Geodesic
Simulation of wave responses from subvertical macrofracture systems using grid-characteristic method
Matematičeskoe modelirovanie, Tome 25 (2013) no. 3, pp. 89-104.

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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.
Keywords: numerical simulation, seismic exploration, fracture patterns, hyperbolic equation systems, grid-characteristic method, non-structured triangular meshes. 
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M. V. Muratov; I. B. Petrov. Simulation of wave responses from subvertical macrofracture systems using grid-characteristic method. Matematičeskoe modelirovanie, Tome 25 (2013) no. 3, pp. 89-104. http://geodesic.mathdoc.fr/item/MM_2013_25_3_a7/

[1] Sheriff R., Geldart L., Seismorazvedka, Mir, M., 1987

[2] Biot M. A., “Mechanics of deformation and acoustic propagation in porous media”, J. Apple Physics, 33:4 (1962), 1482–1498 | DOI | MR | Zbl

[3] Agakhanov S. N., Kvasov I. E., Pankratov S. A., “Chislennoe issledovanie osrednennykh modelei neodnorodnykh sred v zadachakh geofiziki setochno-kharakteristicheskim metodom”, Informatsionnye tekhnologii: modeli i metody, Sbornik nauchnykh trudov, MFTI, M., 2010, 12–21

[4] Hsu C. J., Schoenberg M., “Elastic waves through a simulated fractured medium”, Geophysics, 58:7 (1993), 964–977 | DOI

[5] Willis M. E. at al., “Spatial orientation and distribution of reservoir fractures from scattered seismic energy”, Geophysics, 71:5 (2006), 43–51 | DOI | MR

[6] Molotkov L. A., Bakulin A. V., “Effektivnaya model sloistoi uprugo-poristoi sredy”, DAN, 372:1 (2000), 108–112

[7] Kozlov E. A., “Pressure-dependent seismic response of fractured rock”, Geophysics, 1969, 885–897

[8] Thomsen L., “Weak elastic anisotropy”, Geophysics, 51 (1986), 1954–1966 | DOI

[9] Kondaurov V. I., Fortov V. E., Osnovy termomekhaniki kondensirovannoi sredy, MFTI, M., 2002

[10] Novatskii V. K., Teoriya uprugosti, Mir, M., 1975, 872 pp. | MR

[11] Magomedov K. M., Kholodov A. S., “O postroenii raznostnykh skhem dlya uravnenii giperbolicheskogo tipa na osnove kharakteristicheskikh sootnoshenii”, Zh. vychislitelnoi matematiki i matematicheskoi fiziki, 24:5 (1984), 722–739 | MR

[12] Levyant V. B., Petrov I. B., Kvasov I. E., “Chislennoe modelirovanie volnovogo otklika ot subvertikalnykh makrotreschin, veroyatnykh flyuidoprovodyaschikh kanalov”, Tekhnologii seismorazvedki, 2011, no. 4, 4–29

[13] Levyant V. B., Petrov I. B., Chelnokov F. B., “Klasternaya priroda seismicheskoi energii, rasseyannoi ot zony diffuznoi poverkhnosti i treschinovatosti v massivnykh porodakh”, Geofizika, 2005, no. 6, 5–19

[14] Levyant V. B., Pankratov S. A., Petrov I. B., “Issledovanie kharakteristik prodolnykh i obmennykh voln obratnogo otklika ot zon treschinovatogo kollektora”, Tekhnologii seismorazvedki, 2009, no. 2, 3–11

[15] Kvasov I. E., Pankratov S. A., Petrov I. B., “Chislennoe modelirovanie seismicheskikh otklikov v mnogosloinykh geologicheskikh sredakh setochno-kharakteristicheskim metodom”, Matematicheskoe modelirovanie, 22:9 (2010), 13–21

[16] Kvasov I. E., Pankratov S. A., Petrov I. B., “Chislennoe issledovanie dinamicheskikh protsessov v tverdoi deformiruemoi srede s treschinoi, initsiiruemykh pripoverkhnostnym vozmuscheniem, setochno-kharakteristicheskim metodom”, Mat. modelir., 23:11 (2010), 109–162

[17] Kvasov I. E., Petrov I. B., “Chislennoe modelirovanie volnovykh protsessov v geologicheskikh sredakh v zadachakh seismorazvedki s pomoschyu vysokoproizvoditelnykh EVM”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 52:2 (2012), 330–341 | MR | Zbl

[18] Petrov I. B., Kholodov A. S., “Chislennoe issledovanie nekotorykh dinamicheskikh zadach mekhaniki deformiruemogo tverdogo tela setochno-kharakteristicheskim metodom”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 24:5 (1984), 722–739 | MR | Zbl

[19] Petrov I. B., Kholodov A. S., “O regulyarizatsii razryvnykh chislennykh reshenii uravnenii giperbolicheskogo tipa”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 24:8 (1984), 1172–1188 | MR | Zbl

[20] Petrov I. B., Tormasov A. G., Kholodov A. S., “O chislennom izuchenii nestatsionarnykh protsessov v deformiruemykh sredakh mnogosloinoi struktury”, Izv. AN SSSR, ser. ITT, 1989, no. 4, 89–95