Research On The Three-Dimensional Anisotropic Inversion Of Magnetotelluric Data

Magnetotelluric（MT）method is an important branch of geophysical prospecting for deep Earth structures.For the forward modeling and inversion research as well as application research,electrical anisotropy is increasingly recognized as an important aspect of models required to explain magnetotelluric observations.Anisotropic forward modeling and inversion have become hot topics.However,published research is mainly focused on two-dimensional anisotropy and can not be found yet for the three-dimensional inversion of magnetotelluric data from a model with arbitrary anisotropy.Thus,it needs in-depth study.Based on the three-dimensional forward modeling of the arbitrary anisotropic Earth of my master study,which solves for the magnetic fields,this paper has implemented the corresponding three-dimensional arbitrary anisotropic inversion using nonlinear conjugate gradient method and considering smoothing model constraint as well as anisotropy constraint in its objective function.The arbitrary anisotropic inversion solves for three axial resistivities ρ_x,ρ_y,ρ₂ as well as three rotation angles α_s,α_D,α_L.Besides,using the staggered-grid finite difference method,a forward modeling algorithm for the three-dimensional axial anisotropic model was implemented,which solves for the electric fields.The accuracy has been validated by comparisons with the 1-D analytical solution and the 2-D quasi-analytical solution of anisotropic models.Then the corresponding nonlinear conjugate inversion was implemented with smoothing model constraint as well as anisotropy constraint considered in its objective function.It can solve for three axial resistivities ρ_x,ρ_y,ρ₂.Both of these two inversion algorithms have been parallelized with the MPI implementation.Comparisons have been made for the two algorithms in terms of their formula derivations and the algorithms’ implementation details.These comparisons and a synthetic example demonstrate that the algorithm based on solving for electric fields requires less computer memory and runs much faster than that based on solving for magnetic fields.Theoretical models were designed to generate synthetic magnetotelluric data.Anisotropic inversions of the synthetic datasets validate the effectiveness of these two algorithms.The inversion results demonstrate that the three-dimensional isotropic inversion of anisotropic data can not resolve the true model and the three-dimensional axial anisotropic inversion of arbitrary anisotropic data can not recover the true model as well,while the three-dimensional arbitrary anisotropic inversion can well resolve the true model.Comparisons were made through inverting the real data from Rocky Mountain Trench in British Columbia,Canada with both the three-dimensional isotropic and anisotropic inversion algorithms.The inversion results show that both the isotropic and the anisotropic models can fit the real magnetotelluric data.However,the isotropic model is not consistent with the geological model given by the mapped geology,while the electrical features in the anisotropic model are consistent with the location and dipping direction of a fault discovered by the mapped geology.Both the synthetic and real data inversions show the effectiveness and practicality of the two developed anisotropic inversion algorithms.They also demonstrate the superiority of anisotropic inversion over the isotropic inversion.