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We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…

Analysis of PDEs · Mathematics 2020-09-10 Florian Faucher , Otmar Scherzer , Hélène Barucq

In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…

Analysis of PDEs · Mathematics 2015-12-08 Pengbin Feng , E. T. Karimov

We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated from applications in photoacoustic tomography when one seeks…

Analysis of PDEs · Mathematics 2024-08-26 Shitao Liu , Gunther Uhlmann , Yang Yang

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

Numerical Analysis · Mathematics 2015-05-28 Carlos Borges , Leslie Greengard

The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…

Numerical Analysis · Mathematics 2021-01-05 Aleksey Alekseev , Alexander Bondarev

This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of…

Numerical Analysis · Mathematics 2015-06-19 Thorsten Hohage , Frederic Weidling

In this paper, we study an inverse problem for identifying the initial value in a space-time fractional diffusion equation from the final time data. We show the identifiability of this inverse problem by proving the existence of its unique…

Analysis of PDEs · Mathematics 2024-12-10 Mohamed BenSalah , Salih Tatar

In this paper, we propose a direct probing method for the inverse problem based on the Eikonal equation. For the Eikonal equation with a point source, the viscosity solution represents the least travel time of wave fields from the source to…

Analysis of PDEs · Mathematics 2023-02-21 Kazufumi Ito , Ying Liang

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…

Numerical Analysis · Mathematics 2023-07-06 Yan Chang , Yukun Guo , Tao Yin , Yue Zhao

The omega-square hypothesis assumes that the ground displacement u(t) in the far-field zone decays as the inverse square of frequency in the range ~1-30 Hz. This empirical fact remains theoretically unjustified. Our analysis of the problem…

Geophysics · Physics 2016-04-21 G. Molchan

A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A…

Numerical Analysis · Mathematics 2025-02-11 Thi Thanh Mai Ta , Quang Huy Nguyen , Dinh Nho Hào

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…

Mathematical Physics · Physics 2015-06-12 Kirk D. Blazek , Christiaan C. Stolk , William W. Symes

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem…

Numerical Analysis · Mathematics 2024-04-12 Kamal Aghazade , Ali Gholami , Hossein S. Aghamiry , Hamid Reza Siahkoohi

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…

Analysis of PDEs · Mathematics 2019-06-07 Xia Ji , Xiaodong Liu

In seismic exploration, sources and measurements of seismic waves on the surface are used to determine model parameters representing geophysical properties of the earth. Full-waveform inversion (FWI) is a nonlinear seismic inverse technique…

Numerical Analysis · Mathematics 2019-02-05 Yunan Yang

This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…

Analysis of PDEs · Mathematics 2021-06-16 Yavar Kian

We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…

Analysis of PDEs · Mathematics 2022-10-13 Peijun Li , Xu Wang

The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…

Analysis of PDEs · Mathematics 2014-01-03 Sebastian Acosta , Sum Chow , James Taylor , Vianey Villamizar

The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…

Analysis of PDEs · Mathematics 2015-05-28 Mark Hubenthal

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…