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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">gtcrust</journal-id><journal-title-group><journal-title xml:lang="ru">Геодинамика и тектонофизика</journal-title><trans-title-group xml:lang="en"><trans-title>Geodynamics &amp; Tectonophysics</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2078-502X</issn><publisher><publisher-name>Institute of the Earth's crust of the Russian Academy of Sciences, Siberian Branch</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.5800/GT-2019-10-1-0402</article-id><article-id custom-type="elpub" pub-id-type="custom">gtcrust-767</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ТЕКТОНОФИЗИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TECTONOPHYSICS</subject></subj-group></article-categories><title-group><article-title>МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ФОРМИРОВАНИЯ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ ЭПИПЛАТФОРМЕННЫХ ОРОГЕНОВ</article-title><trans-title-group xml:lang="en"><trans-title>MATHEMATICAL MODELS SIMULATING THE FORMATION OF THE STRESS-STRAIN STATE OF EPIPLATFORM OROGENS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мягков</surname><given-names>Д. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Myagkov</surname><given-names>D. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Дмитрий Сергеевич Мягков - научный сотрудник</p><p>123242, ГСП-5, Москва Д-242, ул. Большая Грузинская, 10</p></bio><bio xml:lang="en"><p>Dmitriy S. Myagkov - Researcher</p><p>10 Bol’shaya Gruzinskaya street, Moscow D-242 123242, GSP-5</p></bio><email xlink:type="simple">Dmitriymyagkov92@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3492-2452</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ребецкий</surname><given-names>Ю. Л.</given-names></name><name name-style="western" xml:lang="en"><surname>Rebetsky</surname><given-names>Yu. L.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Юрий Леонидович Ребецкий - доктор физико-математических наук, заведующий лабораторией</p><p>123242, ГСП-5, Москва Д-242, ул. Большая Грузинская, 10</p></bio><bio xml:lang="en"><p>Yuri L. Rebetsky - Doctor of Physics and Mathematics, Head of Laboratory</p><p>10 Bol’shaya Gruzinskaya street, Moscow D-242 123242, GSP-5</p></bio><email xlink:type="simple">reb@ifz.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт физики Земли им. О.Ю. Шмидта РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>O.Yu. Schmidt Institute of Physics of the Earth of RAS</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>21</day><month>03</month><year>2019</year></pub-date><volume>10</volume><issue>1</issue><fpage>21</fpage><lpage>41</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Мягков Д.С., Ребецкий Ю.Л., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Мягков Д.С., Ребецкий Ю.Л.</copyright-holder><copyright-holder xml:lang="en">Myagkov D.S., Rebetsky Y.L.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.gt-crust.ru/jour/article/view/767">https://www.gt-crust.ru/jour/article/view/767</self-uri><abstract><p>Рассматривается вопрос об источниках формирования природного напряженно-деформированного состояния (НДС) эпиплатформенных орогенов, исследуемого тектонофизическими методами на основе сейсмологических данных. Такого рода данные свидетельствуют о преобладании горизонтальной ориентации осей главного девиаторного растяжения во впадинах и осей главного девиаторного сжатия в хребтах орогенов. Проводится сравнительный анализ НДС коры орогена, источником которого выступают «общепринятые» геодинамические процессы: давление на Евразийскую плиту со стороны Индийской и действие мелкомасштабной термогравитационной астеносферной конвекции. Исследование проводилось методом математического (аналитического) моделирования, основным критерием тектонофизической корректности модели считалось соответствие распределения ориентаций главных осей тензора напряжений в коровой части моделей природным данным. Моделирование показало, что НДС литосферы, формирующееся в обстановке латерального сжатия, менее соответствует искомому. Вторая модель также показала результаты, не вполне соответствующие данным тектонофизической реконструкции напряжений. Однако дополнительный анализ позволил установить, что астеносферная конвекция является более перспективным, с точки зрения тектонофизики, геодинамическим процессом для объяснения эпиплатформенного орогенеза. Мы считаем, что в рамках более сложных и, вероятно, неаналитических математических моделей этот источник нагружения литосферы должен рассматриваться как один из наиболее существенных факторов формирования НДС коры орогенов Центральной Азии.</p></abstract><trans-abstract xml:lang="en"><p>The sources of the natural stress-strain state (SSS) of epiplatform orogens are investigated by tectonophysical methods based on seismological data. According to the available data, the horizontal axes of the main deviatoric extension are dominant in depressions, while in the ridges of the orogens, the axes of the main deviatorial compression are dominant.Our comparative analysis is focused on SSS of the orogenic crust. It is generally accepted that the sources of such SSS are geodynamic processes, including the pressure on the Eurasian Plate from the Indian Plate, and the small-scale thermogravitational asthenospheric convection. In the mathematical (analytical) simulation technique used in our study, the main criterion for the correctness of models in terms of tectonophysics is the correspondence between the orientation pattern of the principal stress tensor axes in the crust model to the natural data. According to Model I, the lithospheric SSS under lateral compression is less consistent with the sought-for SSS. Model II also gives the results that do not fully correspond to the stress data from tectonophysical reconstructions. However, additional analysis suggests that asthenospheric convection is a more promising (from the point of view of tectonophysics) geodynamic process for explaining epiplatform orogenesis. In our opinion, more complex and probably non-analytical mathematical models should consider this source of loading of the lithosphere as one of the most significant factors in the formation of the orogenic crust SSS in Central Asia.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>аналитическое моделирование</kwd><kwd>эпиплатформенный орогенез</kwd><kwd>напряженное состояние горных массивов</kwd></kwd-group><kwd-group xml:lang="en"><kwd>analytical modeling</kwd><kwd>epiplatform orogenesis</kwd><kwd>stress state of mountain ranges</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">РФФИ (проекты № 18-35-00482 и № 16-05-01115) и в рамках Государственного задания ИФЗ РАН</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Ahnert F., 1970. Functional relationships between denudation, relief, and uplift in large, mid-latitude drainage basins. 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