The modal noise covariance matrix for an array of vector sensors

Abstract

A modal noise covariance matrix for an array of vector sensors is presented. It is assumed that the sensors measure pressure and gradients or velocities on three axes. The noise covariance matrix is obtained as a discrete modal sum. The derivation relies on the differentiation of the complex pressure field and the application of a set of Bessel function integrals. The modal representation is restricted to a horizontally stratified environment and assumes that the noise sources form a layer of uncorrelated monopoles. The resulting noise field is horizontally isotropic, but vertically non-isotropic. Particular attention is paid to the effect of the noise source intensity on the normalization of the covariance matrix and, consequently, to the effect of noise on the output of the array of vector sensors.