Doppler sidebands in the cross-spectral density of narrow-band reverberation from a dynamic sea surface

Analytic methods are used to formulate the impact of a random dynamic sea surface on the space-frequency characteristics of bistatic reverberation. A narrow-band point source is positioned beneath the time-dependent surface of a range-independent ocean. The small-waveheight perturbative approximation is invoked, and attention is focused on the Doppler sideband contributions to the reverberation cross-spectral density for an arbitrarily placed receiver pair. The new expression that results is identified as an active scattering generalization of the van Cittert-Zernike theorem from classical partial coherence theory. This work is the first to explicitly predict the sideband structure in the cross-spectral density of the field scattered from a realistic moving sea surface. A numerical example is presented for a shallow source and shallow receivers in a homogeneous ocean.