Modal formulation and paraxial approximation for acoustic wave propagation in waveguides with surface perturbations

Abstract

We propose a modal approach developed in the framework of the paraxial approximation to investigate the effects of deterministic surface perturbations in a planar waveguide. In the first part, the sensitivity of the modal amplitudes is theoretically formulated for a three-dimensional perturbation at the air–water interface. When applied to a broadband ultrasonic signal in a laboratory tank experiment, this approach results in travel-time and amplitude fluctuations that are successfully compared to experimental data recorded between two vertical source–receiver arrays that span the ultrasonic waveguide. The nonlinear shape of the modal amplitude fluctuations is of particular interest and is due to the three-dimensional nature of the surface perturbation. In the second part, a time-harmonic inversion method is built in the paraxial single-scattering approximation to image the dynamic surface perturbation from the modal transmission matrix between two source–receiver arrays. Again, the inversion results for capillary-gravity surface perturbations are successfully compared to similar inversions performed from experimental data processed with a complete set of eigenbeams extracted between the two arrays.