Constraining the magnitude of the largest event in a foreshock–main shock–aftershock sequence

Extreme value statistics and Bayesian methods are used to constrain the magnitudes of the largest expected earthquakes in a sequence governed by the parametric time-dependent occurrence rate and frequency–magnitude statistics. The Bayesian predictive distribution for the magnitude of the largest event in a sequence is derived. Two types of sequences are considered, that is, the classical aftershock sequences generated by large main shocks and the aftershocks generated by large foreshocks preceding a main shock. For the former sequences, the early aftershocks during a training time interval are used to constrain the magnitude of the future extreme event during the forecasting time interval. For the latter sequences, the earthquakes preceding the main shock are used to constrain the magnitudes of the subsequent extreme events including the main shock. The analysis is applied retrospectively to past prominent earthquake sequences.