Physics-Inspired Neural Network for Joint Inversion of Multialtitude 3-D Gravity and Vertical Gradient

Gravity inversion is the pioneer in exploring the structural characteristics of the Earth, the Moon, and other celestial bodies. Classical gravity inversion methods aim to estimate the 3-D subsurface density distribution from the observed 2-D surface gravity anomalies, which is an ill-posed problem. Constraints can provide vertical resolution and reduce uncertainty. However, these methods significantly increase the cost of data acquisition. This article presents a novel joint inversion method to estimate subsurface density anomaly via a physics-inspired neural network. The observed signals in the proposed method are the gravity anomalies on multiple altitudes and their vertical gradients, which provide vertical resolution for gravity inversion. The proposed joint inversion method contains two stages. The proposed inversion model is initially pretrained on the synthetic data. Self-supervised transform learning with a closed loop between inversion and forward models is applied to the target gravity anomalies and their gradients. The loss function is defined by mean absolute error (MAE), cross-gradient loss, and total variation (TV). Experiments on independently and identically distributed (IID) synthetic data, as well as out-of-distributed (OOD) field data, demonstrate the effectiveness of the proposed method.