A stable analytical expression for magnetotelluric/radiomagnetotelluric impedances in anisotropic layered Earth models

Previous closed-form solutions of impedances on layered Earth models were only available for the anisotropic conductivity case under the plane wave electromagnetic incidence. Here, we have developed a numerically stable impedance formula for both magnetotelluric and radiomagnetotelluric problems in layered media with arbitrarily anisotropic conductivity and dielect permittivity. Maxwell equations are first transformed into a set of coupled second-order partial differential equations with the horizontal components of electric field as the variables. Then, the recursive formula of surface impedance is obtained by using the general solutions of the second-order partial differential equations and the tangential continuity condition of electromagnetic fields at each layer interface. To avoid the numerical overflow in both the nominator and denominator of the recursive impedance formula due to large layer thickness or high working frequency, an artificial exponential function with positive exponential factor is used to regularize both the nominator and denominator. It leads numerically stable recursive formula for any layer thickness and working frequency. At the end, a four layered magnetotelluric model with anisotropic conductivities is adopted to validate the newly derived analytical formula and another two synthetic layered Earth models are used to study the effects of conductive anisotropy and dielectric anisotropy on radiomagnetotelluric responses.