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

Abstract

A normal-mode scattering formulation that assumes a finite spatial correlation length in the distribution of scattering features is used to compute single-frequency bottom reverberation for bistatic and monostatic scattering geometries in a shallow water and deep water environment. Spatial correlation of the scattering features allows the superposition of modes scattered within each spatially correlated region and produces diffraction in the scattered field that is not predicted in the limit of a zero spatial correlation length (point scattering). For bistatic scattering geometries, the scattered field computed as a function of scattering location in the horizontal plane exhibits a pattern of diffractive maxima and minima for nonzero spatial correlation lengths. The spatial details of the diffraction pattern and its influence on the scattered energy depend on the frequency and spatial correlation length and can result in a significant reduction in the predicted levels of received reverberation. The greatest sensitivity to finite correlation effects occurs for monostatic scattering geometries because the strongest diffractive effects occur in the backscattering direction. The effects of including modal interference in the incident and scattered field propagation are also examined in this paper. The inclusion of modal interference in the propagating fields imposes an interference pattern on the spatial structure of the scattered field in the horizontal plane, and can cause the temporal dependence of the reverberated return to oscillate about the levels of return predicted when modal interference in the propagating fields is neglected. In agreement with previously published results for bottom backscattering, the effects of including modal interference in the propagating fields were found to be significant for deep water environments that exhibit convergent zone propagation and to be of limited importance for shallow water environments in which the energy incident on the bottom is characterized by a large number of multipaths. The present work includes results which show that the effects of including modal interference in the propagating fields can be important for shallow water environments that exhibit significant bottom penetration.