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so the amount of crust in the mantle would build up. As crust accumulated within
the mantle, its rate of removal would increase. Eventually they might approach a
balance, where the rate of removal equals the rate of addition.
This situation can be analysed in a similar way to the removal of primitive mantle,
and it is explained in Section C.2. The result is that
f
will exponentially approach a
maximum
f
m
=
φ
c
/φ
. With a crustal density of 2900 kg/m
3
and thickness of 7 km,
this gives
f
m
=
0.06. The fraction at any given model time,
t
m
,is
f
m
1
t
m
/τ
)
.
f
=
−
exp (
−
(10.7)
This specifies that
f
starts at zero, initially builds up at the rate 1
/τ
c
, but then the
rate of accumulation slows and
f
approaches
f
m
. After 18 Gyr of model time,
f
will
be 99% of
f
m
.
In other words, the mantle should contain about 6% of subducted, unprocessed
oceanic crust. The reason the amount of crust within the mantle reaches a maximum
is that old subducted crust is removed by melting within melting zones. Thus in
the asymptotic state old subducted crust is removed as fast as it is added. As we
will see later, not all crust melted under ridges may have been removed from the
mantle, so the total amount of crust-derived material may be about double this.
This result quantifies the widespread expectation that, after several billion years
of subducting oceanic crust plus underlying depleted mantle, the mantle will have
substantial heterogeneity of major elements, with accompanying heterogeneity of
trace elements.
10.5 Melting in a heterogeneous mantle
Probably the most important implication of major element heterogeneity is that
the processes of mantle melting and melt extraction will be substantially different
from those in the kind of uniform source that has been commonly assumed. Almost
every aspect of these processes needs to be re-examined.
The main heterogeneity being injected into the mantle is the duality of oceanic
crust and its complementary depleted mantle. The basaltic composition of oceanic
crust forms eclogite at upper-mantle pressures, and eclogite melts at lower tem-
peratures in the upper mantle than does a typical peridotite of average mantle
composition, as is illustrated in Figure 10.11. Thus, as a heterogeneous mixture
of eclogite and peridotite rises under a mid-ocean ridge, it is the eclogite that will
melt first, and it may melt substantially before any peridotite melts. It may even
produce more melt than a comparable homogeneous source [169].
Over the past decade petrological and geochemical studies have addressed the
question of melting in such a heterogeneous source (e.g. [202, 204, 205] and ref-
erences therein). A key factor is that melt derived from eclogite pods will be out
of chemical equilibrium with the surrounding material, peridotite. The melt will
