Inverse Acoustic Problems in Shallow Oceans

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The objective of this research is to develop methods for the direct scattering problem in the case of a non-homogeneous ocean with a non-homogeneous, poro-elastic seabed. With regard to acoustic inverse problems in a shallow ocean, the researchers will investigate the undetermined object problem and the unknown parameters problem. Such research is of importance in investigating estuaries, harbors and coastal waters for the nature of the seabed and the existence of inhomogeneities. The nature of the seabed is of interest to fisheries because it determines the spawning grounds of certain fish species; whereas, inhomogeneities may be caused by sunken wreckage, mines and mineral deposits buried in the seabed. In both inverse problems, an incident acoustic wave is scattered off an object or the sea-floor in order to determine the shape of an object or the physical coefficients of the seabed. Prior work by the investigators have been limited to the case of a homogeneous ocean with a totally reflective seabed. They now have the theory and numerical algorithms in place to extend this procedure to the case of oceans with elastic and/or poro-elastic seabeds. This work will be completed by developing good computational procedures for the ocean with variable index of refraction and elastic and/or poro-elastic seabeds. The PI's development of the mathematical techniques and the software to solve the fully three-dimensional, direct problem for a homogeneous, poro-elastic seabed and a stratified ocean will permit extension of the methodology for solving the unidentified object problem to the case of non-homogeneous oceans with interactive seabeds.