Geometrical theory of shear‐wave splitting: corrections to ray theory for interference in isotropic/anisotropic transitions

Abstract

An S‐wavefront from an isotropic region is expected to separate into two fronts when it passes into a gradually more anisotropic region. Standard ray expansions may be used to continue the waves in the anisotropic region when these two S‐wavefronts have separated sufficiently. However, just inside the anisotropic region the two S‐waves interfere with an effect that is stronger than the usual ω‐1 corrections of the ray method. A waveform distortion can occur and this should be considered when modelling S‐waves in, e.g., subduction zones with regions of isotropy grading into regions of anisotropy. The interference is studied here by local analysis of an integral equation obtained by the Green's function method. It is found that if the elasticity and its first two derivatives are continuous at the isotropy/anisotropy border, then zeroth‐order ray theory may still be used to continue the incident wave into the anisotropic region. The incident displacement is simply resolved into two definite directions at the point where the anisotropy begins. These two directions are the limits of the unique eigenvectors on the anisotropic rays as the point of isotropy (onset of splitting) is approached. If the nth derivative of the elasticity is discontinuous at the isotropy/anisotropy border, then the scattering integral which describes the interference makes a correction to ray theory which is O(ω‐1/n+1) in magnitude. Hence, the interference effect is stronger when the emergence of anisotropy is more gradual. Although the corrections are given by simple expressions, it is not reasonable to specify numerical velocity models up to such high‐order derivatives. For a smooth interpolation scheme, such as cubic splines, it is more practical to monitor the splitting rays obtained by ray tracing and to use the best‐fitting ‘equivalent’ high‐order discontinuity. This will lead to an estimate of the importance of the correction terms. An example is given for a subduction zone model involving olivine alignment in the mantle‐wedge above the slab. Copyright © 1992, Wiley Blackwell. All rights reserved