Mathematical Sciences: Research in Underwater Acoustics

首席研究员将展示如何逆问题 在水下声学的情况下，可以解决有限的 折射率随深度变化的海洋 有两 困难 第一个问题涉及到海洋的相互作用 和底部。 第二个涉及的事实是， 水的折射随深度而变化。 出现问题 海底可以通过假定一个适当的 远场边界条件，而问题的变量 通过替换原始方程组， 用一组更容易处理的平均方程。 的 分析工作将辅以数值模拟。 人们对水下声学感兴趣的一个原因是 能够定位和跟踪潜艇是很重要的 使用卫星。 从本质上讲，卫星向一个 一部分的海洋寻找潜艇，并解释了 返回信号。 这是一个难题，因为海洋是 复杂的介质和返回信号可能会失真 轻易 首席研究员将研究如何改善 通过使用 数学分析和数值模拟。

The principal investigator will show how the inverse problem in underwater acoustics can be solved for the case of finite oceans with a depth-varying index of refraction. There are two difficulties. The first involves the interaction of th> ocean and the bottom. The second involves the fact that the index of refraction of the water varies with depth. The problem with the ocean bottom can be taken care of by postulating an appropriate far-field boundary condition, while the problem with the variable refractivity is solved by replacing the original set of equations with a set of averaged equations that are more tractable. The analytical work will be complemented with numerical simulations. One reason that people are interested in underwater acoustics is that it is important to be able to locate and track submarines using a satellite. Essentially a satellite sends a signal to a part of the ocean to look for a submarine and interprets the return signal. This is a difficult problem because the ocean is a complicated medium and the return signal can be distorted easily. The principal investigator will study ways of improving the interpretation of signals from the ocean by using mathematical analysis and numerical simulations.