Modelling the effect of seismic velocity gradients on the change in geometrical spreading across a boundary

This paper begins with a review on how rays may be traced though isotropic inhomogeneous media separated by curved interfaces. The results are applied to the case of a layer over a half-space in which the seismic velocity var ies linearly with depth and the interface is a horizontal plane. The presen ce of this type of velocity inhomogeneity will affect the observed amplitud es through its influence on the discontinuity in geometrical spreading at a n interface. Analytical results will be compared to an approximate method f or evaluation of geometrical spreading to ensure their accuracy. We show th at the focusing effects due to the presence of velocity gradients become si gnificant in our examples only for large angles of incidence.