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0
a
c
h
2rH
h
ıJ
i
:
ıB
D
(6.109)
Taking into account that the power spectrum of the magnetic noise is proportional
to ıB
2
and replacing
h
ıJ
i
2
by the spectral density of random current fluctuation
F .f / yields
0
a
c
h
2rH
2
‰
.B/
.r;f /
F .f /;
(6.110)
where f
D
!=.2/.
The background atmospheric currents mainly depend on the air conductivity
which, in turn, is subject to violent changes from the action of the winds, precip-
itations, air humidity, pressure and temperature and etc. Thus, there may be many
causes of the background conductivity and current fluctuations. This means that
there may be the same mechanisms, which lead to the flicker-noise spectral density.
Substituting Eq. (
6.103
)forF .!/ and Eq. (
6.91
)for
c
.f / into Eq. (
6.110
), we
finally obtain the rough estimate of the power spectrum
0
aV
a
h
2rH
2
m
K
h
ıJ
i
‰
.B/
.r;f /
:
(6.111)
f
nC2
When h
H, the above equation coincides with the result obtained by Surkov and
Hayakawa (
2007
) to an accuracy of factor 2.
On the basis of the assumption that the ULF atmospheric background current
fluctuations exhibit a power law noise with the spectral index n we have found that
the power spectra of magnetic noise must vary on overall inversely proportional
to f
nC2
. It is interesting to note that if n is close to unity, then the magnetic
noise power spectra vary as f
3
, which is totally compatible with the measured
dependence in the frequency range of 5
10
4
to 5
10
2
Hz (Lanzerotti et al.
1990
).
The theoretical line calculated from Eq. (
6.111
) approximately coincides with
line 3 shown in Fig.
6.14
that is lower, but nearly parallel to the experimental
data shown with line 1. It should be noted that we have considered only a single
atmospheric inhomogeneity as the source of the electromagnetic noise. Meanwhile,
the worldwide thunderstorms, whirlwinds, or hurricanes, which are in progress
around the world at any time, may contribute to the net electromagnetic nose.
Before leaving this section, it should be noted that the ULF electric field noise in
the atmosphere due to background current variations is estimated to be of the order
of 20-0.7 V=.mHz
1=2
/ (Surkov and Hayakawa
2007
). Such electric variations are
practically undetectable since its amplitude lies below the actual electric noise level.
This leads us to the conclusion that the atmospheric electric noise must arise due to
another causes.
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