Geology Reference
In-Depth Information
results from a horizontal line mass (equation (6.7)). The
depth to a line mass or to the centre of a horizontal cylin-
der with the same mass distribution is given by
by
n
1
Â
M
e
=
ga
i
DD
(6.19)
i
2
G
p
zx
=
i
=
1
12
Before using this procedure it is important that the re-
gional field is removed so that the anomaly tails to zero.
The method only works well for isolated anomalies
whose extremities are well defined. Gravity anomalies
decay slowly with distance from source and so these tails
can cover a wide area and be important contributors to
the summation.
To compute the actual mass
M
of the body, the densi-
ties of both anomalous body (
r
1
) and country rock (
r
2
)
must be known:
For any two-dimensional body, the limiting depth is
then given by
(6.16)
zx
<
12
(b) Gradient-amplitude ratio method
. This method re-
quires the computation of the maximum anomaly am-
plitude (
A
max
) and the maximum horizontal gravity
gradient (
A
¢
max
) (Fig. 6.18(b)). Again the initial assump-
tion is made that a three-dimensional anomaly is caused
by a point mass and a two-dimensional anomaly by a line
mass. By differentiation of the relevant formulae, for any
three-dimensional body
M
r
rr
1
e
M
=
(6.20)
(
-
)
1
2
A
A
max
max
z
<
086
.
(6.17)
The method is of use in estimating the tonnage of ore
bodies. It has also been used, for example, in the estima-
tion of the mass deficiency associated with the Chicxu-
lub crater,Yucatan (CamposEnriquez
et al
. 1998), whose
formation due to meteorite or asteroid impact has been
associated with the extinction of the dinosaurs.
¢
and for any two-dimensional body
A
A
max
max
(6.18)
z
<
065
.
¢
Inflection point
(c) Second derivative methods
. There are a number of
limiting depth methods based on the computation of
the maximum second horizontal derivative, or maxi-
mum rate of change of gradient, of a gravity anomaly
(Smith 1959). Such methods provide rather more accu-
rate limiting depth estimates than either the half-width
or gradient-amplitude ratio methods if the observed
anomaly is free from noise.
The locations of inflection points on gravity profiles, i.e.
positions where the horizontal gravity gradient changes
most rapidly, can provide useful information on the na-
ture of the edge of an anomalous body. Over structures
with outward dipping contacts, such as granite bodies
(Fig. 6.19(a)), the inflection points (arrowed) lie near the
base of the anomaly. Over structures with inward dip-
ping contacts such as sedimentary basins (Fig. 6.19(b)),
the inflection points lie near the uppermost edge of the
anomaly.
Excess mass
The excess mass of a body can be uniquely determined
from its gravity anomaly without making any assump-
tions about its shape, depth or density. Excess mass refers
to the difference in mass between the body and the mass
of country rock that would otherwise fill the space oc-
cupied by the body.The basis of this calculation is a for-
mula derived from Gauss' theorem, and it involves a
surface integration of the residual anomaly over the area
in which it occurs.The survey area is divided into
n
grid
squares of area
D
a
and the mean residual anomaly
D
g
found for each square. The excess mass
M
e
is then given
Approximate thickness
If the density contrast
Dr
of an anomalous body is
known, its thickness
t
may be crudely estimated from its
maximum gravity anomaly
D
g
by making use of the
Bouguer slab formula (equation (6.8)):
g
G
D
t
ª
(6.21)
2
pr
D
