Mode separation with one hydrophone in shallow water: A sparse Bayesian learning approach based on phase speed

An approach of broadband mode separation in shallow water is proposed using phase speed extracted from one hydrophone and solved with sparse Bayesian learning (SBL). The approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, is used to build the dictionary matrix for SBL. Given a multi-frequency pressure vector on one hydrophone, SBL estimates a set of sparse coefficients for a large number of atoms in the dictionary. With the estimated coefficients and corresponding atoms, the separated normal modes are retrieved. The presented method can be used for impulsive or known-form signals in a shallow-water environment while no bottom information is required. The simulation results demonstrate that the proposed approach is adapted to the environment where both the reflected and refracted modes coexist, whereas the performance of the time warping transformation degrades significantly in this scenario.