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As a key component of remote-sensing technology, satellite gravity observation offers extensive coverage and high accuracy, effectively compensating for the shortcomings of terrestrial gravity measurements. Three-dimensional gravity data inversion can predict the physical property and spatial distribution of geological formations beneath the surface by analyzing the gravity data. In this paper, the heat source position within the Gonghe Basin’s geothermal system is identified through the analysis of satellite gravity data, and a constrained deep-learning inversion method is proposed. This method adds the fitting data constraints and depth-weighting function into the network model establishment of deep learning, and trains the network through a large number of datasets, so that the network is constrained by physical information in the training process to obtain the results with a better data-fitting accuracy and higher depth resolution. The proposed method is employed to verify the synthetic model data, and the inversion results indicated that, compared to other methods, the deep-learning gravity inversion method with the addition of physical information constraints has a higher inversion accuracy and depth resolution. Finally, the inversion results based on satellite gravity data revealed the presence of numerous low-density bodies in the underground range of 10–35 km in the research area. It is speculated that this part could be the heat source of the geothermal system in the Gonghe Basin. The findings from this study are expected to contribute to a deeper comprehension of the formation of the geothermal system in the region.

In the 3D inversion modeling of gravity and magnetic potential field data, the model weighting function is often applied to overcome the skin effect of inversion results. However, divergence occurs at the the deep area, and artificial weak negative anomalies form around the positive anomalies in the horizontal direction, resulting in a reduction in the overall resolution. To fully utilize the model weighting function, this study constructs a combined model weighting function. First, a new depth weighting function is constructed by adding a regulator into the conventional depth weighting function to overcome the skin effect and inhibit the divergence at the deep area of the inversion results. A horizontal weighting function is then constructed by extracting information from the observation data; this function can suppress the formation of artificial weak anomalies and improve the horizontal resolution of the inversion results. Finally, these two functions are coupled to obtain the combined model weighting function, which can replace the conventional depth weighting function in 3D inversion. It improves the vertical and horizontal resolution of the inversion results without increasing the algorithm complexity and calculation amount, is easy to operate, and adapts to any 3D inversion method. Two model experiments are designed to verify the effectiveness, practicability, and anti-noise of the combined model weighting function. Then the function is applied to the 3D inversion of the measured aeromagnetic data in the Jinchuan area in China. The obtained inversion results are in good agreement with the known geological data.

We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations between calculated and observed data. We also use the depth weighting function based on the eigenvector of gravity gradient tensor to eliminate undesired effects owing to the fast attenuation of the position function. Model data suggest that the extrapolated Tikhonov regularization in conjunction with the depth weighting function can effectively recover the 3D distribution of density anomalies. We conduct density inversion of gravity gradient data from the Australia Kauring test site and compare the inversion results with the published research results. The proposed inversion method can be used to obtain the 3D density distribution of underground anomalies.