Imaging of seabed topography from the scattering of water waves

TL;DR

This paper addresses reconstructing seabed topography from water wave observations, formulating it as an inverse scattering problem, proposing simplifications, and validating a numerical inversion method with synthetic data.

Contribution

It introduces a tractable inverse scattering framework for seabed imaging from water waves, including a stability analysis and a fast numerical inversion technique.

Findings

Proved a conditional stability result for the inverse problem.

Developed a simple, fast numerical inversion method.

Validated the approach with synthetic data simulations.

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.