## 2 Geologic Background and Methods
### Partitioning of Crust-Mantle Heat Flow  
The earth's crustal heat flow originates from two primary sources: first, the radiogenic heat produced by crustal rocks--primarily due to elements such as uranium (U), thorium (Th), and potassium (K)--and second, the thermal energy transferred from the earth's deep mantle. The distribution of heat flow between the crust and mantle not only affects the present activity of the crust and upper mantle but also influences the thermal conditions within the deep mantle, thereby highlighting the fundamental characteristics of geothermal  
Figure 1: Geologic overview map of the study area. 1—Qinghai Nanshan North Marginal Fracture; 2—Daotang River Fracture; 3—Hacheng Fracture; 4—Laji Mountain South Marginal Fracture; 5—Laji Mountain North Marginal Fracture. heat [22]. There is a linear relationship between the heat flow in a region and the rate of radiogenic heat generation in rock formations [23]:  
\[\mathrm{q}=\mathrm{q_{m}}+\mathrm{AD}=\mathrm{q_{m}}+\mathrm{q_{c}}\]  
The mantle heat flow was obtained by modeling the layered crust of the study area and then calculating the heat flow from the heat generation of radioactive elements layer by layer using a similar \"stripping back\" approach \(\mathrm{q_{a}}\). The following is obtained: \(\mathrm{\sum q_{a}=q_{c}}\). The heat flow is obtained by \(\mathrm{q_{m}=q-q_{c}}\). The primary high-temperature anomalies in the tunnels of the study area are located in the Qiabuqiab region of the Gonghe Basin. In this study, the crustal thermal structure of the Qiabuqiab area is derived by calculating stratified heat flux values using the \"stripping back\" method. For rock heat generation rates within a depth of 4.6 km, measured values are adopted; for deeper layers, the heat generation rates of rocks in each zone are computed using the correlation formula relating seismic wave velocity to the deep crustal heat generation rate proposed by [PERSON] and [PERSON] [24]. \[\mathrm{lnA}=\mathrm{16.5-2.47V_{p}}\]  
where (\(\mathrm{V_{p}}\)) represents the seismic wave velocity in km/s. The transverse (shear) wave velocity for the Qiabuqia Valley earthquake was obtained from the natural seismic observation profile along the Qinghai Gonghe-Yushu Highway, which controls the Gonghe Basin (Figure 2); the velocity ratio was taken as 1.709 [18]. In Figure 2, the dashed line is the Moho. The depth of the Moho in the Gonghe Basin is 50-60 km. Based on the seismic velocity profile, the depth of the Moho in the Qiabuqia Valley is taken as 55 km. The geothermal heat flow value in the Qiabuqia region is 106.2 mW/m\({}^{2}\). Of this, 80.4 mW/m\({}^{2}\) is generated by heat from the radioactive decay of elements in the Qiabuqia River Valley, meaning the crustal heat flow is 80.4 mW/m\({}^{2}\) and the mantle heat flow is 25.8 mW/m\({}^{2}\). The crust-to-mantle heat flow ratio in the region is 3.12:1. It is evident that the Gonghe Basin belongs to a 'hot crust, cold mantle' type of crustal thermal structure, while the Qiabuqia Valley exhibits a distinct anomalous heating type of crustal thermal structure. From Figure 2, it can be seen that the distribution of blocks within the crust of the Gonghe Basin is characterized by an alternating arrangement of high-velocity and low-velocity bodies. Notably, there is a significantly large low-velocity block near the Qiabuqia Valley (station 199), where only the vertical band of this low-velocity body can be observed at station 199. This block extends to depths of approximately 22 to 41 km. The terrestrial heat flow is significantly influenced by the low-velocity, high-conductivity layer within the crust. Notably, there is a large low-speed block near the Qiabuqia River Valley (station 199), where a vertical band of this low-speed body can be observed. This low-speed body extends from a depth of approximately 22 to 41 km, and the geothermal heat flow is significantly influenced by the low-speed, high-conductivity layer in the crust. The crustal structure in the study area exhibits a distinct vertical layering.