Geoscience Reference
In-Depth Information
conductivity σ g =10 5 s 1 , 10 6 s 1 , 10 7 s 1 (thin lines) and perfectly conducting
(thick line).
Two curves in the upper right corner of Fig. 8.8 show hodographs of
the 'ground' and 'magnetospheric' waves versus distance. In this example
T = 100 s and ground conductivity σ g =10 6 s 1 . The hodograph of the ground
wave is given in the 4-th quadrant, and the magnetospheric wave in the 2-nd.
Numbers along the curves mark the distance from the source in kilometers.
The radius connected to the origin of the coordinate system and a point on
the curves is ln A. Here A is the amplitude of the horizontal magnetic compo-
nent of the corresponding wave mode and the angle between the radius and
horizontal axis is a phase of the magnetic component.
The hodographs illustrate an interesting feature of both waves. Magne-
tospheric and ground waves propagate along the ground surface with oppo-
site phases. Hence, the total ground field is determined by the difference of
their intensities. In spite of the fact that the intensities of both waves increase
sharply with approach to the source, the intensity of the total field is roughly
double that of the incident wave with A = 1 for the high conductive ground.
Moreover, the intensity of the ground field at distances on the scale of
the skin depth is defined mainly by the magnetospheric wave. Values of d g
for low conductive ( σ g =10 5 s 1 ) , moderate σ g =10 6 s 1 and high conduc-
tive σ g =10 7 s 1 ground are marked by asterisks on the distance axis with
numbers 1 , 2 , 3 , respectively .
It can be seen that the dependence of the field on distance is mainly de-
termined by a ground conductivity. The same figure presents separately the
spatial distribution of a 'ground' G g (8.54) and 'magnetospheric' G m (8.54 )
wave for σ g =10 6 s 1 . In this case the 'ground' wave damps severely from
1000 km , i.e., from distances of the order of skin depth ( d g is marked by
asterisks on the distance axis) the field on the ground is formed by the 'mag-
netospheric' wave. At distances of more than d g , the least spatial gradients
will be found in the curve corresponding to conductivity σ g =10 5 s 1 . One
can say that at distances x
d g the total wave propagates along finitely
conductive ground as if it was a perfect conductor.
Figures. 8.9 and 8.10 depict the dependencies of the b x -component ampli-
tude on distance for dayside (Figure 8.9) and nightside (Fig. 8.10) ionospheric
conditions. In this example σ g =10 6 s 1 . A Gaussian source is chosen, as in
Figure 8.8. The values of the monochromatic source periods are indicated
near each curve. Comparing Fig. 8.9 and 8.10, it can be seen that the field
amplitude reaching the ground surface at night is smaller than daytime. This
is a result of the change of the reflection coecient: the magnetic field is re-
versed in the transition from day to night roughly from +1 to
1. It means
that the electric field is almost compensated at ionospheric levels by day
and is intensified at night. More precisely, for the chosen model the electric
field in the ionosphere is E
1 . 5mV/m at
night ( T = 100 s ) at the 1 nT amplitude in the incident beam. Going to the
ionospheric currents, we obtain that the currents generated by an Alfven wave
0 . 1 mV/m at daytime and E
Search WWH ::




Custom Search