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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">geophystech</journal-id><journal-title-group><journal-title xml:lang="ru">Геофизические технологии</journal-title><trans-title-group xml:lang="en"><trans-title>Russian Journal of Geophysical Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2619-1563</issn><publisher><publisher-name>IPGG SB RAS</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.18303/2619-1563-2022-1-99</article-id><article-id custom-type="elpub" pub-id-type="custom">geophystech-216</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>Статьи</subject></subj-group></article-categories><title-group><article-title>Искусственная нейронная сеть, уменьшающая численную дисперсию, для постобработки результатов сейсмического моделирования</article-title><trans-title-group xml:lang="en"><trans-title>Deep neural network reducing numerical dispersion for post-processing of seismic modeling results</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>Гадыльшина</surname><given-names>К. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Gadylshina</surname><given-names>K. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Младший научный сотрудник лаборатории вычислительной физики горных пород Института нефтегазовой геологии и геофизики СО РАН. Основные научные интересы: методы машинного обучения в приложении к решению задач геофизики.630090, Новосибирск, просп. Акад. Коптюга, 3</p></bio><bio xml:lang="en"><p>Koptyug Ave., 3, Novosibirsk, 630090</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3544-4878</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лисица</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Lisitsa</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Доктор физико-математических наук, заведующий лабораторией вычислительной физики горных пород Института нефтегазовой геологии и геофизики СО РАН. Основные научные интересы: численные методы для моделирования физических процессов в пористых средах.630090, Новосибирск, просп. Акад. Коптюга, 3</p></bio><bio xml:lang="en"><p>Koptyug Ave., 3, Novosibirsk, 630090</p></bio><email xlink:type="simple">LisitsaVV@ipgg.sbras.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Вишневский</surname><given-names>Д. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Vishnevsky</surname><given-names>D. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Научный сотрудник лаборатории вычислительной физики горных пород Института нефтегазовой геологии и геофизики СО РАН. Основные научные интересы: численное моделирование сейсмических волновых полей, высокопроизводительные вычисления.630090, Новосибирск, просп. Акад. Коптюга, 3</p></bio><bio xml:lang="en"><p>Koptyug Ave., 3, Novosibirsk, 630090</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гадыльшин</surname><given-names>К. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Gadylshin</surname><given-names>K. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кандидат физико-математических наук, старший научный сотрудник лаборатории вычислительной физики горных пород Института нефтегазовой геологии и геофизики СО РАН. Основные научные интересы: прямые и обратные задачи сейсмики, применение методов машинного обучения для повышения качества сейсмических данных.630090, Новосибирск, просп. Акад. Коптюга, 3</p></bio><bio xml:lang="en"><p>Koptyug Ave., 3, Novosibirsk, 630090</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Институт нефтегазовой геологии и геофизики им. А.А. Трофимука СО РАН<country>Россия</country></aff><aff xml:lang="en">Trofimuk Institute of Petroleum Geology and Geophysics SB RAS<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>14</day><month>12</month><year>2022</year></pub-date><volume>0</volume><issue>1</issue><fpage>99</fpage><lpage>109</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Гадыльшина К.А., Лисица В.В., Вишневский Д.М., Гадыльшин К.Г., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Гадыльшина К.А., Лисица В.В., Вишневский Д.М., Гадыльшин К.Г.</copyright-holder><copyright-holder xml:lang="en">Gadylshina K.A., Lisitsa V.V., Vishnevsky D.M., Gadylshin K.G.</copyright-holder><license 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.rjgt.ru/jour/article/view/216">https://www.rjgt.ru/jour/article/view/216</self-uri><abstract><p>В работе описан новый подход к сейсмическому моделированию, сочетающий традиционный конечно-разностный метод с глубоким обучением. На первом шаге генерируется обучающий набор данных, рассчитанный для ограниченного числа источников. Этот набор вычисляется путем конечно-разностного моделирования на мелкой пространственно-временной сетке. На втором этапе рассчитываются сейсмограммы для всей системы наблюдения, но с использованием грубой расчетной сетки. На третьем, заключительном этапе происходит обучение искусственной нейронной сети, уменьшающей численную дисперсию, и ее применение ко всему набору данных. На тестовом материале проверена работоспособность такого подхода в задаче подавления численной дисперсии и продемонстрировано десятикратное ускорение расчетов сейсмических волновых полей.</p></abstract><trans-abstract xml:lang="en"><p>The article describes a new approach to seismic modeling that combines calculations using traditional finite difference methods with the deep learning tools. Seismograms for the training data set are calculated using a finite difference scheme with high-quality spatial and temporal discretization. A numerical dispersion mitigation neural network is trained on the training dataset and applied to inaccurate seismograms calculated on a raw grid with a large spatial spacing. The paper presents a demonstration of this approach for 2D model; it is showing a tenfold acceleration of seismic modeling.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Сейсмическое моделирование</kwd><kwd>численная дисперсия</kwd><kwd>глубокое обучение</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Seismic modelling</kwd><kwd>numerical dispersion</kwd><kwd>deep learning</kwd></kwd-group><funding-group xml:lang="ru"><funding-statement>Разработки выполнены при Российского научного фонда (гранты №№ 22-11-00004 и 22-21-00738) и проекта ФНИ № 0266-2022-0022.</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">Abadi M., Agarwal A., Barham P., Brevdo E., Chen Z., Citro C., Corrado G., Davis A., Dean J., Devin M., Ghemawat S., Goodfellow I., Harp A., Irving G., Isard M., Jia Y., Jozefowicz R., Kaiser L., Kudlur M., Levenberg J., Mané D., Monga R., Moore S., Murray D., Olah C., Schuster M., Shlens J., Steiner B., Sutskever I., Talwar K., Tucker P., Vanhoucke V., Vasudevan V., Viégas F., Vinyals O., Warden P., Wattenberg M., Wicke M., Yu Y., Zheng X. 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