1500 km the amplitude and phase of
the attenuation function were calculated for the cases of various path
orientation relative to the geomagnetic field vector, properties of the
underlying surface, and location and geometric dimensions of the irregularity
( ap,
bp, and
zp ).
|
Figure 3
|
|
Figure 4
|
[24] Figures 3 and 4 show the amplitudes and phases of the attenuation
function for the nighttime period. The distance from the source to the
receiver in kilometers is shown at the
x axis.
The underlying surface is wet
soil with a relative dielectric permeability of
em=20 and conductivity of
s=0.01 S m-1.
The radio wave propagation direction is chosen along the
south-north line (the azimuth is
Az=0 ). The following parameters of the
irregularity are chosen:
ap=bp=20 km and
zp=20 km. In Figure 3 the
irregularity is put directly over the signal propagation path ( yp=0 )
in the
region of the minimum of the attenuation function amplitude at the regular
path ( xp=800 km).
At such choice of the coordinates, the effects related
to the presence of the irregularity are best pronounced. It is demonstrated in
Figure 4.
[25] No graphs of the amplitude and phase of the attenuation function for
the daytime are presented in the paper.
Soloviev and Hayakawa [2002]
showed that such irregularities weakly distort the field in the daytime
Earth-ionosphere waveguide. Moreover, the sprites modeled here are observed
mainly at night.
[26] Below we consider the amplitude deviations: the difference in the
attenuation function amplitude values in the undisturbed and disturbed by a
three-dimensional irregularity cases. There exists an influence of the
irregularity on the behavior of the attenuation function phase, but it is less
important than the influence on the amplitude behavior. Since the graphs
showing the phase changes are not such visual as the graphs showing the
amplitude changes, the former are not presented.
|
Figure 5
|
[27] Figure 5 shows the curves of amplitude disturbances corresponding
to the cases when the geomagnetic field is and is not taken into account.
The curves differ considerably from each other, so one may conclude that
taking into account of the magnetic field is important. One can see in Figure 5
and the following figures the presence of not only forward scattering but
backscattering as well.
|
Figure 6
|
|
Figure 7
|
[28] The perturbations in the attenuation function amplitude illustrating
the influence of the irregularity on the field as a function of the propagation
direction relative the magnetic azimuth of the path are shown in Figures 6
and 7. The strongest difference is seen between the field behavior at the
paths with the azimuth
Az=90o and
Az=-90o,
the former and the latter
azimuths corresponding to the eastward and westward propagation,
respectively. The change of the wave propagation direction to the opposite
one ( Az=45o and
Az=225o )
is shown in Figure 7. It is worth noting that
the presence of the irregularity influences these paths in a different way.
|
Figure 8
|
|
Figure 9
|
|
Figure 10
|
[29] Figures 8, 9, and 10 show the influence of the geometric dimensions
of the irregularity on the attenuation function amplitude. Figure 8 shows
curves corresponding to various values of the semiaxes of the cylinder base
of the irregularity. The large and small semiaxes of ellipse are taken to be
equal ( ap=bp ) and to have values of 10 km, 20 km, and 40 km. It is
worth noting that a change of the radius of the cylinder base by a factor of 2
leads to a change in the maximum disturbance in the attenuation function
amplitude approximately by the same factor.
[30] The influence of the cylinder height is shown in Figure 9. The
values of the impedances of the base and sidewall of the cylinder stayed
fixed. The comparison of the changes caused by the irregularity in the form
of a cylinder with impedance of the base
dp=0.5(1+i)10-2 and by the
irregularity of a "spot" type with impedance
dp=(2.38 -i
0.34)10-2 (obtained by recalculation to the waveguide height by the method described
above) is shown in Figure 10. Comparing the curves one can conclude that
taking into account of the possibility of a descent (assent) of the local region
of the waveguide upper wall relative to the level of the regular ionosphere
plays an important role in the study of the irregularity impact on radio wave
propagation.
|
Figure 11
|
[31] Figure 11 illustrates the fact that the influence of the irregularity on
the field in the waveguide depends also on the location of the irregularity
relative to the radio wave propagation path. Figure 11 shows the curves
corresponding to the distance of the cylinder axis from the path line equal to
yp = 0,
yp = 20,
and
yp = 50 km for
ap=bp=20 km and
xp=800 km. At
relatively short distances between the irregularity and path (~50 km), a
decrease of the maximum disturbance in the attenuation function amplitude
by a factor of more than 10 is observed. It should be noted here that for the
considered path, one can estimate the distance by the lateral dimension of
the first Fresnel's zone, the small semiaxes of the latter being ~53 km.
|
Figure 12
|
[32] The position of the observer influences considerably the estimate of
the changes caused by the presence of the irregularity. A shift in the
coordinates of the observational point actually corresponds to a shift in the
irregularity location along and across the radio wave propagation path. The
same shift in the direction lateral to the path would cause much stronger
changes in the irregularity impact than a shift along the path. This
dependence is shown in Figure 12.
|
Figure 13
|
[33] The influence of the underlying surface properties is shown in Figure 13.
The curves are shown corresponding to the following underlying
surfaces: wet soil
( em=20,
s = 0.01 S m-1 )
and seawater
( em=81,
s = 4 S m-1 ).
Figure 13 shows the graph calculated at the value of the
propagation path magnetic azimuth
Az=0.
It is worth noting that stronger
influence of the irregularity is observed if a sea is the underlying surface than
if waves propagate over a land. At other orientation of the wave
propagation path, the character of the amplitude perturbations is the same.
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