Geoscience Reference
In-Depth Information
40
35
30
25
20
η
15
10
5
ζ
0
0
0.02
0.04
0.06
0.08
0.1
η
,
ζ
Fig. 15.1.
Dependencies of
η
(
z
)and
ξ
(
z
) on the dimensionless height
z
=
z/
2
H
for
H
=10km
is proportional to the height distribution of currents which produce magnetic
perturbations (see the second equation in (15.15)).
As it is seen from Fig. 15.1, the current is localized within a layer of
thickness
l
=
l/
(2
H
)
1 at height
z
1
. If the dimensionless scale of the
wave
l
s
=
l
s
/
(2
H
)=
c
s
/
(2
Hω
)=
Ω
−
1
∼
is large in comparison with the
current layer thickness
l
∼
1, then it can be used instead of the real
thick current layer. As
l
1, the condition
l
Ω
−
1
∼
may be rewritten
Ω
1.
Let the plain
z
=
z
1
be a horizontal plane boundary between the at-
mosphere and ionosphere. The atmosphere is nonconductive (i.e.
η
(
z
)=0for
z<z
1
). Above the plane
z
=
z
1
the conductivity changes with a normalized
scale size of the order of 10. Then (15.15) becomes
∂
2
V
∂ z
2
−
2
∂V
∂ z
+
Ω
2
η
(
z
)
A
x
+
Ω
[
Ω
+
iη
(
z
)]
V
=0
,
∂
2
A
x
∂ z
2
=0
,
for
z>z
1
,
∂
2
V
∂ z
2
−
2
∂V
∂ z
+
Ω
2
V
=0
,
∂
2
A
x
∂ z
2
=0
for
z<z
1
.
(15.17)
As to the equation for
A
x
for the region ¯
z>z
1
,
it should be noted that
neglecting the terms
iΩζ
(
z
)
A
x
and
ζ
(
z
)
V
, we lose some effects such as the
excitation of upper ionospheric and magnetospheric resonances because their
influence on the thin layer currents are small and can be ignored in the esti-
mations of the induced ground magnetic fields.
Search WWH ::
Custom Search