Deep Learning-Based Gravity Inversion Integrating Physical Equations and Multiple Constraints

Three-dimensional gravity inversion technology involves inferring the underground density structure based on observed gravity anomaly data. In addition to gravity inversion based on physics-driven methods, deep learning, as a purely data-driven technique, is increasingly gaining attention in geophysical inversion problems. However, purely data-driven methods rely on the implicit relationships within the data during the inversion process, which results in a lack of clear physical significance. This study proposes a three-dimensional gravity inversion method that integrates physical equations with deep learning. Based on the U-Net architecture, the gravity forward equation is incorporated as a physical constraint term, and a composite loss function—comprising three-dimensional mean squared error, a depth-weighting function, and three-dimensional intersection-over-union loss—is constructed to enhance inversion accuracy. Numerical experiments indicate that this method outperforms traditional algorithms in terms of density recovery accuracy and boundary clarity. When applied to gravity anomaly data from the Tangshan earthquake region in China, this method successfully inverted the three-dimensional subsurface density structure, revealing a high-density anomaly beneath the seismic source area, which provides important evidence for understanding the regional earthquake generation mechanism.