Ray tracing in azimuthally anisotropic media-I. Results for models of aligned cracks in the upper crust

Abstract

Ray tracing through gradients in anisotropic materials is complicated by singularities where the two quasi-shear wave slowness sheets cross or touch. Difficulties associated with such points can be removed by explicitly including polarization in the ray tracing equations. Slowness sheet and wavefront plots show the polarization and velocity behavior of various anisotropy models of aligned cracks in the upper crust. A simple scaling of the elastic tensor with depth can be shown to be approximately correct for models of aligned cracks within an isotropic host matrix with a linear velocity gradient. Ray tracing examples for models of aligned cracks within a strong vertical velocity gradient in the uppermost crust demonstrate various features of azimuthal anisotropy, including amplitude and polarization anomalies and shear-wave splitting. Quasi-shear wave polarizations typically twist along ray paths, with stronger twisting near the symmetry axis in hexagonally symmetric media. Strong anisotropy can cause unusual effects, such as ray paths which have three turning points in laterally homogeneous models.

Quasi-shear wave ray tracing by wavefront construction in 3-D, anisotropic media

“…In particular, S-wave propagation in anisotropic media is complicated by the S-wave singularities, where the two qS-wave slowness surfaces cross or touch (Crampin, 1985;Shearer and Chapman, 1989;Coates and Chapman,1990;Červený, 2001;Vavryčuk, 2001). There are three main types of S-wave singularity: point, kiss and line, and they can appear in weakly or strongly anisotropic media (Crampin and Yedlin, 1981;Červený, 2001;Vavryčuk, 2001).…”

“…Processing to measure shear-wave splitting also provides further information on earth properties that cannot be obtained from quasi-compressional (qP) data. For example, shear-wave splitting measured from vertical seismic profiles can be interpreted in terms of crack-induced anisotropy (Crampin, 1985;Shearer and Chapman, 1989;Douma and Crampin, 1990;Horne et al, 1997;Crampin and Chastin, 2003;Nistala and McMechan, 2005). Such information regarding crack properties from qS-wave splitting can provide important insights for understanding reservoir performance (Ramos-Martinez et al, 2000).…”

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

“…Compared with the method of traveltime calculation using eikonal equation, ray tracing methods not only can obtain the traveltime of the seismic wave field, but also can get the ray trajectories in the ground (Shearer and Chapman 1989;Cerveny 2001). Traditional ray tracing methods include shooting methods (Langan et al 1985;Virieux and Farra 1991;Xu et al 2004Xu et al , 2007Xu et al , 2008 and bending methods (Julian and Gubbins 1977;Thurber and Ellsworth 1980;Aki and Richards 1980).…”

Determination of the reference symmetry axis of a generally anisotropic medium which is approximately transversely isotropic

“…The density reduced stiffness tensor in homogeneous anisotropic velocity model 1 by Shearer and Chapman (1989) …”

“…If we inspect stiffness tensor (33) manually, we see that the medium is exactly transversely isotropic. Velocity model 1 by Shearer and Chapman (1989) was first rotated by 45…”