Magnetotelluric impedance consisting of six elements

Abstract This letter addresses two critical questions concerning the validity of the current formulation of the magnetotelluric (MT) method. The first question pertains to its mathematical formulation: specifically, whether solving the fundamental equations in a Cartesian coordinate system is universally valid. The second question concerns the number of impedance elements. Through a simple theoretical consideration, we found that the MT impedance generally consists of nine elements, which reduces to six at the Earth’s surface, whereas conventional MT studies utilize the impedance consisting of only four elements. Should MT studies adopt the 6-element impedance? Based on three-dimensional (3-D) numerical modeling results in both Cartesian and spherical coordinate systems, along with further theoretical analyses, we derived the following implications: (1) The MT impedance comprising four elements and the tipper are unique response functions only in a Cartesian coordinate system. In a spherical coordinate system, they become non-unique and exhibit significant dependence on the source amplitude. (2) The MT impedance consisting of six elements is a unique response function of the Earth, determinable in a spherical coordinate system but undeterminable in a Cartesian coordinate system under the plane-wave approximation. (3) Consequently, it is inappropriate to invert MT impedances obtained from Earth observations using numerical solvers designed for Cartesian coordinate systems. If these implications are validated, most of the theories and numerical solvers developed for Cartesian coordinate systems will need to be replaced by those adapted for spherical coordinate systems, except for cases involving only the primary field.