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In-Depth Information
,
J
1
J
3
o
S
1
h
2
≈
(1
.
49)
where
J
1
and
J
3
are currents induced in the upper layer and in the conductive base-
ment (Berdichevsky and Dmitriev, 2002).
More detailed consideration of the one-dimensional model can be found in the
basic works by Weidelt (1972, 1978) and Weidelt and Kaikkonen (1994) as well
as in the topics by Kaufman and Keller (1981), Whittall and Oldenburg (1992) and
Berdichevsky and Dmitriev (2002).
1.3.2 The Two-Dimensional Impedance Tensor
In the 2D-model the conductivity varies along the vertical axis
z
and one of the
horizontal axes,
x
or
y
, perpendicular to the model strike. The magnetotelluric
field splits into two independent modes: (1) the
TM-mode
(transverse magnetic
mode - the magnetic field is transverse to vertical direction), and (2) the
TE-mode
(transverse electric mode - the electric field is transverse to vertical direction). The
TM- and TE-modes are frequently referred to as the
H-polarization
(the magnetic
field is polarized along the model strike) and the
E
-
polarization
(the electric field is
polarized along the model strike).
Let the
x
-axis run along the strike. Then the TM-mode is presented by compo-
nents
E
y
,
E
z
,
H
x
, where
H
x
obeys the equation
1
grad H
x
di
v
+
i
o
H
x
=
0
(1
.
50)
and
1
H
x
1
H
x
E
y
=
z
,
E
z
=−
,
(1
.
51)
y
while the TE-mode is presented by components
E
x
,
H
y
,
H
z
, where
E
x
obeys the
equation
di
v
grad E
x
+
i
o
E
x
=
E
x
+
i
o
E
x
=
0
(1
.
52)
and
o
1
E
x
o
1
E
x
H
y
=
z
,
H
z
=−
.
(1
.
53)
i
i
y
It is common for the magnetotelluric theory to ignore galvanic coupling between
the ionosphere and the Earth and accept that the electric conductivity of the air
is zero (Berdichevsky and Dmitriev, 2002). If this is the case, we assume that
