3D property inversion of gravity and magnetic data based on a double branch regressive CNN trained by synchronous forward modeling ：a case study of the Western Ross Sea

Joint inversion is an essential technique in potential field data processing. The current methodology largely relies on the geology model of anomalous bodies, especially for deep, complex structures. Inspired by the excellent nonlinear mapping capability of the image semantic segmentation model and the advantages of supervised learning, a regressive, end-to-end, encoder-decoder structural, convolutional neural network with a double-branch structure called PFInvNet(Potential Field Inversion Neural Network) is proposed for joint 3D  inversion of physical properties from gravity and magnetic data. Its input is a four-channel dataset consisting of gravity and magnetic anomalies and their vertical gradients, and its output is a 3D matrix representing the spatial distribution of the remnant density and the magnetic susceptibility, which are predicted independently through the double-branch structure of the decoders and then concatenated in the final layer. For network training, a large amount of precisely labeled sample is exceedingly demanding; thus, forward modeling becomes a prerequisite approach. Two discretized forward modeling algorithms for gravity and magnetic anomalies of 3D homogeneous arbitrary-shaped bodies based on surface integrals are deduced and verified with analytic solutions of the sphere model. Furthermore, the neural network needs to learn from the anomalies generated by various forms of abnormal bodies with different physical properties. Therefore, different sizes and quantities of cuboids are randomly distributed in the model space to simulate different forms of abnormal bodies. The label represents the combined spatial distribution of remanent density and magnetic susceptibility for the cuboids, encompassing both spatial location information and physical properties information. With the help of the Marching Cubes(MC) algorithm, the surface of the cuboids can be easily extracted and divided into a triangular surface mesh. The surface mesh is then used to calculate the gravity and magnetic anomalies synchronously through the forward modeling algorithms. The anomalies are concatenated in the channel direction as a sample. A set of optimal network parameters has been determined, including the weight initialization method, the gradient calculation methods, the loss function, the training hyperparameters, the regularization method, and the normalization method. The PFInvNet is trained with 500 and 10000 pairs of samples and labels, respectively. The analysis and comparison of training results prove that PFInvNet has two crucial features: one is that the branch structure enables independent prediction of magnetic susceptibility and remanent density; the other is efficient anti-overfitting ability and efficient solution-finding ability .The prediction error of small samples is very close to that of large samples and is also not obviously enhanced by the noise-contaminated data , demonstrating the strong generalization and robustness of the network. Finally, the network is tested with magnetic and gravity anomalies of the Victoria Land Basin in the western Ross Sea through transfer learning and retraining, and definite 3D distributions of apparent remnant density and apparent magnetic susceptibility have been obtained and can be checked with geological evidences.