Geoscience Reference
In-Depth Information
5.1.6
Electromagnetic Field at the Atmosphere
and in the Ground
The spectrum of IAR normal modes is its inner property, which is independent of
source of the IAR excitation. Since the general IAR dispersion relation is of main
interest here, the source of the IAR excitation is of minor importance at this point.
In the next section some of the sources will be treated in detail and others in a more
sketchy fashion. For the present we assume that the IAR excitation is due to neutral
wind at the height of E-layer or due to the MHD waves coming from outer space,
since it seems conceptually simpler than the lightning discharge.
Although the conductivity of the atmosphere increases with altitude approxi-
mately as an exponential function with the characteristic scale
z
a
4-7 km (see, for
example, Eq. (
3.1
)), the plane slab model can be applied if the typical lateral sizes
of the source are much greater than both
z
a
and l, i.e., if k
?
l
1 and k
?
z
a
1.In
this approach the atmosphere and the ionosphere are considered as uniform media
in lateral dimension in such a way that the atmospheric conductivity can be char-
acterized via height-integrated conductivity †
a
10
3
1
(e.g., Cole and Pierce
1965
) similar to the height-integrated Pedersen and Hall conductivities (
5.25
)ofthe
ionosphere. In practice †
a
†
P
and †
a
†
H
so that in the first approximation
the neutral atmosphere .
d<
z
<0/ can be considered as an insulator. Neglecting
the displacement current
i!"
0
e
as well, the ULF electromagnetic perturbations in
the atmosphere obey Laplace equation
2
b
D
0:
r
(5.27)
The solid Earth (
z
<
d) is supposed to be a uniform conductor with a
constant conductivity
g
. The conduction current
g
e
in the ground is much
greater than the displacement one for all frequencies of interest here. This implies
that the electromagnetic perturbations in the conducting ground are described by
quasisteady Maxwell equation (
1.15
), which can be rewritten as follows:
2
b
; (5.28)
where
m
D
0
g
1
is the magnetic diffusion coefficient in the ground. The
electric field in the ground is described by an equation analogous to Eq. (
5.28
).
Since the atmosphere is considered as an insulator and there are no sources
of electromagnetic perturbations, the vertical electric current j
z
flowing from the
ionosphere into the atmosphere vanishes at the boundary between the ionosphere
and atmosphere. As shown in Appendix D, this leads to the condition that A
D
0
everywhere in the atmosphere. In this special case the magnetic variations in the
atmosphere is dependent only on the potential ‰. Although the TM mode can be
excited in the atmosphere by the other sources such as lightning discharges and in
this case the TM mode is described by both the potentials A and ǚ. We shall return
to this point later in the end of this section.
i!
b
D
m
r
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