Three‐dimensional magnetotelluric responses for arbitrary electrically anisotropic media and a practical application

Abstract

ABSTRACTElectrical anisotropy in earth media increases the complexity of magnetotelluric responses. Magnetotelluric models based on anisotropic media must be developed to fully understand observed data. This paper presents a three‐dimensional algorithm for calculating magnetotelluric responses of arbitrary anisotropic media in the frequency domain. Using a staggered‐grid finite difference method, the model space is discretized into rectangular blocks with electric fields on the edges of each block and the magnetic fields normal to the faces of each block. The electric field Helmholtz vector equation that considers a full 3 × 3 conductivity tensor is calculated numerically under two orthogonal polarizations. In calculating the boundary values on the four sides of the three‐dimensional anisotropic model, we adopt different procedures for calculating the two‐dimensional responses on the sides in the x and y directions. The responses for a layered anisotropic model and a three‐dimensional isotropic model calculated with this algorithm are compared with the corresponding analytical and numerical solutions, respectively. The comparisons show that the algorithm's approximations are highly precise for a wide frequency band. A typical two‐dimensional anisotropic model and a general three‐dimensional anisotropic model were also constructed, and their responses were calculated. These anisotropic models have ordinary structures but can produce phase rolling out of quadrant magnetotelluric responses, which indicates that considering electrical anisotropy may improve our interpretation of observed data. Using this algorithm, we can model the observed data from the northern Qaidam Basin in northern Tibet, where ultrahigh‐pressure metamorphic rocks are exposed along an old suture, and seismic anisotropy was indicated in neighbouring areas. The phase tensors of the magnetotelluric sites at this location show large skew angles, and the corresponding phase splits are distinct in the off‐diagonal impedance elements. Although the isotropic three‐dimensional electrical structure can model the profile data well, the structure shows a sequence of conductive and resistive bodies in the mid‐lower crust of the north Qaidam Basin, which is very spatially inhomogeneous, and a simple intrinsic anisotropic body can also produce similar surficial responses. Using the three‐dimensional anisotropic algorithm, we found an equivalent anisotropic replacement for this area. The results of the three‐dimensional anisotropy modelling of the magnetotelluric data from the northern Tibetan Plateau show the valuable applicability of the three‐dimensional anisotropic algorithm in testing the qualitative presumption of electrical anisotropy.