Finite correlation and coherent propagation effects in the normal mode formulation of bottom reverberation

A normal mode bottom scattering formulation is presented that includes superposition effects historically omitted in normal mode reverberation treatments. The Bass and Born approximations are used to derive a normal mode expression for the field scattered by random deviations in the bottom surface height, combined with variations in the sediment and substrate density and sound speed. The first superposition effect examined is diffraction introduced by using spatially correlated scattering features rather than the typical point-scattering description. Spatial correlation of the bottom features causes superposition of the fields scattered within each correlated region and produces diffraction that is not predicted in the point-scattering limit. For a bistatic scattering geometry, the scattered field computed assuming correlated scattering features exhibits a series of diffractive maxima and minima as a function of azimuthal scattering angle in the horizontal plane. The central maximum corresponds to forward scattering; the highest order diffractive effects occur for scattering in the back direction. The diffractive effects, which depend on the environment, frequency and spatial correlation length, can cause a substantial reduction in the time-dependent levels of reverberated return in comparison with point-scattering predictions. The second superposition effect examined is caused by the constructive and destructive interference of modes in the incident and scattered field propagation. Modal interference in the propagating fields imposes an interference pattern on the spatial structure of the scattered energy in the horizontal plane and can cause the time-dependent levels of reverberation to oscillate about the levels predicted when the modal interference is neglected. The effects of modal interference in the propagating fields are highly dependent on the scattering geometry but also depend on the environment. The most significant effects occur for monostatic scattering geometries in environments that exhibit convergence zone propagation; the effects can also be important for shallow water waveguides in which the critical angle for bottom penetration is small. The combination of spatially correlated bottom features and modal interference in the propagating fields results in a superposition of the individual effects.