A Constrained Deep Learning Approach for Marine Gravity Field Recovery Based on the Inverse Vening Meinesz Method

Marine gravity is traditionally derived from altimeter data using physics-based methods, which are sensitive to altimeter data noise. Although deep learning methods can capture nonlinear relationships between marine gravity and multi-source data, purely data-driven approaches depend strongly on the quality and spatial distribution of training ship-borne gravity data. To combine the advantages of both methods, this study proposes a hybrid marine gravity recovery method that integrates the Inverse Vening Meinesz (IVM) method into a convolutional neural network (CNN) framework. Specifically, the IVM-derived marine gravity is incorporated into the CNN loss function as a constraint, and distance- and topography-dependent hyperparameters are introduced to control its contribution during training. The gravity model derived by the proposed IVM-constrained CNN method is validated using independent ship-borne gravity observations and a recognized marine gravity model. Assessed by ship-borne data, the proposed method improves accuracy by 28.5% and 6.8% compared with the IVM-derived and CNN-derived gravity models, respectively. Comparisons with the recognized model also indicate that the gravity model derived by the proposed method achieves the highest accuracy among the three models. These results show that embedding IVM constraints into deep learning frameworks can significantly improve the accuracy and robustness of marine gravity recovery.