Geology Reference
In-Depth Information
3
2.5
2
1.5
1
0.5
2
4
6
8
Processing time [Gyr]
Figure 10.22. Final residence time as a function of processing time,
τ
.Curvesare
from the sampling theory (Section 10.7.3) for simple sampling (solid) and two
cases in which a sampling delay has been assumed (dashed). Results from some
numerical models are indicated by the symbols. From Huang and Davies [215].
Copyright American Geophysical Union.
A second requirement is to determine an accurate residence time for the mantle.
This depends on the average plate velocity and on the depth of melting (Eqs (10.1)
and (10.2)). The biggest uncertainty is the depth of melting. Because of mantle
heterogeneity, trace elements are likely to be scavenged from a depth of about
110 km under mid-ocean ridges (Figure 10.11), and we saw in Section 10.4.3 that
this gives a processing time of
τ
4 Gyr. If the melting depth were taken to be the
conventional peridotite melting depth of 60 km, then
τ
=
7.3 Gyr and processing
would be relatively slow. The relationship between residence time (at the end of a
run) and processing time is shown in Figure 10.22, as estimated by the sampling
theory of the next section. This indicates that a processing time in the range 3-4 Gyr
will give residence times in the range 1.5-2 Gyr. However, there are some details
that affect this result, as will be discussed in the next section.
These plots explain the main differences among earlier results. For example,
Davies [203] in two models used an areal spreading rate of only 2.4 km
2
/yr (6 cm/yr
linear spreading rate and an assumed ridge length of 40 000 km) and a melting depth
that decreased to 70 km at present, and this gives a processing time of 7.2 Gyr. The
mean MORB residence times from these models were 2.7 Gyr and 2.6 Gyr, which
is within the range predicted in Figure 10.22. On the other hand, Christensen and
Hofmann's [122] processing time was only 1.5 Gyr and their mean residence time
less than 1.4 Gyr, also within the range predicted in Figure 10.22. Considering the
noble gases in the mantle, van Keken and Ballentine [220, 221] estimated that
the mantle would have been processed and degassed only by 35-70%, but their
models were run at present rates for only 4 Gyr and for only 0.2-1.3 processing
=
