## 3 Results  
### Three-Dimensional Slab Thermal Regime  
The 3-D slab thermal state of the subducting plate is compared with the spatial distribution of seismic events according to the temperature distribution of the plate's inner surface at different vertical distances. Figure 3a exhibits the temperature structure of the incoming plate and the earthquake distribution near the subduction interface with a resolution of 20 \(\times\) 10 \(\times\) 4 km (width \(\times\) length \(\times\) depth). The temperature distribution on internal surfaces of the dipping oceanic lithosphere is measured vertically downward  
Figure 2: Model size and setting (including slab depth and subduction velocity). Colored spheres indicate the earthquakes cataloged in Figure 1. The plotted seismic events are less than 2 km above the interface. The earthquake symbol size mimics the average rupture dimensions for a given magnitude. The colored spheres indicate all M \(>\) 3 earthquakes (IRIS) from 1 January 2000 to December 2010 and all M \(>\) 5.5 earthquakes from 1 January 1900 to December 2000 (Centennial Database).  
from the plate interface at different vertical distances (Figure 3): 0, 4, and 8 km. The comparison between different intraslab depths allowed us to further evaluate the slab geometry-dependent thermal regime.  
Figure 3: Slab temperatures were calculated vertically below the interface at depths of (**a**) 0, (**b**) 4, and (**c**) 8 km. The black dashed lines represent the interface 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]. The blue, purple, and dark red dashed lines represent the isotherm contours of 500, 400, and 300 \({}^{\circ}\)C, respectively.  
The surface temperature of the dipping oceanic lithosphere depended largely on the subduction angle and obliquity along the plate interface geometry. The surface temperature of the slab beneath south-central Alaska (Figure 3a) at a given depth was approximately 50-100 \({}^{\circ}\)C higher than that beneath southwestern Alaska due to a smaller subduction angle and a younger plate (45 vs. 55 Ma). Moreover, the flatness of the slab geometry led to the slow increase of the slab surface temperature from 300 to 600 \({}^{\circ}\)C beneath the offshore of south-central Alaska. In contrast, the slab surface temperature rapidly transitioned from 300 to 500 \({}^{\circ}\)C beneath the offshore of southwestern Alaska due to slab bending. As the slab dip angle decreased from westward to eastward, the distance between the 300 and 500 \({}^{\circ}\)C isotherms on the plate interface increased and finally reached a maximum beneath south-central Alaska. Furthermore, the surface temperature of the slab beneath Kodiak Island in south-central Alaska varied from 300 to 600 \({}^{\circ}\)C in the depth range of 20-55 km, whereas the surface temperature of the slab beneath other islands of southwestern Alaska significantly exceeded 600 \({}^{\circ}\)C at depths of \(>\)50 km. The slab surface temperature beneath the coastline of south-central Alaska decreased southeastward from 600 to 400 \({}^{\circ}\)C. We also observed similar temperature trends inside the subducting plate at various intraslab depths (4 and 8 km), as our calculation results show in Figure 3b,c. However, the slab's surface (0 km) temperature was warmer than that inside the subducting plate below the same location because it is closer to the overlying lithosphere. In addition, when the model takes into account the horizontal convergence velocity and the thermal structure of the incoming and overriding plates [44; 45], its coupling depth remains not fully determined due to the complexity of dehydration and decoupling.