Bottom Interaction Effects on Normal Modes: an Algebraic Approach
We assume that the speed of sound in the water and in the bottom of the ocean is a function of only the depth, and not the range. We also assume that the ocean and its bottom is eventually underlaid with a rigid interface. This problem can be solved by the method of normal modes, involving the eigenvalues and eigenfunctions of a depth dependent ordinary differential equation. We investigate the changes in these eigenvalues and eigenfunctions that result from changes in the depth dependent sound speed within the ocean and its bottom, using a perturbation approach. We formulate the perturbation in terms of an algebraic eigenvalue problem, and we show that it is equivalent to the usual power series expansion in a small parameter.
KeywordsSine Nite Acoustics Carol
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