| Efficient and accurate mathematical codes for the prediction of underwater sound propagation are a critical component of SONAR system development and operation. Shallow water provides a unique set of complications to the problem of acoustic propagation prediction due to range dependence of acoustic properties resulting from a high number of wave interactions with the surface and seafloor and bathymetric variation. In this situation, the modes of vibration of the acoustic wave equation become coupled, with a transfer of energy between adjacent modes occurring upon traversing a horizontal change of environment. While mode methods have been developed for solving this range-dependent problem with varying accuracy, the computational intensity of these solutions makes them unsuitable for use in applications where real-time or near real-time performance is desired. The goal of the research presented herein was to develop, implement, and verify an efficient and rigorous coupled-mode solution for acoustic wave propagation in shallow water range-dependent environments. Particular interest was given to developing a solution that maintains analytical integrity while executing in a time window that is useful for tactical applications. A theoretical framework involving a range-expanded inner product for capturing the coupling between modes as they propagate through a horizontally-variable medium is presented. This framework includes a novel discretization of the range-dependent acoustic medium. A difference equations approach, which implements the inner product to account for non-adiabatic energy transfer between modes, is used to recursively compute reflection and transmission coefficients throughout the discretized environment. Increased efficiency is gained in the method due to the ability to compute coupling via closed-form algebraic expressions and in the application of asymptotic analysis to simplify the transmission and reflection coefficient solutions. |
