Related papers: Waveform inversion with a data driven estimate of …
Full-waveform inversion is a cutting-edge methodology for recovering high-resolution subsurface models. However, one of the main conventional full-waveform optimization problems challenges is cycle-skipping, usually leading us to an…
In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is given. It is proved that there is an…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties.…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
The paper is devoted to the presentation of the non-spectral methods of analysis of the natural measurements of the internal gravity waves in the ocean with the purpose to determine characteristics of the wave-trains composing the measured…
We present a wave-equation inversion method that inverts skeletonized data for the subsurface velocity model. The skeletonized representation of the seismic traces consists of the low-rank latent-space variables predicted by a well-trained…
This paper is concerned with an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite time interval. The unknown obstacle is assumed to be sound-soft one. The governing equation of the wave is…
This paper defines an angular velocity for time-dependent functions on the sphere, and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular…
We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography,…
In the workflow of Full-Waveform Inversion (FWI), we often tune the parameters of the inversion to help us avoid cycle skipping and obtain high resolution models. For example, typically start by using objective functions that avoid cycle…
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…
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…
Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving…
We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…