Theoretical Uniqueness of the Magnetotelluric Inverse Problem for Equal Penetration Discretizable Models

The problem of uniqueness in determining a certain kind of stratified conductivity structure of a medium from its magnetotelluric surface impedance is studied. The model is assumed to belong to the class consisting of homogeneous, isotropic parallel layers lying on top of a homogeneous half-space substratum. An equal penetration discretization is further assumed. It is shown that for this class of models the impedance can be represented in a rational polynomial form of a penetration operator u. From the algebraic properties of these polynomials it is proved that no two such conductivity models can have the same surface impedance.