Illuminating the Hierarchical Segmentation of Faults Through an Unsupervised Learning Approach Applied to Clouds of Earthquake Hypocenters

We propose a workflow for the recognition of the hierarchical segmentation of faults through earthquake hypocenter clustering without prior information. Our approach combines density-based clustering algorithms (DBSCAN and OPTICS), and principal component analysis (PCA). Given a spatial distribution of earthquake hypocenters, DBSCAN identifies first-order clusters, representing regions with the highest density of connected seismic events. Within each first-order cluster, OPTICS further identifies nested higher-order clusters, providing information on their number and size. PCA analysis is applied to first- and higher-order clusters to evaluate eigenvalues, allowing discrimination between seismicity associated with planar features and distributed seismicity that remains uncategorized. The identified planes are then geometrically characterized in terms of their location and orientation in the space, length, and height. This automated procedure operates within two spatial scales: the largest scale corresponds to the longest pattern of approximately equally dense earthquake clouds, while the smallest scale relates to earthquake location errors. By applying PCA analysis, a planar feature outputted from a first-order cluster can be interpreted as a fault surface while planes outputted after OPTICS can be interpreted as fault segments comprised within the fault surface. The evenness between the orientation of illuminated fault surfaces and fault segments, and that of the nodal planes of earthquake focal mechanisms calculated along the same faults, corroborates this interpretation. Our workflow has been successfully applied to earthquake hypocenter distributions from various seismically active areas (Italy, Taiwan, and California) associated with faults exhibiting diverse kinematics.