Geoscience Reference
In-Depth Information
This is the simplest gravity anomaly to calculate. All the others involve more
tedious algebra (for many detailed examples the reader is referred to Telford
et al
. 1990). Here we merely note that the gravity anomaly for an infinitely long
cylinder with anomalous density
ρ
and radius
b
,buried at a depth
d
beneath
the surface, is
G
ρ
2
π
b
2
d
x
2
g
x
=
(5.46)
+
d
2
and the gravity anomaly for a semi-infinite (extending to infinity in the positive
x
direction) horizontal sheet with anomalous density
ρ
and thickness
t
,buried
at depth
d
beneath the surface, is
t
2
+
tan
−
1
x
d
g
z
=
2
G
ρ
(5.47)
Each particular buried body gives rise to its own anomaly. In many cases, the
shape of the anomalous body can be determined from the shape of the gravity
anomaly (e.g., the gravity anomaly due to a sphere is narrower than that due to
an infinite horizontal cylinder and not stretched out in the
y
direction). Gravity
models are, however, unfortunately
not
unique.
These three examples illustrate the fact that, to determine a shallow density
structure, one must perform a detailed local survey. Anomalies due to bodies
buried at depth
d
can be detected only at distances out to perhaps 2
d
from the
body. To resolve details of the density structure of the lower crust (at say 20-
40 km), gravity measurements must be made over an extensive area, because
the widths of these anomalies are much greater (say, five to ten times greater)
than those of the anomalies due to the shallow crustal structure. Likewise, gravity
anomalies due to anomalous bodies in the mantle are of a much longer wavelength
(hundreds of kilometres). Thus, although at first sight it might seem impossible
to extract mantle density information from surface gravity measurements (which
cannot fail to be affected by near-surface density anomalies), application of a
wavelength filter or smoothing of the gravity data does allow such deep struc-
tures to be studied. The opposite is, of course, also true: to study the shallow
structure, one must remove the regional long-wavelength anomaly which is of
deeper origin. However, no amount of processing can always ensure a complete
separation.
5.6 Observed gravity and geoid anomalies
5.6.1 Gravity anomalies
Agravity profile across the Mid-Atlantic Ridge is shown in Fig. 9.11. The maxi-
mum free-air anomaly on this profile is about 100 mgal. The four density models
in Fig. 9.11 yield anomalies that adequately match the measurements, despite
being very different. Note that, as is to be expected, model (c), the deepest model,
