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<front>
<journal-meta>
<journal-id journal-id-type="publisher">NHESSD</journal-id>
<journal-title-group>
<journal-title>Natural Hazards and Earth System Sciences Discussions</journal-title>
<abbrev-journal-title abbrev-type="publisher">NHESSD</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nat. Hazards Earth Syst. Sci. Discuss.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2195-9269</issn>
<publisher><publisher-name></publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/nhessd-2-2981-2014</article-id>
<title-group>
<article-title>Signatures of the self-affinity of fracture and faulting in pre-seismic electromagnetic emissions</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Potirakis</surname>
<given-names>S. M.</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>Eftaxias</surname>
<given-names>K.</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>Balasis</surname>
<given-names>G.</given-names>
<ext-link>https://orcid.org/0000-0001-7342-0557</ext-link>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Kopanas</surname>
<given-names>J.</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>Antonopoulos</surname>
<given-names>G.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Kalimeris</surname>
<given-names>A.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Department of Electronics Engineering, Technological Education Institute (TEI) of Piraeus, 250 Thivon &amp; P. Ralli, 12244, Aigaleo, Athens, Greece</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Department of Physics, Section of Solid State Physics, University of Athens, Panepistimiopolis, 15784, Zografos, Athens, Greece</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, I. Metaxa &amp; Vas. Pavlou St., 15236 Penteli, Greece</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Department of Environmental Technology and Ecology, Technological Education Institute (TEI) of the Ionian Islands, Panagoulas road, 29100, Zante, Greece</addr-line>
</aff>
<pub-date pub-type="epub">
<day>30</day>
<month>04</month>
<year>2014</year>
</pub-date>
<volume>2</volume>
<issue>4</issue>
<fpage>2981</fpage>
<lpage>3013</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 S. M. Potirakis 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://nhess.copernicus.org/preprints/2/2981/2014/nhessd-2-2981-2014.html">This article is available from https://nhess.copernicus.org/preprints/2/2981/2014/nhessd-2-2981-2014.html</self-uri>
<self-uri xlink:href="https://nhess.copernicus.org/preprints/2/2981/2014/nhessd-2-2981-2014.pdf">The full text article is available as a PDF file from https://nhess.copernicus.org/preprints/2/2981/2014/nhessd-2-2981-2014.pdf</self-uri>
<abstract>
<p>Of particular interest is the detection of precursors of an impending rupture. Theoretical,
  numerical studies along with laboratory experiments indicate that precursory signs of an impending
  failure are the sudden drop of fractal dimension and entropy, along with the anticorrelated, for
  large system sizes, rising of Hurst exponent and drop of a frequency–size power-law scaling
  exponent. Based on the widely accepted concept of the self-affine nature of faulting and fracture,
  we examine whether these precursory signs exist in the fracto-electromagnetic emissions resulting
  from the activation of a single fault.</p>
</abstract>
<counts><page-count count="33"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Aggelis, D. G., Soulioti, D. V., Sapouridis, N., Barkoula, N. M., Paipetis, A. S., and Matikas, T. E.: Acoustic emission characterization of the fracture process in fibre reinforced concrete, Constr. Build. Mater., 25, 4126–4131, 2011.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Bahat, D., Rabinovitch, A., and Frid, V.: Tensile Fracturing in Rocks, Springer, New York, 2005.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bouchaud, E.: Scaling properties of cracks, J. Phys.: Condens. Matter, 9, 4319, &lt;a href=&quot;http://dx.doi.org/10.1088/0953-8984/9/21/002&quot;&gt;https://doi.org/10.1088/0953-8984/9/21/002&lt;/a&gt;, 1997.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</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="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Carpinteri, A., Lacidogna, G., and Puzzi, S.: From criticality to final collapse: evolution of the &quot;b-value&quot; from 1.5 to 1.0, Chaos Soliton. Fract., 41, 843–853, &lt;a href=&quot;http://dx.doi.org/10.1016/j.chaos.2009.03.165&quot;&gt;https://doi.org/10.1016/j.chaos.2009.03.165&lt;/a&gt;, 2009a.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Carpinteri, A., Lacidogna, G., and Niccolini, G.: Fractal analysis of damage detected in concrete structural elements under loading, Chaos Soliton. Fract., 42, 2047–2056, &lt;a href=&quot;http://dx.doi.org/10.1016/j.chaos.2009.03.165&quot;&gt;https://doi.org/10.1016/j.chaos.2009.03.165&lt;/a&gt;, 2009b.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Chen, C.-C., Lee, Y.-T., Hasumi, T., and Hsu, H.-L.: Transition on the relationship between fractal dimension and Hurst exponent in the long-range connective sandpile models, Phys. Lett. A, 375, 324–328, &lt;a href=&quot;http://dx.doi.org/10.1016/j.physleta.2010.11.021&quot;&gt;https://doi.org/10.1016/j.physleta.2010.11.021&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Chen, W., Wang, Z., Xie, H., and Yu, W.: Characterization of surface EMG signal based on fuzzy entropy, IEEE T. Neur. Sys. Reh., 15, 266–272, 2007.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Chen, W., Zhuang, J., Yu, W., and Wang, Z.: Measuring complexity using FuzzyEn, ApEn, and SampEn, Med. Eng. Phys., 31, 61–68, 2009.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Contoyiannis, Y. F., Kapiris, P. G., and Eftaxias, K. A.: Monitoring of a pre-seismic phase from its electromagnetic precursor, Phys. Rev. E, 71, 066123, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.71.066123&quot;&gt;https://doi.org/10.1103/PhysRevE.71.066123&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Cowie, P., Vanneste, C., and Sornette, D.: Statistical physics model for spatio-temporal evolution of faults, J. Geophys. Res., 98, 21809–21821, 1993.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Cowie, P., Sornette, D., and Vanneste, C.: Multifractal scaling properties of a growing fault population, Geophys. J. Int., 122, 457–469, 1995.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Eftaxias, K.: Are there pre-seismic electromagnetic precursors? A multidisciplinary approach, in: Earthquake Research and Analysis – Statistical Studies, Observations and Planning, InTech, March, &lt;a href=&quot;http://dx.doi.org/10.5772/28069&quot;&gt;https://doi.org/10.5772/28069&lt;/a&gt;, 460 pp., 2012.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Eftaxias, K. and Potirakis, S. M.: Current challenges for pre-earthquake electromagnetic emissions: shedding light from micro-scale plastic flow, granular packings, phase transitions and self-affinity notion of fracture process, Nonlin. Processes Geophys., 20, 771–792, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-20-771-2013&quot;&gt;https://doi.org/10.5194/npg-20-771-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Eftaxias, K., Kapiris, P., Polygiannakis, J., Bogris, N., Kopanas, J., Antonopoulos, G., Peratzakis, A., and Hadjicontis, V.: Signature of pending earthquake from electromagnetic anomalies, Geophys. Res. Lett., 28, 3321–3324, 2001.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Eftaxias, K., Kapiris, P., Dologlou, E., Kopanas, J., Bogris, N., Antonopoulos, G., Peratzakis, A., and Hadjicontis, 2002 EM anomalies before the Kozani earthquake: a study of their behavior through laboratory experiments, Geophys. Res. Lett., 29, 1228, &lt;a href=&quot;http://dx.doi.org/10.1029/2001GL013786&quot;&gt;https://doi.org/10.1029/2001GL013786&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Eftaxias, K., Potirakis, S. M., and Chelidze, T.: On the puzzling feature of the silence of precursory electromagnetic emissions, Nat. Hazards Earth Syst. Sci., 13, 2381–2397, &lt;a href=&quot;http://dx.doi.org/10.5194/nhess-13-2381-2013&quot;&gt;https://doi.org/10.5194/nhess-13-2381-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Enescu, B. and Ito, K.: Some premonitory phenomena of the 1995 Hyogo-ken Nanbu (Kobe) earthquake, Tectonophysics, 338, 297–314, 2001.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Frankel, A.: High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, &lt;i&gt;b&lt;/i&gt; value, and the scaling of strength on faults, J. Geophys. Res., 96, 6291–6302, &lt;a href=&quot;http://dx.doi.org/10.1029/91JB00237&quot;&gt;https://doi.org/10.1029/91JB00237&lt;/a&gt;, 1991.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Fukui, K., Okubo, S., and Terashima, T.: Electromagnetic radiation from rock during uniaxial compression testing: the effects of rock characteristics and test conditions, Rock Mech. Rock Eng., 38, 411–423, &lt;a href=&quot;http://dx.doi.org/10.1007/s00603-005-0046-7&quot;&gt;https://doi.org/10.1007/s00603-005-0046-7&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Girard, L., Weiss, J., and Amitrano, D.: Damage-cluster distribution and size effect on strength in compressive failure, Phys. Rev. Lett., 108, 225502, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.108.225502&quot;&gt;https://doi.org/10.1103/PhysRevLett.108.225502&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Gokhberg, M., Morgunov, V., and Pokhotelov, O.: Earthquake Prediction, Seismo-Electromagnetic Phenomena, Gordon and Breach Publishers, Amsterdam, 1995.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Guarino, A., Ciliberto, S., Garcimartín, A., Zei, M., and Scorretti, R.: Failure time and critical behaviour of fracture precursors in heterogeneous materials, Eur. Phys. J. B, 26, 141–151, &lt;a href=&quot;http://dx.doi.org/10.1140/epjb/e20020075&quot;&gt;https://doi.org/10.1140/epjb/e20020075&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Gutenberg, B. and Richter, C.: Seismicity of the Earth and Associated Phenomena, 2nd edn., Princeton Univ. Press, Princeton, 1954.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Hadjicontis, V., Mavromatou, C., Antsygina, T. N., and Chishko, K. A.: Mechanism of electromagnetic emission in plastically deformed ionic crystal, Phys. Rev. B, 76, 024106, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevB.76.024106&quot;&gt;https://doi.org/10.1103/PhysRevB.76.024106&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Hadjicontis, V., Mavromatou, C., Mastrogiannis, D., Antsygina, T. N., and Chishko, K. A.: Relationship between electromagnetic and acoustic emissions during plastic deformation of gamma-irradiated LiF monocrystals, J. Appl. Phys., 110, 024907, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3608247&quot;&gt;https://doi.org/10.1063/1.3608247&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Hallgass, R., Loreto, V., Mazzella, O., Paladin, G., and Pietronero, L.: Earthquake statistics and fractal faults, Phys. Rev. E, 56, 1346–1356, 1997.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Hansen, A. and Schmittbuhl, J.: Origin of the universal roughness exponent of brittle fracture surfaces: stress-weighted percolation in the damage zone, Phys. Rev. Lett., 90, 045504, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.90.045504&quot;&gt;https://doi.org/10.1103/PhysRevLett.90.045504&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Hayakawa, M.: Atmospheric and Ionospheric Electromagnetic Phenomena Associated with Earthquakes, Terrapub, Tokyo, 1999.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Hayakawa, M. and Fujinawa, Y.: Electromagnetic Phenomena Related to Earthquake Prediction, Terrapub, Tokyo, 1994.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</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="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Herrmann, H. J. and Roux, S.: Statistical Models for Fracture and Disordered Media, North-Holland, Amsterdam, 1990.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Houle, P. A. and Sethna, J. P.: Acoustic emission from crumpling paper, Phys. Rev. E, 54, 278–283, 1996.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Hurst, H.: Long term storage capacity of reservoirs, T. Am. Soc. Civ. Eng., 116, 770–808, 1951.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Kalimeri, M., Papadimitriou, C., Balasis, G., and Eftaxias, K.: Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy, Physica A, 387, 1161–1172, 2008.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Kapiris, P. G., Eftaxias, K. A., and Chelidze, T. L.: Electromagnetic signature of prefracture criticality in heterogeneous media, Phys. Rev. Lett., 92, 065702, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.92.065702&quot;&gt;https://doi.org/10.1103/PhysRevLett.92.065702&lt;/a&gt;, 2004a.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Kapiris, P. G., Balasis, G. T., Kopanas, J. A., Antonopoulos, G. N., Peratzakis, A. S., and Eftaxias, K. A.: Scaling similarities of multiple fracturing of solid materials, Nonlin. Processes Geophys., 11, 137–151, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-11-137-2004&quot;&gt;https://doi.org/10.5194/npg-11-137-2004&lt;/a&gt;, 2004b.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Karamanos, K., Dakopoulos, D., Aloupis, K., Peratzakis, A., Athanasopoulou, L., Nikolopoulos, S., Kapiris, P., and Eftaxias, K.: Study of pre-seismic electromagnetic signals in terms of complexity, Phys. Rev. E, 74, 016104, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.74.016104&quot;&gt;https://doi.org/10.1103/PhysRevE.74.016104&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Krajcinovic, D.: Damage Mechanics, Elsevier, Amsterdam, 1996.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Kuksenko, V. S., Damaskinskaya, E. E., and Kadomtsev, A. G.: Fracture of granite under various strain conditions, Izvestiya, Physics of the Solid Earth, 47, 879–885, 2011.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Lacidogna, G., Manuello, A., Carpinteri, A., Niccolini, G., Agosto, A., and Durin, G.: Acoustic and electromagnetic emissions in rocks under compression, in: Proceeding of the SEM Annual Conference 2010, Indianapolis, Indiana, USA, 2010, Society for experimental Mechanics Inc., 2010.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Lacidogna, G., Carpinteri, A., Manuello, A., Durin, G., Schiavi, A., Niccolini, G., and Agosto, A.: Acoustic and electromagnetic emissions as precursor phenomena in failure processes, Strain, 47, 144–152, &lt;a href=&quot;http://dx.doi.org/10.1111/j.1475-1305.2010.00750.x&quot;&gt;https://doi.org/10.1111/j.1475-1305.2010.00750.x&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Lavrov, A.: Fracture-induced physical phenomena and memory effects in rocks: a review, Strain, 41, 135–149, 2005.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Lee, Y.-T., Chen, C.-C., Hasumi, T., and Hsu, H.-L.: Precursory phenomena associated with large avalanches in the long-range connective sandpile model II: an implication to the relation between the &lt;i&gt;b&lt;/i&gt;-value and the Hurst exponent in seismicity, Geophys. Res. Lett., 36, L02308, &lt;a href=&quot;http://dx.doi.org/10.1029/2008GL036548&quot;&gt;https://doi.org/10.1029/2008GL036548&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Lee, Y.-T., Chen, C.-C., Lin, C.-Y., and Chi, S.-C.: Negative correlation between power-law scaling and Hurst exponents in long-range connective sandpile models and real seismicity, Chaos Solit. Fract., 45, 125–130, 2012.</mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple">Lei, X.-L., and Satoh, T.: Indicators of critical point behavior prior to rock failure inferred from pre-failure damage, Tectonophysics, 431, 97–111, &lt;a href=&quot;http://dx.doi.org/10.1016/j.tecto.2006.04.023&quot;&gt;https://doi.org/10.1016/j.tecto.2006.04.023&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple">Li, Y. H., Liu, J.-P., Zhao, X.-D., and Yang, Y.-J.: Study on &lt;i&gt;b&lt;/i&gt;-value and fractal dimension of acoustic emission during rock failure process, Rock and Soil Mech., 30, 2559–2563, 2009.</mixed-citation>
</ref>
<ref id="ref48">
<label>48</label><mixed-citation publication-type="other" xlink:type="simple">Lomnitz, C.: Fundamentals of Earthquake Prediction, John Wiley &amp; Sons, Inc, New York, 1994.</mixed-citation>
</ref>
<ref id="ref49">
<label>49</label><mixed-citation publication-type="other" xlink:type="simple">Lopez, J. M. and Schmittbuhl, J.: Anomalous scaling of fracture surfaces, Phys. Rev. E, 57, 6405–6408, 1998.</mixed-citation>
</ref>
<ref id="ref50">
<label>50</label><mixed-citation publication-type="other" xlink:type="simple">Lowen, S. B. and Teich, M. C.: Estimation and simulation of fractal stochastic point processes, Fractals, 3, 183–210, 1995.</mixed-citation>
</ref>
<ref id="ref51">
<label>51</label><mixed-citation publication-type="other" xlink:type="simple">Lu, C., Mai, Y.-W., and Xie, H.: A sudden drop of fractal dimension: a likely precursor of catastrophic failure in disordered media, Phil. Mag. Lett., 85, 33–40, 2005.</mixed-citation>
</ref>
<ref id="ref52">
<label>52</label><mixed-citation publication-type="other" xlink:type="simple">Maes, C., VanMoffaert, A., Frederix, H., and Strauven, H.: Criticality in creep experiments on cellular glass, Phys. Rev. B, 57, 4987–4990, 1998.</mixed-citation>
</ref>
<ref id="ref53">
<label>53</label><mixed-citation publication-type="other" xlink:type="simple">Mandelbrot, B. B.: The Fractal Geometry of Nature, Freeman, New York, 1983.</mixed-citation>
</ref>
<ref id="ref54">
<label>54</label><mixed-citation publication-type="other" xlink:type="simple">Mandelbrot, B. B. and Wallis, J. R.: Noah, Joseph and operational hydrology, Water Resour. Res., 4, 909–918, 1968.</mixed-citation>
</ref>
<ref id="ref55">
<label>55</label><mixed-citation publication-type="other" xlink:type="simple">Matsumoto, H., Ikeya, M., and Yamanaka, C.: Analysis of barberpole color and speckle noises recorded 6 and half hours before the Kobe earthquake, Jpn. J. Appl. Phys., 37, 1409–1411, 1998.</mixed-citation>
</ref>
<ref id="ref56">
<label>56</label><mixed-citation publication-type="other" xlink:type="simple">Mogi, K.: Magnitude frequency relation for elastic shocks accompanying fractures of various materials and some related problems in earthquakes, B. Earthq. Res. I. Tokyo Univ., 40, 831–853, 1962.</mixed-citation>
</ref>
<ref id="ref57">
<label>57</label><mixed-citation publication-type="other" xlink:type="simple">Morgounov, V.: Relaxation creep model of impending earthquake, Ann. Geophys., 44, 369–381, &lt;a href=&quot;http://dx.doi.org/10.4401/ag-3603&quot;&gt;https://doi.org/10.4401/ag-3603&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref58">
<label>58</label><mixed-citation publication-type="other" xlink:type="simple">Mori, Y. and Obata, Y.: Electromagnetic emission and AE Kaiser effect for estimating rock in-situ stress, Report of the Research Institute of Industrial Technology Nihon University, 93, 1–16, 2008.</mixed-citation>
</ref>
<ref id="ref59">
<label>59</label><mixed-citation publication-type="other" xlink:type="simple">Mourot, G., Morel, S., Bouchaud, E., and Valentin, G.: Scaling properties of mortar fracture surfaces, Int. J. Fracture, 140, 39–54, 2006.</mixed-citation>
</ref>
<ref id="ref60">
<label>60</label><mixed-citation publication-type="other" xlink:type="simple">Nitsan, U.: Electromagnetic emission accompanying fracture of quartz-bearing rocks, Geophys. Res. Lett., 4, 333–337, 1977.</mixed-citation>
</ref>
<ref id="ref61">
<label>61</label><mixed-citation publication-type="other" xlink:type="simple">Ohnaka, M.: Acoustic emission during creep of brittle rock, Int. J. Rock Mech. Min., 20, 121–134, 1983.</mixed-citation>
</ref>
<ref id="ref62">
<label>62</label><mixed-citation publication-type="other" xlink:type="simple">Ohnaka, M. and Mogi, K.: Frequency characteristics of acoustic emission in rocks under uniaxial compression and its relation to the fracturing process to failure, J. Geophys. Res., 87, 3873–3884, &lt;a href=&quot;http://dx.doi.org/10.1029/JB087iB05p03873&quot;&gt;https://doi.org/10.1029/JB087iB05p03873&lt;/a&gt;, 1982.</mixed-citation>
</ref>
<ref id="ref63">
<label>63</label><mixed-citation publication-type="other" xlink:type="simple">Papadimitriou, C., Kalimeri, M., and Eftaxias, K.: Nonextensivity and universality in the EQ preparation process, Phys. Rev. E, 77, 036101, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.77.036101&quot;&gt;https://doi.org/10.1103/PhysRevE.77.036101&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref64">
<label>64</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="ref65">
<label>65</label><mixed-citation publication-type="other" xlink:type="simple">Peng, C.-K., Havlin, S., Stanley, H. E., and Goldberger, A. L.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos, 5, 82–87, &lt;a href=&quot;http://dx.doi.org/10.1063/1.166141&quot;&gt;https://doi.org/10.1063/1.166141&lt;/a&gt;, 1995.</mixed-citation>
</ref>
<ref id="ref66">
<label>66</label><mixed-citation publication-type="other" xlink:type="simple">Petri, A., Paparo, G., Vespignani, A., Alippi, A., Costantini, M.: Experimental evidence for critical dynamics in microfracturing processes, Phys. Rev. Lett., 73, 3423, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.73.3423&quot;&gt;https://doi.org/10.1103/PhysRevLett.73.3423&lt;/a&gt;, 1994.</mixed-citation>
</ref>
<ref id="ref67">
<label>67</label><mixed-citation publication-type="other" xlink:type="simple">Ponomarev, A., Zavyalov, A., Smirnov, V., and Lockner, D.: Physical modelling of the formation and evolution of seismically active fault zones, Tectonophysics, 277, 57–81, 1997.</mixed-citation>
</ref>
<ref id="ref68">
<label>68</label><mixed-citation publication-type="other" xlink:type="simple">Ponson, L., Bonamy, D., and Bouchaud, E.: Two-dimensional scaling properties of experimental fracture surfaces, Phys. Rev. Lett., 96, 035506, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.96.035506&quot;&gt;https://doi.org/10.1103/PhysRevLett.96.035506&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref69">
<label>69</label><mixed-citation publication-type="other" xlink:type="simple">Potirakis, S. M., Minadakis, G., and Eftaxias, K.: Analysis of electromagnetic pre-seismic emissions using Fisher information and Tsallis entropy, Physica A, 391, 300–306, &lt;a href=&quot;http://dx.doi.org/10.1016/j.physa.2011.08.003&quot;&gt;https://doi.org/10.1016/j.physa.2011.08.003&lt;/a&gt;, 2012a.</mixed-citation>
</ref>
<ref id="ref70">
<label>70</label><mixed-citation publication-type="other" xlink:type="simple">Potirakis, S. M., Minadakis, G., and Eftaxias, K.: Relation between seismicity and pre-earthquake electromagnetic emissions in terms of energy, information and entropy content, Nat. Hazards Earth Syst. Sci., 12, 1179–1183, &lt;a href=&quot;http://dx.doi.org/10.5194/nhess-12-1179-2012&quot;&gt;https://doi.org/10.5194/nhess-12-1179-2012&lt;/a&gt;, 2012b.</mixed-citation>
</ref>
<ref id="ref71">
<label>71</label><mixed-citation publication-type="other" xlink:type="simple">Potirakis, S. M., Minadakis, G., and Eftaxias, K.: Sudden drop of fractal dimension of electromagnetic emissions recorded prior to significant earthquake, Nat. Hazards, 64, 641–650, &lt;a href=&quot;http://dx.doi.org/10.1007/s11069-012-0262-x&quot;&gt;https://doi.org/10.1007/s11069-012-0262-x&lt;/a&gt;, 2012c.</mixed-citation>
</ref>
<ref id="ref72">
<label>72</label><mixed-citation publication-type="other" xlink:type="simple">Rabinovitch, A., Frid, V., and Bahat, D.: Gutenberg–Richter-type relation for laboratory fracture-induced electromagnetic radiation, Phys. Rev. E, 65, 011401, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.65.011401&quot;&gt;https://doi.org/10.1103/PhysRevE.65.011401&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref73">
<label>73</label><mixed-citation publication-type="other" xlink:type="simple">Raghavendra, B. S. and Narayana Dutt, D.: Computing fractal dimension of signals using multiresolution box-counting method, World Acad. of Sci., Eng., and Technol., 61, 1223–1238, 2010.</mixed-citation>
</ref>
<ref id="ref74">
<label>74</label><mixed-citation publication-type="other" xlink:type="simple">Rundle, J. B., Turcotte, D. L., Shcherbakov, R., Klein, W., and Sammis, C.: Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems, Rev. Geophys., 41, 1019, &lt;a href=&quot;http://dx.doi.org/10.1029/2003RG000135&quot;&gt;https://doi.org/10.1029/2003RG000135&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref75">
<label>75</label><mixed-citation publication-type="other" xlink:type="simple">Sahimi, M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing, Rev. Mod. Phys., 65, 1393–1534, 1993.</mixed-citation>
</ref>
<ref id="ref76">
<label>76</label><mixed-citation publication-type="other" xlink:type="simple">Sahimi, M. and Tajer, S. E.: Self-affine fractal distributions of the bulk density, elastic moduli, and seismic wave velocities of rock, Phys. Rev. E, 71, 046301, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.71.046301&quot;&gt;https://doi.org/10.1103/PhysRevE.71.046301&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref77">
<label>77</label><mixed-citation publication-type="other" xlink:type="simple">Sahimi, M., Robertson, M. C., and Sammis, C. G.: Fractal distribution of earthquakes hypocenters and its relation to fault patterns and percolation, Phys. Rev. Lett., 70, 2186–2189, 1993.</mixed-citation>
</ref>
<ref id="ref78">
<label>78</label><mixed-citation publication-type="other" xlink:type="simple">Sarlis, N. V., Skordas, E. S., and Varotsos, P. A.: Nonextensivity and natural time: the case of seismicity, Phys. Rev. E, 82, 021110, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.82.021110&quot;&gt;https://doi.org/10.1103/PhysRevE.82.021110&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref79">
<label>79</label><mixed-citation publication-type="other" xlink:type="simple">Schmittbuhl, J., Vilotte, J. P., and Roux, S.: Reliability of self-affine measurements, Phys. Rev. E, 51, 131–147, 1995.</mixed-citation>
</ref>
<ref id="ref80">
<label>80</label><mixed-citation publication-type="other" xlink:type="simple">Scholz, C. H.: The frequency–magnitude relation of microfracturing in rock and its relation to earthquakes, B. Seismol. Soc. Am., 58, 399–415, 1968.</mixed-citation>
</ref>
<ref id="ref81">
<label>81</label><mixed-citation publication-type="other" xlink:type="simple">Schiavi, A., Niccolini, G., Terrizzo, P., Carpinteri, A., Lacidogna, G., and Manuello, A.: Acoustic emissions at high and low frequencies during compression tests in brittle materials, Strain, 47, 105–110, 2011.</mixed-citation>
</ref>
<ref id="ref82">
<label>82</label><mixed-citation publication-type="other" xlink:type="simple">Shadkhoo, S., Ghanbarnejad, F., Jafari, G. R., and Tabar, M. R. R.: Scaling behavior of earthquakes&apos; inter-events time series, Cent. Eur. J. Phys., 7, 620–623, 2009.</mixed-citation>
</ref>
<ref id="ref83">
<label>83</label><mixed-citation publication-type="other" xlink:type="simple">Sharon, E. and Fineberg, J.: Confirming the continuum theory of dynamic brittle fracture for fast cracks, Nature, 397, 333, &lt;a href=&quot;http://dx.doi.org/10.1038/16891&quot;&gt;https://doi.org/10.1038/16891&lt;/a&gt;, 1999.</mixed-citation>
</ref>
<ref id="ref84">
<label>84</label><mixed-citation publication-type="other" xlink:type="simple">Silva, R., Franca, G. S., Vilar, C. S., and Alcaniz, J. S.: Nonextensive models for earthquakes, Phys. Rev. E, 73, 026102, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.73.026102&quot;&gt;https://doi.org/10.1103/PhysRevE.73.026102&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref85">
<label>85</label><mixed-citation publication-type="other" xlink:type="simple">Sornette, D.: Self-organized criticality in plate tectonics, in: Spontaneous Formation of Space–Time Sructures and Criticality, edited by: Riste, T. and Sherrington, D., Kluwer Academic Publishers, Dordrecht, 57–106, 1991.</mixed-citation>
</ref>
<ref id="ref86">
<label>86</label><mixed-citation publication-type="other" xlink:type="simple">Sornette, D.: Critical phenomena in natural sciences, in: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer, Berlin, Heidelberg, New York, 2000.</mixed-citation>
</ref>
<ref id="ref87">
<label>87</label><mixed-citation publication-type="other" xlink:type="simple">Sornette, D., Miltenberger, P., and Vanneste, C.: Statistical physics of fault patterns self-organized by repeated earthquakes, Pure Appl. Geophys., 142, 491–527, 1994.</mixed-citation>
</ref>
<ref id="ref88">
<label>88</label><mixed-citation publication-type="other" xlink:type="simple">Sotolongo-Costa, O. and Posadas, A.: Fragment-asperity interaction model for earthquakes, Phys. Rev. Lett., 92, 048501, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.92.048501&quot;&gt;https://doi.org/10.1103/PhysRevLett.92.048501&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref89">
<label>89</label><mixed-citation publication-type="other" xlink:type="simple">Soulioti, D., Barkoula, N. M., Paipetis, A., Matikas, T. E., Shiotani, T., and Aggelis, D. G.: Acoustic emission behavior of steel fibre reinforced concrete under bending, Constr. Build. Mater., 23, 3532–3536, 2009.</mixed-citation>
</ref>
<ref id="ref90">
<label>90</label><mixed-citation publication-type="other" xlink:type="simple">Tsukakoshi, Y. and Shimazaki, K.: Decreased b-value prior to the &lt;i&gt;M&lt;/i&gt; 6.2 Northern Miyagi, Japan, earthquake of 26 July 2003, Earth Planets Space, 60, 915–924, 2008.</mixed-citation>
</ref>
<ref id="ref91">
<label>91</label><mixed-citation publication-type="other" xlink:type="simple">Uyeda, S.: Short-term earthquake prediction: current status of seismo-electromagnetics, Tectonophysics, 470, 205–213, 2009.</mixed-citation>
</ref>
<ref id="ref92">
<label>92</label><mixed-citation publication-type="other" xlink:type="simple">Vettegren, V. I., Kuksenko, V. S., Mamalimov, R. I., and Shcherbakov, I. P.: Dynamics of fractoluminescence, electromagnetic and acoustic emissions upon impact on a granite surface, Izvestiya, Physics of the Solid Earth, 48, 415–420, 2012.</mixed-citation>
</ref>
<ref id="ref93">
<label>93</label><mixed-citation publication-type="other" xlink:type="simple">Warwick, J. W., Stoker, C., and Meyer, T. R.: Radio emission associated with rock fracture: possible application to the great Chilean earthquake of May 22 1960, J. Geophys. Res., 87, 2851–2859, 1982.</mixed-citation>
</ref>
<ref id="ref94">
<label>94</label><mixed-citation publication-type="other" xlink:type="simple">Weeks, J., Lockner, D., and Byerlee, J.: Changes in b-values during movement on cut surfaces in granite, B. Seismol. Soc. Am., 68, 333–341, 1978.</mixed-citation>
</ref>
<ref id="ref95">
<label>95</label><mixed-citation publication-type="other" xlink:type="simple">Wu, Y.-M., Chen, C.-C., Zhao, L., and Chang, C.-H.: Seismicity characteristics before the 2003 Chengkung, Taiwan, earthquake, Tectonophysics, 457, 177–182, 2008.</mixed-citation>
</ref>
<ref id="ref96">
<label>96</label><mixed-citation publication-type="other" xlink:type="simple">Zapperi, S., Nukala, P., and Simunovic, S.: Crack roughness and avalanche precursors in the random fuse model, Phys. Rev. E, 71, 026106, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.71.026106&quot;&gt;https://doi.org/10.1103/PhysRevE.71.026106&lt;/a&gt;, 2005.</mixed-citation>
</ref>
</ref-list>
</back>
</article>