Mathematical Sciences: Research in Underwater Acoustics

首席研究员将展示如何解决具有深度变化折射率的有限海洋的水下声学逆问题。有两个困难。第一种是海洋与海底的相互作用。第二个问题涉及到水的折射率随深度而变化的事实。海底问题可以通过假设一个适当的远场边界条件来解决，而变折射率问题可以通过用一组更容易处理的平均方程来代替原来的方程来解决。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，能够利用卫星定位和跟踪潜艇是很重要的。从本质上讲，卫星向海洋的某一部分发送信号来寻找潜艇，并对返回的信号进行解释。这是一个困难的问题，因为海洋是一个复杂的介质，返回的信号很容易失真。首席研究员将研究如何利用数学分析和数值模拟来改进对海洋信号的解释。

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.