### DETERMINATION OF SEISMIC SIGNAL VELOCITY FROM $\tau$ FUNCTION FOR A CLASS OF ANISOTROPIC MEDIA

V. M. Markushevich and A. S. Tsemahman

Abstract

We extend the $\tau$ method to anisotropic laterally homogeneous media with seismic signal velocity $v$ depending on two variables, $y$ and $\alpha$, where $y$ is depth and $\alpha$ is the angle between the vertical and the ray direction. A special dependence on the angle is introduced, which preserves Snell's law with horizontal velocity replacing velocity independent of direction in an isotropic medium. We also consider the specific case where seismic signal velocity in the horizontal direction increases with depth. In that case we can evaluate the horizontal velocity and the velocity indicatrix by $\tau$ functions of reflected and refracted waves.

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Computational Seismology, Vol. 2.