Reweighted regularized conjugate gradient method (RRCG) for 3D focusing inversion of potential field data

Traditional objective functions in potential field inversions commonly prioritize functionals that emphasize maximal smoothness and stability. Although this approach results in petrophysical images with smooth transitions and gradients, it often fails to delineate the boundaries and central positions of geological bodies accurately. To address this limitation, we build on the core principles of focused inversion imaging techniques and incorporate minimal support functionality into our inversion objective function. This adjustment explicitly includes model parameter variables within the variable weighting functions. In addressing the minimization of the objective function, we introduce reweighted regularization to seek clustered solutions constrained by the L0 norm. Furthermore, to ensure inversion stability and accelerate convergence, we enhance traditional focused inversion by integrating background fields and imposing petrophysical bounds, thereby simplifying the selection of focus factors. As a result, the inversion outcomes are less sensitive to the choices of focus factors, facilitating easier attainment of desired results compared to traditional focused inversion algorithms. This method has been applied to theoretical models and practice to validate its effectiveness and accuracy.