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    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="edn" pub-id-type="custom">HTDPXJ</article-id>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-16283</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/16283</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Геотехнология и инженерная геология</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Geotechnical Engineering and Engineering Geology</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Landslide hazard assessment in Tinh Tuc town, Cao Bang province, Vietnam using Frequency ratio method and the combined Fractal-frequency ratio method</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Оценка оползневой опасности с использованием метода соотношения частот и комбинированного фрактально-частотного метода на примере города Тиньтук провинции Каобанг (Вьетнам)</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Duong</surname>
            <given-names>Binh Van</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Зыонг</surname>
              <given-names>Бинь Ван</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Duong</surname>
              <given-names>Binh Van</given-names>
            </name>
          </name-alternatives>
          <email>duongvanbinh@humg.edu.vn</email>
          <contrib-id contrib-id-type="orcid">0000-0002-8612-2943</contrib-id>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">Российский государственный геологоразведочный университет имени Серго Орджоникидзе (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Department of Engineering Geology, Hydrogeological Faculty, Ordzhonikidzе Russian State Geological Prospecting University (MGRI) (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Fomenko</surname>
            <given-names>Igor K.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Фоменко</surname>
              <given-names>И. К.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Fomenko</surname>
              <given-names>Igor K.</given-names>
            </name>
          </name-alternatives>
          <email>ifolga@gmail.com</email>
          <contrib-id contrib-id-type="orcid">0000-0003-2318-6015</contrib-id>
          <xref ref-type="aff" rid="aff2"/>
        </contrib>
        <aff-alternatives id="aff2">
          <aff>
            <institution xml:lang="ru">Российский государственный геологоразведочный университет имени Серго Орджоникидзе (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Sergo Ordzhonikidze Russian State University for Geological Prospecting (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Nguyen</surname>
            <given-names>Kien Trung</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Нгуен</surname>
              <given-names>Киен Чунг</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Nguyen</surname>
              <given-names>Kien Trung</given-names>
            </name>
          </name-alternatives>
          <email>kien.mgri@gmail.com</email>
          <contrib-id contrib-id-type="orcid">0000-0002-0840-5163</contrib-id>
          <xref ref-type="aff" rid="aff3"/>
        </contrib>
        <aff-alternatives id="aff3">
          <aff>
            <institution xml:lang="ru">Российский государственный геологоразведочный университет имени Серго Орджоникидзе (Ханой, Вьетнам)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Sergo Ordzhonikidze Russian State University for Geological Prospecting (Hanoi, Vietnam)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Zerkal</surname>
            <given-names>Oleg Vladimirovich</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Зеркаль</surname>
              <given-names>О. В.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Zerkal</surname>
              <given-names>Oleg Vladimirovich</given-names>
            </name>
          </name-alternatives>
          <email>igzov@mail.ru</email>
          <contrib-id contrib-id-type="orcid">0000-0002-4775-4091</contrib-id>
          <xref ref-type="aff" rid="aff4"/>
        </contrib>
        <aff-alternatives id="aff4">
          <aff>
            <institution xml:lang="ru">Московский государственный университет имени М.В.Ломоносова (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Lomonosov Moscow State University (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Sirotkina</surname>
            <given-names>Olga N.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Сироткина</surname>
              <given-names>О. Н.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Sirotkina</surname>
              <given-names>Olga N.</given-names>
            </name>
          </name-alternatives>
          <email>onsirotkina@gmail.com</email>
          <contrib-id contrib-id-type="orcid">0000-0001-8171-1960</contrib-id>
          <xref ref-type="aff" rid="aff5"/>
        </contrib>
        <aff-alternatives id="aff5">
          <aff>
            <institution xml:lang="ru">Московский государственный университет имени М.В.Ломоносова (Москва, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Lomonosov Moscow State University (Moscow, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Vu</surname>
            <given-names>Dang Hong</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Ву</surname>
              <given-names>Данг Хонг</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Vu</surname>
              <given-names>Dang Hong</given-names>
            </name>
          </name-alternatives>
          <email>hongdangbg@gmail.com</email>
          <contrib-id contrib-id-type="orcid">0000-0002-4402-0746</contrib-id>
          <xref ref-type="aff" rid="aff6"/>
        </contrib>
        <aff-alternatives id="aff6">
          <aff>
            <institution xml:lang="ru">Вьетнамский институт геонаук и минеральных ресурсов (Ханой, Вьетнам)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Vietnam Institute of Geosciences and Mineral Resources (Hanoi, Vietnam)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2024-04-09">
        <day>09</day>
        <month>04</month>
        <year>2024</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2024</year>
      </pub-date>
      <volume>268</volume>
      <fpage>613</fpage>
      <lpage>624</lpage>
      <history>
        <date date-type="received" iso-8601-date="2023-07-07">
          <day>07</day>
          <month>07</month>
          <year>2023</year>
        </date>
        <date date-type="accepted" iso-8601-date="2023-12-27">
          <day>27</day>
          <month>12</month>
          <year>2023</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2024-08-26">
          <day>26</day>
          <month>08</month>
          <year>2024</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© Binh Van Duong, Igor K. Fomenko, Kien Trung Nguyen, Oleg Vladimirovich Zerkal, Olga N. Sirotkina, Dang Hong Vu</copyright-statement>
        <copyright-year>2024</copyright-year>
        <copyright-holder xml:lang="ru">Бинь Ван Зыонг, И. К. Фоменко, Киен Чунг Нгуен, О. В. Зеркаль, О. Н. Сироткина, Данг Хонг Ву</copyright-holder>
        <copyright-holder xml:lang="en">Binh Van Duong, Igor K. Fomenko, Kien Trung Nguyen, Oleg Vladimirovich Zerkal, Olga N. Sirotkina, Dang Hong Vu</copyright-holder>
        <license xlink:href="http://creativecommons.org/licenses/by/4.0">
          <license-p>CC BY 4.0</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/16283">https://pmi.spmi.ru/pmi/article/view/16283</self-uri>
      <abstract xml:lang="ru">
        <p>Во Вьетнаме, 3/4 территории которого занимают горные регионы, оползни являются одним из наиболее распространенных стихийных бедствий, приводящих к значительному материальному ущербу. Более 500 коммун в 17 горных провинциях на севере страны подвержены высокой и очень высокой опасности в результате развития оползней. Основной целью исследования было составление карт оползневой опасности и сравнительный анализ эффективности применяемых методов для района города Тиньтук, расположенного в провинции Каобанг. Оценка оползневой опасности выполнена с использованием метода соотношения частот (FR) и комбинированного фрактально-частотного метода (FFR). В основе метода FR заложен принцип актуализма, который предполагает, что факторы, приводящие к разрушениям склонов в прошлом и настоящем, могут вызвать оползни в будущем. Метод FFR базируется на определении фрактальной размерности, которая является мерой плотности заполнения оползнями участка исследований. В качестве исходных данных выбраны восемь факторов – высота над уровнем моря, расстояние до дорог, крутизна склонов, геологическое строение, расстояние от разломов, землепользование, экспозиция склона и расстояние до эрозионной сети, представленных в картографическом виде. Достоверность полученных карт оценивалась по площади под кривой ошибок (ROC-AUC), а оценка эффективности модели – с использованием индекса подтверждения (LRclass). Для исследуемой области было выделено пять зон: с очень низкой, низкой, средней, высокой и очень высокой оползневой опасностью. Анализ достоверности полученных карт с использованием индексов AUC и LRclass показал, что модель FFR обладает более высокой степенью достоверности и эффективности (AUC = 86 %, LRclass = 86 %) в сравнении с моделью FR (AUC = 72 %, LRclass = 73 %) и ее использование является более предпочтительным.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>Landslides are one of the most frequent natural disasters that cause significant damage to property in Vietnam, which is characterized by mountainous terrain covering three-quarters of the territory. In 17 northern mountainous provinces of the country, over 500 communes are at a high to very high landslide hazard. The main goal of this study was to establish landslide hazard maps and conduct a comparative evaluation of the efficiency of the methods employed in Tinh Tuc town, Cao Bang province. The landslide hazard assessment was carried out in this study using the combined Fractal-frequency ratio (FFR) and the Frequency ratio (FR) methods. The FR method is based on the actualist principle, which assumes that future landslides may be caused by the same factors that contributed to slope failure in the past and present. The FFR method is based on the determination of the fractal dimension, which serves as a measure of the landslide filling density in the study area. Eight landslide-related factors were considered and presented in cartographic format: elevation, distance to roads, slope, geology, distance to faults, land use, slope aspect, and distance to drainage. Determining the area under the receiver operating characteristic curve (ROC-AUC) and verification index (LRclass) was performed to assess the performance of prediction models and the accuracy of the obtained maps. As a result, five zones were identified for the study area, characterized by very low, low, moderate, high, and very high landslide hazards. The analysis of the reliability of the obtained landslide hazard maps using the AUC and LRclass indices revealed that the FFR model has a higher degree of reliability (AUC = 86 %, LRclass = 86 %) compared to the FR model (AUC = 72 %, LRclass = 73 %); therefore, its use is more effective.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>фрактально-частотный метод</kwd>
        <kwd>факторы оползнеобразования</kwd>
        <kwd>оползневая опасность</kwd>
        <kwd>геоинформационная система</kwd>
        <kwd>ROC-AUC</kwd>
        <kwd>Тиньтук</kwd>
        <kwd>Вьетнам</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>Fractal-frequency ratio method</kwd>
        <kwd>landslide-related factors</kwd>
        <kwd>landslide hazard</kwd>
        <kwd>Geographic Information System</kwd>
        <kwd>ROC-AUC</kwd>
        <kwd>Tinh Tuc</kwd>
        <kwd>Vietnam</kwd>
      </kwd-group>
      <funding-group>
        <funding-statement xml:lang="ru">Исследование выполнено в рамках национального научно-технического проекта № ĐTĐL.CN-81/21.</funding-statement>
        <funding-statement xml:lang="en">The study was conducted as part of the national scientific and technical project under grant N ĐTĐL.CN-81/21.</funding-statement>
      </funding-group>
    </article-meta>
  </front>
  <body/>
  <back>
    <ref-list>
      <ref id="ref1">
        <label>1</label>
        <mixed-citation xml:lang="ru">Quynh Duy Bui, Hang Ha, Dong Thanh Khuc et al. Landslide susceptibility prediction mapping with advanced ensemble models: Son La province, Vietnam // Natural Hazards. 2023. Vol. 116. Iss. 2. P. 2283-2309. DOI: 10.1007/s11069-022-05764-3</mixed-citation>
        <mixed-citation xml:lang="en">Quynh Duy Bui, Hang Ha, Dong Thanh Khuc et al. Landslide susceptibility prediction mapping with advanced ensemble models: Son La province, Vietnam. Natural Hazards. 2023. Vol. 116. Iss. 2, p. 2283-2309. DOI: 10.1007/s11069-022-05764-3</mixed-citation>
      </ref>
      <ref id="ref2">
        <label>2</label>
        <mixed-citation xml:lang="ru">Зыонг В.Б., Фоменко И.К., Ву Х.Д. и др. Региональная оценка оползневой опасности модифицированным методом анализа иерархий в геоинформационной системе (на примере района Шапа провинции Лаокай Вьетнама) // Инженерная геология. 2021. Т. ХVI. № 2. С. 6-20. DOI: 10.25296/1993-5056-2021-16-2-6-20</mixed-citation>
        <mixed-citation xml:lang="en">Duong V.B., Fomenko I.K., Vu H.D. et al. Regional assessment of landslide hazard using modified analytic hierarchies process method in geoinformation system (a study of the Sa Pa District, Lao Cai Province, Vietnam). Engineering Geology World. 2021. Vol. XVI. N 2, p. 6-20 (in Russian). DOI: 10.25296/1993-5056-2021-16-2-6-20</mixed-citation>
      </ref>
      <ref id="ref3">
        <label>3</label>
        <mixed-citation xml:lang="ru">Зыонг В.Б., Фоменко И.К., Нгуен Ч.К. и др. Применение статистических методов на основе ГИС для оценки потенциального развития оползней в районе Шапа, Вьетнам // Известия Томского политехнического университета. Инжиниринг георесурсов. 2022. Т. 333. № 4. С. 126-140. DOI: 10.18799/24131830/2022/4/3473</mixed-citation>
        <mixed-citation xml:lang="en">Duong V.B., Fomenko I.K., Nguyen T.K. et al. Application of GIS-based bivariate statistical methods for landslide potential assessment in Sapa, Vietnam. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering. 2022. Vol. 333. N 4, р. 126-140 (in Russian). DOI: 10.18799/24131830/2022/4/3473</mixed-citation>
      </ref>
      <ref id="ref4">
        <label>4</label>
        <mixed-citation xml:lang="ru">Nguyen Thi Hoa, Nguyen Quoc Phi, Pham Dinh Manh. Assessment of the current status of geological hazards in Nguyen Binh district, Cao Bang province using open data sources (In Vie) / Earth sciences and natural resource for sustainable development. Hanoi, 2022. P. 510-514. URL: https://ersd.humg.edu.vn/ersd/ersd2022/book5 (дата обращения 06.07.2023).</mixed-citation>
        <mixed-citation xml:lang="en">Nguyen Thi Hoa, Nguyen Quoc Phi, Pham Dinh Manh. Assessment of the current status of geological hazards in Nguyen Binh district, Cao Bang province using open data sources (In Vie). Earth sciences and natural resource for sustainable development. Hanoi, 2022, p. 510-514. URL: https://ersd.humg.edu.vn/ersd/ersd2022/book5 (accessed 06.07.2023).</mixed-citation>
      </ref>
      <ref id="ref5">
        <label>5</label>
        <mixed-citation xml:lang="ru">Nguyen Trung Kien, The Viet Tran, Vy Thi Hong Lien et al. Landslide Susceptibility Mapping Based on the Combination of Bivariate Statistics and Modified Analytic Hierarchy Process Methods: A Case Study of Tinh Tuc Town, Nguyen Binh District, Cao Bang Province, Vietnam // Journal of Disaster Research. 2021. Vol. 16. № 4. P. 521-528. DOI: 10.20965/jdr.2021.p0521</mixed-citation>
        <mixed-citation xml:lang="en">Nguyen Trung Kien, The Viet Tran, Vy Thi Hong Lien et al. Landslide Susceptibility Mapping Based on the Combination of Bivariate Statistics and Modified Analytic Hierarchy Process Methods: A Case Study of Tinh Tuc Town, Nguyen Binh District, Cao Bang Province, Vietnam. Journal of Disaster Research. 2021. Vol. 16. N 4, p. 521-528. DOI: 10.20965/jdr.2021.p0521</mixed-citation>
      </ref>
      <ref id="ref6">
        <label>6</label>
        <mixed-citation xml:lang="ru">Krivoguz D., Bespalova L. Landslide susceptibility analysis for the Kerch Peninsula using weights of evidence approach and GIS // Russian Journal of Earth Sciences. 2020. Vol. 20. № ES1003. DOI: 10.2205/2020ES000682</mixed-citation>
        <mixed-citation xml:lang="en">Krivoguz D., Bespalova L. Landslide susceptibility analysis for the Kerch Peninsula using weights of evidence approach and GIS. Russian Journal of Earth Sciences. 2020. Vol. 20. N ES1003. DOI: 10.2205/2020ES000682</mixed-citation>
      </ref>
      <ref id="ref7">
        <label>7</label>
        <mixed-citation xml:lang="ru">Харченко С.В., Шварев С.В. Прогнозирование оползневой опасности в окрестностях Красной Поляны на основе линейного дискриминантного анализа // Вестник Московского университета. Серия 5. География. 2020. № 3. С. 22-33.</mixed-citation>
        <mixed-citation xml:lang="en">Kharchenko S.V., Shvarev S.V. Forecasting landslide hazards in the vicinity of Krasnaya Polyana based on the linear discriminatory analysis. Vestnik Moskovskogo universiteta. Seriya 5. Geografiya. 2020. N 3, p. 22-33 (in Russian).</mixed-citation>
      </ref>
      <ref id="ref8">
        <label>8</label>
        <mixed-citation xml:lang="ru">Нгуен Ч.К., Фоменко И.К., Пендин В.В., Нгуен К.Т. Применение метода анализа иерархий при региональной оценке оползневой опасности (на примере района Северо-Западный Лаокай, Вьетнам) // Геоинформатика. 2017. № 2. С. 53-66.</mixed-citation>
        <mixed-citation xml:lang="en">Nguyen T.K., Fomenko I.K., Pendin V.V., Nguyen Q.T. Application of the method of analysis hierarchies (AHP) under the regional landslide hazard assessment (for example area North-West of Laocai in Vietnam). Geoinformatika. 2017. N 2, p. 53-66 (in Russian).</mixed-citation>
      </ref>
      <ref id="ref9">
        <label>9</label>
        <mixed-citation xml:lang="ru">Anis Z., Wissem G., Vali V. et al. GIS-based landslide susceptibility mapping using bivariate statistical methods in North-western Tunisia // Open Geosciences. 2019. Vol. 11. Iss. 1. P. 708-726. DOI: 10.1515/geo-2019-0056</mixed-citation>
        <mixed-citation xml:lang="en">Anis Z., Wissem G., Vali V. et al. GIS-based landslide susceptibility mapping using bivariate statistical methods in North-western Tunisia. Open Geosciences. 2019. Vol. 11. Iss. 1, p. 708-726. DOI: 10.1515/geo-2019-0056</mixed-citation>
      </ref>
      <ref id="ref10">
        <label>10</label>
        <mixed-citation xml:lang="ru">Ram P., Gupta V., Devi M., Vishwakarma N. Landslide susceptibility mapping using bivariate statistical method for the hilly township of Mussoorie and its surrounding areas, Uttarakhand Himalaya // Journal of Earth System Science. 2020. Vol. 129. Iss. 1. № 167. DOI: 10.1007/s12040-020-01428-7</mixed-citation>
        <mixed-citation xml:lang="en">Ram P., Gupta V., Devi M., Vishwakarma N. Landslide susceptibility mapping using bivariate statistical method for the hilly township of Mussoorie and its surrounding areas, Uttarakhand Himalaya. Journal of Earth System Science. 2020. Vol. 129. Iss. 1. N 167. DOI: 10.1007/s12040-020-01428-7</mixed-citation>
      </ref>
      <ref id="ref11">
        <label>11</label>
        <mixed-citation xml:lang="ru">Langping Li, Hengxing Lan, Changbao Guo et al. A modified frequency ratio method for landslide susceptibility assessment // Landslides. 2017. Vol. 14. Iss. 2. P. 727-741. DOI: 10.1007/s10346-016-0771-x</mixed-citation>
        <mixed-citation xml:lang="en">Langping Li, Hengxing Lan, Changbao Guo et al. A modified frequency ratio method for landslide susceptibility assessment. Landslides. 2017. Vol. 14. Iss. 2, p. 727-741. DOI: 10.1007/s10346-016-0771-x</mixed-citation>
      </ref>
      <ref id="ref12">
        <label>12</label>
        <mixed-citation xml:lang="ru">Sifa S.F., Mahmud T., Tarin M.A., Haque D.M.E. Event-based landslide susceptibility mapping using weights of evidence (WoE) and modified frequency ratio (MFR) model: a case study of Rangamati district in Bangladesh // Geology, Ecology, and Landscapes. 2020. Vol. 4. Iss. 3. P. 222-235. DOI: 10.1080/24749508.2019.1619222</mixed-citation>
        <mixed-citation xml:lang="en">Sifa S.F., Mahmud T., Tarin M.A., Haque D.M.E. Event-based landslide susceptibility mapping using weights of evidence (WoE) and modified frequency ratio (MFR) model: a case study of Rangamati district in Bangladesh. Geology, Ecology, and Landscapes. 2020. Vol. 4. Iss. 3, p. 222-235. DOI: 10.1080/24749508.2019.1619222</mixed-citation>
      </ref>
      <ref id="ref13">
        <label>13</label>
        <mixed-citation xml:lang="ru">Feby B., Achu A.L., Jimnisha K. et al. Landslide susceptibility modelling using integrated evidential belief function based logistic regression method: A study from Southern Western Ghats, India // Remote Sensing Applications: Society and Environment. 2020. Vol. 20. № 100411. DOI: 10.1016/j.rsase.2020.100411</mixed-citation>
        <mixed-citation xml:lang="en">Feby B., Achu A.L., Jimnisha K. et al. Landslide susceptibility modelling using integrated evidential belief function based logistic regression method: A study from Southern Western Ghats, India. Remote Sensing Applications: Society and Environment. 2020. Vol. 20. N 100411. DOI: 10.1016/j.rsase.2020.100411</mixed-citation>
      </ref>
      <ref id="ref14">
        <label>14</label>
        <mixed-citation xml:lang="ru">Polykretis C., Grillakis M.G., Argyriou A.V. et al. Integrating Multivariate (GeoDetector) and Bivariate (IV) Statistics for Hybrid Landslide Susceptibility Modeling: A Case of the Vicinity of Pinios Artificial Lake, Ilia, Greece // Land. 2021. Vol. 10. Iss. 9. № 973. DOI: 10.3390/land10090973</mixed-citation>
        <mixed-citation xml:lang="en">Polykretis C., Grillakis M.G., Argyriou A.V. et al. Integrating Multivariate (GeoDetector) and Bivariate (IV) Statistics for Hybrid Landslide Susceptibility Modeling: A Case of the Vicinity of Pinios Artificial Lake, Ilia, Greece. Land. 2021. Vol. 10. Iss. 9. N 973. DOI: 10.3390/land10090973</mixed-citation>
      </ref>
      <ref id="ref15">
        <label>15</label>
        <mixed-citation xml:lang="ru">Silalahi F.E.S., Pamela, Arifianti Y., Hidayat F. Landslide susceptibility assessment using frequency ratio model in Bogor, West Java, Indonesia // Geoscience Letters. 2019. Vol. 6. № 10. DOI: 10.1186/s40562-019-0140-4</mixed-citation>
        <mixed-citation xml:lang="en">Silalahi F.E.S., Pamela, Arifianti Y., Hidayat F. Landslide susceptibility assessment using frequency ratio model in Bogor, West Java, Indonesia. Geoscience Letters. 2019. Vol. 6. N 10. DOI: 10.1186/s40562-019-0140-4</mixed-citation>
      </ref>
      <ref id="ref16">
        <label>16</label>
        <mixed-citation xml:lang="ru">Karaman M.O., Çabuk S.N., Pekkan E. Utilization of frequency ratio method for the production of landslide susceptibility maps: Karaburun Peninsula case, Turkey // Environmental Science and Pollution Research. 2022. Vol. 29. Iss. 60. P. 91285-91305. DOI: 10.1007/s11356-022-21931-2</mixed-citation>
        <mixed-citation xml:lang="en">Karaman M.O., Çabuk S.N., Pekkan E. Utilization of frequency ratio method for the production of landslide susceptibility maps: Karaburun Peninsula case, Turkey. Environmental Science and Pollution Research. 2022. Vol. 29. Iss. 60, p. 91285-91305. DOI: 10.1007/s11356-022-21931-2</mixed-citation>
      </ref>
      <ref id="ref17">
        <label>17</label>
        <mixed-citation xml:lang="ru">Mandelbrot B. How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension // Science. 1967. Vol. 156. Iss. 3775. P. 636-638. DOI: 10.1126/science.156.3775.636</mixed-citation>
        <mixed-citation xml:lang="en">Mandelbrot B. How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science. 1967. Vol. 156. Iss. 3775, p. 636-638. DOI: 10.1126/science.156.3775.636</mixed-citation>
      </ref>
      <ref id="ref18">
        <label>18</label>
        <mixed-citation xml:lang="ru">Mandelbrot B.B. Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder // International Journal of Fracture. 2006. Vol. 138. Iss. 1-4. P. 13-17. DOI: 10.1007/s10704-006-0037-z</mixed-citation>
        <mixed-citation xml:lang="en">Mandelbrot B.B. Fractal Analysis and Synthesis of Fracture Surface Roughness and Related Forms of Complexity and Disorder. International Journal of Fracture. 2006. Vol. 138. Iss. 1-4, p. 13-17. DOI: 10.1007/s10704-006-0037-z</mixed-citation>
      </ref>
      <ref id="ref19">
        <label>19</label>
        <mixed-citation xml:lang="ru">Захаров В.С. Самоподобие структур и процессов в литосфере по результатам фрактального и динамического анализа: Автореф. дис. … д-ра геол.-минерал. наук. М.: Московский государственный университет имени М.В. Ломоносова, 2014. 35 с.</mixed-citation>
        <mixed-citation xml:lang="en">Zakharov V. S. Self-similarity of structures and processes in the lithosphere based on the results of fractal and dynamic analysis: Abstract of the dissertation for the degree of Doctor of Geological and Mineralogical Sciences. Moscow: Lomonosov Moscow State University, 2014, p. 35 (In Russian).</mixed-citation>
      </ref>
      <ref id="ref20">
        <label>20</label>
        <mixed-citation xml:lang="ru">Mandelbrot B.B. The Fractal Geometry of Nature. New York: W.H.Freeman and Company, 1982. 460 p.</mixed-citation>
        <mixed-citation xml:lang="en">Mandelbrot B.B. The Fractal Geometry of Nature. New York: W.H.Freeman and Company, 1982, p. 460.</mixed-citation>
      </ref>
      <ref id="ref21">
        <label>21</label>
        <mixed-citation xml:lang="ru">Xiaoming Man, Yanguang Chen. Fractal-Based Modeling and Spatial Analysis of Urban Form and Growth: A Case Study of Shenzhen in China // ISPRS International Journal of Geo-Information. 2020. Vol. 9. Iss. 11. № 672. DOI: 10.3390/ijgi9110672</mixed-citation>
        <mixed-citation xml:lang="en">Xiaoming Man, Yanguang Chen. Fractal-Based Modeling and Spatial Analysis of Urban Form and Growth: A Case Study of Shenzhen in China. ISPRS International Journal of Geo-Information. 2020. Vol. 9. Iss. 11. N 672. DOI: 10.3390/ijgi9110672</mixed-citation>
      </ref>
      <ref id="ref22">
        <label>22</label>
        <mixed-citation xml:lang="ru">Husain A., Reddy J., Bisht D., Sajid M. Fractal dimension of coastline of Australia // Scientific Reports. 2021. Vol. 11. № 6304. DOI: 10.1038/s41598-021-85405-0</mixed-citation>
        <mixed-citation xml:lang="en">Husain A., Reddy J., Bisht D., Sajid M. Fractal dimension of coastline of Australia. Scientific Reports. 2021. Vol. 11. N 6304. DOI: 10.1038/s41598-021-85405-0</mixed-citation>
      </ref>
      <ref id="ref23">
        <label>23</label>
        <mixed-citation xml:lang="ru">Luxiao Cheng, Ruyi Feng, Lizhe Wang. Fractal Characteristic Analysis of Urban Land-Cover Spatial Patterns with Spatiotemporal Remote Sensing Images in Shenzhen City (1988-2015) // Remote Sensing. 2021. Vol. 13. Iss. 22. № 4640. DOI: 10.3390/rs13224640</mixed-citation>
        <mixed-citation xml:lang="en">Luxiao Cheng, Ruyi Feng, Lizhe Wang. Fractal Characteristic Analysis of Urban Land-Cover Spatial Patterns with Spatiotemporal Remote Sensing Images in Shenzhen City (1988-2015). Remote Sensing. 2021. Vol. 13. Iss. 22. N 4640. DOI: 10.3390/rs13224640</mixed-citation>
      </ref>
      <ref id="ref24">
        <label>24</label>
        <mixed-citation xml:lang="ru">Lei Gui, Kunlong Yin, Thomas Glade. Landslide displacement analysis based on fractal theory, in Wanzhou District, Three Gorges Reservoir, China // Geomatics, Natural Hazards and Risk. 2016. Vol. 7. Iss. 5. P. 1707-1725. DOI: 10.1080/19475705.2015.1137241</mixed-citation>
        <mixed-citation xml:lang="en">Lei Gui, Kunlong Yin, Thomas Glade. Landslide displacement analysis based on fractal theory, in Wanzhou District, Three Gorges Reservoir, China. Geomatics, Natural Hazards and Risk. 2016. Vol. 7. Iss. 5, p. 1707-1725. DOI: 10.1080/19475705.2015.1137241</mixed-citation>
      </ref>
      <ref id="ref25">
        <label>25</label>
        <mixed-citation xml:lang="ru">Ting-yu Zhang, Ling Han, Heng Zhang et al. GIS-based landslide susceptibility mapping using hybrid integration approaches of fractal dimension with index of entropy and support vector machine // Journal of Mountain Science. 2019. Vol. 16. Iss. 6. P. 1275-1288. DOI: 10.1007/s11629-018-5337-z</mixed-citation>
        <mixed-citation xml:lang="en">Ting-yu Zhang, Ling Han, Heng Zhang et al. GIS-based landslide susceptibility mapping using hybrid integration approaches of fractal dimension with index of entropy and support vector machine. Journal of Mountain Science. 2019. Vol. 16. Iss. 6, p. 1275-1288. DOI: 10.1007/s11629-018-5337-z</mixed-citation>
      </ref>
      <ref id="ref26">
        <label>26</label>
        <mixed-citation xml:lang="ru">Wei Feng, Yaming Tang, Bo Hong. Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China) // Sustainability. 2022. Vol. 14. Iss. 13. № 8098. DOI: 10.3390/su14138098</mixed-citation>
        <mixed-citation xml:lang="en">Wei Feng, Yaming Tang, Bo Hong. Landslide Hazard Assessment Methods along Fault Zones Based on Multiple Working Conditions: A Case Study of the Lixian–Luojiabu Fault Zone in Gansu Province (China). Sustainability. 2022. Vol. 14. Iss. 13. N 8098. DOI: 10.3390/su14138098</mixed-citation>
      </ref>
      <ref id="ref27">
        <label>27</label>
        <mixed-citation xml:lang="ru">Xiaolong Deng, Guangji Sun, Naiwu He, Yonghua Yu. Landslide susceptibility mapping with the integration of information theory, fractal theory, and statistical analyses at a regional scale: a case study of Altay Prefecture, China // Environmental Earth Sciences. 2022. Vol. 81. Iss. 13. № 346. DOI: 10.1007/s12665-022-10470-1</mixed-citation>
        <mixed-citation xml:lang="en">Xiaolong Deng, Guangji Sun, Naiwu He, Yonghua Yu. Landslide susceptibility mapping with the integration of information theory, fractal theory, and statistical analyses at a regional scale: a case study of Altay Prefecture, China. Environmental Earth Sciences. 2022. Vol. 81. Iss. 13. N 346. DOI: 10.1007/s12665-022-10470-1</mixed-citation>
      </ref>
      <ref id="ref28">
        <label>28</label>
        <mixed-citation xml:lang="ru">Hu Q., Zhou Y., Wang S.X. et al. Fractal-based spatial distribution analysis of geological hazards and measurement of spatial association with hazard-related predisposing factors // The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. 2020. Vol. XLII-3/W10. P. 125-131. DOI: 10.5194/isprs-archives-XLII-3-W10-125-2020</mixed-citation>
        <mixed-citation xml:lang="en">Hu Q., Zhou Y., Wang S.X. et al. Fractal-based spatial distribution analysis of geological hazards and measurement of spatial association with hazard-related predisposing factors. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. 2020. Vol. XLII-3/W10, p. 125-131. DOI: 10.5194/isprs-archives-XLII-3-W10-125-2020</mixed-citation>
      </ref>
      <ref id="ref29">
        <label>29</label>
        <mixed-citation xml:lang="ru">Changjiang Li, Tuhua Ma, Leling Sun et al. Application and verification of a fractal approach to landslide susceptibility mapping // Natural Hazards. 2012. Vol. 61. Iss. 1. P. 169-185. DOI: 10.1007/s11069-011-9804-x</mixed-citation>
        <mixed-citation xml:lang="en">Changjiang Li, Tuhua Ma, Leling Sun et al. Application and verification of a fractal approach to landslide susceptibility mapping. Natural Hazards. 2012. Vol. 61. Iss. 1, p. 169-185. DOI: 10.1007/s11069-011-9804-x</mixed-citation>
      </ref>
      <ref id="ref30">
        <label>30</label>
        <mixed-citation xml:lang="ru">Ni Zhihui, Wu Lichun, Wang Ming-hui et al. The Fractal Dimension of River Length Based on the Observed Data // Journal of Applied Mathematics. 2013. Vol. 2013. № 327297. DOI: 10.1155/2013/327297</mixed-citation>
        <mixed-citation xml:lang="en">Ni Zhihui, Wu Lichun, Wang Ming-hui et al. The Fractal Dimension of River Length Based on the Observed Data. Journal of Applied Mathematics. 2013. Vol. 2013. N 327297. DOI: 10.1155/2013/327297</mixed-citation>
      </ref>
      <ref id="ref31">
        <label>31</label>
        <mixed-citation xml:lang="ru">Nikhil Prakash, Andrea Manconi, Simon Loew. A new strategy to map landslides with a generalized convolutional neural network // Scientific Reports. 2021. Vol. 11. № 9722. DOI: 10.1038/s41598-021-89015-8</mixed-citation>
        <mixed-citation xml:lang="en">Nikhil Prakash, Andrea Manconi, Simon Loew. A new strategy to map landslides with a generalized convolutional neural network. Scientific Reports. 2021. Vol. 11. N 9722. DOI: 10.1038/s41598-021-89015-8</mixed-citation>
      </ref>
      <ref id="ref32">
        <label>32</label>
        <mixed-citation xml:lang="ru">Gerzsenyi D., Albert G. Landslide inventory validation and susceptibility mapping in the Gerecse Hills, Hungary // Geo-spatial Information Science. 2021. Vol. 24. Iss. 3. P. 498-508. DOI: 10.1080/10095020.2020.1870872</mixed-citation>
        <mixed-citation xml:lang="en">Gerzsenyi D., Albert G. Landslide inventory validation and susceptibility mapping in the Gerecse Hills, Hungary. Geo-spatial Information Science. 2021. Vol. 24. Iss. 3, p. 498-508. DOI: 10.1080/10095020.2020.1870872</mixed-citation>
      </ref>
      <ref id="ref33">
        <label>33</label>
        <mixed-citation xml:lang="ru">Su Z., Chow J.K., Tan P.S. et al. Deep convolutional neural network–based pixel-wise landslide inventory mapping // Landslides. 2021. Vol. 18. Iss. 4. P. 1421-1443. DOI: 10.1007/s10346-020-01557-6</mixed-citation>
        <mixed-citation xml:lang="en">Su Z., Chow J.K., Tan P.S. et al. Deep convolutional neural network–based pixel-wise landslide inventory mapping. Landslides. 2021. Vol. 18. Iss. 4, p. 1421-1443. DOI: 10.1007/s10346-020-01557-6</mixed-citation>
      </ref>
      <ref id="ref34">
        <label>34</label>
        <mixed-citation xml:lang="ru">Pospehov G.B., Savón Y., Delgado R. et al. Inventory of Landslides Triggered by Hurricane Matthews in Guantánamo, Cuba // Geography, Environment, Sustainability. 2023. Vol. 16. № 1. P. 55-63. DOI: 10.24057/2071-9388-2022-133</mixed-citation>
        <mixed-citation xml:lang="en">Pospehov G.B., Savón Y., Delgado R. et al. Inventory of Landslides Triggered by Hurricane Matthews in Guantánamo, Cuba. Geography, Environment, Sustainability. 2023. Vol. 16. N 1, p. 55-63. DOI: 10.24057/2071-9388-2022-133</mixed-citation>
      </ref>
      <ref id="ref35">
        <label>35</label>
        <mixed-citation xml:lang="ru">Pourghasemi H.R., Yansari Z.T., Panagos P., Pradhan B. Analysis and evaluation of landslide susceptibility: a review on articles published during 2005-2016 (periods of 2005-2012 and 2013-2016) // Arabian Journal of Geosciences. 2018. Vol. 11. Iss. 9. № 193. DOI: 10.1007/s12517-018-3531-5</mixed-citation>
        <mixed-citation xml:lang="en">Pourghasemi H.R., Yansari Z.T., Panagos P., Pradhan B. Analysis and evaluation of landslide susceptibility: a review on articles published during 2005-2016 (periods of 2005-2012 and 2013-2016). Arabian Journal of Geosciences. 2018. Vol. 11. Iss. 9. N 193. DOI: 10.1007/s12517-018-3531-5</mixed-citation>
      </ref>
      <ref id="ref36">
        <label>36</label>
        <mixed-citation xml:lang="ru">Swets J.A. Measuring the Accuracy of Diagnostic Systems // Science. 1988. Vol. 240. Iss. 4857. P. 1285-1293. DOI: 10.1126/science.3287615</mixed-citation>
        <mixed-citation xml:lang="en">Swets J.A. Measuring the Accuracy of Diagnostic Systems. Science. 1988.  Vol. 240.  Iss. 4857,  p. 1285-1293. DOI: 10.1126/science.3287615</mixed-citation>
      </ref>
      <ref id="ref37">
        <label>37</label>
        <mixed-citation xml:lang="ru">Šimundić A.-M. Measures of Diagnostic Accuracy: Basic Definitions // The Journal of the International Federation of Clinical Chemistry and Laboratory Medicine. 2009. Vol. 19. Iss. 4. P. 203-211.</mixed-citation>
        <mixed-citation xml:lang="en">Šimundić A.-M. Measures of Diagnostic Accuracy: Basic Definitions. The Journal of the International Federation of Clinical Chemistry and Laboratory Medicine. 2009. Vol. 19. Iss. 4, p. 203-211.</mixed-citation>
      </ref>
      <ref id="ref38">
        <label>38</label>
        <mixed-citation xml:lang="ru">Haijun Qiu, Yaru Zhu, Wenqi Zhou et al. Influence of DEM resolution on landslide simulation performance based on the Scoops3D model // Geomatics, Natural Hazards and Risk. 2022. Vol. 13. Iss. 1. P. 1663-1681. DOI: 10.1080/19475705.2022.2097451</mixed-citation>
        <mixed-citation xml:lang="en">Haijun Qiu, Yaru Zhu, Wenqi Zhou et al. Influence of DEM resolution on landslide simulation performance based on the Scoops3D model. Geomatics, Natural Hazards and Risk. 2022. Vol. 13. Iss. 1, p. 1663-1681. DOI: 10.1080/19475705.2022.2097451</mixed-citation>
      </ref>
      <ref id="ref39">
        <label>39</label>
        <mixed-citation xml:lang="ru">Sarma C.P., Dey A., Krishna A.M. Influence of digital elevation models on the simulation of rainfall-induced landslides in the hillslopes of Guwahati, India // Engineering Geology. 2020. Vol. 268. № 105523. DOI: 10.1016/j.enggeo.2020.105523</mixed-citation>
        <mixed-citation xml:lang="en">Sarma C.P., Dey A., Krishna A.M. Influence of digital elevation models on the simulation of rainfall-induced landslides in the hillslopes of Guwahati, India. Engineering Geology. 2020. Vol. 268. N 105523. DOI: 10.1016/j.enggeo.2020.105523</mixed-citation>
      </ref>
      <ref id="ref40">
        <label>40</label>
        <mixed-citation xml:lang="ru">Park D.W., Nikhil N.V., Lee S.R. Landslide and debris flow susceptibility zonation using TRIGRS for the 2011 Seoul landslide event // Natural Hazards and Earth System Sciences. 2013. Vol. 13. Iss. 11. P. 2833-2849. DOI: 10.5194/nhess-13-2833-2013</mixed-citation>
        <mixed-citation xml:lang="en">Park D.W., Nikhil N.V., Lee S.R. Landslide and debris flow susceptibility zonation using TRIGRS for the 2011 Seoul landslide event. Natural Hazards and Earth System Sciences. 2013. Vol. 13. Iss. 11, p. 2833-2849. DOI: 10.5194/nhess-13-2833-2013</mixed-citation>
      </ref>
      <ref id="ref41">
        <label>41</label>
        <mixed-citation xml:lang="ru">Tran T.V., Alvioli M., Lee G., An H.U. Three-dimensional, time-dependent modeling of rainfall-induced landslides over a digital landscape: a case study // Landslides. 2018. Vol. 15. Iss. 6. P. 1071-1084. DOI: 10.1007/s10346-017-0931-7</mixed-citation>
        <mixed-citation xml:lang="en">Tran T.V., Alvioli M., Lee G., An H.U. Three-dimensional, time-dependent modeling of rainfall-induced landslides over a digital landscape: a case study. Landslides. 2018. Vol. 15. Iss. 6, p. 1071-1084. DOI: 10.1007/s10346-017-0931-7</mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>
