The Unstructured Nodal Finite Element Modeling Of Three-dimensional Magnetotellurics In General Anisotropic Media

This article first reviews the magnetotelluric anisotropy forward research results by the domestic and foreign experts.Then based on the Coulomb gauge condition,we get the Helmholtz equation of magnetic vector potential and electric scalar potential in the anisotropic media.We use the nodal finite element method based on unstructured tetrahedral element interpolation basis function to calculate the integral in each element,and the matrix of each element is assembled to the overall system of linear equations.Finally,the finite element linear equations system is solved using a preconditioned iterative solver,and the finite element solution is obtained.The three-dimensional general anisotropic forward code of magnetotellurics based on unstructured nodal finite element method is written using Fortran and performed on Intel Fortran compiler.The unstructured grid used for model subdivision is generated using Tet Gen,an open source program for generating tetrahedral grids proposed and compiled by Si Hang.In order to improve the accuracy and practicability of the unstructured finite element algorithm,the mesh is locally refined in different degrees and different ranges by element volume constraints according to the known prior information of the model and the frequencies used in the modeling.To test the accuracy of the three-dimensional finite element forward modeling algorithm,we design three one dimensional isotropic geoelectric models(the three layered model),and two typical one dimensional anisotropic geoelectric models(two layered model and the four layered model).The analytical solutions are compared with the numerical results simulated by the program in this paper to verify the accuracy of the algorithm under different refinement degrees,different frequencies and different underground geological conditions.On the initial mesh,the accuracy of the finite element solution is particularly lower,especially in the high frequency band,where the maximum relative error of apparent resistivity is 40.62% and the maximum error of phase is 7.9degrees.After the refinement of the mesh,the accuracy of the finite element solution is greatly improved,especially for the high frequency band.On the final refined mesh,the relative error of apparent resistivity is 0.9%,and the phase error is 0.8 degree.The numerical results show that the mesh refinement method can effectively improve the accuracy of finite element numerical solutions in a wide frequency range.The more times of mesh refinement and the denser grid is needed for the higher frequencies.For lower frequencies,the mesh refinement does not improve the accuracy significantly.Finally,the characteristics of magnetotelluric response of different geoelectric models are researched and their laws are summarized.By designing a theoretical geoelectric model,the magnetotelluric response characteristics of three dimensional anisotropic anomalous bodies in homogeneous isotropic half space at different burial depths and different rotation angles of anisotropic resistivity are simulated and analyzed.Finally,considering the influence of topography on the magnetotelluric response,the conductivity anisotropy model with the undulated topography is numerically simulated to further verify the accuracy and applicability of the method.