P-wave ray (group) velocities in a weak-anisotropy approximation

Veronique Farra & Ivan Psencik


We test accuracy of the weak-anisotropy approximation of the ray (group)-velocity formulae. The formulae of varying accuracy are applicable to anisotropy of arbitrary symmetry and orientation. They provide the square of the magnitude of the ray velocity as a function of a ray vector, i.e., a unit vector pointing in the direction of the ray-velocity vector. The ray velocity (phase velocity too) is expressed in terms of three elements of the rotated Christoffel matrix, which depend linearly on the parameters specifying the medium. The less accurate formulae are fully independent of the choice of a reference isotropic medium, the most accurate formula depends only slightly on the ratio of S- and P-wave velocities of the reference medium. We show that the accuracy of the formulae is close to the accuracy of the so-called anelliptic approximations, very accurate approximations based on perturbation of elliptical anisotropy.

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Seismic Waves in Complex 3-D Structures, 25 (2015), 157-175 (ISSN 2336-3827, online at http://sw3d.cz).