Three-dimensional magnetotelluric modeling in the spherical and Cartesian coordinate systems: A comparative study

With the increase in the coverage area of magnetotelluric data, three-dimensional magnetotelluric modeling in spherical coordinates and its differences with respect to traditional Cartesian modeling have gradually attracted attention. To fully understand the influence of the Earth’s curvature and map projection deformations on Cartesian modeling, qualitative and quantitative analyses based on realistic three-dimensional models need to be examined. Combined with five representative map projections, a type of model conversion method that transforms the original spherical electrical conductivity model to Cartesian coordinates is described in this study. The apparent resistivity differences between the spherical western United States electrical conductivity model and the corresponding five Cartesian models are then compared. The results show that the cylindrical equal distance map projection has the smallest error. A meridian convergence correction resulting from the deformation of the map projection is introduced to rotate the Cartesian impedance tensor from grid north to geographic north, which reduces differences from the spherical results. On the basis of the magnetotelluric field data, the applicability of the Cartesian coordinate system to western and contiguous United States models is quantitatively evaluated. Precise interpretations of the contiguous United States model were found to require spherical coordinates.