TY - JOUR

T1 - Mathematical Modeling for Thin-Layered Elastic Media in Seismic Exploration

AU - Mitrofanov, G. M.

AU - Karchevsky, A. L.

N1 - Funding Information: The work was carried out within the framework of state assignments for Trofimuk Institute of Petroleum Geology and Geophysics of the Siberian Branch of the Russian Academy of Sciences, project no. FWZZ-2022-0017, and Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0009. Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/5

Y1 - 2022/5

N2 - Some issues of mathematical modeling of wave fields associated with thin-layered objectsin a horizontally layered medium are considered. Systems of partial differential equations thatcorrespond to the theory of elasticity are used when describing wave propagation processes. As aresult, both vertical and horizontal displacement components are obtained; this is important forsetting up and analyzing seismic field work with three-component instruments. In addition, in themathematical statement of the problem, a buried source of the spreading center type is used; thisbrings the model results closer to the real experiment. The solution of the problem written inspectral form is analyzed; this may turn out to be significant when this solution is used to solveinverse dynamic seismic problems. The paper presents not only the computational features of theproposed scheme for solving the problem but also the study of the resulting wave fields from thepoint of view of their use in the processing and interpretation of real seismic data.

AB - Some issues of mathematical modeling of wave fields associated with thin-layered objectsin a horizontally layered medium are considered. Systems of partial differential equations thatcorrespond to the theory of elasticity are used when describing wave propagation processes. As aresult, both vertical and horizontal displacement components are obtained; this is important forsetting up and analyzing seismic field work with three-component instruments. In addition, in themathematical statement of the problem, a buried source of the spreading center type is used; thisbrings the model results closer to the real experiment. The solution of the problem written inspectral form is analyzed; this may turn out to be significant when this solution is used to solveinverse dynamic seismic problems. The paper presents not only the computational features of theproposed scheme for solving the problem but also the study of the resulting wave fields from thepoint of view of their use in the processing and interpretation of real seismic data.

KW - horizontal displacement

KW - horizontally layered isotropic medium

KW - spatial frequency

KW - system of elasticity equations

KW - time frequency

KW - vertical displacement

UR - http://www.scopus.com/inward/record.url?scp=85144233925&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/40f8a62b-e5be-329a-904b-83ee967fd874/

U2 - 10.1134/S1990478922030140

DO - 10.1134/S1990478922030140

M3 - Article

AN - SCOPUS:85144233925

VL - 16

SP - 501

EP - 511

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -