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5.1.4 Final Remarks on the Generalized Impedance Tensor
For many years the magnetotelluric theory defines the impedance of the Earth at two
model levels: (1) the scalar impedance of the horizontally homogeneous medium
excited by a field with linearly varying horizontal components (the Tikhonov-
Cagniard impedance), and (2) the tensor impedance of the horizontally inhomo-
geneous medium excited by a plane wave. The generalized model includes both the
levels and supplements them with a third level, namely, with the tensor impedance
of the horizontally inhomogeneous medium excited by a electromagnetic field with
linearly varying horizontal components and a vertical magnetic component. Appli-
cation of this model can considerably extend the capabilities of magnetotellurics in
zones that are unfavorable for plane-wave approximation of the normal field, say, in
the auroral zones.
Let the normal field consist of three independent modes (two plane-wave modes
and a source-field mode with vertical magnetic component). Hence, we determine 6
components of the generalized impedance tensor. The question is how to solve the
inverse problem using all six components. We can suggest two different approaches
to this problem.
1. Immediate inversion of the generalized impedance tensor. Given a resistivity
model, determine electromagnetic fields excited by each mode of the normal field
and calculate the components of the generalized impedance tensor. Solution of the
inverse problem reduces to the regularized iterative minimization of the misfits of
the generalized impedance tensor.
2. Solution of the inverse problem consists of three stages: (1) synthesis of
the plane-wave magnetotelluric fields from the generalized impedance tensors, (2)
reconstruction of the basic impedance tensor, [
Z
], and the tipper matrix, [
W
], (3)
inversion of [
Z
] and [
W
] using standard methods.
5.2 Synthesis of the Magnetotelluric Field
A common set of magnetotelluric and magnetovariational data usually consists of
the impedance and tipper matrices obtained on the network of autonomous field
stations. We can pave the new ways to the qualitative and quantitative interpretation
of MT and MV data by converting autonomous impedances and tippers into the
synthetic magnetic field and computing the horizontal magnetic tensors that are
slightly subjected to the low-frequency distortions caused by the near-surface local
inhomogeneities and provide sufficiently high sensitivity to the regional structures
(Barashkov, 1986; Dmitriev and Kruglov, 1995, 1996; Dmitriev and Mershchikova,
2002).
We will consider the following conversions:
1. Synthesis of the synchronous magnetic field from the impedance tensors.
2. Synthesis of the synchronous magnetic field from the Wiese-Parkinson matrices.
3. Synthesis of the synchronous magnetic field from the generalized impedance
tensors.
