Geoscience Reference
In-Depth Information
13.4
Geochemical Constraints and an
Integrated Model
2008, for detail). In this case, Independent Com-
ponent Analysis (ICA) is suitable to identify the
independent vectors from the data set (Hyv arinen
et al
. 2001). ICA utilizes non-Gaussianity inher-
ited in the data as a measure of independence: ac-
cording to the central limit theorem, random mix-
ing of non-Gaussian variables approaches Gaus-
sian more than the original variables. In turn, a
linear combination of the observed mixture vari-
ables will be maximally non-Gaussian if it equals
to one of the independent components.
Using ICA, two independent components (IC1
and IC2) that span the major plane have been
identified (Figure 13.8, modified from Iwamori
et al
. 2010), and in fact the two ICs bear indepen-
dent information: IC1 broadly separates OIB from
MORB, while IC2 discriminates the geographical
distribution irrespective of OIB or MORB. Most
of OIB plot in the positive IC1 field, whereas
most of MORB plot in the negative field. Except
for the plume-influenced ridges such as Iceland,
Azores, Galapagos and Red Sea, 83% of MORB
have negative IC1, whereas 95% of OIB have
positive IC1 except for Hawaii and Iceland that
plot mostly in the negative IC1 field. On the
other hand, irrespective of OIB or MORB, oceanic
basalts from the Indian Ocean mostly plot in
the positive IC2 field, whereas the others mostly
plot in the negative field, demonstrating that IC2
tracks geographical provenance.
The vector associated with melting has nega-
tive slopes in
87
Sr/
86
Sr-
204
Pb/
206
Pb and
87
Sr/
86
Sr-
143
Nd/
144
Nd spaces, whereas it exhibits a
positive slope in
143
Nd/
144
Nd-
204
Pb/
206
Pb. The
vector associated with dehydration has neg-
ative slopes in
143
Nd/
144
Nd-
204
Pb/
206
Pb and
87
Sr/
86
Sr-
143
Nd/
144
Nd spaces, whereas it exhibits
a positive slope in
87
Sr/
86
Sr-
204
Pb/
206
Pb.
Based on the geochemical nature of ICs and
a differentiation-recycling model of the mantle
concerning trace elemental and isotopic compo-
sitions proposed by Rudge
et al
. (2005), Iwamori
et al
. (2010) argued the origin of ICs as follows.
IC1 may be related to elemental fractionation
associated with melting and the subsequent ra-
diogenic ingrowth with an average recycling time
of 0.8-2.4 Ga, whereas IC2 are related to aqueous
Mantle compositional variability has been
extensively studied using oceanic basalts as
geochemical messages from the mantle (e.g.,
Hofmann, 2003). Wide compositional variations
have been recognized for both mid-ocean ridge
basalts (MORB) and ocean island basalts (OIB),
and based on their isotopic compositions mainly
of Sr, Nd and Pb, various mantle end-members
have been defined: e.g., EMI and EMII [enriched
mantle I and II], HIMU [high
μ
(238U/204Pb)],
DMM [depleted MORB mantle], PREMA [preva-
lent mantle], and BSE [bulk silicate Earth] (Zindler
& Hart, 1986). Hart
et al
. (1992) and Hanan and
Graham (1996) proposed additional end-members
FOZO [focus zone] and ''C'' [common component]
towards which the arrays defined by individual
oceanic hot spot and MORB broadly converge.
In addition to the studies on the nature of these
end-members, the overall structure of the whole
data is important, and has been investigated using
multivariate statistical analyses. Principal Com-
ponent Analysis (PCA) is one of such methods and
has been frequently used. The most important re-
sult commonly recognized with PCA is that the
data structure is planar in the five dimensional
space of Sr, Nd and Pb isotopic ratios, e.g., based
on 57 data (Zindler
et al
. 1982) or 570 data (Hart
et al
. 1992). The planar structure has been con-
firmed by a recent study with 4288 oceanic basalt
data that cover the major oceans fairly densely
(Iwamori
et al
. 2010). The major plane accounts
for 95.7% of the sample variance, indicating that
only two independent differentiation processes
in terms of Rb-Sr, Sm-Nd and U-Th-Pb parent-
daughter pairs are required to explain most of the
mantle isotopic variability.
We now seek for the independent vectors that
span the major plane based on the statistical char-
acteristics of the data distribution. Principal com-
ponents (PCs) are independent only when the data
form a joint Gaussian distribution, and if the data
distribution is non-Gaussian, PCA fails to extract
the independent features (Iwamori & Albar ede,
