On the elastic profiles of a layered medium from reflection data. Part II: Impulsive point source

Abstract

It is shown that the density and the two Lamé profiles of a layered elastic half-space are uniquely determined from the surface displacement due to an impulsive point source. Two different inversion algorithms are developed which construct these profiles in a direct (noniterative) manner from the surface data. The first algorithm transforms the surface data due to the point source into three reflection coefficients due to SH plane waves at two precritical angles and a P plane wave at normal incidence. From these reflection coefficients, the density and the two Lamé profiles are uniquely determined by the procedure developed in Part I of this series. The second algorithm is based on the modification of Weidelt’s theory to apply to the Radon transform of the surface particle velocity. Although the second algorithm is conceptually similar to the first algorithm it provided the necessary conditions for the existence of the solution.