Spherical magnetotelluric modeling based on non-uniform source

Traditionally, magnetotellurics (MT) rests on an assumption that plane wave is incident vertically into flat Earth. With more and more magnetotellurics data coming in and the expansion of research area, Cartesian approximation and plane wave assumption may no longer be suitable for the large-scale modeling due to the inevitable Earth curve. We have developed a kind of magnetotellurics forwarding code in spherical coordinates based on staggered grid finite difference method. In addition, the electric fields are represented by poloidal-toroidal decomposition, then solved based on spherical harmonic and Bessel function to construct the source model that can be used to replace plane wave. The spherical model is built directly through geographic information like latitude and longitude, and the forward response will be obtained by solving the Maxwell's equations in terms of spherical format. Electric field components defined on curving cell edges are the primary EM field that is computed iteratively utilizing a quasi-minimum residual scheme, with a divergence correction applied periodically. Taking into account the versatility and convenience, this spherical forward code is developed on the open source ModEM which provides a ready framework for rapid implementation of new application or algorithms. Large scale three-dimensional conductive models with different resolution are built and transformed to their corresponding Cartesian models by Lambert Conformal Conic map projection which can maintain the shape of original spherical model. We compare their forward response such as electric fields and apparent resistivity computed from spherical and Cartesian coordinates respectively. Under the combined effect of conductivity distribution and the unavoidable deformation, electric fields and apparent resistivities show stronger difference at the place where conductivity contrasts. All the forward calculations are implemented on the blade server in the form of frequency parallel scheme, spherical model usually takes twice time than Cartesian. According to real bathometry data, we make the China continent and its adjacent sea model to research the forward difference between spherical and Cartesian coordinates.