Modal wavenumber estimation using a Bayesian compressed sensing algorithm

Abstract

In shallow water, low-frequency acoustic propagation is described by modal theory. In this context, the environment acts as a dispersive waveguide, and the geoacoustic properties of the seabed can be inferred from the modal wavenumbers. When considering horizontal aperture (using a horizontal array or a towed source), wavenumber estimation is a well-known problem, equivalent to spectral analysis. In this paper, wavenumber estimation is revisited using Compressed Sensing (CS). Our method benefits from two strong physical hypotheses. Only a few modes are propagating so that the wavenumber spectrum is sparse. Moreover, if the source is broadband, the wavenumbers can be related from one frequency to the next using a general dispersion relationship. Our method resorts to a state-of-the-art Bayesian algorithm exploiting a Bernoulli-Gaussian model. The latter, well-suited to the sparse representations, makes possible a natural integration of the prior dispersion information through a wise choice of the Bernoulli parameters. The whole methodology is assessed on simulated data and successfully applied on marine data.