Geoscience Reference
In-Depth Information
The components of
x
ij
may also be expressed by the spatial distance
s
ij
,
the azimuth
A
ij
, and the zenith angle
z
ij
, which is assumed to be corrected
for refraction. The appropriate relation is
⎡
⎣
⎤
⎦
⎡
⎤
s
ij
sin
z
ij
cos
A
ij
s
ij
sin
z
ij
sin
A
ij
s
ij
cos
z
ij
n
ij
e
ij
u
ij
⎣
⎦
=
x
ij
=
,
(5-68)
where the terrestrial measurement quantities
s
ij
,A
ij
,z
ij
refer to
P
i
, i.e.,
the measurements were taken at
P
i
. Inverting (5-68) gives the measurement
quantities explicitly:
=
n
2
+
e
2
+
u
2
s
ij
,
ij
ij
ij
tan
A
ij
=
e
ij
n
ij
,
(5-69)
u
ij
cos
z
ij
n
2
=
.
ij
+
e
2
ij
+
u
2
ij
Substituting (5-65) for
n
ij
,e
ij
and
u
ij
, the measurement quantities may be
expressed by the components of the vector
X
ij
in the global system.
A note on azimuth and zenith distance
Since the local level coordinates refer to the local plumb line defined by the
astronomical coordinates Φ
,
Λ (Sect. 2.4),
A
and
z
are called astronomical
azimuth and astronomical zenith distance (zenith angle). They will also play
a basic role in Part III.
A final word on the zenith distance. The measured (“astronomical”) az-
imuth is denoted by
A
, and the corresponding ellipsoidal azimuth is denoted
by
α
. Since the ellipsoidal zenith distance is conventionally denoted by
z
,it
would be consistent to indicate the measured (“astronomical”) zenith dis-
tance by
Z
. This symbol, however, is firmly reserved for the third axis of the
XY Z
system, so we exceptionally, but consistently with the rest of the topic,
use the symbol
z
.(Both
A
and
z
will return in the following sections.)
5.10
Combining terrestrial data and GPS
5.10.1
Common coordinate system
So far, GPS and terrestrial networks have been considered separately with
respect to the adjustment. The combination, for example, by a datum trans-
formation, was supposed to be performed after individual adjustments. Now
