Properties of Weak Contrast PP Reflection/Transmission Coefficients for Weakly Anisotropic Elastic Media

Abstract

Approximate formulae for PP reflection/transmission (R/T) displacement coefficients for weak contrast interfaces separating weakly anisotropic media of an arbitrary symmetry are presented. The coefficients have a form of a sum of a well-known approximate PP reflection/transmission coefficient for a weak contrast interface separating two background isotropic halfspaces and a correction due to weak anisotropy. The correction is controlled, linearly, by the so-called weak anisotropy (WA) parameters. The coefficients are defined with respect to an arbitrary isotropic background. The formulae are convenient for description of coefficients of reflection and transmission in low symmetry weakly anisotropic media as well as in media with higher symmetry (orthorhombic, hexagonal) with arbitrarily oriented axes of symmetry. For anisotropies of higher symmetry, for which approximate formulae of other authors exist, we discuss the differences between these and our formulae and effects of these differences on the accuracy of approximate coefficients. Performance of the approximate formulae for R PP coefficients is tested on models with weak anisotropy and weak contrast interfaces as well as on models whose anisotropy and velocity contrast are in no way weak. Even in the latter case, the formulae yield satisfactory results. Accuracy of the approximate R PP coefficient depending on the choice of the background is then investigated. It is shown that the R PP coefficient can be described, approximately, by a formula, whose correction term due to anisotropy is independent of the S-wave background velocity and depends only slightly on the choice of the P-wave background velocity. The formulae for the R PP coefficients commonly used in literature for higher symmetry anisotropies are obtained by linearization of the above mentioned formula. Linearization leads to the dependence of the R PP coefficient on the choice of the S-wave background velocity and, generally, to a slight decrease of accuracy. Presented formulae are convenient for solving an inverse problem: determination of contrasts of parameters of anisotropic media surrounding an interface. Sensitivity of the approximate R PP coefficient to basic weak anisotropy parameters is presented.