Application of the grid-characteristic method on unstructured tetrahedral meshes to the solution of direct problems in seismic exploration of fractured layers. (English. Russian original) Zbl 1336.86002
Comput. Math. Math. Phys. 55, No. 10, 1733-1742 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 10, 1762-1772 (2015).
Summary: Seismic responses from fractured geological layers are mathematically simulated by applying the grid-characteristic method on unstructured tetrahedral meshes with the use of high-performance computer systems. The method is intended for computing complicated spatial dynamical processes in complex heterogeneous media and is characterized by exact formulation of contact conditions. As a result, it can be applied to the simulation of seismic exploration problems, including in regions with a large number of inhomogeneities, examples of which are fractured structures. The use of unstructured tetrahedral meshes makes it possible to specify geological cracks of various shapes and spatial orientations. As a result, problems are solved in a formulation maximally close to an actual situation. A cluster of computers is used to improve the accuracy of the computation by optimizing its duration.
MSC:
| 86A15 | Seismology (including tsunami modeling), earthquakes |
| 86-08 | Computational methods for problems pertaining to geophysics |
| 65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |
Keywords:
grid-characteristic method; unstructured tetrahedral meshes; seismic exploration; fractured media; seismic waves; numerical simulation; high-performance computer systems; parallel algorithmsReferences:
| [1] | R. E. Sheriff and L. P. Geldart, Exploration Seismology (Cambridge Univ. Press, Cambridge, 1982; Mir, Moscow, 1987). |
| [2] | W. Nowacki, Thermoelasticity (Pergamon, Oxford, 1962; Mir, Moscow, 1975). · Zbl 0364.73001 |
| [3] | V. I. Kondaurov and V. E. Fortov, Fundamentals of Thermal Mechanics of Condensed Media (Mosk. Fiz.-Tekh. Inst., Moscow, 2002) [in Russian]. |
| [4] | K. M. Magomedov and A. S. Kholodov, Grid-Characteristic Numerical Methods (Nauka, Moscow, 1988) [in Russian]. · Zbl 0649.65051 |
| [5] | A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Chapman and Hall/CRC, London, 2001). · Zbl 0965.35001 |
| [6] | I. B. Petrov and A. S. Kholodov, “Numerical study of some dynamic problems of the mechanics of a deformable rigid body by the mesh-characteristic method,” USSR Comput. Math. Math. Phys.24(3), 61-73 (1984). · Zbl 0566.73068 · doi:10.1016/0041-5553(84)90044-2 |
| [7] | A. S. Kholodov, “Numerical methods for solving hyperbolic equations and systems,” in Encyclopedia of LowTemperature Plasmas (Yanus-K, Moscow, 2008), Vol. VII-1, Part 2, pp. 141-174 [in Russian]. |
| [8] | V. D. Ivanov, V. I. Kondaurov, I. B. Petrov, and A. S. Kholodov, “Computation of dynamic deformation and fracture of elastoplastic bodies by grid-characteristic methods,” Mat. Model.2(1), 11-29 (1990). · Zbl 0972.74515 |
| [9] | I. B. Petrov and A. S. Kholodov, “Regularization of discontinuous numerical solutions of equations of hyperbolic type,” USSR Comput. Math. Math. Phys.24(4), 128-138 (1984). · Zbl 0577.65079 · doi:10.1016/0041-5553(84)90245-3 |
| [10] | I. B. Petrov, A. G. Tormasov, and A. S. Kholodov, “On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid,” USSR Comput. Math. Math. Phys.30(4), 191-196 (1990). · Zbl 0737.73095 · doi:10.1016/0041-5553(90)90062-W |
| [11] | A. V. Favorskaya, I. B. Petrov, I. E. Kvasov, and A. V. Sannikov, “Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step,” Math. Model. Comput. Simul.5(5), 409-415 (2013). · Zbl 1457.86003 · doi:10.1134/S2070048213050104 |
| [12] | I. B. Petrov and A. V. Favorskaya, “Library of high-order interpolation methods on unstructured triangular and tetrahedral meshes,” Zh. Inf. Tekhnol., No. 9, 30-32 (2011). |
| [13] | C. J. Hsu and M. Schoenberg, “Elastic waves through a simulated fractured medium,” Geophysics58(7), 964-977(1993). · doi:10.1190/1.1443487 |
| [14] | M. E. Willis, at al., “Spatial orientation and distribution of reservoir fractures from scattered seismic energy,” Geophysics71(5), 43-51 (2006). · doi:10.1190/1.2235977 |
| [15] | L. A. Molotkov and A. V. Bakulin, “Effective model of a layered elastic porous medium,” Dokl. Akad. Nauk372(1), 108-112 (2000). |
| [16] | E. A. Kozlov, Medium Models in Exploration Seismology (Gers, Tver, 2006) [in Russian]. |
| [17] | V. B. Levyant, I. B. Petrov, and I. E. Kvasov, “Numerical simulation of wave response of subvertical macrofractures, possible fluid-conducting channels,” Tekhnol. Seismorazvedki, No. 4, 4-29 (2011). |
| [18] | V. B. Levyant, I. B. Petrov, and M. V. Muratov, “Numerical simulation of wave responses from subvertical macrofractures system,” Tekhnol. Seismorazvedki, No. 1, 5-21 (2012). |
| [19] | V. B. Levyant, I. B. Petrov, M. V. Muratov, and S. A. Byko, “Stability analysis of the formation of a front of converted waves from a zone of macrofractures,” Tekhnol. Seismorazvedki, No. 1, 32-45 (2013). |
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