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In-Depth Information
values -highandlow -areaveragedoutatridges
by large-volume mantle sampling.
oceanic-island volcanoes sample this mantle in
different ways and to different extents. Superim-
posed on this sampling difference, is the possibil-
ity of real lateral and vertical heterogeneity hav-
ing scales that cannot be averaged out.
Basalts and hydrothermal fluids having
R
greater than about 8.5---9.0
R
A
are commonly
believed to be
'plume-type' or 'lower-
mantle' helium
.
R
can be significantly higher
than the normal MORB range and these high val-
ues are, by definition 'plume-type' and, by con-
vention, are attributed to the lower mantle. There
is some circular reasoning here; although high
values are rare along the global spreading ridge
system --- except at Iceland and the Red Sea ---
they are excluded, when found, and attributed to
plumes. 'Hotspots' or elevated regions of ridges
Statistics
There are as many low-
R
hotspots as there are
high-
R
hotspots. The statistics (means, medians)
of many hotspot datasets of helium isotopic
ratios are identical or similar to midocean ridge
statistics. The hypothesis that OIB and MORB, as
global datasets, are drawn from the same pop-
ulation cannot be rejected by standard statisti-
cal tests, although selected subsets of these pop-
ulations can differ. The differences in variances
of the datasets are consistent with midocean
ridges sampling a larger volume of a heteroge-
nous mantle than do oceanic islands. Statisti-
cally, the MORB and OIB datasets could be drawn
from the same population, at least for helium iso-
topes. This does not appear to be true for other
isotope systems. The issue is complicated because
mixing relations and averages of ratios involve
also the absolute abundances, not just the ratios.
If the absolute abundance of helium in the var-
ious components differ a lot, then mixtures will
be dominated by the high-[He] members. On the
other hand, if the Sr and Nd contents are similar,
then all components contribute to the observed
average ratios.
If two datasets have the same mean and differ-
ent variances they may be different size samples
from the same distribution. A consequence of
the central limit theorem is that the ratio of
the variances of a large number of samples from
a heterogenous population is inversely propor-
tional to the ratios of the number of samples
contributing to the average. The larger volume
sampled by ridges includes the effect of larger
degreesofpartialmeltingaswellaslargerphys-
ical volumes.
A common hypothesis is that helium iso-
topes in mantle-derived materials represent two
distinct populations, the midocean-ridge (MORB)
reservoir and the oceanic-island (OIB) reservoir.
This based on the observation that
some OIB
samples have higher ratios than the
mean of the MORB distribution
. This is
not a valid statistical argument. The alternative
hypothesis is that the mantle is heterogenous
on various scales and that midocean ridge and
8
6
4
2
0
24
22
20
18
16
Standard deviation
s
statistically inaccessible
max
Xenoliths
Seamounts
mean
14
12
10
8
6
4
2
0
R
R
a
/
MORB
Islands
min
statistically inaccessible
1
2
3 4
V
OLUME OF
S
AMPLED
S
PAC E
5
6
7
8
Fig. 16.7
An illustration of the central limit theorem.
Midocean ridges sample very large volumes whereas
seamounts and xenoliths are small-scale small-volume
samples that more faithfully represent the true heterogeneity
of the mantle. In this example, the range of
R
/
R
a in the mantle
is from 0 to 24. This complete range will only be evident by
taking many small-scale small-volume samples. Large islands
and spreading ridges average over large volumes and cannot
access the whole range. The presence of high values in OIB
samples does not imply that these samples are from a
different part of the mantle.
