Page 56 - Global Tectonics

THE INTERIOR OF THE EARTH 43

where equal; that is, the weights of vertical columns of
unit cross-section, although internally variable, are
identical at the depth of compensation if the region is
in isostatic equilibrium.
Two hypotheses regarding the geometric form of a
local isostatic compensation were proposed in 1855 by
Airy and Pratt.
r

2.11.2 Airy’s hypothesis

Airy’s hypothesis assumes that the outermost shell of
the Earth is of a constant density and overlies a
higher density layer. Surface topography is compen-
sated by varying the thickness of the outer shell in
such a way that its buoyancy balances the surface
load. A simple analogy would be blocks of ice of

varying thickness floating in water, with the thickest
showing the greatest elevation above the surface.
Thus mountain ranges would be underlain by a thick
root, and ocean basins by a thinned outer layer or
antiroot (Fig. 2.29a). The base of the outer shell is
Figure 2.29 (a) Airy mechanism of isostatic
consequently an exaggerated mirror image of the
compensation. h, height of mountain above sea level; z,
surface topography. Consider the columns of unit
depth of water of density r w ; T A , normal thickness of
cross-section beneath a mountain range and a region
crust of density r c ; r, thickness of root; a, thickness of
of zero elevation shown in Fig. 2.29a. Equating their
antiroot; D A , depth of compensation below root; r m ,
weights gives:
density of mantle. (b) The Pratt mechanism of isostatic
compensation. Legend as for (a) except T p , normal
g[hρ c + T Aρ c + rρ c + D Aρ m] = g[T Aρ c + rρ m + D Aρ m] thickness of crust; r h , density of crust beneath mountain;
r z , density of crust beneath ocean; D p , depth of
where g is the acceleration due to gravity. compensation below T p .
Rearranging this equation gives the condition for
isostatic equilibrium:
2.11.3 Pratt’s hypothesis
h c ρ
r =
ρ ( m −ρ ) Pratt’s hypothesis assumes a constant depth to the base
c
of the outermost shell of the Earth, whose density
A similar computation provides the condition for com- varies according to the surface topography. Thus,
pensation of an ocean basin: mountain ranges would be underlain by relatively low
density material and ocean basins by relatively high
density material (Fig. 2.29b). Equating the weights of
)
a = z(ρ c −ρ w columns of unit cross-section beneath a mountain
− )
range and a region of zero elevation gives:
(ρ m ρ c
If one substitutes appropriate densities for the crust, g(T p + h)ρ h = gT p ρ c
mantle, and sea water in these equations they predict
that the relief on the Moho should be approximately which on rearrangement provides the condition for
seven times the relief at the Earth’s surface. isostatic equilibrium of the mountain range: