Geology Reference
In-Depth Information
few hundred million years. Or, rather, the heat would have been reduced to the
level maintained by radioactive heating (heat is heat, and there is of course no
distinction between the initial heat and the radiogenic heat added later). Since
then, the mantle's temperature and convective activity would have been controlled
by radioactive heating. Thus there is no thermal 'vestige of a beginning' in the
mantle, although of course vestiges may have been left in rocks surviving from that
time. The rapid early cooling is also a result of the strong dependence of viscosity
on temperature, because a few hundred degrees higher temperature lowers the
viscosity by orders of magnitude and thus speeds convection and cooling.
The slow cooling since the early transient reflects the slow decay of radioactive
heating. The relatively small temperature change is a significant result, because
it says that we should not expect the mantle to have been radically hotter in the
Archaean. However, plate velocities might have been 10 times greater than at
present during the Archaean. This is because velocity varies as the square of heat
flow, as is implied by Eqs (5.23), and heat flow has dropped by a factor of about 3.
We will see this explicitly below, from a numerical model. Thus tectonic activity
might have been substantially higher.
This calculation quantifies the argument given in Section 4.4, due to Tozer, that
mantle convection is fairly inevitable in an Earth-like planet. If Earth started hot,
it will convect rapidly and cool until its rate of convection is sufficient to remove
the heat generated by radioactivity. If the Earth started cool, the mantle would
not convect at a significant rate, so radioactive heat would accumulate and, given
enough time, it would reach a temperature at which convection would become
vigorous enough to remove the radiogenic heat.
A basic question about Earth's history is whether plate tectonics has operated
throughout Earth's history. There seem to be no decisive arguments either way at
present, substantially because of the limited geological record from early times, as
we will see later. A more general question is whether the mantle convected in such a
way that heat removal was governed by the kind of relationship shown in Eq. (9.6).
This depends on how the upper thermal boundary layer behaved, since it controls
mantle cooling and at present it comprises a set of stiff but mobile plates. Even if
there were no plates, Eq. (9.6) might still apply if the boundary layer was mobile.
On the other hand, its mobility might be limited by rheological or compositional
factors and then our simple thermal evolution might not apply. This point will be
taken up later in this chapter.
9.2 Numerical thermal evolution
Within the last decade computer power has advanced enough to enable the high
resolution required for numerical models of mantle convection when the mantle
