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10 8 m/s
so using r =
0.9 m/yr. This is about 10 times
the velocity of the faster plates. Thus the material in the plumes may flow upwards
relatively rapidly, although of course 1 m/yr is still slow by human standards.
It is also interesting to compare the volumetric flow rate with the rate at which
magma has been erupted along the Hawaiian volcanic chain. The rate at which the
volcanic chain has been constructed over the past 25 Ma has been about 0.03 km 3 /yr
[57, 58]. This is very much less than the plume volumetric flow rate. It implies that
only about 0.4% of the volume of the plume material is erupted as magma at the
surface. Even if there is substantially more magma emplaced below the surface,
such as at the base of the crust under Hawaii [52, 59], the average melt fraction of
the plume is unlikely to be much more than 1%.
Since the magmas show evidence of being derived from perhaps 5-10% partial
melting of the source [56, 60], this probably means that about 80-90% of the plume
material does not melt at all, and the remainder undergoes about 5-10% partial
melting. This result is important for the geochemical interpretation of plume-
derived magmas.
50 km yields u =
3
×
=
7.2.4 Heat flow from the core
If plumes rise from a hot thermal boundary layer formed by heat conducting out of
the core into the base of the mantle, then the plume heat flow should be similar to the
rate of heat loss from the core. This seems to be true, though estimates of the core
heat flux are not easy, and there are some complications in the plume story as well.
The first complication is that the estimate of plume heat flow rate should include
the heat carried by plume heads, which will be discussed a little later in this chapter.
Hill et al. [61] used the frequency of flood basalt eruptions in the geological record
of the past 250 Ma to estimate that plume heads carry approximately 50% of the
heat carried by plume tails. Thus the total heat flow rate in plumes would be
approximately 3.5 TW, still less than 10% of the global heat flow rate.
The second complication is that some careful modelling has shown that the heat
carried by plumes is greater in the deep mantle than in the shallow mantle [62-64].
This is because the temperature excess of plumes is larger at depth. There are
two contributions to this effect, arising from subtleties of convection and adiabatic
gradients, though we don't need to go into details here. Combined, these effects
yield a temperature difference between the plume and the surrounding mantle
of 400-600 C at the bottom versus 200-300 C at the top. Correspondingly, the
excess heat transported by the model plumes in the deep mantle is about 2-3 times
larger than in the shallow mantle. Thus the plume heat flow is likely to be greater
than our estimate above by a factor of 2, with an upper limit of a factor of 3. Thus
plumes are inferred to be carrying 2-3 times 3.5 TW, i.e. 7-10 TW.
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