Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity

TL;DR

This study analyzes a seismicity model with relaxation, showing that the largest events scale with system size, activity is non-stationary, and relaxation influences the size distribution exponent, but the model's robustness remains uncertain.

Contribution

The paper demonstrates that the largest seismic events scale with system size and explores how relaxation affects the avalanche size distribution exponent in a seismicity model.

Findings

Largest events scale with system size without parameter tuning

Seismic activity is inherently non-stationary, supporting the concept of seismic cycles

Relaxation increases the avalanche size distribution exponent b

Abstract

We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with system size, and show that when parameters are appropriately interpreted, the typical size of the largest events scale as the system size, without the necessity to tune any parameter. Secondly, we show that the temporal activity in the model is inherently non-stationary, and obtain from here justification and support for the concept of a "seismic cycle" in the temporal evolution of seismic activity. Finally, we ask for the reasons that make the model display a realistic value of the decaying exponent $b$ in the Gutenberg-Richter law for the avalanche size distribution. We explain why relaxation induces a systematic increase of $b$ from its value $b\simeq 0.4$ observed in the absence of relaxation. However, we have not been able to justify the actual robustness of the model in displaying a consistent $b$ value around the experimentally observed value $b\simeq 1$.