Acoustic error approximation due to Gouy phase in the sea

In order to estimate the statistical phase of underwater propagation for coherent acoustic systems, a calculation of background structure functions, based on wavespeeds, provides a wavefront distortion metric that excludes the phase due to focusing. In 1890, Gouy measured a phase change through the focus that differs for spherical vs cylindrical convergence by a factor of 2 from π/2. Statistics for the locations of the probable focus waist can use structure functions based on the measured sound speed profiles. Phase estimates are susceptible to errors in phase estimation unless results consider the Gouy phase while passing through focus waists. These foci may counteract or average with other errors of estimation, including scattering, type of spreading (cylindrical vs spherical foci), and reflections from the surface and bottom. Oceans have a sufficient range for the spatial derivatives of sound speed profiles to contribute persistently to foci that we show have coherence time and cross-sectional spatial (imaging) coherence. As an alternative, specular point theory can estimate deterministic pressure solutions. Convergence of these ray models that violate the stationary phase requires methods such as catastrophe theory to estimate the focal effects. Sommerfeld had an early comprehensive ray theory description that includes the Gouy phase. Using Flatté’s data, the foci are clearly time and length coherent. Statistically, the mutual coherence function for the Atlantic, Caribbean, and Gulf of Mexico regions shows that even distorted and out-of-phase convergence has full spatial coherence.