<?xml version="1.0"?>
<!DOCTYPE article
PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20190208//EN"
       "JATS-journalpublishing1.dtd">
<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" article-type="research-article" dtd-version="1.4" xml:lang="en">
 <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">47097</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">Wavelet analysis of secular geomagnetic variations</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Wavelet analysis of secular geomagnetic variations</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Rotanova</surname>
       <given-names>N M</given-names>
      </name>
      <name xml:lang="en">
       <surname>Rotanova</surname>
       <given-names>N M</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Bondar</surname>
       <given-names>T N</given-names>
      </name>
      <name xml:lang="en">
       <surname>Bondar</surname>
       <given-names>T N</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Kovalevskaya</surname>
       <given-names>E V</given-names>
      </name>
      <name xml:lang="en">
       <surname>Kovalevskaya</surname>
       <given-names>E V</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 Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Russia</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Russia</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Russia</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Russia</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Russia</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Russia</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <volume>5</volume>
   <issue>5</issue>
   <fpage>375</fpage>
   <lpage>383</lpage>
   <history>
    <date date-type="received" iso-8601-date="2021-11-10T23:23:00+03:00">
     <day>10</day>
     <month>11</month>
     <year>2021</year>
    </date>
   </history>
   <self-uri xlink:href="https://rjes.ru/en/nauka/article/47097/view">https://rjes.ru/en/nauka/article/47097/view</self-uri>
   <abstract xml:lang="ru">
    <p>Temporal characteristics of secular variations SV over the last hundred of years are studied using the wavelet transformation, providing estimates of dispersion and energy parameters of the process analyzed. The presence of abrupt geomagnetic field variations of the intraterrestrial origin in periods of 1969-1970 and 1989-1990 is confirmed. The SV process is, on the whole, nonfractal, and only two largest scales can be regarded as monofractal. The SV scale diagrams obtained from the wavelet analysis not only revealed singularities in the SV field but also provided constraints on variations in its energy parameters throughout the time interval studied. On the basis of the SV phase portrayal constructed in our study, the limits of the SV dynamic system are estimated to be 24.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Temporal characteristics of secular variations SV over the last hundred of years are studied using the wavelet transformation, providing estimates of dispersion and energy parameters of the process analyzed. The presence of abrupt geomagnetic field variations of the intraterrestrial origin in periods of 1969-1970 and 1989-1990 is confirmed. The SV process is, on the whole, nonfractal, and only two largest scales can be regarded as monofractal. The SV scale diagrams obtained from the wavelet analysis not only revealed singularities in the SV field but also provided constraints on variations in its energy parameters throughout the time interval studied. On the basis of the SV phase portrayal constructed in our study, the limits of the SV dynamic system are estimated to be 24.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>geomagnetic field</kwd>
    <kwd>secular variation</kwd>
    <kwd>wavelet analysis</kwd>
    <kwd>attractor.</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>geomagnetic field</kwd>
    <kwd>secular variation</kwd>
    <kwd>wavelet analysis</kwd>
    <kwd>attractor.</kwd>
   </kwd-group>
  </article-meta>
 </front>
 <body>
  <p></p>
 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Alexandrescu, J. Geophys. Res., v. 100, 1995., doi: 10.1029/95JB00314</mixed-citation>
     <mixed-citation xml:lang="en">Alexandrescu, J. Geophys. Res., v. 100, 1995., doi: 10.1029/95JB00314</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Alexandrescu, J. Geophys. Res., v. 101, 1996., doi: 10.1029/96JB01648</mixed-citation>
     <mixed-citation xml:lang="en">Alexandrescu, J. Geophys. Res., v. 101, 1996., doi: 10.1029/96JB01648</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Alperovich, Phys. Chem. Earth, v. 23, 1998., doi: 10.1016/S0079-19469800128-1</mixed-citation>
     <mixed-citation xml:lang="en">Alperovich, Phys. Chem. Earth, v. 23, 1998., doi: 10.1016/S0079-19469800128-1</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Astafyeva, Usp. Fiz. Nauk, v. 166, 1996.</mixed-citation>
     <mixed-citation xml:lang="en">Astafyeva, Usp. Fiz. Nauk, v. 166, 1996.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Braginsky, Geomagn. Aeron., v. 17, 1977.</mixed-citation>
     <mixed-citation xml:lang="en">Braginsky, Geomagn. Aeron., v. 17, 1977.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Cay, TIIER, v. 69, no. 11, 1981.</mixed-citation>
     <mixed-citation xml:lang="en">Cay, TIIER, v. 69, no. 11, 1981.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Chui, Introduction to Wavelets, 2001.</mixed-citation>
     <mixed-citation xml:lang="en">Chui, Introduction to Wavelets, 2001.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Courtillot, Annu. Rev. Earth Planet. Sci., v. 16, 1988.</mixed-citation>
     <mixed-citation xml:lang="en">Courtillot, Annu. Rev. Earth Planet. Sci., v. 16, 1988.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Daubechies, Ten Lectures on Wavelets, 2001.</mixed-citation>
     <mixed-citation xml:lang="en">Daubechies, Ten Lectures on Wavelets, 2001.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Daubechies, CBMS Ser. Appl. Math. Soc. Ind. Appl. Math. Pa., 61, 1992.</mixed-citation>
     <mixed-citation xml:lang="en">Daubechies, CBMS Ser. Appl. Math. Soc. Ind. Appl. Math. Pa., 61, 1992.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">De Michelis, Geophys. J. Int., v. 143, 2000., doi: 10.1046/j.1365-246X.2000.00208.x</mixed-citation>
     <mixed-citation xml:lang="en">De Michelis, Geophys. J. Int., v. 143, 2000., doi: 10.1046/j.1365-246X.2000.00208.x</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Dremin, Usp. Fiz. Nauk, v. 171, no. 5, 2001.</mixed-citation>
     <mixed-citation xml:lang="en">Dremin, Usp. Fiz. Nauk, v. 171, no. 5, 2001.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ducruix, Geophys. J. R. Astron. Soc., v. 61, 1980.</mixed-citation>
     <mixed-citation xml:lang="en">Ducruix, Geophys. J. R. Astron. Soc., v. 61, 1980.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Dyakonov, Wavelets: Theory and Applications, 2002.</mixed-citation>
     <mixed-citation xml:lang="en">Dyakonov, Wavelets: Theory and Applications, 2002.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gilbert, J. Geophys. Res., v. 103, 1998.</mixed-citation>
     <mixed-citation xml:lang="en">Gilbert, J. Geophys. Res., v. 103, 1998.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Golovkov, Geomagn. Aeron., v. 36, 1996.</mixed-citation>
     <mixed-citation xml:lang="en">Golovkov, Geomagn. Aeron., v. 36, 1996.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hide, Phys. Earth Planet. Int., v. 39, no. 4, 1985., doi: 10.1016/0031-92018590143-8</mixed-citation>
     <mixed-citation xml:lang="en">Hide, Phys. Earth Planet. Int., v. 39, no. 4, 1985., doi: 10.1016/0031-92018590143-8</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B18">
    <label>18.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ippolitov, Optika Atm. Okeana, v. 14, no. 4, 2001.</mixed-citation>
     <mixed-citation xml:lang="en">Ippolitov, Optika Atm. Okeana, v. 14, no. 4, 2001.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B19">
    <label>19.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ivanov, Geomagn. Aeron., v. 40, no. 2, 2000.</mixed-citation>
     <mixed-citation xml:lang="en">Ivanov, Geomagn. Aeron., v. 40, no. 2, 2000.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B20">
    <label>20.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Malin, Publicado on volumen conmemorative 75 aniversario del observatorio del Ebro, 1983.</mixed-citation>
     <mixed-citation xml:lang="en">Malin, Publicado on volumen conmemorative 75 aniversario del observatorio del Ebro, 1983.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B21">
    <label>21.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Mallat, IEEE Pattern Anal. Machine Intell., v. 11, 1989., doi: 10.1109/34.192463</mixed-citation>
     <mixed-citation xml:lang="en">Mallat, IEEE Pattern Anal. Machine Intell., v. 11, 1989., doi: 10.1109/34.192463</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B22">
    <label>22.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">McLeod, J. Geophys. Res., v. 90, 1985.</mixed-citation>
     <mixed-citation xml:lang="en">McLeod, J. Geophys. Res., v. 90, 1985.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B23">
    <label>23.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Meyer, Wavelets and Operators, 1992.</mixed-citation>
     <mixed-citation xml:lang="en">Meyer, Wavelets and Operators, 1992.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B24">
    <label>24.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Papitashvili, Geomagn. Aeron., v. 22, 1982.</mixed-citation>
     <mixed-citation xml:lang="en">Papitashvili, Geomagn. Aeron., v. 22, 1982.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B25">
    <label>25.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Rotanova, Geomagn. Aeron., v. 42, 2002.</mixed-citation>
     <mixed-citation xml:lang="en">Rotanova, Geomagn. Aeron., v. 42, 2002.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B26">
    <label>26.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Runcorn, Phys. Earth Planet. Int., v. 41, 1985., doi: 10.1016/0031-92018590022-6</mixed-citation>
     <mixed-citation xml:lang="en">Runcorn, Phys. Earth Planet. Int., v. 41, 1985., doi: 10.1016/0031-92018590022-6</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B27">
    <label>27.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Takens, Lecture Notes in Mathematics, D. Rand and I.-S. Young, Eds., 1981.</mixed-citation>
     <mixed-citation xml:lang="en">Takens, Lecture Notes in Mathematics, D. Rand and I.-S. Young, Eds., 1981.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B28">
    <label>28.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voorhies, J. Geophys. Res., v. 91, 1986.</mixed-citation>
     <mixed-citation xml:lang="en">Voorhies, J. Geophys. Res., v. 91, 1986.</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
