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

**Veronique Farra** **&**
**Ivan Psencik**
### Abstract

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.

### Whole paper

The paper is available in
PDF (501 kB).

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