Chapter 1: Ill-posed Problems in Geophysics
1.1 DIRECT AND INVERSE GEOPHYSICAL PROBLEMS
The philosophy of methods for studying nature is derived from the theory of ill-posed problems, which determines the potentialities and strategy of practical investigations. So, we would like to begin our book dedicated to modern magnetotellurics with a brief introduction to this theory. Here we will consider general geophysical problems.
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.