Nonextensive models for earthquakes.

We have revisited the fragment-asperity interaction model recently introduced by Sotolongo-Costa and Posadas [Phy. Rev. Lett. 92, 048501 (2004)] by considering a different definition for mean values in the context of Tsallis nonextensive statistics and introducing a scale between the earthquake energy and the size of fragment epsilon proportional to r3. The energy-distribution function (EDF) deduced in our approach is considerably different from the one obtained in the above reference. We have also tested the viability of this EDF with data from two different catalogs (in three different areas), namely, the NEIC and the Bulletin Seismic of the Revista Brasileira de Geofísica. Although both approaches provide very similar values for the nonextensive parameter , other physical quantities, e.g., energy density, differ considerably by several orders of magnitude.

[1]  J. Alcaniz,et al.  Constraining nonextensive statistics with plasma oscillation data , 2005, cond-mat/0603175.

[2]  J. Lima,et al.  Relativity, nonextensivity, and extended power law distributions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  S. Abe,et al.  Necessity of q-expectation value in nonextensive statistical mechanics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Funabashi,et al.  Scale-free statistics of time interval between successive earthquakes , 2004, cond-mat/0410123.

[5]  A. M. Scarfone,et al.  Two-parameter deformations of logarithm, exponential, and entropy: a consistent framework for generalized statistical mechanics. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Lukas Hollenstein,et al.  Dark matter distribution function from non-extensive statistical mechanics , 2004, astro-ph/0407111.

[7]  G. Zangari,et al.  Modelling temperature distributions and radon emission at Stromboli Volcano using a non-extensive statistical approach , 2004 .

[8]  C. Tsallis,et al.  Nonextensive Entropy: Interdisciplinary Applications , 2004 .

[9]  J. Alcaniz,et al.  Non-extensive statistics and the stellar polytrope index , 2004, astro-ph/0402245.

[10]  Oscar Sotolongo-Costa,et al.  Fragment-asperity interaction model for earthquakes. , 2004, Physical review letters.

[11]  B. Dybiec,et al.  Resonant activation in the presence of nonequilibrated baths. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  D. Sornette,et al.  Statistical Detection and Characterization of a Deviation from the Gutenberg-Richter Distribution above Magnitude 8 , 2002, cond-mat/0201552.

[13]  R. Silva,et al.  Negative heat capacity and non-extensive kinetic theory , 2003, astro-ph/0306009.

[14]  Masatoshi Shiino,et al.  Stability analysis of mean-field-type nonlinear Fokker-Planck equations associated with a generalized entropy and its application to the self-gravitating system. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  S. Abe.  Geometry of escort distributions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Evaldo M F Curado,et al.  Derivation of nonlinear Fokker-Planck equations by means of approximations to the master equation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Alexander N Gorban,et al.  Duality in nonextensive statistical mechanics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Giorgio Kaniadakis.  Non-linear kinetics underlying generalized statistics , 2001, cond-mat/0103467.

[19]  A. Plastino,et al.  Nonextensive thermostatistics and the H theorem. , 2001, Physical review letters.

[20]  D. Sornette,et al.  Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution , 2000, cond-mat/0011168.

[21]  J. Lima,et al.  Plasma oscillations and nonextensive statistics , 2000 .

[22]  G. J. Rodgers,et al.  Tsallis Entropy and the Transition to Scaling in Fragmentation , 2000, Entropy.

[23]  P. Guimarães.  Proceedings of the 9th Brazilian Workshop on Semiconductor Physics , 1999 .

[24]  A. Plastino.  Tsallis entropy and the Vlasov-Poisson equations , 1999 .

[25]  C. Tsallis.  Nonextensive statistics: theoretical, experimental and computational evidences and connections , 1999, cond-mat/9903356.

[26]  C. Tsallis,et al.  The role of constraints within generalized nonextensive statistics , 1998 .

[27]  A. Plastino,et al.  A Maxwellian path to the q-nonextensive velocity distribution function , 1998, cond-mat/0201503.

[28]  B. Boghosian.  Navier-Stokes equations for generalized thermostatistics , 1998, cond-mat/9812154.

[29]  Didier Sornette,et al.  Discrete scale invariance, complex fractal dimensions, and log‐periodic fluctuations in seismicity , 1996 .

[30]  Loreto,et al.  Self-affine asperity model for earthquakes. , 1995, Physical review letters.

[31]  Christensen,et al.  Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. , 1992, Physical review letters.

[32]  Hans Jürgen Herrmann,et al.  Space-Filling Bearings , 1990 .

[33]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[34]  N. Rivier,et al.  Fragment-size distribution in disintegration by maximum-entropy formalism , 1987 .

[35]  L. Knopoff,et al.  Model and theoretical seismicity , 1967 .

[36]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.