Critical zone of the branching crack model for earthquakes: Inherent randomness, earthquake predictability, and precursor modelling

The branching crack model for earthquakes was developed by Vere-Jones and Kagan in the 1970s and the 1980s, respectively. With some simple and rational assumptions, its simulation results explain the Gutenberg-Richter magnitude-frequency relationship and the Omori-Utsu aftershock decay formula. By introducing the concept of the critical zone, this model can be connected with the asperity model, the barrier model, and the nucleation model through a parameter – criticality. Particularly, the size of the critical zone determines the maximum magnitude of potential earthquakes and the source of their anomalies. The key to earthquake forecasting is to determine whether the concerned area is in a critical state and how large the critical zone is. We discuss what kinds of anomalies are meaningful as candidates of earthquake precursors. Finally, we outline modelling strategies for earthquake precursors with low probability gains that are due to the inherent randomness of earthquake source processes.