Earthquake Productivity Law in the Olami‒Feder‒Christensen‒Zhurkov Model

Abstract—The generalized cellular model based on the of Olami‒Feder‒Christensen cellular automaton model and modified by considering the durability of the material based on the kinetic concept of the strength of solids developed 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 (OFCZ) model. The OFCZ model captures the main statistical regularities and patterns 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 earthquake productivity law, is caused by the kinetic component of the OFCZ model. The dependences of productivity on material strength and temperature of the medium are obtained. The influence of the Zhurkov parameter and the cell transmission (coupling) parameter in the cellular model (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.