A compact derivation of basic relationships to determine subsurface resistivity functions

Abstract

Starting from the magnetic vector potential and the electric scalar potential a compact derivation is given to determine the one-dimensional subsurface resistivity function in different ways, leading to the basic relationships of the classical magnetotelluric and the magnetovariational methods. With measurements on the horizontal ground surface Schmucker’s C-response and the surface impedance can be determined by using two different combinations of the electromagnetic field components. With measurements at more than one height (depth) levels (assuming the knowledge of horizontal and/or vertical gradients) some further theoretical possibilities emerge.

The novelty of the paper lies first of all in the very compact presentation of the one-dimensional case, introducing a local distortion due to a small-size inhomogeneity.