Geoscience Reference
In-Depth Information
Table 11.2. Characteristic values in arc seconds for Molodensky cor-
rections
ξ
i
and
η
i
for deflections of the vertical until
i
= 4, computed
from free-air gravity anomalies
ξ
1
η
1
ξ
2
η
2
ξ
3
η
3
ξ
4
η
4
min
−
2
.
44
−
1
.
94
−
0
.
92
−
0
.
84
−
0
.
35
−
0
.
24
−
0
.
08
−
0
.
12
2
.
36
3
.
654
0
.
88
0
.
86
0
.
21
0
.
20
0
.
05
0
.
09
max
mean
0
.
19
0
.
32
−
0
.
02
−
0
.
02
−
0
.
01
−
0
.
01
0
.
00
0
.
00
rms
0
.
90
0
.
96
0
.
29
0
.
27
0
.
06
0
.
06
0
.
02
0
.
02
Table 11.3. Characteristic values in arc seconds for Molodensky cor-
rections
ξ
i
and
η
i
for deflections of the vertical until
i
= 4, computed
from isostatic gravity anomalies
ξ
1
η
1
ξ
2
η
2
ξ
3
η
3
ξ
4
η
4
min
−
0
.
57
−
0
.
36
−
0
.
06
−
0
.
07
−
0
.
01
−
0
.
02
0
.
00
0
.
00
max
0
.
33
0
.
46
0
.
09
0
.
05
0
.
01
0
.
01
0
.
00
0
.
00
mean
−
0
.
04
0
.
01
0
.
00
−
0
.
01
0
.
00
0
.
00
0
.
00
0
.
00
rms
0
.
11
0
.
09
0
.
02
0
.
02
0
.
00
0
.
00
0
.
00
0
.
00
As Kuhtreiber (1990) showed in his thorough work, there is no rough-
and-ready prescription for finding an optimal smoothing. Trial and error may
be the best approach.
Isostatic reduction might be considered a smoothing method on a geo-
physical basis, cf. Tables 11.2 and 11.3.
Just to give an idea of the order of magnitudes, we take some typical
sizes of the Molodensky corrections in high mountains.
We take two tables from K uhtreiber (1990): the following Tables 11.2 and
11.3 are Kuhtreiber's Tables (8-3) and (8-6). The gravity data are assumed to
be given in a rectangular grid of size 11
.
25
×
18
.
75
. A suitable smoothing
is presupposed. Much better is, of course, the use of
isostatic reduction
,
which should provide a physically meaningful and ecient smoothing. This
is shown by Table 11.3.
To provide some contrast and to include also Molodensky corrections for
the height anomaly
ζ
, we quote also Table 11.4 of a somewhat earlier work
by Kraiger et al. (1987) (denoted as Table 6.1 there). The values are not
directly comparable because test areas and selected methods of integration,
smoothing, data density, etc., are different. Still, they lead to interesting
