Elastodynamic Green’s tensor in vertically transversely isotropic media

Li, Z. and Chesnokov, E.M., 2015. Elastodynamic Green’s tensor in vertically transversely isotropic media. Journal of Seismic Exploration, 24: 259-280. The elastodynamic Green’s tensor in a vertically transversely isotropic (VTI) medium is presented explicitly as an inverse Hankel transform. The asymptotic solution is found by the stationary phase approximation. An approximate formula in weak VTI media is derived based on a novel way of expanding the vertical slowness linearly to anisotropic parameters in which case the stationary-phase points can be found analytically. The approximate solution will become exact when the medium degenerates into an elliptical VTI rather than an isotropic medium.
- Ben-Menahem, A. and Sena, A.G., 1990. Seismic source theory in stratified anisotropic media. J.
- Geophys. Res., 95: 15395-15427. doi: 10.1029/JB095iB10p15395.
- Dellinger, J.A., 1991. Anisotropic Seismic Wave Propagation. Ph.D. Thesis, Department ofGeophysics, Stanford University, Stanford, CA.
- Fuchs, K. and Miiller, G., 1971. Computation of synthetic seismograms with the reflectivity methodand comparison with observations. Geophys. J., 23: 417.doi: 10.1111/j.1365-246X.1971.tb01834.x.
- Gajewski, D., 1993. Radiation from point sources in general anisotropic media. Geophys. J.
- Internat., 113: 299-317. doi: 10.1111/j.1365-246X.1993.tb00889.x.
- Gridin, D., 2000. Far-field asymptotics of the Green tensor for a transversely isotropic solid. Proc.
- Roy. Soc., A 456: 571-591. doi: 10.1098/rspa.2001.0844.
- Hung, S. and Forsyth, D.W., 1998. Modelling anisotropic wave propagation in oceanicinhomogeneous structures using the parallel multidomain pseudo-spectral method. Geophys.
- J. Internat., 133: 726-740. doi: 10.1046/j.1365-246X.1998.00526.x.
- Kennett, B.L.N., 1983. Seismic Wave Propagation in Stratified Media. Cambridge University Press,Cambridge, UK.
- Miiller, G., 1985. The reflectivity method: a tutorial. J. Geophys., 58: 153-174.
- Thomsen, L., 1986. Weak elastic anisotropy. Geophysics, 51: 1954-1966. doi:10.1190/1.1442051.
- Thomsen, L. and Dellinger, J., 2003. On shear-wave triplication in polar-anisotropic media. J. Appl.
- Geophys., 54: 289-296. doi:10.1016/j.jappgeo.2003.08.008.
- Tsvankin, I.D. and Chesnokov, E.M., 1990. Synthesis of body wave seismograms from pointsources in anisotropic media. J. Geophys. Res., 95 (B7): 11317-11331.doi: 10. 1029/JB095iB07p11317.
- Tsvankin, I. and Thomsen, L., 1994. Nonhyperbolic reflection moveout in anisotropic media.Geophysics, 59: 1290-1304. doi:10:1190/1.1443686.
- Tsvankin, I., 1995. Body-wave radiation patterns and AVO in transversely isotropic media.Geophysics, 60: 1409-1425. doi:10.1190/1.1443876.
- Tsvankin, I., 2001. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media.Elsevier Science Publishers, Oxford.
- Vavrycuk, V., and Yomogida, K., 1996. SH-wave Green tensor for homogeneous transverselyisotropic media by higher-order approximations in asymptotic ray theory. Wave Motion, 23:83-93.GREEN’S TENSOR IN VTI MEDIA 275
- Vavrycuk, V., 1997. Elastodynamic and elastostatic Green tensors for homogeneous weaktransversely isotropic media. Geophys. J. Int., 130: 786-800.doi: 10.1111/j.1365-246X. 1997.tb01873.x.
- Vavrycuk, V., 2002. Asymptotic elastodynamic Green function in the kiss singularity inhomogeneous anisotropic solids. Stud. Geophys. Geod., 46: 249-266.doi: 0.1023/A:1019854020095.