Bayesian confidence intervals for the magnitude of the largest aftershock

Aftershock sequences, which follow large earthquakes, last hundreds of days and are characterized by well-defined frequency-magnitude and spatio-temporal distributions. The largest aftershocks in a sequence constitute significant hazard and can inflict additional damage to infrastructure that is already affected by the main shock. Therefore, the estimation of the magnitude of a possible largest aftershock in a sequence is of high importance. In this work, a Bayesian predictive distribution and the corresponding confidence intervals for the magnitude of the largest expected aftershock in a sequence are derived using the framework of Bayesian analysis and extreme value statistics. The analysis is applied to 19 well-known aftershock sequences worldwide to construct retrospectively the confidence intervals for the magnitude of the subsequent largest aftershock by using the statistics of early aftershocks in the sequences.