Direct Method for Identification of Two Coefficients of Acoustic Equation

Direct Method for Identification of Two Coefficients of Acoustic Equation Full article

Journal

Mathematics
, E-ISSN: 2227-7390

Output data

Year: 2023, Volume: 11, Number: 13, Pages: 3029 Pages count : 16 DOI: 10.3390/math11133029

Tags

acoustic equation; inverse problems; direct methods; integral equations

Authors

Novikov Nikita ^1,2,3 , Shishlenin Maxim ^1,2,3

Affiliations

1	Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
2	Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia
3	Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia

Funding (1)

Russian Science Foundation

20-71-00128

We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to obtain both functions by solving two sets of integral equations. The main advantage of the proposed approach is that the method does not use the multiple solution of direct problems, and thus has quite low CPU time requirements. We also consider the variation of the method for the 1D case, where the variation of the wave equation is considered. We illustrate the results with numerical experiments in the 1D and 2D case and study the efficiency and stability of the approach

Novikov N. , Shishlenin M.
Direct Method for Identification of Two Coefficients of Acoustic Equation
Mathematics. 2023. V.11. N13. P.3029. DOI: 10.3390/math11133029 WOS Scopus РИНЦ OpenAlex

Submitted:	May 4, 2023
Accepted:	Jul 3, 2023
Published print:	Jul 7, 2023
Published online:	Jul 7, 2023

Web of science:	WOS:001028277000001
Scopus:	2-s2.0-85164954717
Elibrary:	62239858
OpenAlex:	W4383736541

DB	Citing
OpenAlex	3
Scopus	3
Web of science	2