Forward scattering from the sea surface and the van Cittert-Zernike theorem

The van Cittert-Zernike theorem is used to generate models for the spatial coherence of a sound field that has been forward scattered from the sea surface. The theorem relates the spatial coherence of an observed wave field to the distant source intensity distribution associated with this field. In this case, the sea surface upon ensonification is taken to be the source, and the sea-surface bistatic cross section corrected for transmission loss is taken as a surrogate for the source intensity distribution. Improvements in methodology for generating an estimate of the 2D autocorrelation function for sea surface waveheight variation, necessary to compute the bistatic cross section, are documented in the Appendix. Upon invoking certain approximations, simple expressions for the characteristic length scales of vertical, horizontal, and horizontal-longitudinal coherence, are derived from the theorem. The three coherence length scales identify a coherence volume for the spatial coherence of a sound field arriving via the surface bounce channel. Models for spatial coherence derived from the van Cittert-Zernike theorem without these approximations compare reasonably well with measurements of complex vertical coherence made at 8 kHz and 20 kHz in the East China Sea as part of the 2001 ASIAEX field program. In terms of the ASIAEX field geometries and sea-surface conditions, at frequency of 20 kHz the coherence volume is a vertical layer 0.5 m thick by 3 m in each of the two horizontal dimensions; at 8 kHz these dimensions increase by a factor of 2.5, representing the ratio of the two frequencies.