Space-Frequency Correlations in Multistatic Acoustic Reverberation Due to a Wind-Driven Sea Surface: Theoretical Results at Low Frequency
NAVAL RESEARCH LAB WASHINGTON DC ACOUSTICS SYSTEMS BRANCH
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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 Greens 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 sourcereceiver geometry. Sample sideband calculations are provided to illustrate the results, and system implications are considered.