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Chapter 1
The Magnetotelluric Response Functions
1.1 On the Deterministic Nature of the Impedadance Tensor
At the heart of the magnetotelluric sounding is a one-dimensional model named
after Tikhonov and Cagniard. The Tikhonov-Cagniard model is very simple
(Tikhonov, 1950; Cagniard, 1953). A plane vertically incident monochromatic elec-
tromagnetic wave illuminates the plane Earth consisting of homogeneous isotropic
layers with horizontal boundaries. Introduce a standard reference frame with hori-
zontal axes x
y directed northwards and eastwards respectively, and vertical axis
z directed downwards. On the Earth's surface
,
0
H =
Z 01
H ,
Z
E =
(1
.
1)
Z 0
10
where
E x
E y
H x
H y
E =
,
H =
are the horizontal components of the magnetotelluric field and Z is the scalar
complex-valued Tikhonov-Cagniard impedance . In expanded form
E x
H y =−
E y
H x .
E x =
ZH y ,
E y =−
ZH x ,
=
.
Z
(1
2)
Here the complex electric and magnetic vectors, E
and H , are linearly polarized
in the mutually perpendicular directions.
The rotationally invariant impedance Z is a functional of the Earth's resistiv-
ity
. The reciprocals of Z and
are the admittance Y
=
1
/
Z and the conductiv-
ity
=
1
/
. The inverse MTS problem reduces to reconstruction of
( z )or
( z )
=
,
from the parametric dependence of the impedance Z(z
0
) or the admittance
=
,
Y(z
0
) upon the frequency
.
 
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