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The ocean noise coherence matrix and its rank.

An expression for the cross-spectral density matrix of ocean noise naturally separates into a Toeplitz part and a Hankel part [Harrison (2017). J. Acoust. Soc. Am. 141, 2812-2820]. The Toeplitz part is shown to be substantially rank-deficient for all practical acoustic cases, which has implications for adaptive beam forming. The influence of the Hankel part on passive fathometry is investigated, and its effect on adaptive beam forming is shown to be weak or negligible. Numerical demonstrations of these findings including beam patterns and eigenvalue spectra derived via circulant matrices are given based on a simple half-space with a Rayleigh reflection coefficient. Two sets of experimental data are revisited in this context, deriving eigenvalue spectra, beam patterns, and passive fathometry impulse responses with conventional and adaptive processing and differing amounts of averaging. The solution to a long-standing puzzle of processing inconsistency is suggested.