Geoscience Reference
In-Depth Information
For the coecient transformation
R
SA
of Alfven wave into an FMS-wave,
(7.99) gives
2
Y
∆
sign
I.
The transmission coecient
T
SA
connects the magnetic fields on the ground
b
(
g
)
R
SA
=
κ
S
k
0
and in the ionosphere
b
(
i
y
:
x
b
(
g
x
=
T
SA
b
(
i
y
.
(12.36)
where (7.105) for
T
SA
gives
Y
g
ζ
3
2
Y
∆
sign
I.
Now we can find electric field
E
y
(
z
) in the ionosphere from the ground
magnetic field dividing (12.35) by (12.36), so that
E
y
(
z
)
b
(
g
)
T
SA
=
−
R
SA
T
SA
k
0
κ
S
=
−
exp(
iκ
S
z
)
(12.37)
x
Z
(
m
)
g
sinh(
kh
)
,
R
SA
T
SA
κ
S
k
0
i
k
0
k
=
−
cosh(
kh
)
−
(12.38)
where
h
=
σ
H
Σ
H
zdz.
Z
(
m
)
is the magnetic impedance on the ground surface.
Let
σ
g
= const and let a horizontal scale
k
−
1
g
less than 10
3
km. Then
impedance
Z
(
m
)
=
κ
g
/k
0
≈
ik/k
0
(see (7.28)) and
κ
S
≈
ik
. Equation (12.38)
g
becomes
R
SA
T
SA
kd
g
k
2
d
g
−
=
−
sinh(
kh
)
−
cosh(
kh
)
.
(12.39)
2
i
Hence the ratio of the electric field in the reflected Alfven wave to the ground
magnetic field is independent of the integral ionospheric conductivity. This
follows at once from the continuity of the tangential components of the electric
field in the thin ionospheric model.
Using (12.29), (12.33), (12.34) and (12.37), we find the relations between
Doppler velocity components and magnetic variation on the ground
z
0
R
SA
T
SA
V
2
b
(
g
)
i
ω
k
cos
I
B
0
∂µ
∂N
e
∂N
e
∂z
=
−
exp(
−
kz
)
dz ,
(12.40)
x
0
z
0
R
SA
T
SA
V
3
b
(
g
)
=
iω
exp(
iI
)
B
0
∂µ
∂N
e
N
e
exp(
−
kz
)
dz .
(12.41)
x
0
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