Unobserved microseismicity may sustain earthquake cascades below detection thresholds

The frequency of earthquakes in each region and time typically follows the Gutenberg-Richter law, which describes a logarithmic decrease in occurrence with increasing magnitude. This implies a much higher number of small earthquakes. Since each event redistributes stress and can trigger further seismicity, the absence of a physical lower cut-off in magnitude leads to an unrealistically large number of small events in models, a phenomenon known as the ultraviolet (UV) divergence problem. Despite its theoretical and potentially large practical importance, the existence of a minimum triggering magnitude (m₀) remains unresolved. To address this, we develop a novel version of the Epidemic-Type Aftershock Sequence (ETAS) model, the Fertility-Tapered ETAS, incorporating a magnitude-dependent triggering taper to the standard exponential fertility law, which takes the form of a S-shaped threshold function: f_{m_0}\ \left(m\ -\ m_0\right)=\ \frac{e^{\delta\left(m-m_0\right)}}{1+e^{\delta\left(m-m_0\right)}}. Here, δ controls the transition width between the non-triggering to triggering regimes, describing the gradual strengthening of event triggering for larger earthquakes. Applying this model to regional datasets and AI-enhanced catalogs (Italy, California, China, New Zealand and Turkiye), we find that m₀ is smaller than the smallest recorded earthquakes in the catalogues, even lower than machine-learning-detected thresholds. Our findings imply that even microseismicity contributes to observed aftershock sequences, potentially cascading into larger events. This challenges the assumption of a sharp triggering cutoff usually implemented in standard ETAS models and indicates that a portion of seismicity needed for the reliable estimation of important parameters, such as the branching ratio, remains unobserved. The model provides a solution to resolve the UV-divergence in ETAS-based forecasting models.