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<article 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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Geomagnetism and Aeronomy</journal-id><journal-title-group><journal-title xml:lang="en">Geomagnetism and Aeronomy</journal-title><trans-title-group xml:lang="ru"><trans-title>Геомагнетизм и аэрономия</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0016-7940</issn><issn publication-format="electronic">3034-5022</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">650921</article-id><article-id pub-id-type="doi">10.31857/S0016794024040069</article-id><article-id pub-id-type="edn">RTQHJH</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Статьи</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Verification of the empirical model of ionization of the lower ionosphere during solar flares of different classes</article-title><trans-title-group xml:lang="ru"><trans-title>Верификация эмпирической модели ионизации нижней ионосферы во время солнечных вспышек различного класса</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Ryakhovsky</surname><given-names>I. A.</given-names></name><name xml:lang="ru"><surname>Ряховский</surname><given-names>И. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>ryakhovskiy88@yandex.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Poklad</surname><given-names>Y. V.</given-names></name><name xml:lang="ru"><surname>Поклад</surname><given-names>Ю. В.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>poklad@mail.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Gavrilov</surname><given-names>B. G.</given-names></name><name xml:lang="ru"><surname>Гаврилов</surname><given-names>Б. Г.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>boris.gavrilov34@gmail.com</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Sadovsky Institute of Geospheres Dynamics, Russian Academy of Sciences</institution></aff><aff><institution xml:lang="ru">Институт динамики геосфер им. акад. М.А. Садовского РАН (ИДГ РАН)</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2024-08-23" publication-format="electronic"><day>23</day><month>08</month><year>2024</year></pub-date><volume>64</volume><issue>4</issue><issue-title xml:lang="ru">ГЕОМАГНЕТИЗМ И АЭРОНОМИЯ</issue-title><fpage>512</fpage><lpage>518</lpage><history><date date-type="received" iso-8601-date="2025-02-01"><day>01</day><month>02</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2024, Russian Academy of Sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2024, Российская академия наук</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="en">Russian Academy of Sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://journals.eco-vector.com/0016-7940/article/view/650921">https://journals.eco-vector.com/0016-7940/article/view/650921</self-uri><abstract xml:lang="en"><p>Using the results of measurements of VLF signal parameters propagating in the Earth-D-region of the ionosphere waveguide to assess changes in the state of the lower ionosphere as a result of the impact of X-ray radiation of solar flares, allows us to obtain qualitative data on the nature and magnitude of the impact. Obtaining accurate data on the relationship between changes in electron concentration and flare parameters and reliable prediction of the conditions of propagation of LF radio signals in conditions of strong geophysical disturbances is complicated by the lack of complete information on the frequency spectrum of X-ray radiation at a particular flare and data on the ionization rate of the ionosphere at flares of different classes. The technique of determining the X-ray spectrum in a wide range of wavelengths and calculating the ionization coefficients of the lower ionosphere as a function of the ionizing radiation parameters of flares, presented in [Ryakhovsky et al., 2023], makes it possible to improve the accuracy of estimates of variations in the parameters of the lower ionosphere. The present paper is devoted to verifying the performance of the developed empirical model of the lower ionization of the lower ionosphere at the solar flare front and comparing the results obtained with experimental data on the variation of VLF radio parameters.</p></abstract><trans-abstract xml:lang="ru"><p>Использование результатов измерений параметров ОНЧ-сигналов, распространяющихся в волноводе Земля – <italic>D</italic>-область ионосферы, для оценки изменений состояния нижней ионосферы в результате воздействия рентгеновского излучения солнечных вспышек позволяет получить качественные данные о характере и величине воздействия. Получение точных данных о связи изменений электронной концентрации с параметрами вспышки и надежное прогнозирование условий распространения НЧ-радиоизлучения в условиях сильных геофизических возмущений затрудняется отсутствием полной информации о частотном спектре рентгеновского излучения при конкретной вспышке и данных о скорости ионизации ионосферы при вспышках различных классов. Предложенная авторами ранее методика определения рентгеновского спектра в широком диапазоне длин волн и расчета коэффициентов ионизации нижней ионосферы в зависимости от параметров ионизирующего излучения вспышек позволяет повысить точность оценок вариаций параметров нижней ионосферы. Настоящая статья посвящена проверке работоспособности разработанной эмпирической модели ионизации нижней ионосферы на фронте солнечных вспышек и сравнению полученных результатов с экспериментальными данными по изменению параметров ОНЧ-радиосигналов.</p></trans-abstract><kwd-group xml:lang="en"><kwd>lower ionosphere</kwd><kwd>VLF radiation</kwd><kwd>solar flares</kwd><kwd>X-ray radiation</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>нижняя ионосфера</kwd><kwd>ОНЧ-излучение</kwd><kwd>солнечные вспышки</kwd><kwd>рентгеновское излучение</kwd></kwd-group><funding-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Российский Научный Фонд</institution></institution-wrap><institution-wrap><institution xml:lang="en">Russian Science Foundation</institution></institution-wrap></funding-source><award-id>22-77-00051</award-id></award-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Министерство науки и высшего образования РФ</institution></institution-wrap><institution-wrap><institution xml:lang="en">Ministry of Science and Higher Education of the Russian Federation</institution></institution-wrap></funding-source><award-id>075-03-2022-330</award-id></award-group></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Гаврилов Б.Г., Ряховский И.А., Поклад Ю.В. 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