Physics-Guided Multi-Scale Encoder-Decoder Convolutional Neural Network (CNN) for 3D Density Gravity Inversion

Summary Three-dimensional (3D) gravity inversion for subsurface density reconstruction is a highly ill-posed and non-unique problem due to the intrinsic ambiguity of gravity data and the high dimensionality of the model space. Conventional inversion methods typically rely on iterative optimization with explicit regularization, which can be computationally expensive and sensitive to parameter selection, often leading to smoothed models and limited resolution. In this study, we propose a physics-guided multi-scale encoder-decoder convolutional neural network (CNN) for efficient and physically consistent 3D density gravity inversion. The network establishes a direct nonlinear mapping from two-dimensional gravity anomaly or gravity gradient data to 3D subsurface density models by integrating hierarchical multi-scale feature extraction, dense skip connections, and deep supervision. To enforce geophysical consistency, a gravity forward operator is embedded into the loss function, constraining the inversion results to honor the governing physical laws. Numerical experiments using progressively complex synthetic models-including single-prism, double-prism, inclined staircase structures and irregular complex model-demonstrate that the proposed method accurately recovers density magnitudes, spatial geometry, sharp boundaries, depth discontinuities, and opposing density polarities, while producing gravity responses that closely match the observations. Application to airborne gravity gradient data over the Vinton salt dome further validates the method under realistic conditions, yielding geologically plausible density models compared with previously published conventional regularized and Bayesian inversion approaches. These results indicate that the proposed physics-guided CNN provides a robust, accurate, and computationally efficient alternative for large-scale and complex 3D gravity inversion problems in real-world geophysical applications