Quasi-periodicity of large avalanches in the long-range connective sandpile models and its implication in natural earthquakes

In this study, we investigated the quasi-periodicity of large avalanches using a new modification of sandpile models, i.e., the long-range connective sandpile (LRCS) model. The LRCS model considers the random distant connection between two separated, instead of neighboring, cells and shows interesting precursory behavior before large avalanches. We explore the statistics of recurrence intervals between large events and find a strong dependence on the size L of the sandpile. In the LRCS model, the average recurrence interval W of large avalanches follows the relationship W ∝ L. Having the recurrence intervals of many earthquake fault systems around the world, we propose an empirical rule between those intervals and the corresponding earthquakes’ magnitudes and provide evidence of the quasi-periodic behavior of natural earthquakes. Copyright c © EPLA, 2014 Introduction. – For natural earthquake fault systems, the quasi-periodicity remains an open issue and has great societal importance. Large earthquakes are not periodic; however, they could be quasi-periodic. A typical example showing quasi-periodicity is in the Parkfield, California area. The San Andreas Fault is the primary boundary between the Pacific and the North American plates, and the displacements associated with it are distributed over many fault segments. Studies on the San Andreas Fault have led to the conception of the characteristic earthquake model. The earthquake sequence occurred in the Parkfield segment of the San Andreas Fault in 1857, 1881, 1901, 1922, 1934, and 1966. This is an excellent example of a moderate characteristic earthquake with an average recurring interval of 22 years [1]. These earthquakes repeat with similar features, including faulting mechanisms, epicenter locations, magnitudes, seismic moments, rupture areas, and southeast rupture propagations. The Parkfield earthquake sequence has given seismologists an opportunity to test the applicability of recurrence models in regions characterized by recurring (a)E-mail: [email protected] moderate-sized earthquake. Bakun and Lindh [1] thus predicted in 1985 that the next moderate Parkfield earthquake after 1966 would occur around 1988 and not later than 1993. The earthquake, however, did not occur within the predicted timescale. Surprisingly, in September 2004, an earthquake occurred in Parkfield with comparable magnitude. There was much debate about whether the event that occurred in 2004 was the expected characteristic earthquake and, if so, why it happened 11 years later. We present in this study an answer to this important issue about earthquake recurrences. Sandpile dynamics and self-organized criticality (SOC) are exhibited in many natural and social phenomena, including earthquakes, forest fires, rainfalls, landscapes, drainage networks, stock prices, and traffic jams. Since Bak et al. [2,3] introduced the original nearest-neighboring sandpile model, various numerical and analytical studies of modified sandpile models have been the subject of much research (e.g., [4–12]). Among these approaches, the annealed random-neighbor sandpile models in which an avalanche can propagate within the system were first proposed by Christensen and Olami [5] and then extensively