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

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.. 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.