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

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.