On the Characterization of Objects in Shallow Water Using Rigorous Inversion Methods

Abstract

We are concerned herein with inverse obstacle scattering problems in underwater acoustics, where the goal is to characterize an unknown object from measurements of the pressure field which results from its interaction with a known probing (incident) wave. Two configurations are considered, i.e., an impenetrable, sound-soft or sound-hard object immersed in a shallow-water open waveguide, the source and the receivers also being located in it, and a penetrable object embedded in a semi-infinite sediment, illuminated and observed from a semi-infinite water column. The inverse problem consists in retrieving the contour of the impenetrable object or a contrast function representative of the constitutive physical parameters of the penetrable one. This is done by means of deterministic nonlinearized iterative solution methods, one devoted to each configuration, i.e., the distributed source method and the binary modified gradient method. Both of them attempt to build up a solution by minimizing, in an appropriate L ₂ setting, a two-term cost functional which expresses the discrepancies between the fields computed by means of the retrieved solution and the data, the latter being either the field measured on the receivers or the known incident field on the boundary of the object (impenetrable case) or inside it (penetrable case). In both configurations the well-known ill-posedness of the inverse scattering problem is enhanced either by range filtering or by the limited aspect of the data, a strong regularization being then needed. This is done by introducing, in the inversion algorithms, some a priori information on the object to be retrieved, which consists in the smoothness of its contour or in its homogeneity.