Geology Reference
In-Depth Information
rarely the case and a further correction, the
terrain correc-
tion
(TC), must be made to account for topographic re-
lief in the vicinity of the gravity station.This correction
is always positive as may be appreciated from considera-
tion of Fig. 6.12(c).The regions designated A form part
of the Bouguer correction slab although they do not
consist of rock. Consequently, the Bouguer correction
has overcorrected for these areas and their effect must be
restored by a positive terrain correction. Region B
consists of rock material that has been excluded from
the Bouguer correction. It exerts an upward attraction
at the observation point causing gravity to decrease. Its
attraction must thus be corrected by a positive terrain
correction.
Classically, terrain corrections are applied using a cir-
cular graticule known, after its inventor, as a Hammer
chart (Fig. 6.13), divided by radial and concentric lines
into a large number of compartments. The outermost
zone extends to almost 22 km, beyond which topo-
graphic effects are usually negligible.The graticule is laid
on a topographic map with its centre on the gravity sta-
tion and the average topographic elevation of each com-
partment is determined. The elevation of the gravity
station is subtracted from these values, and the gravita-
tional effect of each compartment is determined by ref-
erence to tables constructed using the formula for the
gravitational effect of a sector of a vertical cylinder at its
axis. The terrain correction is then computed by sum-
ming the gravitational contribution of all compart-
ments. Table 6.1 shows the method of computation.
Such operations are time consuming as the topography
of over 130 compartments has to be averaged for each
station, but terrain correction is the one operation
in gravity reduction that cannot be fully automated.
Labour can be reduced by averaging topography within
a rectangular grid. Only a single digitization is required
as the topographic effects may be calculated at any point
within the grid by summing the effects of the right rec-
tangular prisms defined by the grid squares and their ele-
vation difference with the gravity station.This operation
can effectively correct for the topography of areas distant
J
I
H
G
F
Fig. 6.13
A typical graticule used in the calculation of terrain
corrections. A series of such graticules with zones varying in radius
from 2 m to 21.9 km is used with topographic maps of varying
scale.
Table 6.1
Terrain corrections.
Zone
r
1
r
2
n
Zone
r
1
r
2
n
B
2.0
16.6
4
H
1 529.4
2 614.4
12
C
16.6
53.3
6
I
2 614.4
4 468.8
12
D
53.3
170.1
6
J
4 468.8
6 652.2
16
E
170.1
390.1
8
K
6 652.2
9 902.5
16
F
390.1
894.8
8
L
9 902.5
14 740.9
16
G
894.8
1529.4
12
M
14 740.9
21 943.3
16
r
(
2
2
2
2
)
T
=
0 4191
.
r
-++-+
r
r
z
r
z
21
1
2
n
where
T
= terrain correction of compartment (gu);
r
= Bouguer correction density
(Mg m
-3
);
n
= number of compartments in zone;
r
1
= inner radius of zone (m);
r
2
= outer
radius of zone (m); and
z
= modulus of elevation difference between observation point and
mean elevation of compartment (m).
