SH plane-wave reflection/transmission coefficients in isotropic, attenuating media

Abstract

An attempt is made to extend the applicability of the weak-attenuation concept (WAC) to ray-theory computations. WAC allows an approximate evaluation of effects of attenuation on seismic-wave propagation in smoothly varying laterally inhomogeneous media encountered in most seismological studies. The goal is to find under which conditions WAC could be applicable to layered media. Specifically, if the use of WAC is necessary, under which conditions it can be used for the approximate evaluation of the reflection and transmission coefficients at interfaces separating attenuating media. It turns out that outside critical incidence regions, where the ray theory is not applicable, the effects of attenuation on the reflection and transmission are negligible in comparison with effects of attenuation on wave propagation inside layers. Despite it, the approximate formulae for reflection and transmission coefficients including effects of attenuation are derived and presented. For better insight and simplicity, effects of attenuation on SH plane-wave coefficients at interfaces separating homogeneous, attenuating isotropic half-spaces are studied. The coefficients are expressed in the form of the sum of coefficients in a reference elastic medium plus a perturbation due to weak attenuation. The study is based on the assumption of the validity of the correspondence principle despite indications of its inapplicability in some situations. A fixed frequency is considered. A basic role in the evaluation of coefficients is played by slowness vectors of incident and transmitted waves. They are required to satisfy constraints resulting from the corresponding equation of motion, Snell's law and radiation condition. The resulting formulae for coefficients are singular for the angles corresponding to critical incidence in the reference elastic medium. It is shown that the approximate formulae work well in the subcritical region. Problems arise in the overcritical region of reference elastic media. The problems are related to the inapplicability of the commonly used correspondence principle. An artificial modification of formulae is proposed, which resolves the problem. However, it leads to the violation of the equation of motion and Snell's law constraints.