Session II:
Scaling physics and emergent behaviors at the micro and macro-scale : theory, simulation and observation

2nd ACES (APEC Cooperation for Earthquake Simulation) Workshop in Japan

Correlation length evolution in cellular automata with long-range stress transfer
Dion Weatherley, Meng-Fen Xia, Peter Mora


In recent years, theoretical research in seismology has been stimulated by the infusion of ideas from statistical physics. Bak and Tang (1989) proposed that the Earth's crust is in a state of Self-Organised Criticality (SOC). This proposal was based upon the statistical similarities between earthquake statistics and those of highly simplified models called cellular automata. A SOC system is one which organises into a state in which events of all sizes may occur at any time. Assuming the Earth's crust is SOC, forecasting large earthquakes is seemingly impossible. More recently, it has been proposed in the literature that regional seismicity may be an example of a Critical Point (CP) system. CP systems progressively approach, and retreat from, a critical state in which large events occur. Cumulative energy release prior to the largest events is predicted to follow a power-law time-to-failure relationship, suggesting that intermediate-term forecasting of large earthquakes may be possible. Cellular automata with differing nearest neighbour energy transfer may display behaviour similar to CP systems or SOC systems (Weatherley, 2000). In these models, energy is only transferred to the nearest neighbours of a failed cell. Such short-range interactions lead to unphysical stress discontinuities at the boundaries of ruptures. For this reason, we have devised a new type of automaton with long-range energy transfer. We find that in a certain regime of parameter space, such long-range automata can display behaviour consistent with the critical point hypothesis of earthquakes. Prior to the largest events, long-range stress correlations progressively form due to the action of external loading and small to moderate sized events. Large events only occur when the stress field is sufficiently correlated at large wavelengths. In a significant number of cases, the largest events are preceded by a period of accelerating cumulative energy release.

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