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_Journal of Structural Geology 32 (2010) 741e745_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _A method for measuring the orientations of planar structures in cut core_ _T.G. Blenkinsop a,*, M.G. Doyleb _a Economic Geology Research Unit, School of Earth and Environmental Science, James Cook University, Townsville QLD 4811, Australia_ _b AngloGold Ashanti Ltd, Level 13, St Martins Tower, PO Box Z5046, Perth WA 6831, Australia_ _article info_ _Article history: Received 5 November 2009_ _Received in revised form 19 April 2010_ _Accepted 28 April 2010_ _Available online 6 May 2010_ _Keywords: Drill core Orientated core SC fabrics Structural analysis_ _abstract_ _Exploration drill core is commonly cut in half for assay purposes soon after acquisition. Structural measurements from half core are generally less accurate or more difficult to make using existing techniques than on whole core. This paper proposes a method to determine the orientations of planar features from half core, by measuring two lengths and one angle. The method is rapid, simple and has errors of less than 2 x14 in suitable core. It is also robust for core that is not cut exactly in half. Detailed structural studies can now be made at later stages in exploration after core has been cut, as illustrated here by kinematic analysis of SC and SC’ fabrics._ _? 2010 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Measuring orientations of structures in orientated drill core is an essential part of most exploration programs for mineral deposits. Tens to hundreds of kilometres of drill core might be obtained in order to prove a resource. Drill core may contain the only direct information about the structures that control the orientation and location of the deposit, especially in areas of poor exposure, or where the deposit is under cover. Measurements from drill core are also vital in engineering and geotechnical applications, and in scientific drilling (e.g. Tembe et al., 2006; Louis et al., 2008)._ _Several methods exist for determining the orientation of planar structures from drill core. The most widely used method is probably the measurement of two angles (usually denoted a and b) to specify the orientation of planes relative to the drill core axis and an orientation line on the core, generally marked at the lowest point around the circumference of the core (e.g. Zimmer, 1963; Laing, 1977; Stanley and Hooper, 2003; Holcombe, 2008). Measurements can also be made relative to fabrics of known orientation (e.g. Hinman, 1993; Scott and Berry, 2004), or from cores that intersect the same structure from different orientations (e.g. Versteeg and Morris, 1994). Methods using unorientated slabbed core to constrain the orientation of planar structures have been described by Hesthammer (1998) and Hesthammer & Hendon._ _? Corresponding author. Tel.: ?61 7 4781 4318. E-mail address: Thomas.Blenkinsop@jcu.edu.au (T.G. Blenkinsop)._ _0191-8141 $ e see front matter ? 2010 Elsevier Ltd. All rights reserved. doi:10.1016 j.jsg.2010.04.011_ _A popular alternative is to re-orientate the core in the position from which it was drilled, and to take structural measurements from the core with a compass, as though the core was an outcrop (e.g. Marjoribanks, 1997). Core can be re-positioned using a simple frame (a “rocket launcher”), or a sand box. A new photographic method has been developed recently (https: www. groundmodellingtechnologies.com )._ _These methods are designed to work with full core as retrieved directly from a drill hole. However, in most mining and exploration circumstances, critical intervals of the core are cut in half as soon as possible after drilling for assay purposes. Structural measurements are taken in the brief interval between drilling and sampling, and are rarely as comprehensive as needed. The remaining half core is stored. It is often necessary to revisit this core to collect more detailed measurements, particularly as hypotheses advance about important structures that may control mineralization as the ore body is delineated and mined. However, cut core poses problems for traditional techniques of core structural analysis. Where the half core does not include the lowest point of a plane, b can not be measured directly. Subject to this limitation, the aeb method can be used on half core if a special transparent template is constructed (Rob Scott, pers. comm.), which needs to be customised to the particular core size. Estimation of planar orientations in the rocket launcher or sand box from cut core are generally more difficult and less accurate than for whole core._ _This study proposes and tests a new method to acquire accurate orientations of planar features from core that has been cut, which requires only three simple measurements: two lengths and an angle. It is comparable in simplicity to the aeb method used on full core, and does not require a template._ _2. Principle_ _The orientation of planes is first measured relative to the core, then converted to real orientations using the direction and inclination of the drill hole. An interim frame of reference is used for the initial measurements, in which the bottom-of-core line is vertical and assumed to be at the North end of the core. Fig. 1 shows the essential geometrical elements, and definitions of terms and quantities are given in Table 1. The objective is to calculate the dip and dip bearing of a plane P (Fig. 1). Lines M’N and O’N are two vectors that lie within P. The normal to P, n, is given simply by their cross-product:_ _n ? M0N x O0N_ _(1)_ _The positions of M and O can be measured simply and quickly with a set square or ruler relative to the point N, taking down-hole distances from N as positive. Fig. 2 is a photograph of half core with N, M and O marked up for a plane, as shown in Fig. 1a. These values can be converted to plunges (P) and trends (T) of vectors M’N and O’N by simple trigonometry, assuming that the core is vertical with the bottom-of-core mark in the North position (i.e., the interim frame of reference):_ _TO0N ? 90 ? b_2 If NO < 0?Fig: 1b?_ _(2)_ _PO0N ? Tan?1?NO_2r Sin?b_2???Fig: 1c?_ _(3)_ _TM0N ? b if NM < 0?Fig: 1a?_ _(4)_ _PM0N ? Tan?1?NM_2r??Fig: 1d?_ _(5)_ _Appropriate adjustments are made to the formula to deal with positive values of NO, NM. The formulae also require measurement of b, the angle measured clockwise when viewed down-hole from the bottom-of-core line to near edge of core (Fig. 1), and the radius of the core, r._ _The normal to P in the interim frame of reference is given by Eq. (1). The final, real orientation of P is given by rotating n back into a geographic frame of reference using a rotation matrix derived from the orientation of the drill hole, which is acquired using standard gyroscopic, electronic or camera tools (e.g., Paulsen et al., 2002). Note that NO’ is undefined for b ? 0 or 180 x14: the method as described only works when the core is not cut along the bottom-of-core mark. The latter is standard industry practice, so as to preserve the orientation mark._ _An additional measurement is necessary for core that is not cut exactly in half. The top of such an oversize half core is shown in Fig. 3a. The vector O’N will be given correctly by measurements of NO and b substituted in Eqs. (2) and (3), but the flat face is no longer parallel to b, and distance M0M is no longer equal to the diameter of the core. Equations (4) and (5) must be rewritten:_ _TM0 N ? b ? Cos?1?M0 ? M_2r if NM < 0?Fig: 1a?_ _(6)_ _PM0N ? Tan?1?NM_M0M??Fig: 1d?_ _For undersize half core (Fig. 3b), Eq. (6) becomes:_ _TM0 N ? b ? Cos?1?M0 ? M_2r if NM < 0?Fig: 1a?_ _(8)_ _Interim North O’ r M’ TO’N r M,N,O -Cos-1(M’M 2r) a d M’ PM’N N M’ Far edge Trace of Plane P on core O O’ c flat surface OO’N O O’ PO’N N Near edge N Interim North Bottom-of-core Line Fig. 1. Appearance of half core and points used for calculations. a) View of half core with trace of plane P. b) View of top of half core. c) View of surface OO’N. d) View of flat face of half core._ _T.G. Blenkinsop, M.G. Doyle Journal of Structural Geology 32 (2010) 741e745_ _743_ _Table 1 Definitions of terms and quantities. Refer to Fig. 1 for further explanation. Lengths are measured positive down-hole._ _Term Quantity Definition Near edge Far Edge b M0 N M0 M N O0O r n Edge of half core nearest bottom-of-core line Edge of half core furthest from bottom-of-core line Beta, smallest angle measured clockwise when viewed down-hole from bottom-of-core line to near edge of core. Trace of plane P on flat face of half core Uphole end of line M0N Projection of M0 across flat face of core perpendicular to core axis down-hole end of line MN Point at intersection of plane with bottom-of-core line Intersection of the plane P perpendicular to core axis that passes through O0 with the edge of the core nearest the bottom-of-core mark Radius of whole core Normal to plane P_ _3. Results_ _a Oversize core Interim North O’ r M’ r TO’N r? M,N,O -Cos-1(M’M 2r) b Undersize core Interim North M’ r O’ TO’N r? r M,N,O +Cos-1(M’M 2r) Fig. 3. Geometries of a) Oversize and b) Undersize core. The solid black angle in both cases is Cos-1 (M0M 2r)._ _The orientations of planes derived from the above method were compared with measurements of the same planes using a rocket launcher. The latter measurements could only be obtained for a limited number of planes, because most planes can not be measured at all accurately in the rocket launcher on half core. Fig. 4 is a lower hemisphere, equal area stereoplot of the poles to planes given by this method (black dots) compared to rocket launcher orientations (red triangles). The accuracy of the rocket launcher measurements is unknown, but there is a good match. This correspondence probably indicates that both methods are reasonably accurate._ _4. Error analysis_ _Errors related specifically to the application of this method can be assessed by the angular difference between poles to planes calculated from this method and those measured using a rocket launcher._ Ключевые слова: plane calculated, variation, vector, core cut, simple, excel spreadsheet, set, doyle journal, errors, shear, data, australia, randomly, down-hole, edge core, sand box, trace, reference, frame, hesthammer, doi, converted, jsg, drilling, formula, zimmer, measurement core, arrow, detailed, measurement, mark, oversize core, orientation plane, distance, surface, drill core, angle, interim frame, measured, fabric, frame reference, marjoribanks, angular difference, berry, centre, hinman, length, measurements, structure, accurate, north, sampling, structural, half-core method, view, developed, sense, planar, wong, viewed down-hole, pole, large, measuring, rocket launcher, intersection plane, control, le, geology, normal, interim, treloar, method, aeb method, cut core, range, feature, structural geology, lowest point, relative, positive, oversize, rocket, ?at, quantity, cut, planar orientation, area, box, simple method, larger, scott, edge, laing, wa, application, interim north, term, result, ha, undersize core, direction, vertical, kinematic analysis, drill, sc, accuracy, drill hole, illustrated, sc ’, journal structural, randomly generated, position, difcult, exploration, assay, axis, marked, generally, analysis, mineral, point, launcher, doyle, work, calculated, orientation planar, holcombe, planar feature, undersize, hole, economic, small, intersection, online, orientation, petroleum, blenkinsop doyle, nm, core, elsevier, shear direction, angular, eqs, error, journal structural geology, blenkinsop, plane, face, journal, bottom-of-core, planar structure, difference, calculate, deposit, paulsen