Precursory phenomena associated with large avalanches in the long-range connective sandpile (LRCS) model

Transition on the relationship between fractal dimension and Hurst exponent in the long-range connective sandpile models

“…Large avalanches are then followed by a period of quiescence and a new approach back toward the critical state ( Fig. 2) [11][12][13]. Such process is similar to the dynamical process of the earthquake fault system which repeats by reloading energy and rebuilding correlation lengths towards criticality and the next great event [18][19][20]33,34].…”

“…We have previously proposed a long-range connective sandpile (LRCS) model by introducing randomly remote connections between two separated cells [10][11][12][13]. For a square lattice of L by L cells, we randomly throw sands, one at a time, onto the grid.…”

“…1. We have furthermore assumed that P c depends strongly on topographic change induced by the last event [11][12][13]. Consider that topographic height of the sandpile x at the iteration step t is Z t (x).…”

Local scaling property of seismicity: an example of getting valuable information from complex hierarchical system

“…Now, let us see the result of fractal dimension. Some researches show the decrease of the fractal dimensions before a great rupture (Carpinteri et al, 2009;Goltz, 1997;Kiyashchenko et al, 2004;Lee et al, 2008;Matcharashvili et al, 2000;Radulian and Trifu, 1991). Because the correlation dimension D 2 is the most typical in the fractal dimensions, we only research D 2 in this paper.…”

“…Li (lqdzjybzx@126.com) has also been shown in multifractal research on seismic activity that the spectrum of generalised dimensions and the singularity spectrum display characteristic changes before large earthquakes (Caruso et al, 2006;Dimitriu et al, 2000;Nakaya, 2005;Roy and Padhi, 2007). Some results have confirmed that the decrease in fractal dimension, the steepening of curves in the generalised dimension spectrum and the broadening of the value range in the singularity spectrum, can be taken as indicators of an unstable state of an earthquake system before a large rupture (Carpinteri et al, 2009;Goltz, 1997;Kiyashchenko et al, 2004;Lee et al, 2008;Matcharashvili et al, 2000;Radulian and Trifu, 1991;Telesca et al, 2005;Telesca and Lapenna, 2006). However, there are some shortcomings in the research: the mono-fractal dimension is not sufficient to characterise heterogeneous fractals (Grassberger and Procaccia, 1984;Kentz and Schreiber, 1997), while the generalised dimension spectrum and singularity spectrum can only represent a global description of the scaling properties (Chhabra and Jensen, 1989;Grassberger, 1983).…”