An Efficient Cross-Gradient Joint Inversion Algorithm for Gravity and Magnetic Data Using a Sequential Strategy

The joint inversion methods of gravity and magnetic data have been presented in numerous studies and implemented in many real applications. However, almost all of these existing methods still face the problem of low computational efficiency, although some targeted improvements have been put forward. To further address this issue, this study proposes an efficient algorithm for the joint inversion of gravity and magnetic data. The new algorithm is developed from the idea of structural coupling by using the cross-gradient function and employs a sequential strategy. A new formula for efficient minimization of the structural similarity term is derived innovatively, in which the minimization of the structural coupling term is obtained by a technical combination of an alternating strategy and the randomized singular value decomposition (RSVD) algorithm. Using the proposed new formula, the dimension of the original inverse problem can be reduced greatly. Furthermore, the RSVD algorithm is utilized to perform the independent inversion and determine an optimal regularization parameter. Several comparative tests on a synthetic example show that the proposed efficient method poses great advantage in efficiency compared with the conventional sequential cross-gradient joint inversion (CSCGJI) method. The proposed algorithm is also successfully applied to the real data from a metallic deposit area in Xinjiang province, China.