Most array-processing methods require knowledge of the correlation structur
e of the noise. While such information may sometimes be obtained from measu
rements made when no sources are present, this may not always be possible.
Furthermore, measurements made in-situ can hardly be used to analyze system
performance before deployment. The development of models of the correlatio
n structure under various environmental assumptions is therefore very impor
tant. In this paper, we obtain integral and closed form expressions for the
auto- and cross-correlations between the components of an acoustic vector
sensor (AVS) for a wideband-noise field, under the following assumptions co
ncerning its spatial distribution: 1) azimuthal independence; 2) azimuthal
independence and elevational symmetry; and 3) spherical isotropy. We also d
erive expressions for the cross-covariances between all components of two s
patially displaced AVSs in a narrowband-noise field under the same assumpti
ons. These results can be used to determine the noise-covariance matrix of
an array of acoustic vector sensors in ambient noise. We apply them to a un
iform linear AVS array to asses its beamforming capabilities and localizati
on accuracy, via the Cramer-Rao bound, in isotropic and anisotropic noise.