The inverse scattering problem for acoustic waves

Abstract

Abstract : We first make a distinction between 'scattering' and 'diffraction' and note that the latter is basically a high frequency phenomena whereas the former is more accurately applied to low and intermediate values of the frequency. In this paper we shall not discuss any of the important new results on the 'inverse diffraction problem' but instead refer the reader to the recent paper of Brian Sleeman for a survey of these results. We shall further restrict our attention to the scattering of a plane time harmonic wave by a fixed bounded obstacle situated in a homogeneous medium and in particular to determine information about this obstacle from a knowledge of the asymptotic behavior of the scattered wave. Hence, we are excluding such topics as the scattering of waves by moving obstacles, the determination of the speed of sound in a non-homogeneous medium, and the location of equivalent sources. Finally, we shall only be concerned with determining two basic properties of the scattering obstacle, viz. its shape and/or its surface impedance.