Deep Learning Inversion of Gravity Data With Multiple Physical Constraints

Gravity inversion is an important method for revealing underground density distribution. Traditional deterministic inversions face challenges such as easily becoming trapped in local minimum solutions and sensitivity to initial models, while conventional data-driven deep learning inversions (DD-DLI) also exhibit limitations including dependence on datasets and lack of physical constraints. In this letter, we propose a multi-physical constrained deep learning inversion method (MPC-DLI) for gravity data based on the U-Net. Within an iterative descent inversion framework, the method employs a trained neural network to predict model updates for each iteration. Constraints about forward modeling laws and model smoothness are incorporated into the loss function during the training phase, serving respectively to promote the fitting of observation data and enhance stability. In the prediction phase, a focusing constraint is built into the objective function to yield model results with clear boundaries and pronounced density variations. Synthetic and field data examples are used to demonstrate the effectiveness of the new method.