To the study of the resonance behavior of volcanic structures
UDC
539.422.3DOI:
https://doi.org/10.31429/vestnik-16-3-46-53Abstract
It is known that the geophysical medium in the vicinity of volcanoes is characterized by the presence of significant structural heterogeneities, which differ in their internal structure from the surrounding geological environment. This gives reason to attribute the volcanic structure with heterogeneities to the geological structures of the resonance type, which determine the mechanisms of preparation and development of the catastrophic event, both earthquakes and activation and eruption of the volcano.
It is known that the geophysical environment in the vicinity of volcanoes is characterized by the presence of significant structural heterogeneities, which differ in their internal structure from the surrounding geological environment. This gives reason to attribute the volcanic structure with heterogeneities to the geological structures of the resonance type, which determine the mechanisms of preparation and development of the catastrophic events such as earthquakes, and the activation and eruption of the volcano.
During the study of the volcanic structure resonance behavior modeled by a block structure, it is necessary to analyze the pseudo-differential equations that arise in the implementation process of the block element method and the differential factorization method. By extracting from them the corresponding integral or integro-differential equations, we are able to write out the conditions that describe the so-called "natural viruses", which can be considered as a generalization of the static conditions. Mathematical descriptions of the "viruses" allow us to find the conditions when the localization of selected parameters occurs, possible under certain conditions in reality.
In the paper we study the resonance properties of particular models of volcanic structures. We obtain an expression for the ``virus'' of a volcanic structure modeled by a stamp on an elastic foundation in the form of a layer, as well as establish the existence of system parameters which lead to the occurrence of unlimited resonance.
To study processes in the environment of trap provinces, we present a model of a tectonic plate, represented by a layer of finite thickness with the distributed load applied to the upper surface simulating anthropogenic effect and distributed load applied to lower surface simulating the effect of the environment of mantle plumes. In the model under consideration, we use the integral Fourier transform, which allows us to reduce the dimension of the problem and construct functional relations for obtaining the Fourier images of the main characteristics of the system, which are further determined by applying the inverse Fourier transform using the apparatus of residue theory. The obtained expressions provide an opportunity for studying the laws of the emerging fields of displacements and stresses in the environment of the trap province.
Keywords:
volcanic structure, resonance type, localization conditions, natural viruses, trap provinceFunding information
Отдельные результаты работы получены при поддержке РФФИ (проекты 18-01-00124, 19-08-00145), РФФИ и Администрации Краснодарского края (проект 19-41-230002).
References
- Рогожин Е.А., Овсюченко А.Н., Лутиков А.И., Собисевич А.Л., Собисевич Л.Е., Горбатиков А.В. Эндогенные опасности Большого Кавказа. М.: ИФЗ РАН, 2014. 256 с. [Rogozhin, Ye.A., Ovsyuchenko, A.N., Lutikov, A.I., Sobisevich, A.L., Sobisevich, L.Ye., Gorbatikov, A.V. Endogennyye opasnosti Bol'shogo Kavkaza [Endogenous hazards of the Greater Caucasus]. Izdatelstvo IFZ RAN, Moscow, 2014. (In Russian)]
- Собисевич А.Л. Избранные задачи математической геофизики, вулканологии и геоэкологии. Том 1. М.: ИФЗ РАН, 2012. 512 с. [Sobisevich, A.L. Izbrannyye zadachi matematicheskoy geofiziki, vulkanologii i geoekologii [Selected problems of mathematical geophysics, volcanology and geoecology]. Vol. 1. Izdatelstvo IFZ RAN, Moscow, 2012. (In Russian)]
- Павлова А.В., Павлова А.В., Зарецкая М.В., Капустин М.С., Лозовой В.В. К исследованию волновых процессов в блочной структуре вулканической постройки // Экологический вестник научных центров Черноморского экономического сотрудничества. 2019. Т. 16. № 2. С. 30–37. [Pavlova, A.V., Pavlova, A.V., Zaretskaya, M.V., Kapustin, M.S., Lozovoy, V.V. K issledovaniyu volnovykh protsessov v blochnoy strukture vulkanicheskoy postroyki [To the study of wave processes in the block structure of a volcanic structure]. Jekologicheskij vestnik nauchnyh centrov chernomorskogo jekonomicheskogo sotrudnichestva [Ecological Bulletin of the Scientific Centers of the Black Sea Economic Cooperation], 2019, vol. 16, no. 2, pp. 30–37. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. О "вирусной" теории некоторых аномальных природных явлений // ДАН. 2012. Т. 447. № 1. С. 33–37. [Babeshko, V.A., Yevdokimova, O.V., Babeshko, O.M. O "virusnoy" teorii nekotorykh anomal'nykh prirodnykh yavleniy [On the "viral" theory of some anomalous natural phenomena]. Doklady akademii nauk [Doklady Physics], 2012, vol. 447, no. 1. pp. 33–37. (In Russian)]
- Бабешко В.А., Ритцер Д., Евдокимова О.В., Бабешко О.М. О локализации энергии природных процессов и природные вирусы // ДАН. 2013. Т. 448. № 4. С. 406–409. [Babeshko, V.A., Rittser, D., Yevdokimova, O.V., Babeshko, O.M. O lokalizatsii energii prirodnykh protsessov i prirodnyye virusy [On the localization of the energy of natural processes and natural viruses]. Doklady akademii nauk [Doklady Physics], 2013, vol. 448, no. 4, pp. 406–409. (In Russian)]
- Вильямс Р., Павлова А.В., Ратнер С.В. Исследование "вирусов" вибропрочности при моделировании геологических структур // Экологический вестник научных центров Черноморского экономического сотрудничества. 2003. № 1. С. 33–35. [Vil'yams, R., Pavlova, A.V., Ratner, S.V. Issledovaniye "virusov" vibroprochnosti pri modelirovanii geologicheskikh struktur [The study of ``viruses'' of vibration strength in the modeling of geological structures]. Jekologicheskij vestnik nauchnyh centrov chernomorskogo jekonomicheskogo sotrudnichestva [Ecological Bulletin of the Scientific Centers of the Black Sea Economic Cooperation], 2003, no. 1, p. 33. (In Russian)]
- Ворович И.И., Бабешко В.А., Пряхина О.Д. Динамика массивных тел и резонансные явления в деформируемых средах. М.: Научный мир, 1999. 246 с. [Vorovich, I.I., Babeshko, V.A., Pryakhina, O.D. Dinamika massivnyh tel i rezonansnye javlenija v deformiruemyh sredah [Dynamic Behavior of Massive Bodies and Resonance Phenomena in Deformable Media]. Nauchn. Mir, Moscow, 1999. (In Russian)]
- Ворович И.И., Бабешко В.А. Динамические смешанные задачи теории упругости для неклассических областей. М.: Наука, 1979. 320 с. [Vorovich, I.I., Babeshko, V.A. Dinamicheskiye smeshannyye zadachi teorii uprugosti dlya neklassicheskikh oblastey [Dynamic mixed problems of elasticity theory for non-classical domains]. Nauka, Moscow, 1979. 320 p. (In Russian)]
- Бабешко В.А., Бабешко О.М., Горшкова Е.М., Зарецкая М.В., Павлова А.В., Телятников И.С. Исследование поведения структурно неоднородных сред с изменяющимися свойствами // Экологический вестник научных центров черноморского экономического сотрудничества. 2013. № 3. С. 5–11. [Babeshko, V.A., Babeshko, O.M., Gorshkova, E.M., Zareckaja, M.V., Pavlova, A.V., Teljatnikov I.S. Issledovanie povedenija strukturno neodnorodnyh sred s izmenjajushhimisja svojstvami [Investigation of the behavior of structurally heterogeneous media with changing properties]. Jekologicheskij vestnik nauchnyh centrov chernomorskogo jekonomicheskogo sotrudnichestva [Ecological Bulletin of the Scientific Centers of the Black Sea Economic Cooperation], 2013. no. 3, pp. 5–11. (In Russian)]
Downloads
Downloads
Dates
Submitted
Accepted
Published
How to Cite
License
Copyright (c) 2019 Зарецкая М.В., Бабешко О.М., Павлова А.В., Телятников И.С.
This work is licensed under a Creative Commons Attribution 4.0 International License.
