Earthquake Triggering Power Extends Below Instrumental Detection Limits

Each earthquake redistributes stress within the crust, triggering cascades of aftershocks that theoretically extend to infinitesimally small magnitudes. This unconstrained proliferation poses the ultraviolet (UV)-divergence problem—where infinite small-energy events render models mathematically unstable and physically inconsistent—if a trunction is not introduced in the form of a lower triggering magnitude threshold (m0). Current empirical studies have yet to conclusively determine whether m0 exists or define its value. To address this gap, we introduce a novel ETAS model which replaces the conventional sharp magnitude cutoff for triggering magnitudes with a smooth transition function. It reflects the expected gradual decline in the aftershock-triggering capacity of smaller-magnitude earthquakes, offering a more realistic physical framework than abrupt thresholds. We found that comprehensive calibrations across long-term regional datasets (e.g., Italy, California, China) and AI-enhanced high-resolution catalogs reveal no evidence of m0 above the smallest detected magnitudes. If m0 exists, it likely lies below the completeness magnitude (mc) of instrumental catalogs, approaching mconly in machine-learning-optimized datasets. Moreover, the absence of an observable m0 suggests that most earthquakes be triggered from undetectably small earthquakes. Critically, even minor seismic events (m0