## Approximate relation between the ray vector
and the wave normal in weakly anisotropic media

**Ivan Psencik** ** & **
**Vaclav Vavrycuk**
### Summary

Determination of the ray vector (the unit vector
specifying the direction of the group velocity vector)
corresponding to a given wave normal (the unit vector
parallel to the phase velocity vector or slowness vector)
in an arbitrary anisotropic medium can be performed
using the exact formula following from the ray tracing
equations. The determination of the wave normal from
the ray vector is, generally, a more complicated task,
which is usually solved iteratively. We present a
first-order perturbation formula for the approximate
determination of the ray vector from a given wave
normal and vice versa. The formula is applicable to qP
as well as qS waves in directions, in which the waves
can be dealt with separately (i.e. outside singular
directions of qS waves). Performance of the approximate
formulae is illustrated on models of transversely
isotropic and orthorhombic symmetry. We show that the
formula for the determination of the ray vector from
the wave normal yields rather accurate results even
for strong anisotropy. The formula for the determination
of the wave normal from the ray vector works reasonably
well in directions, in which the considered waves
have convex slowness surfaces. Otherwise, it can yield,
especially for stronger anisotropy, rather distorted
results.

### Keywords

Wave normal, ray vector, weak anisotropy.

### Whole paper

The reprint is available in
PDF (1109 kB !).

*Stud. geophys. geod.*, **46** (2002), 793-807.

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