Mathematical Sciences: Research in Underwater Acoustics

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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.