Coefficient inverse problem for the Helmholtz equation-Reference-Cited by-同舟云学术

Coefficient inverse problem for the Helmholtz equation

Published:2023-03-16 Issue:3 Volume: Page:77-84
ISSN:2619-1563
Container-title:Russian Journal of Geophysical Technologies
language:
Short-container-title:Russian Journal of geophysical technologies

Author:

Sibiryakov E. B.¹^ORCID

Affiliation:

1. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS
Koptyug Ave., 3, Novosibirsk, 630090

Siberian State University of Telecommunications and Information Science
Gurievskaya Str., 51, Novosibirsk, 630090

Abstract

The paper proposed an algorithm for solving the coefficient inverse problem for the Helmholtz equation, which uses the minimization of the functional in the spectral domain. As an example, the parameters of layer on a half-space was found by using of a given function and its derivative on a plain upper boundary in 2D case.

Publisher

Trofimuk Institute of Petroleum Geology and Geophysics (SB RAS)

Subject

General Medicine

Reference8 articles.

1. Anikeev D.V., Kashtan B.M., Blagoveshenskii A.S., Mulder V.A. Exact dynamical method of the inverse seismic problem by integral Gelfand-Levitan equations // Problems of Geophysics. – St. Petersburg University Press, St. Petersburg, 2012. – Vol. 44. – P. 49–81.

2. Kabanikhin S.I. Inverse and Ill-posed Problems. Textbook for Students [in Russian]. – Siberian Scientific Publishing House, Novosibirsk, 2009. – 457 p.

3. Karchevsky A.L. Several remarks on numerical solution of the one-dimensional coefficient inverse problem // Journal of Inverse Ill-Posed Problems. – 2002. – Vol. 10 (4). – P. 361–383, doi: 10.1515/jiip.2002.10.4.361.

4. Karchevsky A.L. A proper flow chart for a numerical solution to an inverse problem by an optimization method // Numerical Analysis and Applications. – 2008. – Vol. 1. – P. 114–122, doi: 10.1134/S1995423908020031.

5. Karchevsky A.L., Fatianov A.G. Numerical solution of the inverse problem for a system of elasticity with the aftereffect for a vertically inhomogeneous medium // Sibirskii Zhurnal Vychislitel’noi Matematiki. – 2001. – Vol. 4 (3). – P. 259–268.