Three-dimensional magnetotelluric inversion with surface topography based on the vector finite element method

In this paper, the three-dimension (3D) Magnetotelluric (MT) inversion algorithm with topography based on the vector finite element method is studied and the 3D inversion program code is developed. In the 3D forward numerical modeling of the MT field, a fast forward modeling scheme based on Parallel Direct Sparse Solver (PARDISO) without divergence correction is adopted. For typical models with topography, under the conditions of medium-scale calculations, comparison shows that the PARDISO method is more than 10 times faster in calculation speed than Bi-Conjugate Gradient (BICG). The correctness of the 3D forward modeling program with topography is also confirmed by tests on a theoretical model and the comparison with the results in previous studies using the finite element method. In 3D inversion, an inversion code of MT with topography based on the Conjugate Gradient (CG) method is compiled in this study to avoid directly calculation of the Jacobian matrix, thus the problem existing in calculation of the Jacobian matrix is turned into solving two "quasi-forward" problems, and the fast forward solution of PARDISO is further applied to the solution of the "quasi-forward" modeling to improve the efficiency of inversion calculation. The developed algorithm is used to carry out 3D inversion of synthetic data of a series of geo-electric models with topography. The inversion results can well reproduce the electrical structure of the theoretical model, which verifies the correctness and reliability of the 3D inversion algorithm developed in this paper. Finally, the algorithm is used to invert the MT measurement data in a mine area. The resultant 3D electrical structure from the inversion clearly reveals geoelectric characteristics of the study area. Data interpretation is conducted successfully by combining the inversion results with geological data available, further verifying the effectiveness of the algorithm proposed in this work.