Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 1 2010 10.5194/npg-17-85-2010 http://www.nonlin-processes-geophys.net/17/85/2010/ http://www.nonlin-processes-geophys.net/17/85/2010/npg-17-85-2010.html http://www.nonlin-processes-geophys.net/17/85/2010/npg-17-85-2010.pdf 85 91 2010-02-24 Variable predictability in deterministic dissipative sandpile M. G. Shnirman A. B. Shapoval shapoval@mccme.ru Institut de Physique du Globe de Paris, UMR 7154, CNRS, France Finance Academy under the Government of the Russian Federation, Russia International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russia It is known that some quiescence precedes the strong events in the Bak–Tang–Wiesenfeld sand-pile (Pepke and Carlson, 1994) We introduce dissipation depending on the propagation of the events into this model such that in the constructed model the growth of activity occurs before the strong events. This fact allows the prediction of them in advance with a certain efficiency. This efficiency is variable in time. The best predictability is observed during subcritical time ranges, while the efficiency is definitely worse in the supercritical state. Bak,~P., Tang,~C., and Wiesenfeld,~K.: Self-Organized Criticality: An Explanation of $1/f$ Noise, Phys. Rev. Lett., 59, 381–384, 1987. De~Menech,~M., Stella,~A L., and Tebaldi,~C.: Rare Events and Breakdown of Simple Scaling in the Abelian Sandpile, Phys. Rev. E, 58, R2677–R2680, 1998. Dhar,~D.: The Abelian Sandpile and Related Models, Physica A, 263, 4–25, 1999. Dhar, D.: Theoretical Studies of Self-Organized Criticality, Physica A, 369, 29–70, 2006. Dickman,~R., Munoz,~M., Vespignani,~A., and Zapperi,~S.: Paths to Self-Organized Criticality, cond-mat/9910454v2", 2000. Geller,~R J., Jackson,~D D., Kagan,~Y Y., and Mulargia,~F.: Earthquakes cannot be predicted, Science, 275, 1616–1617, 1997. Huang,~Q., Sobolev,~G A., and Nagao, T.: Characteristics of the seismic quiescence and activation patterns before the $M=7.2$ Kobe earthquake, January 17, 1995, Tectonophysics, 337, 99–116, 2001. Keilis-Borok,~V I.: Fundamentals of Earthquake Prediction: Four Paradigms, in: Nonlinear Dynamics of the Lithosphere and Earthquake Prediction, edited by: Keilis-Borok,~V I. and Soloviev,~A A., Springer-Verlag, Heidelberg, pp 1–36, 2003. Keilis-Borok,~V I. and Kossobokov,~V G.: Preliminary activation of seismic flow: Algorithm M8, Phys. Earth Planet. Int., 61, 73–83, 1990. Keilis-Borok, V I. and Rotwain,~I M.: Diagnosis of time of increased probability of strong earthquakes in different regions of the world: algorithm CN, Earth Plannet. Inter., 61, 57–72, 1990. Kossobokov,~V. and Shebalin,~P.: Earthquake Prediction, in: Nonlinear Dynamics of the Lithosphere and Earthquake Prediction, edited by: Keilis-Borok,~V I. and Soloviev,~A A., Springer-Verlag, pp 141–208, 2003. Lübeck, S., Rajewsky, N., and Wolf,~D.E.: A deterministic sandpile automaton revisited, Eur. Phys. J. B., 13, 715–721, 2000. Molchan,~G M.: Earthquake Prediction Strategies: A Theoretical Analysis, in: Nonlinear Dynamics of the Lithosphere and Earthquake Prediction, edited by: Keilis-Borok,~V I. and Soloviev,~A A., Springer-Verlag, pp 209–238, 2003. Pepke,~S L. and Carlson,~J M.: Predictability of Self-Organizing Systems, Phys. Rev. E, 50, 236–242, 1994. Shapoval,~A B. and Shnirman,~M G.: Strong events in the sand-pile model, Int. J. Mod. Phys. C, 15, 279–288, 2004. Shapoval,~A B. and Shnirman,~M G.: Earthquake Precursors used for predicting the largest events in the avalanche formation model, Izvestiya, Phys. Solid Earth, 45, 406–413, 2009. Shebalin, P.: Increased correlation range of seismicity before large events manifested by earthquake chains, Tectonophysics, 424, 335–349, 2006. Sornette,~D.: Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth, Proc. Nat. Acad. Sci. USA, 99, 2522–2529, 2002. Wiesenfeld,~K., Theiler,~J., and McNamara, B.: Self-organized criticality in a deterministic automaton, Phys. Rev. Lett., 65, 949–952, 1990. Wyss, M.: Cannot Earthquakes Be Predicted? Science, 278, 487–490, 1997.