ellibsЭлектронные библиотекиRussian Digital Libraries Journal1562-5419Казанский (Приволжский) федеральный университет10.26907/1562-5419-2020-23-6-1192-1212ellibs-256Research ArticleСтатьиПерсистентные гомологии: применение к мониторингу образования трещин при гидроразрыве пластаPersistent Homology: Application To Monitoring Hydraulic FracturingЕрофеевК. Ю.ErofeevK. Y.krllerof@gmail.comЗиятдиновМ. Т.ZiiatdinovM. T.gltronred@gmail.comМокшинЕ. В.MokshinE. V.zhen-moks@yandex.ru20202812202023611921212Copyright © Ерофеев К.Ю., Зиятдинов М.Т., Мокшин Е.В., 20202020Ерофеев К.Ю., Зиятдинов М.Т., Мокшин Е.В.Erofeev K.Y., Ziiatdinov M.T., Mokshin E.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ellibs.elpub.ru/jour/article/view/256

Персистентные гомологии – это инструмент топологического анализа данных, отражающий то, как изменяется топологическая структура данных с изменением масштаба их восприятия. В статье дано применение персистентных гомологий к мониторингу образования трещин при гидроразрыве пласта, что позволяет исследователю естественным образом учитывать априорную информацию.

Persistent homology is a topological data analysis tool which is reflecting changes in topological structure of data along its scale. Application of persistent homology to monitoring hydraulic fracturing which is allowing researchers to consider prior information in a natural way is given in the article

топологический анализ данныхперсистентные гомологиигидроразрыв пластамикросейсмические событияtopological data analysispersistent homologyhydraulic fracturingmicroseismic eventsReferencesHerbert Edelsbrunner, John Harer. Persistent Homology — a Survey // Contemporary Mathematics. 2007. P. 103–120.Herbert Edelsbrunner, John Harer. Persistent Homology — a Survey // Contemporary Mathematics. 2007. P. 103–120.Herbert Edelsbrunner, Donald Kirkpatrick, Rainmund Siedel. On the shape of a set of points in the plane // IEEE Trans. Inform. Theory. 1983. P. 103–120.Herbert Edelsbrunner, Donald Kirkpatrick, Rainmund Siedel. On the shape of a set of points in the plane // IEEE Trans. Inform. Theory. 1983. P. 103–120.Vanessa Robins. Toward computing homology from finite approxima-tions // Topology Proceedings. 1999. V. 24, No. 1. P. 503–532.Vanessa Robins. Toward computing homology from finite approxima-tions // Topology Proceedings. 1999. V. 24, No. 1. P. 503–532.Herbert Edelsbrunner, David Letscher, Afra Zomordian. Topological Per-sistence and Simplification // Discrete Comput. Geom. 2002. V. 28. P. 511–533. DOI: 10.1007/s00454-002-2885-2.Herbert Edelsbrunner, David Letscher, Afra Zomordian. Topological Per-sistence and Simplification // Discrete Comput. Geom. 2002. V. 28. P. 511–533. DOI: 10.1007/s00454-002-2885-2.‪David Cohen-Steiner, Herbert Edelsbrunner, John Harer. Stability of Per-sistence Diagrams // Discrete Comput. Geom. 2007. V. 37. P. 103–120. DOI: 10.1007/s00454-006-1276-5.‬‬‬‬‬‬‪David Cohen-Steiner, Herbert Edelsbrunner, John Harer. Stability of Per-sistence Diagrams // Discrete Comput. Geom. 2007. V. 37. P. 103–120. DOI: 10.1007/s00454-006-1276-5.‬‬‬‬‬‬Xiaojin Zhu. Persistent Homology: An Introduction and a New Text Rep-resentation for Natural Language // IJCAI International Joint Conference on Artificial Intelligence. 2013. P. 1953–1959.Xiaojin Zhu. Persistent Homology: An Introduction and a New Text Rep-resentation for Natural Language // IJCAI International Joint Conference on Artificial Intelligence. 2013. P. 1953–1959.Gurjeet Singh, Facundo Memoli, Tigran Ishkhanov, Guillermo Sapiro, Gunnar Carlsson, Dario L. Ringach. Topological analysis of population activity in visual cortex // Journal of Vision. 2008.V. 8, No. 11. DOI: 10.1167/8.8.11.Gurjeet Singh, Facundo Memoli, Tigran Ishkhanov, Guillermo Sapiro, Gunnar Carlsson, Dario L. Ringach. Topological analysis of population activity in visual cortex // Journal of Vision. 2008.V. 8, No. 11. DOI: 10.1167/8.8.11.Vin de Silva, Robert Ghrist. Homological sensor networks // Notices of the American Mathematical Society. 2007. V. 54, No. 1. P. 10–17.Vin de Silva, Robert Ghrist. Homological sensor networks // Notices of the American Mathematical Society. 2007. V. 54, No. 1. P. 10–17.Frederic Chazal, Steve Y. Oudot, Primoz Skraba, Leonidas J. Guibas. Per-sistence-Based Clustering in Riemannian Manifolds // Journal of the ACM. 2013. V. 60, No. 6. Article No 14. DOI: 10.1145/1998196.1998212.Frederic Chazal, Steve Y. Oudot, Primoz Skraba, Leonidas J. Guibas. Per-sistence-Based Clustering in Riemannian Manifolds // Journal of the ACM. 2013. V. 60, No. 6. Article No 14. DOI: 10.1145/1998196.1998212.Sven Heydenreich, Benjamin Bruck, Joachim Harnois-Deraps. Persistent homology in cosmic shear: constraining parameters with topological data analysis // arXiv:2007.13724.Sven Heydenreich, Benjamin Bruck, Joachim Harnois-Deraps. Persistent homology in cosmic shear: constraining parameters with topological data analysis // arXiv:2007.13724.Moon Duchin, Tom Needham, Thomas Weighill. The (homological) per-sistence of gerrymandering // arXiv:2007.02390.Moon Duchin, Tom Needham, Thomas Weighill. The (homological) per-sistence of gerrymandering // arXiv:2007.02390.James Rutledge, Phillips W.S., House L.S., Zinno R.J. Microseismic map-ping of a Cotton Valley hydraulic fracture using Decimated downhole arrays // SEG Technical Program Expanded Abstracts. 1998. P. 338–341. DOI: 10.1190/1.1820422.James Rutledge, Phillips W.S., House L.S., Zinno R.J. Microseismic map-ping of a Cotton Valley hydraulic fracture using Decimated downhole arrays // SEG Technical Program Expanded Abstracts. 1998. P. 338–341. DOI: 10.1190/1.1820422.Serge A. Shapiro. Fluid-Induced Seismicity.2015. 289 p.Serge A. Shapiro. Fluid-Induced Seismicity.2015. 289 p.T.I. Urbancic, V. Shumila, J.T. Rutledge, R.J. Zinn. Determining Hydraulic Fracture Behaviour Using Microseismicity // Proceedings of 37th U.S. Rock Mech. Symp. 1999. P. 991–996.T.I. Urbancic, V. Shumila, J.T. Rutledge, R.J. Zinn. Determining Hydraulic Fracture Behaviour Using Microseismicity // Proceedings of 37th U.S. Rock Mech. Symp. 1999. P. 991–996.T.I. Urbancic, S.C. Maxwell. Source Parameters of Hydraulic Fracture In-duced Microseismicity // SPE Annual Technical Conference and Exhibition, 2002. DOI: 10.2118/77439-MS.T.I. Urbancic, S.C. Maxwell. Source Parameters of Hydraulic Fracture In-duced Microseismicity // SPE Annual Technical Conference and Exhibition, 2002. DOI: 10.2118/77439-MS.Tatjana Yanovskaya. Основы сейсмологии. Изд-во С.-Пб. ун-та. 2008. 222 с.Tatjana Yanovskaya. Основы сейсмологии. Изд-во С.-Пб. ун-та. 2008. 222 с.Keiiti Aki, Paul G. Richards. Quantitative Seismology // San Francisco, CA: Freeman, 1980. 49 p.Keiiti Aki, Paul G. Richards. Quantitative Seismology // San Francisco, CA: Freeman, 1980. 49 p.

The authors declare that there are no conflicts of interest present.