An Inverse Method for Determining Small Variations in Propagation Speed

Abstract

We consider the inverse problem of determining small variations in propagation speed from observations of signals which pass through the medium of interest and are then observed remotely. We show that the variation satisfies an integral equation of integral transform type with an atypical kernel. In a variety of examples for the scalar and vector wave equation (Maxwell’s equations) and the equations of linear elasticity, we solve this integral equation by elementary means.