Abstract
Applying natural time analysis, which has been introduced by the authors in 2001, to the Japanese seismic data, we find that the system enters the critical stage upon the occurrence of M = 4.2–5.0 earthquakes from 08:36 to 13:14 local time (LT) on 10 March 2011, i.e., almost one day before the M9 Tohoku earthquake on 11 March 2011. Here, we find that just before this period the Tsallis entropic index q of non-extensive statistical mechanics started to show distinct changes. In addition an evident change of q is found upon the occurrence of the M7.3 foreshock at 11:45 LT on 9 March 2011, which exhibits a scaling behavior with a characteristic exponent 1∕3 that conforms to Lifshitz-Slyozov-Wagner theory for phase transitions.
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References
C. Tsallis,Introduction to Nonextensive Statistical Mechanics (Springer, Berlin, 2009)
C. Tsallis, J. Stat. Phys. 52, 479 (1988)
C. Tsallis, Entropy 13, 1765 (2011)
G. Livadiotis,Kappa Distributions: Theory and Applications in Plasmas (Elsevier, Amsterdam Netherlands, 2017)
G. Livadiotis, Europhys. Lett. 122, 50001 (2018)
O. Sotolongo-Costa, A. Posadas, Phys. Rev. Lett. 92, 048501 (2004)
R. Silva, G.S. França, C.S. Vilar, J.S. Alcaniz, Phys. Rev. E 73, 026102 (2006)
F. Vallianatos, V. Karakostas, E. Papadimitriou, Pure Appl. Geophys. 171, 1343 (2014)
G. Michas, F. Vallianatos, P. Sammonds, Earth Planet. Sci. Lett. 431, 150 (2015)
T. Chelidze, F. Vallianatos, L. Telesca,Complexity of Seismic Time Series (Elsevier, Amsterdam, 2018)
S. Abe, G.B. Bagci, Phys. Rev. E 71, 016139 (2005)
N.V. Sarlis, E.S. Skordas, P.A. Varotsos, Phys. Rev. E 82, 021110 (2010)
L. Telesca, Bull. Seismolog. Soc. Am. 102, 886 (2012)
F. Vallianatos, P. Sammonds, Tectonophysics 590, 52 (2013)
F. Vallianatos, G. Michas, G. Papadakis, Physica A 414, 163 (2014)
G. Papadakis, F. Vallianatos, P. Sammonds, Pure Appl. Geophys. 172, 1923 (2015)
G. Papadakis, F. Vallianatos, Acta Geophys. 65, 555 (2017)
Q. Huang, Geophys. Res. Lett. 35, L23308 (2008)
Q. Huang, J. Asian Earth Sci. 41, 421 (2011)
L. Telesca, M. Lovallo, Geophys. Res. Lett. 36, L01308 (2009)
S. Lennartz, V.N. Livina, A. Bunde, S. Havlin, Europhys. Lett. 81, 69001 (2008)
S. Lennartz, A. Bunde, D.L. Turcotte, Geophys. J. Int. 184, 1214 (2011)
J.B. Rundle, J.R. Holliday, W.R. Graves, D.L. Turcotte, K.F. Tiampo, W. Klein, Phys. Rev. E 86, 021106 (2012)
J.B. Rundle, D.L. Turcotte, A. Donnellan, L. Grant Ludwig, M. Luginbuhl, G. Gong, Earth Space Sci. 3, 480 (2016)
J.M. Carlson, J.S. Langer, B.E. Shaw, Rev. Mod. Phys. 66, 657 (1994)
J.R. Holliday, J.B. Rundle, D.L. Turcotte, W. Klein, K.F. Tiampo, A. Donnellan, Phys. Rev. Lett. 97, 238501 (2006)
D.L. Turcotte,Fractals and Chaos in Geology and Geophysics, 2nd edn. (Cambridge University Press, Cambridge, 1997)
P.A. Varotsos, N.V. Sarlis, E.S. Skordas,Natural Time Analysis: The new view of time. Precursory Seismic Electric Signals, Earthquakes and other Complex Time-Series (Springer-Verlag, Berlin, Heidelberg, 2011)
N.V. Sarlis, E.S. Skordas, P.A. Varotsos, Europhys. Lett. 124, 29001 (2018)
P.A. Varotsos, N.V. Sarlis, E.S. Skordas, Entropy 20, 757 (2018)
P.A. Varotsos, N.V. Sarlis, E.S. Skordas, Europhys. Lett. 125, 69001 (2019)
J.B. Rundle, M. Luginbuhl, A. Giguere, D.L. Turcotte, Pure Appl. Geophys. 175, 647 (2018)
M. Luginbuhl, J.B. Rundle, A. Hawkins, D.L. Turcotte, Pure Appl. Geophys. 175, 49 (2018)
M. Luginbuhl, J.B. Rundle, D.L. Turcotte, Pure Appl. Geophys. 175, 661 (2018)
P.A. Varotsos, N.V. Sarlis, H.K. Tanaka, E.S. Skordas, Phys. Rev. E 72, 041103 (2005)
P. Varotsos, N. Sarlis, E. Skordas, Europhys. Lett. 96, 59002 (2011)
S. Uyeda, M. Kamogawa, Eos Trans. AGU 89, 363 (2008)
S. Uyeda, M. Kamogawa, H. Tanaka, J. Geophys. Res. 114, B02310 (2009)
P.A. Varotsos, N.V. Sarlis, E.S. Skordas, M.S. Lazaridou, Tectonophysics 589, 116 (2013)
N.V. Sarlis, E.S. Skordas, P.A. Varotsos, T. Nagao, M. Kamogawa, S. Uyeda, Proc. Natl. Acad. Sci. U. S. A. 112, 986 (2015)
P.A. Varotsos, N.V. Sarlis, E.S. Skordas, Earthquake Sci. 30, 209 (2017)
G. Xu, P. Han, Q. Huang, K. Hattori, F. Febriani, H. Yamaguchi, J. Asian Earth Sci. 77, 59 (2013)
P. Han, K. Hattori, G. Xu, R. Ashida, C.H. Chen, F. Febriani, H. Yamaguchi, J. Asian Earth Sci. 114, 321 (2015)
P. Han, K. Hattori, Q. Huang, S. Hirooka, C. Yoshino, J. Asian Earth Sci. 129, 13 (2016)
H.K. Tanaka, P.A. Varotsos, N.V. Sarlis, E.S. Skordas, Proc. Jpn. Acad. Ser. B 80, 283 (2004)
H. Kanamori, Nature 271, 411 (1978)
N.V. Sarlis, E.S. Skordas, P.A. Varotsos, A. Ramírez-Rojas, E.L. Flores-Márquez, Physica A 517, 475 (2019)
P.A. Varotsos, N.V. Sarlis, E.S. Skordas, M.S. Lazaridou, Appl. Phys. Lett. 91, 064106 (2007)
O. Penrose, J.L. Lebowitz, J. Marro, M.H. Kalos, A. Sur, J. Stat. Phys. 19, 243 (1978)
I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961)
C. Wagner, Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaft für physikalische Chemie 65, 581 (1961)
L. Pitaevskii, E. Lifshitz, inCourse of Theoretical Physics: Physical Kinetics (Pergamon Press Ltd, Oxford, England, 1993), Vol. 10
L.D. Landau, E.M. Lifshitz,Statistical Physics, 3rd edn. (Pergamon Press, Oxford, 1980)
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Skordas, E.S., Sarlis, N.V. & Varotsos, P.A. Precursory variations of Tsallis non-extensive statistical mechanics entropic index associated with the M9 Tohoku earthquake in 2011. Eur. Phys. J. Spec. Top. 229, 851–859 (2020). https://doi.org/10.1140/epjst/e2020-900218-x
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DOI: https://doi.org/10.1140/epjst/e2020-900218-x