Geoscience Reference
In-Depth Information
Topographic-isostatic anomalies
The topographic-isostatic gravity anomalies are - in analogy to the Bouguer
anomalies - defined by
γ.
(3-79)
If any of the topographic-isostatic systems were rigorously true, then the
topographic-isostatic reduction would fulfil perfectly its goal of complete reg-
ularization of the earth's crust, which would become level and homogeneous.
Then, with a properly chosen reference model for
γ
, the topographic-isostatic
gravity anomalies (3-79) would be zero.
The actual topographic-isostatic compensation occurring in nature can-
not completely conform to such abstract models. As a consequence, nonzero
topo-graphic-isostatic gravity anomalies will be left, but they will be small,
smooth, and more or less randomly positive and negative. On account of
this smoothness and independence of elevation, they are better suited for in-
terpolation or extrapolation than any other type of anomalies; see Chap. 9,
particularly Sect. 9.7.
It may be stressed again that for geodetic purposes the topographic-
isostatic model used must be mathematically precise and self-consistent, and
the same model must be used throughout. Refinements include the consid-
eration of irregularities of density of the topographic masses and the consid-
eration of the anomalous gradient of gravity.
∆
g
TI
=
g
TI
−
3.7
The indirect effect
The removal or shifting of masses underlying the gravity reductions change
the gravity potential and, hence, the geoid. This change of the geoid is an
indirect effect
of the gravity reductions.
Thus, the surface computed by Stokes' formula from topographic-isostatic
gravity anomalies, is not the geoid itself but a slightly different surface, the
cogeoid. To every gravity reduction there corresponds a different cogeoid.
Let the undulation of the cogeoid be
N
c
. Then the undulation
N
of the
actual geoid is obtained from
N
=
N
c
+
δN
(3-80)
by taking into account the indirect effect on
N
,whichisgivenby
δN
=
δW
γ
,
(3-81)
where
δW
is the change of potential at the geoid. Equation (3-81) is an
application of Bruns' theorem (2-237).
