Geoscience Reference
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Replace the exact expressions for
R
(
k
) (7.108) and
T
(
k
) (7.105) in (8.6)
by approximate
R
(0)
(
k
) (7.124) and
T
(0)
(
k
) (7.125). With such replacement
we get a good approximation for the magnetic mode on the ground. As for
the transmitted electric mode, its computation must be conducted by exact
formulae for
T
(
k
), which is necessary to define the field at the large distances.
The reflected electric and magnetic fields above the ionosphere are then
(
k
)exp
ikx
k
A
−
dk
+
2
π
E
(
r
)
SS
b
(
r
)
zS
=
k
0
h
k
b
(
i
)
S
−
Φ
2
S
,
1
√
2
π
k
0
h
i∂/∂ x
−
(8.7)
k
2
Γ
1
+
2
π
b
(
r
)
SS
b
(
r
)
SA
=
b
(
i
)
,
Φ
1
S
S
0
(8.8)
Y
sin
I/ XΦ
1
A
−
+
2
π
b
(
r
)
AS
b
(
r
)
AA
=
0
,
k
A
Y
X
sign
IΦ
2
S
(8.9)
R
(0)
AA
b
(
i
A
Y/XΦ
2
A
|
sin
I
|
=
2
π
b
(
r
)
zA
E
(
r
)
SA
−
Φ
2
A
,
Y
sin
I
X
i∂/∂ x
k
0
h
(8.10)
where
X
=
X
+
√
ε
m
|
,
k
=
kh
,
x
=
x/h
,
h
is the height of the ionospheric
sin
I
|
thin conductive layer, and
k
A
−
exp
ikx
∆
(0)
SK
Φ
1(
A,S
)
Φ
2(
A,S
)
=
+
∞
k
2
(
A,S
)
k
dk,
b
(
i
)
1
−∞
+
∞
(
A,S
)
(
k
)
h
b
(
i
)
(
A,S
)
k
=
(
y,x
)
(
x,
+0) exp
ikx
dx.
1
√
2
π
b
(
i
)
b
(
i
)
=
−∞
Low indexes in the integrals denote either Alfven (
A
) or FMS-wave (
S
)
.
Similarly, the dependence of ground electric and magnetic fields on the
horizontal coordinate are given by
2
π
b
(
g
)
SS
E
(
g
)
SS
=
Φ
3
S
Φ
4
S
,
−
(8.11)
=
2
π
b
(
g
)
SA
E
(
g
)
SA
X
sin
I
Φ
3
A
,
Y
(8.12)
Φ
4
A
2
π
b
(
g
)
zS
b
(
g
)
zA
=
,
∂
∂ x
Φ
4
S
(
Y/X
)sin
IΦ
4
A
−
1
ik
0
h
(8.13)
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