Exact seismic velocities for TI media and extended Thomsen formulas for stronger anisotropies

REFERENCES

• Backus, G. E., 1962, Long-wave elastic anisotropy produced by horizontal layering: Journal of Geophysical Research, 67, 4427-4440.

• Berryman, J. G., 1979, Long-wave elastic anisotropy in transversely isotropic media: Geophysics, 44, 896-917.

• Berryman, J. G., and V. Grechka, 2006, Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems: Journal of Applied Physics, 100, 113527.

• Dellinger, J., F. Muir, and M. Karrenbach, 1993, Anelliptic approximations for TI media: Journal of Seismic Exploration, 2, 23-40.

• Fomel, S., 2004, On anelliptic approximations for qP velocities in VTI media: Geophysical Prospecting, 52, 247-259.

• Fowler, P. J., 2003, Practical VTI approximations: A systematic anatomy: Journal of Applied Geophysics, 54, 347-367.

• Grechka, V., and M. Kachanov, 2006a, Effective elasticity of fractured rocks: The Leading Edge, 25, 152-155.

• Grechka, V., and M. Kachanov, 2006b, Effective elasticity of rocks with closely spaced and intersecting cracks: Geophysics, 71, D85-D91.

• Kachanov, M., 1980, Continuum model of medium with cracks: ASCE Journal of Engineering Mechanics, 106, 1039-1051.

• Mensch, T., and P. Rasolofosaon, 1997, Elastic-wave velocities in anisotropic media of arbitrary symmetry-generalization of Thomsen's parameters $\epsilon$, $\delta$, and $\gamma$: Geophysical Journal International, 128, 43-64.

• Musgrave, M. J. P., 1954, On the propagation of elastic waves in aeolotropic media: Proceedings of the Royal Society of London, A226, 339-366.

• Musgrave, M. J. P., 1959, The propagation of elastic waves in crystals and other anisotropic media: Reports on Progress in Physics, 22, 74-96.

• Musgrave, M. J. P., 2003, Crystal Acoustics: Acoustical Society of America, Leetsdale, Pennsylvania, Chapter 8.

• Pederson, Ø., B. Ursin, and A. Stovas, 2007, Wide-angle phase-slowness approximations: Geophysics, 72, S177-S185.

• Postma, G. W., 1955, Wave propagation in a stratified medium: Geophysics, 20, 780-806.

• Rüger, A., 2002, Reflection Coefficients and Azimuthal AVO Analysis in Anisotropic Media: Geophysical Monographs Series, Number 10, SEG, Tulsa, OK.

• Sayers, C. M., and M. Kachanov, 1991, A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics. International Journal of Solids and Structures, 27, 671-680.

• Schoenberg, M., and K. Helbig, 1997, Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth: Geophysics, 62, 1954-1974.

• Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954-1966.

• Thomsen, L., 2002, Understanding Seismic Anisotropy in Exploration and Exploitation: 2002 Distinguished Instructor Short Course, Number 5, SEG, Tulsa, OK.

• Tsvankin, I., 1997, Anisotropic parameters and -wave velocity for orthorhombic media: Geophysics, 62, 1292-1309.

• Tsvankin, I., 2005, Seismic Signatures and Analysis of Reflection Data in Anisotropic Media: Handbook of Geophysical Exploration, Seismic Exploration, Volume 29, Elsevier, Amsterdam.

• Zhu, T., S. H. Gray, and D. Wang, 2005, Kinematic and dynamic ray tracing in anisotropic media: Theory and application: 75th Annual International Meeting, SEG, Expanded Abstracts, 386-389.

• Zhu, T., S. H. Gray, and D. Wang, 2007, Prestack Gaussian-beam depth migration in anisotropic media: Geophysics, 72, S133-S138.

Exact seismic velocities for TI media and extended Thomsen formulas for stronger anisotropies