Modeling of Magnetotelluric Source Amplitude Effect in a Spherical Coordinate System

Xiaoli WAN, Hisayoshi SHIMIZU, Peng YU, Hisashi UTADA

Magnetotelluric (MT) impedances of the three-dimensional (3-D) Earth are typically modeled in a Cartesian coordinate system, neglecting the Earth’s curvature. While this approximation is valid for one-dimensional (1-D) structures, its applicability to 3-D Earth remains uncertain. To evaluate the influence of source configuration—particularly polarization and amplitude—on MT responses, we conducted systematic 3-D forward modeling in a spherical coordinate system with external dipole source excitations, using both oceanic and continental models. Our results show that the spherical MT impedance, unlike its Cartesian counterpart, is generally non-unique and depends on the source amplitude even when three independent sources are applied. The associated tipper estimates are even more strongly affected. This amplitude dependence is not limited to forward modeling but may also influence impedance and tipper estimates derived from real MT observations, since natural source amplitudes vary over time and the Earth’s curvature is always present. As a result, these source amplitude effects may help account for observed seasonal variations in MT responses. To support accurate modeling under such conditions, this study proposes a practical framework based on a rotated spherical coordinate system to improve numerical stability and ensure consistency with real MT observations. This framework will enable rigorous comparisons with Cartesian models and provide a robust basis for 3-D inversion in spherical geometry in the future. The findings offer an additional perspective for interpreting MT responses in complex Earth structures and may serve as a useful complement to conventional modeling approaches.