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Direct Method for Identification of Two Coefficients of Acoustic Equation. / Novikov, Nikita; Shishlenin, Maxim.
в: Mathematics, Том 11, № 13, 3029, 07.2023.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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