Geoscience Reference
In-Depth Information
We can estimate the lithospheric thickness
L
from Eq. (7.61)byspecifying a
temperature for the base of the lithosphere. For example, if we assume the tem-
perature of the asthenosphere at the ridge axis to be 1300
◦
C and the temperature
at the base of the lithosphere to be 1100
◦
C, then we need to find the combination
of
L
and
t
such that
1100
=
1300 erf
L
2
√
κ
t
(7.63)
In other words, we need the inverse error function of 0.846. Using Fig. 7.5 (or
Appendix 5), we can write
L
2
√
κ
t
1
.
008
=
(7.64)
10
−
6
m
2
s
−
1
,
Thus, if
κ
=
L
=
2
.
016
×
10
−
3
√
t
(7.65a)
when
L
is in metres and
t
in seconds, or
L
=
11
√
t
(7.65b)
when
L
is in kilometres and
t
in millions of years (Ma). At 10 Ma this lithosphere
would be 35 km thick, and at 80 Ma it would be 98 km thick. Different choices
for the temperature at the ridge axis and at the base of the lithosphere will yield
slightly different values for the numerical constants in Eq. (7.65)but the 'root
t
'
dependence of lithosphere thickness on age will not change.
The depth of the seabed at any given age can be calculated by using the
principle of isostasy (see Section 5.5.2) and the gradual increase in density of the
lithosphere as it cools. If we take the compensation depth
D
to be in the mantle
beneath the base of the lithosphere, the total mass in a vertical column extending
down to
D
is
D
0
ρ
(
z
)d
z
Isostatic compensation requires that this mass be constant for all columns what-
ever their age. At the ridge axis the lithosphere has zero thickness, and so, taking
z
=
0tobeatsea level, the mass of the column is
D
d
r
ρ
a
d
z
d
r
ρ
w
d
z
+
0
where
ρ
a
the density of the asthenosphere (at
temperature
T
a
) and
d
r
the depth of the water over the ridge axis. The mass of a
column aged
t
is then
ρ
w
is the density of sea water,
D
d
+
L
ρ
a
d
z
where
d
is the water depth and
L
the thickness of the lithosphere. Because the
mass in this column must be the same as the mass in the column at the ridge axis,
d
0
ρ
w
d
z
+
d
+
L
ρ
(
z
)d
z
+
d
