Moveout approximations for P waves in media of monoclinic and higher anisotropy symmetries

Veronique Farra & Ivan Psencik


We derive and test approximate P-wave moveout formulae for monoclinic, orthorhombic or transversely isotropic media with a vertical or horizontal axis of symmetry underlaid by a horizontal reflector coinciding with a symmetry plane. For the derivation of the formulae, we use the weak-anisotropy approximation, in which deviations of anisotropy from isotropy are assumed to be small. Derived traveltime formulae represent an expansion of traveltime with respect to small parameters characterizing the mentioned deviations. In addition to the traveltime formulae, we also present approximate formulae for normal moveout velocities. All resulting formulae are relatively simple, transparent and described by a reduced number of weak-anisotropy parameters specifying the medium. In monoclinic, orthorhombic or transversely isotropic media, the traveltime formulae depend on 8, 5 or 2 weak-anisotropy parameters. The accuracy of the formulae depends strongly on deviations of ray- and phase-velocity directions. Nevertheless, relative traveltime errors of the most accurate moveout formula do not exceed 1% for anisotropies whose strength is around 25%.

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Seismic Waves in Complex 3-D Structures, 24 (2014), 35-58 (ISSN 2336-3827, online at