Geoscience Reference
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τ gr and
τ if are the observed and ionosphere free group delays. The constituent
where
α
is given by
N e ds 2
40
.
31
40
.
31
α =
N e ds 1
=
(
STEC 1
STEC 2 ) .
(79)
c
c
The speed of light c is used for conversion to time delay, s 1 and s 2 are the paths
of wave propagation from the source to the first and second station of the radio inter-
ferometer. This means that VLBI is only sensitive to differences in the ionospheric
conditions. By neglecting higher order ionospheric terms as supported by Hawarey
et al. ( 2005 ) the linearity of Eq. 78 makes it possible to eliminate ionospheric influ-
ences when measurements are carried out at two separated frequency bands.
Ionosphere Free Linear Combination
Nowadays any geodetic VLBI experiment is carried out at two distinct frequency
bands in order to correct for ionospheric influences. Taking the standard bands
(X- and S-band) for such experiments gives two group delay observable, each of
them containing the ionospheric free delay
τ if (which will be the input for any
precise geodetic analysis) and a contribution
α
from the ionosphere, scaled by the
corresponding effective ionosphere frequencies.
f gx ,
τ gx = τ if +
f gs .
τ gs = τ if +
(80)
Here the first letter in the indices stands for group or phase delay and the second
letter represents X- or S-band. Using these equations the unknown parameter
can
be eliminated and the ionospheric free delay observable can be obtained. This is
carried out by a simple linear combination between two of the expressions, given in
Eq. 80 . Considering group delay measurements
α
f gx
f gx
f gs
f gx
τ if =
f gs τ gx
f gs τ gs .
(81)
The right part of Eq. 81 can be considered as the observable, from which all geodetic
target parameter can be determined. Instead of computing the ionosphere-free linear
combination Eq. 81 , one can also compute the ionospheric contribution in X-band
f gs
f gx
f gx =−
τ igx =
f gs gx τ gs ),
(82)
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