Geology Reference
In-Depth Information
15
10
5
0
0
0.2
0.4
0.6
0.8
1
tracer age/model age
Figure 10.23. Histogram of MORB tracer ages (thin black) compared with the
age distribution predicted from the simple sampling theory (solid grey) and with
a sampling delay time of 0.4 Gyr (Earth time) (dashed grey). The tracer ages are
given relative to the final model time. After Huang and Davies [215]. Copyright
American Geophysical Union.
times. From Figure 10.21(b) we would expect 20-70% of the mantle to have been
processed, which is consistent with their results.
10.7.3 Sampling theory
The simple sampling theory that predicts an exponential decline of remaining prim-
itive mantle (Section 10.4.3) and an asymptotic proportion of subducted oceanic
crust (Section 10.4.4) was extended by Huang to estimate the mean residence times
of tracers and even their age distributions [215-217]. The mean residence time as
a function of model time,
t
m
(i.e. equivalent to a model running at present rates,
see Figure 10.10) is
t
R
=
τ
[1
−
exp(
t
m
/τ
)]
.
(10.8)
This gives the solid curve of Figure 10.22 (for
t
m
=
18 Gyr, i.e. after 4.5 Gyr of
evolution in Earth time).
Usually ridges are well separated from trenches, and it takes some time before
any subducted material reaches a ridge melting zone. This will cause a delay before a
tracer is processed, and a corresponding lack of young tracers. This was observed in
the age distributions of tracers [203], an example of which is shown in Figure 10.23.
This effect increases the processing time in the model. The theory was extended to
take account of this by adding a delay time to the processing, and the grey curves
in Figure 10.23 show predicted age distributions without (solid) and with (dashed)
a processing delay, in this case of 0.4 Gyr. Mean ages with processing delays are
included in Figure 10.22 (upper curves) for delays of 0.4 Gyr and 1.2 Gyr [215].
The numerical model results are mostly bracketed by these curves.
