Geology Reference
In-Depth Information
The anomaly of the whole body
D
g
is then found by
summing all such elements which make up the body
G
zz
r
¢-
(
)
g
=
SSS
xyz
¢¢ ¢
D
r
d
d
d
(6.9)
Δ
g
4
X
3
Δ
g
3
If
d
x
¢,
d
y
¢ and
d
z
¢ are allowed to approach zero, then
Δ
g
2
X
Δ
g
1
G
zz
r
(
¢-
)
Ú
Ú
Ú
D
g
=
ddd
xyz
¢
¢
¢
(6.10)
r
3
X
where
Time
Fig. 6.9
The principle of looping. Crosses and circles represent
alternate gravimeter readings taken at two base stations.The verti-
cal separations between the drift curves for the two stations (
D
g
1-4
)
provide an estimate of the gravity difference between them.
2
2
2
(
)
(
)
(
)
r
=
x
¢ -
x
+
y
¢ -
y
+
z
¢ -
z
As shown before, the attraction of bodies of regular
geometry can be determined by integrating equation
(6.10) analytically. The anomalies of irregularly shaped
bodies are calculated by numerical integration using
equations of the form of equation (6.9).
In order to obtain a reduced gravity value accurate to
±1 gu, the reduction procedure described in the follow-
ing section indicates that the gravimeter must be read to
a precision of ±0.1 gu, the latitude of the station must be
known to ±10 m and the elevation of the station must be
known to ±10 mm.The latitude of the station must con-
sequently be determined from maps at a scale of
1 : 10 000 or smaller, or by the use of electronic position-
fixing systems. Uncertainties in the elevations of gravity
stations probably account for the greatest errors in
reduced gravity values on land; at sea, water depths are
easily determined with a precision depth recorder to an
accuracy consistent with the gravity measurements.
In well-surveyed land areas, the density of accurately-
determined elevations at bench marks is normally suffi-
ciently high that gravity stations can be sited at bench
marks or connected to them by levelling surveys. Re-
connaissance gravity surveys of less well-mapped areas
require some form of independent elevation determina-
tion. Many such areas have been surveyed using aneroid
altimeters. The accuracy of heights determined by such
instruments is dependent upon the prevailing climatic
conditions and is of the order of 1-5 m, leading to a rela-
tively large uncertainty in the elevation corrections
applied to the measured gravity values. The optimal
equipment at present is the global positioning system
(GPS) (Davis
et al.
1989), whose constellation of 24
satellites is now complete and an unadulterated signal
is broadcast. Signals from these can be monitored by a
small, inexpensive receiver. Use of differential GPS, that
is, the comparison between GPS signals between a base
6.7 Gravity surveying
The station spacing used in a gravity survey may vary
from a few metres in the case of detailed mineral or geo-
technical surveys to several kilometres in regional recon-
naissance surveys.The station density should be greatest
where the gravity field is changing most rapidly, as accu-
rate measurement of gravity gradients is critical to sub-
sequent interpretation. If absolute gravity values are
required in order to interface the results with other grav-
ity surveys, at least one easily accessible base station
must be available where the absolute value of gravity is
known. If the location of the nearest IGSN station is in-
convenient, a gravimeter can be used to establish a local
base by measuring the difference in gravity between the
IGSN station and the local base. Because of instrumental
drift this cannot be accomplished directly and a pro-
cedure known as
looping
is adopted. A series of alternate
readings at recorded times is made at the two stations and
drift curves constructed for each (Fig. 6.9). The dif-
ferences in ordinate measurements (
D
g
1-4
) for the two
stations then may be averaged to give a measure of the
drift-corrected gravity difference.
During a gravity survey the gravimeter is read at a base
station at a frequency dependent on the drift characteris-
tics of the instrument. At each survey station, location,
time, elevation/water depth and gravimeter reading are
recorded.
