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Related papers: Inverse Random Source Scattering for Elastic Waves

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We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…

Numerical Analysis · Mathematics 2018-03-14 Xia Ji , Xiaodong Liu , Yingxia Xi

We study the direct and an inverse source problem for the radiative transfer equation arising in optical molecular imaging. We show that for generic absorption and scattering coefficients, the direct problem is well-posed and the inverse…

Analysis of PDEs · Mathematics 2008-03-31 Plamen Stefanov , Gunther Uhlmann

This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…

Numerical Analysis · Mathematics 2022-03-14 Lu Zhao , Heping Dong , Fuming Ma

This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…

Analysis of PDEs · Mathematics 2020-02-21 Peijun Li , Xu Wang

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source…

Numerical Analysis · Mathematics 2020-02-14 Vo Anh Khoa , Michael Victor Klibanov , Loc Hoang Nguyen

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…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…

Analysis of PDEs · Mathematics 2020-02-06 Guanghui Hu , Yikan Liu , Masahiro Yamamoto

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

Source footprints represent an inherent problem to full-waveform inversion (FWI). They are caused by the high data sensitivity to the model parameters in the vicinity of the seismic sources and can be exacerbated by source-related errors in…

Geophysics · Physics 2025-06-12 Milad Bader , Robert G. Clapp , Kurt T. Nihei , Biondo Biondi

To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…

Numerical Analysis · Mathematics 2025-07-11 Yunqing Huang , Shihan Zhang

This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…

Analysis of PDEs · Mathematics 2024-10-15 Peijun Li , Zhenqian Li , Ying Liang

This paper investigates the inverse scattering problem of time-harmonic plane waves incident on a perfectly reflecting random periodic structure. To simulate random perturbations arising from manufacturing defects and surface wear in…

Numerical Analysis · Mathematics 2025-07-29 Zhiqi Sun , Yiwen Lin

We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…

Analysis of PDEs · Mathematics 2023-04-25 Shiqi Ma , Leyter Potenciano-Machado , Mikko Salo

Inverse scattering problems of the reconstructions of physical properties of a medium from boundary measurements are substantially challenging ones. This work aims to verify the performance on experimental data of a newly developed…

Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…

Statistics Theory · Mathematics 2015-12-08 Marco A. Iglesias , Kui Lin , Shuai Lu , Andrew M. Stuart

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain…

Analysis of PDEs · Mathematics 2018-04-04 Gang Bao , Guanghui Hu , Yavar Kian , Tao Yin

In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the…

Analysis of PDEs · Mathematics 2014-01-15 Abeer Aldoghaither , Taous-Meriem Laleg-Kirati , Da-Yan Liu

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

We consider a smooth Riemannian metric tensor $g$ on $\R^n$ and study the stochastic wave equation for the Laplace-Beltrami operator $\p_t^2 u - \Delta_g u = F$. Here, $F=F(t,x,\omega)$ is a random source that has white noise distribution…

Analysis of PDEs · Mathematics 2015-06-17 Tapio Helin , Matti Lassas , Lauri Oksanen