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

Veronique Farra & Ivan Psencik


An approximate nonhyperbolic P-wave moveout formula applicable to horizontally layered media of moderate or weak orthorhombic or higher anisotropy symmetry of arbitrary orientation is presented and tested. Weak-anisotropy approximation is used for its derivation, 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 it, 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. Along a 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 transverse isotropy symmetry, 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%. For most offsets, however, the errors are considerably lower.

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Seismic Waves in Complex 3-D Structures, 29 (2019), 7-17 (ISSN 2336-3827, online at http://sw3d.cz).