Geology Reference
In-Depth Information
Thus both the functional form of seafloor subsidence (proportional to the square
root of age) and the amplitude are well accounted for by our theory. This theory
is, basically, that the oceanic lithosphere is a thermal boundary layer formed by
conductive cooling at the Earth's surface.
6.5 The geography of heat flow
The same theory allows us to calculate how the flux of heat reaching the sea floor
by conduction from depth should vary with seafloor age. In Section 5.4 we used
a simple approximation,
q
KT
m
/d
(Eq. 5.11), based on Figure 5.4. Here
K
is
the thermal conductivity, and the formula is an expression of Fourier's law of
conduction, which was introduced in Section 5.4. Substituting from Eq. (6.5) for
d
shows that this simple formula implies that
q
is inversely proportional to the square
root of age:
=
π
κt
.
However, again, here it is useful to use a more accurate formula, based on the
rigorous error-function solution for the temperature profile through the oceanic
lithosphere [1]. This result is
KT
m
4
q
=
KT
m
√
π
κt
.
q
=
(6.12)
3W/m
◦
C and other values as above, this gives a heat flow of 40 mW/m
2
at an age of 100 Ma. This is a good approximation to the observed magnitude of
heat flow through old sea floor (Figure 2.6). Again, treating the oceanic lithosphere
as a thermal boundary layer yields good agreement with both the functional form
of the dependence of heat flow on age and its magnitude.
Using
K
=
6.6 Numerical model of the plate mode
The results just calculated assume that the deeper mantle has no significant effect
on the topography and heat flow, because we have only looked at the cooling
thermal boundary layer at the surface, and have not considered the effect of the
boundary layer subducting and flowing around the mantle. Figure 6.6 shows that
a numerical convection model that includes the subducted lithosphere still yields
similar topography. The topography has a slightly smaller amplitude in this model
than the equivalent simple boundary layer theory, shown dashed, and the form
deviates a little from the square root of age profile. Nevertheless, the numerical
topography is similar within the scatter of the data in Figure 2.5.
