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The three-dimension (3D) inversion of magnetic data is an effective method of recovering underground magnetic susceptibility distributions using magnetic anomaly data. The conventional regularization inversion method has good data fitting; however, its inversion model has the problem of a poor model-fitting ability due to a low depth resolution. The 3D inversion method based on deep learning can effectively improve the model-fitting accuracy, but it is difficult to guarantee the data-fitting accuracy of the inversion results. The loss function of traditional deep learning 3D inversion methods usually adopts the metric of the absolute mean squared error (MSE). In order to improve the accuracy of the data fitting, we added a forward-fitting constraint term (FFit) on the basis of the MSE. Meanwhile, in order to further improve the accuracy of the model fitting, we added the Dice coefficient to the loss function. Finally, we proposed a multi-constraint deep learning 3D inversion method based on UNet++. Compared with the traditional single-constraint deep learning method, the multi-constraint deep learning method has better data-fitting and model-fitting effects. Then, we designed corresponding test models and evaluation metrics to test the effectiveness and feasibility of the method, and applied it to the actual aeromagnetic data of a test area in Suqian City, Jiangsu Province. [ABSTRACT FROM AUTHOR]

The three-dimension (3D) inversion of magnetic data is an effective method of recovering underground magnetic susceptibility distributions using magnetic anomaly data. The conventional regularization inversion method has good data fitting; however, its inversion model has the problem of a poor model-fitting ability due to a low depth resolution. The 3D inversion method based on deep learning can effectively improve the model-fitting accuracy, but it is difficult to guarantee the data-fitting accuracy of the inversion results. The loss function of traditional deep learning 3D inversion methods usually adopts the metric of the absolute mean squared error (MSE). In order to improve the accuracy of the data fitting, we added a forward-fitting constraint term (FFit) on the basis of the MSE. Meanwhile, in order to further improve the accuracy of the model fitting, we added the Dice coefficient to the loss function. Finally, we proposed a multi-constraint deep learning 3D inversion method based on UNet++. Compared with the traditional single-constraint deep learning method, the multi-constraint deep learning method has better data-fitting and model-fitting effects. Then, we designed corresponding test models and evaluation metrics to test the effectiveness and feasibility of the method, and applied it to the actual aeromagnetic data of a test area in Suqian City, Jiangsu Province.