Geology Reference
In-Depth Information
mantle? And if the process, or something like it, began early in Earth history,
then it would have been converting primitive mantle into processed, heterogeneous
mantle. Is there likely to be any primitive mantle left? We can address the second
question first.
The depth of the main melting under mid-ocean ridges (i.e. the depth to the dry
peridotite solidus) is usually taken to be about 60 km, but minor melting or melting
of heterogeneities might occur as deep as 110 km [80, 202]. The present areal rate
of seafloor spreading is 3 km
2
/yr. The rate at which mantle mass is being processed
through the ridge melting zone can then be calculated as
φ
=
ρA
s
d
m
,
(10.1)
where
ρ
is the density of the upper mantle,
A
s
is the areal spreading rate and
d
m
is
the melting depth. The time it would take to process one mantle mass,
M
,atthis
rate is then
=
τ
M/φ.
(10.2)
This can be called the mantle processing time [203]. With the above values, a
density of 3300 kg/m
3
and a mantle mass of 4
10
24
kg, this gives
τ
4Gyr.
This result suggests that most of the mantle will have been processed through
ridge melting zones, but there are two other important things to consider. On the one
hand, the mantle was probably convecting faster in the past, which would increase
the amount of processing. On the other hand, some of the material processed may
have been previously processed, and this reprocessing will not affect the amount
of primitive mantle remaining.
As we saw in Chapter 9, because of higher radioactive heating in the past, the
mantle would have been hotter, would have had a lower viscosity and so would
have convected faster. At present the average plate velocity is about
v
×
=
5cm/yr.
A useful timescale to use here is the
transit time
, which is the time it would take
mantle material to traverse the mantle depth,
D
=
=
3000 km. The transit time is
then
t
t
=
D/v,
(10.3)
and this evaluates to
t
t
60 Myr. If convection had been proceeding at the present
rate for 4.5 Gyr, there would thus have been time for about 75 transits. From a
thermal evolution calculation of the kind presented in Chapter 9 (but neglecting
the early transient cooling), I estimated [203] that in fact there have been about
300 transits, four times as many as assuming a steady rate. At present rates of
convection, it would thus take 4
=
×
4.5 Gyr
=
18 Gyr to accomplish this number of
transits.
