Gradient filtering regularization for 3-D MT inversion based on unstructured tetrahedral discretization

We propose a novel smoothing regularization scheme for 3-D magnetotelluric (MT) inversion based on unstructured tetrahedral discretization. Different from conventional methods that explicitly add smoothing constraints to model parameters, we choose to do the gradient filtering to smooth the model updates in an implicit way. By transforming the model into a constraint domain, the gradient of the objective function for the parameters in the new domain can be taken as a product of transpose of inverse transformation operator and the conventional gradient. Since the transpose of inverse transformation is designed to be an inverse distance interpolation operator for each tetrahedron, the data fitting term in the gradient can be smoothed in a filtering-like process. We compare our new strategy with the conventional explicit smoothing ones by testing on synthetic data for different noise levels, initial models and regularization factors. The numerical results show that suffering from the unequal volume and random centroid location of adjacent tetrahedrons, the inversion results of conventional methods often demonstrate scattered structures in slices. In contrast, our new method recovers the model in a smooth way and the convergence speed is largely improved. Finally, we adopt the USArray data for further testing and find that comparing to conventional inversion methods, our new strategy can provide more reliable underground structures with better data fitting.