A full-field perturbation approach to scattering and reverberation in range-dependent environments with rough interfaces

A perturbation approach to roughness scattering and reverberation in range-dependent environments is developed treating each interface as a superposition of a smooth reference interface, which may include large-scale deterministic features (such as bathymetry changes), and small compared to the acoustic wavelength vertical deviations from this interface that are considered as random roughness perturbations. The reference interface is assumed to be smooth enough to allow analytic or numerical solution for the field in the vicinity of this interface that can then be used in perturbation theory. Expressions for both the reverberation field and average reverberation intensity in a general case of an arbitrary number of rough interfaces are obtained in a form convenient for numerical simulations. In the case of long-range ocean reverberation, several approximations for these expressions are developed, relevant to various environmental scenarios and different types of interfaces: sea-surface, water-sediment interface, buried sediment interfaces, and bottom basement. The results are presented in a simple form and provide a direct relationship of the reverberation intensity with three critical characteristics defined at each interface: (1) local spectrum of roughness, (2) local contrast of acoustic parameters, and (3) two-way full-field transmission intensity calculated taking into account only large-scale changes of the environment.