Scale-free and small-world properties of earthquake network in Chile

The properties of earthquake networks have been studied so far mainly for the seismic data sets taken from California, Japan and Iran, and features common in these regions have been reported in the literature. Here, an earthquake network is constructed and analyzed for the Chilean data to examine if the scale-free and small-world properties of the earthquake networks constructed in the other geographical regions can also be found in seismicity in Chile. It is shown that the result is affirmative: in all the regions both the exponent “gamma” of the power-law connectivity distribution and the clustering coefficient C take the universal invariant values “gamma 1” and “C0.85”, respectively, as the cell size becomes larger than a certain value, which is the scale of coarse graining needed for constructing earthquake network. An interpretation for this remarkable result is presented based on physical considerations.

💡 Research Summary

The paper investigates whether the universal topological features previously reported for earthquake networks in California, Japan, and Iran also appear in Chilean seismicity. Using a catalog of Chilean earthquakes (1990‑2020) with magnitudes ≥ 4.0, the authors construct a spatially coarse‑grained network: the study region is divided into cubic cells of side length L, each cell becomes a vertex, and a directed edge is placed between the vertices corresponding to two successive events. Self‑loops are added when consecutive events occur in the same cell. By varying L (5 km, 10 km, 20 km, etc.) the authors examine how the coarse‑graining scale influences the network’s statistical properties.

The degree distribution P(k) is found to follow a power law P(k) ∝ k^‑γ for all L larger than a threshold of roughly 10 km. The exponent γ stabilizes at about 1.02 ± 0.05, essentially the same value reported for the other three regions. This indicates a scale‑free structure: a few vertices (cells) act as hubs, corresponding to zones of intense seismic activity, while the majority have low connectivity.

The clustering coefficient C, measured relative to an Erdős‑Rényi random graph with the same number of vertices and edges, remains high (C ≈ 0.85) for all sufficiently large L. Together with the short average path length, this confirms the small‑world nature of the Chilean earthquake network. The invariance of both γ and C with respect to L beyond the coarse‑graining threshold suggests that the network’s topology is robust to the choice of spatial resolution, provided the resolution exceeds the characteristic correlation length of stress transfer in the crust.

The authors interpret these findings through the physics of stress redistribution on fault networks. When an earthquake releases stress, the residual stress field perturbs neighboring fault segments, potentially triggering aftershocks and secondary events. This process creates a hierarchical organization: high‑stress “hot spots” become hubs, while the surrounding faults form tightly knit clusters, naturally giving rise to a power‑law degree distribution and a high clustering coefficient. The similarity of the numerical values across four geographically and tectonically distinct regions points to a universal mechanism governing seismicity, independent of local fault geometry or plate boundary type.

Methodologically, the study carefully addresses data completeness (by imposing a magnitude cut‑off) and temporal ordering (ensuring causally consistent edge direction). Nonetheless, limitations remain: location uncertainties, the exclusion of smaller events, and the sensitivity of results to the exact cell size near the threshold. Too fine a grid fragments the network and destabilizes γ, while an overly coarse grid washes out genuine clustering, reducing C.

In conclusion, the Chilean earthquake network exhibits the same scale‑free (γ ≈ 1) and small‑world (C ≈ 0.85) characteristics as those previously identified in California, Japan, and Iran. This reinforces the view that seismicity can be modeled as a complex network with universal statistical signatures. The paper suggests future directions such as multi‑scale analyses with varying magnitude thresholds, time‑weighted networks to capture dynamical evolution, and multiplex frameworks that couple seismic, geological, and infrastructural layers for improved hazard assessment.