On the modeling of the wave process near the seam zone of lithospheric structures

Authors

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-20-3-66-73

Abstract

In order to develop mechanical and mathematical methods for studying deformation-wave processes in the geological environment and the mechanisms of seismicity formation in the seam zones of lithospheric structures, we have solved the problems of modeling the passage of a harmonic signal through a fault. We consider the problem of modeling the passage of a harmonic signal through a fault and conduct a study of the coating-substrate system. Here the deformable foundation (substrate) is described by the model of the linear theory of elasticity. Structures with a fault are considered as a coating, for which the parameters averaged over the thickness are taken. The paper presents an analytical-numerical method for solving boundary value problems of steady-state vibrations in an elastic medium with a coating modeled by extended plates as well as the results of the numerical implementation of the developed algorithms for a problem simulating the dynamics of contacting lithospheric structures under the action of a surface load for one of the possible contact conditions on a fault. The presence of the resonant type structures is usually substantiated by the results of the observatory experiments and the interpretation of geological and geophysical materials. The approach developed in this paper is based on the possibility of using mobile vibroseismic sources to detect faults by producing mono-signals of a certain frequency which can be received at different distances.

Keywords:

medium with coating, harmonic source, rectilinear fault, factorization method

Acknowledgement

The work was carried out with financial support from the Russian Science Foundation and the Kuban Science Foundation (project no. 22-21-20032).

Author Infos

Maxim N. Kolesnikov

канд. физ.-мат. наук, научный сотрудник Научно-исследовательской части Кубанского государственного университета

e-mail: kolesnikov@kubsu.ru

Ilya S. Telyatnikov

канд. физ.-мат. наук, научный сотрудник Научно-исследовательской части Кубанского государственного университета

e-mail: ilux_t@list.ru

References

  1. Лаверов, Н.П. (ред.), Изменение окружающей среды и климата. Т. 1 Сейсмические процессы и катастрофы. Москва, ИФЗ РАН, 2008. [Laverov, N.P. (ed.), Izmenenie okruzhayushchey sredy i klimata. T. 1 Seysmicheskie protsessy i katastrofy = Environmental and climate change. T. 1 Seismic processes and disasters. Moscow, IPE RAS, 2008. (in Russian)]
  2. Di Toro, G., Han, R., Hirose, T., De Paola, N., Nielsen, S., Mizoguchi, K., Ferri, F., Cocco, M., Shimamoto, T., Fault lubrication during earthquake. Nature, 2011, vol. 471, pp. 494–498. DOI: 10.1038/nature09838
  3. Собисевич, Л.Е., Собисевич, А.Л., Фатьянов, А.Г., Длиннопериодные сейсмогравитационные процессы в литосфере. Москва, ИФЗ РАН, 2020. [Sobisevich, L.E., Sobisevich, A.L., Fatyanov, A.G., Dlinnoperiodnye seysmogravitatsionnye protsessy v litosfere = Long-period seismogravitational processes in the lithosphere. Moscow, IFZ RAN, 2020. (in Russian)]
  4. Садовский, М.А., Болховитинов, Л.Г., Писаренко, В.Ф., Деформирование геофизической среды и сейсмический процесс. Москва, Наука, 1987. [Sadovsky, M.A., Bolkhovitinov, L.G., Pisarenko, V.F., Deformirovanie geofizicheskoy sredy i seysmicheskiy protsess = Deformation of the geophysical medium and seismic process. Moscow, Nauka, 1987. (in Russian)]
  5. Варшанина, Т.П., Коробков, В.Н., Плисенко, О.А., Солодухин, А.А., Структурно подобная геодинамическая модель Краснодарского края и республики Адыгея. Москва-Майкоп, Издательский дом Камертон, 2011. [Varshanina, T.P., Korobkov, V.N., Plisenko, O.A., Solodukhin, A.A., A structurally similar geodynamic model of the Krasnodarsky Region and the Republic of Adygea. Moscow-Maikop, Kamerton Publishing House, 2011. (in Russian)]
  6. Бабешко, В.А., Бабешко, О.М, Евдокимова, О.В., К проблеме исследования материалов с покрытиями. Доклады Академии наук, 2006, т. 410, № 1, с. 49–52. [Babeshko, V.A., Babeshko, O.M., Evdokimova, O.V., On the problem of studying materials with coatings. Doklady Akademii nauk = Rep. of the Academy of Sciences, 2006, vol. 410, no. 1, pp. 49–52. (in Russian)]
  7. Babeshko, V.A., Telyatnikov, I.S., Pavlova, A.V., Kolesnikov, M.N., About one approach in prevention of the emerging dangerous phenomena caused by the existence of defect in continuous media. In: Altenbach, H., Mkhitaryan, S.M., Hakobyan, V., Sahakyan, A.V. (eds), Solid Mechanics, Theory of Elasticity and Creep. Advanced Structured Materials, 2023, vol. 185, pp. 57–76. DOI: 10.1007/978-3-031-18564-9_5
  8. Колесников, М.Н., Павлова, А.В., Телятников, И.С., К исследованию влияния дефекта покрытия на поверхностный волновой процесс. Известия вузов. Северо-Кавказский регион. Естественные науки, 2022, № 4, с. 29–41. [Kolesnikov, M.N., Pavlova, A.V., Telyatnikov, I.S., On the study of the influence of a coating defect on the surface wave process. Izvestiya vuzov. Severo-Kavkazskiy region. Estestvennye nauki = Bull. of Universities. North Caucasus region. Natural Sciences, 2022, no. 4, pp. 29–41. (in Russian)]
  9. Вольмир, А.С., Нелинейная динамика пластинок и оболочек. Москва, Наука, 1972. [Volmir, A.S., Nelineynaya dinamika plastinok i obolochek = Nonlinear dynamics of plates and shells. Moscow, Nauka, 1972. (in Russian)]
  10. Гольденвейзер, А.Л., Теория упругих тонких оболочек. Москва, Наука, 1976. [Goldenweiser, A.L., Teoriya uprugikh tonkikh obolochek = Theory of elastic thin shells. Moscow, Nauka, 1976. (in Russian)]
  11. Ворович, И.И., Бабешко, В.А., Динамические смешанные задачи теории упругости для неклассических областей. Москва, Наука, 1979. [Vorovich, I.I., Babeshko, V.A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey = Dynamic mixed problems of the theory of elasticity for non-classical domains. Moscow, Nauka, 1979. (in Russian)]

Issue

Section

Mechanics

Pages

66-73

Submitted

2023-09-07

Published

2023-09-29

How to Cite

Kolesnikov M.N., Telyatnikov I.S. On the modeling of the wave process near the seam zone of lithospheric structures. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 3, pp. 66-73. DOI: https://doi.org/10.31429/vestnik-20-3-66-73 (In Russian)