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

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

Journal

Journal of Physics: Conference Series
ISSN: 1742-6588 , E-ISSN: 1742-6596

Output data

Year: 2021, Volume: 2092, Number: 1, Article number : 012022, Pages count : DOI: 10.1088/1742-6596/2092/1/012022

Authors

Kabanikhin S.I. ^1,2,3 , Novikov N.S. ^1,2 , Shishlenin M.A. ^1,2,3

Affiliations

1	Novosibirsk State University, Russian Federation
2	Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, Russian Federation
3	Sobolev Institute of Mathematics, Novosibirsk, Russian Federation

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.

Kabanikhin S.I. , Novikov N.S. , Shishlenin M.A.
Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem
Journal of Physics: Conference Series. 2021. V.2092. N1. 012022 . DOI: 10.1088/1742-6596/2092/1/012022 Scopus OpenAlex

Scopus:	2-s2.0-85124040575
OpenAlex:	W4200182454

DB	Citing
Scopus	2
OpenAlex	2