Law of earthquake productivity in the Olami‒Feder‒Christensen‒Zhurkov model

The generalized cellular model based on the of Olami‒Feder‒Christensen cellular automaton model and modified by the allowance for the lifetime of the material on the basis of the kinetic concept for strength of solids by Academician S.N. Zhurkov is used to model and clarify the nature of the statistical law of earthquake productivity. The modified model is named Olami‒Feder‒Christensen‒Zhurkov model (OFCZ). The OFCZ model implements the main statistical regularities of seismicity: the Gutenberg‒Richter and Omori‒Utsu laws, the Bath’s law, fractal geometry of seismicity, and the law of earthquake productivity. It is shown that the clustering of model events (analogs of earthquakes), corresponding to the law of earthquake productivity, is due to the kinetic component of the OFCZ model. The productivity dependences on material strength and medium temperature are obtained. The influence of the Zhurkov parameter and the cell coupling parameter in the cellular model (the dissipativity of the model) on the productivity is considered. It is shown that the revealed dependences of productivity on strength and temperature are consistent with the empirical data.