**Appendix A**

**Table A1.** Forecast model parameters distribution from 10,000 MCMC sampling for 2018, Anchorage sequence.


**Figure A1.** Plot of the magnitudes versus sequential numbers of the earthquakes in the study regions for the three sequences: (**a**) 3 November 2002, Mw 7.9 Denali (**b**) 23 January 2018, Mw 7.9 Kodiak (**c**) 30 November 2018, Mw 7.1 Anchorage. The corresponding times in days after each mainshock are depicted by doted vertical lines.

**Figure A2.** The log-log plot of the earthquake decay rates for: (**a**) the 2002, Mw 7.9 Denali sequence with *m* ≥ 3.0; (**b**) the 2018, Mw 7.9 Kodiak sequence with *m* ≥ 3.2 are presented as open squares. The blue solid lines are the corresponding fit of the OU law, Equation (5), to the aftershock sequences. The obtained parameters from the OU law, Equation (5), with the 95% confidence intervals are reported in the legends.

**Figure A3.** The aftershock sequence and corresponding earthquake magnitude for: (**a**) the 2002, Mw 7.9 Denali sequence with *m* ≥ 3.0; (**b**) the 2018, Mw 7.9 Kodiak sequence with *m* ≥ 3.2. The ETAS model fit, Equation (6), for the target time interval of [*Ts*, *Te*]=[0.06, 30] is plotted as a solid blue line, and the obtained set of parameters are reported with 95% confidence intervals. The OU law fit, Equation (5), is plotted as a black dashed line for comparison.

**Figure A4.** The model parameter estimation during the aftershock sequence of the 2018, Anchorage for all the events with magnitude 2.8 and greater. (**a**) The estimated *b*-value, Equation (1), (**b**) the parameters {*<sup>K</sup>*, *c*, *p*} of the OU law, Equation (5), and (**c**) the parameters {*<sup>A</sup>*, *c*, *p*, *α*} of the ETAS model, Equation (6). The error bars represent the 95% confidence intervals during the target time intervals, {1, 2, 3, 4, 5, 6, 7, 10, 14, 21, <sup>30</sup>}, days after the mainshock.

**Figure A5.** The distribution of each parameter and the matrix plot of the pairs of the OU parameters that computed using the MCMC sampling for the 2018, Mw 7.1 Anchorage sequence with *m* ≥ 2.8.

**Figure A6.** The distribution of each parameter and the matrix plot of the pairs of the ETAS parameters computed using the MCMC sampling for the 2018, Mw 7.1 Anchorage sequence with *m* ≥ 2.8.

**Figure A7.** The probabilities to have the largest expected aftershocks to be larger than *m*ex ≥ 5.0, 6.0, 7.0 using the BPD, Equation (12), during a constant target time interval of [*Ts*, *Te*]=[0.06, 2] days and for the varying target time intervals. (**a**) The 3 November 2002, Mw 7.9 Denali sequence with *m* ≥ 3.0. (**b**) The 23 January 2018, Mw 7.9 Kodiak sequence with *m* ≥ 3.2. (**c**) The 30 November 2018, Mw 7.1 Anchorage sequence with *m* ≥ 2.8.

**Figure A8.** The comparison of the probabilities to have the largest expected aftershock during the target time interval of [*Ts*, *Te*]=[0.06, 2] days for the three sequences: (**a**) 3 November 2002, Mw 7.9 Denali (**b**) 23 January 2018, Mw 7.9 Kodiak (**c**) 30 November 2018, Mw 7.1 Anchorage. The blue triangles are computed using the BPD, Equation (12), with an earthquake decay rate given by the ETAS model, Equation (6). The purple squares are computed using BPD, Equation (12), with an earthquake decay rate given by OU law, Equation (5). The green circles give probabilities computed using the EVD, Equation (11). The aftershock magnitudes are modelled using Equation (3).

**Figure A9.** The number of forecasted and observed aftershocks in the forecasting time interval Δ*T* = [1, 2, 5, 7, 10, 14] days for (**a**) The 3 November 2002, Mw 7.9 Denali for *m* ≥ 3.0; (**b**) The 23 January 2018, Mw 7.9 Kodiak for *m* ≥ 3.2; (**c**) The 30 November 2018, Mw 7.1 Anchorage for *m* ≥ 2.8 by using the constant target time interval [*Ts*, *Te*]=[0.06, 2] days. The red squares show the average number of forecasted earthquakes using the ETAS model, Equation (6), and the black triangles illustrate the average number of forecasted earthquakes using OU law, Equation (5). The shading bands represent 95% confidence intervals. The blue circles represents the observed number of earthquakes in the forecast time interval.

**Figure A10.** The number of forecasted and observed aftershocks in the forecasting time interval Δ*T* = 7 days for the three sequences: (**a**) the 3 November 2002, Mw 7.9 Denali sequence for *m* ≥ 3.5; (**b**) the 23 January 2018, Mw 7.9 Kodiak sequence for *m* ≥ 3.5; (**c**) the 30 November 2018, Mw 7.1 Anchorage sequence for *m* ≥ 3.5. The red triangles show the average number of forecasted earthquakes using the ETAS model and the black squares illustrate the average number of forecasted earthquakes using OU law. The shading bands represent 95% confidence intervals. The blue circles represent the observed number of earthquakes in each forecasting time interval.

**Figure A11.** The obtained quantile scores from the M-test for the constant target time interval [*Ts*, *Te*]=[0.06, 2] days for (**a**) The 3 November 2002, Mw 7.9 Denali for *m* ≥ 3.0; (**b**) The 23 January 2018, Mw 7.9 Kodiak for *m* ≥ 3.2; (**c**) The 30 November 2018, Mw 7.1 Anchorage for *m* ≥ 2.8. The red triangles demonstrate the obtained quantile scores from the ETAS model, Equation (6), and the black squares illustrate the quantile scores of OU law, Equation (5). The blue dashed lines represent the 0.025th and 0.05th quantiles.
