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.

翻译：重力勘探因其低成本和高效率已成为重要的地球物理方法。随着人工智能的兴起，基于深度学习（DL）的数据驱动重力反演方法具备传统正则化方法所缺乏的物性恢复能力。然而，现有DL方法受限于先验信息约束不足，导致反演模型存在较大的数据拟合误差和不可靠的结果。此外，反演结果缺乏其他勘探方法的约束与匹配，可能导致结果与已知地质条件相矛盾。本研究提出一种融合先验密度测井信息的新方法以解决上述问题。首先，我们在神经网络（NN）中引入深度加权函数，并在加权密度参数域中对其进行训练。该神经网络在加权正演算子的约束下，展现出改进的反演性能，所得反演模型的数据拟合误差更小。其次，我们将整个网络训练分为两个阶段：首先训练一个大型预训练网络Net-I，然后以密度测井信息作为约束，得到优化的微调网络Net-II。通过在合成模型和Bishop模型中的测试与对比，本方法相较于无约束的数据驱动DL反演方法，其反演质量显著提升。此外，我们还将本方法与传统的聚焦反演（FI）方法及其测井约束变体进行了对比与讨论。最后，我们将此方法应用于墨西哥圣尼古拉斯矿区的实测数据，并与两种近期基于DL的重力反演方法进行了比较分析。