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This article is cited in 9 scientific papers (total in 9 papers)
Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes
V. I. Golubev, I. B. Petrov, N. I. Khokhlov, K. I. Shul'ts
Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
Abstract:
Wave propagation in fractured rock in the course of seismic exploration is studied. The grid-characteristic method on hexahedral meshes is extended to the case of an elastic medium with empty and fluid-saturated cracks. The crack effect on wave propagation in the medium is taken into account by introducing cracks at the stage of grid generation with boundary conditions and conditions on the crack edges specified in explicit form. This method is used to obtain wave patterns near an extended inclined crack. The problem of numerically computing the seismic effect produced by a cluster of vertical and subvertical cracks is given in a complete three-dimensional formulation. The structure of the resulting pattern and the influence exerted by the crack-filling substance on the signal recorded on the surface are examined.
Key words:
hyperbolic equations, grid-characteristic numerical method, mathematical simulation, fractured media.
DOI:
https://doi.org/10.7868/S0044466915030096
 Full text:
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:3, 509–518
Bibliographic databases:
    
UDC:
519.634
MSC: Primary 74L05; Secondary 74J05, 74R10
Received: 27.05.2014
Citation:
V. I. Golubev, I. B. Petrov, N. I. Khokhlov, K. I. Shul'ts, “Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 512–522; Comput. Math. Math. Phys., 55:3 (2015), 509–518
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http://mi.mathnet.ru/eng/zvmmf10177 http://mi.mathnet.ru/eng/zvmmf/v55/i3/p512
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A. Favorskaya, I. Petrov, A. Grinevskiy, “Numerical simulation of fracturing in geological medium”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, ed. C. Zanni-Merk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1216–1224
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P. Stognii, D. Petrov, N. Khokhlov, A. Favorskaya, “Numerical modeling of influence of ice formations under seismic impacts based on grid-characteristic method”, Knowledge-Based and Intelligent Information & Engineering Systems, Procedia Computer Science, 112, eds. C. Zanni-Merk, C. Frydman, C. Toro, Y. Hicks, R. Howlett, L. Jain, Elsevier Science BV, 2017, 1497–1505
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V. I. Golubev, R. I. Gilyazutdinov, I. B. Petrov, N. I. Khokhlov, A. V. Vasyukov, “Simulation of dynamic processes in three-dimensional layered fractured media with the use of the grid-characteristic numerical method”, J. Appl. Mech. Tech. Phys., 58:3 (2017), 539–545
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V. I. Golubev, N. I. Khokhlov, “Otsenka anizotropii seismicheskogo otklika ot treschinovatykh geologicheskikh ob'ektov”, Kompyuternye issledovaniya i modelirovanie, 10:2 (2018), 231–240
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A. V. Favorskaya, S. V. Kabisov, I. B. Petrov, “Modeling of ultrasonic waves in fractured rails with an explicit approach”, Dokl. Math., 98:1 (2018), 401–404
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A. O. Kazakov, “On the calculation of border and contact nodes by grid-characteristic method on non-periodic tetrahedral grids”, Num. Anal. Appl., 11:4 (2018), 298–310
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V. I. Golubev, O. Ya. Voinov, I. B. Petrov, “Seismic imaging of fractured elastic media on the basis of the grid-characteristic method”, Comput. Math. Math. Phys., 58:8 (2018), 1309–1315
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