©2006 Society of Economic Geologists, Inc. Economic Geology, v. 101, pp. 1079–1085
DRILL-HOLE DESIGN FOR DILATIONAL ORE SHOOT TARGETS IN FAULT-FILL VEINS ERIC P. NELSON† Department of Geology and Geological Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401
Abstract Ore along fault-fill veins typically has an uneven distribution, with semilinear high-grade ore shoots separated by lower-grade zones or barren fault segments. Therefore, a successful drill campaign must be optimally designed for intersection of ore shoots and not the intervening zones. However, the typical drill-hole design for fault-fill veins, which targets the vein directly downdip from the highest-grade outcrops, will miss most ore shootss that rake less shoot less than ~80° ~80° to 90° in the structur structure. e. Dilational Dilational ore shoots shoots form form along prepre- or synmineralization faults in localized, elongated structural openings perpendicular to the slip vector. The rake of such ore shoots in fault-fill veins can be predicted using models of stress-controlled fault-fracture kinematics. Equations are presented that use fault-kinematic data to design drill holes for optimal success in targeting such ore shoots. The equations calculate the universal transverse mercator (UTM) coordinates of the drill target given fault-fill vein orientation, slip-vector rake (usually determined from slickenlines), vertical depth to intersect the ore shoot, and the UTM coordinates of geochemically anomalous outcrops along the fault vein. Although the method assumes that fault kinematics control ore-shoot orientation, and is not applicable to all fault-vein ore shoots (such as those formed at intersections of faults or shear zones with permeable beds, other faults, or dikes), the method increases the probability of success for drill-testing ore shoots through optimal drill-hole design.
Introduction According to Guilbert and Park (1986, p. 73), “detailed studies of structure are essential in exploration, and they unquestionably have led to more discoveries of ore than any other approach.” Indeed, many ore deposits are structurally controlled, and the understanding and application of structural models are extremely important in exploration for such deposits. Although structural controls of ore deposits are many (e.g., Newhouse, 1942; Lovering and Goddard, 1950; McKinstry, 1955; Richards and Tosdal, 2001; Nelson et al., 2003), the dominant control is likely that imposed by stressinduced structural permeability (fault-fracture networks) on the flow of hydrothermal mineralizing fluids in the crust (Sibson, 1996). Fault-fill veins (Cox, 1991; Robert et al., 1994), or simply fault veins, are one of the most common and important structurally controlled ore deposit types. They generally consist of quartz and/or carbonate minerals (the most typical gangue minerals) that fill localized open spaces in faults, fault zones, or shear zones and related fractures. Fault-fill veins typically form in the upper, brittle crust where fault-fracture systems are common and may host epithermal vein deposits, but also form in the semibrittle middle crust in hydraulic fault-fracture arrays that host mesothermal deposits (Sibson, et al., 1988; Poulsen and Robert, 1989; Robert and Poulsen, 2001). Many examples of fault-fill vein deposits have been mined and continue to be explored for; classic epithermal examples include the Fresnillo district, México (Ruvalcaba-Ruiz and Thompson, 1988), the Comstock Lode in Nevada (Berger et al., 2003), and the Orcopampa and Caylloma vein systems in Perú (Gibson et al., 1990, 1995; Echavarría et al., 2006), and classic mesothermal examples include the Sigma and Dumont deposits in the Val d’Or district, Canada (Robert, 1990; Robert and Brown, 1986). † E-mail,
[email protected] enelson@mines. edu
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Ore along fault-fill veins typically has an uneven distribution, with irregular or linear high-grade ore shoots separated by lower-grade zones or barren fault segments. Therefore, the successful drill campaign must be optimally designed for intersection of ore shoots and not the intervening zones. The standard and time-honored philosophy of drill-hole design for fault-fill veins is to drill through the hanging wall opposite to dip direction along a line that passes below the highest-grade outcrops. However, this design assumes that ore shoots rake close to 90° in the structure, but many ore shoots have lower rake angles and will be missed in drill holes following this design. As summarized by Poulsen and Robert (1989) and Robert et al. (1994), ore shoots can form in a number of ways, including replacement of deformed objects, as sheared orebodies, and at intersections such as along fault-bedding, faultfault, or fault-dike intersections (e.g., fig. 8.10b in Poulsen and Robert, 1989). However, most shoots probably form in dilatant fault jogs and bends (e.g., Sibson, 1996; Cox et al., 2001), particularly in epithermal brittle fault regimes. Oreshoot orientation (rake) in most fault-fill veins can be predicted, using models of stress-controlled fault-fracture kinematics, to be perpendicular to the slip vector. This paper summarizes the controls on structural permeability in epithermal fault systems and methods of determining slip-vector orientation and presents equations that use fault-kinematic data to design drill holes for optimal success in targeting such ore shoots.
Ore Shoots: Stress-Control Stress-Controlled led Structural Permeability Ore shoots are zones of highest ore grade and/or thickest ore within an overall orebody. In fault-fill veins they typically consist of generally linear zones of thicker vein(s) and/or dilatant breccia bodies that form in localized openings along faults, typically where faults bend or jog (McKinstry, 1948, p. 322; Fig. 1), and can be termed dilational ore shoots. The orientation of this type of ore shoot, given by the rake angle in
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FIG. 1. A. Model of structural opening formed in a fault jog along a normal fault (from Cox et al., 2001) showing the angular relationship between principal stress axes, fault, extension fracture (ore shoot), and sl ip vector. The structural opening represents a high-permeability zone along σ 2 in which mineral precipitation forms ore shoots. B. Example of a mesoscopic quartz-filled opening in a fault jog along a dextral fault, as an analog for the cross section of a dilational ore shoot; the view is along the σ 2 stress axis parallel to the long axis of opening (Akatore region, New Zealand).
the fault plane (or the plane representing the average faultzone orientation) is controlled by the direction of fault slip which, in turn, is controlled by the orientation of the mutually perpendicular maximum, intermediate, and minimum principal stress axes, σ 1, σ 2, σ 3, respectively (Fig. 1A). Such ore shoots are thus kinematically controlled (“kinematic type” ore shoots of Poulsen and Robert, 1989) and form along the direction of maximum structural permeability. In isotropic homogeneous rock, or rock with planar fabrics not optimally oriented for reactivation (Sibson, 1990), the Mohr-Coulomb theory of fracture mechanics (e.g., Davis and Reynolds, 1996, p. 234) can be used to model the geometric relationship between ore shoot orientation and the kinematics of fault-fracture systems. In this model, neoformed faults (i.e., not reactivated faults or faults following preexisting weaknesses) form at an angle of ~30° to σ 1, and σ 2 lies in the fault plane; the slip vector parallels the line of intersection of the σ 1- σ 3 plane with the fault plane (Fig. 1A). Opening-mode fractures (extension fractures) form in the σ 1- σ 2 plane and normal to σ 3, but commonly are elongate in the σ 2 direction. Such fractures may also form in en echelon arrays which develop by hybrid extensional shear (Ramsay and Huber, 1983). The σ 2-axis is parallel to the intersection of faults and associated extension fractures (Sibson, 1996). The common intersection of faults and extension fractures and the elongate nature of many extension veins thus enhance rock-mass permeability along the σ 2 direction (Sibson, 2001). Fluid flow in fault zones is focused in areas of highest fracture aperture and fracture density where fracture-fault interconnectivity is highest, typically in dilational fault jogs and bends. In dilational fault jogs, bends, and horsetail splays, fault orientation deviates from that plane predicted by MohrCoulomb fracture mechanics to have maximum resolved shear stress (Cox et al., 2001) and approaches parallelism with the σ 1- σ 2 plane. Kinematically controlled, or dilational, ore shoots thus form in dilational fault jogs or bends where extension fractures form the join between two en echelon fault segments (Fig. 1) or near fault tips where fault slip is transferred into extension fractures in horse-tail structures 0361-0128/98/000/000-00 $6.00
(McKinstry, 1948; Cox et al., 2001). Dilational ore shoots can occupy hybrid extensional-shear fractures, which also form parallel to σ 2, but obliquely to σ 1 and σ 3; these ore shoots are in jogs or bends that make a lower angle to the fault than pure extension fractures. Note that not all ore shoots in fault-fill veins form in dilational jogs. Examples include ore shoots formed where faults intersect competent rock bodies (Poulsen and Robert, 1989, fig. 8.10b), chemically reactive layers, permeable layers, or other faults (McKinstry, 1948, p. 325), and ore shoots formed in openings where faults with preexisting bends are reacti vated (Guilbert and Park, 1986, p. 84). In addition, some ore shoots in high strain environments may become stretched to ward parallelism with the elongation lineation (Robert and Poulsen, 2001; Twomey and McGibbon, 2001). In these examples, the ore shoots will have different geometric relationships to the slip-vector orientation than those predicted in the dilational jog model. It is thus important for the geologist to identify what is controlling the ore shoot geometry prior to applying the methodology and equations outlined in this contribution. This typically can be done through observations of surface showings and/or observations at other similar mines in the district.
Slip-Vector Orientation in Fault-Fill Veins Importantly, the direction of maximum permeability along which dilational ore shoots form lies within the plane of the controlling fault zone and perpendicular to the fault slip vector. Therefore, if the orientations of the fault plane and slip vector are known, the orientation of ore shoots can be predicted and drill holes can be designed for optimal success. The orientation of controlling fault zones in most cases can be readily identified through strike and dip measurements in outcrop or oriented drill core, and/or through 3-D reconstructions of fault geometry using a minimum of three control points (e.g., x, y, and z position of the fault zone as identified in outcrop, drill core, or inversion modeling of geophysical data). Slip-vector orientation can be determined or modeled in a number of ways, including direct measurement of slip-related strain features and indirect methods (Table 1).
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TABLE 1. Summary of Common Structural Features and Methods Useful in Determining Slip-Vector Orientation (see text for explanation of indirect methods) Slip-related strain features Structural feature Slickenlines, mullions Slickenfibers Slickolites (oblique stylolitic lineations) Second-order fractures (Riedel fractures) S-C type shear fabrics Shear fold hinge line Mineral elongation lineation
Relation to slip line Parallel Parallel Parallel Intersection line with fault is perpendicular S- and C-plane intersection line is perpendicular Commonly perpendicular Parallel
Indirect methods of slip line determination Asymmetric fold analysis (Hansen method) Piercing point analysis—orthographic or combined orthographic/stereographic construction 3-D computer modeling of ore shell
Linear, slip-related strain features parallel to the slip vector include slickenlines and fault corrugations (mullions or wear grooves), slickenfibers (crystal fibers), and slickolites (pressure solution lineations: Ramsay and Huber, 1987, p. 657–658). Other slip-related strain features that can be used to infer slip-vector orientation include second-order fractures (such as those predicted by the Riedel model; e.g., Tchalenko, 1970; Davis and Reynolds, 1996, p. 365), S-C type shear fabric in semibrittle fault rocks (e.g., Ramsay and Huber, 1987, p. 632), and shear folds and mineral-elongation lineations in relatively ductile rocks in fault zones or ductile shear zones. Second-order fractures intersect the fault plane about a line perpendicular to the slip vector. S-C–type fabrics consist of two sets of anastomosing foliations (Berthe et al., 1979) in which the S- and C-foliations intersect about a line perpendicular to the slip vector. Shear-fold (asymmetrical fold) hinges typically, but not always, are perpendicular to the slip vector. For robust fold data (hinge orientation and fold asymmetry of multiple shear folds), a statistical, stereographicbased method can be used to model the slip-vector orientation (Hansen, 1971). Indirect methods of slip-vector determination include piercing point analysis with orthographic and combined orthographic-stereographic construction methods (Marshak and Mitra, 1988, p. 81; Leyshon and Lisle, 1996, p. 56). Modern 3-D computer modeling also can be used to determine slip-vector orientation. For example, Miller and Nelson (2002), using a gOcad™ 3-D model of fault-hosted Zn orebodies in the Pillara mine in Western Australia, showed that the slip vector is normal to the line of intersection between the faults and extension fractures. The slip-vector orientation determined from known ore shoots can then be used in drillhole design for ore shoots in similar faults in a deposit or district. Slickenline and slickenfiber lineations are the most common features used to determine slip-vector orientation and form on the footwall or hanging-wall contact or on internal planes of many quartz-filled fault-fill veins. Slickenfibers form by crystal-fiber growth at the time of vein f ormation and thus record the synmineralization slip-vector orientation. In contrast, slickenlines form by mechanical wear during fault slip on the quartz vein and, therefore, are generated after vein formation and may record postmineralization slip. How0361-0128/98/000/000-00 $6.00
ever, as suggested by the banded textures common in epithermal (and some mesothermal) veins, many fault veins form by repeated slip and fluid-flow events during one protracted tectonic event, with a consistent stress-field orientation implied (Sibson, 1996). Therefore, it can be assumed that fault-vein slickenlines commonly record synmineralization slip, and they can be used with confidence in the method described below. Nonetheless, multiple slickenline orientations on one fault plane usually indicate that fault reactivation has occurred in a postmineralization stress field, and caution must be exercised in determining the synmineralization slip vector. In ductile and semiductile environments, mineral elongation lineations are the most robust slip-vector indicator. However, postmineralization ductile deformation may rotate dilational ore shoots to less than 90° to the slip vector, and in some cases parallel to the slip vector (Robert and Poulsen, 2001). Caution must be exercised in such environments, and the presence of deformed mineralized zones might indicate that the method presented here is not appropriate for drillhole design.
Calculation of Drill Target Location Given a knowledge of the fault-vein and slip-vector orientations near the best geochemically anomalous vein outcrops (e.g., with economic or bonanza grades), the location of which is given in Universal Transverse Mercator (UTM) coordinates (easting and northing: E O, NO), the UTM coordinates of the drill target (ET, NT) can be calculated using the equations shown below (see Appendix for derivations). Data required for the calculation are as follows: s = vein strike, d = vein dip, Rs = slip-vector rake (usually determined from slickenline rake), and v = vertical depth to intersect ore shoot. Parameters and angular relationships used in the calculations are shown in Figures 2 and 3. Fault-vein strike (s) is entered in right-hand–rule format (azimuthal strike, 0° to 360°, is 90º counterclockwise from the dip direction). Slip-vector rake (Rs) is entered in right-hand–rule format measured clockwise from the right-hand–rule strike and is from 0° to 180° (excluding a value of 90° which is not compatible with the equations). The vertical target depth (v) is determined from knowledge of topography, vein dip, and planned drill-hole inclination (i) at the site (Fig. 3C). Note that a dip value of 0° is not compatible with the equations.
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This method first calculates easting and northing offset distances (E, N) from the vein outcrop to the correct drill target (Fig. 3A). The equations for E and N, given in terms of s, d, Rs, and v, are as follows: , and (1)
.
(2)
These values are then added to the UTM coordinates of the outcrop (EO, NO) to determine the UTM coordinates of the drill target (ET, NT). FIG . 2. Schematic block diagram showing a raking line in fault plane (= long axis of ore shoot) and associated angles used in the calculations.
ET = Eo+E, and
(3)
NT = No+N.
(4)
FIG. 3. Schematic map (A), longitudinal section viewed perpendicular to vein (B), and cross section viewed parallel to vein strike (C), showing the angular relationships and parameters used in calculating drill target UTM coordinates. RHR = righthand-rule (explained in text). Note that if Rs > 90°, then R o = (Rs – 90).
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of geochemically anomalous outcrops along the fault vein. Tests of the Method Information required to test the method directly is not This method requires the assumption that fault kinematics available for many examples. However, the orientations of ore control ore shoot orientation, and is not applicable to all faultshoots in a number of ore deposits—such as Pillara, noted vein ore shoots (such as those formed at intersections of above—have been shown to be essentially perpendicular to structures). Nevertheless, the method increases the probabilslip vector in the hosting fault-fill veins, thus validating the ity of successfully drill-testing ore shoots through optimal deconcept that dilational fault jogs perpendicular to the slip vec- sign of drill holes. tor control the orientation of many ore shoots. Other exam Acknowledgments ples in epithermal systems include (1) the strike slip-hosted Rick Sibson, through his excellent writing on structural perCaylloma Ag-Au-base metal quartz vein system in southern meability and discussions on outcrops in New Zealand, Perú, a low- to intermediate-sulfidation deposit hosted in Tertiary volcanic rocks (Fig. 4A; Echavarría et al., 2006), and (2) helped foster development of some of the concepts in this the normal fault-hosted Arcata Ag-Au quartz vein system in paper. Murray Hitzman is thanked for helpful discussions in southern Perú, a low-sulfidation vein deposit also hosted in conceptual development of some ideas in this paper and for Tertiary volcanic rocks (Fig. 4B; Echavarría et al., 2003). Ex- thoughtful review. Lucas Marshall provided a thoughtful reamples in mesothermal shear zone-hosted systems in Val view and field discussions of structural permeability. Dave d’Or, Canada, include the reverse-slip Ferderber deposit (Vu Benson is thanked for his help with transformation equations. et al., 1987, cited in Poulsen and Robert, 1989, fig. 8.10a) and Jeff Hedenquist also offered a helpful review. the reverse-oblique slip Dumont deposit (Belkabir et al., July 17, September 14, 2006 1993, cited in Robert et al., 1994, fig. 3.24a).
Conclusions Kinematically controlled (i.e., dilatant) ore shoots form in localized, elongated structural openings perpendicular to the slip vector along pre- or synmineralization faults. The orientation (rake) of ore shoots thus can be predicted from the slip vector rake. Equations are derived to calculate the UTM coordinates of the drill target, given fault-vein orientation, slip-vector rake (usually determined from slickenlines), vertical depth to intersect the ore shoot, and the UTM coordinates
REFERENCES Belkabir, A., Robert, F., Vu, L., and Hubert, C., 1993, The influence of dikes on auriferous shear zone development within granitoid intrusions: the Bourlamaque pluton, Val d’Or district, Abitibi greenstone belt: Canadian Journal of Earth Sciences, v. 30, p. 1924–1933. Berger, B.R., Tingley, J.V., and Drew, L.J., 2003, Structural localization and origin of compartmentalized fluid flow, Comstock Lode, Virginia City, Nevada: ECONOMIC GEOLOGY, v. 98, p. 387–408. Berthe, D., Choukroune, P., and Jegouzo, P., 1979, Orthogneiss, mylonite and non coaxial deformation of granites; the example of South Armorican shear zone: Journal of Structural Geology, v. 1, p. 31–42.
A
B
FIG. 4. Longitudinal sections of fault-vein deposits with dilational ore shoots perpendicular to slip vector; stereonets show fault-fill veins as great circles and show slip vector (slickenlines) plotted with arrows showing hanging-wall motion. A. Apóstoles 2 vein showing Ag grade contours and steeply raking ore shoots, Caylloma district, Perú (Echavarría et al., 2006). The stereonet shows faults with low-rake slickenlines. B. Baja vein showing Ag grade contours and low-raking ore shoots, Arcata district, Perú (Echavarría et al., 2003). The stereonet shows fault-fill veins with high-rake slickenlines. 0361-0128/98/000/000-00 $6.00
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Cox, S.F., 1991, Geometry and internal structures of mesothermal vein systems: implications for hydrodynamics and ore genesis during deformation: University of Western Australia, Publication no. 25, p. 47–53. Cox, S.F., Knackstedt, M.A., and Braun, J., 2001, Principles of structural control on permeability and fluid flow in hydrothermal systems: Reviews in Economic Geology, v. 14, p. 1–24. Davis, G.H., and Reynolds, S.J., 1996, Structural geology of rocks and regions, second edition, New York, Wiley, 776 p. Echavarría, L., Yagua, T., Nelson, E., and Benavides, J., 2003, Sistema epitermal de Arcata, sur de Perú: III Congreso Internacional de Prospectores y Exploradores—ProExplo 2003, Lima, Perú, April 23–25, 2003, Conference CD-ROM, 17 p. Echavarría, L., Nelson, E., Humphrey, J., Chavez, J., Escobedo, L., and Iriondo, A., 2006, Geological evolution of the Caylloma epithermal vein district, southern Perú: ECONOMIC GEOLOGY, v. 101, p. 843–863. Gibson, P.C., Noble, D.C., and Larson, L.T., 1990, Multistage evolution of the Calera epithermal vein system, Orcopampa district, Southern Peru: First results: E CONOMIC GEOLOGY, v. 85, p. 1504–1519. Gibson, P.C., McKee, E.H., Noble, D.C., and Swanson, K.E., 1995, Timing and interrelation of magmatic, tectonic, and hydrothermal activity at the Orcopampa district, southern Peru: ECONOMIC GEOLOGY, v. 90, p. 2317–2325. Guilbert, J.M., and Park, C.F., Jr., 1986, The geology of ore deposits: New York, Freeman, 985 p. Hansen, E., 1971, Strain facies: New York-Heidelberg-Berlin, Springer-Verlag, 207 p. Leyshon, P.R., and Lisle, R.J., 1996, Stereographic projection techniques in structural geology: Oxford, Butterworth-Heinemann, 104 p. Lovering, T.S., and Goddard, E.N., 1950, Geology and ore deposits of the Front Range, Colorado: U.S. Geological Survey Professional Paper, v. 223, 319 p. Marshak, S., and Mitra, G., 1988, Basic methods of structural geology: Englewood Cliffs, New Jersey, Prentice Hall, 446 p. McKinstry, H.E., 1948, Mining geology: New York, Prentice-Hall, 680 p. ——1955, Structure of hydrothermal ore deposits: E CONOMIC GEOLOGY 50TH ANNIVERSARY V OLUME, p. 170–225. Miller, J. McL., and Nelson, E.P., 2002, Three-dimensional strain during basin formation—orthorhombic fault patterns and associated MVT mineralization, Lennard shelf, Western Australia [abs.]: Geological Society of America Annual Meeting, Program with Abstracts, v. 34, p. 113. Nelson, E.P, Echavarría, L., and Caine, J.S., 2003, Structural openings and the localization of ore bodies: III Congreso Internacional de Prospectores y Exploradores—ProExplo 2003, Lima, Perú, April 23–25, 2003, Conference CD-ROM, 25 p. Newhouse, W.H., 1942, Ore deposits as related to structural features: New York, Hafner Publishing Co., 280 p.
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Poulsen, K.H., and Robert, F., 1989, Shear zones and gold: Practical examples from the southern Canadian Shield, in J.T. Burnsall, ed., Mineralization and shear zones: Geological Association of Canada, Short Course Notes 6, p. 239–266. Ragan, D.M., 1985, Structural geology: An introduction to geometrical techniques, third edition: New York, John Wiley and Sons, Inc., 393 p. Ramsay, J., and Huber, M., 1983, The techniques of modern structural geology, Volume 1. Strain analysis: London, Academic Press, 307 p. ——1987, The techniques of modern structural geology, Volume 2. Folds and fractures: London, Academic Press, p. 309–700. Richards, J.P., and Tosdal, R.M., eds., 2001, Structural control on ore genesis: Reviews in Economic Geology, v. 14, 180 p. Robert, F., 1990, Structural setting and control of gold-quartz veins in the Val d’Or area, southeastern Abitibi subprovince, in Ho, S.E., Robert, F., and Groves, D.I., compilers, Gold and base metal mineralization in the Abitibi subprovince, Canada, with emphasis on the Quebec segment: University of Western Australia, Publication 24, p. 164–209. Robert, F., and Brown, A.C., 1986, Archean gold-bearing quartz veins at the Sigma mine, Abitibi greenstone belt, Quebec. Part I. Geologic relations and formation of the vein system: E CONOMIC GEOLOGY, v. 81, p. 578–592. Robert, F., and Poulsen, K.H., 2001, Vein formation and deformation in greenstone gold deposits: Reviews in Economic Geology, v. 14, p. 111–155. Robert, F., Poulsen, K.H., and Dube, B., 1994, Structural analysis of lode gold deposits in deformed terranes: Geological Survey of Canada, Open File Report 2850. 136 p. Ruvalcaba-Ruiz, D.C., and Thompson, T.B., 1988, Ore deposits at the Fresnillo mine, Zacatecas, Mexico: ECONOMIC GEOLOGY, v. 83, p. 1583–1597. Sibson, R.H., 1990, Rupture nucleation on unfavorably oriented faults: Bulletin of the Seismological Society of America, v. 80, p. 1580–1604. ——1996, Structural permeability of fluid-driven fault-fracture meshes: Journal of Structural Geology, v. 18, p. 1031–1042. ——2001, Seismogenic framework for hydrothermal transport and ore deposition: Reviews in Economic Geology, v. 14, p. 25–50. Sibson, R.H., Robert, R., and Poulsen, K.H., 1988, High-angle reverse faults, fluid pressure cycling, and mesothermal gold-quartz deposits: Geology, v. 16, p. 551–555. Tchalenko, J.S., 1970, Similarities between shear zones of different magnitudes: Geological Society of America Bulletin, v. 81, p. 1625–1640. Twomey, T., and McGibbon, S., 2001, The geological setting and estimation of gold grade of the high-grade zone, Red Lake mine, Goldcorp Inc.: Exploration and Mining Geology, v. 10, p. 1–34. Vu, L., Darling, R., Béland, J., and Popov, V., 1987, Structure of the Federber deposit, Belmoral Mines Ltd., Val D’Or, Quebec: Canadian Institute of Mining and Metallurgy Bulletin, v. 80, no. 907, p. 68–77.
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APPENDIX Equation Derivation This method first calculates distances from the vein outcrop to the drill target in coordinates perpendicular and parallel to vein strike (X and Y, respectively; Fig. 3A). The easting and northing offset distances for the drill target (E, N) are then determined using a coordinate transformation. These values are then added to the UTM coordinates of the outcrop (E O, NO) to determine the UTM coordinates of the drill target (ET, NT). The final equations for E and N (eq. A7 and A8, respectively) are given in terms of s, d, Rs, and v, and are derived below. The value X is related to the vertical drill intersection distance and the dip of the fault vein (Fig. 3C): X = v / tan(d).
Substituting equation (A1), this equation becomes Y = v / [tan(d) ⋅ tan(90+Rs) ⋅ cos(d)].
The calculated X and Y values are then converted to values parallel to easting and northing coordinates through a transformation matrix using the strike (s):
The resulting equations are as follows: E = Xcos(s) + Ysin(s)
(A7)
(A2)
N = -Xsin(s) + Ycos(s)
The rake of the ore shoot (R o) is related trigonometrically to the apparent rake ( β) and the fault vein dip (d) as follows (Ragan, 1985, eq. 4.5): tan(Ro) = tan( β) / cos(d), and thus, tan( β) = tan(Ro)⋅cos(d).
(A3)
In kinematically-controlled, dilational ore shoots the slip vector is perpendicular to the ore shoot in the fault-fill vein, and therefore, Ro = 90+Rs.
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or (A8)
Finally, the values E and N are added to the UTM coordinates of the outcrop to obtain the UTM coordinates of the drill target:
(A4)
Note that Rs is given in right-hand-rule format, and if Rs > 90°, then Ro = (Rs – 90). Therefore, substituting equations (A3) and (A4), equation (A2) becomes Y = X / tan(90+Rs) ⋅ cos(d).
or
(A1)
The map view (Fig. 3A) shows that Y is related to X and the apparent rake angle ( β) of the ore shoot seen in plan view: Y = X / tan( β).
(A6)
(A5).
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ET = Eo+E, and
(A9)
NT = No+N.
(A10)
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