Earthquakes, model systems and connections to q-statistics

Czasopismo : Acta Geophysica
Tytuł artykułu : Earthquakes, model systems and connections to q-statistics

Autorzy :
Vallianatos, F.
Technological Educational Institute of Crete, Laboratory of Geophysics and Seismology, Crete, Greece,,
Tsallis, C.
Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil,,
Sotolongo-Costa, O.
Catedra de Sistemas Complejos “Henri Poincare”, Universidad de La Habana,,
Celikoglu, A.
Department of Physics, Faculty of Science, Ege University, Izmir, Turkey,,
Abstrakty : In this work, we make an attempt to review some of the recent studies on earthquakes using either real catalogs or synthetic data coming from some model systems. A common feature of all these works is the use of q -statistics as a tool.

Słowa kluczowe : earthquake model, q-statistics, statistical mechanics,
Wydawnictwo : Instytut Geofizyki PAN
Rocznik : 2012
Numer : Vol. 60, no. 3
Strony : 535 – 546
Bibliografia : Abe, S. (2003), Geometry of escort distribution, Phys. Rev. E 68, 031101, DOI: 10.1103/PhysRevE.68.031101.
Abe, S., and N. Suzuki (2004), Aging and scaling of earthquake aftershocks, Physica A 332, 533-538, DOI: 10.1016/j.physa.2003.10.002.
Bath, M. (1965), Lateral inhomogeneities of upper mantle, Tectonophysics 2, 6, 483-514, DOI: 10.1016/0040-1951(65)90003-X.
Celikoglu, A., U. Tirnakli, and S.M.D. Queiros (2010), Analysis of return distributions in the coherent noise model, Phys. Rev. E 82, 021124, DOI: 10.1103/Phys-RevE.82.021124.
Christensen, K., and Z. Olami (1992), Scaling, phase transition, and nonuniversality in a self-organized critical cellular-automaton model, Phys. Rev. A 46, 4, 1829-1838, DOI: 10.1103/PhysRevA.46.1829.
Darooneh, A. H., and A. Mehri (2010), A nonextensive modification of the Gutenberg–Richter law: q-stretched exponential form, Physica A 389, 509-514, DOI: 10.1016/j.physa.2009.10.006.
Gutenberg, B., and C.F. Richter (1944), Frequency of earthquakes in California, Bull. Seismol. Soc. Am. 34, 185-188.
Kagan, Y.Y., and D.D. Jackson (1991), Seismic gap hypothesis: ten years after, J. Geophys. Res. 96, B13, 21419-21431, DOI: 10.1029/91JB02210.
Newman, M.E.J. (1996), Self-organized criticality, evolution and the fossil extinction record, Proc. R. Soc. London, Ser. B 263, 1605-1610, DOI: 10.1098/rspb.1996.0235.
Newman, M.E.J., and K. Sneppen (1996), Avalanches, scaling, and coherent noise, Phys. Rev. E 54, 6, 6226-6231, DOI: 10.1103/PhysRevE.54.6226.
Olami, Z., H.J.S. Feder, and K. Christensen (1992), Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes, Phys. Rev. Lett. 68, 1244-1248, DOI: 10.1103/PhysRevLett.68.1244.
Omori, F. (1894), On the aftershocks of earthquakes, J. Coll. Sci. Imp. Tokyo 7, 111-200.
Silva, R., G.S. Franca, and J.S. Vilar (2006), Nonextensive models for earthquakes, Phys. Rev. E 73, 026102, DOI: 10.1103/PhysRevE.73.026102.
Sneppen, K., and M.E.J. Newman (1997), Coherent noise, scale invariance and intermittency in large systems, Physica D 110, 209-222, DOI: 10.1016/S0167-2789(97)00128-0.
Sornette, D. (1999), Earthquakes: from chemical alteration to mechanical rupture, Phys. Rep. 313, 237-291, DOI: 10.1016/S0370-1573(98)00088-X.
Sotolongo-Costa, O., and A. Posadas (2004), Fragment-asperity interaction model for earthquakes, Phys. Rev. Lett. 92, 048501, DOI: 10.1103/Phys-RevLett.92.048501.
Tirnakli, U. (2004), Aging in earthquakes model. In: C. Beck, G. Benedeck, A. Rapisarda, and C. Tsallis (eds.), Complexity, Metastability and Nonextensivity. Proc. 31st Workshop of Int. School of Solid State Physics Erice, Sicily, Italy, 20-26 July 2004, World Scientific, Singapore, 350-354.
Tirnakli, U., and S. Abe (2004), Aging in coherent noise models and natural time, Phys. Rev. E 70, 056120, DOI: 10.1103/PhysRevE.70.056120.
Tsallis, C. (1988), Possible generalization of Boltzmann–Gibbs statistics, J. Stat. Phys. 52, 479-487, DOI: 10.1007/BF01016429.
Tsallis, C. (2009), Introduction to Nonextensive Statistical Mechanics–Approaching a Complex World, Springer, New York, DOI: 10.1007/987-0-387-85359-8.
Tsallis, C., and U. Tirnakli (2010), Nonadditive entropy and nonextensive statistical mechanics—Some central concepts and recent applications, J. Phys. Conf. Ser. 201, 012001, DOI: 10.1088/1742-6596/201/1/012001.
Tsallis, C., G. Bemski, and R.S. Mendes (1999), Is re-association in folded proteins a case of nonextensivity?, Phys. Lett. A 257, 93-98, DOI: 10.1016/S0375-9601(99)00270-4.
Turcotte, D.L. (1997), Fractals and Chaos in Geology and Geophysics, Cambridge University Press, Cambridge.
Vallianatos, F. (2009), A non-extensive approach to risk assessment, Nat. Hazards. Earth Syst. Sci. 9, 211-216, DOI: 10.5194/nhess-9-211-2009.
Vallianatos, F., and P. Sammonds (2010), Is plate tectonics a case of non-extensive thermodynamics? Physica A 389, 4989-4993, DOI: 10.1016/j.physa.2010.06.056.
Vallianatos, F., and P. Sammonds (2011), A non-extensive statistics of the faultpopulation at the Valles Marineris extensional province, Mars, Tectonophysics 509, 50-54, DOI: 10.1016/j.tecto.2011.06.001.
Zhang, G.Q., U. Tirnakli, L. Wang, and T.L. Chen (2011), Self organized criticality in a modified Olami-Feder-Christensen model, Eur. Phys. J. B 82, 83-89, DOI: 10.1140/epjb/e2011-10941-4.
Cytuj : Vallianatos, F. ,Tsallis, C. ,Sotolongo-Costa, O. ,Celikoglu, A. , Earthquakes, model systems and connections to q-statistics. Acta Geophysica Vol. 60, no. 3/2012