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The pioneering work has been done by Sunkel (1983). Later work, espe-
cially by Sunkel et al. (1987), Kuhtreiber (1998, 2002 a, 2002 b), and Erker
et al. (2003) has refined, extended and perfected the gravity field in Austria,
but the 1983 work is good for an introduction.
Sunkel (1983) used least-squares collocation to calculate the geoid for the
main part of Austria from a very good material of deflections of the vertical.
Gravity anomalies of a comparable quality were not yet available in 1983. In
addition to an isostatic reduction (Sect. 8.14) according to Airy-Heiskanen
( T = 30 km), he also removed a global trend by means of an earth gravity
model, represented by a spherical-harmonic expansion up to a certain degree
N . In particular, he used the model of Rapp (1981) with N = 180.
After removing the topographic-isostatic trend T TI and this global trend
T EM (remember, EM denotes earth model), there remains a residual anoma-
lous potential δT ,givenby
T EM + T TI .
δT = T
T TI
(11-10)
Since the earth model potential T EM is represented by a spherical-harmonic
expansion up to degree N , it may be appropriate to consider, for the isostatic
reduction, only the effect for degrees N> 180 (or, say, N> 360), replacing
T TI by
T CN
=( T TI ) N> 180 = T TI − T TI ,
(11-11)
TI
where T TI represents a spherical-harmonic expansion for T TI truncated at
degree N = 180. This explains Eq. (11-11).
The observations i =[ ξ, η, g ], which represent linear functionals L i T ,
are reduced in the same way, obtaining
L i T EM + L i T TI = L i δT .
i
L i T TI
(11-12)
Adding the earth model reduction to the computational procedure outlined
at the end of the preceding section, we thus have the flow diagram of Ta-
ble 11.1.
Data
The topography in Austria is rather varied, with elevations up to 3800 m.
The density of astrogeodetic stations was 10 to 20 km; the total number of
deflections data used was 521. No gravity anomalies were used in this first
computation.
The topographic-isostatic reduction of the deflections of the vertical was
made using a rather crude digital terrain model consisting of mean elevations
for 20 ×
20 rectangles. It has been obtained by digitizing a map 1 : 500 000.
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