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On the Motivation and Foundation of Natural Time Analysis: Useful Remarks

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Języki publikacji
EN
Abstrakty
EN
Since its introduction in 2001, natural time analysis has been applied to diverse fields with remarkable results. Its validity has not been doubted by any publication to date. Here, we indicate that frequently asked questions on the motivation and the foundation of natural time analysis are directly answered if one takes into account the following two key points that we have considered as widely accepted when natural time analysis was proposed: first, the aspects on the energy of a system forwarded by Max Planck in his Treatise on Thermodynamics; second, the theorem on the characteristic functions of probability distributions which Gauss called Ein Schönes Theorem der Wahrscheinlichkeitsrechnung (beautiful theorem of probability calculus). The case of the time series of earthquakes and of the precursory Seismic Electric Signals are discussed as typical examples.
Czasopismo
Rocznik
Strony
841--852
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • Section of Solid State Physics and Solid Earth Physics Institute, Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece
autor
  • Section of Solid State Physics and Solid Earth Physics Institute, Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece
  • Section of Solid State Physics and Solid Earth Physics Institute, Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece
Bibliografia
  • Applebaum, D. (2013), Lévy Processes and Stochastic Calculus, Cambridge Studies in Advanced Mathematics, Vol. 116, Cambridge University Press, Cambridge.
  • Bauer, M. (2011), A definition of energy, Physics Today 64, 8, 10, DOI: 10.1063/ PT.3.1198.
  • Coopersmith, J. (2010), Energy, the Subtle Concept. The Discovery of Feynman’s Blocks from Leibniz to Einstein, Oxford University Press, Oxford, 416 pp.
  • Crystal, L. (2011), Review of “Energy, the subtle concept: The discovery of Feynman’s blocks from Leibniz to Einstein” by J. Coopersmith, Physics Today 64, 4, 61-62, DOI: 10.1063/1.3580497.
  • Feller, W. (1971), An Introduction to Probability Theory and Its Applications, 2nd ed., John Wiley & Sons, New York.
  • Flores-Márquez, E.L., C.A. Vargas, L. Telesca, and A. Ramírez-Rojas (2014), Analysis of the distribution of the order parameter of synthetic seismicity generated by a simple spring-block system with asperities, Physica A 393, 508-512, DOI: 10.1016/j.physa.2013.07.015.
  • Holliday, J.R., J.B. Rundle, D.L. Turcotte, W. Klein, K.F. Tiampo, and A. Donnellan (2006), Space-time clustering and correlations of major earthquakes, Phys. Rev. Lett. 97, 23, 238501, DOI: 10.1103/PhysRevLett.97.238501.
  • Huang, Q. (2015), Forecasting the epicenter of a future major earthquake, Proc. Natl. Acad. Sci. USA 112, 4, 944-945, DOI: 10.1073/pnas.1423684112.
  • Jaynes, E.T. (2003), Probability Theory: The Logic of Science, Cambridge University Press, Cambridge.
  • Johnson, N.L., S. Kotz, and A.W. Kemp (1992), Univariate Discrete Distributions, John Wiley & Sons, New York, 565 pp.
  • Kolmogorov, A.N. (1950), Foundations of the Theory of Probability, Chelsea Publishing Co., New York.
  • Planck, M. (1945), Treatise on Thermodynamics, Dover Publ., New York, 297 pp.
  • Ramírez-Rojas, A., L. Telesca, and F. Angulo-Brown (2011), Entropy of geoelectrical time series in the natural time domain, Nat. Hazards Earth Syst. Sci. 11, 219-225, DOI: 10.5194/nhess-11-219-2011.
  • Rundle, J.B., J.R. Holliday, W.R. Graves, D.L. Turcotte, K.F. Tiampo, and W. Klein (2012), Probabilities for large events in driven threshold systems, Phys. Rev. E 86, 2, 021106, DOI: 10.1103/PhysRevE.86.021106.
  • Vargas, C.A., E.L. Flores-Márquez, A. Ramírez-Rojas, and L. Telesca (2015), Analysis of natural time domain entropy fluctuations of synthetic seismicity generated by a simple stick-slip system with asperities, Physica A 419, 23- 28, DOI: 10.1016/j.physa.2014.10.037.
  • Varotsos, P., N. Sarlis, and M. Lazaridou (1996), Reply to “Rebuttal to reply by Varotsos and Lazaridou: Towards plainly successful prediction” by Paul W. Burton, Geophys. Res. Lett. 23, 11, 1389-1390, DOI: 10.1029/ 96GL01259.
  • Varotsos, P.A., N.V. Sarlis, and E.S. Skordas (2001), Spatio-temporal complexity aspects on the interrelation between seismic electric signals and seismicity, Pract. Athens Acad. 76, 294-321.
  • Varotsos, P.A., N.V. Sarlis, and E.S. Skordas (2002a), Long-range correlations in the electric signals that precede rupture, Phys. Rev. E 66, 011902, DOI: 10.1103/PhysRevE.66.011902.
  • Varotsos, P., N. Sarlis, and E. Skordas (2002b), Seismic electric signals and seismicity: On a tentative interrelation between their spectral content, Acta Geophys. Pol. 50, 3, 338-354.
  • Varotsos, P.A., N.V. Sarlis, E.S. Skordas, and M.S. Lazaridou (2008), Fluctuations, under time reversal, of the natural time and the entropy distinguish similar looking electric signals of different dynamics, J. Appl. Phys. 103, 014906, DOI: 10.1063/1.2827363.
  • Varotsos, P.A., N.V. Sarlis, and E.S. Skordas (2009), Detrended fluctuation analysis of the magnetic and electric field variations that precede rupture, Chaos 19, 2, 023114, DOI: 10.1063/1.3130931.
  • Varotsos, P.A., N.V. Sarlis, and E.S. Skordas (2011a), Natural Time Analysis: The New View of Time. Precursory Seismic Electric Signals, Earthquakes and other Complex Time Series, Springer Verlag, Berlin Heidelberg.
  • Varotsos, P.A., N.V. Sarlis, and E.S. Skordas, S. Uyeda, and M. Kamogawa (2011b), Natural time analysis of critical phenomena, Proc. Natl. Acad. Sci. USA 108, 28, 11361-11364, DOI: 10.1073/pnas.1108138108.
  • Yates, D.S., D.S. Moore, and D.S. Starnes (2002), The Practice of Statistics, 2nd ed., W.H. Freeman, New York.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę
Typ dokumentu
Bibliografia
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