Seismic quiescence and b-value decrease before large events in forest-fire model

Forest fire models may be interpreted as a simple model for earthquake occurrence by translating trees and fire into stressed segments of a fault and their rupture, respectively. Here we adopt a twodimensional forest-fire model in continuous time, and focus on the temporal changes of seismicity and the b-value. We find the b-value change and seismic quiescence prior to large earthquakes by stacking many sequences towards large earthquakes. As the magnitude-frequency relation in this model is directly related to the cluster-size distribution, decrease of the b-value can be explained in terms of the change in the cluster-size distribution. Decrease of the b-value means that small clusters of stressed sites aggregate into a larger cluster. Seismic quiescence may be attributed to the decrease of stressed sites that do not belong to percolated clusters.