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We propose a 3-D parallel joint inversion framework for gravity and MT data based on Gramian structural constraints. This approach discretizes the inversion model using unstructured tetrahedral meshes and improves the efficiency of forward modeling and sensitivity calculations for both gravity and MT data through a parallel scheme. Subsequently, the objective function is minimized using the Gauss-Newton method, with model updates facilitated by the MINRES solver and line search techniques. The results from the synthetic model demonstrate that joint inversion significantly enhances the inversion outcomes for gravity and MT data, and the correlation between residual density and resistivity is stronger.