Extension of path‐integral theory to shallow‐water coherence.

Abstract

A path‐integral approach to the mutual coherence function of acoustic signals propagating in deep water was developed in the late 1970’s. This theory requires a single dominant ray path that interacts weakly with the boundaries, a restriction which has precluded direct application to acoustic propagation in shallow water. Here, path‐integral theory is extended to the mutual coherence of mode amplitudes defined over the horizontal plane. In this domain, the mode amplitudes follow a principal ray that has no interaction with lateral boundaries. The mutual coherence is found to be related to the spectrum of sound‐speed fluctuations via a Fourier transform along a direction transverse to the acoustic propagation path. For sound‐speed fluctuations generated by a linear internal‐wave field, solutions are obtained that predict the mutual coherence with no free parameters. Such solutions were computed for a winter environment existent during an experiment that took place on the New Jersey shelf in December 2003. Comparison between theoretical and measured coherence is encouraging with respect to both the power‐law behavior at short separations, and the transition to saturation at large separations. [Work supported by the Office of Naval Research.]