Mathematical modelling of the elastic behavior of structured geophysical media
From the viewpoint of modern concepts of nonlinear geophysics, the presence of the hierarchicalblock structure, anisotropy and heterogeneities is the defining property of the natural medium in particular of the Earth.s crust. A lot of achievements of modern self-organization theory in geophysicsare...
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Інститут геофізики ім. С.I. Субботіна НАН України
2017
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| Назва видання: | Геофизический журнал |
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| Цитувати: | Mathematical modelling of the elastic behavior of structured geophysical media / N.V. Olali, D.B. Vengrovich, M.P. Malezhyk // Геофизический журнал. — 2017. — Т. 39, № 5. — С. 92-104. — Бібліогр.: 9 назв. — англ. |
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From the viewpoint of modern concepts of nonlinear geophysics, the presence of the hierarchicalblock structure, anisotropy and heterogeneities is the defining property of the natural medium in particular of the Earth.s crust. A lot of achievements of modern self-organization theory in geophysicsare based on the existence of basic structured media models. The structure plays a key role in Earth.scrust dynamic that is important for tectonic stress origin and localization as well as for next stress-relieved processes. As shown in [Starostenko et al., 2001], it is necessary to describe such a structuredmedia at the micro-, meso- and macro-level as a sets of interacting blocks. Mathematical models created in such a way in particular numerical models of the dynamics of block-structured lithosphere allow us to describe reliably such tectonic processes as the formation and evolution of the rift sedimentary basins [Starostenko et al., 2001], Earth.s crust compression in the subduction zones [Vengrovich, 2017], or faster tectonic processes of halo kinesis [Vengrovich, 2010]. The mechanism of localaccumulation and emission of energy in the seismic waves form, which could be a way of creating anew model of earthquake source, was revealed during the investigation of rifting [Starostenko et al.,1996] and new subduction process modelling in the frame of block-structured lithosphere theory.However tectonic and seismic processes go far beyond the spatial and temporal scales. Used approaches need to be implemented in numerous models on the micro and mesolevel where it is extremelycostly to calculate the dynamics of a huge number of interacting blocks. Therefore, we propose themathematical model of the elastic behavior of the structured geophysical media allowing to obtainanalytical dependencies between its elastic parameters and structure. We describe such environment in the first approximation as an elastic solid matrix with the inclusions of granules with excellentrheological properties. As usual rock formations keep irregular positions of particles different shapesand sizes in the space. These particles can be separated from the binder by fracturing. However, inthis paper, we neglect nonregularity, fracturings, cap it all the granules will be considered as spherical. We combined the optical method of photo-elasticity studies [Malezhyk, 2001; Sirotin, Shaskol-skaja, 1975; Sneddon, 1958; Christensen, 1979] and numerical calculations (FEM model) of stress fi-elds dynamic in structured media using finite element analysis, overall, in such a way the proposedanalytical model will be proofed. |
| format |
Article |
| author |
Olali, N.V. Vengrovich, D.B. Malezhyk, M.P. |
| spellingShingle |
Olali, N.V. Vengrovich, D.B. Malezhyk, M.P. Mathematical modelling of the elastic behavior of structured geophysical media Геофизический журнал |
| author_facet |
Olali, N.V. Vengrovich, D.B. Malezhyk, M.P. |
| author_sort |
Olali, N.V. |
| title |
Mathematical modelling of the elastic behavior of structured geophysical media |
| title_short |
Mathematical modelling of the elastic behavior of structured geophysical media |
| title_full |
Mathematical modelling of the elastic behavior of structured geophysical media |
| title_fullStr |
Mathematical modelling of the elastic behavior of structured geophysical media |
| title_full_unstemmed |
Mathematical modelling of the elastic behavior of structured geophysical media |
| title_sort |
mathematical modelling of the elastic behavior of structured geophysical media |
| publisher |
Інститут геофізики ім. С.I. Субботіна НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/127669 |
| citation_txt |
Mathematical modelling of the elastic behavior of structured geophysical media / N.V. Olali, D.B. Vengrovich, M.P. Malezhyk // Геофизический журнал. — 2017. — Т. 39, № 5. — С. 92-104. — Бібліогр.: 9 назв. — англ. |
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Геофизический журнал |
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AT olalinv mathematicalmodellingoftheelasticbehaviorofstructuredgeophysicalmedia AT vengrovichdb mathematicalmodellingoftheelasticbehaviorofstructuredgeophysicalmedia AT malezhykmp mathematicalmodellingoftheelasticbehaviorofstructuredgeophysicalmedia |
| first_indexed |
2023-10-18T20:53:36Z |
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2023-10-18T20:53:36Z |
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1796151383527784448 |
| spelling |
irk-123456789-1276692017-12-25T03:03:13Z Mathematical modelling of the elastic behavior of structured geophysical media Olali, N.V. Vengrovich, D.B. Malezhyk, M.P. From the viewpoint of modern concepts of nonlinear geophysics, the presence of the hierarchicalblock structure, anisotropy and heterogeneities is the defining property of the natural medium in particular of the Earth.s crust. A lot of achievements of modern self-organization theory in geophysicsare based on the existence of basic structured media models. The structure plays a key role in Earth.scrust dynamic that is important for tectonic stress origin and localization as well as for next stress-relieved processes. As shown in [Starostenko et al., 2001], it is necessary to describe such a structuredmedia at the micro-, meso- and macro-level as a sets of interacting blocks. Mathematical models created in such a way in particular numerical models of the dynamics of block-structured lithosphere allow us to describe reliably such tectonic processes as the formation and evolution of the rift sedimentary basins [Starostenko et al., 2001], Earth.s crust compression in the subduction zones [Vengrovich, 2017], or faster tectonic processes of halo kinesis [Vengrovich, 2010]. The mechanism of localaccumulation and emission of energy in the seismic waves form, which could be a way of creating anew model of earthquake source, was revealed during the investigation of rifting [Starostenko et al.,1996] and new subduction process modelling in the frame of block-structured lithosphere theory.However tectonic and seismic processes go far beyond the spatial and temporal scales. Used approaches need to be implemented in numerous models on the micro and mesolevel where it is extremelycostly to calculate the dynamics of a huge number of interacting blocks. Therefore, we propose themathematical model of the elastic behavior of the structured geophysical media allowing to obtainanalytical dependencies between its elastic parameters and structure. We describe such environment in the first approximation as an elastic solid matrix with the inclusions of granules with excellentrheological properties. As usual rock formations keep irregular positions of particles different shapesand sizes in the space. These particles can be separated from the binder by fracturing. However, inthis paper, we neglect nonregularity, fracturings, cap it all the granules will be considered as spherical. We combined the optical method of photo-elasticity studies [Malezhyk, 2001; Sirotin, Shaskol-skaja, 1975; Sneddon, 1958; Christensen, 1979] and numerical calculations (FEM model) of stress fi-elds dynamic in structured media using finite element analysis, overall, in such a way the proposedanalytical model will be proofed. З точки зору сучасної нелінійної геофізики неоднорідність, наявність ієрархічної блоковоїструктури, анізотропія є визначальними властивостями природного середовища, зокрема земної кори. Багато досягнень сучасної теорії самоорганізації в геофізиці ґрунтуються на вже споруджуваних базових моделях структурованих середовищ. Структура грає ключову роль в динаміці земної кори, вона має велике значення для виникнення тектонічних напружень, їх локалізації і наступних процесів їх вивільнення. Як показано в роботі [Старостенко и др., 2001], такіструктуровані середовища необхідно описати на мікро-, мезо- і макрорівнях у рамках моделейвзаємодіючих блоків, які дозволяють достовірно описати такі тектонічні процеси, як формування і еволюція рифтових осадових басейнів, стиснення земної кори в зонах субдукції [Венгрович2017], соляну тектоніку [Венгрович, 2010]. Використовувані підходи для розрахунку динамікивеличезного числа взаємодіючих блоків дуже затратні. Запропоновано математичну модельпружної поведінки структурованого геофізичного середовища, що дозволяє в певних випадкахотримати аналітичні залежності між її пружними параметрами і структурою. Середовище описано в першому наближенні твердою матрицею з включенням гранул з іншими реологічнимивластивостями. Представлені чисельні (модель МСЕ) і аналітичні розрахунки полів напруженьв реальних середовищах для моделей з внутрішньою періодичною структурою, порівнянняяких підтверджує широкі межі застосування запропонованої аналітичної моделі.Ґ 2017 Article Mathematical modelling of the elastic behavior of structured geophysical media / N.V. Olali, D.B. Vengrovich, M.P. Malezhyk // Геофизический журнал. — 2017. — Т. 39, № 5. — С. 92-104. — Бібліогр.: 9 назв. — англ. 0203-3100 DOI: doi.org/10.24028/gzh.0203-3100.v39i5.2017.112345 http://dspace.nbuv.gov.ua/handle/123456789/127669 550.34 en Геофизический журнал Інститут геофізики ім. С.I. Субботіна НАН України |