Abstract
The coupling ray theory bridges the gap between the isotropic and anisotropic ray theories, and is considerably more accurate than the anisotropic ray theory. The coupling ray theory is often approximated by various quasi-isotropic approximations.
Commonly used quasi-isotropic approximations of the coupling ray theory are discussed. The exact analytical solution for the plane S wave, propagating along the axis of spirality in the 1-D anisotropic “oblique twisted crystal” model, is then numerically compared with the coupling ray theory and its three quasi-isotropic approximations. The three quasi-isotropic approximations of the coupling ray theory are (a) the quasi-isotropic projection of the Green tensor, (b) the quasi-isotropic approximation of the Christoffel matrix, (c) the quasi-isotropic perturbation of travel times. The comparison is carried out numerically in the frequency domain, comparing the exact analytical solution with the results of the 3-D ray tracing and coupling ray theory software. In the oblique twisted crystal model, the three studied quasi-isotropic approximations considerably increase the error of the coupling ray theory. Since these three quasi-isotropic approximations do not noticeably simplify the numerical implementation of the coupling ray theory, they should deffinitely be avoided. The common ray approximations of the coupling ray theory do not affect the plane wave, propagating along the axis of spirality in the 1-D oblique twisted crystal model, and should be studied in more complex models.
Similar content being viewed by others
References
Bakker, P.M., 2002. Coupled anisotropic shear wave raytracing in situations where associated slowness sheets are almost tangent. Pure Appl. Geophys., 159, 1403–1417.
Bucha, V. and Bulant, P. (eds.), 2002. SW3D-CD-6 (CD-ROM). In: Seismic Waves in Complex 3-D Structures, Report 12, pp. 247–247, Dep. Geophys., Charles Univ., Prague, online at “http://sw3d.mff.cuni.cz”.
Bucha, V., Bulant, P. and Klimeš, L. (eds.), 2001. SW3D-CD-5 (CD-ROM). In: Seismic Waves in Complex 3-D Structures, Report 11, pp. 357–357, Dep. Geophys., Charles Univ., Prague, online at “http://sw3d.mff.cuni.cz”.
Bulant, P. and Klimeš, L., 2002. Numerical algorithm of the coupling ray theory in weakly anisotropic media. Pure Appl. Geophys., 159, 1419–1435.
Bulant, P., Klimeš, L. and Pšenčík, I., 1999. Comparison of ray methods with the exact solution in the 1-D anisotropic “twisted crystal” model. In: Seismic Waves in Complex 3-D Structures, Report 8, pp. 119–126, Dep. Geophys., Charles Univ., Prague, online at “http://sw3d.mff.cuni.cz”.
Bulant, P., Klimeš, L. and Pšenčík, I., 2000. Comparison of ray methods with the exact solution in the 1-D anisotropic “twisted crystal” model. In: Expanded Abstracts of 70th Annual Meeting (Calgary), pp. 2289–2292, Soc. Explor. Geophysicists, Tulsa.
Bulant, P., Klimeš, L., Pšenčík, I. and Vavryčuk, V., 2004. Comparison of ray methods with the exact solution in the 1-D anisotropic “simplified twisted crystal” model. Stud. Geophys. Geod., 48, in press.
Červený, V., 2001. Seismic Ray Theory. Cambridge Univ. Press, Cambridge.
Coates, R.T. and Chapman, C.H., 1990. Quasi-shear wave coupling in weakly anisotropic 3-D media. Geophys. J. Int., 103, 301–320.
Klimeš, L., 2002. Second-order and higher-order perturbations of travel time in isotropic and anisotropic media. Stud. Geophys. Geod., 46, 213–248.
Klimeš, L., 2003. Common ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium. In: Seismic Waves in Complex 3-D Structures, Report 13, pp. 119–141, Dep. Geophys., Charles Univ., Prague, online at “http://sw3d.mff.cuni.cz”.
Klimeš, L., 2004. Analytical one-way plane-wave solution in the 1-D anisotropic “simplified twisted crystal” model. Stud. Geophys. Geod., 48, 75–96.
Klimeš, L. and Bulant, P., 2004. Errors due to the common ray approximations of the coupling ray theory. Stud. Geophys. Geod., 48, 117–142.
Lakhtakia, A., 1994. Elastodynamic wave propagation in a continuously twisted structurally chiral medium along the axis of spirality. J. Acoust. Soc. Am., 95, 597–600, erratum: J. Acoust. Soc. Am., 95 (1994), 3669.
Lakhtakia, A. and Meredith, M.W., 1999. Shear axial modes in a PCTSCM. Part IV: Bandstop and notch filters. Sensors and Actuators A, 73, 193–200.
Pšenčík, I., 1998. Green's functions for inhomogeneous weakly anisotropic media. Geophys. J. Int., 135, 279–288.
Pšenčík, I. and Dellinger, J., 2001. Quasi-shear waves in inhomogeneous weakly anisotropic media by the quasi-isotropic approach: A model study. Geophysics, 66, 308–319.
Thomson, C.J., Kendall, J-M. and Guest, W.S., 1992. Geometrical theory of shear-wave splitting: corrections to ray theory for interference in isotropic/anisotropic transitions. Geophys. J. Int., 108, 339–363.
Vavryčuk, V., 1999. Applicability of higher-order ray theory for S wave propagation in inhomogeneous weakly anisotropic elastic media. J. Geophys. Res., 104B, 28829–28840.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bulant, P., Klimeš, L. Comparison of Quasi-Isotropic Approximations of the Coupling Ray Theory with the Exact Solution in the 1-D Anisotropic “Oblique Twisted Crystal” Model. Studia Geophysica et Geodaetica 48, 97–116 (2004). https://doi.org/10.1023/B:SGEG.0000015587.83872.90
Published:
Issue Date:
DOI: https://doi.org/10.1023/B:SGEG.0000015587.83872.90