Journal ArticleDOI
A method of solving the inverse scattering problem for the wave equation
TLDR
In this article, the problem of finding the variable characteristics of an inhomogeneous layer from the scattered field when the plane wave incident on the layer is unknown, is considered, and equations are obtained whereby both the wave shape and the parameters of the medium can be found.Abstract:
The problem of finding the variable characteristics of an inhomogeneous layer from the scattered field when the plane wave incident on the layer is unknown, is considered Equations are obtained whereby both the wave shape and the parameters of the medium can be found. The equations are solved by an iterative regularization method.read more
Citations
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Journal ArticleDOI
On local solvability of inverse dissipative scattering problems
TL;DR: In this paper, a necessary and sufficient condition of solvability of the inverse dissipative scattering problem with data given on a finite time interval was established, based on a step-by-step split method for numerical solution of a system of the Gel'fand - Levitan integral equations under nonlocal boundary conditions.
Journal ArticleDOI
Solving the Inverse Generalized Problem of Vertical Seismic Profiling
A. V. Baev,N. V. Kutsenko +1 more
TL;DR: In this article, the authors investigated whether the wave propagation problem in a vertically nonhomogeneous medium is well-posed and showed that the regular part of the solution is an L 2 function and the inverse problem is thus reducible to minimizing the error functional.
Journal ArticleDOI
Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media
TL;DR: In this article, a three-dimensional inverse scattering problem for the acoustic wave equation is studied and a necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law.
Journal ArticleDOI
On t-local solvability of inverse scattering problems in two-dimensional layered media
TL;DR: In this article, the solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method.
Journal ArticleDOI
Imaging of Layered Media in Inverse Scattering Problems for an Acoustic Wave Equation
TL;DR: In this article, a necessary and sufficient condition for the unique solvability of two-dimensional inverse scattering problems in the form of the law of energy conservation has been established, and it is proved that for each pulse oscillation source located on the boundary of a half-plane, the energy flow of the scattered waves is less than the energy flux of waves propagating from the boundary.
References
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Book
Approximate Solution of Operator Equations
TL;DR: The theory of approximate methods for solving mathematical problems has been studied extensively in the literature, see as discussed by the authors for a survey of some of the most important results in functional analysis. But the authors' aim has not been to give an exhaustive account, even of the principal known results.
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Identification of a Dissipation Coefficient by a Variational Method
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