Cross-correlations of diffuse noise in an ocean environment 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 predicted travel times based on the known array sensor spacing and measured sound speed at the site and are stable temporally (i.e., unbiased estimates). Data from the Shallow Water 2006 experiment demonstrates the effectiveness of this approach and that the signal-to-noise ratio builds up as the square root of time, as predicted by theory.

Acoustic Green's function extraction from ambient noise in a coastal ocean environment

“…These arguments suggest that conditions for noise interferometry are at least as favorable at r = 50 km, h = 5km as under conditions that we have reported on. Also, we note that, independent of water depth and details of propagation conditions, better results (e.g., shorter required coherent stacking time to extract Green's function estimates with adequate signal‐to‐noise ratio) are expected [ Burov et al , ; Leroy et al , ; Menon et al , ; Goncharov et al , ; Fried et al , ] if point measurements are replaced by vertical array measurements, even short arrays. With these comments in mind, we are optimistic about the potential of using noise interferometry as the basis for tomographic inversions at ranges longer than those considered in this letter.…”

Spatial filtering in ambient noise crosscorrelation

“…Wapenaar [10] demonstrated that one-side illumination is compensated by the heterogeneity of the medium. If loud sources are present in the environment, the crosscorrelations might be dominated by the arrivals coming from these sources, and therefore they do not approximate the Green's function between the receivers [11].…”

“…Leroy et al [14] proposed to enhance the emeregence rate of crosscorrelation peaks by considering a reference covariance matrix that multiply the sampled covariance. Menon et al [11] have shown that directional sources can be removed by reducing the largest eigenvalues by a statistical analysis of the eigenvalues of the covariance matrix. The passive fathometer [15,16] is another example of combination of beamforming technique and crosscorrelation, in this case on a vertical array, beamformed to look upward and downward to remove horizontally propagating noise.…”

Sequential Geoacoustic Filtering and Utilizing Ambient Noise for Geoacoustic Inversion

“…A new direction is taken in Menon [2012aMenon [ , 2012bMenon [ , 2012cMenon [ 2013 and where random matrix theory is used to analyze noise cross-spectral density matrices. A random matrix is a matrixvalued random variable, i.e., the elements are stochastic variables.…”