Geoscience Reference
In-Depth Information
Fig. 2
Typical channel distribution of a geodetic VLBI experiment (the video channel bandwidth
is not to scale) (modified from Hobiger (
2005
))
source which is observed for a certain amount of time in order to cross-correlate
the signals. Thereby, so-called fringe phases are the main observables which can
be either used for radio astronomical or geodetical purposes. Most of the geodetic
experiments are using several video channels per frequency band (see Fig.
2
) in order
to derive a group delay measurement from the slope of the fringe phases across the
covered band.
Thus, other than GNSS which operates with a single carrier, VLBI derived group
delays are not assigned to a reference frequency that is actually observed. In a process,
called band-width synthesis, phase and group delays are obtainedwithin the so-called
fringe fitting procedure by finding the values which maximize the delay resolution
function. It can be shown (see e.g. Sekido
2001
) that bandwidth synthesis, which
takes advantage from Fourier operations, is equivalent to a least squares solution if
the correlation amplitude
ρ
i
of each channel
i
corresponds to the weight of the phase
observable. Thus, one can derive an analytical expression for the so-called effective
frequency to which ionosphere group delays can be assigned to. As discussed e.g. in
Hobiger (
2005
) one can express this frequency as
2
N
N
N
2
1
ρ
i
·
1
ρ
i
(
f
i
−
f
0
)
−
1
ρ
i
(
f
i
−
f
0
)
i
=
i
=
i
=
f
gr
=
,
(77)
N
N
N
N
ρ
i
f
i
−
f
i
−
f
0
1
ρ
i
(
f
i
−
f
0
)
·
1
ρ
i
·
1
ρ
i
f
i
i
=
i
=
1
i
=
i
=
where
f
0
is a reference sky frequency and
f
i
is the reference frequency of each chan-
nel from which fringe phases are obtained. Equation
77
provide the theoretical basis
for the treatment of multi-band delays and their ionospheric contributions in the same
way as it would be done for single frequency observations. Instead of the observing
frequency the effective ionosphere frequency, computed from the frequency distrib-
ution has to be taken to express the ionospheric contribution (measured in TECU) to
units of time. The equation reads:
f
gr
,
τ
gr
=
τ
if
+
(78)