## Ray amplitudes of seismic body waves in laterally inhomogeneous media

**Vlastislav Cerveny** ** & **
**Ivan Psencik**
### Summary

The most complicated part in the computation of ray amplitudes of
seismic body waves in laterally inhomogeneous media with curved
interfaces lies in the evaluation of the geometrical spreading.
Geometrical spreading can be simply expressed in terms of the Jacobian *J*
of the transformation from the Cartesian into ray coordinates. Several
systems of ordinary differential equations to compute the function *J*
are suggested. For general three-dimensional media, in which
the velocity changes with all the three spatial coordinates, a system
of three non-linear ordinary differential equations of the first order
is derived. If the velocity does not depend on one coordinate,
the system of equations reduces to only one non-linear differential
equation. The initial conditions for these differential equations
at point (or line) source and at points of intersection of the ray
with curved interfaces are presented.

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*Geophys. J. R. astr. Soc.*, **57** (1979), 91-106.

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