Space-Frequency Correlations in Multistatic Acoustic Reverberation Due to a Wind-Driven Sea Surface: Theoretical Results at Low Frequency

Analytic methods are used to assess the impact of the two-dimensional (2-D) wave spectrum of a wind-driven sea on multistatic low-frequency surface reverberation. The problem is initially posed with a narrowband source beneath a time-dependent sea surface in an ocean that can have depth dependence and bottom layering. The propagated signal interacts with the slower moving surface waves to produce a narrowband scattered field. The small-waveheight approximation is applied to a deterministic sea surface to express the scattered field in terms of the surface elevation and the Green's function for a perfectly calm sea. Randomness is then incorporated into the surface description, and its impact is formulated for an arbitrarily placed pair of receivers. The three-dimensional (3-D) cross-spectral density (CSD) of the reverberation is reduced to a sum of baseband and sideband terms formulated as multiple mean-sea-surface integrals. The sideband result is identified as an active scattering generalization of the van Cittert-Zernike theorem from partial coherence theory. The focus is then narrowed to shallow deployment in a homogeneous ocean, and stationary-phase estimates are used to produce analytic expressions for the CSD. The zero-Doppler component and Bragg-Doppler sidebands are expressed in terms of the power spectrum of the source, the power spectrum and directionality of the surface waves, and the multistatic source/receiver geometry. Sample sideband calculations are provided to illustrate the results, and system implications are considered.