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1
50.
600 Myr
(a)
1500 Myr
2000 Myr
4500 Myr
(b)
Fertile
Actual
0
0.
0
3
0
4500
Tracer concentration
Time (Ma)
Figure 9.8. (a) Horizontally averaged tracer density versus height in the model of
Figure 9.5. There is a gradient of tracer content in the upper mantle, representing
a gradient in basaltic content. (b) Thickness of the oceanic crust calculated from
the same model (Actual), and what it would have been if the uppermost mantle
had average fertility, i.e. average basaltic content (Fertile).
-2.5
1.5
log(Viscosity)
Figure 9.9. Viscosity at 600 Myr in the model of Figure 9.5. Viscosity depends on
temperature, hotter fluid having lower viscosity. Superimposed on this is a depth
dependence in which the viscosity of the lower mantle is 30 times the viscosity of
the upper mantle.
More recent results have revealed a different way out of the paradox [123, 155].
Figure 9.8(a) shows a gradient of tracer concentration in the upper mantle of the
model in Figure 9.5. This occurs because the upper mantle has a lower viscosity,
especially earlier in Earth history when it was hotter (see Figure 9.9). This lower
viscosity offers less resistance to sinking tracers, which settle through the upper
mantle and then (mostly) remain in suspension in the lower mantle, which has a
viscosity 30 times higher. This implies that the uppermost mantle would be depleted
in its basaltic component, because old oceanic crust would tend to sink deeper into
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