Scaling and Clustering in Southern California Earthquake Sequences: Insights from Percolation Theory

Earthquake activity poses significant risks to both human survival and economic development. However, earthquake forecasting remains a challenge due to the complex, poorly understood interactions that drive seismic events. In this study, we construct an earthquake percolation model to examine the relationships between earthquakes and the underlying patterns and processes in Southern California. Our results demonstrate that the model can capture the spatiotemporal and magnitude characteristics of seismic activity. Through clustering analysis, we identify two distinct regimes: a continuous increase driven by earthquake clustering, and a discontinuous increase resulting from the merging of clusters dominated by large, distinct mega-earthquakes. Notably, in the continuous increase regime, we observe that clusters exhibit a broader spatiotemporal distribution, suggesting long-range and long-term correlations. Additionally, by varying the magnitude threshold, we explore the scaling behavior of earthquake percolation. The robustness of our findings is confirmed through comparison with multiple shuffling tests.