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The idea certainly has some attractive features. First, a large amount of oceanic crust could have
been created during early Archean times, and this process would certainly deplete the mantle in in-
compatible elements. Since heat flow was presumably higher in the early Archean than today, it is
quite possible that plate velocities were higher then, implying more rapid creation and destruction
of oceanic crust. Chase and Patchett (1988) calculate that if the rate of oceanic crust creation through
time has decreased in proportion to radioactive heat production in the Earth, some 2 × 1023 g of oce-
anic crust would have been created by
3.5 Ga. If the percentage melting in-
14
MM
volved in the creation of oceanic crust
Sediments
GI
12
is 10% (which is roughly the case for
Arcs
CM
present oceanic crust), melt would
Basalts/Komatiites
KR
10
have been extracted from some 2 ×
IA
1024 g of mantle, or about half the
Moon
8
SA
µ f
NW
mass of the mantle, by 3.5 Ga. The
Nd
MA
Sm/Nd= 0.4
SO
resulting depletion in Nd relative to
RM
CS
6 UO
FF
Sm would be sufficient to produce the
PB
AN
NF
BA
µ values observed in the early Ar- 4
Nd
ARS
chean rocks preserved in continents.
CO
BE/
2
Yet another possibility is that an
AM
IS
early continental crust did form, but
DM
it was subsequently destroyed and re-
0 1.0 2.0 3.0 4.0
cycled into the mantle. This possi-
Time (Ga)
bility was first suggested by R. L.
Figure 11.19. µ in rock suites for which there is little evi-
Nd
Armstrong in 1968, long before the
dence of involvement of much older crust in their genesis
isotopic data in Figure 11.19 were
(after Smith and Ludden, 1989).
494 November 25, 1997
W. M W hit e Geochemistry
Chapter 11: The Mantle and Core
available. Armstrong argued that the continental crust reached its present mass by about 4.0 Ga and
crustal mass has subsequently remained constant. Armstrong was the first to recognize the possibility
that plate tectonics, which then was a new and revolutionary theory, provided a means of transport-
ing material from the crust to the mantle. In ArmstrongÕs model, new continental crust is continually
created, but this creation is balanced by destruction of crust through erosion, deposition of the sedi-
ments on the oceanic crust, and subduction of this sediment into the mantle.
There are a number of reasons to believe that continental crust has been recycled into the mantle.
As we shall see in the next chapter, there have clearly been additions to the continental crust
through geologic time. If there has been no accompanying destruction of crust, the volume and mass of
crust should have increased through geologic time. Armstrong pointed out that this should have led
to flooding of the continents, as the oceans are confined to a smaller and smaller area. But this has
not occurred. Armstrong also noted that virtually no deep ocean pelagic sediment is preserved on con-
tinents, implying that it is carried into the mantle during subduction. Though it was at one time
widely believed that the sedimentary veneer on the oceanic crust is scraped off or ÒobductedÓ in sub-
duction zones, careful study of several trenches shows little or no accumulation of sediment despite
tens of millions of years of continuous subduction.
From a geochemical perspective, growth of the continental crust through time should lead to in-
creasing incompatible element depletion of the upper mantle. This leads, for example, to an increase
in the Sm/Nd ratio through time, which should result in the µ of the mantle following a concave
Nd
upward path (Figure 11.20). In actuality, µ in the depleted mantle appears to follow a linear evo-
Nd
lution, implying that the mass of the continents has not grown through time. However, there is an al-
ternative explanation, proposed by Patchett and Chauvel (1984). They pointed out that if a growing
continental mass could still result in constant Sm/Nd of the mantle if the volume of the depleted
mantle grew.
Let's consider now consider the question of the volume of mantle that would have to be depleted in
incompatible elements to create the continental crust. We start by assuming that the Earth consists of
three reservoir: the continental crust, the volume of mantle depleted in incompatible elements as a re-
sult of formation of this crust, and an undepleted, or primitive mantle (Figure 11.21). For any radioac-
tive decay system we can write a series of mass balance equations. For the Nd isotope system, we as-
sume that the bulk Earth has µ of so, so we may write:
Nd
j
11.1
£j MjC jµ Nd =0
j
where Mj is the mass of the jth reservoir, Cj is the concentration of Nd in that reservoir, and µ is the
Nd
value of µ in that reservoir. We also assume the Sm/Nd is chondritic. WeÕll use fSm/Nd to denote the
Nd
relative deviation of the Sm/Nd ratio from the chondritic value, i.e.:
147
Sm/144Nd 147Sm/144NdCHUR
f = 11.2
Sm/Nd
147
Sm/144NdCHUR
Then we may write a similar mass balance for the Sm/Nd ratio for the Earth:
j
11.3
£j MjC jfSm/Nd =0
The mass balance for the Nd concentration is:
j o
11.4
£j MjCNd =MoCNd
where Mo is the mass of the silicate Earth and Co Nd in the concentration of Nd in the silicate Earth.
Finally, the masses of our three reservoirs must sum to the mass of the silicate Earth:
11.5
£j Mj =Mo
Since the half-life of 147Sm is long compared to the age of the Earth, we may use the approximation:
495 November 25, 1997
W. M W hit e Geochemistry
Chapter 11: The Mantle and Core
e» t = » t + 1 (?)
Fd
and hence:
CRUST
143
Nd/144Nd = 143Nd/144Ndi + 147Sm/144Nd » t 11.6
F
F' (?)
The equation may be transformed into epsilon notation, in which
case it becomes:
DEPLETED MANTLE
i
µ E" µ +fSm/NdQt
Nd Nd 11.7
i
where µ is the initial value of µ (i.e., at t = 0), and Q and
Nd
Nd
fSm/Nd are defined as:
PRIMITIVE MANTLE
4 147
10 » Sm/144NdCHUR
Q = 11.8
Nd
143
Nd/144NdCHUR
QNd is a constant with a value of 25.13 Ga-1.
CORE
a
Assuming that the crust has grown from primitive mantle, then
c
c
. .
µ =fSm/NdQTc 11.9
Nd
M
Md CRUST u
where Tc is the average age of the crust. If the Earth consists of C1
M1
only three reservoirs for Nd, namely the continental crust, de-
UPPER MANTLE
pleted mantle, and primitive mantle, and if the depleted mantle
and crust evolved from a reservoir initially identical to primitive
mantle the mass balance equation 11.1,11.3, and 11.4 must hold for
M2 C2
crust and depleted mantle alone. In this case, these equations can
be combined with 11.9 to derived a relationship between the mass
of the crust and the mass of the depleted mantle:
c c c c LOWER MANTLE
C C Qf T
Nd Nd Sm/Nd
Mdm/Mc = 1
o o
dm 11.10
C3
C C M3
µ
Nd Nd b
Nd
Thus the mass ratio of depleted mantle to crust can be calculated
Figure 11.21. The three reservoir
if we know the Sm/Nd ratio of the crust, the µ of the depleted
Nd
model of the mantle. The de-
mantle, and the concentration of Nd in the crust and in primitive
pleted mantle is the source of
mantle. Figure 11.22 is a plot showing the solutions of 11.10 as a
MORB and has µ = +10, the
Nd
dm
function of TC for various values of µ obtained by DePaolo (1980).
lower mantle is primitive and
Most estimates of the average age of the crust are between 2 and
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