Joint inversion of gravity and magnetic data using total variation stabilizer and crossgradient constraint

It is well-known that the solution of the individual potential field inversion problem, either gravity or magnetic, is non-unique. One efficient strategy to reduce the uncertainty of the solution, and to improve the obtained results, is the simultaneous joint inversion of two or more data sets. In this case, different geophysical data sets are used simultaneously in an inversion algorithm. Depending on the coupling between different model parameters, the algorithm provides the solutions, which satisfy the observed data and coupling constraint. Combined with regularization, this is an effective strategy to obtain a reliable subsurface model. In this study, an algorithm for the joint inversion of gravity and magnetic data using anisotropic total variation (TV) stabilizer is developed. The anisotropic TV stabilizer consists of the individual L1-norm of the gradient of the model parameters in three orthogonal directions. Therefore, our algorithm preserves the edge of the subsurface targets and provides focus models. Here, the relationship between different model parameters is enforced using the cross-gradient coupling. This constraint uses the model topology in order to enhance the structural similarity of the reconstructed models. Then, the information from both data sets can be used to provide reliable models. This simplifies the interpretation of the subsurface targets. The developed algorithm is validated on two different synthetic examples. The results indicate that the algorithm is practical and can provide focus and similar models. Finally, we invert the gravity and magnetic data obtained over kimberlite pipes BK54 and BK55 in Orapa, Botswana. The reconstructed models are consistent with the geological and borehole information from the survey area.