Sparse Magnetization Vector Inversion Based on Modulus Constraints

Magnetization vector inversion (MVI) is an effective method for simultaneously determining the distribution of magnetization intensity and direction without knowing the direction of magnetization beforehand. Nevertheless, the presence of serious non-uniqueness in MVI imposes challenges in achieving accurate and reliable results. To improve the accuracy of MVI, we propose a method that incorporates a modulus constraint, informed by an analysis of the model constraints in two different frameworks. We employ a sparse operator on the magnetization magnitude and obtain an explicit expression for the magnetization components, establishing correlation constraints among them. Synthetic test results show that this method can achieve models with clear boundaries and consistent magnetization directions. Furthermore, the application of a sparse operator to the gradient’s modulus of the magnetization magnitude helps recover inclined structures. However, the dispersed magnetization directions suggest that we should also constrain the magnetization direction, simultaneously. The inversion of magnetic data measured over the Zaohuohexi iron-polymetallic deposit in Qinghai Province, northwest China, verified the proposed approach’s effectiveness.