## 4 Discussion and Conclusions  
To describe the three aftershock sequences which occurred in the Alaska region, statistical models were used in this study. To be more precise, the frequency-magnitude statistical analysis was performed using the GR relation, and the occurrence rates of the aftershock sequence were estimated by the OU law and the ETAS model. The EVD and BPD approaches were used to calculate the probability of having the largest expected aftershock above a certain magnitude during evolution of each sequence for various training and forecasting time intervals. The frequency-magnitude distributions and estimated GR parameters for analyzed sequences are shown in Figure 3. The frequency-magnitude distribution of the Denali aftershock sequence, was characterized by a broad distribution of event magnitudes which led to a relatively low \(b\)-value (0.749 \(\pm\) 0.053) (Figure 3). The 2002, Denali mainshock was followed by several large aftershocks with the largest being 5.6 magnitude which occurred in the first 24 h after the mainshock. The frequency-magnitude statistical analysis of the aftershock sequence of the Kodiak 7.9 magnitude earthquake with the cut-off magnitude 3.2 for the target time interval \([T_{s},\,T_{e}]=[0,\,30]\) days was performed (Figure 3). The frequency-magnitude distribution of the 2018, Kodiak sequence indicates a typical GR fit with \(b\)-value (1.035 \(\pm\) 0.059). The mainshock was followed by several large aftershocks with the largest being 5.5 magnitude event. It should be noted the epicenter of the 2018, Kodiak earthquake was located in a remote area in the North Pacific. The analysis of the 2018 Anchorage sequence produced the \(b\)-value of 0.906 \(\pm\) 0.082 (Figure 3). The largest aftershock with a magnitude 5.8, was close to the expected magnitude from [PERSON]'s law [5] which states that the largest aftershock is on average 1.2 magnitudes lower than the mainshock. In order to analyze the occurrence rate of the aftershock sequence of the selected mainshocks, the Omori-Utsu law, Equation (5), and the ETAS model, Equation (6), were utilized. The obtained results from the analysis of the decay rate of the aftershock sequences show that the parameter \(p\) is comparable for both models (the OU law and the ETAS model) except for the 2018 Kodiak sequence. Computing the probability of having a largest expected aftershock with a magnitude above a given value during different forecasting time intervals after the mainshock was one of the main objectives of this work. The EVD and BPD approaches were used to accomplish this objective. The obtained result of this analysis indicates that the BPD method using the ETAS model is more conservative than BPD using the OU law and the EVD approach. In addition, for the aforementioned approaches, the probabilities of having an earthquake with magnitude 6 and above were calculated for both cases (Figures 9 and A8). Moreover, in order to compare characteristics of analyzed sequences the probabilities to have the largest expected aftershocks to be larger than \(m_{\rm ex}\geq\) 5.0, 6.0, 7.0 were estimated by using the BPD, Equation (12), for both cases (Figures 8 and A7). The results of this analysis show that the Anchorage sequence had a lower potential to generate aftershocks with \(m_{\rm ex}\geq\) 5.0, 6.0, 7.0 compared to other analyzed sequences. These statistical results can be explained directly by the number of events in the aftershock sequence and the magnitude of the mainshock. This increases the probability of occurrence of an aftershock with a certain magnitude in a predefined time interval after the mainshock. In the present implementation of the EVD and BPD analysis we used the unbounded GR distribution. It was suggested that more realistic truncated magnitude distribution can be more appropriate for forecasting [52; 53]. This can be easily incorporated in the analysis as well.