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Licensed Unlicensed Requires Authentication Published by De Gruyter November 17, 2015

Fast Toeplitz linear system inversion for solving two-dimensional acoustic inverse problem

  • Sergey I. Kabanikhin , Nikita S. Novikov EMAIL logo , Ivan V. Oseledets and Maxim A. Shishlenin


The coefficient inverse problem for the acoustic equation is considered. We propose the method for reconstructing the density based on the N-approximation by the finite system of one-dimensional problems and the two-dimensional M. G. Krein approach. The two-dimensional analogue of the M. G. Krein approach is applied to reduce the non-linear inverse problem to a family of linear integral equations. We consider the fast algorithm for solving the relevant linear system, based on using the block-Toeplitz structure of the matrix. The algorithm applied to the M. G. Krein equation allows to obtain the solution of the whole family of the integral equations by solving only one linear system. Results of numerical calculations are presented.

Funding source: RFBR

Award Identifier / Grant number: 14-01-00208

Funding source: RFBR

Award Identifier / Grant number: 15-01-09230

Funding source: the Ministry of Education and Science of the Russian Federation and the Ministry of Education and Science of the Republic of Kazakhstan

Award Identifier / Grant number: MES 1760/GF: project NTP 04.03.02 “Creating methodological basis of geological-geophysical studies of focal zones UNE in igneous rocks”

Funding source: Russian Science Foundation

Award Identifier / Grant number: 14-01-000659

Received: 2015-9-1
Revised: 2015-10-27
Accepted: 2015-10-27
Published Online: 2015-11-17
Published in Print: 2015-12-1

© 2015 by De Gruyter

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