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Mathematical Modeling of Dynamic Processes in Seismic Activity Zones

  • Alexandr KimEmail author
  • Yuriy Shpadi
  • Yuriy Litvinov
Conference paper
Part of the Springer Proceedings in Earth and Environmental Sciences book series (SPEES)

Abstract

Mathematical modeling of wave processes in a tense medium in the event of a sudden rupture with contacting banks was carried out using an analytical solution by Kim A.S. for a dynamic problem simulating the process of an earthquake. The displacement field in the zone of final rupture with viscous contact of the banks is obtained. The results of numerical analysis confirm the theoretical conclusions about the presence of a time interval during which the influence of the ends of the rupture on the movement of its banks can be neglected, and this time interval increases with increasing viscosity at the rupture. A computer visualization of the development in time of the total field of displacements in the focal zone was carried out, taking into account the field of repeated cylindrical waves, when a complete release of stresses occurs at the final rupture. It has been established that on the trunk rupture, reverse displacements of the banks of the rupture can occur, and the total displacement field in the rupture zone tends to its static state.

Keywords

Mathematical model Earthquake Seismic wave Analytical solution Reverse displacement at rupture Computer visualization 

Notes

Acknowledgements

The work was carried out in the framework of the project № 0118PК00799 RBP-008 RK.

Supplementary material

481850_1_En_10_MOESM1_ESM.mp4 (564 kb)
Supplementary material 1 (MP4 563 kb)

References

  1. 1.
    Adushkin, V.: Actual problems of geomechanics crust. Electron. Sci. Inf. J. 1(16), 1–33 (2001) (in Russian), Bulletin of the OGGGGN RASGoogle Scholar
  2. 2.
    Kocharyan, G., Ostapchuk, A., Markov, V., Pavlov, D.: Some problems of geomechanics of the continental crust faults. Fiz. Earth 3, 51–64 (2014) (in Russian)Google Scholar
  3. 3.
    Hayakawa, M.: On the fluctuation spectra of seismo-electromagnetic phenomena. Nat. Hazards Earth Syst. Sci. 301(11), 301–308 (2011).  https://doi.org/10.5194/nhess-11-301-2011ADSCrossRefGoogle Scholar
  4. 4.
    Namgaladze, A., Klimenko, M., Klimenko, V., Zakharenkova, I.: Physical mechanism and mathematical modeling of earthquake ionospheric precursors registered in total electron content. Geomagn. Aeron. 49(2), 252–262 (2009).  https://doi.org/10.1134/s0016793209020169ADSCrossRefGoogle Scholar
  5. 5.
    Kim, A.: Mechanics of Non-stationary Processes in the Focal Zones of the Earth’s Crust. Publisher Gylym Ordasy, Almaty (2017) (in Russian)Google Scholar
  6. 6.
    Martynyuk, P.: On the Dynamic Loading of a Half-Plane with a Crack Under Conditions of Antiplane Deformation, vol. 22, pp. 216–230. Continuum Dynamics, Novosibirsk (1975) (in Russian)Google Scholar
  7. 7.
    Fleetman, L.: Waves caused by the instantaneous discontinuity of the elastic medium. J.: Appl. Math. Mech. 27(4), 618–628 (1963) (in Russian)Google Scholar
  8. 8.
    Richards, P.: Dynamic motions near an earthquake fault a three-dimensional solution. Bull. Seismol. Soc. Am. 66(1), 1–32 (1976)MathSciNetGoogle Scholar
  9. 9.
    Dragoni, M., Santini, S.: A two-asperity fault model with wave radiation. Phys. Earth Planet. Inter. 248, 83–89 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Wu, F., Thomson, K., Kuenzler, H.: Stick-slip propagation velocity and seismic source mechanism. Bull. Seismol. Soc. Am. 62(6), 1621–1628 (1972)Google Scholar
  11. 11.
    Chang, K., Segall, P.: Injection-induced seismicity on basement faults including poroelastic stressing. J. Gephys. Res. 121(4), 2708–2726 (2016).  https://doi.org/10.1002/2015JB012561ADSCrossRefGoogle Scholar
  12. 12.
    Zhang, H., Ge, Z.: Rupture pattern of the Oct 23, 2011 Van-Merke Eastern Turkey earthquake. Earthq. Sci. 27(3), 257–264 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Kim, A.: On shear waves in the focal zone in case of a sudden rupture. In: Proceedings of the Scientific and Technical Society KAHAK, vol. 2, pp. 4–31 (2015) (in Russian)Google Scholar
  14. 14.
    Kim, A.: Non-stationary processes in nidal zone at sudden appearance of break. In: The 24th International Congress of Theoretical and Applied Mechanics (ICTAM-2016), Book of Papers, pp. 2263–2264. Montréal, Canada (2016)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of IonosphereAlmatyKazakhstan
  2. 2.Institute of Space Techniques and TechnologiesAlmatyKazakhstan

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