P. Schmoldt, PhD - MTNet - DIAS

6. Using magnetotellurics to gain information about the Earth
estimators exhibit a breakdown point of zero, meaning that the smallest amount of erroneous
data may seriously bias the final estimate [Smirnov, 2003]. An approach with a
considerable higher breakdown point (ε ∗ = 50 %) was presented by Siegel [1982] using a
repeated median algorithm, and an application for MT processing has been developed by
Smirnov [2003]. Therein, the author uses a reduced M-estimator to supplement the initial
Siegel estimator approximation in order to enhance the performance for short time-series.
6.3. Deriving subsurface structure using
magnetotelluric data
Deriving the distribution of Earth properties and thereby enhancing knowledge about geological
processes is the aim of most geophysical investigations. In MT, the electric properties
of the Earth are studied, which are usually derived through an inversion of the dataset
(cf. Sec. 6.3.3). Overviews about general principles of inversion processes and related
theory are given, among others, by Aster et al. [2005]; Tarantola [2005]; their application
for MT problems was reviewed by Avdeev [2005]; Börner [2010]; Siripunvaraporn
[2010]. Here a condensed description of the parts relevant for MT inversion is given;
namely a characterisation of common forward modelling methods, followed by an illustration
of the basic inversion approach, and lastly an examination of the non-uniqueness
problem of MT inversion. Thereafter, different solvers for the MT inversion problem are
discussed and common inversion codes are presented. At first, however, the principles of
traditional analytical transformations are illustrated.
6.3.1. Analytical direct transformation
Analytical approaches aim to find mathematical relationships between MT response data
and the resistivity-depth distribution of the subsurface. The three most commonly used
relations for 1D MT transformation were derived by Niblett and Sayn-Wittgenstein [1960],
Bostick [1977], and Weidelt et al. [1980]. All approaches calculate the resistivity at the
so-called Niblett-Bostick depth δNB from a given apparent resistivity ρa and the magnetic
permeability µ0 at the related period, i.e.
δNB =
ρa(T)T
2πµ0
. (6.13)
The Niblett-Bostick depth is related to the skin depth δs as δs = √ 2δNB (cf. Sec. 3.3),
hence referring to a depth at which the amplitude of the wave F0 is reduced by a factor
e − 1 √ 2 (approximately F0/2):
114
F(δNB) = F0e −
πµ0
ρaT δNB
= F0e − 1 √
2 . (6.14)