## qP-wave phase velocities in arbitrary weak
anisotropic media - a perturbation approach

**Dirk Gajewski** ** & **
**Ivan Psencik**
### Abstract

We present simple formulae for *qP* wave phase velocities in weakly
but arbitrarily anisotro-pic media. For their derivation, we use the
well-known formula for the first-order perturbation of the *qP* wave
phase velocity, see e.g. Backus (1965). The formula for phase velocity
in a generally anisotropic medium corresponds exactly to the one
already derived by Sayers (1994). We discuss its sensitivity to the
elastic parameters and specify it for special cases of anisotropy
frequently encountered in practice. We consider the case of an
orthorhombic medium with axes of symmetry coinciding with general
coordinate axes, a transversely isotropic medium and a medium with
a horizontal axis of hexagonal symmetry. In all the cases, the
formulae for the phase velocity contain nondimensional parameters,
which represent a generalization of Thomsen's (1986) parameters. The
formula for transversely isotropic medium reduces to the well-known
formula derived by Thomsen (1986).

66th Ann. Internat. Mtg., Soc.Expl.Geophys.,
Expanded Abstracts, 1507-1510, 1996.