Three-dimensional regularized inversion of magnetotelluric data with a minimum support gradient constraint

Regularization is an effective technique to obtain stable solutions for 3D magnetotelluric (MT) inversion. Smooth constraints are commonly used in traditional inversion algorithms. It is unsuitable if anomalies occur in block patterns. In some cases, it is necessary to obtain sharp boundaries. Some studies have proposed stabilizing functionals to obtain clear and sharp boundaries, such as minimum support (MS) and minimum gradient support (MGS) functionals; however, the optimal value of the focusing parameter should be selected to produce reliable inversion results. In this study, we expanded a new stabilizing functional that we called minimum support gradient (MSG) stabilizing functional as a stabilizer in 3D MT inversion. We developed a Gauss-Newton (GN) algorithm based on the edge-based finite-element method (FEM) to invert the MT data. In the inversion process, the forward modeling and the adjoint problem are solved by the Math Kernel Library (MKL) PARDISO parallel direct solver. we also parallelized the inversion program over frequencies by using Message Passing Interface (MPI) to further speed up the inversion process. Two synthetic models are tested to compare the inversion results for different stabilizing functionals. Compared to traditional smooth inversion, the MSG inversion can clearly distinguish the boundaries of the anomalies. The inverted resistive targets are closer to the true test model. Additionally, the MSG inversion results are stable and robust for a wide range of focusing parameter values, indicating that our method is effective and easy to implement. Finally, the proposed algorithm is applied to the long MT data from the USArray component of EarthScope project in the United States.