Chapter 7: Transformations
Published:January 01, 2002
7.1 CONVERSION OF IMPEDANCE TO A FORM USEFUL FOR INTERPRETATION
The difficulty in interpreting MT data consists of the fact that the inverse magnetotelluric problem is ill-posed, and its operator cannot be written in a closed form. Therefore, the basic method of interpretation is iterative optimization using regularizing operators. The optimization is carried out within the class of parametric solutions forming an interpretation model. This model is conceived from a priori concepts about the geology of the area under study and the physical properties of the rocks, as well as from the results of magnetotelluric observations. Thus, it is important to present the results of the magnetotelluric observations in a form that is convenient for direct geoelectric evaluations and conclusions. The frequency curve for the impedance (or the admittance) does not meet this need, since it is not particularly expressive and gives only a rough qualitative picture. However, a considerable improvement can be made by transformations using reasonably simple continuous operators. The transformed magnetotelluric data are expressed in geoelectric terms, such as “resistivity,” “conductivity,” and “depth.” The analysis of these data helps us to determine the type of geoelectric structure, to construct an interpretation model, and to evaluate some of its parameters.
In this chapter, we will describe several interesting impedance and admittance transformations that are used more or less widely in magnetotelluric practice. Before developing these transformations, we would like to gain a better insight into the skin effect in layered media.
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.