Short communication Long-range connective sandpile models and its implication to seismicity evolution Chien-chih Chen a, ⁎, Ling-Yun Chiao b , Ya-Ting Lee a , Hui-wen Cheng a , Yih-Min Wu c a Department of Earth Sciences and Graduate Institute of Geophysics, National Central University, Jhongli, Taiwan 320, ROC b Institute of Oceanography, National Taiwan University, Taipei, Taiwan 106, ROC c Department of Geosciences, National Taiwan University, Taipei, Taiwan 106, ROC ABSTRACT ARTICLE INFO Article history: Received 2 October 2007 Received in revised form 31 March 2008 Accepted 2 April 2008 Available online 10 April 2008 Keywords: Self-organized criticality Sandpile model Long-range connection Seismicity b values We propose a new variant of the sandpile model, the long-range connective sandpile model, by means of introducing randomly internal connections between two separated distant cells. The long-range connective sandpile model demonstrates various self-organized critical states with different scaling exponents in the power-law frequency-size distributions. We found that a sandpile with higher degree of randomly internal long-range connections is characterized by a higher value of the scaling exponent for the distribution, whereas the nearest neighbor sandpile is possessed of a lower scaling exponent. Our numerical experiments on the long-range connective sandpile models imply that higher degree of random long-range connections makes the earthquake fault system more relaxant that releases accumulated energy more easily and produces fewer catastrophic events, whereas lower degree of long-range connections possibly caused by fracture healing very likely motivates accelerating seismicity of moderate events. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Many geophysical phenomena are scale invariant and exhibit the power-law distribution (Turcotte, 1997; Dodds and Rothman, 2000), which is the only statistical distribution not including a characteristic scale. A striking example is the Gutenberg–Richter relation for the frequency–magnitude statistics of earthquakes. The scaling exponent and its associated variation is then a matter of fundamental importance in such power-law distribution. Specifically, in the study of seismicity evolution, the scaling exponent in the Gutenberg–Richter relation, which is well known as the b-value, has been very often discussed in the literature and considered as a monitoring index related to the forthcoming large earthquakes (Smith, 1986; Urbancic et al., 1992; Wiemer and Wyss, 1994; Henderson et al., 1994; Guo and Ogata, 1995; Legrand et al., 1996; Wyss, 1997; Lapenna et al., 1998; Henderson et al., 1999; Barton et al., 1999; Oncel and Wilson, 2004; Wyss et al., 2004; Mandal et al., 2005; Wu and Chiao, 2006). The reductions in the b-value before a large earthquake have been reported in many researches. The reduced b-value is probably caused by the quiescence of smaller earthquakes and/or the activation of moderate earthquakes (e.g. Chen, 2003; Chen et al., 2005; Wu and Chiao, 2006). For example, observed before the 1999 M w 7.6 Chi-Chi, Tectonophysics 454 (2008) 104–107 ⁎ Corresponding author. Institute of Geophysics, National Central University, Jhongli, Taiwan 320, ROC. Tel.: +886 3 422 715165653; fax: +886 3 422 2044. E-mail address: chencc@ncu.edu.tw (C. Chen). Taiwan earthquake were the quiescence of earthquakes with magnitudes smaller than 4 (Fig. 4 in Wu and Chiao, 2006) and activation of events with magnitudes larger than 5 (Fig. 3 in Chen, 2003). Numerical experiments in tending to comprehend seismicity had mainly been based on simple conceptual models such as the spring– slider model of Burridge and Knopoff (1967), the sandpile model of Bak et al. (1987), the block structure model of Gabrielov et al. (1990), and the lattice-solid model of Mora and Place (1994). Among them two types of simple cellular automata models are the spring–slider model (Burridge and Knopoff, 1967) and the sandpile model (Bak et al., 1987). In the sandpile model a hallmarked state, which is very well known as the self-organized criticality (SOC) state and characterized by the frequency-size power-law distribution, is established solely because of the dynamical interactions among individual elements of the system. Since the concept of self-organized criticality was introduced in Bak et al. (1987), earthquakes have been identified as an example of this phenomenon in nature (Bak and Tang, 1989; Sornette and Sornette, 1989; Ito and Matsuzaki, 1990) and the observation of the Gutenberg–Richter law has been suggested to be the manifestation of the self-organized critical state of the dynamics of the earthquake faults. For earthquake studies, the sandpile model sheds new insights into the earthquake physics in addition to those derived from earlier, much complicated spring–slider models (Burridge and Knopoff, 1967; Rundle and Jackson, 1977; Carlson et al., 1994). Here we propose to 0040-1951/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2008.04.004 Contents lists available at ScienceDirect Tectonophysics journal homepage: www.elsevier.com/locate/tecto