# Three-Dimension Inversion of Magnetic Data Based on Multi-Constraint UNet++
## 6 Conclusions  
Magnetic prospecting is an indispensable exploration method in applied geophysics, and it is widely used in searching for various metal deposits, such as iron, copper, and gold ores. In addition, magnetic exploration can also be used to study the formation of structures, especially for the study of various intrusive structures. The 3D inversion of magnetic data is an effective method of restoring the magnetic susceptibility distribution in an underground space using magnetic anomaly data, which play an important guiding role in resource exploration and development, and can help geophysical interpreters to quickly delineate the scope of target ore bodies. The conventional regularization inversion method has an issue with poor model fitting, so an inversion method has been developed based on deep learning to improve the model-fitting effect; however, the data-fitting effect of its inversion results is still poor. In order to solve this problem, this study proposed a multi-constraint DL inversion method on the basis of a single-constraint DL. While ensuring the model-fitting effect, the data-fitting effect is also significantly improved. The loss function of traditional deep learning 3D inversion methods usually adopts the absolute mean squared error (MSE). In order to improve the accuracy of the data fitting, we added a forward-fitting constraint term (FFit) based on the MSE. At the same time, in order to further improve the accuracy of the model fitting, we added the _Dice_ coefficient to the loss function and finally proposed a multi-constraint deep learning 3D inversion method based on UNet++. In order to quantitatively analyze the model-fitting and data-fitting effects of the inversion results, we used the model-fitting and data-fitting differences to compare the advantages and disadvantages of the inversion method. In addition, nine test models were designed to measure the merits of the method, and to compare it with the single-constraint deep learning method. The conclusion is that multi-constraint deep learning has smaller differences in model fitting and data fitting, which means a higher inversion accuracy. Finally, we applied the multi-constraint DL inversion method to the measured magnetic data of Suqian City, Jiangsu Province. Through the inversion results of the magnetic anomalies, three fault zones in this area were successfully identified. In addition, the results also contain depth information, which can be used to locate magnetic anomalies in three-dimensional space. Therefore, the multi-constraint DL method has significant application prospects in the field of data inversion.  
Figure 24: Interpretation of inversion results of real data: (**a**) contour map of magnetic anomaly of measured data (black dashed line indicates fracture, same below); (**b**) top view of multi-constraint DL inversion results.  
**Author Contributions:** Conceptualization, J.J. and X.Z.; methodology and writing--review and editing, J.J. and S.Z.; result interpretation and project administration, P.Y. and H.L.; writing--review and editing and supervision, T.L. and S.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported in part by the Ningxia Key Research and Development Plan under Grant 2023 BEG02066, in part by the National Natural Science Foundation of China under Grant 42204141, in part by the Scientific Research Project of the Education Department of Jilin Province under Grant JJKH20241293 KJ, and in part by the Fundamental Research Funds for the Central Universities under Grant 2023-JCXK-15.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All the data required by the paper has been included in the paper, and other data needs to be kept confidential.  
**Conflicts of Interest:** The authors declare no conflicts of interest.