Geology Reference
In-Depth Information
Water,
ρ
w
h
I
Lithosphere,
ρ
l
d-h
Mantle,
ρ
m
Figure 6.5. Subsidence of the sea floor due to thermal contraction.
d
below a mid-ocean ridge will shrink as the lithosphere moves away, so that a
similar column away from the ridge will occupy a height
d
h
, as illustrated in
Figure 6.5. In other words the volume of a unit-area column changes from
d
−
×
1
×
1m
2
1m
2
. The fractional change in volume is then
h/d
,and
according to Eq. (5.2b) in our earlier discussion of thermal expansion
to (
d
−
h
)
×
1
×
h/d
=
αT
(6.6a)
or
=
h
αT d,
(6.6b)
where
α
is the volume coefficient of thermal expansion and
T
is the average
change in temperature in the column. Equation (6.5) implies that
h
is proportional
to the square root of the age of the sea floor. For an age of 100 Ma, using
α
=
3
×
10
−
5
◦
C
−
1
,
T
10
−
6
m
2
/s, the lithosphere thickness given by
Eq. (6.5) is then 127 km, and the thermal contraction is
h
650
◦
C, and
κ
=
=
=
2.5 km. However, there
is another consideration.
Equation (6.6b) would give the subsidence of the surface of the lithosphere if
there was no ocean, but the presence of the water causes an isostatic adjustment:
the weight of the water weighs the surface down further. Isostatic balance requires
that there is no horizontal pressure gradient under the lithosphere, otherwise the
material under the lithosphere would flow horizontally and that would raise one
side and lower the other. We can take isostatic balance into account: the ideas are
not hard to understand, though the topic-keeping is a little messy.
To simplify our expressions, let's ignore the weight of the water above the level
of the mid-ocean ridge crest, because that is the same for both columns and does
not change the balance. We must also allow that the actual subsidence after isostatic
balance has been established,
h
I
, is different from the subsidence just due to thermal
contraction,
h
. Then the height of the right-hand column of rock plus water is
(
d-h
+
h
I
) and the pressure under it is
P
r
=
g
[
ρ
l
(
d
−
h
)
+
ρ
w
h
I
]
,
(6.7)
