Geoscience Reference
In-Depth Information
3.6
Isostatic reduction
3.6.1
Isostasy
One might be inclined to assume that the topographic masses are simply
superposed on an essentially homogeneous crust. If this were the case, the
Bouguer reduction would remove the main irregularities of the gravity field
so that the Bouguer anomalies would be very small and would fluctuate
randomly around zero. However, just the opposite is true. Bouguer anoma-
lies in mountainous areas are systematically negative and may attain large
values, increasing in magnitude on the average by 100 mgal per 1000 m of
elevation. The only explanation possible is that there is some kind of mass
deficiency under the mountains. This means that the topographic masses are
compensated in some way.
There is a similar effect for the deflections of the vertical. The actual
deflections are smaller than the visible topographic masses would suggest.
In the middle of the nineteenth century, J.H. Pratt observed such an effect
in the Himalayas. At one station in this area he computed a value of 28
for the deflection of the vertical from the attraction of the visible masses
of the mountains. The value obtained through astrogeodetic measurements
was only 5 . Again, some kind of compensation is needed to account for this
discrepancy.
Two different theories for such a compensation were developed at almost
exactly the same time, by J.H. Pratt in 1854 and 1859 and by G.B. Airy in
1855. According to Pratt, the mountains have risen from the underground
somewhat like a fermenting dough. According to Airy, the mountains are
floating on a fluid lava of higher density (somewhat like an iceberg floating
on water), so that the higher the mountain, the deeper it sinks.
Pratt-Hayford system
This system of compensation was outlined by Pratt and put into a mathe-
matical form by J.F. Hayford, who used it systematically for geodetic pur-
poses.
The principle is illustrated in Fig. 3.9. Underneath the level of compen-
sation there is uniform density. Above, the mass of each column of the same
cross section is equal. Let D be the depth of the level of compensation, reck-
oned from sea level, and let 0 be the density of a column of height D .Then
the density of a column of height D + H ( H representing the height of the
topography) satisfies the equation
( D + H ) = D 0 ,
(3-48)
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