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+
J
E2
x
J
H
y
J
E2
x
Z
N
J
H2
y
J
H1
y
J
E1
x
−
−
Z
xx
=
+
J
H2
x
J
H
y
,
1
+
J
H2
x
+
J
H1
y
J
H1
y
−
J
H1
x
Z
N
1
J
H
x
+
+
J
E1
x
J
H
x
J
E1
x
J
H2
x
J
E2
x
+
−
Z
xy
=
+
J
H2
x
J
H
y
,
1
+
J
H2
x
+
J
H1
y
J
H1
y
−
J
H1
x
Z
N
1
J
H
y
+
+
J
E2
y
J
H
y
J
E2
y
J
H1
y
J
E1
y
−
+
−
Z
yx
=
+
J
H2
x
J
H
y
,
1
+
J
H2
x
+
J
H1
y
J
H1
y
−
J
H1
x
+
J
E1
y
J
H
x
J
E1
y
Z
N
J
H1
x
J
H2
x
J
E2
y
+
−
+
J
H2
x
J
H
y
.
Z
yy
=
1
+
J
H2
x
+
J
H1
y
J
H1
y
−
J
H1
x
Thus, we have deduced the complex-valued
impedance tensor
[
Z
] that transforms
the horizontal magnetic field
H
into the horizontal electric field
E
:
E
=
[
Z
]
H
,
(1
.
15)
where
⎡
⎤
⎡
⎤
E
x
E
y
Z
xx
Z
xy
Z
yx
Z
yy
H
x
H
y
⎣
⎦
,
⎣
⎦
.
E
=
,
[
Z
]
=
H
=
The impedance tensor is functionally deterministic, being independent of the nor-
mal field intensity and polarization. It reflects the electrical structure of the Earth.
Now we can explain why the earliest magnetotelluric experiments were doomed
to failure. Applying the Tikhonov-Cagniard relations (1.1), (1.2) to the field
observed over the horizontally inhomogeneous Earth, we get a pseudoimpedance
⎧
⎨
E
x
H
y
=
H
x
H
y
Z
xy
+
Z
xx
Z
pseudo
=
⎩
E
y
H
x
=−
Z
yy
H
y
H
x
−
Z
yx
−
that depends on an arbitrary ratio between magnetic components. With unstable
field polarization,
Z
pseudo
may dramatically change.
The impedance tensor [
Z
] has a second-order square matrix with
Z
xx
,
Z
yy
on
the principal diagonal (on the “diagonal”) and
Z
xy
,
Z
yx
on the secondary diagonal
(on the “antidiagonal”). By virtue of (1.14) these response functions depend on the
normal impedance
Z
N
characterizing the one-dimensional layered background and
on the three-dimensional integrals
J
summing the effects of excess currents arising
within inhomogeneities. Clearly
Z
xx
,
Z
yx
carry the information on
vertical and horizontal variations in the Earth's conductivity. Note, however, that
the basic information on the vertical distribution of the conductivity is given by
Z
yy
and
Z
xy
,
