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

**Veronique Farra** **&**
**Ivan Psencik**
### Summary

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.

### Keywords

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.