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A fast algorithm for the large-scale joint inversion of gravity and magneticdata is developed. It uses a nonlinear Gramian constraint to impose correlationbetween density and susceptibility of reconstructed models. The globalobjective function is formulated in the space of the weighted parameters, butthe Gramian constraint is implemented in the original space, and the nonlinearconstraint is imposed using two separate Lagrange parameters, one for eachmodel domain. This combined approach provides more similarity between thereconstructed models. It is assumed that the measured data are obtained on auniform grid and that a consistent regular discretization of the volume domainis imposed. The sensitivity matrices exhibit a block Toeplitz Toeplitz blockstructure for each depth layer of the model domain. Forward and transposeoperations with the matrices can be implemented efficiently using twodimensional fast Fourier transforms. This makes it feasible to solve for largescale problems with respect to both computational costs and memory demands, andto solve the nonlinear problem by applying iterative methods that rely only onmatrix vector multiplications. As such, the use of the regularized reweightedconjugate gradient algorithm, in conjunction with the structure of thesensitivity matrices, leads to a fast methodology for large-scale jointinversion of geophysical data sets. Numerical simulations demonstrate that itis possible to apply a nonlinear joint inversion algorithm, with $L_p$-normstabilisers, for the reconstruction of large model domains on a standard laptopcomputer. It is demonstrated, that the p=1 choice provides sparse reconstructedsolutions with sharp boundaries, and $p=2$ provides smooth and blurred models.Gravity and magnetic data obtained over an area in northwest of MesoproterozoicSt. Francois Terrane, southeast of Missouri, USA are inverted.

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