Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem

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Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem. / Kabanikhin, Sergey I.; Novikov, Nikita S.; Shishlenin, Maxim A.

In: Journal of Physics: Conference Series, Vol. 2092, No. 1, 012022, 20.12.2021.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{178632cddeca442d8edbb701323b6b66,

title = "Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem",

abstract = "In this article we propose the numerical solution of the one dimensional inverse coefficient problem for seismic equation. We use a dynamical version of Gelfand-Levitan-Krein approach for reducing a nonlinear inverse problem for recovering the shear wave's velocity and the density of the medium to two sequences of the linear integral equations. We propose numerical algorithm for solving these equations based on a fast inversion of a Toeplitz matrix. The proposed numerical methods base on the structure of the problem and therefore improve the efficiency of the algorithms, compared with standard approaches. We present numerical results for solving considered integral equations.",

author = "Kabanikhin, {Sergey I.} and Novikov, {Nikita S.} and Shishlenin, {Maxim A.}",

note = "Funding Information: The research of N.S. Novikov was supported by RFBR, project number 18-31-00409. Publisher Copyright: {\textcopyright} 2021 Institute of Physics Publishing. All rights reserved.; 11th International Scientific Conference and Young Scientist School on Theory and Computational Methods for Inverse and Ill-posed Problems ; Conference date: 26-08-2019 Through 04-09-2019",

year = "2021",

month = dec,

day = "20",

doi = "10.1088/1742-6596/2092/1/012022",

language = "English",

volume = "2092",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem

AU - Kabanikhin, Sergey I.

AU - Novikov, Nikita S.

AU - Shishlenin, Maxim A.

PY - 2021/12/20

Y1 - 2021/12/20

N2 - In this article we propose the numerical solution of the one dimensional inverse coefficient problem for seismic equation. We use a dynamical version of Gelfand-Levitan-Krein approach for reducing a nonlinear inverse problem for recovering the shear wave's velocity and the density of the medium to two sequences of the linear integral equations. We propose numerical algorithm for solving these equations based on a fast inversion of a Toeplitz matrix. The proposed numerical methods base on the structure of the problem and therefore improve the efficiency of the algorithms, compared with standard approaches. We present numerical results for solving considered integral equations.

AB - In this article we propose the numerical solution of the one dimensional inverse coefficient problem for seismic equation. We use a dynamical version of Gelfand-Levitan-Krein approach for reducing a nonlinear inverse problem for recovering the shear wave's velocity and the density of the medium to two sequences of the linear integral equations. We propose numerical algorithm for solving these equations based on a fast inversion of a Toeplitz matrix. The proposed numerical methods base on the structure of the problem and therefore improve the efficiency of the algorithms, compared with standard approaches. We present numerical results for solving considered integral equations.

UR - http://www.scopus.com/inward/record.url?scp=85124040575&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/2092/1/012022

DO - 10.1088/1742-6596/2092/1/012022

M3 - Conference article

AN - SCOPUS:85124040575

VL - 2092

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012022

T2 - 11th International Scientific Conference and Young Scientist School on Theory and Computational Methods for Inverse and Ill-posed Problems

Y2 - 26 August 2019 through 4 September 2019

ER -

ID: 35427403