Geoscience Reference
In-Depth Information
3.6.2
Topographic-isostatic reductions
The objective of the topographic-isostatic reduction of gravity is the
regular-
ization
of the earth's crust according to some model of isostasy. Regulariza-
tion here means that we are trying to make the earth's crust as homogeneous
as possible. The topographic masses are not completely removed as in the
Bouguer reduction but are shifted into the interior of the geoid in order
to make up the mass deficiencies that exist under the continents. In the
topographic-isostatic model of Pratt and Hayford, the topographic masses
are distributed between the level of compensation and sea level, in order to
bring the crustal density from its original value to the constant standard
value
0
. In the Airy-Heiskanen model, the topographic masses are used to
fill the roots of the continents, bringing the density from
0
=2
.
67 g/cm
3
to
1
=3
.
27 g/cm
3
.
In other terms, the topography is removed together with its compensa-
tion, and the final result is ideally a homogeneous crust of density
0
and
constant thickness
D
(Pratt-Hayford) or
T
(Airy-Heiskanen).
Thus we have three steps:
1. removal of topography,
2. removal of compensation,
3. free-air reduction to the geoid.
Steps 1 and 3 are known from Bouguer reduction, so that the techniques of
Sect. 3.4 can be applied to them. Step 2 is new and will be discussed now
for the two main topographic-isostatic systems.
Pratt-Hayford system
The method is the same as for the terrain correction, Sect. 3.4, Eq. (3-32).
The attraction of the (negative) compensation is again computed by
A
C
=
∆
A,
(3-65)
where the attraction of a vertical column representing a compartment is
given by (3-22) with
b
=
D,
c
=
D
+
H
P
(3-66)
and
replaced by the density defect ∆
. If the preceding Bouguer reduction
were done with the original density
of the column expressed by
D
D
+
H
0
=
(3-67)
according to (3-48), then ∆
would be given by (3-50).
