Geoscience Reference
In-Depth Information
are assumed.
For a spheroidal earth, the columns will converge slightly towards its
center, and other refinements may be introduced. We may postulate either
equality of mass or equality of pressure; each postulate leads to somewhat
different spherical refinements. It may be mentioned that for computational
reasons Hayford used still another, slightly different model; for instance, he
reckoned the depth of compensation
D
from the earth's surface instead of
from sea level.
Airy-Heiskanen system
Airy proposed this model, and Heiskanen gave it a precise formulation for
geodetic purposes and applied it extensively. Figure 3.10 illustrates the prin-
ciple. The mountains of constant density
0
=2
.
67 g cm
−
3
(3-55)
float on a denser underlayer of constant density
1
=3
.
27 g cm
−
3
.
(3-56)
The higher they are, the deeper they sink. Thus, root formations exist under
mountains, and “antiroots” under the oceans.
We denote the density difference
1
−
0
by ∆
. On the basis of assumed
numerical values, we have
0
=0
.
6gcm
−
3
.
∆
=
1
−
(3-57)
Denoting the height of the topography by
H
and the thickness of the cor-
responding root by
t
(Fig. 3.10), then the condition of floating equilibrium
is
t
∆
=
H
0
,
(3-58)
so that
0
∆
H
=4
.
45
H
t
=
(3-59)
results. For the oceans, the corresponding condition is
t
∆
=
H
(
0
−
w
)
,
(3-60)
where
H
and
w
are defined as above and
t
is the thickness of the antiroot
(Fig.3.10),sothatweget
t
=
0
−
w
H
=2
.
73
H
(3-61)
1
−
0
