Sequential joint inversion of gravity and magnetic data via the cross‐gradient constraint

Different geophysical methods use different model parameterizations and inversion algorithms. Thus, combining these different inversion systems and yet adding the nonlinear cross‐gradient constraint in a joint inversion framework might be a big challenge, for instance, as explained further by Moorkamp et al. in 2011, there is a complex interaction between the data misfit terms, regularization and cross‐gradient terms and an imperfect fit to the data is expected. In this paper, we use a sequential algorithm for a two‐dimensional joint inversion of gravity and magnetic data, which tries to avoid these issues by decoupling the gravity inversion, the magnetic inversion and the cross‐gradient minimization processes. The efficiency of the algorithm and developed code is demonstrated by the joint inversion of noisy synthetic data. The results show a significant improvement in the respective models obtained by introducing the cross‐gradient joint inversion over the models obtained by separate inversions for synthetic data and then for field data targeting potash ore source in the AjiChai salt deposit in north‐western Iran. In this application case, the lower density of salt minerals such as potash, compared to its surrounding sedimentary sequences, motivates a gravity study. Furthermore, the relative lower susceptibility of these salt minerals, alongside their diamagnetic effect, makes them a suitable target for magnetic surveys. Separate gravity and magnetic studies had been performed over the deposit; however, a constitutive relationship between density and magnetization within the area of interest supporting a joint inversion had not been established. In this paper, we apply the sequential cross‐gradient approach to perform the first full joint inversion for the AjiChai salt deposit. The magnetic inversion here is performed to recover the magnetization amplitudes rather than the magnetization vector. In fact, we assume there is no remanent magnetization and, therefore, that the magnetization vector is constant and parallel to the geomagnetic field direction. The constructed density and magnetization models are of high concordance with available geological information and previous studies including drilling results. In addition, unlike previous separate inversion models, the models are structurally and geometrically similar.