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

Ivan Psencik, Milosz Wcislo & Patrick F. Daley


An attempt is made to extend the application of the weak-attenuation concept (WAC), allowing for the approximate evaluation of effects of weak attenuation on seismic-wave propagation in smooth laterally inhomogeneous media to layered media. This should be done by including the approximate evaluation of the reflection and transmission coefficients at interfaces separating weakly attenuating media. For simplicity, effects of weak attenuation on SH plane-wave reflection and transmission coefficients, related to interfaces separating weakly attenuating isotropic half-spaces, are studied. The study is based on the assumption of validity of the correspondence principle. 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 coming from corresponding wave equations and Snell’s law. 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. Certain problems arise in the overcritical region for media with higher attenuation in the half-space with the incident wave. Problem of the applicability of the correspondence principle in these situations is indicated. An artificial modification of formulae is proposed, which fixes the problems. It, however, leads to the violation of the wave-equation constraint. Since the effects of attenuation on the reflection or transmission coefficient are weak, their omission in modeling should not lead to significant errors.

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Seismic Waves in Complex 3-D Structures, 29 (2019), 45-69 (ISSN 2336-3827, online at