Geoscience Reference
In-Depth Information
the waves incident on and backscattered from the radar range
r
i
(upgoing and downgoing
waves, respectively). In addition,
κ
i
is a random variable related to the radar cross section
(RCS) of the scatterers at the range
r
i
(e.g., randomly moving ionospheric electrons).
We now consider an
x
polarized radar antenna transmitting
k
×
k
×
x
p
1
=
(73)
k
×
k
×
x
|
|
polarized waves field in
k
direction. On reception, the same antenna would be co-polarized
with incoming fields of identical polarization direction
p
1
.
For an orthogonal
y
polarized
antenna
k
×
k
×
y
p
2
=
(74)
k
×
k
×
y
|
|
would be the polarization direction of co-polarized fields. Let's assume that these two
antennas, located at the geomagnetic equator, scan the ionosphere from north to south to
construct power maps of the backscattered signals. In every pointing direction, narrow pulses
are transmitted so that range filtering effects (due to the convolution of the pulse shape with
the response of the ionosphere) can be ignored. In transmission, only the first antenna (
x
polarized) is excited, while, in reception, both antennas are used to collect the backscattered
signals. The two antennas then provide us with co- and cross-polarized output voltages
k
)
∝
κ
i
p
1
Π
i
p
1
k
)
∝
κ
i
p
2
Π
i
p
1
,
v
1
(
and
v
2
(
(75)
sampled at each range
r
i
, where the two-way propagator matrix
Π
i
(defined above) is
dependent on the electron density and magnetic field values along
k
up to the radar range
r
i
.As
κ
i
is a random variable, the statistics of voltages (75) would be needed to characterize
the scattering targets. For instance, the mean square values of
v
1
and
v
2
can be modeled as
2
2
|
v
1
|
∝
σ
v
Γ
1
and
|
v
2
|
∝
σ
v
Γ
2
,
(76)
2
where
is the volumetric RCS of the medium, which is dependent on the electron
density, temperature ratio, and magnetic aspect angle at any given range. In addition,
σ
v
=
|
κ
i
|
Γ
1
and
Γ
2
are polarization coefficients defined as
p
1
Π
i
p
1
p
2
Π
i
p
1
2
2
Γ
1
=
Γ
2
=
and
.
(77)
To simulate radar voltages using the model described above, an ionosphere with the electron
density and
T
e
/
T
i
profiles displayed in Figure 14 was considered. In addition, the magnetic
field was computed using the International Geomagnetic Reference Field (IGRF) model (e.g.,
Olsen et al., 2000). Finally, the simulations were performed for a 50 MHz radar at the location
of the Jicamarca ISR in Peru and antenna polarizations
x
and
y
were taken to point in SE and
NE directions as at Jicamarca.
Let us first analyze magnetoionic propagation effects on the simulated radar voltages,
disregarding scattering effects.
Γ
2
are
displayed in Figure 15 as functions of distance and altitude from the radar (in the plots,
the positive horizontal axis is directed north).
For this purpose, polarization coefficients
Γ
1
and
Note that, at low altitudes, where there is
