Inversion of Magnetic Data Based on L1 Norm and Total Variation Regularization

For magnetic inversion, recovering the location and boundaries of causative bodies is challenging. In this study, we propose an improved magnetic inversion method based on the L1 norm of the model and its gradients total variation (TV1). Four weights for the L1 norm and TV1 penalties are introduced in the L1-TV1 inversion, and their effects are discussed comprehensively. These weights are crucial for the inversion, controlling the shape, boundaries, and resolution of the resultant model. Based on extensive synthetic model tests, appropriate parameters are given to achieve good inversion performance. Numerical experiments demonstrate that the proposed approach can reproduce a consistent model with the real solution. Finally, we apply this method to the inversion of the actual data in the Yeshan region, east Jiangsu Province, China, and successfully image the underground magnetic structure.