The bathymetry is uniquely determined from single-time surface wave data with logarithmic stability under a local fatness condition on bottom profiles.
Lannes.The water-waves problem: mathematical analysis and asymptotics, volume 188
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Uniqueness and stability in bottom detection through surface measurements of water waves
The bathymetry is uniquely determined from single-time surface wave data with logarithmic stability under a local fatness condition on bottom profiles.