Relation between waveguide and nonwaveguide (half-space) scattering from a rough interface

A formal solution of the scattering field from a rough interface has been derived. Under the Bass perturbation theory, both waveguide and nonwaveguide (half-space) scattering from a rough interface (the sea bottom) can be calculated analytically. By using an identical definition of ‘‘scattering coefficient,’’ a relation between the waveguide scattering (the modal S matrix) Mljs and the nonwaveguide scattering (conventional plane-wave scattering) coefficient ms has been found: Mljs= (2π)2ms/‖V(θl)V(θj)‖, where V(θl) and V(θj) represent the reflection coefficients of the plane interface for the modal incident angles θl and θj, respectively. Consequently, based on this relation, the ms data measured in the conventional sense (half-space) can be bridged into a shallow water reverberation prediction or vice versa.