First-order ray tracing for qS waves in inhomogeneous weakly anisotropic media

Abstract

First-order ray tracing equations and paraxial ray tracing system are derived for quasi-shear waves propagating in a smooth inhomogeneous weakly anisotropic medium. The first-order equations are based on explicit formulae in terms of slowness vector and elastic parameters. They only depend on 15 independent combinations of elastic parameters. For isotropic media, they reduce to exact equations. The behaviour of the approximate equations is studied in the vicinity of singularities. Ray tracing equations behave properly if the wave mode is changed when the ray crosses the conical or the intersection singularity, but the paraxial ray tracing system may be singular. A second-order correction of the traveltime is obtained by integration along the approximate rays. Comparison of the exact and approximate traveltimes in transversely isotropic and orthorhombic homogeneous media shows small relative errors except in the close vicinity of cusps. © 2005 RAS.