Stochastic propagation of the mutual coherence function in the deep ocean

We present a computer-implemented algorithm for underwater acoustic propagation based upon a theoretical formulation which simultaneously incorporates probabilistic random volume scattering and deterministic refraction and diffraction. The model, called the Combined Effects Model, adds the vertical scattering caused by the random inhomogeneities in the ocean to the multipath features produced by the mean sound-speed structure. The analysis is based on the two-point coherence function which describes the acoustic field in terms of position and the direction of energy flux, and as such is directly related to the field as seen by an acoustic array. Basic to the theoretical formulation is a locally quadratic approximation on the index of refraction. Although multipath interference effects (which are apparent when the coherence function is calculated directly from a propagation algorithm) are lost with this assumption, estimates for the output of a vertical array are not significantly affected. The incorporation of random volume scatter with realistic background sound-speed structure results in the distribution of arriving energy being smoothed over vertical arrival angles. This effect depends on the magnitude of the strength of the fluctuating field. The multipath structure can still exist for over 100 km, for signals below a few hundred Hz, in the presence of a typical scattering field or can deteriorate in the first few kilometers in the presence of strong scatter.