Modeling Magnetotelluric Source Amplitude Effect in a Spherical Coordinate System

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. These source amplitude effects highlight the need for careful treatment of MT responses in spherical geometry, especially when comparing with conventional Cartesian models. To address this, this study introduces a practical framework based on a rotated spherical coordinate system, which improves numerical stability and facilitates consistent interpretation of real MT observations. While complementary to the main focus of this study, this framework provides a useful basis for future 3-D inversion in spherical geometry and strengthens the connection between theoretical modeling and observational practice.