An Inverse Initial Boundary Value Problem for the Wave Equation in the Presence of Imperfections of Small Volume

Abstract. We consider for the wave equation the inverse problem of identifying locations and certain properties of the shapes of small conductivity inhomogeneities in a homogeneous background medium from dynamic boundary measurements on part of the boundary and for a finite interval in time. Using as weights particular background solutions constructed by a geometrical control method, we develop an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to very effective computational identification algorithms.