Chapter 3: Statement of the Magnetotelluric Problem
3.1 THE TIKHONOV-CAGNIARD TRANSFORMATIONS
The unfortunate peculiarity of magnetotellurics lies in the fact that we solve a geoelectric problem in which the source of an electromagnetic field is unknown (more exactly, it is known, but only in a very general way). How can we avoid this difficulty? The fundamental idea for the magnetotelluric method can be formulated as follows. Because we do not have precise information on the distribution of currents in the magnetosphere or the ionosphere, we must abandon a traditional geoelectric concept based on the study of the relationship between electromagnetic fields and their sources, and proceed to determine the electric conductivity of the earth by studying the ratios between the electric and magnetic fields, or between the various components of the magnetic field. This idea of Tikhonov’s opened a new period in the development of the technology of geoelectric methods and electric exploration.
Figures & Tables
Magnetotellurics in the Context of the Theory of Ill-Posed Problems
In 1950, A. N. Tikhonov published a paper, “On determination of electric characteristics of deep layers of the earth’s crust” in the proceedings of the Academy of Sciences of the USSR (Doklady, Akademia Nauk SSSR). In this paper, Tikhonov examined the relations between the horizontal components Ex, Hy of the magnetotelluric field (the natural time-varying electromagnetic field of cosmic origin), and introduced the impedance Z = Ex/Hy as a quantity characterizing the electric conductivity of the earth’s interior. A one-dimensional model disregarding the lateral effects was used for impedance interpretation. In this way, the feasibility of sounding the earth through the magnetotelluric observations at a single point on the earth’s surface was demonstrated, and new information about conductivity in the mantle was obtained.
This simple idea gave impetus to the development of a new geophysical method called magnetotelluric sounding, or MT sounding, or simply MTS. This method is a variation of frequency sounding. With all its strengths and weaknesses, it has found wide utility in commercial electric exploration and deep geoelectric investigations. A new branch of geophysics, given the name magnetotellurics, has come into being.