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In-Depth Information
datum, or lack of it in the case of the valley below the
datum, affects gravity. When the gravity station is located
on topography above the survey datum, it is located on a
layer of rock that contributes mass between the gravity
meter and the datum. The rock layer increases the meas-
ured value of gravity. Its effect is compensated by the
Bouguer correction (g
BOU
), which assumes that the Earth
is
flat, i.e. not curved, and that the rock layer is a horizontal
slab of uniform density extending to infinity in all direc-
tions, i.e. the hatched area comprising zones A and A
0
in
Fig. 3.16b
.
It is given by:
level in the survey area, as this reduces the thickness of the
slab and will reduce errors due to variations in density
between the surface and the datum. The use of variable
or constant Bouguer density and the consequences thereof
are described in detail by Vajk (
1956
).
Using the average crustal density of 2.67 g/cm
3
, the
Bouguer correction is 1.12 gu/m, so station height needs
to be known with an accuracy of about 10 cm in order to
calculate the Bouguer correction to an accuracy of 0.1 gu.
Note that the likelihood of non-uniform density is not
accounted for in this calculation.
The infinite flat-slab model of the Bouguer correction
does not account for the curvature of the Earth
g
BOU
¼
2
π
G
ρ
h
top
ð
3
:
17
Þ
s surface.
This can be included in the reduction process by using
spherical cap correction; see LaFehr (
1991
). The spherical
cap correction is a more appropriate model in areas of
rugged terrain, particularly where there are very large
changes in station height.
'
where h
top
is the height (m) of the topography, or the
thickness of the slab (m);
is the Bouguer density (g/cm
3
),
the average density of the slab between the gravity station
and the datum level; and G the universal gravitational
constant given in
Section 3.2.1.1
.
This reduces to:
ρ
g
BOU
¼
0
:
4192
ρ
h
top
gu
ð
3
:
18
Þ
3.4.5.3
Terrain correction
The Bouguer correction assumes that the rock occupying
the height interval between the datum level and the station
is a uniform slab extending to in
nity in all directions.
Referring to
Fig. 3.16b
, the Bouguer correction removes the
effect of the mass in zones A and A
0
. It fails to account for
mass above the slab (B), i.e. mass above the gravity station.
In contrast, the correction accounts for too much mass in
regions where the topographic surface is below than the
station, i.e. the non-existent mass where the slab is above
the actual ground surface (A
0
). The terrain correction
explicitly addresses these limitations and therefore must
be used in conjunction with the Bouguer correction.
gravitational attraction of the mass above the slab (in zone
B) acts against the gravitational attraction of the subsurface
to
The Bouguer correction is subtracted from the free-air
gravity, noting that height is negative for stations below
the datum level so the Bouguer correction is then negative.
The Bouguer correction is an approximation as it does
not account for variable topography around the station
(the top of the slab is flat). Furthermore, selecting the
appropriate Bouguer density can be a problem. The aver-
used but other values are appropriate for particular
geological environments. For example, values as low as
1.8 g/cm
3
may be used in sedimentary basins, 0.917 g/cm
3
for ice-covered areas.
Since it is unlikely that the density of the rocks under-
lying the entire survey area will be the same, a variable
Bouguer density may be more appropriate. The subsurface
geology and density distribution needs to be known to
determine the appropriate Bouguer density which, obvi-
ously, is a problem since determining subsurface density
variations is the aim of the gravity survey itself (an example
of the geophysical paradox; cf.
Section 1.3
)
. If variable
density is chosen based on outcrop geology, an explicit
assumption is being made that the geology is consistent
vertically downwards to the datum level, which may well
not be the case. Selecting a single density is usually the only
practical solution, reflecting an acceptance of one
'
pull
'
the gravity sensor up. The observed gravity is then
'
and a positive correction is required. In the lower-
lying area, zone A
0
, the Bouguer correction has assumed that
mass is present here and in so doing has over-corrected; it
has taken mass away, reducing the gravitational attraction.
Since the Bouguer correction is subtracted, the corrected
gravity is too small and again a positive correction compen-
sates for this.
The terrain correction is the gravitational attraction, at
the gravity station, of all the hills above the Bouguer slab
and all the valleys occupied by the slab. It is obtained by
determining the mass of the hills and the mass deficiencies
of
too low
'
s ignor-
ance. The resulting errors are small, except in rugged
terrain. If variable density is chosen, the datum level should
be as high as possible, for example the lowest topographic
'
the valleys using topographic information and the
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