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<front>
<journal-meta>
<journal-id journal-id-type="publisher">NPG</journal-id>
<journal-title-group>
<journal-title>Nonlinear Processes in Geophysics</journal-title>
<abbrev-journal-title abbrev-type="publisher">NPG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nonlin. Processes Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1607-7946</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/npg-21-1059-2014</article-id>
<title-group>
<article-title>Nonlinear fluctuation analysis for a set of 41 magnetic clouds measured by the Advanced Composition Explorer (ACE) spacecraft</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ojeda González</surname>
<given-names>A.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Gonzalez</surname>
<given-names>W. D.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mendes</surname>
<given-names>O.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Domingues</surname>
<given-names>M. O.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Rosa</surname>
<given-names>R. R.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>DGE/CEA/National Institute for Space Research, INPE 12227-010 São José dos Campos, SP, Brazil</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>LAC/CTE/National Institute for Space Research, INPE 12227-010 São José dos Campos, SP, Brazil</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Laboratory of Physics and Astronomy, IP &amp; D/University of Paraíba Valley, UNIVAP 12244-000 São José dos Campos, SP, Brazil</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Junior Postdoctoral Fellow &amp;ndash; CNPq, Brasilia-DF, Brazil</addr-line>
</aff>
<pub-date pub-type="epub">
<day>30</day>
<month>10</month>
<year>2014</year>
</pub-date>
<volume>21</volume>
<issue>5</issue>
<fpage>1059</fpage>
<lpage>1073</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 A. Ojeda González et al.</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/1059/2014/npg-21-1059-2014.html">This article is available from https://npg.copernicus.org/articles/21/1059/2014/npg-21-1059-2014.html</self-uri>
<self-uri xlink:href="https://npg.copernicus.org/articles/21/1059/2014/npg-21-1059-2014.pdf">The full text article is available as a PDF file from https://npg.copernicus.org/articles/21/1059/2014/npg-21-1059-2014.pdf</self-uri>
<abstract>
<p>The statistical distribution of values in the signal and the autocorrelations
(interpreted as the memory or persistence) between values are attributes of
a time series. The autocorrelation function values are positive in a time
series with persistence, while they are negative in a time series with anti-persistence.
The persistence of values with respect to each other can be
strong, weak, or nonexistent. A strong correlation implies a &quot;memory&quot; of
previous values in the time series. The long-range persistence in time series
could be studied using semivariograms, rescaled range, detrended fluctuation
analysis and Fourier spectral analysis, respectively. In this work,
persistence analysis is to study interplanetary magnetic field (IMF) time series. We use data from
the IMF components with a time resolution of 16 s. Time intervals
corresponding to distinct processes around 41 magnetic clouds (MCs) in the period between
March 1998 and December 2003 were selected. In this exploratory study, the
purpose of this selection is to deal with the cases presenting the three
periods: plasma sheath, MC, and post-MC. We calculated one exponent of
persistence (e.g., α, β, &lt;i&gt;Hu&lt;/i&gt;, &lt;i&gt;Ha&lt;/i&gt;) over the
previous three time intervals. The persistence exponent values increased
inside cloud regions, and it was possible to select the following threshold
values: &amp;alpha;&lt;sub&gt;(&lt;i&gt;j&lt;/i&gt;)&lt;/sub&gt; = 1.392,
&lt;i&gt;Ha&lt;/i&gt;&lt;sub&gt;(&lt;i&gt;j&lt;/i&gt;)&lt;/sub&gt; = 0.327, and &lt;i&gt;Hu&lt;/i&gt;&lt;sub&gt;(&lt;i&gt;j&lt;/i&gt;)&lt;/sub&gt; = 0.875. These values are
useful as another test to evaluate the quality of the identification. If the
cloud is well structured, then the persistence exponent values exceed
thresholds. In 80.5% of the cases studied, these tools were able to
separate the region of the cloud from neighboring regions. The Hausdorff
exponent (&lt;i&gt;Ha&lt;/i&gt;) provides the best results.</p>
</abstract>
<counts><page-count count="15"/></counts>
<funding-group>
<award-group id="gs1">
<funding-source></funding-source>
<award-id>483226/2011-4</award-id>
<award-id>150595/2013-1</award-id>
<award-id>483226 /2011-4</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Fundação de Amparo à Pesquisa do Estado de São Paulo</funding-source>
<award-id>2012/072812-2</award-id>
</award-group>
<award-group id="gs3">
<funding-source>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior</funding-source>
<award-id>1236-83/2012</award-id>
</award-group>
</funding-group>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Assireu, A. T., Rosa, R. R., Vijaykumar, N. L., Lorenzzetti, J. A., Rempel, E. L., Ramos, F. M., Sá, L. D. A., Bolzan, M. J. A., and Zanandrea, A.: Gradient patter analysis of short nonstationary time series: an application to Lagrangian data from satellite tracked drifters, Physica D, 168–169, 397–403, &lt;a href=&quot;http://dx.doi.org/10.1016/S0167-2789(02)00527-4&quot;&gt;https://doi.org/10.1016/S0167-2789(02)00527-4&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Baroni, M. P. M. A., Wit, A. D., and Rosa, R. R.: Detrended fluctuation analysis of numerical density and viscous fingering patterns, Europhys. Lett., 92, 64002, &lt;a href=&quot;http://dx.doi.org/10.1209/0295-5075/92/64002&quot;&gt;https://doi.org/10.1209/0295-5075/92/64002&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bashan, A., Bartsch, R., Kantelhardt, J. W., and Havlin, S.: Comparison of detrending methods for fluctuation analysis, Physica A, 387, 5080–5090, &lt;a href=&quot;http://dx.doi.org/10.1016/j.physa.2008.04.023&quot;&gt;https://doi.org/10.1016/j.physa.2008.04.023&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Bolzan, M. J. A., Ramos, F. M., Sá, L. D. A., Neto, C. R., and Rosa, R. R.: Analysis of fine-scale canopy turbulence within and above an Amazon forest using Tsallis&apos; generalized thermostatistics, J. Geophys. Res., 107, 8063, &lt;a href=&quot;http://dx.doi.org/10.1029/2001JD000378&quot;&gt;https://doi.org/10.1029/2001JD000378&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Bothmer, V. and Schwenn, R.: The structure and origin of magnetic clouds in the solar wind, Ann. Geophys., 16, 1–24, &lt;a href=&quot;http://dx.doi.org/10.1007/s00585-997-0001-x&quot;&gt;https://doi.org/10.1007/s00585-997-0001-x&lt;/a&gt;, 1998.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Bryce R. M. and Sprague K. B.: Revisiting detrended fluctuation analysis, Sci. Rep., 2, 1–6, 2012.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Buldyrev, S. V., Goldberger, A. L., Havlin, S., Mantegna, R. N., Matsa, M. E., Peng, C.-K., Simons, M., and Stanley, H. E.: Long-range correlation properties of coding and noncoding DNA sequences: genbank analysis, Phys. Rev. E, 51, 5084–5091, 1995.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Burlaga, L. F.: Magnetic clouds, in: Physics of the Inner Heliosphere, Vol. 2, edited by: Schwenn, R. and Marsch, E., Springer-Verlag, New York, 1–2, 1991.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Burlaga, L. F., Sittler, E., Mariani, F., and Schwenn, R.: Magnetic loop behind an interplanetary shock: Voyager, Helios and IMP 8 observations, J. Geophys. Res., 86, 6673–6684, 1981.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Calzadilla, M. A. and Lazo, B.: Sheffield Space Plasma Meeting (2001) multipoint measurements vs. theory, in: Inproceedings, ESA: Non-lineal time series analysis of Dst geomagnetic index, ESA Publications Division, SP-492, 24–26 April 2001, edited by: Warmbein, B., Sheffield, UK, 121–125, 2001.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Campos-Velho, H. F., Rosa, R. R., Ramos, F. M., Pielke, R. A., Degrazia, G. A., Neto, C. R., and Zanandrea, A.: Multifractal model for eddy diffusivity and counter-gradient term in atmospheric turbulence, Physica A, 295, 219–223, 2001.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Dasso, S., Mandrini, C., Démoulin, P., Luoni, M., and Gulisano, A.: Large scale MHD properties of interplanetary magnetic clouds, Adv. Space Res., 35, 711–724, 2005.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Heneghan, C. and McDarby, G.: Establishing the relation between detrended fluctuation analysis and power spectral density analysis for stochastic processes, Phys. Rev. E, 62, 6103–6110, 2000.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., and Stanley, H. E.: Effect of trends on detrended fluctuation analysis, Phys. Rev. E, 64, 011114, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.64.011114&quot;&gt;https://doi.org/10.1103/PhysRevE.64.011114&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Hurst, H. E.: Long-term storage capacity of reservoirs, T. Am. Soc. Civ. Eng., 116, 770–808, 1951.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Hurst, H. E., Black, R. P., and Simaika, Y. M.: Long-Term Storage: an Experimental Study, Constable, London, 145 pp., 1965.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Huttunen, K. E. J., Schwenn, R., Bothmer, V., and Koskinen, H. E. J.: Properties and geoeffectiveness of magnetic clouds in the rising, maximum and early declining phases of solar cycle 23, Ann. Geophys., 23, 625–641, &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-23-625-2005&quot;&gt;https://doi.org/10.5194/angeo-23-625-2005&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., and Stanley, H. E.: Multifractal detrended fluctuation analysis of nonstationary time series, Physica A, 316, 87–114, 2002.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Kay, S. and Marple, S. J.: Spectrum analysis – a modern perspective, Proc. IEEE, 69, 1380–1419, &lt;a href=&quot;http://dx.doi.org/10.1109/PROC.1981.12184&quot;&gt;https://doi.org/10.1109/PROC.1981.12184&lt;/a&gt;, 1981.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Klausner, V., Ojeda, G. A., Domingues, M. O., Mendes, O., and Papa, A. R. R.: Study of local regularities in solar wind data and ground magnetograms, J. Atmos. Sol.-Terr. Phy., 112, 10–19, &lt;a href=&quot;http://dx.doi.org/10.1016/j.jastp.2014.01.013&quot;&gt;https://doi.org/10.1016/j.jastp.2014.01.013&lt;/a&gt;, 2014.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Klein, L. W. and Burlaga, L. F.: Interplanetary magnetic clouds at 1 AU, J. Geophys. Res., 87, 613–624, 1982.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Lepping, R. P., Acuña, M. H., Burlaga, L. F., Farrell, W. M., Slavin, J. A., Schatten, K. H., Mariani, F., Ness, N. F., Neubauer, F. M., Whang, Y. C., Byrnes, J. B., Kennon, R. S., Panetta, P. V., Scheifele, J., and Worley, E. M.: The WIND magnetic field investigation, Space Sci. Rev., 71, 207–229, 1995.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Little, M., McSharry, P., Moroz, I., and Roberts, S.: Nonlinear, biophysically-informed speech pathology detection, in: ICASSP 2006 Proceedings, 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, 14–19 May 2006, Toulouse, France, 1080–1083, &lt;a href=&quot;http://dx.doi.org/10.1109/ICASSP.2006.1660534&quot;&gt;https://doi.org/10.1109/ICASSP.2006.1660534&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Malamud, B. D. and Turcotte, D. L.: Self-affine times series: I. Generation and analyses, Adv. Geophys., 40, 1–90, &lt;a href=&quot;http://dx.doi.org/10.1016/S0065-2687(08)60293-9&quot;&gt;https://doi.org/10.1016/S0065-2687(08)60293-9&lt;/a&gt;, 1999.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Mandelbrot, B. B.: The Fractal Geometry of Nature, W. H. Freeman and Company, New York, 480 pp., 1983.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Mandelbrot, B. B. and Ness, J. W. V.: Fractional brownian motions, fractional noises and applications, SIAM Rev., 10, 422–437, 1968.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Mandelbrot, B. B. and Wallis, J. R.: Some long-run properties of geophysical records, Water Resour. Res., 5, 321–340, 1969.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Mcsharry, P. E. and Malamud, B. D.: Quantifying self-similarity in cardiac inter-beat interval time series, in: Computers in Cardiology, IEEE, Lyon, 459–462, &lt;a href=&quot;http://dx.doi.org/10.1109/CIC.2005.1588136&quot;&gt;https://doi.org/10.1109/CIC.2005.1588136&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Narock, T. W. and Lepping, R. P.: Anisotropy of magnetic field fluctuations in an average interplanetary magnetic cloud at 1 AU, J. Geophys. Res., 112, A06108, &lt;a href=&quot;http://dx.doi.org/10.1029/2006JA011987&quot;&gt;https://doi.org/10.1029/2006JA011987&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Ojeda, G. A., Calzadilla, M. A., Lazo, B., Alazo, K., and Savio, S.: Analysis of behavior of solar wind parameters under different IMF conditions using two nonlinear dynamics techniques, J. Atmos. Sol.-Terr. Phy., 67, 1859–1864, &lt;a href=&quot;http://dx.doi.org/10.1016/j.jastp.2004.12.014&quot;&gt;https://doi.org/10.1016/j.jastp.2004.12.014&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Ojeda, G. A., Mendes, O., Calzadilla, M. A., and Domingues, M. O.: Spatio-temporal entropy analysis of the magnetic field to help magnetic cloud characterization, J. Geophys. Res., 118, 5403–5414, 2013.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Ojeda, G., A., Mendes, O., Domingues, M. O., and Menconi, V. E.: Daubechies wavelet coefficients: a tool to study interplanetary magnetic fluctuations, Geofis. Int., 53, 101–115, 2014.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Pelletier, J. D. and Turcotte, D. L.: Self-affine times series: 2. Applications and models, Adv. Geophys., 40, 91–166, 1999.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Peng, C.-K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L.: Mosaic organization of DNA nucleotides, Phys. Rev. E, 49, 1685–1689, 1994.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Percival, D. B. and Walden, A. T.: Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge University Press, Cambridge, New York, NY, USA, p. 583, 1993.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Price, C. P. and Newman, D. E.: Using the R/S statistic to analyze AE data, J. Atmos. Sol.-Terr. Phy., 63, 1387–1397, 2001.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Priestley, M. B.: Spectral Analysis and Time Series, Academic Press, London, New York, 890 pp., 1981.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Ramos, F. M., Bolzan, M. J. A., Sá, L. D. A., and Rosa, R. R.: Atmospheric turbulence within and above an Amazon forest, Physica D, 193, 278–291, &lt;a href=&quot;http://dx.doi.org/10.1016/j.physd.2004.01.026&quot;&gt;https://doi.org/10.1016/j.physd.2004.01.026&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Rosa, R. R., Sharma, A. S., Valdivia, J. A.: Characterization of asymmetric fragmentation patterns in spatially extended systems, Int. J. Mod. Phys. C., 10, 509–514, 1999.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Rosa, R. R., Karlický, M., Veronese, T. B., Vijaykumar, N. L., Sawant, H. S., Borgazzi, A. I., Dantas, M. S., Barbosa, E. B. M., Sych, R. A., and Mendes, O.: Gradient pattern analysis of short solar radio bursts, Adv. Space Res., 42, 844–851, 2008.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Ruzmaikin, A., Feynman, J., and Robinson, P.: Long-term persistence of solar activity, Sol. Phys., 149, 395–403, 1994.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Sharma, A. S. and Veeramani, T.: Extreme events and long-range correlations in space weather, Nonlin. Processes Geophys., 18, 719–725, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-18-719-2011&quot;&gt;https://doi.org/10.5194/npg-18-719-2011&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Tapiero, C. and Vallois, P.: Run length statistics and the Hurst exponent in random and birth-death random walks, Chaos Soliton. Fract., 7, 1333–1341, &lt;a href=&quot;http://dx.doi.org/10.1016/0960-0779(96)00032-X&quot;&gt;https://doi.org/10.1016/0960-0779(96)00032-X&lt;/a&gt;, 1996.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Tsurutani, B. T., Sugiura, M., Iyemori, T., Goldstein, B. E., Gonzalez, W. D., Akasofu, S. I., and Smith, E. J.: The nonlinear response of AE to the IMF Bs driver: A spectral break at 5 hours, Geophys. Res. Lett., 17, 279–282, 1990.</mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Turcotte, D. L.: Fractals and chaos in geology and geophysics, 2nd revised Edn., Cambridge University Press, New York, USA, 1997.</mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple">Vanouplines, P.: Rescaled range analysis and the fractal dimension of pi, University Library, Free University Brussels, Brussels, Belgium, 1995.</mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple">Veronese, T., Rosa, R., Bolzan, M., Fernandes, F. R., Sawant, H., and Karlicky, M.: Fluctuation analysis of solar radio bursts associated with geoeffective X-class flares, J. Atmos. Sol.-Terr. Phy., 73, 1311–1316, &lt;a href=&quot;http://dx.doi.org/10.1016/j.jastp.2010.09.030&quot;&gt;https://doi.org/10.1016/j.jastp.2010.09.030&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple">Voss, R. F.: Random fractals: characterization and measurement, in: Scaling Phenomena in Disordered System, edited by: Pynn, R. and Skjeltorp, A., Springer, USA, 1–11, &lt;a href=&quot;http://dx.doi.org/10.1007/978-1-4757-1402-9_1&quot;&gt;https://doi.org/10.1007/978-1-4757-1402-9_1&lt;/a&gt;, 1985a.</mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple">Voss, R. F.: Random fractal forgeries, in: Fundamental Algorithms for Computer Graphics, NATO ASI, F17, edited by: Earnshaw, R. A., Springer-Verlag, Berlin, Heidelberg, 805–835, 1985b.</mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple">Voss, R. F.: Characterization and measurement of random fractals, Phys. Scripta, 13, 27–32, 1986.</mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple">Wei, H. L., Billings, S. A., and Balikhin, M.: Analysis of the geomagnetic activity of the &lt;i&gt;D&lt;sub&gt;st&lt;/sub&gt;&lt;/i&gt; index and self–affine fractals using wavelet transforms, Nonlin. Processes Geophys., 11, 303–312, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-11-303-2004&quot;&gt;https://doi.org/10.5194/npg-11-303-2004&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple">Zheng, H., Song, W., and Wang, J.: Detrended fluctuation analysis of forest fires and related weather parameters, Physica A, 387, 2091–2099, 2008.</mixed-citation>
</ref>
</ref-list>
</back>
</article>