P. Schmoldt, PhD - MTNet - DIAS

6.3. Deriving subsurface structure using magnetotelluric data
Analytical direct transformations can provide a first insight to the subsurface structures
and their results can be used to create a starting model for subsequent inversion. Moreover,
depth estimations from analytical transformations are also commonly used during
processing of MT data, e.g. strike estimation (Sec. 9.6.1).
Niblett-Bostick transformation
The so-called Niblett-Bostick transformation refers to the two independently-developed
formulations by Niblett and Sayn-Wittgenstein [1960], and Bostick [1977]. Both equations
use apparent resistivity values ρa (or its inverse apparent conductivity σa) and its depthderivative
to derive a 1D resistivity-depth (or conductivity-depth) profile, i.e. Niblett and
Sayn-Wittgenstein [1960]:
and Bostick [1977]:
with
∂σa(T)
σNB(δNB) = σa(T) + δNB , (6.15)
m(T) =
∂δNB
1 + m(T)
ρNB(δNB) = ρa(T)
1 − m(T)
∂ log(ρa(T))
∂ log(T)
= T
ρa(T)
(6.16)
∂ρa(T)
, (6.17)
∂T
in where δNB is given in Equation 6.13. It was shown by Jones [1983b] that the transformation
by Niblett and Sayn-Wittgenstein and Bostick are equivalent. Jones [1983b]
further points out that an alternative expression of the Bostick resistivity at depth δNB can
be used, i.e.
π
ρW(δNB) = ρa(T) − 1 . (6.18)
2φ(T)
This formulation is related to the ‘appproximate phase’ [Weidelt et al., 1980] (next paragraph)
and uses phase φ(T) and apparent resistivity ρa(T) information at one period to
estimate the resistivity. The resistivity is derived directly without the extra step of calculating
the apparent resistivity gradient, which speeds up the calculation process; however,
the two formulations yield different resistivity estimates (i.e. ρW ρNB).
Schmucker and Weidelt transformation
Like the formulation in Equation 6.18, and unlike the approaches by Niblett and Sayn-
Wittgenstein and Bostick (Eqs. 6.15-6.16), the ρ ∗ − z ∗ transform [Schmucker, 1987] uses
phase information φ(T) and does not require prior calculation of the derivative. The transformation
calculates the resistivity for a depth z ∗ which is equivalent to the skindepth δs
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