Internal-wave-induced, ocean-acoustic fluctuations: Comparison between path-integral approximations and parabolic-equation simulations

Numerical simulations of sound propagation have proven to be valuable tools in attempts to connect ocean structures to features of a travelling acoustic signal. Two possible methods of modelling the propagating sound are compared in this dissertation: the use of a parabolic wave equation and the implementation of corrections to ray theory based on path-integral techniques. Simulations using the parabolic equation allow for an accurate examination of a multi-frequency source, include some distinctly wave-based phenomena such as interference, and offer a direct way to develop predictions regarding the sound intensity. However, such simulations frequently require a great deal of computational resources. Also, the extraction of statistical acoustic quantities can involve a significant amount of analysis. The path-integral approximations used, conversely, greatly reduce the necessary computational time and the calculation of certain acoustic fluctuations becomes straightforward. This technique estimates the effect of internal waves on the acoustic signal by using integrals along ray paths of the average internal-wave-induced speed fluctuations. These ray trajectories are determined by the average sound-speed dependence on depth. The conditions under which these path-integral corrections to geometrical acoustics can be expected to offer sufficient accuracy have been investigated.; Parabolic-equation simulations have been performed to a maximum range of 1000 km, with two different temperate sound-speed profiles. The sound speed was perturbed by internal waves conforming to the Garrett-Munk (GM) spectral model. The acoustic frequency and the strength of the internal waves were varied in order to provide a range of circumstances under which the path-integral approximations could be compared to wave calculations. Predictions of the bias and variance of travel time, pulse spread and coherence in depth using the path-integral approximations were compared to results from the parabolic equation. For most purposes, reasonable accuracy was achieved in variance estimates over the entire 1000 km range, and in bias predictions for the first few hundred kilometers of propagation. Predicted depth-coherence lengths and pulse spreads were, however, significantly smaller and larger, respectively, than simulation results in most instances.