Earthquake and avalanche statistics show a magnitude distribution (Gutenberg-Richter) and a distribution of consecutive times (Omori). In order to describe such phenomena within a statistical physics approach we generalize our Local Growth Global Reset (LGGR) model for resets to arbitrary lower states of the unobserved background variable.

This variable is the accumulated stress for quakes, and the quakes themselves are the jumps between two such values. In a given class of transition rates between states with different stress values an analytic determination of the stationary PDF is possible. We utilize these findings to real-world data from various earthquakes.

A. Gergely, T.S. Biró, F. Járai-Szabó, Z. Néda, Statistics of earthquakes based on the extended LGGR model, Physica A Statistical Mechanics and its Applications 650 (2024) 129983.