Gravity reduction - Physical Geodesy - page 152

3. Rigorously , free-air anomalies can even be considered as resulting from
a mass-transporting gravity reduction, in a similar sense as the iso-
static anomaly. Just imagine that you transport the masses above the
geoid into its interior in such a way that the external potential remains
unchanged ! This reminds us of Rudzki's reduction (geoid potential re-
mains constant) but is rather different. The most important advantage
is that the free-air anomaly in the present sense leaves the external po-
tential unchanged which nowadays is much more important than the
geoid. The greatest disavantage is that it cannot be computed: we do
not know how to shift the masses so that the external masses remain
unchanged. In logical terms, the Rudzki reduction is constructive -
we are told how to do it -, whereas the present reduction is non-
constructive - we do not know how to do it directly. More about this
in Sects. 8.2, 8.6, 8.9, and 8.15. We shall, thus, attempt to cut the
di cult cake into easier pieces.

These are the main methods that have been proposed for the reduction of
gravity. A simple overview is given by Fig. 3.16.

Pratt Airy Rudzki Helmert

H H H H

T

H

D t

Fig. 3.16. Topography and compensation for different gravity reductions