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Geoinformatika 2018; 2(66) : 59-66

УДК 550.830, 539.3

ALGORITHM OF MODELING ACOUSTIC WAVES DISTRIBUTED IN A LAYER-BLOCK MEDIUM WITH COMPOSITE HIERARCHICAL INCLUSIONS

O.A. Khachai 1, A.Yu. Khachai 2, O.Yu. Khachai 2

1Institute of Geophysics. Yu.P. Bulashevich UB RAS, Amundsen, 100, 620016, Ekaterinburg, Russian Federation, olgakhachay@yandex.ru
2Ural Federal University. B.N. Yeltsin, Mira, 19, 620002, Yekaterinburg, Russian Federation, andrey.khachay@gmail.com, khachay@yandex.ru

Purpose. A geological or artificial environment with a multilevel hierarchical structure and strength properties requires regular study of the stability of its state. For this purpose, a new method was developed for modeling acoustic monitoring by longitudinal and transverse waves of a layered-block medium with several inclusions with different physico-mechanical hierarchical structures.
Design/methodology/approach. An iterative process of solving a direct problem is developed for the case of an acoustic field penetrating into three hierarchical inclusions of l, m and s-th rank, based on the use of two-dimensional integral-differential equations. The degree of inclusion hierarchy is determined by the values ​​of their ranks, which can be different.
Findings. Hierarchical inclusions are located in different layers one on top of the other: the top layer is anomalously plastic, the second is anomalously resilient, and the third is anomalously dense. The degree of filling of inclusions of each rank for all three hierarchical inclusions can be different.
Practical value /implications. Iterative modeling algorithms have been constructed in the seismic case in the acoustic approximation for a complex hierarchical heterogeneity. For the first time, the proposed iterative algorithm for modeling a composite complex hierarchical environment can be used to monitor stability studies of complex hierarchical structures under various mechanical influences. This algorithm can be extended to more complex multi-faceted hierarchical environments with different physical and mechanical functions. The  article is devoted to the analysis of the propagation of nonlinear acoustic waves through materials containing hierarchical structures with different physical and mechanical properties. The simulation results can be used to monitor studies of the stability of geological and mechanical structures of a complex hierarchical structure under various mechanical influences.

Keywords: complex hierarchical environment, acoustic field, iterative algorithm, integral-differential equations and direct problem.

 

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References:

  1. Panin V.E., Likhachev V.A., Grinyaev Yu.V. Structural levels of deformation of solids. Novosibirsk: Science, 1985. 254 p. [in Russian].
  2. Hachay O.A., Khachay A.Yu. On the integration of seismic and electromagnetic active methods for mapping and monitor¬ing the state of two-dimensional heterogeneities in an N-layer medium. Bulletin of SUSU. A series “Computer technologies, management, radio electronics”, 2011. no 2(219), pp. 49—56 [in Russian].
  3. Hachay O.A., Khachay A.Yu. Modeling of the seismic field in the acoustic approximation of two-phase hierarchically het-erogeneous media. Bulletin of SSSU, series “Computational mathematics and computer science”, 2014. V. 3, no 1. pp. 33—43 [in Russian].
  4. Hachay O.A., Khachay A.Yu. Reflection of noneqiulibrium two-phase filtration processes in oil saturated hierarchical media in active wave geophysical monitoring data. Mining Information and Analytical Bulletin, 2014. no 4, pp. 232—238 [in Russian].
  5. Hachay O.A., Khachai O.Yu., Khachai A.Yu. Integration of acoustic, gravitational and geomechanical fields in hierarchical environments. Mining Information and Analytical Bulletin, 2017. no 4, pp. 328—336 [in Russian].
  6. Hachay O.A., Khachay A.Yu. Modeling of the seismic and electromagnetic field in hierarchically heterogeneous media. Bulletin of SSSU, series “Computational mathematics and computer science”, 2014. V. 2, no 2, pp. 48—55 [in Russian].
  7. Khachai A.Yu. An algorithm for solving a direct dynamic seismic problem when a horizontal point layer is excited in an arbitrary layer of an N-layer elastic isotropic medium. Informatics and mathematical modeling, Ekaterinburg: USU, 2006a, pp. 170—278 [in Russian].
  8. Khachai A.Yu. Algorithm for solving a direct dynamic seismic problem when excited by a point source of a vertical force located in an arbitrary layer of an N-layer elastic isotropic medium. Informatics and mathematical modeling. Ekaterinburg: USU, 2006b, pp. 279—310 [in Russian].
  9. Hachay O.A., Khachay A.Yu. Modeling the propagation of a seismic field in a layered-block elastic medium with hierar¬chical plastic inclusions. Mining Information and Analytical Bulletin, 2016. no 12, pp. 318—326 [in Russian].
  10. Kolsky G.G. Stress waves in solids. Moscow. Publishing in foreign literature, 1955. 216 p. [in Russian].