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)


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.


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



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)


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© 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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