Inverse Acoustic Problems in Shallow Oceans

本研究的目的是发展非均匀海洋和非均匀多孔弹性海床的直接散射问题的方法。对于浅海声反演问题，研究对象不确定问题和参数不确定问题。这种研究对于调查河口、港口和沿海水域的海底性质和不均匀性的存在具有重要意义。渔业对海底的性质很感兴趣，因为它决定了某些鱼类的产卵场；然而，不均匀性可能是由沉没的残骸、海底埋藏的地雷和矿床引起的。在这两个反问题中，入射声波从物体或海底散射出来，以确定物体的形状或海底的物理系数。调查人员先前的工作仅限于具有完全反射海床的均匀海洋的情况。他们现在已经有了理论和数值算法，可以将这一过程扩展到具有弹性和/或多孔弹性海床的海洋。这项工作将通过为具有可变折射率和弹性和/或多孔弹性海床的海洋开发良好的计算程序来完成。PI开发了数学技术和软件，以解决均匀、多孔弹性海床和分层海洋的完全三维直接问题，这将允许将解决不明物体问题的方法扩展到具有相互作用海床的非均匀海洋的情况。

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.