Spatial Correlation in Arbitrary Noise Fields

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 wavenumber-frequency spectrum. The approach is particularly attractive when the field can be adequately represented by a relatively small number of harmonics. Both two- and three-dimensional fields are considered. [This work was performed at the University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego, California 92132.]