INVERSE PROBLEMS FOR A PERTURBED DISSIPATIVE HALF-SPACE

This paper addresses the scattering of acoustic and electromagnetic wa ves from a perturbed dissipative half-space. For simplicity, the pertu rbation is assumed to have compact support. Section 1 discusses the ap plication that motivated this work and explains how the scalar model u sed here is related to Maxwell's equations. Section 2 introduces three formulations for direct and inverse problems for the half-space geome try. Two of these formulations relate to scattering problems, and the third to a boundary value problem. Section 3 shows how the scattering problems can be related to the boundary value problem. This shows that the three inverse problems are equivalent in a certain sense. In sect ion 4, the boundary value problem is used to outline a simple way to f ormulate a multi-dimensional layer stripping procedure. This procedure is unstable and does not constitute a practical algorithm for solving the inverse problem. The paper concludes with three appendices, the f irst two of which carry out a careful construction of solutions of the direct problems and the third of which contains a discussion of some properties of the scattering operator.