Geoscience Reference
In-Depth Information
conducting sides of the Earth-Ionosphere cavity. Furthermore, some electromag-
netic energy can penetrate through the conductive E-layer thereby exciting the shear
and magnetosonic Alfvén waves which are radiated into the magnetosphere.
Let Q be the quality/energy-factor, which is defined as
f
max
f
;
Q
D
(4.27)
where f
max
is the central frequency corresponding to the local maximum/resonance
of power spectrum and f is its full width at semi-height/half of the maximum.
The Q-factor can be defined as
e
T
D
N
e
;
Q
D
(4.28)
where
e
is the relaxation time or the time which is necessary to decrease the
amplitude of damping oscillation by the factor e (base of natural logarithm), T is the
period of damping oscillations, and N
e
denotes the number of wave periods keeping
within a relaxation time. Furthermore, the Q-factor is inversely proportional to
energy dissipation for a period of oscillations. Typical values of the Q-factors for
various Schumann resonances observed at mid-latitudes are as follows: Q
1
D
4:6,
Q
2
D
6:0, Q
3
D
6:6, Q
4
D
6:8, and Q
5
D
7:0 (e.g., see Bliokh et al. (
1980
)).
For the fundamental mode .n
D
1/ the relaxation time
e
D
Q
1
=.f
1
/
0:2 s.
On average approximately 10
2
strokes per second occur worldwide due to the global
lightning activity, and thus within 0:2 s of damping interval of the fundamental mode
about 20 lightnings may occur. The vast majority of individual lightning strokes
are randomly distributed in time, so that their electromagnetic fields are added
incoherently thereby producing quasi-permanent excitation of the normal modes
in the Earth-Ionosphere cavity.
In a more complete theory complications due to the field attenuation in
conducting layers of the ionosphere and of the Earth may be included. Numerical
modeling permits of fitting adequately the theoretical and experimental values of
both the eigenfrequencies and Q-factors.
4.2.3
Solution of the Problem in a More Accurate Model
Before leaving this section, it is useful to revise the solution of the problem
derived above in order to take into account the effect of wave damping. Substituting
Eq. (
4.19
)forU into Eqs. (
4.6
) and (
4.7
) yields
C
n
n
C
@
P
n
.cos /;
X
0
m.!/
2R
e
1
2
B
'
D
(4.29)
n
D
1
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