Geoscience Reference
In-Depth Information
(a)
(b)
Figure 5.6.
(a) An illustration of Airy's hypothesis of isostasy. The upper layer has
density
ρ
u
, and the substratum has density
ρ
s
. Isostatic compensation is achieved
by variation in the thickness of the upper layer: mountains have deep roots and
ocean basins have anti-roots. (b) An illustration of Pratt's hypothesis of isostasy.
Density of sea water,
ρ
w
; density of substratum,
ρ
s
; densities of upper layer beneath
mountains of heights
h
2
and
h
1
,
ρ
2
and
ρ
1
; density of upper layer beneath ocean of
depth
d
,
ρ
u
; and compensation
depth,
D
. Isostatic compensation is achieved by a lateral variation of density beneath
surface features. Material beneath mountains is less dense; material beneath ocean
basins is more dense.
ρ
d
; density of upper layer beneath land at sea level,
Pratt's hypothesis
Pratt assumed that the depth of the base of the upper layer is level and that
isostatic equilibrium is achieved by allowing this upper layer to be composed of
columns of constant density (Fig. 5.6(b)). Taking the base of the upper layer as
the compensation depth and equating the masses above this level in each column
of unit cross-sectional area gives
ρ
u
D
=
(
h
1
+
D
)
ρ
1
=
(
h
2
+
D
)
ρ
2
=
ρ
w
d
+
ρ
d
(
D
−
d
)
(5.28)
Thus, in this model, compensation is achieved by mountains consisting of and
being underlain by material of low density,
ρ
1
=
ρ
u
D
h
1
+
D
(5.29)
and the oceans being underlain by material of higher density,
ρ
u
D
−
ρ
w
d
D
−
d
ρ
d
=
(5.30)
