Cross-correlations of diffuse ocean noise using eigenvalue based statistical inference

Abstract

Cross-correlations of diffuse noise fields can be used to extract environmental information. The influence of directional sources (usually ships), often results in a bias of the travel time estimates obtained from the cross-correlations. Using an array of sensors, insights from random matrix theory on the behavior of the eigenvalues of the sample covariance matrix (SCM) in an isotropic noise field are used to isolate the diffuse noise component from the directional sources. A sequential hypothesis testing of the eigenvalues of the SCM reveals eigenvalues dominated by loud sources that are statistical outliers for the assumed diffuse noise model. Travel times obtained from cross-correlations using only the diffuse noise component (i.e., by discarding or attenuating the outliers) converge to the expected travel times (i.e., unbiased estimates) and are stable temporally. Data from the Shallow Water 2006 experiment demonstrates the effectiveness of this approach and that the SNR builds up as the square root of time, as predicted by theory.