Covariance of Surface-Generated Noise in a Deep Ocean

Abstract

The space-time covariance of surface-generated noise is investigated using a model that assumes that the covariance of the pressure is specified for all pairs of points on a plane and that the acoustic pressure satisfies a wave equation with constant coefficients in the semiinfinite region below this plane. It is shown that one may imagine the noise to be generated by a plane distribution of statistically dependent dipole sources. Alternatively, one may imagine dependent omnidirectional sources if the surface covariance of the normal derivative of the pressure is specified. A second noise model employs ray theory and supposes that the noise is generated by a plane distribution of statistically independent directional point sources. The covariance functions predicted by the two models at points in deep water are compared and are shown to be equal when the covariance on the plane of the first model is properly related to the source directionality in the second model. This relationship allows us to specify a surface covariance function for a given source directionality and conversely. Surface covariance functions corresponding to the common source directionalities (cos)m are investigated, and directionality is examined for Gaussian surface covariance.