Geoscience Reference
In-Depth Information
P
P
0
H
P
Q
H
Q
0
H
QQ QQ'
0
=
0
Q'
Fig. 3.14. Rudzki reduction as a plane approximation
Rudzki gravity at the geoid becomes, in analogy to (3-72),
A
T
+
A
C
+
F,
(3-96)
where
A
C
=
∆
A
with
b
=
H
,
c
=
H
+
H
P
, the density being equal to
that of topography.
Since the indirect effect is zero, the cogeoid of Rudzki coincides with the
actual geoid, but the gravity field outside the earth is changed, which to-
day is in the center of attention. In addition, the Rudzki reduction does not
correspond to a geophysically meaningful model.
Nevertheless, it is impor-
tant conceptually
. Regard it an interesting historic curiosity, but never even
consider to use it!
g
R
=
g
−
3.9
The condensation reduction of Helmert
Here the topography is condensed so as to form a surface layer (somewhat
like a glass sphere made of very thin but very heavy and robust glass) on the
geoid so that the total mass remains unchanged. Again, the mass is shifted
along the local vertical (Fig. 3.15).
We may consider Helmert's condensation as a limiting case of an isostatic
P
H
%
geoid
·%
=
H
Fig. 3.15. Helmert's method of condensation
