Geology Reference
In-Depth Information
that any initial excess temperature would decay away within a few hundred million
years, and it's useful to know that.
The early transient cooling also establishes the temperature difference between
the core and the lower mantle. This temperature difference is required to drive
mantle plumes, and Figure 9.1(b) shows the plume heat flow,
Q
C
, rising from
zero at the start. This quantifies the evolution sketched in Figure 7.3, where it
was argued that plumes are inevitable if the core is hotter than the mantle. After
the early transient cooling, the mantle temperature is maintained by radioactive
heating. You can see this from Figure 9.1(b), where the heat loss,
Q
S
, drops rapidly
until it is just above the heat generation, after which it tracks the heat generation
fairly closely.
Q
S
is always a little higher than
Q
R
because the mantle is cooling.
(If
Q
R
were constant instead of declining, and there were no core heat flow, then
Q
S
would approach it asymptotically.)
Figure 9.1(c) shows the mantle temperature on an expanded scale, and it declines
by only about 200
◦
C in the slow cooling phase, although the heat loss declines by
a factor of 3-4. The reason the temperature does not decline very much is because
the mantle viscosity depends so strongly on temperature (Chapter 4). It takes only
a modest change in temperature to increase the viscosity substantially, and thus to
slow the convection and reduce the heat loss substantially.
The core temperature declines only slowly, reflecting the low heat loss,
Q
C
,
which is controlled not by the core but by the thermal boundary layer at the base
of the mantle, which regulates how much heat can escape through the mantle.
Q
C
is controlled mainly by two quantities, the temperature difference between the
mantle and the core, and the viscosity within the thermal boundary layer, which
is controlled by
T
C
. Because
T
C
does not decline very much, the heat carried
by plumes does not vary a lot through the age of the Earth in this calculation
(Figure 9.1(b)). It also happens that (
T
C
−
T
L
) declines only slowly in this calcula-
tion, which contributes to
Q
C
declining only slowly: it peaks at 16 TW and declines
to 7.6 TW at present. Thus this calculation suggests that plumes may have been
only moderately more active in the past than they are now.
We will use this simplified thermal evolution model as a reference case, as we
discuss potential variations and complications below. Because of its simplifications,
it requires some parameters to specify simple results of complicated processes. For
example, when Eq. (9.6) is used, an additional adjustment factor is included (Section
B.2) to compensate for the simplified approximations used in its derivation. This
approach has therefore become known as parametrised convection, as distinct from
the numerical convection (below) in which the physics is left freer to work itself out.
For the moment, the parametrised model suggests some significant lessons. If
the Earth started hot, due to the gravitational energy released during accretion and
core formation, then that 'primordial heat' would have been removed within a
