Normal mode extraction using sparse Bayesian learning in shallow water

Abstract

The low-frequency signals propagating in the shallow-water waveguides are dispersive. They are composed of several normal modes according to the normal mode theory. For the vertical array data, the horizontal wavenumbers and the associated multi-frequency modal depth functions were estimated using block sparse Bayesian learning (Niu et al., JASA 2020), while a priori knowledge of sea bottom, moving source, and source locations is not needed. For the impulsive or known-form signals received by one hydrophone, the sparse Bayesian learning (SBL) approach can be also used to extract the modes (Niu et al., JASA 2021). It uses the approximate modal dispersion relation, connecting the horizontal wavenumbers (phase velocities) for multiple frequencies, to build the dictionary matrix for SBL. Different from warping transforms based on the group slowness (or group speed) dispersion curves, mode separation using SBL is performed in frequency domain based on the phase speed (or equivalently horizontal wavenumbers) dispersion relation. 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.