Ray-Based Model for Spatial Coherence of Ocean-Surface-Generated Noise and Its Approximation in a Triplet Array

Abstract

In this paper, a ray-based noise model is developed to calculate the two-point spatial coherence function for ocean-surface-generated noise in a hydrophone triplet, which consists of three hydrophones arranged as an equilateral triangle with side length $d$ . While existing ray-based models employ the semianalytic approach, this model is more generally formulated for the 3-D noise field with vertical and azimuthal directivity using a ray-tracing model. Moreover, we derive a Maclaurin series of the formulated spatial coherence function for the ratio of the hydrophone spacing and the acoustic wavelength $\lambda $ . This series explicitly reveals the feature of spatial coherence for the noise field as a function of the orientation of the hydrophone pair and the ocean environmental coefficients. At small $d/\lambda $ , the leading-order terms alone provide a good approximate solution for the spatial coherence function, which enables rapid computation of six coherence functions for the hydrophone triplet. Especially, for the ocean environment with weakly azimuth-dependent ocean bathymetry, the contribution from each term in the derived series is analyzed and a simpler formula for the spatial coherence function is suggested.