Noise Covariance and Vertical Directivity in a Deep Ocean

Abstract

Under the assumption that deep-water ocean noise is a superposition of uncorrelated plane waves, the covariance can be expressed in terms of the noise directivity. We propose a simple directivity function that agrees with experimental results and use it to study the covariance for the case of vertical receiving points. We investigate covariance versus spacing for zero time delay and various directivities and bandwidths. When almost all of the noise arrives from the horizontal, the zero-delay covariance is always positive; when most of the noise arrives from overhead, it is negative for some spacings. We present contours of constant covariance as a function of spacing and time delay for various directivities and a narrow frequency band. We also examine covariance for single-frequency noise. Vertical noise with steering towards the vertical and horizontal noise with steering towards the horizontal are found to give the same covariance values. We examine maximum covariance over time delay and also that delay for which maximum covariance occurs. Numerous comparisons are made between our predictions and published experimental results. Finally, covariance for horizontal receiving points is considered.