Simulation of Dynamic Processes in Three-Dimensional Layered Cracked Media with the Use of the Grid-Characteristic Numerical Method
V. I. Golubev1, R. I. Gilyazutdinov1, I. B. Petrov1, N. I. Khokhlov1, A. V. Vasyukov2
1Moscow Institute of Physics and Technology, Dolgoprudny, 141700, Russia
2Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia
Keywords: трещиноватые среды, математическое моделирование, численные методы, параллельные алгоритмы, прямые задачи сейсмической разведки, композитные материалы, cracked media, mathematical simulation, numerical methods, parallel algorithms, direct seismic prospecting tasks, composite materials
Abstract
This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer cracked media. The dynamic processes are described using the defining system of equations in partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic method on curvilinear structural grids. The cracked nature of the medium is accounted for by explicitly selecting the boundaries of individual cracks and setting special boundary conditions in them. The various models of the heterogeneous deformed medium having a cracked structure are considered: a homogeneous medium, a medium with horizontal boundaries, and media with inclined and curvilinear boundaries. The wave fields detected on the surface are obtained, and their structure is analyzed. It is demonstrated that it is possible to detect waves propagating from a cracked medium even in the case of nonparallel (inclined and curvilinear) boundaries of geological layers.
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