  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.
