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Volume 9, Number 4
24 April 2008
Q04033, doi:10.1029/2007GC001753
AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES
Published by AGU and the Geochemical Society
ISSN: 1525-2027
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Decoupled isotopic record of ridge and subduction zone
processes in oceanic basalts by independent component
analysis
Hikaru Iwamori
Department of Earth and Planetary Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
([email protected])
Francis Albarède
Laboratoire des Sciences de la Terre, UMR CNRS 5570, Ecole Normale Supérieure de Lyon and Université Claude
Bernard Lyon 1, F-69007 Lyon, France
[1] Isotopic variability in oceanic basalts indicates possible interactions among multiple mantle
components or geochemical end-members. Beyond the standard principal component analysis, which
has been used so far to identify mantle components, the relatively new independent component analysis is
well suited for extracting independent features in multivariate compositional space. Radiogenic isotopic
compositions of oceanic basalts from the Atlantic and South Indian oceans, including both mid-ocean ridge
basalts (MORB) and ocean island basalts (OIB), show that two independent compositional vectors
(referred to as independent components or ICs) account for most of the observed variations with three
isotopic ratios of Pb (856 MORB and 781 OIB) or five isotopic ratios of Pb, Sr, and Nd (672 MORB and
597 OIB). In both cases, the first IC distinguishes OIB from MORB, while another maps the geographical
distribution of a mantle component and in particular the DUPAL anomaly. This property shows that the
two ICs indeed distinguish independent information and reflect two distinctive geodynamic processes, a
feature which is not present in the conventional analysis of mantle isotopic variability. The first IC that
distinguishes OIB from MORB is similar to the isotopic trend reproduced in the MORB-recycling model
of Christensen and Hofmann (1994). The second IC that discriminates geographical distribution is
characterized by simultaneous enrichment/depletion of Pb, Rb, and Nd relative to U-Th, Sr, and Sm,
respectively, which can be explained by elemental fractionation associated with aqueous fluid-mineral
reactions. These geochemical characteristics, together with the fact that most of the observed
multidimensional isotopic space is spanned by the joint distribution of the two ICs, indicate
independent but overlapping differentiation processes which mostly take place within the depleted
mantle domain. They are likely to reflect ridge versus subduction zone processes, or melting versus
interaction with aqueous fluid. We use the regional distribution of the second, ‘‘enriched’’ IC to redefine
the DUPAL anomalous mantle and show that in addition to its Southern Ocean type locality, it also
distributes itself broadly in the Northern Hemisphere.
Components: 8433 words, 7 figures.
Keywords: oceanic basalt; isotope; independent component analysis; ridge; subduction zone.
Index Terms: 1040 Geochemistry: Radiogenic isotope geochemistry; 1038 Geochemistry: Mantle processes (3621); 1032
Geochemistry: Mid-oceanic ridge processes (3614, 8416).
Copyright 2008 by the American Geophysical Union
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Received 13 July 2007; Revised 20 February 2008; Accepted 21 February 2008; Published 24 April 2008.
Iwamori, H., and F. Albarède (2008), Decoupled isotopic record of ridge and subduction zone processes in oceanic basalts by
independent component analysis, Geochem. Geophys. Geosyst., 9, Q04033, doi:10.1029/2007GC001753.
1. Introduction
[2] One of the well-accepted concepts of mantle
isotope geochemistry is that the isotope compositions of radiogenic elements (e.g., Sr, Nd and Pb)
in terrestrial basalts can be broken down into
individual mantle components. These components
are inherited from geochemical reservoirs with a
distinctive history, such as ancient residues of
melting at ridge crests or recycled oceanic crust,
and with characteristic isotopic properties resulting
from long-term isolation. The geochemical nature
and spatial distribution of these components are
thought to provide key information on differentiation and convection of the Earth’s mantle. For this
reason, extensive efforts have been made to identify the geochemical mantle components present in
mid-ocean ridge basalts (MORB) and ocean island
basalts (OIB) [e.g., White, 1985; Zindler and Hart,
1986; Hofmann, 1997].
[3] Principal component analysis (PCA) has been
regarded as the most efficient way to identify these
mantle components [e.g., Zindler et al., 1982;
Allègre et al., 1987; Blichert-Toft et al., 2005].
Principal components are those linear combinations
of observables with the largest possible variance.
As will be shown later, however, the core assumption of PCA, which holds that the data constitute a
single multivariate Gaussian population, is clearly
invalidated for the isotope compositions of oceanic
basalts. In this case, the principal components (PCs)
do not form a true base, i.e., a set of independent
vectors describing uniquely the isotopic variability.
A promising tool for the analysis of geochemical
mantle components is independent component
analysis (ICA), which has been established in
Information Science over the past 15 years (e.g.,
see the textbooks by Hyvärinen et al. [2001] and
Amari [2002]). As with PCA, the core assumption
is that the data can be accounted for by a linear
combination of mutually independent components,
but without the condition that the population is
unique with a multivariate Gaussian distribution.
ICA deconvolves a data set into independent components (ICs) by finding the directions that maximize the non-Gaussianity through criteria such as a
higher-order cumulant or negentropy (see below) of
the projected data distribution [Hyvärinen et al.,
2001]. A caveat is that the term ‘‘component’’ as
used for both PCA and ICA refers to a vector or a
direction, which unfortunately conflicts with the
well-entrenched denomination of geochemical
mantle components. In order to avoid such confusion, we hereafter use ‘‘component’’ for describing
the statistical distribution in both PCA and ICA and
‘‘end-member’’ for the geochemical mantle components with specific compositions, such as Depleted MORB Mantle (DMM).
[4] The relevance of statistical distributions, typically normal versus lognormal, underlying elemental and isotopic data on oceanic basalts has been
discussed by different authors under different perspectives. Allègre and Lewin [1995] investigated
different geochemical properties in basalts and concluded that the underlying distributions could be
normal, lognormal, fractal or multifractal. Meibom
and Anderson [2004] conjured up the central limit
theorem to argue that the complexity and multiplicity of melting and mixing events in the mantle lead
to near-Gaussian histograms. Rudge et al. [2005]
argued that isotopic ratios are not normally distributed and analytically elaborated statistical distributions from melting-recycling models. They derived
expressions for the higher central moment and
particularly the skewness of the distributions of
isotopic ratios, which provides a background theory
for non-Gaussian histograms. These authors only
considered models with linearized radioactive decay, a constraint later released by Rudge [2006]. By
examining databases, Albarède [2005] used statistical tests (notably quantile-quantile plots and comparison between corresponding means and modes)
to show that normal distributions do not do justice to
actual histograms of isotopic ratios in MORB. We
will see in particular that the non-Gaussianity of
isotope distributions appears nowhere more clearly
than in two-dimensional diagrams of Pb-isotopic
ratios in oceanic basalts.
[5] In this study, we examined the compositional
space of a maximum of six isotopic ratios
(204Pb/206Pb, 207Pb/206Pb, 208Pb/206Pb, 87Sr/86Sr,
143
Nd/ 144 Nd, 177 Hf/ 176 Hf) with an algorithm
known as FastICA [Hyvärinen, 1999] for oceanic
basalts from the Atlantic and South Indian oceans.
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The data set includes both MORB from the literature [Agranier et al., 2005; Meyzen et al., 2005,
2007, and references therein] (most of which can
be found in the PetDB database http://www.petdb.
org) and OIB from GEOROC database (http://
georoc.mpch-mainz.gwdg.de/georoc/). On the basis
of the geochemical characteristics of the two ICs in
the five-dimensional space of Pb-Sr-Nd isotopic
ratios, the origin of isotopic heterogeneity and the
differentiation processes of the mantle are discussed.
The detected ICs naturally leads to redefinition of
the DUPAL anomaly, showing that the enriched
signature distributes broadly into the Northern
Hemisphere.
2. Principles of Independent
Component Analysis
[6] Independent component analysis (ICA) is a
statistical and computational technique designed
for revealing the hidden sources and factors that
underlie the distribution of multivariate observations [Hyvärinen et al., 2001]. In this model, the
observed multivariate data are assumed to be linear
mixtures of unknown latent variables. No assumption about the specific processes by which these
variables mix is made. Contrary to principal components, the latent variables are required to be
mutually independent but do not form a multivariate Gaussian distribution. They are referred to as
independent components (ICs), or equivalently as
the sources or factors of the observed data. The
core concepts and principles of ICA will now be
described. To avoid ambiguity, let us first review
the definition of ‘‘independent’’ versus ‘‘correlated’’ variables. Two random variables X and Y are
independent if their joint probability density function (pdf), fXY(x, y), can be factored as the product
of two pdfs of the single variables X and Y, i.e.,
fXY ð x; yÞ ¼ fX ð xÞfY ð yÞ
ð1Þ
[e.g., Hamilton, 1964]. Any distribution of n
normal variables can always be decomposed in
the linear combination of n independent variables.
Noting E the expectation (mean value), two
variables X and Y are correlated if their covariance
covð X ; Y Þ ¼ E ð XY Þ E ð X Þ EðY Þ
ð2Þ
and the associated correlation coefficient are
different from zero. From these equations, it
follows that independent variables are not correlated, whereas uncorrelated variables are not
necessarily independent. As a special case, un-
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correlated Gaussian variables are independent, but
this does not in general hold for non-Gaussian
variables. Let us use a simple example to
demonstrate that the PCs of non-Gaussian data
are uncorrelated but may not be independent
[Hyvärinen et al., 2001; Amari, 2002]. Figure 1a
shows the joint distribution of two independent
variables, s1 and s2, with uniform probability
density in the range of s1 2 [1,1] and s2 2
[1,1]. Clearly the original variables, s1 and s2, are
independent and their correlation coefficient is
zero. Let us mix s1 and s2 to produce two mixed
variables x1 = 2(s1 + s2) and x2 = 14(s2 s1) as in
Figure 1b. In this case, the PCs lie along the
diagonal axes, x1 and x2, which maximize the
variance of the data distribution projected on each
axis. Since the expectation E[x1x2] = E[(s22 s21)/2]
= 0, x1 and x2 are uncorrelated. However, it is clear
that x1 and x2 (hence the two PCs) are not
independent: when x1 departs from the mean value,
we recognize that the modulus of x2 becomes
smaller, and therefore information on x2 can be
extracted from x1. ICA achieves the goal of
extracting the independent components, s1 and s2,
from the multivariate data set as follows.
[7] First, the observed multivariate variables and
data (e.g., x1 and x2 in Figure 1b), which are
assumed to be linear mixtures of unknown independent variables, are centered and scaled by the
standard deviations along the PCs. This procedure
is called ‘‘whitening’’ [e.g., see Hyvärinen et al.,
2001, chapter 6], and transforms the variables and
the data in Figure 1b to those in Figure 1a where
the transformed variables x10 and x20 and the two
PCs lie along the diagonal axes. In this whitened
space of Figure 1a, any orthogonal pair of two
variables, including x10 and x20, are uncorrelated
but not necessarily independent. ICA searches
for the independent pair from these orthogonal
pairs by maximizing non-Gaussianity instead of
maximizing variance as for PCA. Figure 1c shows
the marginal probability density corresponding to
the joint distribution shown in Figure 1a: ps1(s1)
(probability
density projected on s1, red line)
0
and px01(x1) (that projected on x10, green line) are
plotted, together with a Gaussian distribution
(black line) plotted for reference. It shows that
ps1(s1) deviates significantly from the Gaussian dis0
tribution (large non-Gaussianity), whereas px01(x1)
deviates to a lesser extent (smaller non-Gaussianity).
In the whitened space, the independent components
have the maximum non-Gaussianity of all the
possible sets of uncorrelated components. This
is because, according to the central limit theorem,
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Figure 1. A simple example showing joint non-Gaussian distribution and the corresponding marginal probability
density. (a) The joint distribution of two independent components, s1 and s2, with uniform probability density in the
range of s1 2 [1, 1] and s2 2 [1, 1]. The diagonal axes, x10 and x20, correspond to linear transformation (i.e.,
whitening) of mixed variables x1 and x2 in Figure 1b. (b) The two variables x1 = 2(s1 + s2) and x2 = 14(s2 s1) are
produced by mixing of s1 and s2. The two nonorthogonal variables s10 and s20 correspond to the transformed (i.e.,
to the joint distribution
dewhitened) s1 and s2 in Figure 1a. (c) The marginal probability density, p, corresponding
0
0
shown in Figure 1a: ps1(s1) (probability density projected on s1, red line) and px1 (x1 ) (that projected on x10, green line)
are plotted, together with a Gaussian distribution (black line) for reference.
random mixing of non-Gaussian variables approaches Gaussian more than the original variables.
Therefore, a linear combination of s1 and s2 (i.e.,
Siaisi, where ai are the mixing coefficients), such
as x10 or x20 in Figure 1a, are closer to Gaussian
than si.
ICs. Nonorthogonal ICs in the original space and
oblique PCs with respect to ICs therefore reflect
the non-Gaussian character of the observed data.
We will show the data distribution and the
extracted ICs in both original and whitened spaces
in the following analyses of the oceanic basalts.
[8] In turn, a linear combination of the observed
mixture variables (e.g., Sibixi0, where bi are the
mixing coefficients) will be maximally non-Gaussian
if it equals to one of the independent components
[Hyvärinen et al., 2001, chapter 8]. In the example
of Figure 1a, x10 and x20 are rotated around the
center to find the ICs (i.e., s1 and s2) that give
maximum non-Gaussianity. Then the ICs can be
linearly backtracked to the original space (e.g., s10
and s20 in Figure 1b). The two ICs are therefore
nonorthogonal in the original space (Figure 1b),
which contrasts with the orthogonal relationship
between PCs. Independent components may be
orthogonal, but on the condition that the variables
are uncorrelated Gaussian variables. In such a case,
however, non-Gaussianity is zero for all the components and ICA cannot extract a unique set of
[9] Whitening removes correlation from the original data set and also determines the proportion of
the total variance that the components account for.
As is commonly assumed in both PCA and ICA,
components which account for a small proportion
of the variance are judged to be unimportant
signals. In this study we follow this conventional
procedure to determine the number of ICs,
although ICA can potentially extract ICs as many
as the number of the observed variables based on
non-Gaussianity criteria.
[10] At this point, application of ICA to the isotopic space of oceanic basalts is straightforward:
first, the observed isotopic compositions are centered and scaled by the standard deviations along
the PCs (i.e., whitened), and second the original
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function G(y) = 1a exp(ay2/2) with a constant a
is selected among the choices suggested in the
FastICA algorithm to hold robustness against
outliers [Hyvärinen, 1999]. J(y) is zero if y is
exactly Gaussian, and increases as y deviates from
Gaussian. It should be noted that, unlike principal
components, the independent components cannot
be ranked according to the proportion of variance
they account for. Because the ICs are independent,
there is no common measure of their respective
importance. The FastICA software package for
MATLAB/Octave is available at http://www.cis.
hut.fi/projects/ica/fastica/.
3. Independent Components of Isotopic
Compositions of Oceanic Basalts
Figure 2. Index map showing the distribution of
oceanic basalts used in the analysis. The four colors
correspond to the four geographical regions: north of
47°N (black), intermediate latitude between 47°N and
35°S in the Atlantic Ocean (red), south of 35°S in the
Atlantic Ocean (green), and Indian Ocean (blue).
Crosses correspond to mid-ocean ridge basalts, while
solid dots correspond to ocean island basalts. These
colors and symbols are used in Figures 3 – 5.
axes are rotated until the projection of the whitened
data gives histograms with maximum non-Gaussianity. Such axes correspond to a set of independent compositional base vectors that create the
observed compositional space. Entropy H is an
information theory parameter which characterizes
the randomness and lack of structure of a random
variable Y with pdf fY(y) and defined as:
Z
H ¼
fY ð yÞ log fY ð yÞdy
ð3Þ
D
where D is the domain of definition of the variable
Y. Normal variables have the largest entropy of all
the real-valued random variables with the same
mean and variance [Hyvärinen, 1999]. In this
study, the non-Gaussianity is measured by the
negentropy, which is the difference between the
entropy of the observed measurements and that of a
normal variable with the same mean and variance.
Negentropy J(y) is approximated by
J ðyÞ c½ EfGð yÞg EfGðnÞg2
ð4Þ
where y is the whitened and projected data, c is an
arbitrary constant, n is the Gaussian variable of
zero mean and unit variance, and the contrast
[11] In total, 1637 data sets are available with the
three Pb isotopic ratios (856 MORB and 781 OIB),
while 1269 data sets are available with the five
ratios of Pb, Sr and Nd (672 MORB and 597 OIB),
and 461 data sets exist for all six ratios (393
MORB and 68 OIB) (Figure 2). First, we examine
the three Pb-isotopic ratios, for which mixing of
different mantle geochemical end-members forms a
truly linear trend suitable for ICA, as a large
number of high-quality data recently have become
available. Because counting statistics and thermal
noise affect small signals much more so than strong
signals, couples of isotopic ratios with a minor or
otherwise noisy isotope as the denominator,
such as 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb,
are strongly correlated. Albarède et al. [2004]
calculated the correlation coefficient between
206
Pb/204Pb and 207Pb/204Pb introduced by Poisson
counting statistics on 204Pb variables and found it
equal to 0.96. Such a correlation of purely analytical origin interferes with geochemical correlations,
e.g., because of the mixing of mantle geochemical
end-members. The effect of analytical error correlations is particularly critical because the range of
207
Pb/204Pb variations cannot be neglected with
respect to analytical errors. In contrast, the correlation coefficient between 204 Pb/ 206 Pb and
207
Pb/206Pb due to counting statistics is only
0.16, which makes the correlation between counting uncertainties essentially negligible with respect
to those of more geochemical significance. The
normalization to 206Pb is routinely used for early
Solar System chronology and the parameters of the
207
Pb/206Pb versus 204Pb/206Pb isochron are easily
derived from those of the more conventional
207
Pb/204Pb versus 206Pb/204Pb isochron [Tera
and Wasserburg, 1972] (see Appendix A). For
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Figure 3. Independent components (compositional vectors/lines labeled IC1 and IC2) in the 204Pb/206Pb207
Pb/206Pb-208Pb/206Pb system, for 1637 data sets (856 MORB and 781 OIB data). The ICs have been calculated
according to the FastICA algorithm based on the approximation of negentropy as a measure of non-Gaussianity
[Hyvärinen, 1999]. Principal components (PC1 and PC2) are also shown. The isotopic data are compiled from
literature (the PetDB database, Agranier et al. [2005], and Meyzen et al. [2005, 2007]) for MORB and the GEOROC
database for OIB. From the GEOROC database, basaltic rocks with SiO2 contents between 53 and 35 wt % were
selected. (a) 204Pb/206Pb-208Pb/206Pb plot of the data, ICs and PCs. (b) IC1-IC2 plot where the data and the vectors
are decomposed into the two ICs. In both diagrams, the data distribution is sharply cut off at the edges, with several
internal subgroups or array-like structures. These characteristics clearly show a strong non-Gaussianity of the data
distribution. In each figure, the labels ‘‘IC1’’ and ‘‘IC2’’ are placed along the positive axes of ICs. Widths of the ICs
in Figure 3a represent the ranges obtained by perturbing the data points with their analytical uncertainties (1s for
204
Pb/206Pb, 207Pb/206Pb and 208Pb/206Pb has been estimated to be 1800, 800 and 800 ppm, respectively, on the basis
of the maximum uncertainties reported in the references of the data sources). The distribution in slope of the
perturbed ICs shows a normal distribution, and the ranges shown in Figure 3a approximately correspond to 3s of the
distribution. The colors and symbols are the same as in Figure 2. Approximate locations of conventional mantle
geochemical end-members are also shown by light grey symbols: asterisk, HIMU [Zindler and Hart, 1986]; circle,
FOZO [Hart et al., 1992; Stracke et al., 2005] or C [Hanan and Graham, 1996]; plus, depleted MORB mantle
(D-DMM) [Workman and Hart, 2005]; square, EM-I [Zindler and Hart, 1986]; cross, EM-II [Zindler and Hart,
1986].
these reasons, we use 206Pb as the denominator for
the Pb isotopic ratios, although the detected ICs are
almost identical in both 206Pb- and 204Pb-normalized spaces (Appendix A and Figure A1).
[12] The principal components are determined for
reference (Figure 3). The first component, PC1
(97.3% of the population variance), corresponds
to the longest axis of the overall data distribution as
it is defined to give the maximum variance of the
projected data. However, the second component,
PC2 (2.7% of the population variance), is not
useful in describing the data, either individually
or in groups. These features are similar to those
determined for North Atlantic MORB [BlichertToft et al., 2005]. Two independent components
(ICs), i.e., independent compositional base vectors
to represent the observed compositional space, also
cover 99.9% of the population variance, but are
clearly oblique with respect to the PCs (Figure 3a).
[13] This feature is similar to Figure 1b in the
simple example for homogeneous joint distribution. Although the overall elongation of data distribution in the original space obscures the
relationship between the PCs and ICs, the obliquity
is obvious in the whitened space (Figure 3b),
where the data points and vectors are broken down
into the two ICs. The obliquity between PCs and
ICs always occurs when the data constitute a
multivariate non-Gaussian population. Figure 3b
is similar to Figure 1a (homogeneous joint distribution of the two independent components in the
whitened space) in terms of the overall data distribution and the two PCs close to the diagonal axes,
indicating that the observed isotopic data is clearly
non-Gaussian.
[14] In Figure 3b, most OIB lie in the field of
positive IC1 values, except for Iceland, which is
situated on a spreading ridge, whereas most
MORB have negative IC1, except for the plume6 of 15
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influenced ridge basalts [e.g., Schilling, 1973;
White et al., 1976; Hanan et al., 1986]. In contrast,
IC2 discriminates the geographical distribution:
most of the basalts from northern and central
latitudes have negative IC2 values, while basalts
from the South Atlantic and Indian Ocean mostly
plot in the field of positive IC2 values. Such a clear
separation indicates that, contrary to the PCs, the
two ICs may be independent and reflect the effect
of two separate geodynamic processes to span most
of the observed compositional space. On the other
hand, although a linear trend nearly parallel to IC2
through EM-I (enriched mantle 1 [Zindler and
Hart, 1986]), FOZO (focal zone [Hart et al.,
1992]) or C (common component [Hanan and
Graham, 1996]), and HIMU (high-U/Pb mantle
[Zindler and Hart, 1986]) roughly limits the data
distribution on the positive-IC1 margin, some data
lie outside the polyhedron defined by connecting
the conventional mantle geochemical end-members, especially for negative IC1 values. This
indicates that mixing of the end-members cannot
fully explain the observed compositional space. An
alternative interpretation of Figure 3b will be
proposed later.
[15] As a next step, the five-dimensional isotopic
space with Pb, Sr and Nd was explored using ICA,
and again two dominant components were identified, which together account for 97.7% of the
population variance. An additional 1.9% of the
total variance is covered by inclusion of the third
component. It is not clear whether such a small
share actually indicates the presence of an additional geochemical component or reflects the nonlinear character of mass balance relationships in 5
dimensions including Sr and Nd. The inclusion of
three components creates metastable solutions that
locally maximize non-Gaussianity, indicating that
the major robust features are adequately represented by the two ICs shown in Figure 4.
10.1029/2007GC001753
[16] This result, i.e., the presence of only two
major components covering more than 90% of
the population variance, has already been shown
by PCA for oceanic basalts [Zindler et al., 1982;
Allègre et al., 1987; Hart et al., 1992], although the
ICs are different from the PCs (Figure 4e). The two
ICs in the space with five isotopic ratios are
essentially the same as in Figure 3: IC1 separates
OIB from MORB, and IC2 discriminates geographical distribution in both the OIB and MORB
fields. We checked that essentially the same result
is obtained for the subspace with only the three
variables 204Pb/206Pb, 87Sr/86Sr and 143Nd/144Nd
and with the four variables of the three Pb plus Nd
isotopic ratios, which shows the robustness of the
two ICs.
[17] The conventional mantle geochemical endmembers do not span the entire space of observed
compositions (Figure 4e). In addition, in the original space (e.g., Figures 4a – 4d), some of the
conventional end-members significantly deviate
from the two-dimensional plane spanned by the
two ICs. Note that, in Figures 3–5, the labels
‘‘IC1’’ and ‘‘IC2’’ are placed along the positive
axes of ICs. EM-I and EM-II, which refer to those
suggested by Zindler and Hart [1986] on the basis
of extensive extrapolation of the data trends, plot in
the field with positive IC1 and positive IC2, but do
not plot in the same field in Figure 4d (and Figure
4b for EM-I). Assuming a 143Nd/144Nd for EM-I,
its 87 Sr/ 86 Sr should be more radiogenic (by
0.002) if it is to be consistent with the actual
data (Indian MORB or OIB) and the IC axes, i.e.,
to plot in the IC plane. Similarly, EM-II should
correspond to lower 87Sr/86Sr values (by 0.002)
so as to plot in the IC plane. In contrast, HIMU,
FOZO/C and DMM plot consistently in all the
diagrams: HIMU and FOZO/C plot in the field of
positive IC1 and negative IC2, while DMM (DDMM and A-DMM) falls along the IC1 axis.
These end-members plot within the actual data or
Figure 4. Independent components (IC1 and IC2) in the 204Pb/206Pb-207Pb/206Pb-208Pb/206Pb-87Sr/86Sr-143Nd/144Nd
system, for 1269 data sets (672 MORB and 597 OIB data). For the data sources and ICA procedure, see Figure 3.
(a – d) The plot of data and ICs in the original space. (e) The IC1-IC2 plot where the data and PCs are decomposed
into the two ICs. In each figure, the labels ‘‘IC1’’ and ‘‘IC2’’ are placed along the positive axes of ICs. Widths of
the ICs in Figures 4a – 4d represent the ranges obtained by perturbing the data points with their analytical
uncertainties (1s for 204Pb/206Pb, 207Pb/206Pb, 208Pb/206Pb, 87Sr/86Sr and 143Nd/144Nd has been estimated to be
450, 200, 200, 40 and 50 ppm, respectively, on the basis of those reported in the references of the data sources).
The distribution in slope of the perturbed ICs shows a normal distribution, and the ranges shown in Figures 4a – 4d
approximately correspond to 3s of the distribution. The colors and symbols are the same as in Figure 3, with an
additional symbol: light grey triangle, average depleted MORB mantle (average DMM) [Workman and Hart,
2005]. The light grey dashed line in Figure 4c represents the trend reproduced in the MORB-recycling model of
Christensen and Hofmann [1994].
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on a slight extension of the actual data trends and
therefore plot in the two-dimensional IC plane,
which accounts for 97.7% of the population variance. A slight deviation from the plane, however,
distorts the data plot in the view nearly parallel to
10.1029/2007GC001753
the IC plane: in Figure 4d, some of the Indian OIB
(blue dots) plot slightly above the plane toward
higher 87Sr/86Sr and 143Nd/144Nd values, which
makes them appear closer to the IC2 axis.
Figure 4
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Figure 5. Independent components (IC1 and IC2) in the 204 Pb/ 206 Pb- 207 Pb/ 206 Pb- 208 Pb/ 206 Pb87
Sr/86Sr-143Nd/144Nd-177Hf/176Hf system, for 461 data with the complete six ratios (393 MORB and 68 OIB data
sets). For the data sources and ICA procedure, see Figure 3. (a– f) The plot of data and ICs in the original space.
(g) The IC1-IC2 plot where the data and PCs are decomposed into the two ICs. In each figure, the labels ‘‘IC1’’ and
‘‘IC2’’ are placed along the positive axes of ICs. Widths of the ICs in Figures 5a – 5f represent the ranges obtained by
perturbing the data points with their analytical uncertainties (1s for 204Pb/206Pb, 207Pb/206Pb, 208Pb/206Pb, 87Sr/86Sr,
143
Nd/144Nd and 177Hf/176Hf has been estimated to be 450, 200, 200, 40, 50 and 35 ppm, respectively, on the basis of
those reported in the references of the data sources). The distribution in slope of the perturbed ICs shows a normal
distribution, and the ranges shown in Figures 5a – 5f approximately correspond to 3s of the distribution. The colors
and symbols are the same as in Figure 4.
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[18] We also explored the six-dimensional space by
adding Hf to the previous isotopic systems (Figure 5).
Again two dominant components are identified,
which together account for 95.2% of the population
variance. However, in this case, the two calculated
ICs are different from those of Figures 3 and 4, and
are closer to the PCs (Figure 5g). The clear
MORB-OIB separation and geographical discrimination are lost in the process. The geometries of
data distribution and two ICs in the diagrams of
Pb-Nd isotopic ratios (Figure 5c) and Pb-Hf isotopic
ratios (Figure 5d) are similar, which is consistent
with a high correlation between Nd- and Hf-isotopic
ratios with almost identical slopes of the two ICs
(Figure 5f). Also, most of the population variance
(95.2%) is covered by the two components, which
is similar to the result in the five-dimensional space
with Pb-Sr-Nd isotopic ratios in Figure 4. A
remarkable difference between Figures 4 and 5 lies
with the number of data: because Hf isotope
analysis has only recently become routine, the
number of MORB data (393) far exceeds that of
OIB data (68) (Figure 5), which contrast with the
more balanced situation when Hf is omitted with
672 MORB and 597 OIB data (Figure 4). This
imbalance significantly modifies the overall as well
as internal structures of the data distribution, and
results in the different ICs in Figure 5 relative to
those in Figure 4. A larger number of data sets with
the complete six isotopic ratios is nevertheless
required to judge whether, as argued by Salters
and Hart [1991] and Blichert-Toft et al. [2005], the
Hf-isotopic ratio contains statistically unique information distinct from the information conveyed by
the Pb-Sr-Nd systems.
strained, namely by using either extreme data or an
extension of observed trends where no actual
datum exists. There is room, therefore, for shifting
the composition of some mantle geochemical endmembers to make them suitable as components of
the ICs, as was discussed for EM-I and EM-II in
the previous section. By contrast, the present study
suggests that the literature mantle geochemical
end-members may not necessarily represent unique
compositions. The essential feature of Figure 3b
and Figure 4e is that the variations along the two
IC directions are created by two independent
processes. When these two processes overlap, they
will create the observed compositional variability.
The ICA shown in Figures 3 and 4 suggest that the
two components that have been identified are
independent, which we take as an indication that
they were created by distinct geodynamic processes. Since MORB and OIB roughly are symmetrically distributed around a depleted mantle
composition in the IC space (although it is slightly
more enriched compared to the average depleted
MORB mantle (A-DMM) [Workman and Hart,
2005] as in Figure 4e), we argue that these processes occur as two differentiation processes mostly within the depleted mantle domain. The dual
structure of the geochemical data demonstrated by
ICA is robust and suggests that it reflects the two
dominant geodynamic processes with distinct elemental fractionation processes in the Earth, the
ridge and subduction zone processes. In addition,
the overlap of two independent components
reflects mutual processing: products from ridge
activity are processed at subduction zones and
ridges potentially remelt materials recycled through
the subduction zones.
4. Discussion
[21] Segregation and long isolation of MORB/
eclogite from its harzburgitic residue and subsequent recycling can reproduce a broad trend in the
Pb and Nd isotope space observed in oceanic
basalts [Christensen and Hofmann, 1994], whose
slope is similar to the IC1 direction. For example,
in Figure 4c (204Pb/206Pb versus 143Nd/144Nd), the
isotopic variation produced in the MORB-recycling model, which is slightly curved because of
the faster rate of 238U decay relative to 147Sm
[Christensen and Hofmann, 1994], is nearly parallel to IC1. The slopes of IC1 in Figures 4a–4d
suggest that IC1 originates from elemental fractionation associated with simultaneous increases
(or decreases) in U/Pb, Th/Pb, Rb/Sr and Nd/Sm,
which is consistent with that associated with melting [e.g., Beattie, 1993; Green, 1994; Salters and
Longhi, 1999]. Although the range and slope of the
[ 19 ] Since ICA uses non-Gaussianity criteria
throughout, a preliminary question is whether the
data can safely be considered as nonnormal. In
spite of convective stirring, the mantle is not
homogeneous because new heterogeneities are
continuously created by melting at ridges and
subduction of the oceanic plates. As shown by
Rudge et al. [2005], such a regime tends to a steady
state, and the resultant distribution of geochemical
variables are skewed and non-Gaussian.
4.1. Origin of Geochemical Independent
Components
[20] The conventional view of mantle geochemical
end-members is that their compositions are unique,
although such compositions are only loosely con-
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trend depend on several physical parameters such
as density contrast between MORB/eclogite and
peridotite, the MORB/eclogite-rich portion can
form a source region of OIB, whereas the residual
harzburgitic portion represents DMM [Christensen
and Hofmann, 1994]. These features coincide with
those of IC1, separating OIB from MORB.
[22] What IC2 reflects in contrast is likely to be
subduction zone processes. In Figures 4b and 4c,
the slope of IC2 has an opposite sign to that of IC1
and MORB-recycling trend that reflects elemental
fractionation associated with melting, while both
IC1 and IC2 exhibit the same sign in Figures 3a,
4a, and 4d. These features indicate that IC2 originates from elemental fractionation with simultaneous increases (or decreases) in Pb/U, Pb/Th, Rb/
Sr and Nd/Sm. Such fractionation can occur associated with aqueous fluid-mineral reactions
[Brenan et al., 1995; Keppler, 1996; Kogiso et
al., 1997], and therefore suggests that aqueous
fluid processes in subduction zones create the
IC2 variation superimposed on the IC1 variability.
[23] Dehydration of the subducted oceanic crust
concentrates more Pb, Rb and Nd in the aqueous
fluid than U-Th, Sr and Sm, respectively, leading to
a negative IC2 value of the dehydrated rocks, while
hydration of the rocks can produce positive IC2.
Clear differences between IC1 and IC2 also exist in
relative magnitude of fractionation between the
different parent/daughter pairs. Figures 3a, 4a,
and 4d show that a differentiation process responsible for the IC2 variation fractionates U/Pb more
than Th/Pb, and Rb/Sr more than Nd/Sm when
compared to IC1. These differences can be
explained by some of the experimental results on
elemental partitioning among aqueous fluids, silicate melts and minerals [e.g., Beattie, 1993; Green,
1994; Brenan et al., 1995; Keppler, 1996; Kogiso
et al., 1997; Salters and Longhi, 1999], although
they are not readily inferred consistently from all
the experimental data, since the partition coefficients significantly vary depending on a number of
parameters, such as pressure, temperature, bulk
composition, oxygen fugacity, alkali-chloride
contents in fluids, mineralogy of the coexisting
solid, and experimental configurations (e.g., static
equilibrium or dehydration mobility experiments).
However, considering the robust feature with
simultaneous increases (or decreases) in Pb/U,
Pb/Th, Rb/Sr and Nd/Sm, and that it must reflect
a first-order differentiation process within the
depleted mantle domain as dominant as ridge
10.1029/2007GC001753
melting, we propose that IC2 is related to aqueous
fluid processes in subduction zones as follows.
[24] During subduction of oceanic plates, altered
MORB and oceanic mantle generate aqueous fluids
and leave residues of dehydration. Fluids migrate
upward and hydrate the overlying mantle wedge
that may also contain recycled MORB and residual
rocks circulated by corner flow, and cause flux
melting and arc magmatism [Iwamori, 2007].
Hydration and dehydration at subduction zones of
both the basaltic and refractory parts of the oceanic
lithosphere and in the mantle wedge accounts for
the overprinting of the IC1 geochemical variability
by a distinct IC2 signature. The ubiquitous presence of this IC2 component in the source of both
OIB and MORB (Figures 3b and 4e) simply
reflects that most of the subducted oceanic lithosphere and the overlying mantle wedge go through
the hydration-dehydration processes at subduction
zones [Iwamori, 2007], in agreement with Li
isotope evidence [Elliot et al., 2006].
[25] Melting in subduction zones also contributes
to mantle differentiation, producing the continental
crust and a residue [Tatsumi, 2000]. In terms of the
nature of elemental differentiation, which reflects
the effect of mineral/melt partitioning, the effect of
melting in subduction zones may be similar to that
at mid-ocean ridges. In fact, EM-II, which is
analogous to continental crustal material recycled
in the mantle [White and Duncan, 1996], has a
positive IC1 and IC2 value (Figures 3b and 4e),
reflecting both melting and aqueous fluid processes
in subduction zones. Therefore, IC1 probably
reflects melting processes, whereas IC2 reflects
interaction of the mantle with aqueous fluid, regardless of the geodynamic sites where these
processes take place. It is unclear at this stage
how exactly the two elementary processes are
separated in the IC space, partly because the
aqueous fluid and melting processes are strongly
coupled in subduction zones, as is suggested by
numerical modeling of H2O transportation and
melting in subduction zones [Iwamori, 1998], trace
element modeling of aqueous fluid, peridotite and
island arc basalts [Ayers, 1998], and (231Pa/235U)(230Th/238U) variations of arc lavas [Thomas et al.,
2002].
4.2. Geodynamic Implications
[26] The nature and possible origin of the ICs have
several geodynamic implications. The existence of
FOZO, or C, and the local trends toward it [Hart et
al., 1992; Hanan and Graham, 1996] have been
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Figure 6. Distribution of IC2 values in oceanic basalts from the Atlantic and Indian oceans based on Figure 4e with
the five isotopic ratios of Pb, Sr, and Nd. Circles correspond to MORB, while stars correspond to OIB. In each
location, the IC2 variability is shown by the size of the color-coded symbols (smaller for the higher IC2 values).
Contours for positive IC2 values are shown by solid lines, while broken lines have been drawn arbitrarily or with
reference to the Pb-isotopic ratios of Figure 3b.
interpreted as representing mixing between the
ambient mantle and a plume, or a diapir, rising
from the core-mantle boundary [Hart et al., 1992]
or the transition zone [Hanan and Graham, 1996].
In the IC space, FOZO, or C, is characterized by a
positive IC1 and negative IC2 value (Figures 3b
and 4e), corresponding to the melt component-rich
(e.g., MORB/eclogite-rich) portion that has experienced dehydration in subduction zones, e.g.,
subducted oceanic crust. Because of its high
density and viscosity, the subducted oceanic crust
can be segregated from the subducted oceanic
mantle and accumulated near the base of a convecting system for subsequent prolonged isolation
[Christensen and Hofmann, 1994; Karato, 1997] to
develop the isotopic characteristics suitable for
FOZO or C. Its prevailing nature as a common
source of oceanic basalts can be explained by the
significant volume of subducted oceanic crust
present in the mantle. However, the local trends
toward FOZO or C, which are in general oblique to
the ICs (Figures 3b and 4e), are minor structures
within the IC space. Likewise, ICA shows
no evidence for incorporation of what could represent a primordial mantle component or an early
enriched reservoir into the observed depleted domain, which is consistent with 142Nd evidence
[Boyet and Carlson, 2005]. The lack of a clear
correlation between Pb-isotopic compositions and
3
He/4He in oceanic basalts [Hanan and Graham,
1996] also suggests that the incorporation of primordial components is largely decoupled from the
major mantle processes identified by ICA.
[27] Finally, the detected ICs call for a redefinition
of the criteria used to identify the DUPAL anomaly.
Hart [1984] defined three criteria on the basis of
Sr- and Pb-isotopic ratios and their deviations from
a Northern Hemisphere reference line. Although
the overall distribution of the contours clearly
shows the anomaly in the Southern Hemisphere,
the three types of contours are not consistent with
each other, especially in the Atlantic Ocean [see
Hart, 1984, Figure 2]. In the IC space, the five
isotopic ratios of Pb, Sr and Nd have been considered simultaneously, in which case a simpler and
more consistent criterion can be obtained. As a
result, as shown by Figure 6, the realm of the
enriched region defined by a positive IC2 value is
different from the DUPAL domain of Hart [1984]:
the enriched signature distributes itself in the
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Northern Hemisphere, which is consistent with
occurrence of a DUPAL signature along the Nansen-Gakkel Ridge [Mühe et al., 1993]. This could
have an important implication on mantle dynamics:
if the enriched region was initially confined to a
distinct domain (e.g., because it represents a mantle
domain contaminated by extensive Pangeatic subduction [Anderson, 1982; Zindler and Hart,
1986]), the disposition of the IC2 domain and the
amplitude of the anomaly may provide unique
information on the long-term mantle flow and
material transport. Accounting for mantle isotopic
variability in terms of the independent differentiation processes identified by ICA rather than by
interactions among mantle geochemical end-members with unique compositions is therefore bridging
the gap between geochemical observations and
mantle dynamics.
5. Conclusions
[28] Independent component analysis has been
applied to the isotopic compositional space of
oceanic basalts. Two statistically independent components have been found, which characterize two
independent features: one opposes mid-ocean ridge
basalts to ocean island basalts, while the other
maps geographically regional isotopic properties.
The distribution of the data in the IC space demonstrates that the observed compositional space is
created by the joint distribution of the two ICs,
indicating that two distinct differentiation processes
mutually overlap, rather than by interaction among
the conventional mantle geochemical end-members
with unique compositions. The geochemical characteristics of the two ICs oppose the variations due
to melting from those caused by interaction of
aqueous fluid with the mantle, both at mid-ocean
ridges and at subduction zones. The ICs provide a
new quantitative measure for describing the isotopic heterogeneity of the mantle. As a result, a new
criterion is proposed for the definition of the
DUPAL anomaly. It is shown that the DUPAL
signature is present both in the Southern Hemisphere and the Northern Hemisphere, which
possibly reflects a large-scale feature of the mantle
flow.
Appendix A: 204Pb Normalization
Versus 206Pb Normalization
[29] Let a = 206Pb/204Pb, b = 207Pb/204Pb and g =
208
Pb/204Pb. For a system evolving in time from 0
to t and with identical Pb isotope compositions at
10.1029/2007GC001753
t = 0, the conventional 207 Pb/ 204 Pb versus
Pb/204Pb isochron can be written as:
206
b ¼ b0 þ sða a0 Þ
ðA1Þ
1 el235U t 1
137:88 el238U t 1
ðA2Þ
where
s¼
and l are the decay constants of the different U
isotopes. Dividing the first equation by a gives:
b b0 sa0
þs
¼
a
a
ðA3Þ
which is the equation of a straight line in a
207
Pb/206Pb versus 204Pb/206Pb plot. In contrast
with the conventional 207 Pb/ 204 Pb versus
206
Pb/204Pb isochron, in which the age is obtained
from the slope, the age in this so-called ‘‘inverse’’
isochron plot is read from the intercept.
[30] Let a = a + Da, b = b + Db and g = g + Dg,
where a, b and g represent the mean values of a, b
and g, respectively. Since a Da, b Db and
g Dg, the transformation from 204Pb-normalized variables (a, b, g) to 206Pb-normalized variables (x, y, z) can be linearized as follows:
1 1
Da
1
a
a a
ðA4Þ
y¼
b b
Db Da
1þ
a
a a
b
ðA5Þ
z¼
g g
Dg Da
1þ
g
a
a a
ðA6Þ
x¼
Since ICA searches for the components as linear
combinations of original variables with maximum
non-Gaussianity, any linear transformation, such as
those expressed in (A4) to (A6), should lead to
identical results. Figure A1 shows the result of ICA
with 204Pb-normalized variables for the same data
set as in Figure 3. In spite of the slight nonlinearity
of transformation, the ICs obtained in the 204Pb
(Figure A1) and 206Pbnormalized space (Figure 3)
are essentially identical. However, because the
transformation from 204Pb-normalized variables to
206
Pb-normalized variables, while it is approximately linear, is not orthogonal, the PCs are
different (Figure 3). In both cases described by
Figures 3 and A1, the PCs are oblique with respect
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Figure A1. Independent components (compositional vectors/lines labeled IC1 and IC2) in the
206
Pb/ 204 Pb- 207 Pb/ 204 Pb- 208 Pb/ 204 Pb system. The data and symbols are the same as in Figure 3.
(a) 206Pb/204Pb-208Pb/204Pb plot of the data, ICs and PCs. (b) IC1-IC2 plot where the data and the vectors are
decomposed into the two ICs. (c) 206Pb/204Pb-208Pb/204Pb plot of the data, together with ICs and PCs which are
obtained in the 204Pb-normalized space and are then transformed into the 206Pb-normalized space (compare with
Figure 3a).
to the ICs, which reflects the non-Gaussian
character of the data populations.
Acknowledgments
[31] We thank Matt Miller and Yoshi Tatsumi for discussion
and help and Dan McKenzie, John Rudge, Vincent Salters, and
Bill White for constructive reviews. Janne Blichert-Toft
obliged with a careful editing of the manuscript. F.A. would
like to thank the Earthquake Research Institute for their
generous invitation to visit the University of Tokyo and the
Program SEDIT of the Institut National des Sciences de
l’Univers for financial support.
References
Agranier, A., J. Blichert-Toft, D. Graham, V. Debaille,
P. Schiano, and F. Albarède (2005), The spectra of isotopic
heterogeneities along the mid-Atlantic Ridge, Earth Planet.
Sci. Lett., 238, 96 – 109.
Albarède, F. (2005), The survival of mantle geochemical
heterogeneities, in Earth’s Deep Mantle: Structure, Composition, and Evolution, Geophys. Monogr. Ser., vol. 160,
edited by R. D. van der Hilst et al., pp. 27 – 46, AGU,
Washington, D. C.
Albarède, F., P. Telouk, J. Blichert-Toft, M. Boyet, A. Agranier,
and B. Nelson (2004), Precise and accurate isotopic measurements using multiple-collector ICP-MS, Geochim. Cosmochim. Acta, 68, 2725 – 2744.
Allègre, C. J., and E. Lewin (1995), Scaling laws and geochemical distributions, Earth Planet. Sci. Lett., 132, 1 – 13.
Allègre, C. J., B. Hamelin, A. Provost, and B. Dupre (1987),
Topology in isotopic multispace and origin of the mantle chemical heterogeneities, Earth Planet. Sci. Lett., 81, 319 – 337.
Amari, S. (2002), Independent component analysis and the
circumference (in Japanese), in Development of Multivariate
Analysis, Frontier of Statistical Science, vol. 5, edited by
S. Amari et al., pp. 1 – 63, Iwanami, Tokyo.
14 of 15
Geochemistry
Geophysics
Geosystems
3
G
iwamori and albarE`de: decoupled isotopic record by ica
Anderson, D. L. (1982), Hotspots, polar wander, Mesozoic
convection and the geoid, Nature, 297, 391 – 393.
Ayers, J. (1998), Trace element modeling of aqueous fluidperidotite interaction in the mantle wedge of subduction
zones, Contrib. Mineral. Petrol., 132, 390 – 404.
Beattie, P. (1993), Uranium-thorium disequilibria and partitioning on melting of garnet peridotite, Nature, 363, 63 – 65.
Blichert-Toft, J., A. Agranier, M. Andres, R. Kingsley, J.-G.
Schilling, and F. Albarède (2005), Geochemical segmentation of the Mid-Atlantic Ridge north of Iceland and ridge-hot
spot interaction in the North Atlantic, Geochem. Geophys.
Geosyst., 6, Q01E19, doi:10.1029/2004GC000788.
Boyet, M., and R. W. Carlson (2005), 142Nd evidence for early
(>4.53 Ga) global differentiation of the silicate Earth,
Science, 309, 576 – 581, doi:10.1126/science.1113634.
Brenan, J. M., H. F. Shaw, F. J. Ryerson, and D. L. Phinney
(1995), Mineral-aqueous fluid partitioning of trace elements
at 900°C and 2.0 GPa: Constraints on the trace element
chemistry of mantle and deep crustal fluids, Geochim. Cosmochim. Acta, 59, 3331 – 3350.
Christensen, U. R., and A. W. Hofmann (1994), Segregation of
subducted oceanic crust in the convecting mantle, J. Geophys. Res., 99, 19,867 – 19,884.
Elliot, T., A. Thomas, A. Jeffcoate, and Y. Niu (2006), Lithium
isotope evidence for subduction-enriched mantle in the
source of mid-ocean-ridge basalts, Nature, 443, 565 – 568.
Green, T. H. (1994), Experimental studies of trace-element
partitioning applicable to igneous petrogenesis—Sedona 16
years later, Chem. Geol., 117, 1 – 36.
Hamilton, W. C. (1964), Statistics in Physical Science, 230 pp.,
Ronald, New York.
Hanan, B. B., and D. W. Graham (1996), Lead and helium
isotope evidence from oceanic basalts for a common deep
source of mantle plumes, Science, 272, 991 – 995.
Hanan, B. B., R. H. Kingsley, and J.-G. Schilling (1986), Pb
isotope evidence in the South Atlantic for migrating ridgehotspot interactions, Nature, 322, 137 – 144.
Hart, S. R. (1984), A large-scale isotope anomaly in the Southern Hemisphere mantle, Nature, 309, 753 – 757.
Hart, S. R., E. H. Hauri, L. A. Oschmann, and J. A. Whitehead
(1992), Mantle plumes and entrainment: Isotopic evidence,
Science, 256, 517 – 520.
Hofmann, A. W. (1997), Mantle geochemistry: The message
from oceanic volcanism, Nature, 385, 219 – 229.
Hyvärinen, A. (1999), Fast and robust fixed-point algorithms
for independent component analysis, IEEE Trans. Neural
Networks, 10, 626 – 634.
Hyvärinen, A., J. Karhunen, and E. Oja (2001), Independent
Component Analysis, John Wiley, Hoboken, N. J.
Iwamori, H. (1998), Transportation of H2O and melting in
subduction zones, Earth Planet. Sci. Lett., 160, 65 – 80.
Iwamori, H. (2007), Transportation of H2O beneath the Japan
arcs and its implications for global water circulation, Chem.
Geol., 239, 182 – 198.
Karato, S. (1997), On the separation of crustal component
from subducted oceanic lithosphere near the 660 km discontinuity, Phys. Earth Planet. Inter., 99, 103 – 111.
Keppler, H. (1996), Constraints from partitioning experiments
on the composition of subduction-zone fluids, Nature, 380,
237 – 240.
Kogiso, T., Y. Tatsumi, and S. Nakano (1997), Trace element
transport during dehydration processes in the subducted
oceanic crust: 1. Experiments and implications for the origin
of ocean island basalts, Earth Planet. Sci. Lett., 148, 193 –
205.
10.1029/2007GC001753
Meibom, A., and D. L. Anderson (2004), The statistical upper
mantle assemblage, Earth Planet. Sci. Lett., 217, 123 – 139.
Meyzen, C. M., J. N. Ludden, E. Humler, B. Luais, M. J.
Toplis, C. Mèvel, and M. Storey (2005), New insights into
the origin and distribution of the DUPAL isotope anomaly in
the Indian Ocean mantle from MORB of the Southwest Indian Ridge, Geochem. Geophys. Geosyst., 6, Q11K11,
doi:10.1029/2005GC000979.
Meyzen, C. M., J. Blichert-Toft, J. N. Ludden, E. Humler,
C. Mèvel, and F. Albarede (2007), Isotopic portrayal of the
Earth’s upper mantle flow field, Nature, 447, 1069 – 1074.
Mühe, R., C. W. Devey, and H. Bohrmann (1993), Isotope and
trace element geochemistry of MORB from the NansenGakkel ridge at 86° north, Earth Planet. Sci. Lett., 120,
103 – 109.
Rudge, J. F. (2006), Mantle pseudo-isochrons revisited, Earth
Planet., Sci. Lett., 249, 494 – 513.
Rudge, J. F., D. McKenzie, and P. H. Haynes (2005), A theoretical approach to understanding the isotopic heterogeneity
of mid-ocean ridge basalt, Geochim. Cosmochim. Acta, 69,
3873 – 3887.
Salters, V. J. M., and S. R. Hart (1991), The mantle sources of
ocean ridges, islands and arcs: The Hf-isotope connection,
Earth Planet. Sci. Lett., 104, 364 – 380.
Salters, V. J. M., and J. Longhi (1999), Trace element partitioning during the initial stages of melting beneath midocean ridges, Earth Planet. Sci. Lett., 166, 15 – 30.
Schilling, J.-G. (1973), Iceland mantle plume, geochemical
evidence along Reykjanes Ridge, Nature, 242, 565 – 571.
Stracke, A., A. W. Hofmann, and S. R. Hart (2005), FOZO,
HIMU, and the rest of the mantle zoo, Geochem. Geophys.
Geosyst., 6, Q05007, doi:10.1029/2004GC000824.
Tatsumi, Y. (2000), Continental crust formation by crustal delamination in subduction zones and complementary accumulation of the enriched mantle I component in the mantle,
Geochem. Geophys. Geosyst., 1(12), doi:10.1029/
2000GC000094.
Tera, F., and G. J. Wasserburg (1972), U-Th-Pb systematics in
lunar highland samples from the Luna 20 and Apollo 16
missions, Earth Planet. Sci. Lett., 17, 36 – 51.
Thomas, R. B., M. M. Hirschmann, H. Cheng, M. K. Reagan,
and R. L. Edwards (2002), (231Pa/235U)-(230Th/238U) of
young mafic volcanic rocks from Nicaragua and Costa Rica
and the influence of flux melting on U-series systematics of
arc lavas, Geochim. Cosmochim. Acta, 66, 4287 – 4309.
White, W. M. (1985), Sources of oceanic basalts: Radiogenic
isotopic evidence, Geology, 13, 115 – 118.
White, W. M., and R. A. Duncan (1996), Geochemistry and
geochronology of the Society Islands: New evidence for
deep mantle recycling, in Earth Processes: Reading the
Isotopic Code, Geophys. Monogr. Ser., vol. 95, edited by
A. Basu and S. Hart, pp. 183 – 206, AGU, Washington, D. C.
White, W. M., J.-G. Schilling, and S. R. Hart (1976), Evidence
for the Azores mantle plume from strontium isotope geochemistry of the Central North Atlantic, Nature, 263, 659 –
663.
Workman, R. K., and S. R. Hart (2005), Major and trace element composition of the depleted MORB mantle (DMM),
Earth Planet. Sci. Lett., 231, 53 – 72.
Zindler, A., and S. R. Hart (1986), Chemical geodynamics,
Annu. Rev Earth Planet. Sci., 14, 493 – 571.
Zindler, A., E. Jagoutz, and S. Goldstein (1982), Nd, Sr and Pb
isotopic systematics in a three-component mantle: A new
perspective, Nature, 298, 519 – 523.
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