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magma can have such high La/Yb, Rb/Sr and Pb-
isotope ratios that derivation from an enriched
source is indicated, but the Sr- and Nd-isotope
ratios imply derivation from an ancient depleted
reservoir. Many island, island-arc and continen-
tal basalts have these characteristics. These appar-
ently paradoxical results simply mean that ratios
do not average as do concentrations. An addi-
tional complication is that the melt components,
and the mixed hybrid, can experience crystal frac-
tionation while mixing. Magma mixtures and
evolved magmas do not necessarily define simple
mixing lines.
they do not have to be recycled into the deep
lower mantle before they return to the surface.
Observed magmas are blends or mixtures of com-
ponents, or partial melts therefrom, with various
isotopic signatures followed by variable degrees
of crystal fractionation and reactions with the
crust and mantle on the way to the surface. Trace-
element and isotope ratios of mixtures can have
anti-intuitive properties.
The recipes and mathematics of mixtures
Rocks, and the mantle, are composed of compo-
nents .LetuscallthemA,B,C...Thefractionof
each component in the mix is x , y , z ...The
mixture itself, M, has properties that are the
appropriate weighted average of the properties
of the components. It is straightforward to con-
struct a rock, or a mantle, or a fruitcake, if
we know all the ingredients and the propor-
tions in which they occur. It is not straight-
forward to infer the ingredients and the mix-
ing ratios if we just have samples from M, or
if we know the ingredients but not the pro-
portions. Our inferences depend on assumptions
and how we sample M. There are techniques,
known as geophysical inverse theory,
sampling theory and the central limit
theorem (CLT) for approaching these kinds of
problems.
Consider first, the fruitcake. The components
are bits of fruit and dough. Every large bite is
more-or-less the same. Every tiny bite is different,
a different bit of fruit or a different combination.
The big bites have very little variance in com-
position or taste, while the compositions (tastes)
of the small bites have enormous scatter. This is
a consequence of the CLT. One cannot infer the
composition of the fruitcake from the homoge-
nous big bites, one can only infer the average
taste.
Consider next, the rock. A rock is composed
of minerals, inclusions and intergranular mate-
rial. By grinding up a large sample, one infers the
average composition of the rock. Many such sam-
ples from a homogenous outcrop will give similar
results. That is, there will be little scatter or vari-
ance. However, if very small samples are taken,
there will be enormous variance, a reflection of
The isotope zoo
A large number of components in MORB and
OIB have been proposed and labeled. These are
primarily based on isotopic characteristics. A
short list is: EM1, EM2, HIMU, DUPAL, C,
PHEM, PREMA, FOZO, LOMU, LONU and Q.
The origin of the isotope species in
the mantle zoo is a matter of considerable
controversy. In the isotope geochemistry liter-
ature these are attributed to the lower mantle
and to plumes but there is no evidence that
this is the case. There is considerable evidence
that all these species originated at the surface
of the Earth, in the crust or in the lithosphere,
and may have evolved in the shallow mantle.
Various kinds of altered and recycled materials
have been proposed as contributors or ancestors
to these species. Among the suggestions are
oceanic sediments, recycled oceanic crust with
some pelagic sediments (EM1), continental sed-
iments or dehydrated oceanic sediments (EM2),
altered oceanic crust and sediments or ancient
altered MORB (HIMU), delaminated lower conti-
nental crust (EM1, DUPAL), peridotites, and high
3 He/U and low U and Th bubbles in depleted
lithosphere, restites or cumulates (FOZO). Some
EM components of the mantle have oxygen
isotopic compositions similar to MORB and peri-
dotite xenoliths, ruling out a large contribution
of subducted sediment and other sources that
were proposed on the basis of Sr and Nd isotopes
alone.
All of these species may co-exist in the shal-
low mantle, along with the sources of MORB;
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