Temporal coherence of normal modes in an ocean waveguide.

Abstract

Temporal coherence is a measure of sound correlation in time, and the temporal coherence time refers to the time it takes for the signal to become uncorrelated. Over 20 experiments have been conducted over the past 40 years to measure the temporal coherence of sound propagation to a long distance. The experimental results in shallow and deep water were recently analyzed by Yang [J. Acoust. Soc. Am. 120, 2595–2614 (2006); J. Acoust. Soc. Am. 124, 113–127 (2008); J. Acoust. Soc. Am. 125, 1247 (2009)]. A theoretical treatment is given in this paper for the temporal coherence of normal modes using the path integral approach and also the perturbation expansion of the coupled normal-mode equation to the first order of sound-speed-perturbation squared. For a typical shallow water and deep water environment with internal waves present, the coherence time of the acoustic field (averaged over the source and receiver depths) decreases as −3/2 power of frequency due to mode coupling, as is observed in data. Not including mode-coupling, the coherence time of the acoustic field decreases as −1 power of frequency, same as that predicted for acoustic rays. The coherence time decreases as −1/2 power of range in all cases. (Work supported by the Office of Naval Research.)