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Properties of a Finite Stochastic Cellular Automaton Toy Model of Earthquakes

Białecki M.

Acta Geophysica

2015

Vol. 63, no. 4

923--956

Finite version of Random Domino Automaton - a recently proposed toy model of earthquakes - is investigated in detail. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown that for a system of large size, these equations are coincident with RDA equations. We demonstrate a non-existence of exact equations for size N ≥ 5 and propose appropriate approximations, the quality of which is studied in examples obtained within the framework of Markov chains. We derive several exact formulas describing properties of the automaton, including time aspects. In particular, a way to achieve a quasi-periodic like behaviour of RDA is presented. Thus, based on the same microscopic rule - which produces exponential and inverse-power like distributions - we extend applicability of the model to quasi-periodic phenomena.

On Mechanistic Explanation of the Shape of the Universal Curve of Earthquake Recurrence Time Distributions

Białecki M.

Acta Geophysica

2015

Vol. 63, no. 5

1205--1215

This paper outlines an idea for an explanation of a mechanism underlying the shape of the universal curve of the Earthquake Recurrence Time Distributions. The proposed simple stochastic cellular automaton model is reproducing the gamma distribution fit with the proper value of parameter γ characterizing the Earth’s seismicity and also imitates a deviation from the fit at short interevent times, as observed in real data. Thus the model suggests an explanation of the universal pattern of rescaled Earthquake Recurrence Time Distributions in terms of combinatorial rules for accumulation and abrupt release of seismic energy.