Approximate P-wave reflection coefficient in weakly-to-moderately anisotropic media of arbitrary tilt

Veronique Farra & Ivan Psencik


There is an evident need for simple and transparent approximate formulae for reflection/transmission coefficients, which could find applications in the amplitude-versus-offset (AVO) or amplitude-versus-azimuth (AVA) studies. It is desirable that such formulae are applicable to a broad type of media, and parameterized in a unique way utilizable in other related studies. We offer such an approximate formula for the P-wave reflection coefficient. It is based on the weak-contrast and weak-anisotropy approximations. The coefficient is applicable to any type of weak-to-moderate anisotropy. It is specified in terms of weak-anisotropy (WA) parameters, which represent an alternative to the commonly used elements of the stiffness matrix. They represent a unique set of parameters capable to describe any type of anisotropy. They can also be used for the specification of other related concepts as the reflection moveout or the geometrical spreading. Presented tests illustrate high accuracy and flexibility of the formula.

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Seismic Waves in Complex 3-D Structures, 30 (2020), 47-61 (ISSN 2336-3827, online at