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A Description of Seismicity Based on Non-extensive Statistical Physics: A Review

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Earthquakes and Their Impact on Society

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Abstract

Earthquakes have always been one the most intriguing natural phenomena for mankind. The abruptness of the shaking ground and the devastating consequences for the human environment were always attracting people’s fear and wonder. Despite the large amount of effort that has been dedicated in understanding the physical processes that lead to the birth of an earthquake and the significant progress that has been achieved in this field, the prediction of an upcoming earthquake still remains a challenging question.

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References

  • Abe, S., & Suzuki, N. (2003). Law for the distance between successive earthquakes. Journal of Geophysical Research, 108(B2), 2113.

    Article  Google Scholar 

  • Abe, S., & Suzuki, N. (2005). Scale-free statistics of time interval between successive earthquakes. Physica A, 350, 588–596.

    Article  Google Scholar 

  • Bak, P., Christensen, K., Danon, L., & Scanlon, T. (2002). Unified scaling law for earthquakes. Physical Review Letters, 88, 178501.

    Article  Google Scholar 

  • Bak, P., & Tang, C. (1989). Earthquakes as a self-organized critical phenomenon. Journal of Geophysical Research, 94, 635–637.

    Article  Google Scholar 

  • Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of 1/f noise. Physical Review Letters, 59, 381–384.

    Article  Google Scholar 

  • Bak, P., Tang, C., & Wiesenfeld, K. (1988). Self-organized criticality. Physical Review A, 38, 364–374.

    Article  Google Scholar 

  • Beck, C., & Schlogl, F. (1993). Thermodynamics of chaotic systems: An introduction. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Bell, A. F., Naylor, M., & Main, I. G. (2013). Convergence of the frequency-size distribution of global earthquakes. Geophysical Research Letters, 40, 2585–2589.

    Article  Google Scholar 

  • Berrill, J. B., & Davis, R. O. (1980). Maximum entropy and the magnitude distribution. Bulletin of the Seismological Society of America, 70, 1823–1831.

    Google Scholar 

  • Bird, P. (2003). An updated digital model of plate boundaries. Geochemistry, Geophysics, Geosystems, 4(3), 1027.

    Article  Google Scholar 

  • Burridge, L., & Knopoff, L. (1967). Model and theoretical seismicity. Bulletin of the Seismological Society of America, 57, 341–371.

    Google Scholar 

  • Caruso, F., Pluchino, A., Latora, V., Vinciguerra, S., & Rapisarda, A. (2007). Analysis of self-organized criticality in the Olami-Feder-Christensen model and in real earthquakes. Physical Review E, 75, 055101.

    Article  Google Scholar 

  • Chakrabarti, B. K., & Benguigui, L. G. (1997). Statistical physics of fracture and breakdown in disordered systems. Oxford: Oxford Science Publications.

    Google Scholar 

  • Corral, A. (2004). Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes. Physical Review Letters, 92, 108501.

    Article  Google Scholar 

  • Darooneh, A. H., & Dadashinia, C. (2008). Analysis of the spatial and temporal distributions between successive earthquakes: Nonextensive statistical mechanics viewpoint. Physica A, 387, 3647–3654.

    Article  Google Scholar 

  • De Rubeis, V., Hallgas, R., Loreto, V., Paladin, G., Pietronero, L., & Tosi, P. (1996). Self-affine asperity model for earthquakes. Physical Review Letters, 76, 2599–2602.

    Article  Google Scholar 

  • Engdahl, E. R., & Villaseñor, A. (2002). Global seismicity: 1900–1999. International Handbook of Earthquake and Engineering Seismology, Part A, Chapter 41, (pp. 665–690). Academic Press, Waltham.

    Google Scholar 

  • Ferri, G. L., Martínez, S., & Plastino, A. (2005). Equivalence of the four versions of Tsallis’s statistics. Journal of Statistical Mechanics: Theory and Experiment P04009.

    Google Scholar 

  • Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.

    Google Scholar 

  • Hasumi, T. (2007). Interoccurrence time statistics in the two-dimensional Burridge-Knopoff earthquake model. Physical Review E, 76, 026117.

    Article  Google Scholar 

  • Hasumi, T. (2009). Hypocenter interval statistics between successive earthquakes in the two-dimensional Burridge-Knopoff model. Physica A, 388, 477–482.

    Article  Google Scholar 

  • Herrmann, H. J., & Roux, S. (1990). Modelization of fracture in disordered systems. Statistical Models for the Fracture of Disordered Media (pp. 159–188). Elsevier: North-Holland.

    Google Scholar 

  • Hirata, T., & Imoto, M. (1991). Multifractal analysis of spatial distribution of micro earthquakes in the Kanto region. Geophysical Journal International, 107, 155–162.

    Article  Google Scholar 

  • Kagan, Y. Y. (1994). Observational evidence for earthquakes as a nonlinear dynamic process. Physica D: Nonlinear Phenomena, 77, 160–192.

    Article  Google Scholar 

  • Kagan, Y. Y. (1997). Seismic moment-frequency relation for shallow earthquakes: Regional comparison. Journal of Geophysical Research, 102, 2835–2852.

    Article  Google Scholar 

  • Kagan, Y. Y., & Jackson, D. D. (1991). Long-term earthquake clustering. Geophysical Journal International, 104, 117–133.

    Article  Google Scholar 

  • Kagan, Y. Y., & Jackson, D. D. (2000). Probabilistic forecasting of earthquakes. Geophysical Journal International, 143, 438–453.

    Article  Google Scholar 

  • Kagan, Y. Y., & Jackson, D. D. (2013). Tohoku earthquake: A surprise? Bulletin of the Seismological Society of America, 103, 1181–1194.

    Article  Google Scholar 

  • Kagan, Y. Y., & Knopoff, L. (1980). Spatial distribution of earthquakes: The two point correlation function. Geophysical Journal Royal Astronomical Society, 62, 303–320.

    Article  Google Scholar 

  • Kanamori, H. (1978). Quantification of earthquakes. Nature, 271, 411–414.

    Article  Google Scholar 

  • Kawamura, H., Hatano, T., Kato, N., Biswas, S., & Chakrabarti, B. K. (2012). Statistical physics of fracture, friction and earthquakes. Review of Modern Physics, 84, 839–884.

    Article  Google Scholar 

  • Knapmeyer, M., Oberst, J., Hauber, E., Wahlisch, M., Deuchler, C., & Wagner, R. (2006). Working model for spatial distribution and level of Mars’ seismicity. Journal of Geophysical Research, 111, E11006.

    Article  Google Scholar 

  • Krajcinovic, D., & Van Mier, J. G. M. (2000). Damage and fracture of disordered materials. New York: Springer.

    Book  Google Scholar 

  • Lay, T., & Wallace, T. C. (1995). Modern global seismology. New York: Academic Press.

    Google Scholar 

  • Lei, X. L., Kusunose, K., Nishizawa, O., Cho, A., & Satoh, T. (2000). On the spatiotemporal distribution of acoustic emissions in two granitic rocks under triaxial compression: the role of preexisting cracks. Geophysical Research Letters, 27, 1997–2000.

    Article  Google Scholar 

  • Lei, X., Nishizawa, O., Kusunose, K., & Satoh, T. (1992). Fractal structure of the hypocenter distribution and focal mechanism solutions of AE in two granites of different grain size. Journal of Physics of the Earth, 40, 617–634.

    Article  Google Scholar 

  • Lucchitta, B. K., McEwen, S., Clow, G. D., Geissler, P. E., Singer, R. B., Schultz, R. A., & Squyres, S. W. (1992). The canyon system of Mars. In H. H. Kieffer, B. M. Jakosky, C. W. Snyder, & M. S. Matthews (Eds.), Mars (pp. 453–492). USA: University of Arizona Press.

    Google Scholar 

  • Main, I. (1996). Statistical physics, seismogenesis, and seismic hazard. Reviews of Geophysics, 34, 433–462.

    Article  Google Scholar 

  • Main, I. G., & Al-Kindy, F. H. (2002). Entropy, energy, and proximity to criticality in global earthquake populations. Geophysical Research Letters, 29(7), 25–1

    Google Scholar 

  • Main, I. G., & Burton, P. W. (1984). Information theory and the earthquake frequency-magnitude distribution. Bulletin of the Seismological Society of America, 74, 1409–1426.

    Google Scholar 

  • Main, I. G., Meredith, P. G., & Jones, C. (1989). A reinterpration of the precursory seismic b-value anomaly from fracture mechanics. Geophysical Journal, 96, 131–138.

    Article  Google Scholar 

  • Main, I. G., Meredith, P. G., & Sammonds, P. R. (1992). Temporal variations in seismic event rate and b-values from stress corrosion constitutive laws. Tectonophysics, 211, 233–246.

    Article  Google Scholar 

  • Mandelbrot, B. B. (1983). The fractal geometry of nature. San Francisco: Freeman.

    Google Scholar 

  • Mège, D., & Masson, P. (1996). A plume tectonics model for the Tharsis province, Mars. Planetary and Space Science, 44, 1499–1546.

    Article  Google Scholar 

  • Michas, G., Vallianatos, F., & Sammonds, P. (2013). Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece). Nonlinear Processes in Geophysics, 20, 713–724.

    Article  Google Scholar 

  • Nature Debates. (1999). Nature debates: Is the reliable prediction of individual earthquakes a realistic scientific goal? Available from http://www.nature.com/nature/debates/.

  • Olami, Z., Feder, H. J. S., & Christensen, K. (1992). Self-organized criticality in a continuous nonconservative cellular automaton modeling earthquakes. Physical Review Letters, 68, 1244–1247.

    Article  Google Scholar 

  • Omori, F. (1894). On the aftershocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo 7, 111–200.

    Google Scholar 

  • Papadakis, G., Vallianatos, F., & Sammonds, P. (2013). Evidence of nonextensive statistical physics behavior of the Hellenic Subduction Zone seismicity. Tectonophysics, 608, 1037–1048.

    Article  Google Scholar 

  • Papadakis, G., Vallianatos, F., & Sammonds, P. (2014). A nonextensive statistical physics analysis of the 1995 Kobe earthquake, Japan. Pure and Applied Geophysics (accepted).

    Google Scholar 

  • Picoli, S., Mendes, R. S., Malacarne, L. C., & Santos, R. P. B. (2009). q-distributions in complex systems: A brief review. Brazilian Journal of Physics, 39, 468–474.

    Article  Google Scholar 

  • Prigogine, I. (1980). From being to becoming: Time and complexity in physical systems. San Francisco: Freeman and Co.

    Google Scholar 

  • Queirós, S. M. D. (2005). On the emergence of a generalised gamma distribution, application to traded volume in financial markets. Europhysics Letters, 71, 339–345.

    Article  Google Scholar 

  • Rundle, J. B., Gross, S., Klein, W., Ferguson, C., & Turcotte, D. L. (1997). The statistical mechanics of earthquakes. Tectonophysics, 277, 147–164.

    Article  Google Scholar 

  • Rundle, J. B., Turcotte, D. L., Shcherbakov, R., Klein, W., & Sammis, C. (2003). Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems. Reviews of Geophysics, 41, 4.

    Article  Google Scholar 

  • Sammonds, P. (2005). Plasticity goes supercritical. Nature Materials, 4, 425–426.

    Article  Google Scholar 

  • Sammonds, P., & Ohnaka, M. (1998). Evolution of microseismicity during frictional sliding. Geophysical Research Letters, 25, 699–702.

    Article  Google Scholar 

  • Scholz, C. H. (1998). Earthquakes and friction laws. Nature, 391, 37–42.

    Article  Google Scholar 

  • Scholz, C. H., & Mandelbrot, B. B. (1989). Fractals in geophysics. Basel: Birkhuser.

    Book  Google Scholar 

  • Schultz, R. A. (1995). Gradients in extension and strain at Valles Marineris, Mars. Planet Space Science, 43, 1561–1566.

    Article  Google Scholar 

  • Schultz, R. A. (1997). Displacement–length scaling for terrestrial and Martian faults: Implications for Valles Marineris and shallow planetary grabens. Journal of Geophysical Research, 102, 12009–12015.

    Article  Google Scholar 

  • Schultz, R. A. (2003). Seismotectonics of the Amenthes Rupes thrust fault population, Mars. Geophysical Research Letters, 30, 1303–1307.

    Article  Google Scholar 

  • Schultz, R. A., Hauber, E., Kattenhorn, S., Okubo, C., & Watters, T. (2010). Interpretation and analysis of planetary structures. Journal of Structural Geology, 32, 855–875.

    Article  Google Scholar 

  • Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal 27, 379–423, 623–656.

    Google Scholar 

  • Silva, R., Franca, G. S., Vilar, C. S., & Alcaniz, J. S. (2006). Nonextensive models for earthquakes. Physical Review E, 73, 026102.

    Article  Google Scholar 

  • Sornette, D. (2004). Critical phenomena in natural sciences, chaos, fractals, self-organization and disorder: Concepts and tools (2nd ed.). Heidelberg: Springer.

    Google Scholar 

  • Sornette, A., & Sornette, D. (1989). Self-organized criticality and earthquakes. Europhysics Letters, 9, 197–202.

    Article  Google Scholar 

  • Sotolongo-Costa, O., & Posadas, A. (2004). Fragment-asperity interaction model for earthquakes. Physical Review Letters, 92(4), 048501.

    Article  Google Scholar 

  • Telesca, L. (2010a). Analysis of Italian seismicity by using a nonextensive approach. Tectonophysics, 494, 155–162.

    Article  Google Scholar 

  • Telesca, L. (2010b). Nonextensive analysis of seismic sequences. Physica A, 389, 1911–1914.

    Article  Google Scholar 

  • Telesca, L. (2010c). A non-extensive approach in investigating the seismicity of L’Aquila area (central Italy), struck by the 6 April 2009 earthquake (ML = 5.8). Terra Nova, 22, 87–93.

    Article  Google Scholar 

  • Telesca, L. (2011). Tsallis-based nonextensive analysis of the southern California seismicity. Entropy, 13, 1267–1280.

    Article  Google Scholar 

  • Telesca, L. (2012). Maximum likelihood estimation of the nonextensive parameters of the earthquake cumulative magnitude distribution. Bulletin of the Seismological Society of America, 102(2), 886–891.

    Article  Google Scholar 

  • Telesca, L., Cuomo, V., Lapenna, V., Vallianatos, F., & Drakatos, G. (2001). Analysis of the temporal properties of Greek aftershock sequences. Tectonophysics, 341, 163–178.

    Article  Google Scholar 

  • Telesca, L., Lapenna, V., & Macchiato, M. (2003). Spatial variability of the time-correlated behaviour in Italian seismicity. Earth and Planetary Science Letters, 212, 279–290.

    Article  Google Scholar 

  • Telesca, L., Lapenna, V., & Vallianatos, F. (2002). Monofractal and multifractal approaches in investigating scaling properties in temporal patterns of the 1983–2000 seismicity in the western Corinth graben, Greece. Physics of the Earth and Planetary Interiors, 131, 63–79.

    Article  Google Scholar 

  • Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52, 479–487.

    Article  Google Scholar 

  • Tsallis, C. (2001). Non extensive statistical mechanics and its applications. In S. Abe, & Y. Okamoto (Eds.), Berlin: Springer.

    Google Scholar 

  • Tsallis, C. (2009). Introduction to nonextensive statistical mechanics: Approaching a complex world. Berlin: Springer.

    Google Scholar 

  • Tsallis, C., Bemski, G., & Mendes, R. S. (1999). Is re-association of folded proteins a case of non-extensivity? Physics Letters A, 257, 93–97.

    Article  Google Scholar 

  • Tsekouras, G. A., & Tsallis, C. (2005). Generalized entropy arising from a distribution of q indices. Physical Review E, 71, 046144.

    Article  Google Scholar 

  • Turcotte, D. L. (1997). Fractals and chaos in geology and geophysics (2nd ed.). Cambridge, UK: Cambridge University Press.

    Book  Google Scholar 

  • Utsu, T., Ogata, Y., & Matsura, R. S. (1995). The centenary of the Omori formula for a decay law of aftershock activity. Journal of Physics of the Earth, 43, 1–33.

    Article  Google Scholar 

  • Vallianatos, F. (2009). A non-extensive approach to risk assessment. Natural Hazards and Earth System Sciences, 9, 211–216.

    Article  Google Scholar 

  • Vallianatos, F. (2013). On the non-extensivity in Mars geological faults. Europhysics Letters, 102, 28006.

    Article  Google Scholar 

  • Vallianatos, F., Benson, P., Meredith, P., & Sammonds, P. (2012a). Experimental evidence of a non-extensive statistical physics behaviour of fracture in triaxially deformed Etna basalt using acoustic emissions. Europhysics Letters, 97, 58002.

    Article  Google Scholar 

  • Vallianatos, F., Kokinou, E., & Sammonds, P. (2011a). Non extensive statistical physics approach to fault population distribution. A case study from the Southern Hellenic Arc (Central Crete). Acta Geophysica, 59, 1–13.

    Article  Google Scholar 

  • Vallianatos, F., Michas, G., & Papadakis, G. (2014). Non-extensive and natural time analysis of seismicity before the Mw 6.4, 12 Oct 2013 earthquake in the south west segment of the Hellenic arc. (submitted).

    Google Scholar 

  • Vallianatos, F., Michas, G., Papadakis, G., & Sammonds, P. (2012b). A non-extensive statistical physics view to the spatiotemporal properties of the June 1995, Aigion earthquake (M6.2) aftershock sequence (West Corinth rift, Greece). Acta Geophysica, 60, 758–768.

    Google Scholar 

  • Vallianatos, F., Michas, G., Papadakis, G., & Tzanis, A. (2013). Evidence of non-extensivity in the seismicity observed during the 2011–2012 unrest at the Santorini volcanic complex, Greece. Natural Hazards and Earth System Sciences, 13, 177–185.

    Article  Google Scholar 

  • Vallianatos, F., & Sammonds, P. (2010). Is plate tectonics a case of non-extensive thermodynamics? Physica A, 389, 4989–4993.

    Article  Google Scholar 

  • Vallianatos, F., & Sammonds, P. (2011). A non-extensive statistics of the fault-population of the Valles Marineris extensional province, Mars. Tectonophysics, 509, 50–54.

    Article  Google Scholar 

  • Vallianatos, F., & Sammonds, P. (2013). Evidence of non-extensive statistical physics of the lithospheric instability approaching the 2004 Sumatran-Andaman and 2011 Honsu mega-earthquakes. Tectonophysics, 590, 52–58.

    Article  Google Scholar 

  • Vallianatos, F., & Triantis, D. (2012). Is pressure stimulated current relaxation in amphibolite a case of non-extensivity? Europhysics Letters, 99, 18006.

    Article  Google Scholar 

  • Vallianatos, F., Triantis, D., & Sammonds, P. (2011b). Non-extensivity of the isothermal depolarization relaxation currents in uniaxial compressed rocks. Europhysics Letters, 94, 68008.

    Article  Google Scholar 

  • Vallianatos, F., Triantis, D., Tzanis, A., Anastasiadis, C., & Stavrakas, I. (2004). Electric earthquake precursors: From laboratory results to field observations. Physics and Chemistry of the Earth, 29, 339–351.

    Article  Google Scholar 

  • Varotsos, P. A., Sarlis, N. V., & Skordas, E. S. (2001). Spatio-temporal complexity aspects on the interrelation between seismic electric signals and seismicity. Practica of Athens Academy, 76, 294–321.

    Google Scholar 

  • Varotsos, P. A., Sarlis, N. V., & Skordas, E. S. (2011). Natural time analysis: The new view of time, precursory seismic electric signals, earthquakes and other complex time series. Berlin: Springer.

    Book  Google Scholar 

  • Vilar, C. S., Franca, G. S., Silva, R., & Alcaniz, J. S. (2007). Nonextensivity in geological faults. Physica A, 377, 285–290.

    Article  Google Scholar 

  • Wada, T., & Scarfone, A. M. (2005). Connection between Tsallis’ formalisms employing the standard linear average energy and ones employing the normalized q-average energy. Physics Letters A, 335, 351–362.

    Article  Google Scholar 

  • Zaslavsky, G. M. (1999). Chaotic dynamics and the origin of statistical laws. Physics Today, 52, 39–45.

    Article  Google Scholar 

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Acknowledgments

The work was supported by the THALES Program of the Ministry of Education of Greece and the European Union in the framework of the project entitled ‘‘Integrated understanding of Seismicity, using innovative Methodologies of Fracture mechanics along with Earthquake and non-extensive statistical physics—Application to the geodynamic system of the Hellenic Arc. “SEISMO FEAR HELLARC”, (MIS 380208).

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Vallianatos, F., Michas, G., Papadakis, G. (2016). A Description of Seismicity Based on Non-extensive Statistical Physics: A Review. In: D'Amico, S. (eds) Earthquakes and Their Impact on Society. Springer Natural Hazards. Springer, Cham. https://doi.org/10.1007/978-3-319-21753-6_1

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