## Calculation of the slowness vector from
the ray vector in anisotropic media

**Vaclav Vavrycuk**
### Summary

The wave quantities needed in constructing wave fields propagating in
anisotropic elastic media are usually calculated as a function of the slowness
vector, or of its direction called the wave normal. In some applications,
however, it is desirable to calculate the wave quantities as a function of
the ray direction. In this paper, a method of calculating the slowness vector
for a specified ray direction is proposed. The method is applicable to general
anisotropy of arbitrary strength with arbitrary complex wave surface.
The slowness vector is determined by numerically solving a system of
multivariate polynomial equations of the sixth order. By solving the equations,
we obtain a complete set of slowness vectors corresponding to all wave types
and to all branches of the wave surface including the slowness vectors along
the acoustic axes. The wave surface can be folded to any degree. The system of
equations is further specified for rays shot in the symmetry plane of
an orthorhombic medium and for a transversely isotropic medium. The system
is decoupled into two polynomial equations of the fourth order for
the P-SV waves, and into equations for the SH wave, which yield an explicit
closed-form solution. The presented approach is particularly advantageous in
constructing ray fields, ray-theoretical Green functions, wavefronts
and wave fields in strong anisotropy.

### Keywords

Acoustic axis, anisotropy, elasticity, ray theory.

### Whole paper

The reprint is available in
PDF (198 kB).

*Proc. R. Soc. A*, **462** (2006), 883-896.

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