Geoscience Reference
In-Depth Information
source. In the real world, sampling at volcanoes
involves
1 Scrabble game
melting,
recrystallization
and
incom-
20
plete extraction, as well as statistics.
Fast spreading oceanic ridges process large
volumes of the mantle and involve large degrees
of melting. A consequence of the central
limit theorem is that the variance of samples
drawn from a heterogenous population (reser-
voir) depends inversely on the sampled volume
(Anderson, 2000b; Meibom & Anderson, 2003).
The homogeneity of a sample population (e.g.
all MORB samples) can thus simply reflect the
integration effect of large volume sampling. The
presumed homogeneity of the MORB source may
thus be an illusion.
The 'MORB reservoir' is thought to be homoge-
nous because some isotopic ratios show less
scatter in MORB than in ocean-island basalts
(OIB). The common explanation is that MORB
are derived from a well-stirred, convecting part
of the mantle while OIB are derived from a dif-
ferent, deeper reservoir. Alternatively, the
homo-
geneity of MORB can be explained as a
consequence of the sampling process
.
The standard, two-reservoir model of geochem-
istry is reinforced by questionable -- from a sta-
tistical point of view -- data filtering practices.
Samples that are judged to be contaminated by
plumes (i.e. OIB-like samples) are often removed
from the dataset prior to statistical analysis.
Sometimes the definition of plume influence is
arbitrary. For example, isotopic ratios that exceed
an arbitrary cutoff may be eliminated from the
dataset. In this way, the MORB dataset is forced to
appear more homogenous than it really is. This
method is commonly applied to
3
He/
4
He. Despite
this, various ridges still have different means and
variances, and these depend on spreading rate
and ridge maturity.
The
upper mantle
,
sub-continental lithosphere
,and
lower mantle
are usually treated as distinct and
accessible
geochemical reservoirs
. There is evidence,
however, for ubiquitous small- to moderate-scale
heterogeneity in the upper mantle, referred to
as the
statistical upper mantle assem-
blage (SUMA).
This heterogeneity is the result
of processes such as inefficient melt extrac-
tion and long-term plate tectonic recycling of
sedimentary and crustal
components
. The SUMA
18
average by ones
average by twos
average by threes
16
14
12
10
8
6
4
2
0
0
24
6
8
10
12
14
16
18
20
22
24
26
ABCDE FGH I J K LMNOPQRS TUVWXY Z
Fig. 12.1
The distribution of letters, and their assigned
numerical values, in a Scrabble game. Also shown are average
values for two and three-letter combinations, illustrating the
smoothing effect of the CLT. One might conclude that the
various combinations represent different bags, or reservoirs,
of letters.
were a distribution of normalized helium iso-
topic ratios one might conclude that the popula-
tion that was being sampled by four-letter words
did not contain the extreme values that one- and
two-letter words were sampling. The lower curve
in Figure 12.1 approximates the helium isotope
histogram for MORB; the other curves look more
like OIB statistics.
SUMA -- sampling upon melting and
averaging
In dealing with the mantle, one is dealing with
a heterogenous system -- heterogenous in prop-
erties and processes. In geochemical box mod-
els the mantle is viewed as a collection of large,
discrete and isolated
reservoirs
, with definite loca-
tions and compositions. In petrological models
there are distinct
components
that can be inti-
mately mixed. The
sampling process
usually envis-
aged is similar to using a dipper in a bucket of
water. In models based on
sampling theory
the vari-
ous products of mantle differentiation are viewed
as averages, different kind of samples from a
heterogenous population; a homogenous product
does
not
imply
a
homogenous
or
well-mixed
