## 1. Introduction

[2] In the estimation of seismicity tendency, the Gutenberg-Richter *b*-value and the Hurst exponent are two parameters which are widely used. Many literatures considered the *b*-value as a monitoring index related to the forthcoming large earthquakes [*Smith*, 1986; *Urbancic et al.*, 1992; *Wiemer and Wyss*, 1994; *Henderson et al.*, 1994; *Legrand et al.*, 1996; *Henderson et al.*, 1999; *Wyss et al.*, 2004; *Wu and Chiao*, 2006]. Reductions in the *b*-values before large earthquakes 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 [*Chen*, 2003; *Chen et al.*, 2005; *Wu and Chiao*, 2006]. Another parameter, the Hurst exponent, is based on the rescaled range (R/S) analysis, which was proposed by a hydrologist H. E. Hurst [*Hurst*, 1951]. The R/S analysis can figure out the statistical properties of time series and has also been used to analyze time series of earthquakes as the attempt on predicting future earthquake trends. Many groups of researchers have applied the R/S analysis to investigate the long-term correlation of seismicity [*Cisternas et al.*, 2004; *Goltz*, 1997; *Lomnitz*, 1994; *Telesca et al.*, 2001; *Chen et al.*, 2008c]. Each research group constructed their own time series for the R/S analysis from the earthquake catalogues. For example, *Cisternas et al.* [2004] had constructed the cumulative seismic moment as a function of time for conducting the R/S analysis of the seismicity in the Marmara Sea Region, Turkey. They showed the time variation of seismicity is persistent with the Hurst exponent *H* of 0.82. Also, *Telesca et al.* [2001] had analyzed the temporal fluctuations in *H* for the waiting time of earthquakes occurred in southern Italy and found the values of *H* range from 0.5 to 0.92. They also found a good correlation, with a correlation coefficient about −0.64, between the spectral power-law exponent of geo-electrical signals and the Hurst exponent of seismicity in Italy.

[3] In the present work, we calculate the Hurst exponent *H* and the power-law exponent *B* of the frequency-size distributions of avalanches in a modified sandpile model, the long-range connective sandpile (LRCS) model [*Chen et al.*, 2008a, 2008b; *Lee et al.*, 2008]. The upper-case *B* is exclusively used for the scaling exponent of the power-law frequency-size distribution of avalanches for differencing from the low-case *b* in the Gutenberg-Richter relation [*Gutenberg and Richter*, 1949]. The LRCS model differs from the original sandpile (BTW) model in the aspect of releasing grains to nearest neighboring cells. The LRCS model can release storing energy to remote cells, which is reminiscent of seismic wave propagations [*Chen et al.*, 2008a, 2008b; *Lee et al.*, 2008]. We show the increase in *H* values accompanied with the decrease in *B* values prior to large avalanches, which mimics the observed precursory phenomena of the Gutenberg-Richter *b*-values in real seismicity. Most importantly, we present the negative correlation between *B* and *H* in the LRCS model.