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Accurate prediction of shallow water flows relies on precise bottom topography data, yet direct bathymetric surveys are expensive and time-consuming. In contrast, remote sensing platforms such as radar or satellite altimetry provide…

Numerical Analysis · Mathematics 2026-03-13 Falko Ruppenthal , Dmitri Kuzmin

In this article, we propose an inverse technique that accurately reconstructs the ocean's density stratification profile simply from free surface elevation data. Satellite observations suggest that ocean surface contains the signature of…

Fluid Dynamics · Physics 2019-06-27 Subhajit Kar , Anirban Guha

Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming and expensive.…

Numerical Analysis · Mathematics 2024-06-03 Judith Angel , Jörn Behrens , Sebastian Götschel , Marten Hollm , Daniel Ruprecht , Robert Seifried

Bathymetry reconstruction is an important problem in various fields, including oceanography and environmental monitoring. This paper presents a Bayesian inference approach to reconstructing bathymetries from point measurements of the water…

Applications · Statistics 2026-04-22 Lars Stietz , Sebastian Götschel , Peter Schleper , Daniel Ruprecht

In this letter a new method based on modified self-organizing maps is presented for the reconstruction of deep ocean current velocities from surface information provided by satellites. This method takes advantage of local correlations in…

Atmospheric and Oceanic Physics · Physics 2017-05-24 Christopher Chapman , Anastase Alexandre Charantonis

In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…

Analysis of PDEs · Mathematics 2023-08-22 Vishal Vasan , Manisha , Didier Auroux

We propose a novel data-driven approach for high-resolution bathymetric reconstruction from sidescan. Sidescan sonar (SSS) intensities as a function of range do contain some information about the slope of the seabed. However, that…

Robotics · Computer Science 2022-06-17 Yiping Xie , Nils Bore , John Folkesson

Precise three-dimensional (3D) reconstruction of wave free surfaces and associated velocity fields is essential for developing a comprehensive understanding of ocean physics. To address the high computational cost of dense visual…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Jiabin Liu , Zihao Zhou , Jialei Yan , Anxin Guo , Alvise Benetazzo , Hui Li

The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…

Fluid Dynamics · Physics 2017-11-22 Philippe Bonneton , David Lannes

Accurate mapping of ocean bathymetry is a multi-faceted process, needed for safe and efficient navigation on shipping routes and for predicting tsunami waves. Currently available bathymetry data does not always provide the resolution to…

Fluid Dynamics · Physics 2020-03-12 N. K. -R. Kevlahan , R. A. Khan

This paper investigates the geometric inverse problem of recovering the bottom shape from surface measurements of water waves. Using the general water-waves system on a bounded subdomain of the fluid domain, we address this inverse problem,…

Analysis of PDEs · Mathematics 2026-04-08 Noureddine Lamsahel , Lionel Rosier

Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed,…

Fluid Dynamics · Physics 2015-03-02 Robin Ming Chen , Samuel Walsh

We present a method for reconstructing two-dimensional velocity fields at specified length scales using observational data from tracer particles in a flow, without the need for interpolation or smoothing. The algorithm, adapted from…

Fluid Dynamics · Physics 2010-04-28 Douglas H. Kelley , Nicholas T. Ouellette

Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath.…

Computational Engineering, Finance, and Science · Computer Science 2020-12-23 Ajinkya Kadu , Tristan van Leeuwen , Wim A. Mulder

We propose a fast, stable, and direct analytic method to detect underwater channel topography from surface wave measurements, based on one-dimensional shallow water equations. The technique requires knowledge of the free surface and its…

Mathematical Physics · Physics 2025-10-07 Lamsahel Noureddine , Carole Rosier

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…

Analysis of PDEs · Mathematics 2026-03-30 Adrian Kirkeby

A model based on a convolutional neural network (CNN) is designed to reconstruct the three-dimensional turbulent flows beneath a free surface using surface measurements, including the surface elevation and surface velocity. Trained on…

Fluid Dynamics · Physics 2023-04-12 Anqing Xuan , Lian Shen

Reconstructions of sea level prior to the satellite altimeter era are usually derived from tide gauge records; however most algorithms for this assume that modes of sea level variability are stationary which is not true over several…

Data Structures and Algorithms · Computer Science 2020-09-04 Alina Nitzke , Benjamin Niedermann , Luciana Fenoglio-Marc , Jürgen Kusche , Jan-Henrik Haunert

A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the…

Pattern Formation and Solitons · Physics 2011-12-09 Katie Oliveras , Vishal Vasan , Bernard Deconinck , Diane Henderson

Recovering 3D geometry of underwater scenes is challenging because of non-linear refraction of light at the water-air interface caused by the camera housing. We present a light field-based approach that leverages properties of angular…

Computer Vision and Pattern Recognition · Computer Science 2022-04-06 Yuqi Ding , Zhang Chen , Yu Ji , Jingyi Yu , Jinwei Ye
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