World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Tsallis and Levy Statistics in the Preparation of an Earthquake : Volume 15, Issue 3 (06/05/2008)

By Contoyiannis, Y. F.

Click here to view

Book Id: WPLBN0003978328
Format Type: PDF Article :
File Size: Pages 10
Reproduction Date: 2015

Title: Tsallis and Levy Statistics in the Preparation of an Earthquake : Volume 15, Issue 3 (06/05/2008)  
Author: Contoyiannis, Y. F.
Volume: Vol. 15, Issue 3
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Eftaxias, K., & Contoyiannis, Y. F. (2008). Tsallis and Levy Statistics in the Preparation of an Earthquake : Volume 15, Issue 3 (06/05/2008). Retrieved from

Description: Department of Physics and Chemistry, Techological Education Institute (TEI) of Chalkis, Greece. Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are distributed along the activated fault and sustain the system. (ii) The initial MHz part is thought to be due to the fracture of highly heterogeneous system that surrounds the family of asperities. Interestingly, the MHz EM time-series can be described in analogy with a thermal second order phase transition. Herein we focus on the MHz pre-seismic activity, and especially on the naturally arising question: what is the physical mechanism that organizes the heterogeneous system in its critical state? Combining ideas of Levy and Tsallis statistics and criticality with features hidden in the precursory MHz time-series we argue that a Levy walk type mechanism can organize the heterogeneous system to criticality. Based on a numerically produced truncated Levy walk, we propose a way to estimate in the stage of critical fluctuations: (i) the associated Levy index-a, which describes quantitatively the underlying Levy dynamics, and (ii) the range of values where the nonextesitive Tsallis index q is restricted. We also show that the kHz EM activity could not be described by a truncated Levy mechanism. This result further indicates an abrupt sweep of the population of asperities that sustain the system.

Tsallis and Levy statistics in the preparation of an earthquake

Alemany, P. and Zanette, D.: Fractal random walks from a variational formalism for Tsallis entropies, Phys. Rev. E, 49, R956–R958, 1994.; Antoniou, N., Contoyiannis, Y., Diakonos, F., Karanikas, A., and Ktorides, C.: Pion production from a critical QCD phase, Nucl. Phys. A, 693, 799–824, 2001.; Baldovin, F. and Robledo, A.: Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: Rigorous nonextensive solutions, Europhys. Lett., 60, 518–524, 2002.; Buiatti, M., Grigolini, P., and Montagnini, A.: Dynamic Approach to the Thermodynamics of Superdiffusion, Phys. Rev. Lett., 82, 3383–3387, 1999.; Contoyiannis, Y. and Diakonos, F.: Criticality and imtermittency in the order parameter space, Phys. Lett. A, 268, 286–292, 2000.; Contoyiannis, Y., Diakonos, F., and Malakis, A.: Intermittent dynamics of critical fluctuations, Phys. Rev. Lett., 89, 035701/1–4, 2002.; Contoyiannis, Y., Kapiris, P., and Eftaxias, K.: Monitoring of a preseismic phase from its electromagnetic precursors, Phys. Rev. E, 71, 066123/1–14, 2005.; Contoyiannis, Y., Diakonos, F., Papaefthimiou, G., and Theophilidis, G.: Criticality in the relaxation phase of the spontaneous contracting atria isolated from the heart of the frog (Rana ridibunda), Phys. Rev. Lett., 93, 098101/1–4, 2004.; Contoyiannis, Y. and Diakonos, F.: Abrupt transition in a sandpile model, Phys. Rev. E, 73, 031303/1–5, 2006.; Diakonos, F., Pingel, D., and Schmelcher, P.: A stochastic approach to the construction of full-chaotic maps with prescribed statistical properties, Phys. Lett. A, 264, 162–170, 1999.; Kapiris, P., Eftaxias, K., and Chelidze, T.: The electromagnetic signature of prefecture criticality in heterogeneous media, Phys. Rev. Lett., 92, 065702/1–4, 2004.; 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, 016104/1–21, 2006.; Karamanos, K., Peratzakis, A., Kapiris, P., Nikolopoulos, S., Kopanas, J., and Eftaxias, K.: Extracting pre-seismic electromagnetic signatures in terms of symbolic dynamics, Nonlin. Processes Geophys., 12, 835–848, 2005.; Koponen, I.: Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process, Phys. Rev. E, 52, 1197–1199, 1995.; Mantegna, R. and Stanley, H.: Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Levy Flights, Phys. Rev. Lett., 73, 2946–2949, 1994.; Pingel, D., Schmelcher, P., and Diakonos, F.: Theory and examples to the inverse Frobenious-Perron problem for complete chaotic maps, Chaos, 9, 357–366, 1999.; Robledo, A.: Critical fluctuations, Intermittent dynamics and Tsallis statistics, Physica A, 344, 631–636, 2004.; Scafetta, N. and West, B.: Multiscaling Comparative Analysis of Time Series and Geophysical Phenomena, Complexity, 10, 51–56, 2005.; Schuster, H.: Deterministic Chaos. An Introduction, VCH, 1989.; Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52 479–487, 1988.; Vilar, C., Franca, G., Silva, R., and Alcaniz, J.: Nonextensivity in geological faults?, Physica A, 377, 285–290, 2007.


Click To View

Additional Books

  • Limits and Characteristics of the Multif... (by )
  • Intermittency, Non-gaussian Statistics a... (by )
  • Anomalous Diffusion in Geophysical and L... (by )
  • Hamiltonian Approach to the Derivation o... (by )
  • Non-linear Quenching of Current Fluctuat... (by )
  • Grid Preparation for Magnetic and Gravit... (by )
  • Mitigation of Coupled Model Biases Induc... (by )
  • Statistical Analysis of Stromboli Vlp Tr... (by )
  • Variational Data Assimilation with Super... (by )
  • Stability and Nonlinear Regimes of Flow ... (by )
  • Extremum Statistics: a Framework for Dat... (by )
  • Scaling of Peak Flows with Constant Flow... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.