Zamorano-Aliaga, SSZamorano-AliagaLecaros, R.R.LecarosLopez-Rios, J.J.Lopez-RiosOrtega, J. H.J. H.Ortega2025-04-232025-04-23202010.1088/1361-6420/abafeehttps://sic.vriic.usach.cl/entities/publication/175ac296-0a51-4bd5-b2b0-428bbbab5deeIn this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water-waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water-waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation.en-USfree boundary value problemswater-waves equationsgeometric inverse problemsstabilitysize estimatenon-local operatorshttps://doi.org/10.1088/1361-6420/abafee