## 3 Data Testing
### Synthetic Data Testing
The results of our processing of real measured data are consistent with previous studies, indicating the practical application capabilities of our algorithm. Figure 8: Real measured gravity data corresponding to Gonghe Basin. Figure 7: (**a**) Distribution of faults, wells and hot springs in the Gonghe Basin and surrounding areas; the red boxes represent the study and inversion region (revised from [PERSON] et al. [33]); (**b**) location of the research area. ## 4 Conclusions

The gravity exploration method plays an important role in ore exploration and oil and gas exploration. For example, in the case of metal minerals, gravity exploration can be used to find ore directly (such as chromite, magnetite, etc.) according to the characteristics of high density. In the geological exploration of oil, gas and coal fields, gravity exploration can be used to delineate sedimentary basins, study the thickness of sedimentary layers, and find the structures related to oil, gas and coal fields according to the characteristics of low density. The 3D inversion algorithm for gravity data can produce a reasonable density distribution and provide reference for further geological interpretation. However, as the number of observed data and model parameters increases, the inversion process faces problems of high memory consumption and long calculation time. Therefore, it is necessary to develop fast algorithms that can handle large-scale data. We study a 3D fast smoothing constraint algorithm for gravity data based on an optimized conjugate gradient flow. The algorithm is implemented in Python language, and PyQt gravity data inversion software is developed. In the data tests, the inversion obtains satisfactory 3D density distribution imaging results. It can be seen from the performance test records that the acceleration algorithm is scalable and can accelerate the inversion quickly. The new algorithm avoids generating an \(N\times N\) large matrix in the whole operation process, reducing memory consumption, which leads to a faster speed in the iterative process. Compared to other GPU-based parallel algorithms, our proposed method is equally efficient computationally. Moreover, the calculation time required for a single iteration is at least 350 times faster than that of the traditional algorithm, making our proposed acceleration algorithm efficient and practical for large-scale gravity data inversion. Therefore, this paper provides a new strategy for the rapid inversion of large-scale gravity data, saves the computational cost (time and memory) of data processing and provides important guidance for further ore and oil and gas exploration. Conceptualization, S.Z. and H.J. ; methodology; writing--review and editing, S.Z. ; result interpretation; project administration, P.Y. and J.J.; writing--review and editing; supervision, T.L. and Z.Z. ; project administration. All authors have read and agreed to the published version of the manuscript. Ministry of Science and Technology of the People's Republic of China under Grant 2020 YFE0201300, and National Natural Science Foundation of China under Grant 42274187 and Grant 42074119, and Natural Science Foundation of Jilin Province under Grant 20220101147 JC. Not applicable. The authors declare no conflict of interest. Figure 9: Real measured gravity data inversion results. ## References

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