Imaging of seabed topography from the scattering of water waves

Abstract

We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic dependence of the forward and inverse problem. Moreover, we propose a useful model simplification that makes the inverse problem much more tractable. As water waves allow for observations of the full wave field, it differs quite a lot from the classical inverse scattering problems, and we utilize this to prove a conditional stability result for the inverse problem. Last, we develop a simple and fast numerical inversion method and test it on synthetic data to verify our analysis.