The unidentified object problem in a shallow ocean

This work addresses the inverse problem of the identification of a passive three-dimensional impenetrable object in a shallow-water environment. The latter is assumed to have flat perfectly reflecting (sound-soft top and sound-hard bottom) boundaries and therefore acts as a guide for acoustic waves. These waves are employed to interrogate the object and the scattered acoustic wavefield is measured on the surface of a (virtual) vertically oriented cylinder (of finite or infinite radius, corresponding to near- or far-field measurements) fully enclosing the object. The direct scattering problem is resolved in approximate manner by employing, in a local manner, the known separated-variable solution for a scattering by a vertically oriented cylinder in a perfect waveguide. The inverse problem is resolved in the same manner (i.e., with the same approximate field ansatz) by least-squares matching of theoretical fields (for trial objects) to the measured field. Examples are given of successful shape reconstructio...