When multiple scattering is negligible, classical single-scattering models proposed by Ingenito represent each waveguide mode as a superposition of up- and down-going plane waves. However, when the target is embedded in a strongly stratified waveguide with a depth-dependent sound-speed profile, the incident field in the target vicinity can no longer be approximated by a local plane wave, rendering the plane-wave incidence assumption underlying classical single-scattering models invalid. To address this limitation, this paper presents a generalized Fourier expansion (GFE) framework in which each waveguide mode is further expanded over a set of orthogonal basis functions and the corresponding scattering matrix is constructed under the resulting modal–angular representation, thereby enabling accurate reproduction of incident-field refraction and modal coupling effects during scattering. Numerical simulations verify the effectiveness of the proposed method. The proposed approach provides a computationally efficient correction to classical single-scattering models, enabling more accurate estimation and prediction of target scattering fields in waveguides with arbitrary sound-speed profiles.
Nie et al. (Fri,) studied this question.