The Magnetotelluric Impedance Tensor and its Properties

Abstract

A consistent definition of the linear relationship between the electric field true vector E and magnetic field pseudovector H yields a true magnetotelluric impedance tensor T. The true tensor nature of T admits diagonalisation in terms of classical eigenstate decomposition. Eigenstate analysis of T is in agreement with biorthogonal methods. Physical properties of the electromagnetic energy at the surface of the earth define hermitian forms that can be viewed as surface functions of the field polarization parameters. Geometrical and physical properties of these surfaces establish the result that the eigenvectors of all the hermitian forms have the same principal directions. This property links the vertical magnetic field with T, reduces the degrees of freedom of T from eight to six, provides a single principal direction that facilitates the interpretation of magnetotelluric data and shows that when T is defined, defining the tipper is unnecessarily restrictive. Synthetic data from a 3D model is used to illustrate the main result.