Joint 3D inversion of gravity and magnetic data using deep learning neural networks

Three-dimensional (3D) joint inversion of geophysical data is often non-unique, non-linear on a large scale, and is complicated for most conventional model-driven approaches that use additional regularization terms in the objective function. In recent years, with the development of computing devices and artificial intelligence, processing large-scale data using data-driven methods is no longer difficult, and great progress has been made in the inversion of single geophysical dataset using the deep learning. In this work, we explore the feasibility of using deep learning methods for 3D joint inversion. In particular, we propose two methods based on modified U-Net architectures: (1) early fusion that constructs a single network and requires different types of data to be preprocessed to share the same size; (2) late fusion that employs multiple branches of network designed for different types of data, but feature-fused together before the final loss is calculated. Our synthetic examples focus on the joint 3D inversion of gravity and magnetic inversion for mineral exploration; the model is parameterized by an ore body represented by an ellipsoid with an arbitrary size, position and orientation in the 3D space. We have found that the performance of the early fusion mostly relies on the data preprocessing, but the early fusion has obvious advantages in its simplicity and efficiency; the late fusion is a more stable choice and highly flexible in cases where data are in different sizes. Our results have proven the feasibility and the basic workflow of 3D joint inversion using the deep learning methods.