Geoscience Reference
In-Depth Information
geodetic observations, specifically for Global Navigation Satellite Systems (GNSS)
and Very Long Baseline Interferometry (VLBI) observations. In particular, we sum-
marize existing models as well as strategies based on observations at two or more
frequencies to eliminate first and higher order delays. Finally, we review various
space geodetic techniques (including satellite altimetry and radio occultation data)
for estimating values and maps of TEC.
1 Group and Phase Velocity
The characteristic of an electromagnetic wave propagating in space is defined by
its frequency
f
and wavelength
. In a dispersive medium, the propagation veloc-
ity of an electromagnetic wave is dependent on its frequency. In such a medium
the propagation velocities of a sinusoidal wave and a wave group are different.
The propagation velocity of a sinusoidal wave with a uniform wavelength is called
the phase velocity
λ
ν
ph
, while the propagation velocity of the wave group is referred
to as group velocity
ν
gr
. Within the vacuum the phase and group velocities are the
same, but in the real conditions, this is not the case. Following Wells (
1974
)the
velocity of phase is
ν
ph
=
λ
f
.
(1)
In general, the carrier waves propagate with the phase velocity. For the group
velocity we have (Hofmann-Wellenhof et al.
1993
)
df
d
2
ν
gr
=−
λ
.
(2)
λ
According to Bauer (
2003
) for Global Navigation Satellite Systems (GNSS),
modulated code signals propagate with the group velocity.
By forming the differential of Eq.
1
we get
d
ν
ph
=
fd
λ
+
λ
df
.
(3)
This equation can be re-arranged to
df
d
1
λ
d
ν
ph
d
f
λ
.
=
−
(4)
λ
λ
Substituting Eq.
4
into Eq.
2
yields the relation between group and phase velocities
d
ν
ph
d
ν
gr
=
ν
ph
−
λ
.
(5)
λ
In a non-dispersive media phase and group velocities are the same and are equal
or lower than the speed of light
c
299792458ms
−
1
in vacuum.
As we know the wave propagation velocity in a medium depends on the refractive
index
n
of that medium. So in principle we have
=
