Perturbation from isotropic to anisotropic heterogeneous media in the ray approximation

Abstract

In this paper, perturbation methods are used to obtain ray results in slightly anisotropic, heterogeneous media from a nearby isotropic medium. The advantage of this approach is that rays computed by available 2‐D isotropic ray‐tracing algorithms can be used to approximately compute, by perturbation, ray theoretical results in more general 3‐D slightly anisotropic, heterogeneous media. The perturbation approach also makes possible an efficient computation of ray sensitivity operators necessary in seismic tomography studies. In order to compute approximate ray results for quasi‐shear waves, degenerate perturbation theory must be used in order to split a single shear wave in an isotropic medium into two quasi‐shear waves in a nearby anisotropic medium. The perturbation approach is tested on an effectively anisotropic model of aligned cracks within a linear, vertical velocity gradient. Perturbed traveltimes, ray paths and particle motions of quasi‐compressional and quasi‐shear waves for such an anisotropic medium are compared with exact ray results. Good agreement between the exact and perturbed results is found. Copyright © 1991, Wiley Blackwell. All rights reserved