## 3 Results
### Frequency-Magnitude Statistics Analysis  
The aftershocks of the three mainshocks within elliptical regions as shown in Figure 1 were used to obtain the frequency-magnitude statistics. The fitting of Equation (2) was done to all three sequences and during specific target time intervals. To estimate the parameter \(\beta\) from Equation (2) the MLE approach was used [41]. The model parameter uncertainties were estimated using the method of Tinti and Mulargia [42]. In addition, the method of goodness of fit test [50] was utilized to estimate the magnitude of completeness \(m_{c}\) for thethree sequences. Specifically, \(m_{0}\) was selected as the magnitude above which at least 95% of the observed data are modeled by Equation (2). The results are presented in Figure 3. Moreover, to investigate how the earthquake magnitudes evolve over time, they are plotted versus the sequential number in Figure 11. This can be used to inspect the early magnitude incompleteness of aftershock sequences and can be used to justify the use of a chosen magnitude threshold [51].  
In order to analyze the frequency-magnitude statistics of the 2002, Denali earthquake sequence, \(m_{0}=3.0\) was considered as a cut-off magnitude, and the analysis was performed during \([T_{s},\ T_{e}]=[0,\ 30]\) days after the mainshock occurrence on 3 November 2002 (22:12:41 UTC) for the earthquakes within the elliptical region given in Figure 1a. The total number of aftershocks during the selected time interval was 771 with the maximum magnitude 5.6, respectively. The fit of the GR relation is demonstrated in Figure 3. The estimated \(b\)-value and \(a\)-value for the analyzed earthquake sequence are \(0.749\pm 0.053\) and \(5.134\pm 0.176\), respectively. The magnitude-frequency statistics analysis of the 2018, Kodiak earthquake sequence was performed during \([T_{s},\ T_{e}]=[0,\ 30]\) days after the mainshock that occurred on 23 January 2018 (09:31:4 UTC) for earthquakes with the cut-off magnitude \(m_{0}=3.2\) within an elliptical region shown in Figure 1b. In total 1207 earthquakes with the magnitude ranging from 3.2 to 5.5 occurred in the analyzed elliptical region during the specified time interval. The estimated \(b\)-value and \(a\)-value for selected earthquake sequence are \(1.035\pm 0.059\) and \(6.394\pm 0.214\), respectively (Figure 3). For analyzing the frequency-magnitude statistics of the 2018, Anchorage earthquake sequence, \(m_{0}=2.8\) was considered as a cut-off magnitude, and the analysis was carried out during \([T_{s},\ T_{e}]=[0,\ 30]\) days after the mainshock occurrence on 30 November 2018 (17:29:29 UTC) for the earthquakes within an elliptical region of Figure 1c. In total 476 earthquakes within the magnitude range of 2.8-5.2 occurred in the analyzed spatiotemporal window. The obtained \(b\)-value and \(a\)-value for Anchorage earthquake sequence are \(0.906\pm 0.082\) and \(5.216\pm 0.246\) respectively. The fit of the GR relation is plotted in Figure 3.  
Figure 3: The frequency-magnitude statistics of aftershock sequences for 30 days from the mainshock occurrence. The lines are the Gutenberg–Richter scaling fit, Equation (1). The open symbols represent the cumulative numbers corresponding to each aftershock sequence. The estimated \(a\) and \(b\)-value with 95% confidence intervals are given in the legend. The cumulative numbers of aftershocks for the 2002, Denali aftershocks for \(m\geq 3.0\) are plotted as red circles, the 2018, Kodiak aftershocks for \(m\geq 3.2\) cumulative numbers are plotted as purple diamonds, and blue squares are used to depict the 2018, Anchorage aftershocks for \(m\geq 2.8\).