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

**Vaclav Vavrycuk**
### Abstract

The wave quantities needed in constructing the wave fields propagating in anisotropic elastic media are usually
calculated as a function of the slowness vector or its direction called the wave normal. In some applications,
however, it is desirable to calculate the wave quantities as a function of a 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 an arbitrary strength having arbitrary complex triplications. The slowness vector is determined
by numerical solving a system of multivariate polynomial equations of 6th order. Solving the equations,
we obtain a complete set of slowness vectors corresponding to all wave types and to all branches of the triplicate
wave surface. The system of equations is further specified for rays shot in a symmetry plane of an orthorhombic
medium and for a transversely isotropic medium. The system is decoupled into two polynomial equations of the
4th order for the P-SV waves, and separately into the equations for the SH waves, which yield an explicit
closed-form solution. The presented approach is particularly advantageous in constructing ray fields, ray-theoretical
Green functions and wave fields in strong anisotropy.

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In: Seismic Waves in Complex 3-D Structures, Report 15,
pp. 217-234, Dep. Geophys., Charles Univ., Prague, 2005.

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