## A new approximation of the velocity-depth distribution
and its application to the computation of seismic wave fields

**Vlastislav Cerveny**
### Summary

A new approximation of the velocity-depth distribution in a vertically
inhomogeneous medium is suggested. This approximation guarantees
the continuity of velocity and of its first and second derivatives
and does not generate false low-velocity zones. It is very suitable
for the computations of seismic wave fields in vertically inhomogeneous
media by ray methods and its modifications, as it removes many false
anomalies from the travel-time and amplitude-distance curves of seismic
body waves. The ray integrals can be evaluated in a closed form;
the resulting formulae for rays, travel times and geometrical
spreading are very simple. They do not contain any transcendental
functions (such as ln(*x*) or sin^{-1}(x))
like other approximations; only
the evaluation of one square root and of certain simple arithmetic
expressions for each layer is required. From a computational point
of view, the evaluation of ray integrals and of geometrical spreading
is only slightly slower than for a system of homogeneous parallel
layers and even faster than for a piece-wise linear approximation.

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*Stud. geophys. geod.*, **24** (1980), 17-27.

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