Enhanced 3D Gravity Inversion Using ResU-Net with Density Logging Constraints: A Dual-Phase Training Approach

2026-01-06

AI Summary

This study addresses the common issue in deep learning–based gravity inversion where the absence of geological prior constraints leads to geologically implausible and distorted results. To overcome this limitation, the authors propose a two-stage training framework that incorporates density well-log priors. In the first stage, a depth-weighting function is introduced in the weighted density parameter domain, and a ResU-Net is trained using a physics-informed weighted forward operator. In the second stage, the model is fine-tuned with well-log constraints to enhance physical consistency and generalization. Evaluated on synthetic models, the Bishop model, and real-world data from the San Nicolás mining district in Mexico, the proposed method consistently outperforms both unconstrained deep learning approaches and traditional focusing inversion—including its well-constrained variants—demonstrating significant improvements in the accuracy and geological plausibility of 3D gravity inversion.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• gravity inversion
• deep learning
• prior constraints
• density logging
• data fitting error

Innovation

• ResU-Net
• gravity inversion
• density logging constraints
• dual-phase training
• depth weighting