## 3 Results
### Aftershock Decay Rate Modelling  
To begin with, we obtained the first-order approximation to the background seismicity rate within the presented elliptical regions in Figure 1 for each analyzed aftershock sequence. In this evaluation the background rate was estimated as the ratio of the number of earthquakes to the number of days, during the time interval that started on 1 January 2000, and ended 30 days before each mainshock. The estimated background rates, the corresponding time intervals, and cut-off magnitude for each analyzed mainshock are reported in Table 3.  
Subsequently, the aftershock decay rate was modeled by using the OU law, Equation (5), for the three sequences during the target time interval of \([T_{s},\,T_{e}]=[0.001,\,30]\) days. The obtained parameters of the OU model with 95% confidence interval and the model fits are shown for the Anchorage sequence in Figure 4 and for the Denali and Kodiak sequences in Figure 2.  
The estimated set of parameters of the OU law, Equation (5), with 95% confidence intervals for the 2002, Denali earthquake sequence are \(\omega=\{K=202.72\pm 48.35,\,c=0.29\pm 0.13,\,p=1.22\pm 0.11\}\) (Figure 2a). Similarly for the 2018, Kodiak earthquake sequence the obtained parameters of the OU law, Equation (5) with 95% confidence intervals are \(\omega=\{K=225.91\pm 46.84,\,c=0.31\pm 0.18,\,p=0.88\pm 0.09\}\) (Figure 2b). Finally, for the 2018, Anchorage earthquake sequence the estimated parameters of the OU law are \(\omega=\{K,\,c,\,p\},\,\{76.71\pm 11.25,\,0.06\pm 0.03,\,1.17\pm 0.1\}\), respectively. The fit of the OU law and the estimated parameters from Equation (5) are demonstrated in Figure 4.  
Furthermore, we used the ETAS model, Equation (6), to estimate the aftershock decay rate during the target time interval \([T_{s},\,T_{e}]=[0.06,\,30]\) days for the three aftershock sequences. For comparison we present the OU fit and the ETAS model fit for the 2018, Anchorage earthquake sequence in Figure 5. A similar plot for the other two sequences is  
Figure 4: The log-log plot of the aftershock decay rate for the 2018, Mw 7.1 Anchorage aftershock sequence with magnitudes \(m\geq 2.8\) are presented as open squares. The blue solid line is the corresponding fit of the OU law, Equation (5), to the aftershock sequence. The obtained parameters from the OU law, Equation (5), with the 95% confidence intervals are reported in the legend. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Start Time** & **End Time** & \(m_{0}\) & \(\mu\) **(Events per Day)** \\ \hline Denali & 1 January 2000 & 3 October 2002 & 3.0 & 0.1 \\ Kodiak & 1 January 2000 & 23 December 2017 & 3.2 & 0.005 \\ Anchorage & 1 January 2000 & 30 October 2018 & 2.8 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Background Seismicity Rate. given in Figure A3. Figure 6 illustrates the fit of the ETAS model in transformed time for the 2018, Anchorage earthquake sequence. Finally, the statistical properties of the aftershock sequence initiated by the M7.1 Anchorage, Alaska, earthquake are investigated in detail during several additional target time intervals. Specifically, the sequence was analyzed during several target time intervals starting from the occurrence of the mainshock and ending at \(\overline{T}_{e}=[1,\,2,\,3,\,4,\,5,\,6,\,7,\,10,\,14,\,21,\,30]\) days. The evolution of the estimated parameters with 95% confidence intervals for both models OU and ETAS during 2018, Mw 7.1 Anchorage earthquake sequences are shown in Figure A4. Obtained estimations for the \(b\)-value of the GR relation, Equation (1) with 95% confidence intervals are demonstrated in Figure A4. The evolution of the OU model parameters are shown in Figure A4. We presented the evolution of the estimation of the ETAS model parameters in Figure A4. Figure 5: The aftershock sequence and corresponding earthquake magnitudes during 2018, Mw 7.1 Anchorage sequence with \(m\geq 2.8\).