction, depending on the orientation of its particle-displacement vector. Those deformations sense a different earth resistance in directions parallel to and normal to various symmetry planes in real-earth media. The logic of that nonmathematical approach appeals to people who are interested in the geo geolog logic ic and pet petrop rophys hysical ical inf inform ormatio ation n that mult multicom icompon ponent ent seis seismic mic data can provide and are less concerned about theory and mathematics. A second approach that is helpful for distinguishing one-component (1C), 3C, and 9C wavefield behavior focuses on the mathematics of the reflectivity equation associated with each mode of the full-elastic seismic wavefield. The mathematical structure of the reflectivity equatio equation n associated with with each seismic wave mode describes describes why and how petrophyspetrophysical properties of the propagation medium affect different wave modes in different ways. The logic of that analytical approach is appreciated by scientists who are comfortable with mathemati mathematics. cs. All of these concepts lead to the development of a new seismic-interpretation science based on multicomponent seismic data called elastic wavefield seismic stratigraphy. The

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Multicomponent Seismic Technology

principles of this science are discussed in Chapter 6. The fundamental assumption of elastic-wavefield elasticwavefield seismic stratigraphy stratigraphy is that any mode of an elastic wavefield can provide uniquee rock, fluid, or sequenc uniqu sequencee inform information ation across some stratigr stratigraphic aphic intervals that cannot be obtained with the other wave modes of the elastic wavefield.

Vector-based thinking A thought process based on vector concepts has to be used when developing and applying multicomponent seismic technology, regardless of whether the effort involves 9C, four-component (4C), or 3C data. For decades, much seismic technology has been scalar based. For scalar data, it is not necessary to know the direction that a seismic wave mode moves the earth to use the data. In multicomponent seismic technology, it is man manda dato tory ry to kn know ow th thee dir direct ectio ion n of ea earth rth dis displ place acemen mentt (v (vect ector or-b -bas ased ed th thin inki king ng)) when any step is taken to create, process, or interpret multicomponent data. That fundamental principle will be used when discussing almost every concept and application in this book.

Vector sources If the objective is to conduct a multicomponent seismic survey that will produce all possible wave modes, then each source station must be occupied by sources that generate three orthogonal source-displacement vectors. The three displacement vectors then must propagate through the earth as three independent illuminating wavefields. Such sources will be called vector sources (Figure 1). Full-vector source illumination requires that one illuminating wavefield (designated as wave mode c in Figure 1) has a displacement vector oriented normal to its wavefront and that two illuminating wavefields (designated as wave modes a and b) have orthogonal displacement vectors that are tangent to their respective wavefronts. The displacement vector that is normal to its associated wavefront generates compressional-wave (P-wave) data. The displacement vectors that are tangent to their wavefronts create shear-wave (S-wave) data.

Wave components Three independent, vector-based seismic wave modes propagate in a simple homogeneous earth: a compressional mode, P, and two shear modes, SV and SH (Figure 2). Those are the three modes we try to create with three orthogonal source-displacement vectors and then record with three orthogonal vector sensors. Each mode travels through real-earth media at a different velocity, and each mode distorts the earth in a specific direction. The directions of distortion are different for each mode. The propagation velocities of the SH and SV shear modes differ by only a few percent, but both shear velocities (V S) are significantly less than the P-wave velocity (V P). The velocity ratio V P/V S can vary by an order of magnitude in earth media, from a value of 50 or more in deepwater, unconsolidated, solidat ed, near-seafloor near-seafloor sediment to a value of 1.5 in a few dense, well-consolidated well-consolidated rocks.

Chapter 1: Basic Concepts

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Figure 1. Distinction between vector and scalar seismic sources. A full-vector source should cause three orthogonal displacement vectors to propagate through the earth. Two seismic properties are measured measure d for a vector seismic source: the direction and timevarying magnitude magnitude of the particle displacement created within the earth. A scalar source also creates a vecto vec torr di disp spla lacem cemen entt of th thee ea eart rth, h, bu butt the only seismic property that is measure meas ured d is the tim time-v e-vary arying ing chan change ge of the mag magnitu nitude de of ear earth th mov movemen ement, t, not the direct direction ion of that movement. The distinction between scalar and vecto vec torr so sour urces ces is not how th thee so sour urce cess function functio n but how they are used. The classic example of scalar seismic data da ta is da data ta ge gene nera rate ted d by a ma mari rine ne ai airr gun and recorde recorded d by hydrop hydrophones. hones.

Figure 2. A fullfull-elasti elastic, c, multicomponent seismic wavefield propagating in a hom homogen ogeneous eous iso isotro tropic pic earth consists of a compressional mode P and two shear modes, SV and SH. A key distinction among those wave modes is that each mode distorts the earth in a different direction along its propagation path. The direction in which each mode displaces the earth is indicated by doubleheaded arrows.

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Figure 3. Distinction between SH and SV shear-wave displacements displ acements in isotr isotropic opic media. SV displa displacement cement occurs occ urs in the ver vertic tical al plan planee that pas passes ses thr through ough the sou source rce station and the observation point. SH displacement is normal to that plane.

When P- and S-waves propagate in an isotropic medium, the orientations of the P, SV, and SH disp di splac laceme ement nt ve vecto ctors rs rel relati ative ve to the propagation direction of each mode are defined as in Figure 2. For such media, a convenient way to di dist stin ingu guis ish h be betw twee een n SH an and d SV shear modes is to imagine a verti ve rtical cal pla plane ne pa pass ssin ing g thr throu ough gh a source station and a receiver station. SV vector displacement occurs cu rs in th thee ve vert rtic ical al pl plan ane; e; SH vector displacement is normal to the plane (Figure 3). The vertical plane passing through the coordinates of a source station, a receiver station, and a reflection point produced by this source-receiver pair is called a sagittal plane.

Sensing the earth’s fabric Real-earth media are anisotropic, not isotropic. In such media, the physical character and elastic properties of the internal fabric of a small volume of earth depend on the direction in which the internal fabric of that volume is tested. Different elastic constants (fabric) are sensed when the earth is distorted perpendicular to its bedding planes versus being displaced parallel to those planes or when the earth is displaced perpendicular to fractures versus parallel to fractures. For decades, the principal seismic data used in oil and gas applications have been P-wave modes, and those P modes commonly have been treated as scalar data. Even when P-wave data are analyzed as vector data, the particle-disparticle-displac pl acem emen entt ve vect ctor or of a PP-wa wave ve mo mode de st stil illl se sens nses es th thee ea eart rth h fa fabr bric ic in on only ly on onee di dire rect ctio ion, n, wh whic ich h does not provide a full definition of earth fabric. The advantage of multicomponent seismic data is that P, SH, and SV wave modes sense the earth’s fabric in three orthogonal directions (Figure 2). Each wave mode thus carries unique earth-fabric information — such as direction-dependent information about elastic constants, grain cementation, pore geometry, anisotropy axes, and lateral variations in rock and fluid types — when it leaves a target interval and travels to receiver stations. The technology challenges are to preserve this increased amount of geologic information when processing processing multicomponent multicomponent seismic data and then to correctly interpret the geolog geologic ic messages contained in the P, SH, and SV data volumes that are created. A simple argument helps explain why P-wave and S-wave particle-displacement vectors sense different different earth fabric in anisotropic anisotropic media and thus cause P-wave sequences and


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Figure 4. A simple experiment illustrates illustrates that a layere layered d (VTI) medium exhibits exhibits a dif different ferent fabric (or strength) when its elasticity is tested in directions normal to and parallel to its layering.

facies to differ from S-wave sequences and facies even though both images are correct depictions of the geology illuminated by P and S wavefields. Assume that an elastic wavefield is traveling vertically through a horizontally layered medium. Such a medium is anisotropic and is called a VTI medium (vertical symmetry axis passing through transversely isotropic layers). The P-wave particle-displacement vector associated with that wave wa vefie field ld se sens nses es th thee fa fabr bric ic of th thee me medi dium um in a di dire rect ctio ion n no norm rmal al to th thee la laye yeri ring ng,, whereas the companion S-wave particle-displacement vector senses the fabric in a direction parallel to layering. The elastic constants of the medium differ in those two displacement directions. Forr ex Fo exam ampl ple, e, fo forc rces es of di difffe fere rent nt ma magn gnit itud udes es ha have ve to be ap appl plie ied d to fle flex x a de deck ck of pl play ayin ing g cards or the sheets of a notepad when those forces are directed normal to layering and parallel to layering (Figure 4). In this simple demonstration, the medium is the same at th thee co comm mmon on po poin intt wh wher eree th thee fo forc rces es ar aree ap appl plie ied, d, bu butt th thee st stre reng ngth th (o (orr fa fabr bric ic)) of th thee ma mate teri rial al is not the same in the two force directions. Thus, P-wave seismic sequences and facies some so metim times es di difffe ferr fr from om SS-wa wave ve se sequ quen ences ces an and d fa facie ciess acr acros osss a st stra ratig tigra raph phic ic in inter terva vall because a vertical P-wave particle-displacement vector and a horizontal S-wave particledisplacement vector sense different elastic properties of the layered-rock system within that interva interval. l.

Wave-mode terminology An appropriate, descriptive descriptive vocabu vocabulary lary is requir required ed to discus discusss multicom multicomponent ponent seismic technology. If three orthogonal source-displacement vectors are created at a source station and three orthogonal vector sensors record the distinct wavefields associated with each of those source displacements, displacements, the result is 9C data. Nine-co Nine-componen mponentt seismic data contain all poss po ssib ible le wa wave ve mo mode des. s. In th this is di disc scus ussi sion on,, th thee wa wave ve mo mode dess wi will ll be de desi sign gnat ated ed as PP-P, P, SH SH-S -SH, H, SV-S SV -SV, V, PP-SV SV,, an and d SV SV-P -P in a si simp mple le iso isotro tropic pic ea earth rth.. In th that at no nomen mencla clatu ture re,, th thee ter term m

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preceding the hyphen defines the downgoing wavefield, and the term following the hyphen specifies the upgoing wavefield. Three-component data are generated when three orthogonal vector sensors occupy the receiver stations but only a P-wave source is used to generate the illuminating wavefield. Two wave modes are provided by 3C data: the P-P mode and the P-SV mode. When a vertical-displacement force is applied to the surface of an elastic half-space, an illuminating SV wavefield is created at the source station in addition to an illuminating P wavefield. Thus, 3C data should be expanded to include an SV-SV mode, but efforts to use SV-SV modes produced by P-wave sources are difficult to find in the literature. When possible, concepts are explained assuming that P- and S-waves propagate in simple isotropic isotropic media. Althou Although gh this book is not intended to be a treatise on multicom multicompoponent wave propagation in anisotropic earth media, fractured rocks and tectonic-stressed rocks are so common that P and S propagation in those types of anisotropic earth conditions are discussed in several sections, particularly in Chapters 4 and 8. S-wave S-w ave pro propag pagatio ation n in ani anisotr sotropi opicc med media ia is par particu ticularl larly y imp import ortant. ant. A she shear ar wav wavee that propagates in an earth that has vertical fractures or that has a significant difference between its maximum and minimum horizontal stress vectors throughout the overburden above a seismic target will segregate into two daughter modes called the fast-S mode and the slow-S mode. The daughter modes travel at different velocities, as their names imply, and they have orthogonal, not parallel, displacement vectors. The displacement vector of the fast-S mode is oriented parallel to the isotropy plane that is parallel to the vertical fractures (or parallel to the maximum horizontal stress if a stress condition is used to describe the propagation medium). The displacement vector of the slow-S mode is oriented normal to this isotropy plane. In the literature, the term S1 sometimes is used to refer to the fast-S mode, and S 2 is used to indicate the slow-S mode. This wave physics is mentioned here only to complete this discussion of terminology. Examples of fast-S and slow-S wave physics will be shown in later discussions. Thee va Th vario rious us op optio tions ns fo forr acq acquir uiring ing mu multi ltico comp mpon onen entt se seism ismic ic da data ta an and d th thee sp spec ecific ific wave modes that are associated with each acquisition option are tabulated in Figure 5. Note how many S-wave modes are involved in multicomponent seismic data, particularly in fractured-earth media in which S-wave splitting occurs (the phenomenon of an S-wave mode separating into a fast and a slow component). One terminology error encountered in multicomponent seismic applications is that people often use the term shear wave and do not specify which particular shear mode is being considered. Each shear mode listed in Figure 5 is unique and can provide geologic information not available in its companion shear modes. Thus, we always should strive to define the specific shear mode(s) we are dealing with in any multicomponent seismic procedure.

Multicomponent reflectivities Each wave mode listed in Figure 5 has a unique reflectivity equation that relates the reflection amplitude and phase of that mode to elastic impedances of the earth. Those


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differing reflectiv differing reflectivity ity equaa) Dataacquisition tion ti onss ar aree of ofte ten n th thee mo most st option Source Receiver Captured mode (s) comp co mpel elli ling ng ev evid iden ence ce to 9C XYZ XYZ P-P, P-SV, SV-SV, SV-P, SH-SH convin con vince ce math mathemat ematical ically ly 6C YZ XYZ P-P, P-SV, SH-SH 4C Z or A XYZH P-P, P-SV oriented orient ed investi investigators gators that 3C Z XYZ P-P, P-SV dif ifffer eren entt ea earrth fa fabr bric ic is 1C Z Z P-P sens se nsed ed by ea each ch ve vect ctor or of X = radial, Y = transverse, Z = vertical, H = hydrophone, A = air gun. thee thr th three ee or orth thog ogon onal al pa parrb) Dataticle-displaceme ticle-di splacement nt vector vectorss acquisition invo in volv lved ed in mu multi ltico comp mpoooption Source Receiver Captured mode (s) nent seismic imaging. 9C XYZ XYZ P-P, P-SV1, P-SV2, SV1-SV1, SV2-SV2 Developing Develop ing express expressions ions SV1-P, SV2-P, SH1-SH1, SH2-SH2 6C YZ XYZ P-P, P-SV1, P-SV2, SH1-SH1, SH2-SH2 for reflectivity equations of 4C Z or A XYZH P-P, P-SV1, P-SV2 thee va th vari rio ous mo mod des of a mu mull3C Z XYZ P-P, P-SV1, P-SV2 ticomponent seismic wave1C Z Z P-P X = radial, Y = transverse, Z = vertical, H = hydrophone, A = air gun. field involves cumbersome and an d ted tedio ious us alg algeb ebra. ra. Th Thee Options ns for acquiring multicomponent multicomponent seismic Figure 5. Optio mathematics of reflectivity data and the seismic modes that are associated with each calculations is not particuoption. Part (a) applies to an isotropic earth. Part (b) applies larly complex because it is to an anisotropic medium in which S-wave splitting occurs. essentially basic trigonomSubscript 1 defines a fast-S mode; subscript 2 indicates a slow-S mode. etry and algebra. However, several published analyses of re refle flect ctiv ivit ity y eq equa uati tion onss contain typographical and notational errors because the equations contain many terms and inv involv olvee num numero erous us petr petroph ophysi ysical cal par paramet ameters ers.. The There re are mult multiple iple opp opport ortuni unities ties for making simple blunders, such as writing cosine when sine should be used, forgetting to include a parameter in an expression, inadvertently altering the algebraic sign of a term, or writing an incorrect subscript on a parameter. Some of those published errors have persisted in the literature for years. Because those types of errors are easy to make when reflectivity equations are developed, many researchers prefer to copy the equations from sources that have been proved over time to be error free. That approach will be followed in this discussion. Reflectivity equations published by Aki and Richards (1980) and by Ru¨ ger (2001) are among the sources sourc es that are popula popularr with many resear researchers. chers. The terminology terminology used by Aki and Richar Richards ds (1980) will be followed in this section. A distinct reflectivity equation is needed for each of the wave modes listed in Figure 5. The simplest reflectivity equation is the one associated with the SH-SH mode, which is defined in Figure 6. Also shown in Figure 6 is an illustration of the single-interface earth model used in the deriva derivation tion of the reflectiv reflectivity ity equations that follow. That model and its associated SH-SH reflectiv reflectivity ity equatio equation n incorp incorporate orate the notatio notation n for petrophysical petrophysical properties used by Aki and Richards (1980). In that nomenclature, a and b represent represent P-wave and S-wave velocities, respectively. The terms V P and V S are used for those velocities in the rem remaind ainder er of thi thiss boo book. k. Add Additio itional nal petr petroph ophysi ysical cal par paramet ameters ers app appear earing ing in the

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reflectivity equations are bulk density (r ), ), P-wave angle (i), S-wave angle (j), and horizontal slowness (p). As P- and S-waves propagate through an isotropic medium and reflect and refract at interfaces, the horizontal slowness associated with those waves is defined as p

=

sin(i)/V P

=

sin( si n( j)/V S .

(1)

In equation 1, angles i and j define P and S raypath directions as those modes approach and leave lea ve an int inter erfa face. ce. Sn Snell ell’s ’s law re requ quir ires es the ho hori rizo zont ntal al slo slown wness ess of ev ever ery y refl reflec ected ted and tra trans ns-mitted mode to be identical to the horizontal slowness of the incident wave that caused the reflection and transmission. Indices 1 and 2 attached to parameters refer, respectively, to the r b cos j 1 – r 2b 2 cos j 2 SHSHR = 1 1 layer above the interface and to r 1b 1 cos j 1 + r 2b 2 cos j 2 the layer below the interface. In SHSHR Figure 6 and subsequent figures, SH subscripts R a and nd T refer, respec j 1 tively tiv ely,, to re refle flecte cted d an and d tra trans ns-r 1 b 1 mitted modes. The notation for r 2 b 2 j 2 a reflected SH mode is the SHSHT same as the nomenclature used in Figure 5 except that the hyRayp Ra ypat ath h Part artic icle le di disp spla lace ceme ment nt (n (norm ormal al to ra rayp ypat ath) h) phen is omitted. The development of reflecFigure 6. Reflecti Reflectivity vity equation for the SH-SH seismic seismic mode. tivity equations associated with seismicmodesotherthantheSHSH mode requires that a polarity co conv nven entio tion n be est estab ablis lished hed forr inc fo incid ident ent an and d tr tran ansmi smitte tted d P and SV par particl ticle-d e-displ isplacem acement ent vectors at an interface. The particle-displaceme ticle-d isplacement nt polarit polarities ies assume su med d by Ak Akii an and d Ri Rich char ard ds (1980) for P and SV modes at an int interf erface ace whe where re impe impedan dance ce increases increas es downw downward ard are defined in Figure 7. If the particle-displacementt vector of an incident placemen incident,, Figure 7. Analysis of P and SV reflectivities requires that refle re flect cted ed,, or tr tran ansm smit itte ted d P or a polarity (algebraic sign) convention be assumed for SV mode points in the direction particle-dis partic le-displaceme placement nt vector vectors. s. The formulations for P and indicated for that mode in FigSV reflectivities that follow in Figures 9 through 14 are ure 7, the displacement vector based on this polarity convention recommended by Aki has a positive algebraic sign. If and Richards (1980). The impedance of the lower layer is assumed assum ed to be greater than the impedan impedance ce of the upper layer. the particle-displacement vector


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for any mode points in the opposite direction indicated by the model, that displacement vector is assigned a negative algebraic sign. The Aki and Richards (1980) formulation of reflectivity equations allows both downgoing and upgoing P and SV modes to be incident on the interface between two elastic layers. For each incident mode, four scattered wave modes are generated — upgoing P, downgoing P, upgoing SV, and downgoing SV (Figure 8). Relationships between the directions of P and SV wavefield propagation and the orientations of P and SV particledisplacement vectors that have positive algebraic signs are defined in Figure 8. By al allo lowi wing ng fo four ur sc scat atte tere red d mode mo dess fo forr ea each ch of th thee fo four ur in inci cide dent nt Incident Scattered modes, Aki and Richards (1980) SV1 deve de velo lope ped d 16 eq equa uati tion onss to de de-SV1 scrib sc ribee th thee to total tal re reflec flectio tion n/transP1 P1 mis isssion physic icss of P an and d SV wave wa vefiel fields ds at an in inter terfa face. ce. On Only ly four of the 16 equations will be r 1 a 1 b 1 used in this discussion — the two r 2 a 2 b 2 reflecti refl ectivity vity equ equatio ations ns ass associa ociated ted P2 with wi th a do down wngo goin ing g P mo mode de an and d P2 the two reflectivity equations reSV2 sult su ltin ing g fr fro om a do down wngo goin ing g SV SV2 mode. To shorten the mathematRaypath Par ticle displacement icall de ica descr scrip iptio tion n of th thee refl reflec ectiv tiv-ity eq equa uatio tions ns,, Ak Akii an and d Ri Rich char ards ds Figure 8. Each incident P and SV mode (left) creates (1980) introduced the nine terms two reflected modes and two transmitted modes (right) at an interface. Notation used by Aki and Richards (1980). list li sted ed in Fi Figu gure re 9. Wi With th th thos osee te term rmss being used, the reflectivity equation ti onss as asso soci ciat ated ed wi with th a do down wn-going P mode then are defined in Variables: Figure 10, and the two reflectivity a = r 2(1 – 2b 22 p2) – r 1(1 – 2b 12 p2) b = r 2(1 – 2b 22 p2) + 2r 1b 12 p2 equa eq uatio tions ns pr prod oduc uced ed by a do down wn-d = 2(r 2b 22 – r 1b 12) c = r 1(1 – 2b 12 p2) + 2r 2 b 22 p2 going SV-mode are given in Figure 11. Cosine-dependent terms: All wave modes listed in cos i1 cos i2 cos j1 cos j2 E=b +c F=b +c a 1 a 2 b 1 b 2 Figures 10 and 11 have a subscript cos i1 cos j2 cos i2 cos j1 we are interested interested in only G=a–d H=a–d R because we a 1 a 2 b 2 b 1 reflected wavefields wavefields in this discusD = EF + GHp 2 sion. As noted in the text accomNotation: pany pa nyin ing g Fi Figu gure re 6, th thee no nota tati tion on i = P angl e j = S V a n gl e p = horizontal slowness used us ed to id iden enti tify fy th thos osee re refle flect cted ed 1= top layer 2 = bottom layer p = sin(i)/a = = sin(j)/ b b modes is identical to the nomenclat cl atur uree in Fi Figu gure re 5 ex exce cept pt th that at Figure 9. Mathematical terms needed for P and SV the hyphen is omitted. The reflecreflectivity equations as developed by Aki and Richards (1980). tivity equations in Figure 10 are

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Figure 10. Reflectivity equations for downgoing downgo ing P-mode illumination illumination developed by Aki and Richards (1980). Horizontal slowness is defined by equation 1. These two reflectivity equations are the ones of interest in 3C and 4C seismic imaging. Terms a, b, c, d, D, F, and H are defined defined in Fig Figure ure 9. Note how complicated those expressions are compared with the reflectivity equation for the SH mode (Figure 6).

Figure 11. Reflectivity equations for downgoing SV-mode illumination developed by Aki and Richards (1980). Horizontal slowness is defined by equati equ ation on 1. Terms Terms a, b, c, d, D, E, and H are defined in Figure 9. Compare the complexity complex ity of those expressions expressions with the simpler expression for the reflectivity equation of the SH mode (Figure 6).

PRR =

b

PSVR = –2

cos i1 cos i2 cos i1 cos j2 F– a+d –c Hp2 D a 1 a 2 a 1 b 2 cos i1 cos i2 cos j2 ab + c d pa 1 /(b 1D) a 1 a 2 b 2

i = P angle 1 = top layer

SVPR = 2 SVSVR = i = P angle 1 = top layer

j = SV angle 2 = bottom layer

cos j2

p = horizontal slowness p = sin(i)/ a a = = sin(j)/ b b

cos i1 cos j1 pb 2 /(a 2D) a 1 b 2 b 1 cos j1 cos j2 cos i1 cos j2 b –c E + a + d a Hp2 b 1 b 2 b 2 1 ac + bd



of particular interest because they describe the P-P and P-SV modes involved in 3C and 4C seismic technology. Any downgoing wave mode could be used to acquire 3C seismic data, but in this text, 3C and 4C seismic technology will be restricted to data produced by P-wave illumination.. Thi tion Thiss con concep ceptt that that 3C and and 4C seism seismic ic data req requir uiree a downg downgoin oing g P wav wavefiel efield d is stan standar dard d practice in the seismic industry. The reflectivity equations in Figures 6 and 11 thus apply to 9C seismic technology, not to 3C seismic technology, because those equations are produced, respectively, respectively, by SH-mod SH-modee and SV-mode illumination, not by P-mod P-modee illumina illumination. tion. To permit convenient comparison of the reflectivity physics associated with each 3C and 9C seis seismic mic mod mode, e, the for forego egoing ing equ equatio ations ns are pos positio itioned ned in a side side-by -by-si -side de for format mat in Figure 12. Figure 12a describes 3C (or 4C) reflectivity. Figure 12b describes 9C reflectivity. Key principles illustrated by those equations can now be noted.

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†

Three-component Three-compon ent seismic data are a subset of 9C seismic data, as shown shown by the P-P and P-SV reflectivities shown at the top of Figure 12a and 12b. Only one S-wave mode (P-SV) (P-SV) is provided by 3C data, whereas 9C data provide three S-wave modes (SV-SV, SH-SH, and P-SV).


a) PPR = b PSVR = –2

b)

3C technology cos i1 cos i2 cos i1 cos j2 –c F– a+d Hp2 D a 1 a 2 a 1 b 2 cos i1 cos i2 cos j2 ab + c d pa 1 /(b 1D) a 1 a 2 b 2

PPR =

9C technology

b

PSVR = –2

SVPR = 2 SVSVR =

cos i1 cos i2 cos i1 cos j2 –c F– a+d Hp2 D a 1 a 2 a 1 b 2 cos i1 cos i2 cos j2 ab + c d pa 1 /(b 1D) a 1 a 2 b 2

cos j2 cos i1 cos j1 ac + bd pb 2 /(a 2D) a 1 b 1 b 2 cos j1 cos j2 cos i1 cos j2 b –c E+ a+d Hp2 D b 1 b 2 a 1 b 2

SHSHR =

i = P angle 1 = top layer


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r 1b 1 cos j 1 – r 2b 2 cos j 2 r 1b 1 cos j 1 + r 2b 2 cos j 2


Figure 12. Side-by-side comparison of (a) 3C (or 4C) and (b) 9C reflectivity equations.

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The reflectivity equations equations for the three S-wave modes (P-SV, SV-SV, SV-SV, SH-SH) differ from one another. Each S mode thus will create images across layered interfaces that differ from one another. Thee SV sh Th shea earr mo mode de an and d th thee P co comp mpre ress ssio iona nall mo mode de ar aree li link nked ed to ea each ch ot othe her, r, an and d en ener ergy gy is exchanged between those two modes during reflection. The SH shear mode is not linked to either P or SV, and no energy energy exchange between between SH and those modes occurs during reflection. Thee on Th only ly wa way y to ge gene nera rate te a re refle flect cted ed SH mo mode de is to us usee an SH so sour urce ce fo forr il illu lumi min nat atio ion n. An SH mode thus is never available in 3C or 4C seismic data because those data are generated by a P source. SH-SH reflectivity reflectivity is simpler mathematically mathematically than SV-SV and P-SV reflectivities. reflectivities. This fact implies that SH shear-wave data might be easier to interpret than SV-SV and P-SV data. Only Onl y one P-wave P-wave mode (P(P-P) P) is avai availabl lablee with 3C data; 9C data provide provide two P-wave modes (P-P and SV-P).

This analysis leads to the conclusion that differences in the mathematical structure of the reflectivity equations for various seismic wave modes cause those modes to react to changes in the earth’s elastic constants in different ways. The result is that one mode sometimes images stratal surfaces and produces seismic sequences and facies that are different from those of the other modes. That fact is particularly important when assessing the relative value value of 3C and and 9C S-wave imaging. imaging. Because Because 9C data allow three independe independent nt S-wave S-wave images to be made but 3C data provide only one S-wave image, 9C S-wave data should provide more petrophysical, stratigraphic-sequence, and facies information than do 3C data because each 9C S-mode potentially can reveal rock and fluid information that its companion compan ion S-mode S-modess cannot cannot..

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The complex reflectivity equations associated with illuminating P and SV modes can be simplified when the petrophysical properties of the two earth layers at an interface are similar. The definition of similar earth parameters is arbitrary, but in most instances, it is reasonable to assume that variations of less than 20% in bulk density (r ) and in velocities boundary ary satisfy the appro approximation ximation of similarity between the two earth V P and V S across a bound layers lay ers at th that at bo boun unda dary ry.. In su such ch in insta stanc nces, es, th thee len lengt gthy hy,, ted tedio ious us mat mathem hemati atical cal des descr crip iptio tions ns of reflectivity equations for an illuminating P mode (Figure 10) simplify to the expressions given in Figure 13. The reflectivity equations for an illuminating SV mode reduce to the simpler expressions given in Figure 14. Those modified equations are adequate for most multicomponent seismic modeling exercises and for most multicomponent seismic data analyses. They also allow the individual contributions of density contrasts (Dr ) and velocity contrasts (Da, Db ) to reflectiv reflectivity ity to be determined more easily than do the equations listed in Figures 10 and 11. An example of the principle that the reflectivity of each mode of an elastic wavefield at an interface differs from the reflectivities of its companion modes is illustrated in Figure 15. Vertical axis Ri,S in Figure 15 is S-S reflectivity at an interface. The term S-S is us used ed fo forr th this is no norm rmal al-i -inc ncid iden ence ce an anal alys ysis is be beca caus usee SH SH-S -SH H an and d SV SV-S -SV V ha have ve th thee sa same me re refle flecctivity tiv ity for normal normal inci inciden dence ce at an inte interfa rface. ce. Horizon Horizontal tal axis axis b is th thee ra rati tio o of th thee ve velo loci city ty ra rati tio o V P/V S across the interface, and quantity Ri,P labeled on each curve is P-P reflectivity at the interface. Those curves show that there are interfaces that †

are invisibl invisiblee to P waves (the curve curve labeled labeled Ri,P unless b 1.0 are invisible invisible to S waves (the horizontal horizontal line Ri,S unless b 1.0

¼

0) but are not invisible to S waves

¼

†

¼

0) but are not invisible to P waves

¼

Figure 13. Simplified formulation used by Aki and Richards (1980) for P-wave reflectivity that can be used when two elastic media at an interface have similar petrophysical properties. Horizontal slowness is defined by equation equati on 1.

PPR = PSVR =

1 2

1 Dr Da Db (1 – 4b 2p2) r + – 4b 2p2 2 a b 2 cos i

–pa cos i cos j 1 – 2b 2p2 + 2b 2 2 cos j a b – 4b 2p2 – 4b 2

a , b , r = = mean values i = P angle j = SV angle

Figure 14. Simplified formulation used by Aki and Richards (1980) for SV reflectivity that can be used when two elastic media at an interface have similar petrophysical properties. Horizontal slowness is defined by equation equati on 1.

SVPR =

Dr

r

Db

cos i cos j a b

b

= Da , Db , Dr =

[(Value 2) – (Value 1)] p = horizontal slowness p = sin(i)/ a = sin(j)/ b a = b

cos j b PSVR, a cos i

SVSVR = –

1 2

1 Dr (1 – 4b 2p2) r – – 4b 2p2 2 cos2 j

a , b , r = = mean values i = P angle j = SV angle

= Da , Db , Dr =

Db

b

[(Value 2) – (Value 1)] p = horizontal slowness p = sin(i)/ a a = = sin(j)/ b b


†

†

13

cause cause PP-P P an and d SS-S S re refle flecctions to be in phase (shaded regi re gion ons) s),, an and d ot othe hers rs cau cause se P-P and S-S reflections to be opposite polarity (unshaded regions) are robust robust P-P reflectors reflectors but weak S-S reflectors (elliptical domains A), and others are robust S-S reflectors but weak P-P reflectors (elliptical domains B)

Any co Any comb mbin inat atio ion n of PP-P P and S-S sequences and facies thus can be encountered when interp int erpreti reting ng mult multicom icompon ponent ent seism se ismic ic da data, ta, de depen pendin ding g on ho how w the V P/V S velocity ratio varies across acr oss inte interfa rfaces ces illu illumin minated ated by an elastic wavefield.

Horizontaldisplacement sources and SH/SV illumination

Figure 15. Relationships between normal-incidence S-wave reflectivity reflecti vity Ri,S and P-wave reflectivity Ri,P for differing contrasts of the V P/V S velocity ratio across an interface. For normal incidence, there is no distinction between SH-SH and SV-SV reflectivity. After McCormack et al., 1984, Figure 1.

The preceding section discusses distinctions between reflected S-wave modes involved in 9C and 3C seismic data acquisition. To further appreciate how 3C and 9C S-wave data differ, dif fer, it is equally importa important nt to consider distinctions between the downg downgoing oing illumination patternss of 9C and 3C S-wave modes. The reflectiv pattern reflectivity ity equations developed developed in the previous section assume that the illuminating wave mode, whether it is a P, SV, or SH mode, is a plane wave rather than a radiation pattern generated by a finite source. We now consider radiation patterns produced by finite-size vector sources. A map view of the particle-displacement wavefield produced by a horizontal-displacement vector source is illustrated in Figure 16. It is assumed that the source introduces a horizontal horizo ntal displacement displacement S oriented from left to right over the finite earth-to-source earth-to-source contact area. are a. This sou source rce-di -displa splaceme cement nt vec vector tor con conver verts ts into the par particl ticle-d e-disp isplace lacemen mentt vect vectors ors shown distributed over the image space. All particle-displacement vectors are drawn with equal equ al length length bec becaus ausee the intent intent of Fig Figure ure 16 is is to sho show w orienta orientation tionss of the vect vectors ors acro across ss the image space, not their relative magnitudes. magnitudes. The key point is that at every image coordinate

14


encircling the source station, the particledisplacement vector always is oriented in the dir directi ection on of the sou sourcerce-dis displac placemen ementt vector. Gray arrows G1 through G4 indicate the positive orientation direction of a horizontal vector seismic sensor at four locations around the source station. The principle illustrated in Figure 3 will be used to define SV and SH shear modes mo des pr prod oduc uced ed by th this is ve vecto ctorr so sour urce ce shown in Figure 16. If a vertical plane is constructed through source station S and sensor stations G2 and G4, the propagating par particl ticle-d e-disp isplace lacemen mentt vec vector tor is con con-strained to that plane. Thus, sensors G2 and G4 measure SV shear motion. If a vertical plane is constructed through the sour so urce ce st stat atio ion n an and d se sens nsor or st stat atio ions ns G1 particle-displacement ement Figure 16. Map view of particle-displac and G3, the particle-displacement vector wavefield propagating away from a horizontalis normal to that plane. Sensors G1 and displacement displ acement vector source. From Beecherl and G3 thus measure SH shear motion. If a Hardage, Harda ge, 2004. vertical plane is constructed through the source station and arbitrary point A, the particle-displace particledisplacement ment vector has components parallel to and normal to that plane. A sensor at point A thus would record a mixture of SV and SH shear motion. This exercise demonstrates that a single horizontal-displacement source produces both SH and SV modes and that those modes radiate away from the source station in asymmetr me tric ical al pa patt tter erns ns.. Th Thee pr prop opor orti tion onss of SH an and d SV en ener ergi gies es th that at ar arri rive ve at an im imag agee co coor ordi dina nate te vary according to the azimuth from the source station to the image point. Mathematical expressions that describe the geometric shape of P, SV, and SH radiation patterns produced by seismic sources in an isotropic earth are described by White (1983). In map view, SH and SV radiation patterns produced by a horizontal-displacement source have the appearance of the diagrams shown in Figure 17. Viewed from directly above the horizontal-displacement source, SV and SH modes propagate away from the source station as expand expanding ing circles. Becaus Becausee SV radiation from a horizo horizontal-dis ntal-displacemen placementt source is more energetic than SH radiation, SV radiation circles are drawn larger than SH radiation circles. These four circles indicate which parts of the image space each mode affects and the magnitude of the mode illumination that reaches each image coordinate. Thee re Th rela lati tive ve si size zess of th thes esee SH an and d SV ci circ rcle less ar aree qu qual alit itat ativ ivee an and d ar aree no nott in inte tend nded ed to be ac accu cu-rate in a quantitative sense. A hor horizo izontal ntal sou source rce-dis -displa placeme cement nt vect vector or ori orient ented ed in the Y dir directi ection on (Fig (Figure ure 17a 17a)) causes SV modes to radiate in the + Y and –Y directions and SH modes to propagate in the + X and – X dir directi ections ons.. A hor horizon izontal tal sou source rce-di -displa splaceme cement nt vect vector or oriented oriented in the X


15

Figure 17. Map view of SH and SV illumination patterns for orthogonal (X and Y) horizontaldisplacement sources. The rela relative tive magn magnitud itudes es of the SH and SV patterns are suggestive rather than precise. From Beecherl and Hardage, 2004.

direction directi on (Fig (Figure ure 17b 17b)) caus causes es SV mod modes es to radiate in the + X an and d – X di dire rect ctio ions ns and an d SH mo mode dess to pr prop opag agat atee in th thee + Y and –Y directions. If a line is drawn from the source station to intersect one of the radiation circles, the distance to the intersection sect ion poi point nt ind indicat icates es the magn magnitud itudee of that particular mode displacement in the azimuth direction of that line. The orientation of the particle-displacement vector remains constant across the image space, as indicated in Figure 16, but the magniFigure 18. Source-receiver geometry used by tudes of the SH and SV particle-displaceRobertson Rober tson and Corrig Corrigan an (1983) to study SH and ment vectors vary with azimuth, as shown SV radiation patterns created by a horizontal by th thee SH an and d SV rad adia iati tio on ci cirrcl cles es in vibrator. Figure 17. A se seri ries es of fie field ld ex expe peri rime ment ntss th that at verifies the SH and SV radiation patterns produced by a horizontal force vector has been publish pub lished ed by Rob Roberts ertson on and Cor Corrig rigan an (19 (1983) 83).. The sou sourcerce-rec receive eiverr test geo geometr metry y they used us ed is sh show own n in Fi Figu gure re 18 18.. At se sele lect cted ed so sour urce ce st stat atio ions ns,, a ho hori rizo zont ntal al vi vibr brat ator or wa wass po posi siti tion oned ed so that its baseplate motion was oriented at small azimuth increments of 10 relative to the known orientations of the downhole geophones (Figure 19a). The responses of the downhole sensors acquired in one test are plotted in Figure 19b. Visual inspection of those wiggle-trace displays shows that the SV mode is more robust than the SH mode, as indicated by the SH and SV radiation patterns drawn in Figure 17. Numerical analysis of those test data produces the SH and SV radiation patterns drawn in Figure 20. The plotted data points are scaled versions of the amplitude responses of the wigglewig gle-trac tracee data displ displayed ayed in Fig Figure ure 19b. 19b. The num number ber writte written n bes beside ide each each data point point spe speccifies the azimuth orientation (in degrees) of the baseplate measured from the azimuth of the X (SV) geophone, which is the same coordinate parameter used to identify the wiggle traces displayed in Figure 19b. The resulting radiation patterns are a map view of the 8

16


Orientations ations of the downhole downhole horizontal horizontal geophones used in this test by Robertson Robertson and Figure 19. Orient Corrigan (1983) are shown in the center of the figure. Part (a) describes the manner in which the horizontal vibrator was maneuvered at surface source stations relative to those geophones. The baseplate was positioned first so that its first motion was aligned with the positive polarity of the downhole Y (or SH) geophone. The baseplate then was repositioned at azimuth increments of 10 until it aligned with the negative polarity of the X (or SV) geophone geophone.. Part (b) plots the responses of the downhole geophones for each baseplate orientation. Note the opposite polarities of the SV and SH data. 8

Figure 20. Map view of SH and SV radiation patterns produced by a horizontal force vector F oriented as sho how wn by th thee ve vect ctor or dr draw awn n at th thee plot origin (Rober (Robertson tson and Corri Corri-gan, 1983).


17

SH and SV illumination produced by the X-oriented (or SV) horizontal force vector drawn at the origin. Those experimental data are the basis for drawing the SH and SV radiation patterns shown in Figure 17. Those data again confirm that the SV mode is more energetic than the SH mode. A principle established established in this experiment experiment is that it is essential to know the directio direction n of the first motion of the baseplate baseplate of a horizontal horizontal vector. The first movement movement defines the positive polarity of the horizontal force vector created by the vibrator and is essential information for keeping data polarities consistent during S-wave data acquisition. By repeating this data acquisition at several offset source stations, a vertical view of SH and SV radiation patterns can be created. The results produced along one source profile extending away from the buried 3C geophone are displayed in Figure 21. Those dat ataa on once ce ag agai ain n co confi nfirm rm th that at th thee SV mo mode de is mo more re en ener erge geti ticc th than an th thee SH mo mod de. Because the SH and SV lobes have essentially the same geometric shape, they will illuminate min ate equ equival ivalent ent geo geolog logy. y. Bot Both h rad radiati iation on lob lobes es hav havee rea reason sonable able ampl amplitud itudes es at sma small ll takeoff angles of 10 from vertical. These walkaway VSP investigations are particularly important for defining the velocities of wave modes produced by seismic sources. By analyzing traveltime behavior along alo ng ray raypath pathss ass associa ociated ted with the sou source rce-re -receiv ceiver er geo geometr metry y illu illustra strated ted in Fig Figure ure 18, Robertson and Corrigan (1983) found the SH and SV velocity behavior illustrated in Figure 22. Those data show that SH and SV modes propagate with different velocities, which is a critical distinction between these two S-wave modes. The features of these velo ve locit city y su surf rface acess co conf nfor orm m to the theory for wave propagation ti on in ho hori rizo zont ntal ally ly la laye yere red d (vertic (ve rtical al tran transver sverse se iso isotro tropic pic [VTI [V TI]) ]) me medi diaa pu publ blis ishe hed d by Levin (1979, 1980), which is repeated in Figure 23. 8

Vertical-displacement source sou rcess and con conver verted ted-S (P-SV) illumination The shea shear-w r-wave ave rad radiati iation on associated with P-to-SV mode conver con versio sion n is much dif differ ferent ent from that produced by a horizontal izo ntal-di -displ splacem acement ent sou source. rce. Section and map views of PSV radiation patterns are provide vi ded d in Fi Figu gure ress 24 an and d 25 25,, respectively. The section view (Fig (F igur uree 24 24)) in indi dica cate tess an ai airr

Figure 21. Section view of SH and SV radiation lobes. After Robertson and Corrigan, 1983, Figure 15.

18


gun operating in a water environm vir onment ent (a scal scalar ar sou source rce). ). The con conver vertedted-SV SV rad radiati iation on patterns in the diagram apply equally well to land-based operations in which the energy source is a vertical-displacement source such as a vertical vibrator or an explosive in a shot hole. In both 3C (land) and 4C (marine) data acquisition, the SV radiation pattern associatedwiththeP-SVmode is produced in the subsurface at th thee PP-to to-S -SV V co conv nver ersi sion on Figure 22. SH and SV velocity behavior. After Robertson point, not at the surface-based and Corrigan, 1983, Figure 11. source station, as is the case for a horizontal-displacement source (Figures 16 and 17). ThemapviewinFigure25 shows the downgoing-P mode prop pr opag agati ating ng aw away ay fr from om th thee source station, with SV radiation patterns being produced at su subs bsur urfa face ce in inte terf rfac aces es at every point along the P wavefront. Dotted circles indicate thee ge th geom omet etri ricc sh shap apee of th thee conver con verted ted-SV -SV rad radiati iation on that is created at each subsurface P-to-SV conversion point. A Figure 23. Comparison of SH, SV, and P velocity behavior key point to note is that the for elastic wave propagation in horizon horizontally tally layered (vert (vertical ical orie or ient ntat atio ion n of th thee SV pa parrtransverse trans verse isotropic [VTI]) media. After Levin, 1979, Figticle-d ticl e-disp isplace lacemen mentt vec vector tor is ure 5. not in a fixed direction as it is for a hor horizon izontaltal-dis displac placeement source (Figure 16), but it varies with azimuth direction. The P and S particle-displace pl acemen mentt ve vecto ctors rs or orien ientat tatio ions ns sh show own n in Fi Figu gure re 25 ar aree co corr rrec ectt fo forr an iso isotr trop opic ic ea earth rth where the total SV displacement is oriented in the radial direction in which the P-wave is propagating. In an anisotropic earth, an SV particle-displacement vector might have both radial and transverse components. Distinctions between 3C and 9C S-wave target illuminations are easier to visualize if SV and SH radiation patterns associated with each type of data are viewed in a sideby-s by -sid idee fo form rmat, at, as in Fi Figu gure re 26 26.. Th Thos osee rad radiat iatio ion n pa patte ttern rnss ar aree de descr script iptiv ivee of SS-wa wave ve


19

propag prop agat atio ion n in an is isot otro ropi picc eart ea rth, h, no nott in an an anis isot otro ropi picc earth. ear th. Ana Analysi lysiss of tho those se illu illu-minati min ation on be beha havio viors rs lea leads ds to several conclusions. †

†

†

†

†

A 3C P-wave P-wave source source generates at es on only ly a co conv nver erte tedd-SV SV Swave mode. A 9C horizontal-dis taldisplac placemen ementt sou source rce creates at es bot oth h SH an and d SV mo mode dess. An An SH SS-wa wave ve mo mod de ca can n be created by only an SH source, which by definition Figure 24. Section view of P-SV radiation pattern. is a pu pure re ho hori rizo zont ntal al-d -dis is-placementt source placemen source.. A 9C horizo horizontal-di ntal-displaceme splacement nt source creates SH and SV modes in the earth volume immediately around aro und its sur surfac face-st e-statio ation n coo coordi rdinate nates. s. A 3C Pwave source creates a converted-SV mode at subsurface coordinates remote from the source station. In 9C illumination, all SH and SV particle-displacemen plac ementt vect vectors ors thr throug oughou houtt the pro propag pagatio ation n medium are oriented in the same direction as the horizon hor izontal tal sou sourcerce-disp displace lacement ment vect vector or that created the modes. In 3C illumination, orientation Figure 25. Map view of P-SV illuof the SV particle-displacement vector varies with mination pattern. azimuth direction away from the source station. In 9C tar target get illu illumina mination tion,, SH and SV par particl ticle-d e-disp isplace lacemen mentt vect vectors ors have a con constan stantt algebraic sign (polarity) throughout the propagation medium. In 3C illumination, the particle-displacement vector of the converted-SV mode has an opposite algebraic sign (polarity) for any two propagation azimuths that differ by 180 . In 9C dat dataa acqu acquisit isition ion,, SH and SV mod modes es illu illumina minate te the subsurfa subsurface ce with a dif differ ferent ent intensity intensi ty in each azimuth direction. In 3C data acquisition, acquisition, the conver converted-SV ted-SV mode illuminates the subsurface with the same intensity in all azimuth directions. 8

†

A final observation about 3C and 9C S-wave illumination is based on the principles shown in Figure 27. This diagram illustrates distinctions between the polarizations of SV modes in 3C and 9C seismic data as seen in map view around a source station. SH-mode polarization is not included in the illustration because a 3C source cannot create an SH mode. For each source, polarization behavior of the SV mode is defined in terms of inline and crossline vector components in each of the four quadrants that surround the source position.

20


Side-by-side -side comparison comparison of (a) 3C and (b) 9C S-wave illumination illumination patterns. Figure 26. Side-by

Figure 27. Distin Distinctions ctions between between (a) 3C SV-mod SV-modee polarization and (b) 9C SV-mode polarization. polarization.

When a P-wave source occupies the source station, the downgoing P wavefield illuminates all four quadrants with equal intensity (Figure 27). However, inline and crossline vector sensors measure a different polarization for one or both of the P-source SV displacements in each image quadrant, as illustrated in Figure 27a. In contrast, a single horizontaldisplacement source does not illuminate all four quadrants around a source station with equal intensity. Two orthogonal horizontal-displacement sources must occupy a source station in 9C data acquisition to create equivalent SV and SH illumination in all azimuth directions directio ns throu throughout ghout the propag propagation ation medium. Those ortho orthogonal gonal sources create the same SV polarization in all quadrants (Figure 27b), which is significantly different from 3C SV polarization behavior.


21

Vertical-displacement sources and direct-SV illumination The most common type of source used in onshore seismic data acquisition is one that applies a vertical-displacement force to the earth. Among those sources are vertical weight droppers and thumpers, explosives in a shot hole, and vertical vibrators, the latter being prob pr obab ably ly the mo most st wid widel ely y us used ed of al alll on onsh shor oree so sour urces ces.. Su Such ch so sour urce cess ar aree vi viewe ewed d tr trad aditi ition onall ally y as only P-wave sources, but they also produce robust SV wavefields. A theoretical calculation, similar to that done by Miller and Pursey (1954) and by White (1983), illustrates how energy is distributed between P-wave and SV-shear modes when a vertical force is applied to an elastic half-sp half-space ace (Figure 28). This calculation shows that a vertical-force source produces more SV energy than P energy and that at takeoff angles of 20 and more, this direct-SV mode is significantly stronger than the P mode. One shortcoming shortc oming of this particular SV radiatio radiation n is that it does not result in a robust illumination of geology directly below the source station, whereas its companion P radiation does. To take advantage of the direct-SV mode produced by vertical-displacement onshore sources, only two changes need to be done in data-acquisition programs: 8

1) Deploy 3C geophone geophoness rather than single-co single-componen mponentt geophones. geophones. 2) Use longer longer recordin recording g times to acco accommo mmodate date the slower slower propagat propagation ion velocity velocity of the downgoing and upgoing direct-SV mode. A definitive way to illustrate the P and direct-SV radiation produced by a verticaldisplacement source is to analyze its downgoing wavefield using vertical seismic profile (VSP (V SP)) da data. ta. Fi Figu gure re 29 pr prov ovid ides es on onee ex examp ample le of VS VSP P da data ta acq acqui uire red d in th thee De Delaw lawar aree Basin of New Mexico with a vertical vibrator used as a source. The downgoing mode la-

Figure 28. Cross Cross-secti -section on views of the P and SV radiati radiation on pattern patternss produced produced when a vertic vertical al force force F is applied to the surface of the earth. Calculations are shown for two values of the Poisson’s ratio of the earth layer. This analysis focuses only on body waves and ignores horizontally traveling energy along the earthearth-air air interface. Semicircles Semicircles indicate the relati relative ve strength of the radiation. Radial lines define the takeoff angle relative to vertical. In each model, more SV energy is generated than P energy, but vertical-force sources often are viewed only as P-wave sources.

22


beled SV is not a tube wave because beca use it pro propag pagates ates with a velocity of approximately 2400 m/s (80 8000 00 ft/s), almost twice the velocity of a flu fluid id-b -bor orne ne tu tube be wa wave ve.. Thee do Th down wngo goin ing g P an and d di di-rect-SV illuminating wavelets le ts pr prod oduc uced ed by thi thiss ve verrtical-d tica l-displ isplacem acement ent sou source rce aree la ar labe bele led d an and d ex exte tend nded ed back to the surface source station to illustrate that an SV mo mode de is pr prod oduc uced ed di di-rectly at the source. The ab abse sen nce of dat ataa cove co vera rage ge acr acros osss th thee sh shalallowest 3000 ft of str trat ataa leav avees some doubt as to where the downgoing event SV is created, so a second example of VSP data proFigure 29. VSP data acquir acquired ed using a vertical-displaceme vertical-displacement nt duced by a vertical vibrator source (a vertical vibrator). Data shown here are the responses of in a south Texas well is the downhole vertical geophones, which are not ideal sensors to illu il lust stra rate ted d in Fi Figu gure re 30 30.. emphasize SV modes. Even so, there is a robust direct-SV event. Again, this popular verticalThe downgoing P and direct-SV illuminating wavelets are traced displacement source creates back to their common point of origin at the source station. a rob robust ust dir directect-SV SV wav wavefiel efield d in addition to the customary P wavefield. In this example, the downgoing SV mode can be extended back to the source station at the earth surface with confidence. These VSP data examples show that one of the most popular onshore P-wave seismic sources — a vertical vibrator — is an efficient producer of direct-SV radiation and creates an SV-SV mode that can be used. An equally popular P-wave source is a shot-hole explosive. si ve. An ex expl plos osiv ivee sh shot ot als also o ap appl plies ies a ve vert rtica ical-d l-disp isplac laceme ement nt forc forcee to th thee ea earth rth an and d ge gene nera rates tes a robust direct-SV mode. An example of a downgoing explosive-generated SV mode radiating directly from a shot-hole station has been published by Li et al. (2007) and by Liu et al. (2007). The explosive-source VSP data acquired by Li et al. (2007) are illustrated in Figure 31. The SV mode exhibited by those data is produ produced ced at the same earth coordinate coordinate as the P mode and is an obvious source-generated direct-SV wave. The propagation medium at that location has unusually low V P and V S velocities. The SV mode produces a large population of robust upgoing SV reflections that are obvious in these raw, unprocessed data.


23

SV-SV imaging with shot-hole explosives Based on th Based thee ev evide idenc ncee (Fig (F igure ure 31) tha thatt sho shot-h t-hole ole explosives produce a directSV mode, Li et al. (2007) acqu ac quir ired ed a 2D exp explos losiv iveesourcee seismic line and prosourc cessed the data to create PP, PP-SV SV,, an and d SV SV-S -SV V im im-ages ag es.. Th Thee re resu sult ltss ar aree di dissplay pl ayed ed in Fi Figu gure re 32 32.. Th Thee SV-S SV -SV V mo mode de pr prod oduc uces es an image im age of th thee ge geol olog ogy y tha thatt is as good as that provided by th thee P-P P-P and PP-SV SV mo mode des. s. The SV-SV data provide an excellent image of geology acro ac ross ss th thee ga gass-sa satu tura rate ted d structure at the left end of thee pro th rofil file, e, wh wher erea eass PP-P P data da ta ar aree af affe fecte cted d str stron ongly gly by the gas cloud embedded in the structure.

Techniques used to measure V P/V S from seismic data The velocity ratio V P/ V S is not measured directly when whe n inte interpr rpretin eting g P-w P-wave ave and an d SS-wa wave ve sei seismi smicc da data. ta. Inste In stead ad,, a tra trave velti ltime me rat ratio io deter ermin mined ed,, DTS/DTP is det where DTS is the time requi uire red d fo forr th thee SS-wa wave ve to travel verticall vertically y across a dedefined fine d str stratig atigrap raphic hic inte interva rvall of thic thickne kness ss DZ, and DTP is th thee ve vert rtic ical al tr trav avel elti time me

Figure 30. VSP example of a vertical-displacement source (vertical vibrator) creating a robust direct-SV wavefield in addition to a P wavefield. In this instance, the source was offset only 100 ft from the VSP well. (a) Vertical geophone response. (b) Horizo Horizontal ntal geophone respon response. se.

24


required for the P-wave to traverse the same interval. This seismic traveltime paramet parameter er DT has units of milliseconds and is not to be confused with the slo slowne wness ss par paramet ameter er Dt, which has units of microseco se cond ndss per fo foo ot. By de defifinition, niti on, the velo velociti cities es V P and V S are V P

= D Z /DT P

and V S

= D Z /DT S .

(2)

Thus, V P /V S

= DTS /DTP .

(3)

This simple but effective technique for calculating V P/ V S is illustrated in Figure 33 when the V P/V S ratio is to be dete de term rmin ined ed fr from om VS VSP P da data ta and an d in Fi Figu gurre 34 wh when en th thee ratio is to be determined from surface-recorded P-P and S-S Figure 31. VSP data generated by a 20-kg explosive detrefle flecti ction on da data, ta, wh wher eree S can onated in a 40-m shot hole. (a) Vertical geophone response. response. (b) re Horizontal geophone response. A robust SV mode is generated be either the SH mode or the directly at the source station. After Li et al., 2007. Courtesy of SV mode. Yanpeng Li. Used by permission. A critical assumption that can be made when V P/V S ratios are determined from seismic-reflection data is that S-wave reflections AS and BS, between tw een wh which ich in inter terva vall tim timee DTS is me meas asur ured ed,, mu must st ma mark rk th thee to top p an and d ba base se of ex exac actl tly y th thee sa same me stratigraphic interval DZ defined by P-wave reflections reflections Ap and BP, between which interval time DTp is measured. measured. The import importance ance and challen challenge ge of depthdepth-register registering ing surface-re surface-recorded corded P and S data so that this assumption can be made with reasonable confidence warrants a separate chapter in this book (Chapter 5). If 3C and 4C data are the only available multicompone multicomponent nt data and P-P and P-SV reflections can be defined that originate at interfaces A and B bounding a layer of thickness d, then the V P/V S velocity ratio across that interval can be calculated using the equation written in Figure 35. This raypath model applies for normal-incidence conditions only. Slant raypaths are drawn only to allow all segments of the raypaths to be labeled. TB and TA are the image times of the reflections from interfaces B and A, respectively,


25

Figure 32. (a) P-P, (b) P-SV, and (c) SV-SV images produced from data generated by shot-hole expl ex plos osiv ives es.. Th Thee SV SV-S -SV V im imag agee is eq equi uiva vale lent nt in qu qual alit ity y to th thee PP-P P an and d PP-SV SV im imag ages es.. St Stru ruct ctur uree A at th thee left end of the profile has gas-saturated sediments. P-P data cannot image through the gas cloud. In contrast, P-SV and SV-SV data do, with the gas-saturation having no effect on the SV-SV image. After Li et al., 2007. Courtesy of Yanpeng Li. Used by permission.

DT

is the interval time (TB – TA), and subscripts PP and PS define which wave mode is being considered. For P-SV data, the term V S in the V P/V S ratio is the velocity of the SV shear mode. That distinction is important because SH and SV velocities are equal for vertical wave propagation, but they differ when measured along slant travel paths (Figure 23). An advantage of using VSP data to determine V P/V S is that one can be confident that the P and S wavelet phases used for traveltime measurements are determined at precisely the same depth coordinates. Lash (1980) was one of the first to do a VSP-based investigatio ga tion n to ext exten end d th thee inv invest estiga igatio tion n of V P/V S behavio behaviorr fro from m the labo laborat ratory ory fre freque quency ncy range to the field-seismic frequency range. The major finding of Lash’s analysis is summarized in Figure 36, which depicts V P,V S, and V P/V S as functions of depth in the sand-shale sequen seq uence ce pen penetra etrated ted by the VSP well well.. Tho Those se sed sedimen iments ts are reas reasona onably bly con consol solidat idated ed below a depth of approximately 1500 m (5000 ft). If the data analysis is restricted to depths greater than 1500 m, the 3C VSP data show that at this test site, the ratio V P/V S in shale-dominated intervals is always greater than V P/V S in sand-dominated intervals. The ratio V P/V S, when measured at seismic frequencies, thus segregates into distinct numerical ranges according to lithology, just as it does in the high-frequency laboratory tests discussed in Chapter 4.

26


Potential for improved spatial resolution

Figure 33. Determining V P/V S ratios using VSP data. In this technique, the one-way traveltimes DTS and DTP required for vertically traveling P and S waves to traverse the same depth interval (DZ) are measured, and the velocity ratio V P/V S is simply the ratio of the traveltimes DTS/DTP. The labeling implies that the wavefields are downgoing, but upgoing reflection events also can be used. Using VSP data to determine V P/V S ratios across specific rock-type intervals and stratigraphic sequences is an excellent way to establish whether surface-based measurements of V V P/ V S behavior near a VSP well are capable of distinguishing between rock type 1 and rock type 2 penetrated by the well.

When S-wave data have a frequency bandwidth equivalentt to th en that at of PP-wa wave ve da data ta,, then th en an SS-wa wave ve im imag agee ha hass a better bett er spa spatial tial res resolu olution tion than does do es it itss co comp mpan anio ion n PP-wa wave ve image ima ge.. Th This is im impr prov oveme ement nt in spati sp atial al res resol olut ution ion oc occu curs rs be be-cause at any specific frequency f , the spatial wavelengths l of S-wave and P-wave data are, respectively,

lS

=

V S f

(4)

and lP

=

V P f

.

(5)

Figure 34. Determining V P/V S rat ratios ios usi using ng sur surface face-bas -based ed sei seismi smicc refl reflect ection ion dat data. a. In thi thiss tec techni hnique, que, two-way traveltime DTP is measured between P-wave reflections AP and BP, which span depth interval DZP. That traveltime is compared with two-way time DTS between two S-wave events AS and BS that are interpreted to be generated at the top and base of the same depth interval. This technique generates valid V P/V S ratios as long as the assumption DZP DZS is true. ¼


27

Thus, lS is shorter than lP by a factor of V S/V P. When shorter wavelengths exist in the imaging wavefield, the spatial resolution increases. In most documented comparisons of surface-recorded P and S images, S-wave data tend to have a reduced frequency bandwidth compared with their companion P-wave data, da ta, wit with h th thee re resu sult lt th that at P an and d S im image agess hav havee ap appr prox oxima imatel tely y th thee sam samee wa wave velen lengt gths hs and the same spa spatial tial res resolu olution tion.. How However ever,, a phe phenom nomeno enon n of sho shortrt-dis distanc tancee cro crossw sswell ell seismic profiling is that the S wavefields that are recorded often have approximately the same sa me fr freq equen uency cy ba band ndwi widt dth h as do th thee P wa wave vefiel fields ds.. Th Thee SS-wav wavee da data ta th ther eref efor oree hav havee Figure 35. This raypath diagram illustrates illus trates how to calcula calculate te V P/V S velocity ratios using stacked or migrated P-P and P-SV images, preferably prefer ably migrat migrated ed data.

b) 0

a) 0 0.3

0.3

0.6

0.6 V P

0.9

0.9

V S

1.2

1.2 ) m k ( 1.5 h t p e 1.8 D

1.5 1.10 1.28

2.4

Approximate base Miocene

2.62

Anahuac shale Approximate top Frio

2.4

2.7

2.3

2.93

(40%–60% sand)

2.7

Base Frio

Base Frio

3.0

3.0

2.32

0.82

Anahuac shale (90% shale) Approximate top Frio

2.4

1.28

2.7

(65%–75% sand) Approximate base Miocene

2.0

2.1

0.98

2.1

3.3 0 .3

1.8

2.8

90% shale

3.3 0.6

0 .9

1.2 1.5 1.8 Velocity (km/s)

2.1

2 .4

2 .7

3 .0

2. 0

3 .0

4. 0 V P / V VS

5.4

6. 0

Figure 36. (a) V P and V S values and (b) V P/V S ratios determined from 3C VSP data recorded in a Tertiary section of the Texas Gulf Coast. At the test site, sediments are reasonably consolidated at depths below 1.5 km. The VSP-measured interval velocities are labeled on the respective curves in part (a), and sand and shale content is labeled on the V P/V S curve (b) for depths greater than 1.5 km. For those labeled depths, V P/V S in shale-dominated intervals is always greater than V P/V S in sand-dominated intervals, which is the same behavior documented by Domenico (1984). Velocity decrease at the base of the Frio is the result of overpressure. After Lash, 1980, Figure 5.

28


wavelengths that are shorter than the wavelengths in the P wavefields, and crosswell Swave images have better spatial resolution than do P-wave images, as demonstrated by the example displayed in Figure 37.

Receiver well

a)

P-wave Distance (ft)

Sonic (P-wave)

0

92

Source well 184

Sonic (P-wave)

1700 520

530

) t f ( h t 1750 p e D

) m ( h t p e D

540

1800 16 20 Velocity (kft/s)

0

28 Distance (m)

S y n t he t i c

b)

Receiver well

S-wave

Sonic (P-wave)

Distance (ft) 92

0

56

16 2 0 Velocity (kft/s) Synthetic Source well

184

Sonic (P-wave)

1700 520

530

) t f ( h t 1750 p e D

) t f ( h t p e D

540

1800 16 2 0 Velocity (kft/s)

0 Synthetic

28 Distance (m)

56

16 20 Velocity (kft/s) S y nt h e t i c

Figure 37. (a) High-resolution High-resolution crosswell crosswell P-wave image of a carbonate reservoir system. system. (b) Crosswell S-wave image of the same interwell space. As indicated by the increased number of SS-wa wave ve re refle flecti ction on pea peaks ks an and d tr trou ough ghss ac acro ross ss a gi given ven de dept pth h in inte terv rval al,, the SS-wa wave ve dat dataa ex exhib hibit it a bet bette terr spatial resolution than do the P-wave data. The S-wave image also reveals an internal reservoir sequence (shaded) that cannot be seen in the P-wave image. The S-wave data thus demonstrate important new information about the reservoir architecture that is not seen with the P-wave data. After Lazaratos et al., 1995, Figure 12.


29

One situation in which S-wave data have a frequency content approximately the same as P-wave data occurs in the first few hundred meters of seafloor sediment when data are acquired in deep water using 4C seafloor sensors. Studies have shown that for deepwater, near-seafloor strata, the converted P-SV mode has a frequency content equivalent to the frequency content of the P-P mode, and SV velocity can be less than 100 m/s (Backus et al., 2006). As a result, the dominant wavelength of the P-SV mode across near-seafloor strata is an order of magnitude shorter than the dominant wavelength of the P-P mode, and the spatial resolution of P-SV data can be matched by P-P data only when the frequency content of the P-P mode is increased to a range of 5 to10 kHz. An example of this wave physics is illustrated in Figure 8 of Chapter 7.

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