P-wave reflection-moveout approximation for horizontally layered media of tilted weak-to-moderate orthorhombic symmetry

An approximate nonhyperbolic P-wave moveout formula applicable to horizontally layered media of weak-to-moderate orthorhombic or higher-symmetry anisotropy of arbitrary orientation is presented and tested. Weak-anisotropy approximation is used for the derivation of the formula, in which the square of the reflection traveltime is expanded in terms of weak-anisotropy (WA) parameters specifying the anisotropy of the layers. Due to the use of the weak-anisotropy approximation, the proposed formula is applicable to any offset. Its accuracy decreases with increasing strength of anisotropy. The relation between traveltimes and WA parameters in the formula is transparent and relatively simple. For any offset along an arbitrarily chosen single surface profile, the formula depends in each layer on its thickness, on the auxiliary reference P-wave velocity, on, at most, six WA parameters describing P-wave orthorhombic or higher-symmetry anisotropy, and on three Euler angles specifying the orientation of symmetry elements in the layer. Performed tests indicate that the maximum relative traveltime error does not exceed 2.5% for P-wave anisotropy about 25%. Often, the errors are considerably lower. (C) 2020 Elsevier B.V. All rights reserved.