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 Компьютерные исследования и моделирование, 2019, том 11, выпуск 6, страницы 1077–1082 (Mi crm763)

THE 3RD BRICS MATHEMATICS CONFERENCE

Application of mathematical fracture models to simulation of exploration seismology problems by the grid-characteristic method

M. V. Muratov, I. B. Petrov

Moscow Institute of Physics and Technology, 9 Institutskii per., Dolgoprudny, Russia

Аннотация: In real problems of exploration seismology we deal with a heterogeneity of the nature of elastic waves interaction with the surface of a fracture by the propagation through it. The fracture is a complex heterogeneous structure. In some locations the surfaces of fractures are placed some distance apart and are separated by filling fluid or emptiness, in some places we can observe the gluing of surfaces, when under the action of pressure forces the fracture surfaces are closely adjoined to each other. In addition, fractures can be classified by the nature of saturation: fluid or gas. Obviously, for such a large variety in the structure of fractures, one cannot use only one model that satisfies all cases.
This article is concerned with description of developed mathematical fracture models which can be used for numerical solution of exploration seismology problems using the grid-characteristic method on unstructured triangular (in 2D-case) and tetrahedral (in 3D-case) meshes. The basis of the developed models is the concept of an infinitely thin fracture, whose aperture does not influence the wave processes in the fracture area. These fractures are represented by bound areas and contact boundaries with different conditions on contact and boundary surfaces. Such an approach significantly reduces the consumption of computer resources since there is no need to define the mesh inside the fracture. On the other side, it allows the fractures to be given discretely in the integration domain, therefore, one can observe qualitatively new effects, such as formation of diffractive waves and multiphase wave front due to multiple reflections between the surfaces of neighbor fractures, which cannot be observed by using effective fracture models actively used in computational seismology.
The computational modeling of seismic waves propagation through layers of mesofractures was produced using developed fracture models. The results were compared with the results of physical modeling in problems in the same statements.

Ключевые слова: grid-characteristic method, exploration seismology problems, mathematical modeling, mathematical models of fractures, mesofractures, physical modeling.

 Финансовая поддержка Номер гранта Российский научный фонд 19-11-00023

DOI: https://doi.org/10.20537/2076-7633-2019-11-6-1077-1082

Полный текст: PDF файл (4298 kB)
Полный текст: http://crm.ics.org.ru/.../2866
Список литературы: PDF файл   HTML файл

Тип публикации: Статья
УДК: 519.63
Поступила в редакцию: 22.05.2019
Принята в печать:14.11.2019
Язык публикации: английский

Образец цитирования: M. V. Muratov, I. B. Petrov, “Application of mathematical fracture models to simulation of exploration seismology problems by the grid-characteristic method”, Компьютерные исследования и моделирование, 11:6 (2019), 1077–1082

Цитирование в формате AMSBIB
\RBibitem{MurPet19} \by M.~V.~Muratov, I.~B.~Petrov \paper Application of mathematical fracture models to simulation of exploration seismology problems by the grid-characteristic method \jour Компьютерные исследования и моделирование \yr 2019 \vol 11 \issue 6 \pages 1077--1082 \mathnet{http://mi.mathnet.ru/crm763} \crossref{https://doi.org/10.20537/2076-7633-2019-11-6-1077-1082} 

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