Mathematical modeling for thin-layered elastic media in seismic exploration

G. M. Mitrofanov ; A. L. Karchevsky

Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 120-134

Résumé

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.

Détail

Keywords: system of elasticity equations, vertical displacement, horizontal displacement, horizontally layered isotropic medium, time frequency, spatial frequency. .