Weak-anisotropy approximations of P-wave phase and ray velocities for anisotropy of arbitrary symmetry

Veronique Farra & Ivan Psencik


We test the accuracy of the previously derived weak-anisotropy approximations of the P-wave phase and ray (group) velocities. The formulae are of varying accuracy, and are applicable to weak or moderate anisotropy of arbitrary symmetry and orientation. They have a form of expressions for squares of phase velocity depending on the phase-velocity direction and of ray velocity depending on the ray-velocity direction. Both velocities are expressed in terms of three elements of the rotated Christoffel matrix, which depend linearly on the parameters specifying the medium, the weak-anisotropy (WA) parameters. The least accurate formulae are fully independent of the choice of a reference isotropic medium and depend linearly on weak-anisotropy parameters. The most accurate formulae depend only slightly on the ratio of S- and P-wave velocities of a reference medium, their dependence on weak-anisotropy parameters being quadratic. We show that the accuracy of the formulae is quite high, in fact, in some cases, it is close to the accuracy of the so-called anelliptic approximations, very accurate approximations based on a perturbation of the elliptical anisotropy.


Weak anisotropy, P wave, phase velocity, ray velocity.

Whole paper

The reprint can be obtained from Ivan Psencik.

Stud. geophys. geod., 60 (2016), 403-418.