Part II: One-dimensional Magnetotellurics
4.1 SPECTRAL DECOMPOSITION OF THE FIELD IN A SPHERICAL MODEL
As a first step, we must consider a spherical model of the earth (Figure 11). Let the earth, of radius R, have a radial piecewise constant distribution of conductivity, ?(r), and be surrounded by a nonconducting atmosphere. Magnetic permeability of the earth is taken to be equal to the permeability of a vacuum, ? = ?0 = 4? × 10?7 H/m. The model is excited (inductively!) by an external nonuniform magnetic field.
5.1 SPECTRAL DECOMPOSITION OF THE FIELD IN A PLANE MODEL
We will now examine the complete problem, including both inductive and galvanic mechanisms of field excitation (Dmitriev and Berdichevsky, 1979).
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.