Compact magnetization vector inversion

SUMMARY Magnetization vector inversion (MVI) has attracted considerable attention in recent years since by this inversion both distribution of the magnitude and direction of the magnetization are obtained; therefore, it is easy to distinguish between the magnetic causative bodies especially when magnetic data are affected by different remanent magnetization. In this research, the compact magnetization vector inversion is presented: a 3-D magnetic modelling is proposed from surface data measurements to obtain compact magnetization distribution. The equations are solved in data-space least squares and the algorithm includes a combination of two weights as depth weighting and compactness weighting in the Cartesian system. The re-weighted compactness weighting matrix handles sparsity constraints imposed on the magnitude of magnetization for varying Lp-norms ($0 \le p \le 2$). The low value of the norm leads to more focused or compact inversion, and using a large value of p obtains a smooth model. The method is validated with two synthetic examples, the first is a cube that has significant remanent magnetization and the second consists of two causative cube bodies with significant different magnetization directions at different depths. The case study is the magnetic data of Galinge iron ore deposit (China) that the apparent susceptibility and magnetization directions are reconstructed. The compact model reveals that the results agree with drilling and geological information.