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Along with the impedance tensor [
Z
] we can introduce its inverse
[
Z
]
−
1
[
Y
]
=
,
(1
.
18)
which is the
admittance tensor
transforming the horizontal electric field
E
into the
horizontal magnetic field
H
=
[
Y
]
E
.
In the matrix form
Y
xx
Y
xy
=
,
.
[
Y
]
(1
19)
Y
yx
Y
yy
where
Z
yy
Z
xx
Z
yy
−
Z
xy
Z
xx
Z
yy
−
Y
xx
=
Z
xy
Z
yx
,
Y
xy
=−
Z
xy
Z
yx
,
Z
yx
Z
xx
Z
yy
−
Z
xx
Z
xx
Z
yy
−
Y
yx
=−
Z
xy
Z
yx
,
Y
yy
=
Z
xy
Z
yx
,
and
H
x
=
Y
xx
E
x
+
Y
xy
E
y
,
H
y
=
Y
yx
E
x
+
Y
yy
E
y
.
The impedance and admittance tensors carry the same information about the geo-
electric structure of the Earth, and from this point of view, it makes no difference
which of them is used as fundamental. Cagniard chose the impedance and appar-
ent resistivity, and this suited geophysicists who got accustomed to the apparent
resistivity measured with the DC vertical sounding method. There is little point in
abandoning this tradition, though we have to realize that the layered Earth consti-
tutes a system consisting of parallel-connected conductors (the Earth's layers), and
the most natural way of characterizing such a system would seem to be as an admit-
tance, and therefore, as an apparent conductivity. It is not an accident that in many
magnetotelluric problems, it is easier to deal with the admittance (Berdichevsky
and Dmitriev, 2002). Consider, for instance, a one-dimensional model where the
admittance constitutes the weighted complex conductance :
∞
0
z
i
0
Y
(
z
)
dz
=
.
Y
(
z
)
e
dz
0
In concluding we note that model under consideration offers the linear relation-
ships between the electric fields measured at different sites of the Earth's surface.
Let us consider horizontal electric fields
E
at two sites: at an observation site and
at a base (reference) site B. According to (1.13)
