*Article* **The Analysis of the Aftershock Sequences of the Recent Mainshocks in Alaska**

**Mohammadamin Sedghizadeh \* and Robert Shcherbakov**

> Department of Earth Sciences, University of Western Ontario, London, ON N6A 5B7, Canada; rshcherb@uwo.ca **\*** Correspondence: msedghiz@uwo.ca

> **Abstract:** The forecasting of the evolution of natural hazards is an important and critical problem in natural sciences and engineering. Earthquake forecasting is one such example and is a difficult task due to the complexity of the occurrence of earthquakes. Since earthquake forecasting is typically based on the seismic history of a given region, the analysis of the past seismicity plays a critical role in modern statistical seismology. In this respect, the recent three significant mainshocks that occurred in Alaska (the 2002, Mw 7.9 Denali; the 2018, Mw 7.9 Kodiak; and the 2018, Mw 7.1 Anchorage earthquakes) presented an opportunity to analyze these sequences in detail. This included the modelling of the frequency-magnitude statistics of the corresponding aftershock sequences. In addition, the aftershock occurrence rates were modelled using the Omori–Utsu (OU) law and the Epidemic Type Aftershock Sequence (ETAS) model. For each sequence, the calculation of the probability to have the largest expected aftershock during a given forecasting time interval was performed using both the extreme value theory and the Bayesian predictive framework. For the Bayesian approach, the Markov Chain Monte Carlo (MCMC) sampling of the posterior distribution was performed to generate the chains of the model parameters. These MCMC chains were used to simulate the models forward in time to compute the predictive distributions. The calculation of the probabilities to have the largest expected aftershock to be above a certain magnitude after a mainshock using the Bayesian predictive framework fully takes into account the uncertainties of the model parameters. Moreover, in order to investigate the credibility of the obtained forecasts, several statistical tests were conducted to compare the performance of the earthquake rate models based on the OU formula and the ETAS model. The results indicate that the Bayesian approach combined with the ETAS model produced more robust results than the standard approach based on the extreme value distribution and the OU law.

> **Keywords:** epidemic type aftershock sequence model; extreme value distribution; Bayesian predictive distribution
