Geoscience Reference
In-Depth Information
10
7
s
−1
σ
g
=1
×
(1+i)/d
(n)
d
(n)
= c(2
k
n
=
0.01
πσ
(n)
)
−
1/2
ω
0.008
10
6
s
−1
10
6
s
−1
3
×
1
×
=10
5
, 10
6
, 10
7
s
−1
σ
k
10
6
s
−1
k
3
0.006
2
×
10
5
s
−1
5
×
0.004
10
4
s
−1
10
5
s
−1
3
×
1
×
0.002
k
2
k
1
0
−5
0
5
10
15
x 10
−3
Re
k
Fig. 8.6.
The plot of the root
k
(1)
S
versus ground conductivity obtained by a
numerical solution of (8.36) for the 100 s wave period and the Pedersen conductivity
Σ
P
=0
.
116
×
10
9
km/s
Electric Mode
It has been shown in Chapter 7 that, far from cuts
Γ
m
and
Γ
g
(see Fig. 8.1),
function
X
sin
I
∆
A
≈−
=const
,
i.e. all singularities of an electric mode are located close to cuts
Γ
m
and
Γ
g
.
Analysis carried out in Appendix 8.C demonstrates that the damping
coecients of these waves, except the basic one, are greater than
h
−
1
(
h
is the
thickness of the atmosphere) and increase in proportion to the mode number.
The expression for the basic mode
κ
(0)
(type TEM-wave in the terminology
adopted in waveguide theory) for
√
ε
g
>>
{
X, Y
}
and
k
0
hX
1
,
is
√
β
h
k
(0)
=exp
iπ
4
β
=
k
0
hε
a
sin
2
I
X
,
,
(8.39)
where
I
is the inclination of the geomagnetic field,
ε
a
is atmospheric dielectric
permeability,
h
is the atmosphere thickness (in km).
β
can be estimated for
the typical values of the ionospheric conductivities (see Table 7.1) as
10
−
7
T
−
1
10
−
5
T
−
1
day,
night,
β
∝
where
T
is the period of the wave (in s).
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