Direct Method for Identification of Two Coefficients of Acoustic Equation

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Direct Method for Identification of Two Coefficients of Acoustic Equation. / Novikov, Nikita ; Shishlenin, Maxim.

In: Mathematics, Vol. 11, No. 13, 3029, 07.2023.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c0c4259bdbcc4a3fac129d97a76c74e7,

title = "Direct Method for Identification of Two Coefficients of Acoustic Equation",

abstract = "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.",

keywords = "acoustic equation, direct methods, integral equations, inverse problems",

author = "Nikita Novikov and Maxim Shishlenin",

note = "The work has been supported by the Russian Science Foundation under grant 20-71-00128 “Development of new algorithms for parameters identification of geophysics based on the direct methods of data processing”.",

year = "2023",

month = jul,

doi = "10.3390/math11133029",

language = "English",

volume = "11",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "13",

}

RIS

TY - JOUR

T1 - Direct Method for Identification of Two Coefficients of Acoustic Equation

AU - Novikov, Nikita

AU - Shishlenin, Maxim

N1 - The work has been supported by the Russian Science Foundation under grant 20-71-00128 “Development of new algorithms for parameters identification of geophysics based on the direct methods of data processing”.

PY - 2023/7

Y1 - 2023/7

N2 - 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.

AB - 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.

KW - acoustic equation

KW - direct methods

KW - integral equations

KW - inverse problems

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85164954717&origin=inward&txGid=4edc7bd3f74c6e2df20474b63853fc09

UR - https://www.mendeley.com/catalogue/65ccb05c-c496-3f10-80b6-401b28e97718/

U2 - 10.3390/math11133029

DO - 10.3390/math11133029

M3 - Article

VL - 11

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 13

M1 - 3029

ER -

ID: 59258325