## 3 Data Testing
### Synthetic Data Testing
In addition, we also performed a simple comparison between our proposed acceleration algorithm and the GPU parallel acceleration inversion algorithm developed by [PERSON] et al. [24]. The GPU parallel algorithm developed by [PERSON] et al. [24] takes approximately 6 s for a single iteration with the 100 \(\times\) 100 \(\times\) 20 mesh number. The time required for a single iteration of our algorithm at this partition scale is usually no more than 2 s. This explains our method can reduce computer memory usage and computation time for large-scale data inversion. ### Real Data Testing

The proposed method is applied to the gravity anomaly data of the Gonghe Basin in the northeastern Qinghai-Tibet Plateau (Figure 7). The inner and peripheral areas of the Gonghe Basin show abundant geothermal resources [27]. On the east side of the basin, the temperature of the Zhacang and Qunlianhai hot springs reached 93-96 \({}^{\circ}\)C, exceeding the local boiling point. In 2017, a high-temperature dry hot rock mass of 236 \({}^{\circ}\)C was discovered at 3705 m depth in Qiapuqia in the Gonghe Basin, northeast of the Tibetan Plateau. This is the first time that the shallowest and hottest hot dry rock has been discovered in China, further confirming that the geothermal resources in Gonghe Basin are rich and are attracting renewed interest in evaluating geothermal resources in this region [28]. Several hot springs \begin{table}
\begin{tabular}{c c c c c} \hline  & **40 \(\times\) 40 \(\times\) 20** & **50 \(\times\) 50 \(\times\) 20** & **80 \(\times\) 80 \(\times\) 20** & **100 \(\times\) 100 \(\times\) 20** \\ \hline Traditional algorithm & 107.54 & 282.98 & 4954.16 & - \\ Model I Acceleration algorithm & 8.75 & 20.39 & 167.59 & 350.71 \\ speedup & 12.55 & 13.88 & 29.56 & - \\ Traditional algorithm & 104.24 & 241.50 & 4483.66 & - \\ Model II Acceleration algorithm & 8.52 & 20.33 & 162.28 & 350.33 \\ speedup & 12.23 & 11.88 & 27.63 & - \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of calculation time of different mesh number in the pre-processing stage. \begin{table}
\begin{tabular}{c c c c c} \hline  & **40 \(\times\) 40 \(\times\) 20** & **50 \(\times\) 50 \(\times\) 20** & **80 \(\times\) 80 \(\times\) 20** & **100 \(\times\) 100 \(\times\) 20** \\ \hline Traditional algorithm & 19.90 & 34.83 & 641.34 & - \\ Model I Acceleration algorithm & 0.037 & 0.095 & 0.69 & 1.81 \\ speedup & 537.84 & 366.63 & 929.48 & - \\ Traditional algorithm & 19.25 & 33.60 & 728.13 & - \\ Model II Acceleration algorithm & 0.031 & 0.091 & 0.515 & 1.23 \\ speedup & 620.97 & 369.23 & 1413.84 & - \\ \hline \end{tabular}
\end{table} 
Table 3: Comparison of calculation time of single iteration for different mesh number. and geothermal wells are located in and around the basin [29; 30], and a granite basement with hot dry rock is approximately 2 km underground [31; 32]. The Institute of Geological Survey of Jilin University collected the gravity anomaly data of the Gonghe region used in this study (Figure 8). After grid processing, the measured data revealed that the grid spacing was 500 m, and the range of the entire measuring area was 33 \(\times\) 25 km as shown in Figure 7. In this paper, the inversion maximum depth is set at 9 km, and the underground space of the inversion target area is divided into 66 \(\times\) 50 \(\times\) 60 closely spaced upright prism units, each with a size of 500 m \(\times\) 500 m \(\times\) 150 m. The density constraint range of inversion is controlled at \([-1,1]\)g/cm\({}^{3}\), the maximum number of iterations is set at \(k\) = 200, and the cutoff error is set at \(\varepsilon=0.01\). After 110 iterations the inversion was terminated, with a total time of 221.8 s, including 114.7 s for the iteration time. Figure 9 illustrates the 3D imaging display of gravity survey data inversion results. The cap layer has weak density characteristics, and its thickness is generally less than 3 km.