## 4 Discussion  
### Subduction Thermal Regime and Earthqu  
We compared the slab thermal regime with the M \(>\) 3 earthquakes near the interplate surface from 1900 to 2010, plotted as colored spheres in Figure 3. The features of the Alaskan earthquake distribution (Figure 3a) show that most of the seismic events are distributed beneath the offshore forearc. The interplate 300-500 \({}^{\circ}\)C geotherms are outlined 100-200 km southward of offshore Alaska and are accompanied by frequent seismic ruptures on the subduction interface. Moreover, a large number of recorded M \(>\) 5 earthquakes are clustered near Kodiak Island (Figure 3a). In contrast, regular earthquakes with recorded magnitudes  
Figure 5: Slab water content (wt%) was calculated at depths of (**a**) 0 (subduction interface) and (**b**) 8 km vertically below the interface. The black dashed lines represent the isodepth contours of 25, 50, and 75 km. The yellow and gray dashed circles represent the slow slip event patches in the Upper Cook (2008–2012, [17]) and Lower Cook Inlets (2010–2011, [18]). The green dashed line indicates low-frequency earthquakes [20]. Bold blue lines indicate the 1992.0–2004.8 (\(\sim\)M 7.8) Slow Slip Event, and bold red lines indicate the 2009.85–2011.81 (\(\sim\)M 7.2) Slow Slip Event [21; 22].  
of M3-M5.5 were mostly distributed below offshore of southwestern Alaska and the east side of south-central Alaska. The slab surface temperatures of these regular earthquakes below southwestern Alaska were less than 600 \({}^{\circ}\)C, whereas the slab surface temperatures of these regular earthquakes below south-central Alaska were more than 600 \({}^{\circ}\)C. [PERSON] et al. [49] have suggested that the intermediate-depth earthquakes beneath south-central Alaska occur in the temperature range of 500-900 \({}^{\circ}\)C. This is consistent with our results. The SSEs occurring in the Upper and Lower Cook Inlets are also located in regions with slab surface temperatures over 600 \({}^{\circ}\)C below south-central Alaska.  
By comparing our work with previous results [50], [PERSON] et al. [35] suggested that the interplate temperature below south-central Alaska is predicted to gradually increase from 300 to 800 \({}^{\circ}\)C with increasing depth (Figure S5) rather than rapidly increasing from 400-600 \({}^{\circ}\)C to 800-1100 \({}^{\circ}\)C. In this study, we compared the P-T conditions with those of previous studies (e.g., [50; 51; 52; 53; 54; 55]) to further verify that our results were reasonable (Figure S6). In general, globally exhumed rock records [52; 54] are suggested to well-constrain the global subduction thermal regime. We found that our P-T results (blue curve in Figure S6) are concordant with the results from [PERSON] et al. [51], [PERSON] et al. [52], and [PERSON] and Johnson [54]. Compared with other models (e.g., [50; 53; 55]), the temperature in our model is warmer than that in the decoupling models (orange curves in Figure S6) at pressures \(<\) 2.5 GPa (depth \(<\) 70 km) because these models assumed maximum plate decoupling depths. Hence, the thermal structure of the subducting plate beneath south-central Alaska and southwestern Alaska that we obtained based on the 3-D model is acceptable.