Coupled Mode Propagation in Elastic Media

In a variety of applications in shallow water acoustics, coupled mode theory is an attractive model. In addition to the parabolic equation technique (PE), it is the only other numerically efficient model that provides the solution of the wave equation in a range-dependent environment. However, while the parabolic equation technique for propagation in the ocean over a bottom modeled as a fluid has been hugely successful, up to date there is no PE model that can produce reliable results for propagation over an elastic bottom. It is the goal of this work to use elastic coupled mode theory to develop a range-dependent propagation model for waves in an ocean overlying an elastic bottom. To accomplish this goal, we plan to use the elastic coupled mode theory developed in [1], the acoustic version of which was successfully applied to the acoustic wedge in [2]. In this method, as in its acoustic counterpart, the range-dependent waveguide is divided into small stair-steps, and the field from one stair step to the next is propagated by the coupled mode differential equation, here referred to as the coupled mode engine. The coupled mode engine uses a marching technique similar to the one used in the PE method, except that in this case the grid spacing is determined by the width of the stair-steps, which is determined by the degree at which the water depth changes as a function of range. During this process, it computes the mode coupling matrices from the knowledge of the local modes and their depth derivatives. By combining the coupled mode engine with an elastic normal mode model, we plan to develop a model for propagation of waves in a range-dependent environment overlying an elastic bottom.