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In-Depth Information
3. Find a distribution
ρ
(
s
) within the class
C
ρ
with minimal difference be-
tween theoretical and experimental FLR-frequencies using a fitting proce-
dure.
ULF-Magnetospheric Diagnostics
Below, we describe a technique to determine experimentally the necessary pa-
rameters of the ULF-structure. It follows from (8.26) that upon transmission
through the ionosphere, the width
δ
of the resonance peak, as observed on the
ground, is increased compared to its value above the ionosphere,
δ
i
, namely
δ
=
δ
i
+
h
, where
h
is the height of the ionospheric
E
-layer. We rewrite (8.26)
for the amplitude and phase characteristics of the magnetic
H
-component at
the ground in the form
H
(
x, f
)=
b
R
(
f
)
1
iζ
,
(11.3)
−
where
ζ
=(
x
x
r
)
/δ
denotes the normalized distance from the FLR-point
x
R
(
f
).
b
R
(
f
) is the amplitude of the pulsations at the FLR-point, and
x
is the
coordinate of a magnetic shell, as measured along the geomagnetic meridian.
A principal problem of the experimental determination of FLR-parameters
is that in most events the input into the ULF-spectral content from the reso-
nant magnetospheric response and the one from the 'source' are comparable.
So in most cases, a spectral peak does not necessarily correspond to a local
resonant frequency, and the width of a spectral peak cannot be directly used
to determine the Q-factor of the FLR. This ambiguity can be resolved with the
help of the experimental methods listed below and in particular the gradient
method.
−
Gradient Method
Using precise measurements of the gradients of spectral amplitude and phase
along a small baseline, one can exclude the influence of the source spectrum
and reveal the relatively weak resonant effects. The following simple relation-
ships, stemming from the properties of function (11.3), describe the specific
features of the ratio
G
(
f
) between amplitude spectra and the difference of
phase spectra
∆ψ
(
f
) of magnetic
H
-components, recorded at points
x
1
and
x
2
(
∆x
=
x
1
−
x
2
>
0):
=
1+
ζ
2
1+
ζ
1
1
/
2
G
(
f
)=
|
H
(
x
1
,f
)
|
,
(11.4)
|
H
(
x
2
,f
)
|
∆ψ
(
f
) = arctan
ζ
2
−
.
ζ
1
1+
ζ
1
ζ
2
(11.5)
The typical features of functions (11.4), (11.5), schematically shown in
Fig. 11.1, are
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