Inverse Acoustic Problems in Shallow Oceans

本研究的目的是开发的直接散射问题的方法的情况下，一个非均匀的海洋与非均匀的，多孔弹性海床。 对于浅海中的声学反问题，研究人员将研究未知目标问题和未知参数问题。 这种研究对于调查河口、港口和沿海沃茨的海底性质和不均匀性的存在具有重要意义。 海底的性质与渔业有关，因为它决定了某些鱼种的产卵场;而海底的沉没残骸、地雷和矿藏可能造成不均匀性。 在这两个逆问题中，入射声波从物体或海底散射，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海底完全反射的均匀海洋的情况。 他们现在有了理论和数值算法，可以将这一程序扩展到具有弹性和/或多孔弹性海床的海洋。 这项工作将通过为折射率可变的海洋以及弹性和/或多孔弹性海床制定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全三维直接问题，这将使解决不明物体问题的方法能够扩展到海床相互作用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.