Geoscience Reference
In-Depth Information
3.4
Bouguer reduction
The objective of the Bouguer reduction of gravity is the complete removal
of the topographic masses, that is, the masses outside the geoid.
The Bouguer plate
Assume the area around the gravity station
P
to be completely flat and
horizontal (Fig. 3.5), and let the masses between the geoid and the earth's
surface have a constant density
. Then the attraction
A
of this so-called
Bouguer plate is obtained by letting
a →∞
in (3-13), since the plate,
considered plane, may be regarded as a circular cylinder of thickness
b
=
H
and infinite radius. By well-known rules of the calculus, we obtain
A
B
=2
πGH
(3-27)
as the attraction of an infinite Bouguer plate. With standard density
=
2
.
67 g cm
−
3
this becomes
A
B
=0
.
1119
H
[mgal]
(3-28)
for
H
in meters.
Removing the plate is equivalent to subtracting its attraction (3-27) from
the observed gravity. This is called
incomplete Bouguer reduction
.Notethat
this is the usual “plane” Bouguer plate; for a truly “spherical” Bouguer plate
we would have 4
π
instead of 2
π
(Moritz 1990: p. 235).
To continue and complete our gravity reduction, we must now apply the
free-air reduction
F
as given in (3-26). This combined process of removing
the topographic masses and applying the free-air reduction is called
complete
Bouguer reduction
. Its result is Bouguer gravity at the geoid:
g
B
=
g
−
A
B
+
F.
(3-29)
P
H
P
0
Fig. 3.5. Bouguer plate
