Application of Fractures Mathematical Models in Exploration Seismology Problems Modeling

  • Maksim V. MuratovEmail author
  • Igor B. Petrov
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 133)


This chapter is about description of developed mathematical models of fractures, which can be used for numerical solution of exploration seismology problems with use of grid-characteristic method on unstructured triangular (in 2D-case) and tetrahedral (in 3D-case) meshes. The base of developed models is the concept of infinitely thin fracture, which aperture does not influence on wave processes in fracture area. These fractures are represented by boundaries and contact boundaries with different conditions on contact and boundary surfaces. Such approach significantly reduces the consumption of computer resources by the absence of the mesh definition inside of fracture necessity. On the other side, it lets state the fractures discretely in integration domain, therefore one can observe qualitative new effects, such as diffractive waves forming and multi-phase wave front due to multiple reflections between surfaces of neighbor fractures, which are not available to observe by use of effective models of fractures actively used in computational seismic.


Grid-characteristic method Exploration seismology problems Mathematical modeling Mathematical models of fractures 



Research is supported by grant of Russian Science Foundation (project No 14-11-00263).


  1. 1.
    Kozlov, E.A.: Medium models in exploration seismology. Nedra, Tver (2006). (in Russian)Google Scholar
  2. 2.
    Leviant, V.B., Petrov, I.B., Kvasov, I.E.: Numerical modeling of seismic response from subvertical macrofractures as possible fluid conduits. Seismic Technol. 4, 41–61 (2011)Google Scholar
  3. 3.
    Bakulin, A., Grechka, V., Karaev, N., Anisimov, A., Kozlov, E.: Physical modeling and theoretical studies of seismic reflections from a fault zone. SEG, 1674–1677 (2004)Google Scholar
  4. 4.
    Willis, M.E., Burns, D.R., Rao, R., Minsley, B., Toksöz, M.N., Vetri, L.: Spatial orientation and distribution of reservoir fractures from scattered seismic energy. Geophysics 71(5), O43–O51 (2006)CrossRefGoogle Scholar
  5. 5.
    Leviant, V.B., Petrov, I.B., Muratov, M.V.: Numerical simulation of wave responses from subvertical macrofractures system. Seismic Technol. 1, 5–21 (2012)Google Scholar
  6. 6.
    Biryukov, V.A., Muratov, M.V., Petrov, I.B., Sannikov, A.V., Favorskaya, A.V.: Application of the grid-characteristic method on unstructured tetrahedral meshes to the solution of direct problems in seismic exploration of fractured layers. Comput. Math. Math. Phys. 55(10), 1733–1742 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Magomedov, K.M., Kholodov, A.S.: Grid-characteristic numerical methods. Nauka, Moscow (1988). (in Russian)zbMATHGoogle Scholar
  8. 8.
    Petrov, I.B., Kholodov, A.S.: Numerical study of some dynamic problems of the mechanics of a deformable rigid body by the mesh-characteristic method. Computational Math. and Math. Phys. 24(3), 61–73 (1984)CrossRefGoogle Scholar
  9. 9.
    Aurenhammer, F.: Voronoi diagrams—a study of fundamental geometric data structure. ACM Comput. Surveys 23, 345–405 (1991)CrossRefGoogle Scholar
  10. 10.
    Edelsbrunner H.: Geometry and topology for mesh generation. Cambridge University Press (2006)Google Scholar
  11. 11.
    Leviant, V.B., Miryakha, V.A., Muratov, M.V., Petrov, I.B.: Seismic responses of vertical fractures depending on their thickness. Seismic Technol. 3, 16–30 (2015)Google Scholar
  12. 12.
    Muratov, M.V., Petrov, I.B., Kvasov, I.E.: Numerical solution of exploration seismology problems in areas of fractures reservoirs. Math. Models Comput. Simulation 28(7), 31–44 (2016)zbMATHGoogle Scholar
  13. 13.
    Karaev, N.A., Lukashin, YuP, Prokator, O.M., Semenov, V.P.: Physical modeling of fractured media. Seismic Technol. 2, 64–73 (2008)Google Scholar
  14. 14.
    Karaev, N.A., Leviant, V.B., Petrov, I.B., Karaev, G.N., Muratov, M.V.: Detection and charaterisation of fracture systems from P- to S-scattering: potentiality checks by physical modeling and simulations. Seismic Technol. 1, 22–36 (2016)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (MIPT)DolgoprudnyRussian Federation

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