Geoscience Reference
In-Depth Information
Again, we can use a template in polar coordinates (Fig. 2.20) for theoretical
considerations or a rectangular grid (Fig. 2.21) for numerical computations.
For a surplus mass ∆
m
+
,
H>H
p
,wehave
b
=
H − H
P
,
c
= 0 ;
(3-33)
and for a mass deficiency ∆
m
−
,
H<H
P
,
b
=
c
=
H
P
− H.
(3-34)
By adding the terrain correction
A
t
to (3-29), the
refined Bouguer gravity
g
B
=
g
−
A
B
+
A
t
+
F
(3-35)
is obtained. The Bouguer reduction and the corresponding Bouguer anoma-
lies ∆
g
B
are called
refined
or
simple
, depending on whether the terrain cor-
rection has been applied or not.
In practice it is convenient to separate the Bouguer reduction into the
effect of a Bouguer plate and the terrain correction, because the amount of
the latter is usually much less. Even for mountains 3000 m in height, the
terrain correction is only of the order of 50 mgal (Heiskanen and Vening
Meinesz 1958: p. 154).
Unified procedure
It is also possible to compute the total effect of the topographic masses,
A
T
=
A
B
−
A
t
,
(3-36)
in one step by using columns with base at sea level (Fig. 3.7), again sub-
P
H
H
P
P
0
Fig. 3.7. Bouguer reduction
