Subdimension Method in Gravity and Magnetic Inversion

We developed a new potential data inversion method with no use of regularization or depth weight. Generally, ill-posed inverse problems are solved by Tikhonov-type regularization or image compactness methods to specify the solution behavior. Since different regularization forms and their coefficients cause various results, determining an appropriate regularization is not an easy task. We proposed a new approach that stabilizes the inversion by projection rather than regularization. In our method, the original equation is projected into a subspace in which the kernel matrix is less ill-conditioned than the original matrix. Notably, we set the subspace dimension equal to the quantity of data, which allows our method to perform without extra parameters. An approximate solution is obtained in a single subspace inversion, whereas the final result is obtained by averaging the results from multiple subspaces. We implemented the projection based on a random cuboid because it has good computational properties and can constrain the inversion by dividing the region. Synthetic tests show that our method outperforms conventional methods in complex situations, such as geological bodies stacked in the vertical direction. The application to field data also validates the robustness of our method by imaging geothermal features in Gonghe Basin, Qinghai Province, China. In the figure, (a) shows the gravity anomaly of models overlapping in depth. The conjugate gradient (CG) inversion methods can rarely solve such problems regardless of what values of alpha are assigned (in (d), (e), (f)). The shallow model is recovered with inaccurate depth, and the deeper shows artifacts. In subdimension(SD) methods, the two targets can be distinguished but are unclear when there is no space division((b)). When we layer the underground space, the two bodies can be recovered well ((c)).