Spatial correlation in arbitrary noise fields with application to ambient sea noise

Explicit expressions are developed for the cross-spectral density between pairs of sensors and the wavenumber-frequency spectrum projected onto the line joining these sensors, when they are placed in arbitrary positions in noise fields which are described by an arbitrary directional distribution of uncorrelated plane waves. The approach is to expand the directional distribution in spatial harmonics. Each harmonic leads to a corresponding term, with the same coefficient, in series representations for the cross-spectral density function and the wave-number-frequency spectrum. The approach particularly attractive when the field can be adquately represented by a relatively small number of harmonics. Both two- and three-dimensional fields are considered. The approach is applied to the vertical directionality of ambient sea noise and is related to some existing models of ambient sea noise. Some new models are presented. Results are compared with reported experimental data and found to be in good agreement over a wide frequency range.