Investigation of the Elastic Waves Anisotropy Using the Grid-characteristic Computational Method and Explicit Treatment of Cracks

One of the factors characterizing oil and gas deposits is the anisotropy of seismic wave propagation in fractured rock. This paper presents a technique for studying the anisotropy of seismic wave propagation from a point source in a medium filled with a system of equally oriented cracks. The P-wave...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023, Vol.44 (1), p.341-353
Main Authors: Khokhlov, N. I., Favorskaya, A. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Anisotropy
Boundary value problems
Cartesian coordinates
Crack propagation
Domains
Elastic anisotropy
Elastic waves
Finite element method
Geometry
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Natural gas exploration
Numerical methods
Oil exploration
P waves
Point sources
Probability Theory and Stochastic Processes
Propagation
Seismic waves
Wave equations
Wave propagation
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Summary:One of the factors characterizing oil and gas deposits is the anisotropy of seismic wave propagation in fractured rock. This paper presents a technique for studying the anisotropy of seismic wave propagation from a point source in a medium filled with a system of equally oriented cracks. The P-wave amplitude and arrival time anisotropy factors dependent on the cracks number were investigated. The cracks number was varied from 200 up to 1800. The effect of anisotropy relative to the axes of the Cartesian coordinate mesh of the numerical method used is neutralized by appropriate normalization. We applied the grid-characteristic method on Cartesian computational meshes and the model of infinitely thin fluid-saturated cracks. This fracture model is a special case of the Linear Slip Model (LMS, Schoenberg model). Mathematically, the problem under consideration is a solution of the initial-boundary value problem of the elastic wave equation with multiple contact boundaries inside the integration domain. The anisotropy of the wave field arises from multiple reflections between these boundaries. This formulation of the problem is more preferable than the solution of the anisotropic wave equation without contact boundaries inside the integration domain, since it allows more accurate calculation of the wave field, even though it requires large computational resources.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223010201