Abstract
The velocities of two Devonian-Mississippian shales have been measured to confining pressures of 200 MPa in a laboratory study of anisotropy and wave propagation. Both samples were found to be transversely isotropic at elevated pressures with the main symmetry axis perpendicular to bedding. The elastic constants of the shales were used to calculate phase and group velocity surfaces as a function of angle to the bedding normal. Multiple velocity measurements in non-symmetry directions, not undertaken in previously published studies of shales, have been used to confirm features observed on calculated velocity surfaces. It is demonstrated that velocities measured in non-symmetry directions are phase velocities. Group velocities were found to be significantly lower than the corresponding phase velocities of the shales due to their high anisotropies. Shear wave splitting was found to be negligible for propagation directions within approximately 30° of the bedding normals.
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Alexandrov, K.S. and Ryzhova, T.V.: 1961, ‘Elastic Properties of Rock-Forming Minerals, 1, Pyroxenes and Amphiboles’,Bull. Acad. Sci. USSR, Geophys. Ser., English Trans. 9, 1165–1168.
Auld, B.A.: 1990,Acoustic Fields and Waves in Solids, Vol. 1, Robert E. Krieger Pub. Co., Malabar, Florida.
Babuska, V.: 1972, ‘Elasticity and Anisotropy of Dunite and Bronzitite’,J. Geophys. Res. 77, 6955–6965.
Baker, D.W. and Carter, N.L.: 1972, ‘Seismic Velocity Anisotropy Calculated for Ultramafic Minerals and Aggregates’,Am. Geophys. U. Mon. 16, 157–166.
Banik, N.C.: 1984, ‘Velocity Anisotropy of Shales and Depth Estimation in the North Sea Basin’,Geophysics 49, 1411–1419.
Birch, F.: 1960, ‘The Velocity of Compressional Waves in Rocks to 10 Kilobars, 1’,J. Geophys. Res. 65, 1083–1102.
Brocher, T. M. and Christensen, N.I.: 1990, ‘Seismic Anisotropy Due to Preferred Mineral Orientation Observed in Shallow Crustal Rocks in Southern Alaska’,Geology 18, 737–740.
Carrion, P., Costa, J., Pinheiro, J.E.F. and Schoenberg, M.: 1992, ‘Cross-Borehole Tomography in Anisotropic Media’,Geophysics 57, 1194–1198.
Cheadle, S.P., Brown, R.J. and Lawton, D.C.: 1991, ‘Orthorhombic Anisotropy: A Physical Seismic Modeling Study’,Geophysics 56, 1603–1613.
Christensen, N.I.: 1966, ‘Elasticity of Ultrabasic Rocks’,J. Geophys. Res. 71, 5921–5932.
Christensen, N. I. and Ramananantoandro, R.: 1971, ‘Elastic Moduli and Anisotropy of Dunite to 10 Kilobars’,J. Geophys. Res. 76, 4003–4010.
Christensen, N.I.: 1984, ‘The Magnitude, Symmetry, and Origin of Upper Mantle Anisotropy Based on Fabric Analyses of Ultramafic Tectonites’,Geophys. J. R. astr. Soc. 76, 89–111.
Christensen, N.I.: 1985, ‘Measurements of Dynamic Properties of Rock at Elevated Temperatures and Pressures’, in H.J. Pincus and E. R. Hoskins (eds.),Measurements of Rock Properties at Elevated Temperatures and Pressures, American Society for Testing and Materials, Philadelphia, Pa., pp 93–107.
Crampin, S.: 1985, ‘Evaluation of Anisotropy by Shear Wave Splitting’,Geophysics 50, 142–152.
Crosson, R. L. and Lin, J.W.; 1971, ‘Voigt and Reuss Prediction of Anisotropy Elasticity of Dunite’,J. Geophys. Res. 76, 570–578.
Dellinger, J. and Vernik, L.: 1992, ‘Do Core Sample Measurements Record Phase or Group Velocity?’,62nd. Ann. Internat. Mtg., Soc. Explor. Geophys. Expanded Abstracts, 662–665.
Eaton, D.W.: 1993, ‘Discussion of “Ultrasonic Velocity and Anisotropy of Hydrocarbon Source Rocks” by Vernik, L. and Nur, A.’,Geophysics 58, 758–759.
Harder, S.: 1985, ‘Inversion of Phase Velocities for the Anisotropic Elastic Tensor’,J. Geophys. Res. 90, 10,275–10,280.
Hearmon, R.F.S.: 1961,An Introduction to Applied Anisotropic Elasticity, Oxford University Press, Oxford.
Hess, H.H.; 1964, ‘Seismic Anisotropy of the Uppermost Mantle Under Oceans’,Nature 203, 629–631.
Johnston, J.E. and Christensen, N.I.: 1992, ‘Shear Wave Reflectivity, Anisotropies, Poisson's Ratios, and Densities of a Southern Appalachian Paleozoic Sedimentary Sequence’,Tectonophysics 210, 1–20.
Jones, L.E.A. and Wang, H.F.: 1981, ‘Ultrasonic Velocities in Cretaceous Shales from the Williston Basin’,Geophysics 46, 288–297.
Justice, M.G., McCormack, M.D. and Lee, S.S.: 1986, ‘Anisotropy in the Morrow Formation of Southeast New Mexico’, in S.H. Danboom and S.N. Domenico (eds.),Shear Wave Exploration, Society of Exploration Geophysicists Geophysical Development Series, 1, pp. 154–164.
Kumazawa, M.: 1969, ‘The Elastic Constants of Single Crystal Orthopyroxene’,J. Geophys. Res. 74, 5973–5980.
Lo, T., Coyner, K.B. and Toksoz, M.N.: 1986, ‘Experimental Determination of Elastic Anisotropy of Berea Sandstone, Chicopee Shale, and Chelmsford Granite’,Geophysics 51, 164–171.
Lynn, H.B., and Thomsen L.A.: 1990, ‘Reflection Shear Wave Data Collected Near the Principal Axes of Azimuthal Anisotropy’,Geophysics 55, 147–156.
McCormack, M.D., Dunbar, J.A. and Sharp, W.W.: 1984, ‘A Case Study of Stratigraphic Interpretation Using Shear and Compressional Seismic Data’,Geophysics 49, 509–520.
Musgrave, M.J.P.: 1970,Crystal Acoustics, Holden Day, San Francisco.
Pacalo, R.E.G., Weidner, D.J. and Gasparik, T.: 1992, ‘Elastic Properties of Sodium-Rich Majorite Garnet’,Geophys. Res. Lett. 19, 1895–1898.
Sano, O., Kudo, Y. and Mizuta, Y.: 1992, ‘Experimental Determination of Elastic Constants of Oshima Granite, Barre Granite, and Chelmsford Granite’,J. Geophys. Res. 97, 3367–3379.
Seront, B., Mainprice, D. and Christensen, N. I.: 1993, ‘A Determination of the Three Dimensional Seismic Properties of Anorthosite: Comparison Between Values Calculated from the Petrofabric and Direct Laboratory Measurements’,J. Geophys. Res. 98, 2209–2221.
Thomsen, L.: 1986, ‘Weak Elastic Anisotropy’,Geophysics 51, 1954–1966.
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Johnston, J.E., Christensen, N.I. Elastic constants and velocity surfaces of indurated anisotropic shales. Surv Geophys 15, 481–494 (1994). https://doi.org/10.1007/BF00690171
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DOI: https://doi.org/10.1007/BF00690171