An Approximate Propagation Speed Inversion Over a Prescribed Slab

Abstract

An algorithm is proposed which facilitates an explicit velocity profile inversion in the presence of a presumedly known, background slab. The formulation is outlined within the confine of the so called, “distorted wave” Born approximation in which the background effects are properly accounted for. A plane wave excitation is considered.

The presence of a non-negligible background slab presents the following, previously unencountered, difficulties. Firstly, the slab’s multiple reflections impose a sequential reconstruction procedure, in which each iterative step yields the reconstruction of a finite spatial slab. This contrasts the one-step reconstruction, achieved by Bleistein and Cohen over a homogeneous background.

Secondly, difficulties associated with the reality of limited band measurements may be magnified. Finite bandwidth data may render the inversion procedure nonunique.