Large-scale focusing joint inversion of gravity and magnetic data with Gramian constraint

A fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. It uses a nonlinear Gramian constraint to impose correlation between density susceptibility reconstructed models. The global objective function formulated in space weighted parameters, but implemented original space, imposed using two separate Lagrange one each model domain. This combined approach provides more similarity assumed that measured are obtained on uniform grid consistent regular discretization volume domain imposed. sensitivity matrices exhibit block Toeplitz structure depth layer Forward transpose operations with can be efficiently dimensional Fourier transforms. makes it feasible solve large scale problems respect both computational costs memory demands, problem by applying iterative methods rely only matrix vector multiplications. As such, use regularized reweighted conjugate gradient algorithm, conjunction matrices, leads methodology geophysical sets. Numerical simulations demonstrate possible apply $L_p$-norm stabilisers, reconstruction domains standard laptop computer. demonstrated, p=1 choice sparse solutions sharp boundaries, $p=2$ smooth blurred Gravity over an area northwest Mesoproterozoic St. Francois Terrane, southeast Missouri, USA inverted.