## 2 Geologic Background and Methods
### Calculation of Geothermal Values and Prediction of Deep Temperatures in the Study Area  
Heat flow density, also known as geodetic heat flow, quantifies the transfer of heat from the earth's interior to its surface per unit area and time before being released into space. This phenomenon is a comprehensive quantitative representation of the thermal state of the deep crust or lithosphere at the surface. The standard unit for heat flow is milliwatts per square meter (mW/m\({}^{2}\)). The heat flow value is typically determined using Equation (2). \[\mathrm{Q}=-\mathrm{K}\frac{\mathrm{dT}}{\mathrm{d}Z} \tag{2}\]  
In the formula, \(\mathrm{Q}\) is the earth's heat flow, and the unit is mW/m\({}^{2}\); \(\mathrm{K}\) is the thermal conductivity of the rock, and the unit is W/(m\(\cdot\)K); \(\mathrm{dT}/\mathrm{d}Z\) is the earth's temperature gradient, and the unit is \({}^{\circ}\mathrm{C}/\mathrm{km}\); the negative sign represents the direction of the earth's heat flow is opposite to the direction of the earth's temperature gradient. In this study, the data from the deep borehole test wells in the early stage of the study area were collated, and temperature measurements from six representative wells along the tunnel were selected (Figure 6); the temperature measurement data were used to find the ground temperature gradient using the least squares method. To determine the thermal conductivity of the drill core, a representative rock type is selected, the arithmetic mean of the thermal conductivities of the same rock type in the borehole is calculated, and the overall thermal conductivity is obtained by using the summation average method according to the thickness of different lithological layers. The present-day geothermal heat flow values for boreholes SZK03, SZK04, SZK05, SZK13, SZK10, and SZK30 were  
Figure 5: Schematic diagram of model meshing. obtained as 89.52 mW/m\({}^{2}\), 51.32 mW/m\({}^{2}\), 34.78 mW/m\({}^{2}\), 46.94 mW/m\({}^{2}\), 34.14 mW/m\({}^{2}\), and 70.77 mW/m\({}^{2}\), respectively (Table 1). The spatial distribution of these values indicates significantly higher geothermal heat flow on the Gonghe Basin side compared to the Xining Basin, which aligns with geological observations. The two wells with the highest geothermal heat flow values, SZK03 and SZK30, are both located in the Gonghe Basin and near the northern margin of the Qinghai-Nanshan Fault zone. The strata in these areas consist of granite with high thermal conductivity and heat generation rates. It can be observed that the deep heat flow is dominated by the rapid upwelling through high-permeability faults and the high radioactive heat generation rate of the granites in the crust, leading to the high geothermal heat flow values in this region. SZK13 and SZK04 are located in the transition zone between the Gonghe Basin and the Xining Basin, with strata consisting of sandstone and gravel with relatively low thermal conductivity and heat generation rates. A noticeable decline in geothermal heat flow is observed here, further supporting the previously described 'hot crust, cold mantle' thermal structure of the Gonghe Basin. SZK10 and SZK05 have crossed the Lajishan Fault and are now situated in the Xining Basin, where the geothermal heat flow values are further reduced compared to the Gonghe Basin, which is consistent with the actual conditions. Figure 6: Temperature measurement curve of the temperature measurement well. Equation (3) is used to calculate the temperature of the surrounding rock at the bottom of the sub-borehole square model. Due to practical constraints, it is not feasible to measure the temperature at every point along the tunnel. Therefore, this study employs the Kriging interpolation method to estimate the temperature at the bottom along the tunnel [25; 26].