A linear sampling method for near-field inverse problems in elastodynamics

  title={A linear sampling method for near-field inverse problems in elastodynamics},
  author={S. Nintcheu Fata and Bojan B. Guzina},
  journal={Inverse Problems},
The problem of reconstructing underground obstacles from near-field, surface seismic measurements is investigated within the framework of a linear sampling method. Although the latter approach has been the subject of mounting attention in inverse acoustics dealing with far-field wave patterns in infinite domains, there have apparently not been any attempts to apply this new method to the interpretation of near-field elastic wave forms such as those relevant to the detection of subterranean… 
A linear sampling method for the inverse transmission problem in near-field elastodynamics
Elastic-wave shape reconstruction of buried penetrable scatterers from near-field surface measurements is examined within the framework of the linear sampling method. The proposed inversion scheme is
A linear sampling method for inverse scattering stodynamics elastodynamics problems in the time domain elastodynamics problems in the time domain
This paper, deals with detecting and identifying unknown scatters (e.g., obstacles) in an elastic background solid through the use of elastic illuminating waves. In this regards, the Linear Sampling
A linear sampling approach to inverse elastic scattering in piecewise-homogeneous domains
The focus of this study is a 3D inverse scattering problem underlying non-invasive reconstruction of piecewise-homogeneous (PH) defects in a layered semi-infinite solid from near-field, surface
Near-field imaging of small perturbed obstacles for elastic waves
Consider an elastically rigid obstacle which is buried in a homogeneous and isotropic elastic background medium. The obstacle is illuminated by an arbitrary time-harmonic elastic incident wave. This
Elastic Scatterer Reconstruction via the Adjoint Sampling Method
It is shown that the adjoint statement elevates the performance of the linear sampling method when dealing with scarce illuminating sources and that a combined use of the existing formulation together with its adjoint counterpart represents an effective tool for exposing an undersam...
The factorization method in inverse elastic scattering from penetrable bodies
The present work is concerned with the extension of the factorization method to the inverse elastic scattering problem by penetrable isotropic bodies embedded in an isotropic host environment for
The linear sampling method for the transmission problem in 2D anisotropic elasticity
In the present work, the problem of reconstructing the shape of two-dimensional elastic anisotropic inclusions embedded in isotropic media is investigated within the framework of the linear sampling


On the stress-wave imaging of cavities in a semi-infinite solid
Computational framework for the BIE solution to inverse scattering problems in elastodynamics
AbstractThe focus of this paper is a computational platform for the non-intrusive, active seismic imaging of subterranean openings by means of an elastodynamic boundary integral equation (BIE)
Topological derivative for the inverse scattering of elastic waves
To establish an alternative analytical framework for the elastic-wave imaging of underground cavities, the focus of this study is an extension of the concept of topological derivative, rooted in
The linear sampling method for the transmission problem in three-dimensional linear elasticity
In this paper the sampling method for the shape reconstruction of a penetrable scatterer in three-dimensional linear elasticity is examined. We formulate the governing differential equations of the
Summary A rigorous treatment of the singular visco-elastodynamic solutions for a semi-infinite multilayered solid is presented. It is shown explicitly via an asymptotic analysis of the propagator
A simple method for solving inverse scattering problems in the resonance region
This paper is concerned with the development of an inversion scheme for two-dimensional inverse scattering problems in the resonance region which does not use nonlinear optimization methods and is
On the far‐field operator in elastic obstacle scattering
We investigate the far-field operator for the scattering of time-harmonic elastic plane waves by either a rigid body, a cavity, or an absorbing obstacle. Extending results of Colton & Kress for
A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems
A method for solving the inverse scattering problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods.
An Introduction to the Mathematical Theory of Inverse Problems
  • A. Kirsch
  • Mathematics
    Applied Mathematical Sciences
  • 2021
This book introduces the reader to the area of inverse problems. A relatively new branch of Applied Mathematics, the study of inverse problems is of vital interest to many areas of science and