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v
o
h
2
hf
4
π
i
E
x
(
y
)
E
x
E
x
(
y
)[
S
1
(
y
)
S
1
]
dy
=
E
x
(
y
)
−
=
−
(
|
y
| −
v
)
2
−
v
v
h
2
f
2
E
x
(
y
)[
S
1
(
y
)
S
1
]
dy
,
=−
Z
N
−
π
(
|
y
| −
v
)
2
−
v
v
h
2
f
2
H
y
(
y
)
E
x
(
y
)[
S
1
(
y
)
S
1
]
dy
,
=−
−
.
(7
57)
π
(
|
y
| −
v
)
2
−
v
v
2
h
2
hf
4
E
x
(
y
)[
S
1
(
y
)
S
1
]
dy
H
z
(
y
)
=−
−
π
(
|
y
| −
v
)
3
−
v
v
2
h
2
f
2
Z
N
E
x
(
y
)[
S
1
(
y
)
S
1
]
dy
,
=−
−
i
o
π
(
|
y
| −
v
)
3
−
v
whence
E
x
(
y
)
H
y
(
y
)
=
Z
N
a
(7
.
58)
H
z
dH
y
dy
−
i
o
=
Z
N
.
b
Equation (7.58a) means that the Leontovich condition (Leontovich, 1948) is sat-
isfied in the far zone
The ratio between
E
x
and
H
y
equals the
normal impedance
Z
N
no matter how strong the magnetotelluric anomalies are. Here
the longitudinal impedance
Z
, defined by magnetotelluric ratio
E
x
/
|
y
| −
v
>>
h
eff
.
H
y
, coincides
with the normal impedance
Z
N
:
Z
N
H
y
(
y
)
Z
N
H
y
(
y
)
E
x
(
y
)
E
x
(
y
)
+
E
x
(
y
)
H
y
(
y
)
=
+
Z
(
y
)
=
(
y
)
=
=
Z
N
.
(7
.
59)
H
y
(
y
)
+
H
y
H
y
(
y
)
+
H
y
(
y
)
Equation (7.58b) suggests that along with estimation (7.59), we can estimate
Z
N
using the magnetovariational ratio (1.3). Taking into account that
H
y
y
=
0, we
write
H
z
dH
y
dy
H
z
H
z
dH
y
dy
−
i
o
=−
i
o
=−
i
o
=
Z
N
.
(7
.
60)
dH
y
dy
dH
y
dy
+
Note that (7.60) is valid for a field with quadratic spatial variation of
H
y
, while
(7.59) is valid for a field with linear spatial variation of
H
y
(Weidelt, 1978; Dmitriev
