Geology Reference
In-Depth Information
Models that include tracers of dense subducted oceanic crust usually form accu-
mulations at the base, as in Figures 9.5 and 9.10. The tracer concentration profiles
of Figure 10.18 also reveal the accumulations. These results, and those of others
[218, 219], confirm the results of Christensen and Hofmann [122] and support the
hypothesis of Hofmann and White [74] that plumes acquired an additional com-
plement of basalt-composition material from the D
layer. These models therefore
offer a straightforward explanation for the enrichment of OIBs relative to MORBs.
Although this explanation is plausible, it is not easy to quantify, in terms of
how much additional basaltic component a plume is likely to carry. There will
be a physical limit, because the negative buoyancy of the basaltic component will
counter the positive thermal buoyancy of the plume, and if there is too much basaltic
component the plume would no longer ascend. There have been some instructive
models of thermochemical plumes ([81-84]; Chapter 7), but their behaviour is
not simple, as there is a tendency for heavy and light components to separate.
Nevertheless, it ought to be possible to establish what amounts are plausible, and
whether they are consistent with the observed enrichments of OIBs.
10.7.2 Residence times
The extraction of reliable ages from such models has required a couple of issues
to be clarified. Christensen and Hofmann [122] obtained residence times of about
1.3 Gyr, but the models were run for only 3.6 Gyr at steady conditions, leaving
the possibility that longer runs would have yielded larger residence times. Davies
[203] ran models for 18 Gyr at steady conditions and obtained residence times up
to 2.7 Gyr. On the one hand, this seemed to dispose of the previously perceived
difficulty of mantle heterogeneities surviving for billions of years. On the other, it
raised questions as to the source of the large residence times, which might have
been due to using better plate simulations, to having a high-viscosity lower mantle
(which the C&H models lacked) or to different assumptions about melting.
Subsequent studies [215-217] have demonstrated that residence times and
degree of processing are controlled almost entirely by the rate at which material is
processed through mid-ocean ridge melting zones (
φ
in Eq. (10.1)) or, equivalently,
by the processing time
τ
(Eq. (10.2)). Other factors, such as the stiffness of sub-
ducted plates, the viscosity of the lower mantle, the vigour of convection (in other
words the Rayleigh number), the dimensionality (two-dimensional versus three-
dimensional) and the presence of toroidal flow (horizontal shearing) have only
secondary effects. An example of a three-dimensional model with heavy tracers is
shown in Figure 10.20.
It is important, however, to run the models for a sufficient time. Figure 10.21(a)
shows that the average residence times of tracers are still increasing even after
