A Hybrid Attention-Gating Deep Learning Framework for 3D Joint Inversion of Gravity and Magnetic Data

The inherent limitations of individual geophysical methods and the sparsity of observational data often render inversion results unstable and non-unique. Joint inversion of multiphysics data exploits the complementary sensitivities of different physical fields regarding depth, resolution, and boundary features, thereby significantly mitigating the ambiguity of single-method inversion and enhancing interpretation reliability. Traditional joint inversion approaches primarily fall into two categories: spatial structure-based and physical parameter-based constraints. The former relies on the similarity of property distribution patterns, which struggles to decouple non-homologous anomalies, while the latter is often constrained by the unreliability of empirical relationships under complex geological conditions. Recently, deep learning methods based on the U-Net architecture have achieved joint inversion by establishing constraints based solely on spatial structural similarity (Hu et al., 2025) or physical parameter correlations (Guo et al., 2021). Although promising, these methods often fail to accurately characterize non-homologous anomalies in complex geological environments.

This study proposes a dual-stream 3D U-Net architecture incorporating a hybrid attention-gating mechanism. In terms of methodology, we first construct a training dataset based on rock physics data that encompasses both statistical correlations and structural discrepancies. Regarding the network architecture, independent encoders are employed to extract 3D features from gravity and magnetic data, respectively. A cross-attention module is then utilized to capture deep structural correlations, thereby enhancing cooperative inversion in homologous regions. Subsequently, a gated fusion module is introduced as an adaptive feature selector to effectively disentangle inconsistent features in non-homologous regions. Finally, the prediction models are generated through independent decoders.

During the joint inversion implementation phase, the network takes preliminary independent inversion results as input to predict high-fidelity models that integrate physical and geological priors. We incorporate these predicted models as reference models into the regularization term of the joint inversion objective function, constructing a deep-prior-based constraint. During iterative optimization, this constraint guides the inversion trajectory toward the fine geological structures predicted by deep learning by minimizing the discrepancy between the inverted and reference models, while ensuring the fit to observational data. This mechanism achieves an organic integration of data-driven and physics-driven approaches.

References

• Hu, Y. Su, X. Wu, Y. Huang and J. Chen, "Successive Deep Perceptual Constraints for Multiphysics Joint Inversion," in IEEE Transactions on Geoscience and Remote Sensing, vol. 63, pp. 1-14, 2025, Art no. 5907114. 
• Guo, H. M. Yao, M. Li, M. K. P. Ng, L. Jiang and A. Abubakar, "Joint Inversion of Audio-Magnetotelluric and Seismic Travel Time Data With Deep Learning Constraint," in IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 9, pp. 7982-7995, Sept. 2021.