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 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Russian Journal of Earth Sciences</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Russian Journal of Earth Sciences</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Russian Journal of Earth Sciences</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">1681-1208</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">46570</article-id>
   <article-id pub-id-type="doi">10.2205/2021ES000766</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>ОРИГИНАЛЬНЫЕ СТАТЬИ</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>ORIGINAL ARTICLES</subject>
    </subj-group>
    <subj-group>
     <subject>ОРИГИНАЛЬНЫЕ СТАТЬИ</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Numerical algorithms for structural magnetometry inverse problem solving</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Numerical algorithms for structural magnetometry inverse problem solving</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Martyshko</surname>
       <given-names>P S</given-names>
      </name>
      <name xml:lang="en">
       <surname>Martyshko</surname>
       <given-names>P S</given-names>
      </name>
     </name-alternatives>
     <email>pmart3@mail.ru</email>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Fedorova</surname>
       <given-names>N V</given-names>
      </name>
      <name xml:lang="en">
       <surname>Fedorova</surname>
       <given-names>N V</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Rublev</surname>
       <given-names>A L</given-names>
      </name>
      <name xml:lang="en">
       <surname>Rublev</surname>
       <given-names>A L</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Institute of Geophysics UB RAS</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Geophysics UB RAS</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Institute of Geophysics UB RAS</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Geophysics UB RAS</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Institute of Geophysics UB RAS</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Geophysics UB RAS</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <volume>21</volume>
   <issue>3</issue>
   <history>
    <date date-type="received" iso-8601-date="2021-10-29T12:49:31+03:00">
     <day>29</day>
     <month>10</month>
     <year>2021</year>
    </date>
   </history>
   <self-uri xlink:href="https://rjes.ru/en/nauka/article/46570/view">https://rjes.ru/en/nauka/article/46570/view</self-uri>
   <abstract xml:lang="ru">
    <p>New methods for studying the anomalous magnetic field of the lithosphere and modeling the sources of anomalies in different layers of the Earth's crust are given in this article. The interpretation consists of three stages: separation of anomalies from the sources in different layers of the Earth's crust, data conversion to the magnetic pole and solving the inverse problem of finding the surface of sources. To isolate anomalies from different layers of the earth's crust, we used a technique based on the subsequent continuation of magnetic data up and down. Calculation of the vertical component of the anomalous magnetic field by its absolute value and conversion to the pole is based on the approximation of the anomalies of the magnetic induction modulus through a set of singular sources - magnetized rods. To solve the nonlinear inverse problem and calculate the boundaries separating layers with different magnetization, the method of local corrections was applied. The new computer technology was created using parallel computing in the multiprocessor computer systems. To demonstrate the developed methods, we chose the region of Western Urals 300 km &amp;#x00D7;230&quot; role=&quot;presentation&quot;&gt;×230</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>New methods for studying the anomalous magnetic field of the lithosphere and modeling the sources of anomalies in different layers of the Earth's crust are given in this article. The interpretation consists of three stages: separation of anomalies from the sources in different layers of the Earth's crust, data conversion to the magnetic pole and solving the inverse problem of finding the surface of sources. To isolate anomalies from different layers of the earth's crust, we used a technique based on the subsequent continuation of magnetic data up and down. Calculation of the vertical component of the anomalous magnetic field by its absolute value and conversion to the pole is based on the approximation of the anomalies of the magnetic induction modulus through a set of singular sources - magnetized rods. To solve the nonlinear inverse problem and calculate the boundaries separating layers with different magnetization, the method of local corrections was applied. The new computer technology was created using parallel computing in the multiprocessor computer systems. To demonstrate the developed methods, we chose the region of Western Urals 300 km &amp;#x00D7;230&quot; role=&quot;presentation&quot;&gt;×230</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>Magnetic anomaly</kwd>
    <kwd>Earth’s crust</kwd>
    <kwd>modelling</kwd>
    <kwd>parallel algorithms</kwd>
    <kwd>inverse problem</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>Magnetic anomaly</kwd>
    <kwd>Earth’s crust</kwd>
    <kwd>modelling</kwd>
    <kwd>parallel algorithms</kwd>
    <kwd>inverse problem</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="en">The Russian Science Foundation (Grant No. 20-17-00058) is acknowledged for supporting this research.</funding-statement>
   </funding-group>
  </article-meta>
 </front>
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 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Byzov, D., L. Muravyev, N. Fedorova (2017) , The approximation of anomalous magnetic field by array of magnetized rods, AIP Conference Proceedings, 1863, p. 560051, https://doi.org/10.1063/1.4992734
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Byzov, D., L. Muravyev, N. Fedorova (2017) , The approximation of anomalous magnetic field by array of magnetized rods, AIP Conference Proceedings, 1863, p. 560051, https://doi.org/10.1063/1.4992734
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Chursin, A. V., A. M. Prut'yan, N. V. Fedorova (2008) , Digital anomalous magnetic field map of the Northern, Middle, Southern Urals and adjacent territories of the East-European and West-Siberian platforms, Litosfera, 6, p. 63-72 (in Russian)
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Chursin, A. V., A. M. Prut'yan, N. V. Fedorova (2008) , Digital anomalous magnetic field map of the Northern, Middle, Southern Urals and adjacent territories of the East-European and West-Siberian platforms, Litosfera, 6, p. 63-72 (in Russian)
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Druzhinin, V. S., P. S. Martyshko, et al. (2015) , Tectonodynamic Model of the Earth's Crust of the Urals and Neighboring Areas, Doklady Earth Sciences, 463, no. 1, p. 659-662, https://doi.org/10.1134/S1028334X15070090
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Druzhinin, V. S., P. S. Martyshko, et al. (2015) , Tectonodynamic Model of the Earth's Crust of the Urals and Neighboring Areas, Doklady Earth Sciences, 463, no. 1, p. 659-662, https://doi.org/10.1134/S1028334X15070090
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Fedorova, N. V. (2005) , Modeling of the magnetic field variation in relation to the origin of the Manchazh secular trend anomaly, Izvestiya. Physics of the Solid Earth, 41, no. 5, p. 355-362
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Fedorova, N. V. (2005) , Modeling of the magnetic field variation in relation to the origin of the Manchazh secular trend anomaly, Izvestiya. Physics of the Solid Earth, 41, no. 5, p. 355-362
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Fedorova, N. V., A. L. Rublev (2019) , Numerical Modeling of Magnetic Anomalies Sources in the South Urals Earth Crust, Russian Geology and Geophysics, 60, no. 11, p. 1310-1318, https://doi.org/10.15372/RGG2019106
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Fedorova, N. V., A. L. Rublev (2019) , Numerical Modeling of Magnetic Anomalies Sources in the South Urals Earth Crust, Russian Geology and Geophysics, 60, no. 11, p. 1310-1318, https://doi.org/10.15372/RGG2019106
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Fedorova, N. V., A. L. Rublev, et al. (2017) , Magnetic anomalies and model of the magnetization in the Earth's crust of circumpolar and polar the sectors of Ural region, Geofizicheskiy Zhurnal, 39, no. 1, p. 111-122, https://doi.org/10.24028/gzh.0203-3100.v39i1.2017.94014
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Fedorova, N. V., A. L. Rublev, et al. (2017) , Magnetic anomalies and model of the magnetization in the Earth's crust of circumpolar and polar the sectors of Ural region, Geofizicheskiy Zhurnal, 39, no. 1, p. 111-122, https://doi.org/10.24028/gzh.0203-3100.v39i1.2017.94014
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              IAGA, (1995) , Division V, Working Group 8, International Geomagnetic Reference Field, 1995 Revision, J. Geomag. Geoelectr., 47, no. 12, p. 1257-1261, https://doi.org/10.5636/jgg.47.1257
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              IAGA, (1995) , Division V, Working Group 8, International Geomagnetic Reference Field, 1995 Revision, J. Geomag. Geoelectr., 47, no. 12, p. 1257-1261, https://doi.org/10.5636/jgg.47.1257
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Lavrentiev, M. M. (1967) , Some Improperly Posed Problems of Mathematical Physics, 76 pp., Springer, New York, https://doi.org/10.1007/978-3-642-88210-4
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Lavrentiev, M. M. (1967) , Some Improperly Posed Problems of Mathematical Physics, 76 pp., Springer, New York, https://doi.org/10.1007/978-3-642-88210-4
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Martyshko, P. S., I. L. Prutkin (2003) , Technology for separating the gravity sources by the depth, Geofiz. Zh., 25, no. 3, p. 159-170, https://doi.org/10.3997/2214-4609-pdb.38.F193 (in Russian)
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Martyshko, P. S., I. L. Prutkin (2003) , Technology for separating the gravity sources by the depth, Geofiz. Zh., 25, no. 3, p. 159-170, https://doi.org/10.3997/2214-4609-pdb.38.F193 (in Russian)
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Martyshko, P. S., N. V. Fedorova, et al. (2014) , Studying the Structural Features of the Lithospheric Magnetic and Gravity Fields with the Use of Parallel Algorithms, Izvestiya. Physics of the Solid Earth, 50, no. 4, p. 508-513, https://doi.org/10.1134/S1069351314040090
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Martyshko, P. S., N. V. Fedorova, et al. (2014) , Studying the Structural Features of the Lithospheric Magnetic and Gravity Fields with the Use of Parallel Algorithms, Izvestiya. Physics of the Solid Earth, 50, no. 4, p. 508-513, https://doi.org/10.1134/S1069351314040090
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Martyshko, P. S., I. V. Ladovskii, A. G. Tsidaev (2010) , Construction of regional geophysical models based on the joint interpretation of gravitaty and seismic data, Izvestiya. Physics of the Solid Earth, 46, no. 11, p. 931-942, https://doi.org/10.1134/S1069351310110030
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Martyshko, P. S., I. V. Ladovskii, A. G. Tsidaev (2010) , Construction of regional geophysical models based on the joint interpretation of gravitaty and seismic data, Izvestiya. Physics of the Solid Earth, 46, no. 11, p. 931-942, https://doi.org/10.1134/S1069351310110030
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Mayer, V. I., F. I. Nikonova, N. V. Fedorova (1985) , A numerical optimization procedure for interpreting gravity and magnetic-anomalies, Izvestiya, Fizika Zemli, 5, p. 46-57
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Mayer, V. I., F. I. Nikonova, N. V. Fedorova (1985) , A numerical optimization procedure for interpreting gravity and magnetic-anomalies, Izvestiya, Fizika Zemli, 5, p. 46-57
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Olsen, N. (2002) , A model of geomagnetic field and its secular variation for epoch 2000 estimated from Orsted data, Geophysical Journal International, 149, no. 2, p. 454-462, https://doi.org/10.1046/j.1365-246X.2002.01657.x
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Olsen, N. (2002) , A model of geomagnetic field and its secular variation for epoch 2000 estimated from Orsted data, Geophysical Journal International, 149, no. 2, p. 454-462, https://doi.org/10.1046/j.1365-246X.2002.01657.x
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Prutkin, I. L. (1986) , The solution of three-dimensional inverse gravimetric problem in the class of contact surfaces by the method of local corrections, Physics of the Solid Earth, 22, no. 1, p. 49-55
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Prutkin, I. L. (1986) , The solution of three-dimensional inverse gravimetric problem in the class of contact surfaces by the method of local corrections, Physics of the Solid Earth, 22, no. 1, p. 49-55
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Puchkov, V. N. (2009) , The evolution of the Uralian orogen, Geological Society, London, Special Publications, 327, no. 1, p. 161-195, https://doi.org/10.1144/SP327.9
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Puchkov, V. N. (2009) , The evolution of the Uralian orogen, Geological Society, London, Special Publications, 327, no. 1, p. 161-195, https://doi.org/10.1144/SP327.9
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
