Inverse Problems in Shallow Oceans

[402539]吉尔伯特这项研究旨在调查浅海中的直接和反向声学问题。该方法将使用均匀化来推导海洋海底系统的确定性和随机微分方程。有几个开放的问题仍然与确定性问题有关，如远场的正确表述，未确定的包含问题，以及基本奇异解的存在性的证明和找到它的有效计算方法。均匀化方法产生确定性模型作为零阶项，一阶通过提出随机微分方程来体现介质的随机性。本研究的目的是研究这种随机微分方程，并提出和研究与之相关的随机逆问题。＊＊＊

9402539 Gilbert The research seeks to investigate direct and inverse acoustic problems in shallow oceans. The approach would be to use homogenization to derive the deterministic and stochastic differential equations for the ocean seabed system. There are several open problems still associated with the deterministic problem such as a correct formulation of the farfield, the unidentified inclusion problem, and for that matter, the proof of the existence of the fundamental singular solution and an efficient computational method for finding it. The homogenization approach produces the deterministic model as the zero order term and the first order takes in the random nature of the media by proposing a stochastic differential equation. The research is aimed at studying this stochastic differential equation and to pose and investigate the random inverse problems associated with it. ***