A coupled bispectral, temporal and spatial coherence function of the pressure field, scattered from a moving sea surface

Abstract

Fluctuations in the scattering of high-frequency sound from the moving sea surface is of significance, particularly in underwater acoustic communication systems using adaptive methods. Surface scattering may statistically be described using coherence functions, especially for higher frequencies when the coherent part of the pressure field is virtually nonexistent. Previous studies have presented coherence functions as a function of either spatial and temporal variations of the channel, but with a fixed signal carrier frequency or two signal frequencies and temporal channel variations (or some of the several possible Fourier transform duals). Here, a coupled bispectral, temporal and spatial coherence function is presented. The coherence function is derived from the pressure field, given by the two-dimensional Kirchhoff–Helmholtz integral for two monochromatic tones evaluated at separate receiver positions. The channel variations are caused by a wind-driven, gravity-wave dispersed sea surface with a Pierson–Moskowitz spectrum. The derivation of the coherence function involves numerical integration. Numerical results are compared to earlier model data from the literature. [Work sponsored by the Danish Technical Research Council.]