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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 3, Pages 120–134
DOI: https://doi.org/10.33048/SIBJIM.2021.25.311
(Mi sjim1187)
 

Mathematical modeling for thin-layered elastic media in seismic exploration

G. M. Mitrofanovabc, A. L. Karchevskyd

a Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, pr. Acad. Koptyuga 3, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
c Novosibirsk State Technical University, pr. Karla Marksa, 20, Novosibirsk 630073, Russia
d Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
References:
Abstract: Some issues of mathematical modeling of wave fields associated with thin-layered objects of a horizontally-layered medium are considered. When describing the processes of wave propagation, systems of differential equations in partial derivatives are used, which correspond to the theory of elasticity. As a result, both vertical and horizontal displacement components are obtained, which is important for setting up and analyzing seismic field work with three-component instruments. In addition, in the mathematical formulation of the problem, a buried source of the expansion center type is used, which brings the model results closer to the real experiment. The solution of the problem written in the spectral form is analyzed, which may turn out to be significant when it is used to solve inverse dynamic seismic problems. The paper presents not only the computational features of the proposed scheme for solving the problem, but also the study of the resulting wave fields from the point of view of their use in the processing and interpretation of real seismic data.
Keywords: system of elasticity equations, vertical displacement, horizontal displacement, horizontally layered isotropic medium, time frequency, spatial frequency. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWZZ-2022-0017
FWNF-2022-0009
Received: 13.05.2022
Revised: 31.05.2022
Accepted: 22.06.2022
Document Type: Article
UDC: 519.633.6:550.8.055
Language: Russian
Citation: G. M. Mitrofanov, A. L. Karchevsky, “Mathematical modeling for thin-layered elastic media in seismic exploration”, Sib. Zh. Ind. Mat., 25:3 (2022), 120–134
Citation in format AMSBIB
\Bibitem{MitKar22}
\by G.~M.~Mitrofanov, A.~L.~Karchevsky
\paper Mathematical modeling for thin-layered elastic media in seismic exploration
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 3
\pages 120--134
\mathnet{http://mi.mathnet.ru/sjim1187}
\crossref{https://doi.org/10.33048/SIBJIM.2021.25.311}
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