Geoscience Reference
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thebasicheterogeneityofrocks.However,the
mean of all the small samples will be close to
themeansofthelargesamples.Thisisanother
consequence of the CLT. The homogeneity of the
large samples does not mean that the rock is
homogenous; it simply means that large-scale,
large-volume averages have been taken. Multiple
microprobe analyses of the same rock would tell
a different story. Some small-scale samples would
give extreme compositions, compositions not evi-
dent in any of the large-volume averages. This
doesnotmeanthattheycomefromadifferent
rock.
Finally, consider the mantle. We have homoge-
nous samples of MORB from midocean ridges,
which are enormous blending and averaging
machines. Seamounts on the flanks of oceanic
ridges provide smaller volume samples from the
same mantle, and these exhibit enormous vari-
ance. Ocean-island basalts also exhibit a wide
range of compositions, partly a reflection of
the large-scale heterogeneity of the mantle and
partly a reflection of the nature and scale of
the sampling process. Sometimes the magmas
bring up small fragments, or xenoliths, from
the mantle. These are highly variable in com-
position and sometimes exhibit a greater range
of compositions than one observes globally in
basalts. Midocean-ridge basalts are blends of mag-
mas and solid materials from huge volumes, and,
as expected, they show little variance, at least in
some properties. MORB is not a component or a
reservoir ;itisanaverage,andwillbetreatedas
such below.
Considering all of this, how does one infer
the composition of the mantle? One approach is
to assume that one knows the composition and
volume of the major reservoirs such as the crust
and the upper mantle and then to attribute dis-
crepancies to the lower mantle or other hidden
reservoirs. The pyrolite model assumes that the
mantle is composed of known amounts and com-
positions of a mafic and an ultramafic compo-
nent. A more objective approach is to make a
list of all the materials that are known to enter
and leave the mantle and construct a compos-
ite from these that satisfies certain constraints.
These constraints might include the total vol-
ume of the crust (one of the components), the
sumofthecomponentsis1,andtheratiosof
some of the components should be chondritic.
This is the approach taken in the following. It is
clearly important to know something about the
various components; magmas, ultramafic rocks,
crust, kimberlites and so on. Most of the com-
ponents are also mixtures of other components.
In some cases, and for some elements, it may
be important to consider mineral components,
such as zircon and rutile, or rare magmas such
as carbonatites. The reason for this is the same
reason that one must include the crust in any
mass balance in spite of the fact that it has a very
small total volume. Some rocks have concentra-
tions of some elements that exceed the crustal
concentrations by an order of magnitude; one
cannot ignore such rocks. For a complete mass
balance one cannot even ignore the oceans and
the atmosphere; iodine and chlorine, for exam-
ple, are concentrated on the atmosphere and the
biosphere.
In addition to all the above, one must always
remember that isotopic and trace-element ratios
do not average and mix as do concentrations or
absolute abundances.
The inverse approach
The inverse approach is more widely used in
geophysics than in geochemistry. The problem
is one of inferring mantle chemistry from var-
ious products of differentiation, which them-
selves are averages. One alternative approach is
to use petrological insight to pick the most rep-
resentative constituents for the mantle, and to
adjust their proportions to satisfy certain key
constraints or assumptions.
The refractory elements can be assumed to be
in the Earth in chondritic ratios but we do not
know the absolute concentrations or their distri-
bution. In order to estimate absolute concentra-
tions, and the volatile and siderophile content
of the mantle, we seek a linear combination of
components that gives chondritic ratios for the
refractory elements. We can then estimate such
key ratios as Rb/Sr, K/U and U/Pb that involve non-
refractory elements. In essence, we replace the
five basic building blocks of mantle chemistry, ol,
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