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Elastic Anisotropy of a Metamorphic Rock Sample of the Canadian Shield in Northeastern Alberta Judith Chan & Douglas R. Schmitt Rock Mechanics and Rock Engineering ISSN 0723-2632 Volume 48 Number 4 Rock Mech Rock Eng (2015) 48:1369-1385 DOI 10.1007/s00603-014-0664-z 1 23 Your article is protected by copyright and all rights are held exclusively by SpringerVerlag Wien. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”. 1 23 Author's personal copy Rock Mech Rock Eng (2015) 48:1369–1385 DOI 10.1007/s00603-014-0664-z ORIGINAL PAPER Elastic Anisotropy of a Metamorphic Rock Sample of the Canadian Shield in Northeastern Alberta Judith Chan • Douglas R. Schmitt Received: 28 January 2014 / Accepted: 5 October 2014 / Published online: 8 November 2014 Ó Springer-Verlag Wien 2014 Abstract The presence of fractures and textures cause metamorphic rock masses to be seismically anisotropic. Neglect of this anisotropy in the processing of field seismic data causes problems in the final reflection images both in terms of their quality and in the true positioning of subsurface features. To quantify the degree of seismic anisotropy in the subsurface, one method is to estimate the anisotropic parameters from the elastic stiffnesses of a rock sample. Using the ultrasonic pulse transmission method, measurements of the compressional and shear wave phase velocities as a function of confining pressure are used to calculate the elastic stiffnesses of a metamorphic granite core sample from the Precambrian basement in northeastern Alberta. Velocities are measured parallel, normal and oblique to an identified foliation plane of the sample assumed to be a transversely isotropic medium. The compressional wave velocities are measured to be in the range of 5,352–6,019 m/s along the foliation plane and 4,752–5,396 m/s normal to the foliation plane over the range of confining pressures from 0 to 60 MPa. Besides providing valuable in situ velocity information for the velocity models, the results also confirm the anisotropic behavior of the metamorphic rock with the estimated compressional and shear wave anisotropy valued at 12 and 8 %, respectively. Such degree of seismic anisotropy should be taken into consideration at the seismic scale when working with three-dimensional geophysical models J. Chan (&) D. R. Schmitt Department of Physics, Institute for Geophysical Research, University of Alberta, 4-181 CCIS, Edmonton, AB T6G 2E1, Canada e-mail: [email protected] D. R. Schmitt e-mail: [email protected] of the Precambrian basement to minimize any out-of-plane anomalies in the final seismic sections. Keywords Seismic anisotropy Elastic moduli Ultrasonic pulse transmission Metamorphic rocks Canadian Shield 1 Introduction Study of the metamorphic cratonic rocks is uncommon in Alberta because most of the province is blanketed with the thick sedimentary successions of the Western Canada Sedimentary Basin (WCSB). Recently, however, there has been interest in evaluating the potential of geothermal energy in Alberta as one means towards reducing greenhouse gas emissions. Part of this effort includes studies within a serendipitously provided borehole-of-opportunity (Hunt well) drilled to a depth of nearly 2.4 km in which the lower 1.9 km is drilled through Canadian Shield rock. An exhaustive geophysical program that included wireline logging and vertical and walk-away seismic profiling was carried out to characterize the rock mass in the borehole with the geothermal gradient recently reported (Majorowicz et al. 2014). A very limited amount of core material exists, and here we describe measurements of the elastic anisotropy on one sample of this material. This paper presents the results of the velocity measurements, elastic constants, and the anisotropic parameters of the sample based on the assumption that the sample material has hexagonal, or transversely isotropic (TI), symmetry. The goal is to quantify the degree of seismic anisotropy of the rock sample under in situ pressure conditions similar to the in situ stresses. Seismic velocities were measured in three orientations with respect to a 123 Author's personal copy 1370 visible foliation plane in the sample. The results of these measurements are intended to assist first in the interpretation of seismic anisotropy measurements in walk-away borehole seismic measurements and, second, to provide measures of the general mechanical properties to assist interpretations of the stress state at depth. A brief theoretical overview of the in situ stress field and the theory of elasticity are first provided in the next section, followed by the experimental setup and the results of the study. 2 Background Seismic anisotropy is a general property of the rocks in the Earth’s crust that affects propagation velocities, particle motion polarizations, and amplitudes of the seismic waves. Anisotropy also further complicates the modeling of such waves (Vavryčuk and Boušková 2009). Study of anisotropy offers the opportunities to estimate the stress field (and fracture orientation), infer the spatial variation of fractures, predict fluid saturation, and monitor the subsurface pressure changes and fluid pathways in the potential subsurface reservoirs. The anisotropic behaviors of rocks to small fractures can be modeled by effective media, whereas modeling of larger fractures that have an impact on the reflection, transmission and diffraction features on seismic data becomes more complicated. Many crystalline metamorphic formations are geologically heterogeneous in nature due to their compositional and structural variations. Seismic anisotropy is one aspect of this heterogeneity and in the case of metamorphic rocks this anisotropy can be caused by the metamorphic textures of anisotropic minerals and by cracks oriented in a preferred direction. The latter case may be related to the regional tectonic stress system that controls the closure and opening of microfractures on a crustal scale (Crampin 1990). An understanding of the in situ stress fields, confining pressure and their relation to rock mechanics helps to predict the geometry of induced fractures and the amount of pressure needed for fracture propagation (Tester et al. 2006). With the rapid development of incorporating anisotropic velocity models in seismic methods, it has become increasingly important to understand the effect of velocity anisotropy for both seismic imaging and in characterizing the rock mass. In general, seismic methods serve as good preliminary imaging of the basement rocks since they offer coverage over a broad area of interest when deep boreholes are not commonly available. However, the effect of anisotropy in seismic imaging can generate problems in the conventional data processing routine. This includes the sideslip and smearing of depth-migrated seismic images leading to the improper positioning of a target structure 123 J. Chan, D. R. Schmitt (e.g., Alkhalifah and Larner 1994; Vestrum et al. 1999; Vestrum and Lawton 2010). Metamorphic rock is commonly assumed to have isotropic, transversely isotropic, or orthorhombic symmetry based on the degree of foliation and mineral alignment (e.g., Kern and Wenk 1990; Takanashi et al. 2001; Cholach et al. 2005). An isotropic rock has no detectable texture and its physical properties are identical regardless of the direction through which it is viewed. Foliated (with no lineation) and layered rocks are considered as transversely isotropic with a rotational axis of symmetry perpendicular to the foliation plane. A foliated rock with clear preferential crystallographic alignments of the minerals that are manifested as a lineation parallel to the foliation plane is expected to have three orthogonal planes of symmetry, i.e., orthorhombic symmetry. By assuming a type of fabric symmetry and undertaking laboratory measurements of seismic wave velocities, the correlating elastic constants with respect to the fabric symmetry can be estimated. The behaviors of elastic wave velocities and seismic anisotropy in metamorphic rocks have long been reported using laboratory measurements and seismic field methods. Large-scale anisotropy had been found to contaminate tomographic images with false structures in the upper mantle when only isotropic velocity models were used (e.g., Wang and Zhao 2009; Eken et al. 2012). Errors in the lateral positioning of the subsurface features also arise if an isotropic earth was assumed in seismic data processing (e.g., Issac and Lawton 1999; Godfrey et al. 2002; Vestrum and Lawton 2010). Johnson and Wenk (1974) measured the physical properties of 110 metamorphic rocks from the Central Alps under the assumption of orthorhombic symmetry. The sample was prepared with respect to the visible mesoscopic fabric directions and elastic wave velocities were measured using the ultrasonic pulse transmission technique. Strong anisotropy was observed in the thermal and elastic properties of the samples. It was found that the pattern of correlations between the various scalar physical properties became more complex in the presence of small openings between grains. Laboratory velocity measurements of rock samples were also used to assist in the interpretation of in situ seismic velocity data. Kern and Schenk (1988) investigated the relationship of velocity anisotropy with the chemical and mineralogical characteristics of metamorphic rocks from the Serre Mountains of southern Italy. Using the structural and stratigraphic field data, and by determining the pressure and temperature derivatives of the compressional and shear wave velocities, they generated a model seismic profile that showed the velocity variation as a result of mineralogical change with depth. It was found that the degree of anisotropy was controlled by the elastic Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample anisotropy of mineral constituents as well as by the modal concentration, distribution, and preferred orientation of mineral constituents at high confining pressure. Furthermore, Poisson’s ratio was found to be more sensitive to lithology than the compressional (P-) and shear (S-) wave velocities alone. Kern et al. (2002) examined the physical properties of metamorphic rocks from the Sulu terrain, China under ultrahigh pressure (up to 600 MPa). Chemical composition and metamorphic grade were known to contribute to the change in mineralogy, and this was evident in the relationship between P-wave velocities and Poisson’s ratio. The measured in situ velocities of P- and S-waves increased with density and metamorphic grade of the rocks. They were compared with the near-intrinsic velocities from seismic measurements (refraction and reflection) which led to the conjecture that fractures play an important role in the in situ seismic properties of the seismic crustal profile. Reflectivity in the seismic profile was suggested to be due to the shear deformation-induced (lattice preferred orientation-related) seismic anisotropy. Vilhelm et al. (2010) compared the velocities determined in the laboratory to those measured in the surface seismic records in the Ivrea zone in northwestern Italy. This zone is composed of strongly metamorphic rocks including an ultra-mafic peridotite massif that was selected for rock sampling. It was found that the laboratory and field-scale velocities differ significantly up to a scale of 41 %. The discrepancy can be due to the frequency of the applied seismic signals, density of parallel cracks, and fracture stiffness observed in the outcrops that were otherwise undetected by the smaller scale rock samples. This study demonstrated that it can be difficult to directly transfer laboratory-measured velocities to a field-scale study. Cholach et al. (2005) measured the P- and S-wave speeds in three orthogonal directions and with three orthogonal polarizations on a suite of 35 metavolcanics and metasediments from an exposed mid-crustal shear zone in the Canadian Shield near Flin Flon, Manitoba. These samples visually displayed a range of textures indicative of isotropic, transversely isotropic, and orthorhombic symmetries; and both strong shear wave splitting and high values of anisotropy were observed. Interestingly, averaging of the elastic properties of this suite suggested that the larger formation would be close to having transverse isotropic symmetry. In situ quantification of seismic anisotropy can be done using multi-offset and multi-azimuths vertical seismic profiling (VSP). Rabbel (1994) observed the presence of shear wave birefringence in the near-offset VSP of the KTB borehole in Oberpfalz, Germany. Velocity for direct compressional and split shear waves was picked from the 1371 near-offset VSP. The polarization direction of the faster shear wave was found to coincide with the steeply dipping rock formation of dominantly biotite gneiss. Under the assumption of hexagonal-type symmetry, the average anisotropy of the gneiss was estimated using the leastsquares fit method with known seismic velocities and angles of wave propagation. Moreover, the final reported anisotropy was found to agree with the laboratory measurements performed on the rock samples from the borehole. Significant seismic anisotropy was observed in the Outokumpu scientific borehole in Finland using walk-away VSP. Schijns et al. (2012) found that the reported anisotropy from the VSP data could not be fully explained alone by the intrinsic rock anisotropy measured in the laboratory (Kern et al. 2008). As such, forward modeling of the VSP results was undertaken to predict an overall anisotropy of schist by incorporating the intrinsic material properties obtained from core measurements and the oriented crack anisotropy. The modeling results revealed that the phase velocities in an intrinsically orthorhombic medium containing a set of aligned cracks would be consistent with the in situ P-wave velocities from the walk-away VSP. Most of the Canadian Shield Craton is made up of Precambrian igneous and high-grade metamorphic rock. The Canadian Shield is exposed in the northeastern part of Alberta where the crystalline basement can be traced unambiguously into the subsurface dipping gently southwest at 4–5 m/km and overlain by the Phanerozoic successions of the WCSB. Recent research interests in characterizing the basement rocks in northern Alberta arise in investigating the feasibility of geothermal energy development in Alberta. Existing geothermal gradient studies suggested that deep drilling into the metamorphic Canadian Shield is required in northeastern Alberta to reach the target temperature for higher enthalpy geothermal exploitation (Majorowicz et al. 2012). In Alberta, there were over 489,000 boreholes drilled in Western Canada until 2011 (Canadian Association of Petroleum Producers (CAPP) 2013). However, boreholes drilled deep into the Precambrian basement in Alberta are extremely rare because these low porosity and permeability rocks are not considered prospective for hydrocarbons. As such, our understanding of the basement rocks, let alone their seismic anisotropy, remains limited. However, commercial interests seeking to test novel hypotheses of hydrocarbon generation drilled a deep borehole (hereafter referred to as Hunt well after its owner) through nearly 2,000 m of metamorphic cratonic rocks in NE Alberta (Chan 2013). This borehole extends deep into the basement rocks and thus provides a unique opportunity for researchers to study the in situ physical properties of the metamorphic rocks. Currently, the Hunt well is believed to 123 Author's personal copy 1372 J. Chan, D. R. Schmitt be the deepest borehole drilled into the metamorphic Canadian Shield in Alberta. Source O * x Horizontal Position 3 Theoretical Background According to the theory of linearized elasticity, a linear relation (Eq. 1) between stress and strain can be applied to characterize the material properties at a particular point by the generalized Hooke’s Law. In an elastic medium, the stress–strain relationship is related in the form of the generalized Hooke’s Law: rij ¼ Cijkl ekl ð1Þ where rij, ekl denote the variables of stress and strain as second-rank tensors, respectively, Cijkl are the components of the elastic stiffness tensor C (or elastic constants) as fourth-rank tensor with 81 components, and i, j, k, l = 1, 2, 3 indicates one of the three orthogonal axes. Einstein summation convention applies here for each instance of a repeated index on the same side of the equation (Auld 1990). Equation (1) can be further reduced from four indices ijkl down to two indices mn by introducing the Voigt notation (Nye 1985): Cijkl ¼ Cmn ði; j; k; l ¼ 1; 2; 3; m; n ¼ 1; . . .; 6Þ ð2Þ which then simplify the generalized Hooke’s Law into to a matrix equation: rI ¼ cIJ eJ ð3Þ where rI and eJ are the 6 9 1 vectors containing independent components of stress and strain tensors, respectively (Auld 1990). Each CIJ is one of the components of a 6 9 6 symmetric matrix with 21 independent elastic stiffnesses that is symmetric about the diagonal: 32 3 2 3 2 e1 C11 C12 C13 C14 C15 C16 r1 6 r2 7 6 C12 C22 C23 C24 C25 C26 76 e2 7 76 7 6 7 6 6 r3 7 6 C13 C23 C33 C34 C35 C36 76 e3 7 76 7 6 7¼6 6 r4 7 6 C14 C24 C34 C44 C45 C46 76 e4 7 ð4Þ 76 7 6 7 6 4 r5 5 4 C15 C25 C35 C45 C55 C56 54 e5 5 r6 C16 C26 C36 C46 C56 C66 e6 where the indices I and J are related to the ij in according to the cyclical notation I, J = 1, 2, 3, 4, 5, 6 when ij or kl = 11, 22, 33, 13 or 31, 23 or 32, 12 or 21, respectively. The Christoffel equation is an eigenvalue problem in which known elastic constants can be used to calculate the phase velocities of the elastic waves. Detailed derivations need not be repeated here but can be found for example in the monograph published by Musgrave (1970). The equations for linking velocities and elastic constants simplify 123 d 3.1 Elasticity Vertical Position D P Pl an e W av ef ro nt Wave Front Surface z Fig. 1 The relationship between ray (group, D) and phase velocities (d). The axis of symmetry is along the z direction. Image adapted from Daley and Hron (1979) and Kebaili and Schmitt (1997) substantially when wave behavior is discussed within a plane of symmetry and along the principal axis (e.g., Brugger 1965; Fedorov 1968; Musgrave 1970; Aki and Richards 1980; Crampin 1981; Nye 1985). 3.2 Anisotropy Metamorphic rocks are more heterogeneous in nature as presence of foliations and lineations result in strong intrinsic anisotropy due to the preferential alignment of minerals, textural–structural features such as bedding and foliation, and pores and cracks (e.g., Crampin 1981; Mainprice and Nicolas 1989; Kern and Wenk 1990). An important point to note when dealing with wave propagation in anisotropic media is that care must be taken in the definition of the wave speed itself. Figure 1 shows the shape of a wavefront in the x–z plane at time t after the source of the elastic wave was activated at position O. An observer at point P on the wavefront, a straight distance D from point O, would calculate a group velocity Vray = D/t under the assumption that he was in the far field from a point source. However, this observer cannot know from his single vantage point whether or not the arrival he sees lies along the front of a plane wave that would have conveniently passed through the origin O at t = 0. This plane wave front is tangent to locus of the point source wave front at the observation point P; and the phase velocity of this plane wave is instead given by Vphase = d/t. In an isotropic medium d = D but once the material becomes anisotropic this is no longer generally true. Ray (group) velocity is the velocity of energy propagation along a ray path at propagation angle /, whereas phase velocity is the velocity of a mono-frequency plane wave at propagation angle h. These two velocities are equivalent in an Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample Fig. 2 Symmetry of a transversely isotropic medium where elastic properties are rotationally symmetric about the z-axis. Arrows of the same color indicate waves propagating at the same speed while their directions indicate the wave’s polarization isotropic material, but while linked to one another still need to be considered separately for an anisotropic material to properly relate the velocities to elastic constants. This is an important point as determining the CIJ directly from the wave speeds requires knowledge of the phase (plane wave) velocities. This must be considered in the experimental design particularly with regards to the dimensions of the transmitting and receiving transducers, the distance of propagation between them, and the degree of ‘side-slip’ of the beam due to the preferred path of the wave’s energy flow through the medium (Dellinger and Vernik 1994; Vestrum 1994; Kebaili and Schmitt 1997; Mah and Schmitt 2001). Modeling for more anisotropic shales (Meléndez Martı́nez 2014) demonstrates that plane (or group) wave speeds are observed in the current experiments. 1373 plane wave propagation direction relative to the axis of symmetry. P, SV and SH indicate the polarization vectors in the compressional, vertical (i.e., parallel to the rotational axis of symmetry z) and horizontally polarized shear directions, respectively. For example, VSH90 refers to the propagating S-wave that is horizontally polarized with respect to the symmetry axis (i.e., at 90° from the symmetry axis). The Hunt well sample is presumably a TI sample with the foliation plane as the plane of symmetry. In TI media, VP0 is different from VP90 and VS0 is also different from VSH90. The S-waves propagating parallel to the symmetry axis do not split and do not need separate polarization labels as related by VSV0 = VSH0. Another special characteristic of TI media is that VSH0 = VSV90. This form of symmetry is similar to a crystal that could be described in the Voigt-form stiffness matrix C (Musgrave 1970): 3 2 C11 2C66 C13 0 0 0 C11 6 C11 2C66 C11 C13 0 0 0 7 7 6 6 C13 C13 C33 0 0 0 7 7 CIJ ¼ 6 6 0 0 0 C44 0 0 7 7 6 4 0 0 0 0 C44 0 5 0 0 0 0 0 C66 ð5Þ The expressions for deriving the elastic constants from phase velocities were developed by Brugger (1965), Daley and Hron (1977) and Thomsen (1986) as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi C33 þ C44 þ ðC11 C33 Þ sin2 h þ DðhÞ VP ð h Þ ¼ ð6Þ 2q sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi C33 þ C44 þ ðC11 C33 Þ sin2 h DðhÞ VSV ðhÞ ¼ 2q ð7Þ 3.3 Transverse Isotropy Many rocks have structure with hexagonal symmetry and elastically will be transversely isotropic in which the elastic properties are the same in a plane that is perpendicular to a symmetry axis (i.e., z-axis, Fig. 2) but different parallel to the axis. To avoid confusion, it must be pointed out that this differs from the sixfold optical symmetry observed in the minerals. Transverse isotropy requires five independent elastic constants that are dependent on the angle between the propagation direction and the symmetry axis. Many low- to medium-grade metamorphic rocks often have well-developed bedding or foliation planes and behave as transversely isotropic (TI) elastic solids (Gupta 2011). Figure 2 illustrates the symmetry of a TI medium. The subscripts 0 and 90 correspond to the angle h of the sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C66 sin2 h þ C44 cos2 h VSH ðhÞ ¼ q ð8Þ where q is the density of the rock and h is the angle between the direction of wave propagation and the sample’s rotational axis of symmetry. D(h) is denoted by: h DðhÞ ðC33 C44 Þ2 þ2 2ðC13 þ C44 Þ2 ðC33 C44 Þ i ðC11 þ C33 2C44 Þ sin2 h 1=2 h i 2 2 4 þ ðC11 þ C33 2C44 Þ 4ðC13 þ C44 Þ sin h ð9Þ Note that the wave front surface for the VSH mode will always take an elliptical form according to Eq. (8). 123 Author's personal copy 1374 J. Chan, D. R. Schmitt As there are five independent elastic coefficients a minimum of five different measured velocities are needed to calculate the stiffness constants of the material. For a TI material these equations simplify significantly in the symmetry directions where the P- and S-waves propagate as pure modes, i.e., modes in which the longitudinal and shear particle motions are parallel and perpendicular, respectively, to the direction of the wave propagation with: 2 C11 ¼ qVP90 ð10Þ 2 C33 ¼ qVP0 ð11Þ 2 C44 ¼ qVSH0 ð12Þ 2 C66 ¼ qVSH90 ð13Þ C12 ¼ C11 2C66 ð14Þ where VP90, VP0, VSH0, and VSH90 are P- and S-wave velocities in different directions as indicated in Fig. 2. SH refers to the shear wave with particle motions perpendicular to the z-axis and is the component vibrating along the foliation plane. The remaining elastic stiffness C13 requires that an additional wave speed to be measured at an angle offset from the symmetry axis. Conveniently taking the velocity measurements at 45° from the symmetry axis, C13 can be obtained using the following equation: C13 ¼ C44 h i1=2 2 2 þ C11 þ C44 2qVp45 C33 þ C44 2qVp45 c¼ C66 C44 VSH90 VSH0 ¼ 2C44 VSH0 ðC13 þ C44 Þ2 ðC33 C44 Þ2 2C33 ð C33 C44 Þ VP45 VP90 ¼4 1 1 VP0 VP0 ð18Þ d¼ ð19Þ where e is a measure of the P-wave anisotropy, c is a measure of SH-wave anisotropy, and d is an expression related to the anellipticity of the P-wave wavefront. e, c, d are dimensionless and have values smaller than 0.5, but frequently much smaller (Sheriff 2002). These three parameters are useful in quantifying anisotropy when simple inspection of the elastic moduli do not present obvious indications of anisotropy. It is worth noting that all of the studies on the anisotropy of metamorphic rocks described earlier made measurements in directions aligned with visible foliations and lineations. However, as examination of the above equations demonstrates, the full set of elastic stiffnesses requires that wave speeds must also be measured at angles away from these directions and to our knowledge this is very rarely accomplished (e.g., Sano et al. 1992; Pros et al. 1998, 2003; Takemura and Oda 2005; Sarout et al. 2007; Nara et al. 2011). Such information, however, is crucial to a full understanding of the wave behavior and for this reason in this study we take care to specially machine our sample to allow for measurements perpendicular, parallel, and at 45° from the symmetry axis. ð15Þ or C13 4 Experimental Procedure 31=2 2 2 2 2 4q2 Vp45 VSV45 ðC11 C33 Þ2 7 6 ¼ C44 þ 4 5 4 ð16Þ Equation (16) is an alternative expression to Eq. (15) proposed by Hemsing (2007) to estimate C13 using a combination of VP45 and VSV45 to reduce the degree of uncertainty. SV refers to shear waves whose polarization lies in the vertical plane (i.e., the plane containing the material’s axis of symmetry). To relate the elastic constants (C11, C13, C33, C44 and C66) to P- and S-wave velocities measured parallel and perpendicular to the symmetry axis, Thomsen (1986) suggested three parameters for quantifying the weak anisotropic behavior of TI materials: e¼ C11 C33 VP90 VP0 ¼ 2C33 VP0 123 ð17Þ 4.1 Sample Preparation Limited core samples from the Hunt well were available from the Core Research Centre of the Alberta Energy Regulator at two different depth intervals: 1656.5–1,657.8 m and 2,347.5–2,364.3 m in the 2.4 km deep borehole (AOC GRANITE 7-32-89-10) located in NE Alberta (latitude 56°450 N, longitude 111°330 W). A rock sample was selected from a depth of 2,350.3 to 2,350.5 m. It is a foliated granite composed mainly of quartz and feldspars. Other minerals present in the rock are biotite, garnet, pyroxene, hematite, magnetite, ilmenite, titanite, zircon, monazite and apatite (Walsh 2013; G. Njiekak, personal communication, January 23, 2014). Some samples also display schlieren textures. Thin sections were made to provide microscopic analysis of the textural features in the sample. Aggregates of elongated quartz and the presence of feldspar bands provide evidence of the preferentially Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample Fig. 3 Thin sections taken under plane-polarized (left) and crosspolarized (right) lights. The preferential orientation of minerals and microcracks are indicated by the yellow arrows. Two evident zones of 1375 microcracks are annotated by the letters A and B for a comparative interpretation between the photographs Fig. 4 Photographs of the metamorphic rock sample a before and b, c after sample preparation. Due to limited cores available, the sample has to be carefully cut along the dotted blue lines with respect to the identifiable foliation plane to obtain a sample with the largest dimension possible from the core 123 Author's personal copy 1376 oriented fabric displayed by the study rock. Furthermore, microcracks are seen parallel to the felsic bands (Fig. 3). P- and S-wave velocities were measured in three different directions: parallel, perpendicular and at 45° to the foliation plane. The sample was cut, ground flat and parallel on opposing surfaces, on a diamond grinding disk in three different angles relative to the apparent direction of the foliation plane to ensure good surface contacts for the transducers. This minimized the errors in velocity measurements and improved pulse transmission from one surface of the sample to another (Meléndez Martı́nez and Schmitt 2013). The final sample size was 8.15 cm (length) 9 7.00 cm (width) 9 4.50 cm (height) with the 45° surfaces 3.80 cm apart (Fig. 4). Error for each measured dimension is estimated to be 0.05 cm. After grinding, the sample was placed in the oven to vacuum dry at 45 °C for over 12 h as a precautionary measure to ensure that the sample is fully dry. Bulk density of the sample was measured in the laboratory using a mercury (Hg) injection porosimeter and a bulk density value of 2.62 g/cm3 was reported at 0.0036 MPa (i.e., at low pressure before any Hg could intrude the sample). A bulk density geophysical log (i.e., Compton scattering) was also available and this provided a density of 2.65 g/cm3 at 2,350.40 m, which closely agrees with the density value measured in the laboratory. A grain density of 2.66 g/cm3 was also reported from the Hg porosimeter and reveals a low porosity of 1.45 %. The main component for transmitting and receiving elastic waves in the laboratory are the transducers. For this experiment, ultrasonic transducers composed of longitudinally and transversely polarized piezoelectric ceramics and copper foil electrodes are used. The transmitting transducer converts the electrical pulse to a mechanical signal, which is transmitted through the rock. The receiving transducer changes the wave back into an electrical pulse, which is then amplified and displayed on the oscilloscope screen. The type of vibration generated is determined by the polarization of the piezoelectric ceramic. Longitudinal wave (P-wave) PZT ceramics were in the form of circular discs with a diameter of 20 mm and the transverse wave (S-wave) ceramics were square plate with a length of 15 mm. Both were made from APC’s 851 material (APC International Ltd. 2011). The piezoelectric material is a ceramic made from lead zirconate titanate with a resonant frequency operating at 1 MHz. This material is capable of producing an electrical potential with applied stress such as a mechanical vibration. Six pairs of piezoelectric transducers were mounted on the aforementioned surfaces relative to the foliation plane to generate and record the P- and S-waves (Fig. 5). Thin copper strips were bonded beneath and on top of the transducers as electrodes using CircuitWorksÒ CW2400 123 J. Chan, D. R. Schmitt Fig. 5 Schematic diagram showing the placement of six pairs of transducers on the sample. The subscripts indicate the direction with respect to the axis of symmetry and the dashed lines represent the direction of wave propagation. Image adapted from Wong et al. (2008) Fig. 6 Schematic diagram of the experimental setup conductive epoxy. The copper foil attached to the underside of the transducer acted as a ground for the transducers. Insulated electrical wires were soldered to the electrodes, and the entire sample was then sealed in a flexible urethane compound (FlexaneÒ 80 Putty) to protect the sample from the hydraulic oil inside the pressure vessel that is used as Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample 1377 the confining pressure medium. This assemblage was then placed in the pressure vessel. A voltage is applied to the transmitting transducer, which then sends a frequency pulse through the sample and is detected by the transducer on the opposite ends. 4.2 Data Acquisition The ultrasonic pulse transmission technique was used to study the dependence of seismic velocity under varying confining pressure condition with a QuizixTM Q5000 pump system. The transmitted signal of the elastic waves was generated using a JSR-PR35 pulse generator that was connected to the electrical wires of the transmitting transducers and the propagated signal was recorded by a digital oscilloscope developed by National Instrument (Fig. 6). In situ peak vertical stress for the sample is determined based on the density of the overburden and the depth in which it was extracted from. Vertical stress (Sv) is often assumed to be equivalent to the overburden weight by integrating the densities of overlying rocks according to the following equation: Sv ð hÞ ¼ Zh qðhÞgdh ð20Þ 0 where h is the overburden depth, q is the average density value and g is the acceleration of gravity. The vertical stresses expected in the Hunt well were calculated by integrating the borehole density log. The negative value arises under the assumption that both g and h are positive numbers with the compressional stress increasing with depth (Schmitt et al. 2012). The in situ peak pressure for the sample was found to be close to 60 MPa. The travel times were recorded in 3 MPa increments between 0 and 15 MPa, and in 5 MPa increments between 15 and 60 MPa during both the compression (pressurization) and decompression (depressurization) cycles conducted at room temperature. The maximum confining pressure of 60 MPa was selected to recreate the in situ pressure conditions similar to those at depth. After reaching the target confining pressure, waveforms were recorded after a waiting period (5 min) to allow the pressure condition to stabilize in the pressure vessel. This step was also taken to ensure the opening or closing of any cracks or pores in the sample. The travel time and amplitude of the wave were recorded at each pressure interval and each waveform trace was constructed from at least 300 progressively stacked records to minimize the random noise effects (Fig. 7). The recorded travel time across the sample in a direction normal to the wave front is defined as the phase travel time. Phase velocities are obtained using the known distance that the wave has traveled normal to the plane wave front and the measured phase travel time (Vestrum 1994). Travel time was interpreted from the first extremum value of the waveform on each stacked record (Molyneux and Schmitt 1999). It was also observed that the signal amplitudes were stronger with pressure due to the combined effects of the closing of microcracks, influence of pressure on the stiffness of rock forming minerals and the improved surface contacts. 5 Results To investigate the anisotropic properties of the metamorphic core sample from the Hunt well, P- and S-wave phase velocities were measured at a confining pressure of up to 60 MPa in three different directions with respect to the visible foliation plane during both the pressurization and depressurization cycles of the measurements. Arrival times for P- and S-waves were then interpreted from the first extremum of the stacked waveforms. At 0–3 MPa, the waveforms for S-waves for both the pressurization and depressurization cycles were relatively noisier compared to all other waveforms at higher confining pressures. P- and S-wave velocities were thereafter calculated using the measured distances between the pulsing and receiving surfaces of the sample which were plotted as a function of confining pressure in Fig. 8. Numerous sources of error need to be considered when calculating the velocities from the measurements. They include the travel time delay through the piezoelectric ceramic transducers (Meléndez Martı́nez 2014), the uncertainty in the complete parallelism of the sample surfaces (0.05 cm) and the accuracy of the travel time picks from the recorded waveforms (0.01 ls). At low confining pressures, the anisotropic character of pore space geometry was suggested to have an influence on seismic anisotropy (e.g., Kern and Schenk 1988). The initial increase in velocity with pressure is often explained by the closing of microcracks and pores in the rock sample. In other words, the closing of cracks under pressure would increase the elastic stiffness which consequently leads to the rapid increase of velocities. Microcracks could be originated from sources such as stress relief during coring and are present in many rocks. The small changes in the anisotropic parameters of the sample show that there is minute stress dependence with the cracks closing at below 9 MPa. As such, the anisotropic behavior of the sample is mainly attributed to its intrinsic properties. At high confining pressures, velocities in all three directions increase linearly at a similar rate as a result of the intrinsic effect of the mineral components (e.g., Birch 1961; Kern and Schenk 1988). Figure 8 shows that the velocity gradient is significantly higher at lower confining pressure (0–9 MPa). The velocity gradient gradually decreases as the pressure 123 Author's personal copy 1378 J. Chan, D. R. Schmitt Fig. 7 Waveforms of P- and S-waves propagating a, b along the foliation plane, c, d normal to foliation plane, and e, f at 45° with respect to the foliation plane. The lengths of the travel paths are 0.070, 0.045 and 0.038 m, respectively increases which reflects the intrinsic effects of pressure on the mineralogical velocities of the rock sample. The fastest P-wave velocities were measured along the foliation plane from 5,352 to 6,019 m/s. Velocities for P-waves measured across and oblique to the foliation plane are quite similar at 4,752–5,396 m/s and 4,810–5,337 m/s, respectively. Figure 9a is useful in demonstrating whether the sample is an isotropic medium. If a sample is isotropic, it is expected that C11 = C33 and C44 = C66. This is not the case for this sample which demonstrates the anisotropic behavior of the rock. As the cracks closed under the influence of increasing pressure, the velocity gradients of the propagative waves also decreased as they encountered less low-rigidity material (air) and cracks. This led to the increase in the elastic stiffnesses that eventually approached the constant linear level when all the cracks are closed at high confining pressure. It is also possible that the 123 stiffnesses of the sample can be affected by other minerals in smaller proportions. Figure 9b shows the change in the anisotropic parameters under pressure. The three anisotropic parameters remained relatively stable beyond a confining pressure of 9 MPa. A sudden sharp decrease of S-wave anisotropy at low confining pressures could be due to the erroneous travel time picks in the noisy waveforms as mentioned earlier at low confining pressures. The anisotropic parameters e and c were obtained from the P- and S-wave velocities (Eqs. 17, 18) in the axial directions and have reported values of 12 and 8 %, respectively. These values indicate that the sample is considered as moderately anisotropic (Table 1) as suggested by Thomsen (1986) when the anisotropic parameters exceed 10 %. In between 0 and 3 MPa, c and d experience greater changes that could be attributed to the uncertainties in the first extremum Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample (a) P-Wave Velocities 5800 5600 5400 Velocity (m/s) Fig. 8 a P- and b S-wave velocities as a function of confining pressure between 0 and 60 MPa for the pressurization (solid line) and depressurization (dashed line) cycle. The hysteresis effect is observed in both the pressurization and depressurization cycles 1379 5200 5000 4800 V P90 V P45 4600 V P0 4400 0 10 20 30 40 50 60 70 Confining Pressure (MPa) (b) S-Wave Velocities 3100 3000 2900 Velocity (m/s) 2800 2700 2600 2500 VSH90 2400 VSH45 2300 2200 VSH0 0 10 20 30 40 50 60 70 Confining Pressure (MPa) picking of the S-wave waveforms. The third anisotropic parameter d contains off-diagonal elastic stiffnesses and is related to the short-spread normal moveout velocities in TI media with a reported value of 13 %. 6 Discussion P-wave velocity anisotropy of the most common metamorphic rocks is typically almost orthorhombic or transversely isotropic (Barberini et al. 2007). The anisotropy in rocks is primarily due to the preferred orientation of the constituent minerals, textural–structural features, pores, and cracks. As the confining pressure increases, the effect of microcracks on anisotropy is expected to diminish, and the remaining anisotropy is more likely to result from layering and preferred orientation of minerals, i.e., intrinsic anisotropy. For most types of symmetry, Backus (1970) reported that the phase and group velocities are identical in magnitude along the principal axes in the case of weak anisotropy. The propagating velocity as a function of pressure is primarily dependent upon mineralogy and porosity (Gupta 2011). The effects of cracks and pores in the anisotropic nature of the rocks should be expected to decrease as the applied confining pressure progressively 123 Author's personal copy 1380 J. Chan, D. R. Schmitt Fig. 9 Display of a elastic constants and b anisotropic parameters as a function of confining pressure (a) Elastic Constants 120 C11 C33 C44 C66 C13 100 (GPa) 80 60 40 20 0 0 10 20 30 40 50 60 50 60 Confining Pressure (MPa) (b) Anisotropic Parameters 0.5 Anisotropic Parameters 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 0 10 20 30 40 Confining Pressure (MPa) increases along with the closing of the cracks which in turn would result in the increase of P- and S-wave velocities (Walsh 1965). In this study, velocity measurements obtained during the initial pressurization cycle are slightly lower than the velocities measured during depressurization. This effect is called hysteresis in which the physical property that has been changed does not return to its original state after the cause of the change has been removed (Gardner et al. 1965). The cracks that were closed during the pressurization cycle would be expected to open at a lower pressure 123 than the original closing pressure associated with the frictional adjustment of crack faces and grain boundaries. Alternatively, it is also possible that some cracks or pore spaces do not re-open during the depressurization cycle as a result of the irreversible change in grain contacts and reduction of porosity in the rock sample (Ji et al. 2007). The hysteresis effect is generally smaller if sufficient time is allowed for data measurements at each confining pressure step. P-wave velocities parallel to the foliation plane are greater than those in the perpendicular and oblique Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample 1381 directions. The high gradients in P- and S-wave velocities at low confining pressures suggest that velocities are largely controlled by the microcracks, as observed in Fig. 8. Thomsen parameters also experience similar sharp gradient with the decrease in values at lower confining pressures. At higher pressures, layering and the preferred orientation of minerals are expected to have greater effects on the anisotropic behavior of the rock as opposed to the cracks. Microscopic analysis of the thin sections of the rock sample is used to verify the interpretations with the presence of microcracks and aggregates of elongated quartz oriented in the same direction (Fig. 3). P and S-wave velocities at 45° are unexpectedly measured to be lower Table 1 Thomsen parameters obtained from the rock sample during the pressurization cycle Pressure (MPa) e c d 0 0.13 ± 0.06 0.27 ± 0.06 0.18 ± 0.02 3 0.12 ± 0.06 0.20 ± 0.05 0.24 ± 0.03 6 0.12 ± 0.06 0.08 ± 0.04 0.16 ± 0.02 9 0.12 ± 0.06 0.08 ± 0.04 0.13 ± 0.02 12 0.12 ± 0.06 0.08 ± 0.04 0.13 ± 0.02 15 0.13 ± 0.06 0.08 ± 0.04 0.14 ± 0.02 20 25 0.13 ± 0.06 0.12 ± 0.06 0.08 ± 0.04 0.07 ± 0.04 0.14 ± 0.02 0.12 ± 0.02 30 0.12 ± 0.06 0.08 ± 0.04 0.12 ± 0.02 35 0.12 ± 0.06 0.08 ± 0.04 0.13 ± 0.02 40 0.13 ± 0.06 0.08 ± 0.04 0.13 ± 0.02 45 0.13 ± 0.06 0.07 ± 0.04 0.14 ± 0.02 50 0.13 ± 0.06 0.08 ± 0.04 0.14 ± 0.02 55 0.13 ± 0.06 0.07 ± 0.04 0.13 ± 0.02 60 0.12 ± 0.06 0.07 ± 0.04 0.13 ± 0.02 Table 2 Elastic constants estimated from the recorded waveforms during the pressurization cycle Pressure (MPa) C11 (GPa) than the velocities measured normal to the foliation plane. One possible explanation for this is the heterogeneity of the sample that could not be identified from the surface of the selected sample for this experiment. Five independent elastic stiffnesses C11, C13, C33, C44 and C66 are calculated from the phase velocities according to Eq. 10 through Eq. 15 (Table 2) and are plotted in Fig. 9a. Elastic constants gradually increase with the increase in confining pressure up to 60 MPa. The calculated C11 and C33 are dependent on the P-wave velocities whereas C44 and C66 are dependent on the S-wave velocities. The results indicate that C11 [ C33 [ C13 [ C66 [ C44. Through error propagations, the uncertainties for C11, C33, C66 and C44 are expected to be lower compared to that for C13 due to the buildup of uncertainties in the equation (Eq. 15). An interpretation of Fig. 9a also reveals that the hysteresis effect is also noticeable in the elastic constants similar to the observation of the velocity measurements. In the case of a weakly TI medium, the dependence of Thomsen parameters (e, c, d) on the phase velocities is illustrated using Thomsen (1986) approximations (Fig. 10). One of Thomsen’s (1986) phase velocity equations Vp(h) = VP0 (1 ? d sin2 h cos2 h ? e sin4 h) demonstrates d as the dominant factor which controls the anisotropic features of most situations in exploration geophysics. Changes in d relative to e illustrate the anellipticity of the propagating P-wave wavefront and controls whether the wavefront is concave (positive anellipticity, d \ e), elliptical (d = e), or convex (negative anellipticity, d [ e). An important note to mention is that the original elastic equations for the P and SV curves do not actually follow the ellipse or circle in Fig. 10 as they are illustrated using Thomsen approximations. The above demonstrates that we have been able to calculate a complete set of elastic stiffnesses for this rock C33 (GPa) C44 (GPa) C66 (GPa) C13 (GPa) 0 75.1 ± 2.9 59.2 ± 3.1 15.3 ± 0.7 23.6 ± 0.8 38.1 ± 4.4 3 79.7 ± 3.2 64.3 ± 3.5 17.3 ± 0.8 24.1 ± 0.8 43.3 ± 4.8 6 86.9 ± 3.5 70.3 ± 3.9 21.4 ± 1.0 24.8 ± 0.8 37.7 ± 5.0 9 89.4 ± 3.6 71.8 ± 4.0 21.6 ± 1.0 25.0 ± 0.8 36.9 ± 5.0 12 89.5 ± 3.6 72.1 ± 4.0 21.7 ± 1.0 25.1 ± 0.8 37.4 ± 5.1 15 90.7 ± 3.7 72.3 ± 4.0 21.8 ± 1.0 25.1 ± 0.8 38.1 ± 5.1 20 91.7 ± 3.7 72.5 ± 4.0 21.9 ± 1.0 25.4 ± 0.8 38.1 ± 5.1 25 92.0 ± 3.8 73.9 ± 4.1 22.1 ± 1.0 25.4 ± 0.8 38.0 ± 5.2 30 92.3 ± 3.8 74.0 ± 4.1 22.3 ± 1.0 25.7 ± 0.8 37.6 ± 5.2 35 92.6 ± 3.8 74.2 ± 4.1 22.4 ± 1.0 25.9 ± 0.9 38.4 ± 5.2 40 94.0 ± 3.9 74.6 ± 4.1 22.5 ± 1.0 26.0 ± 0.9 38.5 ± 5.3 45 94.0 ± 3.9 74.9 ± 4.2 22.7 ± 1.0 26.0 ± 0.9 39.0 ± 5.3 50 94.7 ± 3.9 75.3 ± 4.2 22.8 ± 1.0 26.2 ± 0.9 39.2 ± 5.3 55 60 94.8 ± 3.9 95.0 ± 3.9 75.8 ± 4.2 76.4 ± 4.3 22.9 ± 1.0 23.1 ± 1.0 26.4 ± 0.9 26.5 ± 0.9 39.2 ± 5.3 39.6 ± 5.4 123 Author's personal copy 1382 J. Chan, D. R. Schmitt 2.0 (Bourbie et al. 1987). From the dipole shear sonic imager log recorded for the Hunt well, the Vp/Vs ratio has an average value of 1.71 between 1,012 and 1,865 m interval (Chan 2013). Current laboratory measurements report averaged Vp/Vs ratios in the range of 1.82–1.90 along the three directional variations at 2,350 m depth which reveals an increase in Vp/Vs with depth. At this point, it is unclear whether the increase in Vp/Vs could be attributed to any geological significance. 7 Conclusions Fig. 10 Illustration of the anisotropic parameter behavior of e, c, and d of a weak transversely isotropic medium. The ellipsoids of the longitudinal (dark grey) and SH polarization shear waves (light grey) are included for references sample using the observed wave speeds under the assumption that the material is transversely isotropic. However, in light of the illustration in Fig. 10 it is important to return to the observed wave speeds in Fig. 8 where VP45 \ VP90 and VSH45 \ VSH90. While under certain circumstances the former is allowed, the latter case is not. There are a number of possible reasons for this discrepancy that include heterogeneity of the sample, a misalignment of the true intrinsic transversely isotropic symmetry axes from those chosen visually based on the foliation, or the sample having a lower intrinsic symmetry. Our observations here serve as a caution with regards to determining the elastic stiffnesses from velocity measurements assumptions that the visible foliation and lineation, as is assumed in nearly all measurements of the anisotropy of metamorphic rocks, provide the true reference orientations for the intrinsic anisotropy. Besides analyzing the velocity measurements and elastic stiffnesses, the ratio of P- and S-wave velocities (Vp/Vs) can be used as an indicator of the presence of fluids and fractures that are controlled mainly by rock type and pore fluid. Existing literature has reported that such increase suggests greater fracture density, higher metamorphic grade, larger fluid content and/or changes in mineral composition (e.g., Sanders et al. 1995; Sibbit 1995; Kern et al. 2002; Boness and Zoback 2004; Newman et al. 2008). In the crystalline rock environment, Vp/Vs values generally range from 1.6 to 123 Seismic anisotropy may be caused by the presence of fractures and anisotropic minerals oriented in a preferred direction. To determine the elastic properties and to quantify the directional dependence of a metamorphic rock over a range of confining pressures, compressional and shear wave velocities were measured using the ultrasonic pulse transmission technique on a core sample from the Hunt well, Alberta, Canada. Laboratory measurements are performed up to a confining pressure of 60 MPa and the recorded velocities are presented in graphs. Under the assumption that the symmetry of this sample is transversely isotropic, velocities were measured parallel, perpendicular, and at 45° with respect to the visually selected foliation plane. The graphical results reveal a gradual increase in velocity as a function of confining pressure which reflects the closing of microcracks. The hysteresis effect is observed in both the velocity measurements and the anisotropic parameter plots during the pressurization and depressurization cycles. The elastic constants and Thomsen’s anisotropic parameters are calculated to estimate the degree of seismic anisotropy; e and c are reported to be 12 and 8 %, respectively, which indicate the anisotropic behavior of the metamorphic rock sample. The results can be explained by the preferential alignment of minerals and microcracks. It was also observed that there is little variation in Thomsen parameters for confining pressures beyond 9 MPa after the closure of microcracks. As the confining pressure increases, the alignment of minerals (i.e., intrinsic effect) and cracks become the dominant factors in the anisotropic behavior of the rocks with the lessening effect of the microcracks. However, it might be possible to observe the decreasing gradient of anisotropic parameters as a result of the complete closure of microcracks and the preferred alignment of mineral combination if higher confining pressure is applied to the rock sample. The overall results of the laboratory measurements confirm the anisotropic behavior of the metamorphic rock and could be useful in the construction of velocity models in the seismic processing workflow. This could help to Author's personal copy Elastic Anisotropy of a Metamorphic Rock Sample remove the anomalies caused by the directional dependence in the seismic velocities and further enhance the imaging of seismic reflection profiles. An alternative approach for identifying seismic anisotropy is the analysis of shear wave birefringence. This was not performed on the rock sample that was made available at the time but should be considered in the future measurements of other samples. The comparison of seismic velocities between laboratory measurements and field seismic data is complicated by the frequency ranges of the respective data sets due to dispersion effects. A single rock sample is used to showcase the presence of anisotropy in the crystalline basement, but it is not a representation of the entire crystalline basement rock section. However, the result of this data does provide an indication of the seismic intrinsic anisotropy in the crystalline basement rocks of the study borehole, which suggests that the use of an isotropic velocity model in conventional seismic processing workflow might cause imaging problems as a result of seismic anisotropy. Seismic anisotropy has also been analyzed using walkaway VSP in the Hunt well (Chan 2013). Furthermore, recent acquisition of the sonic scanner in the borehole is also expected to provide and verify the results reported in this paper. It is expected that an integration of the laboratory measurements (this paper), walk-away VSP and sonic scanner interpretations can extend the seismic anisotropy analysis from a single depth interval to other depth levels in the borehole. Acknowledgments The authors would like to thank Lucas Duerksen and Randolf Kofman for their assistance in setting up the laboratory equipment in the Rock Physics Laboratory of the Experimental Geophysics Group (EGG) at the University of Alberta, and Gautier Njiekak for his assistance in analyzing the thin sections. Core samples were generously on loan from the Alberta Core Research Centre in Calgary. This research was sponsored by funding from Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Research Chairs Program, and the Geothermal Theme of the Helmholtz-Alberta Initiative (HAI). We would also like to thank our reviewer for insightful and observant feedback. References Aki K, Richards PG (1980) Quantitative seismology, theory and methods, vol 1. W. H Freeman and Company, San Francisco Alkhalifah T, Larner K (1994) Migration error in transversely isotropic media. Geophysics 59(9):1405–1418. doi:10.1190/1. 1443698 APC International Ltd. 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