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In-Depth Information
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
.