Abstract:
The aim of this paper is formation and propagation of scattered waves analysis. These waves form the response of fracture patterns on seismograms. The initial pulse is a plane wavefront spreading into the medium. The periodic structure of scattered wave response from system (claster) of subvertical macrofractures is studying in this paper. Basing on numeric simulation the ways of this fracture patterns geometric characteristics estimation are concluded. The grid-characteristic method with triangular computational mesh is used in the paper. Boundary conditions on surfaces of fractures and on integration domain boundaries take into account the characteristic properties of the determining hyperbolic equations system. This numeric method lets make the numeric algorithms on the integration domain boundaries and the boundaries between different media the most correctly, take into account the physics of the problem. For this reason this method is the most appropriate for numeric solution of dynamic problems with pronounced wave character in heterogeneous media, in particular for analyzing problem of seismic waves interaction with fracture patterns.
Citation:
M. V. Muratov, I. B. Petrov, “Simulation of wave responses from subvertical macrofracture systems using grid-characteristic method”, Mat. Model., 25:3 (2013), 89–104; Math. Models Comput. Simul., 5:5 (2013), 479–491
This publication is cited in the following 16 articles:
I. A. Mitskovets, N. I. Khokhlov, “Simulation of propagation of dynamic perturbations in porous media by the grid-characteristic method with explicit description of heterogeneities”, Comput. Math. Math. Phys., 63:10 (2023), 1904–1917
I. A. Mitkovets, N. I. Khokhlov, “Grid-characteristic method using superimposed grids in the problem of seismic exploration of fractured geological media”, CMIT, 7:3 (2023), 28
I. B. Petrov, M. V. Muratov, “The application of grid-characteristic method in solution of fractured formations exploration seismology direct problems (review article)”, Math. Models Comput. Simul., 11:6 (2019), 924–939
Petrov I.B. Muratov V M., “Mathematical Modeling of Spatial Wave Responses By Grid-Characteristic Method on Irregular Computational Meshes”, Lobachevskii J. Math., 40:4, SI (2019), 499–506
A. V. Favorskaya, M. S. Zhdanov, N. I. Khokhlov, I. B. Petrov, “Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid-characteristic method”, Geophys. Prospect., 66:8 (2018), 1485–1502
A. Favorskaya, I. Petrov, V. Golubev, N. Khokhlov, “Numerical simulation of earthquakes impact on facilities by 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, 1206–1215
A. Favorskaya, I. Petrov, A. Grinevskiy, “Numerical simulation of fracturing in geological medium”, 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, 1216–1224
A. V. Favorskaya, V. I. Golubev, “About applying Rayleigh formula based on the Kirchhoff integral equations for the seismic exploration problems”, Computer Research and Modeling, 9:5 (2017), 761–771
Voroshchuk D.N. Miryaha V.A. Petrov I.B. Sannikov A.V., “Discontinuous Galerkin Method For Wave Propagation in Elastic Media With Inhomogeneous Inclusions”, Russ. J. Numer. Anal. Math. Model, 31:1 (2016), 41–50
M. V. Muratov, I. B. Petrov, I. E. Kvasov, “Chislennoe reshenie zadach seismorazvedki v zonakh treschinovatykh rezervuarov”, Matem. modelirovanie, 28:7 (2016), 31–44
A. I. Sukhinov, A. E. Chistyakov, A. A. Semenyakina, A. V. Nikitina, “Chislennoe modelirovanie ekologicheskogo sostoyaniya Azovskogo morya s primeneniem skhem povyshennogo poryadka tochnosti na mnogoprotsessornoi vychislitelnoi sisteme”, Kompyuternye issledovaniya i modelirovanie, 8:1 (2016), 151–168
Petrov I., International Conference on Computer Simulation in Physics and Beyond 2015, Journal of Physics Conference Series, 681, IOP Publishing Ltd, 2016
Alena Favorskaya, Igor Petrov, Nikolay Khokhlov, “Numerical Modeling of Wave Processes During Shelf Seismic Exploration”, Procedia Computer Science, 96 (2016), 920
V. A. Miryaha, A. V. Sannikov, I. B. Petrov, “Discontinuous Galerkin method for numerical simulation of dynamic processes in solids”, Math. Models Comput. Simul., 7:5 (2015), 446–455
A. I. Sukhinov, D. S. Khachunts, A. E. Chistyakov, “A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation”, Comput. Math. Math. Phys., 55:7 (2015), 1216–1231
I. B. Petrov, A. V. Favorskaya, N. I. Khokhlov, V. A. Miryaha, A. V. Sannikov, V. I. Golubev, “The monitoring state of a moving train using high performance systems and modern computational methods”, Math. Models Comput. Simul., 7:1 (2015), 51–61
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