Related papers: Inverse problem for the nonlinear long wave runup …
This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of…
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of shallow water theory. The wave shoaling in bays, when the depth varies smoothly along the channel axis,…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
New data was obtained for a frequency band that had not been so well-studied for sea surface probing applications before. During the described 2-weeks sea experiment 1-3 kHz tonal pulses were emitted from a platform, located on the northern…
In this article we study the problem of recovering the initial data of the two-dimensional wave equation from Neumann measurements on a convex domain with smooth boundary in the plane. We derive an explicit inversion formula of a so-called…
The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the…
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…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
We study an inverse initial-data problem for a nonlinear Schr\"odinger equation in which the initial wave field is reconstructed from lateral measurements. Our approach combines a Legendre-polynomial-exponential-time dimensional reduction…
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem,…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
Modeling ocean surface waves under complex ocean current conditions is of crucial importance to many naval applications. For example, traveling ships and underwater vehicles generate spatially heterogeneous currents behind them through…
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…
Ocean waves are complex and often turbulent. While most ocean wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much…
We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…
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…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…