MODELLING THE EFFECT OF SEISMIC VELOCITY GRADIENTS ON THE CHANGE IN GEOMETRICAL SPREADING ACROSS A BOUNDARY

Abstract

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 varies linearly with depth and the interface is a horizontal plane. The presence of this type of velocity inhomogeneity will affect the observed amplitudes through its influence on the discontinuity in geometrical spreading at an interface. Analytical results will be compared to an approximate method for evaluation of geometrical spreading to ensure their accuracy. We show that the focusing effects due to the presence of velocity gradients become significant in our examples only for large angles of incidence.