Imaging of seabed topography from the scattering of water waves

2024/06/09 by Adrian Kirkeby, Kirkeby, Adrian
Earth and Planetary Sciences · #35J05 #35R30 #65J20 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Underwater Acoustics Research

paper · pdf · doi:10.48550/arxiv.2406.05878

openalex publication_date 2024/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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