Distribution related to all samples and extreme events in any seismic cluster generated by the Epidemic Type Aftershock Sequence (ETAS) model

Earthquake forecasting at different time scales is one of the most challenging goal for seismologists and geophysicists. The delivery of reliable forecasts is crucial to reduce seismic risk and establish rational operational strategies, but the task is demanding due to the complex nature of the earthquake phenomenon. Seismic events are characterized by self-organized criticality, and can be labeled as extreme, rare events, making the probability theory a fundamental tool to resort to.

Retrospective studies in statistical seismology mainly focus on the evolution of aftershocks following a large event, the results being then used for analyses of prospective type. However, much attention is also paid to the largest event in the earthquake sequence, because the forecasting of extreme events might be crucial to prevent significant damage or casualties.

In this study, we derive the probability of extreme events in any seismic cluster generated by the Epidemic Type Aftershock Sequence (ETAS) model, a benchmark in statistical seismology for any probabilistic earthquake forecasting application. Specifically, we compute the probability for the largest event within any ETAS cluster to occur at a specific space, time, and magnitude point, considering both the temporal and the spatial components of the process. The results obtained shed light on understanding the distinguishing features between mainshocks and foreshocks, and may actively contribute to operational forecasting in assigning, in real-time, the probability for any new event to be the largest of an ongoing seismic sequence.