Geoscience Reference
In-Depth Information
anomaly is large and negative; all the indications are that the mountains are not
in isostatic equilibrium. The isostatic anomaly calculated for Airy-type compen-
sation for
D
30 km confirms this.
Figure 5.8(c) shows the case in which the mountains are totally uncompen-
sated. Then the Bouguer anomaly is exactly zero since all the excess gravitational
attraction is provided by the material above sea level, whereas the free-air anomaly
is very large and positive. The isostatic anomaly is, in this case, also very large
and positive.
To determine what form the compensation takes, the gravity anomaly must
be calculated for a number of possible subsurface density structures and various
compensation depths. A zero isostatic anomaly indicates that a correct density
distribution and compensation depth have been determined (as in Fig. 5.8(a)).
Unfortunately, it is often not possible to distinguish unequivocably amongst the
various hypotheses or compensation depths because gravity is insensitive to minor
changes in the deep density structure. In addition, small shallow structures can
easily hide the effects of the deeper structure. To determine the extent and shape
that any compensating mass takes, it is helpful to have additional information on
the structure of the crust, such as that given by seismic-refraction and -reflection
experiments.
The continents and oceans are in broad isostatic equilibrium. This is mainly
achieved by variations in crustal thickness (Airy's hypothesis), although, for
example, the mid-ocean ridges are partially compensated by lower-density rocks
in the mantle (Pratt's hypothesis). Gabbro, a typical oceanic rock, is denser than
granite, a typical continental rock, so Pratt's hypothesis also plays a role in this
isostatic balancing of oceanic and continental crust.
=
Example: isostasy and seismic reflection
The many deep continental reflection lines from around the British Isles produced a
result that was initially very surprising. The results of the lines showed that,
although the structure of the upper crust varies from sedimentary basins to
outcropping crystalline rocks, the clear reflection identified as the Moho is
nevertheless generally horizontal and arrives at about 10 s two-way time on
unmigrated sections. The reflection typically shows neither any depression (pull
down) beneath basins nor elevation (pull up) beneath the crystalline rocks. It is
possible that this feature may be just a desire of the eye of the seismic interpreter to
find a suitable candidate for the Moho reflection at about this depth, but it is more
likely that the feature is real and a consequence of isostasy.
Let us modify the Airy and Pratt isostatic compensation models to include a
depth-dependent density
ρ
(
z
)(Warner 1987). For the British reflection lines, which
were shot in relatively shallow water, Airy-type isostatic compensation (Eq. (5.23))
requires
t
1
0
ρ
1
(
z
)d
z
=
t
2
0
ρ
2
(
z
)d
z
+
(
t
1
−
t
2
)
ρ
m
(5.37)
