用井下密度数据约束深度网络，提升重力反演精度与地质一致性。

Gravity exploration has become an important geophysical method due to its low cost and high efficiency. With the rise of artificial intelligence, data-driven gravity inversion methods based on deep learning (DL) possess physical property recovery capabilities that conventional regularization methods lack. However, existing DL methods suffer from insufficient prior information constraints, which leads to inversion models with large data fitting errors and unreliable results. Moreover, the inversion results lack constraints and matching from other exploration methods, leading to results that may contradict known geological conditions. In this study, we propose a novel approach that integrates prior density well logging information to address the above issues. First, we introduce a depth weighting function to the neural network (NN) and train it in the weighted density parameter domain. The NN, under the constraint of the weighted forward operator, demonstrates improved inversion performance, with the resulting inversion model exhibiting smaller data fitting errors. Next, we divide the entire network training into two phases: first training a large pre-trained network Net-I, and then using the density logging information as the constraint to get the optimized fine-tuning network Net-II. Through testing and comparison in synthetic models and Bishop Model, the inversion quality of our method has significantly improved compared to the unconstrained data-driven DL inversion method. Additionally, we also conduct a comparison and discussion between our method and both the conventional focusing inversion (FI) method and its well logging constrained variant. Finally, we apply this method to the measured data from the San Nicolas mining area in Mexico, comparing and analyzing it with two recent gravity inversion methods based on DL.