ArticlePDF Available

Element chemostratigraphy of the Devonian/Carboniferous boundary – A compositional approach

Authors:

Abstract and Figures

The Devonian/Carboniferous (D/C) boundary is a critical interval in the Phanerozoic history, which is associated with vigorous climatic perturbations, continental glaciation, global sea-level fall and rapidly increased extinction rates in marine realms. In many sections world-wide, these global changes left a marked lithological signature, in particular the Hangenberg black shale (products of deep-shelf anoxia) and the overlying Hangenberg sandstone (sudden siliciclastic influx into predominantly carbonate depositional environments). Both layers bear a distinct geochemical signature. Even though either or both of these two lithologies are absent at many sections, their correlative counterparts can be indicated by subtle geochemical markers. We studied elemental geochemistry of fourteen D/C boundary sections in six key areas across Europe with the aim to select globally correlatable elemental proxy for the D/C boundary. Analysis of raw/log-transformed geochemical data (EDXRF, c.p.s. units), presenting the standard approach here, indicates that concentrations of terrigenous elements (Al, K, Rb, Ti and Zr) are mainly controlled by diluted Ca (carried by marine calcium carbonate) in limestone facies and, accordingly, their variations can be related to carbonate production in the sea rather than to terrigenous input from continent. Nevertheless, due to the relative nature of geochemical observations, reliance solely on statistical processing of raw data might lead to incomplete picture of multivariate data structure and/or biased interpretations. For this reason, the aim of this contribution is to discuss the logratio alternatives of the standard statistical methods, which may better reflect the relative nature of the data. For this purpose, principal component analysis was employed to reveal main geochemical patterns and while the geochemical signature of the D/C boundary was further analysed using Q-mode clustering that leads to predicative orthonormal logratio coordinates – balances. The comprehensive picture of the multivariate data structure provided by these statistical tools makes them a primary choice for exploratory compositional data analysis. At the same time, it turns out that the standard and compositional approaches have synergic effects. This fact can be extensively used in further geochemical studies.
Content may be subject to copyright.
Element chemostratigraphy of the Devonian/Carboniferous boundary
a compositional approach
K. FAČEVICOVÁ1*, O. BÁBEK2, K. HRON3, T. KUMPAN4
1Department of Mathematical Analysis and Applications of Mathematics Palacký University
Olomouc, Czech Republic, kamila.facevicova@gmail.com
2Department of Geology Palacký University Olomouc, Czech Republic
3Department of Mathematical Analysis and Applications of Mathematics Palacký University
Olomouc, Czech Republic
4Department of Geological Sciences Masaryk University Brno, Czech Republic
*corresponding author
The Devonian/Carboniferous (D/C) boundary is a critical interval in the Phanerozoic history, which is
associated with vigorous climatic perturbations, continental glaciation, global sea-level fall and rapidly
increased extinction rates in marine realms. In many sections world-wide, these global changes left a
marked lithological signature, in particular the Hangenberg black shale (products of deep-shelf anoxia)
and the overlying Hangenberg sandstone (sudden siliciclastic influx into predominantly carbonate
depositional environments). Both layers bear a distinct geochemical signature. Even though either or
both of these two lithologies are absent at many sections, their correlative counterparts can be
indicated by subtle geochemical markers. We studied elemental geochemistry of fourteen D/C
boundary sections in six key areas across Europe with the aim to select globally correlatable elemental
proxy for the D/C boundary. Analysis of raw/log-transformed geochemical data (EDXRF, c.p.s. units),
presenting the standard approach here, indicates that concentrations of terrigenous elements (Al, K,
Rb, Ti and Zr) are mainly controlled by diluted Ca (carried by marine calcium carbonate) in limestone
facies and, accordingly, their variations can be related to carbonate production in the sea rather than to
terrigenous input from continent. Nevertheless, due to the relative nature of geochemical observations,
reliance solely on statistical processing of raw data might lead to incomplete picture of multivariate
data structure and/or biased interpretations. For this reason, the aim of this contribution is to discuss
the logratio alternatives of the standard statistical methods, which may better reflect the relative nature
of the data. For this purpose, principal component analysis was employed to reveal main geochemical
patterns and while the geochemical signature of the D/C boundary was further analysed using Q-mode
clustering that leads to predicative orthonormal logratio coordinates balances. The comprehensive
picture of the multivariate data structure provided by these statistical tools makes them a primary
choice for exploratory compositional data analysis. At the same time, it turns out that the standard and
compositional approaches have synergic effects. This fact can be extensively used in further
geochemical studies.
Keywords: element geochemistry; compositional biplot; dendrogram; logratio coordinates;
Devonian/Carboniferous boundary; variation matrix
1. Introduction
In geochemistry, most of data are compositional in nature (Aitchison, 1986; Pawlowsky-
Glahn and Buccianti, 2011; Pawlowsky-Glahn et al., 2015a). It is not just indicated by units,
in which observations are measured or expressed, like mg/kg, ppm, or percentages, but
inherently also in the fact that ratios between components form the primary source of
information. As a consequence, any sum of components (compositional parts) is irrelevant. In
particular, in geochemical practice it rarely happens that the input observations sum up to a
constant given by the mode of used representation. For example, to make mg/kg units sum up
to unity (one million) it would mean that all elements in the rock were identified and
analyzed. From this perspective, it is much more convenient to treat the data as
compositional, if their parts convey quantitatively expressed relative contributions on a
whole, formed by the given composition. The above properties also imply that compositional
data carry exclusively relative information (Pawlowsky-Glahn et al., 2015a).
Accordingly, when the relative structure of geochemical observations is of the sole interest,
applying standard statistical tools to the input concentrations may lead to misleading results,
because compositional data obey different geometrical rules. These inherent features can be
expressed by principles of compositional data analysis (Egozcue, 2009): scale invariance,
permutation invariance and subcompositional coherence. From the practical perspective, the
most important one is scale invariance stating that information in a composition does not
depend on the particular units in which the composition is represented. Specifically,
proportional positive vectors represent the same composition. The latter two principles
provide a solid theoretical basis of any reasonable (not exclusively) statistical processing, and
they all are needed to build a sound geometrical setting that would reflect inherent properties
of geochemical (compositional) data. It is provided by the Aitchison geometry (Billheimer et
al., 2001; Pawlowsky-Glahn and Egozcue, 2001; Egozcue et al., 2003), defining an algebraic-
geometrical structure of the sample space of compositions, formed by equivalence classes of
proportional positive vectors (or by simplex for a given constant-sum representation of
compositions). As the majority of statistical methods rely on Euclidean geometry in real space
(Eaton, 1983), it is necessary to transform the compositions prior to standard statistical
analysis with such as the principal component analysis (PCA) and/or visualization. The
definition of compositional data implies that any such transformation (from geometrical
reasons, referred to as coordinates) should be formed by ratios between parts that form the
elemental information in compositional data. Or, even better, by log-ratios (Aitchison, 1986)
that symmetrize positions of components in the ratio and are mathematically easier to handle.
For a standard geochemical analysis, it is preferred to deal with the original compositional
parts, not their log-ratios. However, with all consequences that imply from the nature of
compositions considered, this is frequently not satisfactory. Nevertheless, if interpretation in
terms of single original part is required, centred logratio (clr) coordinates provide a
compositional alternative to raw data. Each part of vector of these coordinates

 
 
 (1)
where g(x) stands for geometric mean



 , (2)
represents a dominance of with respect to the complete composition. Because the resulting
vector has components, a redundancy condition arises,  , leading to
singular covariance matrix of . Although this affects applicability of some statistical
approaches, like the class of robust methods (Filzmoser et al., 2009a), it is still possible to
employ them for most of exploratory tools including PCA. For more discussion about the use
of clr coordinates in geochemical context, see McKinley et al. (2016).
Not all geochemical data must necessarily be treated as compositional, especially if total
abundances are relevant for the analysis. However, from the methodological perspective,
analyzing solely raw data still cannot be recommended. Instead, compositional data should be
treated as standard positive observations that induce again specific geometrical features, e.g.,
their relative scale (Mateu-Figueras and Pawlowsky-Glahn, 2008). Beside the (clr) coordinate
representation, the usual log-transformation   seems to be meaningful
for these situations (Pawlowsky-Glahn et al., 2015b).
The D/C boundary geochemical dataset provides a suitable working material to test the
applicability of the compositional approach. The data comprise marine carbonate rocks, which
alternate with several siliciclastic layers each confined to a specific stratigraphic interval.
These layers are correlatable across the six studied areas and provide thus a common feature
of all the studied sections. They comprise the Hangenberg black shale, sandstone and grey
shale, collectively referred to as the Hangenberg event sensu lato, HBS s.l. (costatus-kockeli
Interregnum, uppermost Famennian) and the Lower Alum Shale, LAS (crenulata Zone,
middle Tournaisian) (Kaiser et al., 2011). Their geochemical signature reflects rapid
siliciclastic influx into shelf seas (sandstones and grey shales of the HBS s.l.), increased
organic productivity in pelagic settings and global development of water bottom anoxia (black
shales of the HBS s.l. and LAS) and effects of dilution by biomineralized calcium carbonate
(interlayered carbonates) (Kumpan et al., 2014a,b, 2015; Bábek et al., 2016). Developed
more-or-less in all of the studied sections, this signature is modulated by such local factors as
different source of the siliciclastics and variable depositional settings. All these factors
contribute to a complex structure of the geochemical data.
The aim of the manuscript is to demonstrate, that not just statistical analysis based on the
compositional approach, being definitively the most relevant from the theoretical perspective,
but also analysis of raw data or their log-transformation bring some benefits to the overall
analysis. The reason is that the effect of the concrete scale of data cannot be frequently simply
removed as it is the case of the compositional approach (scale invariance). Practical
experiences indicate that even considering absolute scale of the original (raw) data, being
methodologically rather incorrect, can reveal some further interesting features. The aim of the
practical part is not to provide an exhaustive comparison, but to demonstrate that just
combination of different approaches (though not necessarily theoretically sound) leads to
complex understanding of the multivariate data structure. Nevertheless, following the
compositional approach that reflects predominant geometrical features of data at hand, one is
on the “safe side”. As an adjacent goal, inspired by quasimetric structure of the variation
matrix, the paper extends the use of Q-mode clustering, introduced in van den Boogaart and
Tolosana-Delgado (2013) for alternative agglomerative clustering procedures. All statistical
calculations were conducted with software R (R Core Team, 2016) and its package
compositions (van den Boogaart et al., 2013; van den Boogaart et al., 2013).
2. Materials and Methods
2.1. Data description
The study material includes elemental geochemistry of carbonate and siliciclastic bed
successions across the Devonian/Carboniferous (D/C) boundary. The dataset includes 1884
samples from 14 sections studied in six major Variscan massifs of Europe (Rhenish Massif,
Germany; Namur-.Dinant Basin, Belgium and northern France; Moravo-Silesian Zone of the
Bohemian Massif, Czech Republic; Carnic Alps, Austria and Italy; Montagne Noire of the
Massif Central, southern France and Pyrenees, southern France) . Figure representing position
of the studied sections in the major outcrops of Variscan massifs in Europe is attached as a
Supplementary Material. The geological settings and stratigraphy of the sections were
recently summarized by Kumpan et al., (2014a,b, 2015) and Bábek et al. (2016). Samples for
element geochemistry were taken from the studied sections with a vertical step of 5 to 25 cm
(rarely with 1 cm or 50 to 60 cm) depending on overall section thickness and required detail.
The average sampling density was one sample per 11.5 cm.
All the samples were analysed by energy-dispersive X-ray fluorescence (EDXRF) using a
MiniPal 4.0 instrument (PANalytical, Netherlands) with an Rh lamp (30 kV) and Peltier
cooled Si PIN detector. The samples were ground to <63 m particle size and filled into
plastic cells 25 mm in diameter and with Mylar foil bottoms. Eighteen elements were
analysed (Al, Ca, Cr, Cu, Fe, K, Mn, Ni, P, Pb, Rb, S, Si, Sr, Ti, Y, Zn and Zr). Al and Si
signals were acquired for 300 s at 5 kV/400 μA with a Kapton filter under He flush (99.996%
purity); K, Ti, Fe, and Mn and Fe for 200 s at 12 kV/200 μA with a thin Al filter in air; and Zr
for 500 s at 30 kV/200 μA with an Ag filter in air. Total analysis time was set at 800 s per
sample. The EDXRF results are given in counts per second (cps). The EDXRF analytical
results for Ca, Si, Al, K, Ti, Mn, Fe, Sr, and Zr (in cps) were calibrated through inductively
coupled plasma mass spectrometry (ICP-MS) analysis of 11 samples (Lesní lom, Křtiny, and
Grüne Schneid sections) by an accredited analytical laboratory of the Technical University of
Ostrava, Czech Republic, using an X Series 2 ICP-MS instrument (Thermo Scientific). The
quality of the ICP-MS analytical data was checked by measuring 2709a standard reference
material (SRM) (San Joaquin Soil, NIST, USA). EDXRF results for Cr, Rb, Y, Cu, Zn, Ni,
and Pb were calibrated by ICP-MS (Element2, Thermo Scientific) at the Geological Institute,
Czech Academy of Sciences, Prague, using calibration equations from an external set of 17
samples from lower Devonian carbonates and shales of the Prague Basin, Czech Republic.
Data quality from the Geological Institute was checked by analysing 1d SRM (Argillaceous
limestone, National institute of Standards and Technology). Calibration curves of the EDXRF
vs. ICP-MS results suggest that all target elements were above EDXRF detection limits while
the high correlation coefficients (R2 = 0.93 to 0.99 generally; only slightly lower for Mn: R2 =
0.893, Cr: R2 = 0.887, and Ni: R2 = 0.722) indicate the good reproducibility of the EDXRF
signal. P and S were not calibrated. All element ratios and enrichment factors mentioned
throughout this paper are based on uncalibrated EDXRF (cps) data.
The elemental composition sensitively reflects basic lithological and paleoenvironmental
changes at the D/C boundary. Particularly effective are the following element groups with
similar geochemical behavior:
a) Ca, which is driven by marine CaCO3 production in benthic and pelagic settings (Sageman
and Lyons, 2005);
b) Al, K, Rb and Ti, which are bound to siliciclastic minerals derived from continent, in
particular clay minerals and silt-sized heavy minerals and phyllosillicates (Ross and Bustin,
2009; Sageman and Lyons, 2005; Vijver et al., 2008);
c) Si and Zr, which tend to concentrate in coarse-grained siliciclastic minerals (Schnetger et
al., 2000; Jones et al., 2012) also derived from continent (heavy minerals, quartz, feldspars)
but Si is also linked to organic pelagic production in the sea (radiolarians and sponge
spicules);
d) Zn, Ni, Cu, Pb, S and P - productivity-sensitive elements, which tend to concentrate in
organic matter-rich sediments such as the Hangenberg black shale and Lower Alum shale
(Bout-Roumazeilles et al., 2013; Fralick and Kroberg, 1997; Sageman and Lyons, 2005;
Śliwiński et al., 2010; Tribovillard et al., 2006).
e) redox-sensitive elements such as Fe and Mn, which are highly mobile across sub-bottom
redox gradients (Haese et al., 1998).
The advantage of the dataset is in the detailed knowledge about distinct sedimentary layers
with expected geochemical behavior, which include: layer 1) Upper Devonian carbonates;
layer 2) Uppermost Devonian black shales of the Hangenberg (HBE) event interval; layer 3)
Uppermost Devonian sandstones and non-black shales of the Hangenberg (HBE) interval;
layer 4) Lower Carboniferous carbonates and layer 5) Lower Carboniferous black shales and
cherts of the Lower Alum Shale interval. Figure representing chronostratigraphy,
biostratigraphy, lithostratigraphy and thickness of the studied sections is attached as a
Supplementary Material.
2.2. Exploration of compositional variation structure
Covariance structure of compositional data reflects the fact that the source information is
contained in pairwise log-ratios. Accordingly, in the compositional context the multivariate
variability is captured by the variation matrix (Aitchison, 1986), defined as
 

  

 

 
 
 
   (3)
Its interpretation is intuitive. A non-diagonal element of the variation matrix is zero, or nearly
so, if and only if the respective compositional parts are proportional, or nearly so. In other
words, proportionality here replaces covariance (correlation) between variables from standard
multivariate statistics. Consequently, elements of variation matrix can also be used as a
measure of dissimilarity between compositional parts, for example for the purpose of
clustering of compositional parts (Montero-Serrano et al., 2010, Pawlowsky-Glahn et al.,
2011; van den Boogaart and Tolosana-Delgado, 2013; McKinley et al., 2016). From the basic
(metric) properties of distances the following are obviously fulfilled,
           (4)
i.e., non-negativity, identity of indiscernibles and symmetry. On the other hand, triangular
inequality is not fulfilled in general, only its generalized form
    (5)
for a constant    that corresponds to quasimetrics (Xia, 2009) can be derived. According
to Fišerová and Hron (2011) it holds true that
   
, (6)
resulting in   . It is shown (Xia, 2009) that many well-known results for the usual metrics
still hold true in quasimetric space that makes them a natural generalization of the basic
metric settings. These findings are inspirative for Q-mode clustering, introduced in the next
section. Finally, a matrix relationship exists between the variation matrix and covariance
matrix of clr coordinates (Aitchison, 1986), which is useful for practical computations.
Variation structure of compositional data can be visualized using compositional biplots
(Aitchison and Greenacre, 2002). Similarly as for a standard PCA biplot (Gabriel, 1971),
which is used to reduce dimensionality of input data, compositional biplot displays as well
scores and loadings of the first two principal components in one planar graph. The scores are
usually marked as points in order to capture multivariate data structure; loadings are
represented by arrows and stand for the input variables. While in the standard biplot original
(log-transformed) variables are considered, in the compositional case clr coordinates are
usually represented. This also affects the interpretation of loading vectors. While in the
standard case the length of the arrow and the cosine of the angle between two arrows
approximate standard deviation of the corresponding variable and correlation between
variables, respectively, interpretation of clr variables needs to be taken into account in the
compositional case. Consequently, the length of the arrow cannot be interpreted as a single
original part but as a representation of its dominance to an “average part” in the composition
(Filzmoser et al., 2012). Instead of interpreting correlation between two clr coordinates, which
is affected by the zero sum constraint of variables, it is preferred to consider links between
vertices, approximating pairwise logratio variances (elements of the variation matrix). In
particular, link between vertices of and approximates 
; if the vertices
coincide, or nearly so, then and are proportional, or nearly so. An enhanced
interpretation of compositional biplot in terms of covariance structure of pairwise log-ratios
can be found, e.g., in Pawlowsky-Glahn et al. (2015a).
2.3. Pattern identification
In order to assess the log-ratio patterns in the geochemical signature of the D/C boundary
rocks, it is necessary to search for such variables which are responsible for the general
geochemical patterns. In particular they include the detrital-input sensitive elements (Al, Ti,
Rb, Zr), grain-size sensitive ones (Si, Zr), organic productivity sensitive ones (P, S, Ca, Ni,
Zn, Cu) and redox-sensitive ones (Fe, Ni, Mn) (see section 2.1). For the case, when total
abundances are informative as well, the log-transformed original variables or their
combinations would be appropriate for this purpose. Nevertheless, it seems that for carbonate
rocks rather relative contributions of the EDXRF signal (in cps) are of interest. This is
reflected also by recent practice in the field, where ratios between elementary components
such as Zr/Rb, K/Al and Rb/K are considered to indicate the lithological changes across the
D/C boundary (Kumpan et al., 2015; Bábek et al., 2016). The previous section implies that,
referring to relative structure of compositional data, single compositional parts are not
appropriate to serve as feature variables, because they necessarily (directly or indirectly) rely
on the other components in the actual composition. All relative information about single
compositional parts is extracted using clr coordinates (1); on the other hand, this information
might be too complex due to different and possibly antagonistic patterns of log-ratios
aggregated there (Reimann et al., 2012; McKinley et al., 2016). Taking simply all possible
pairwise log-ratios into account would need an exhaustive search, therefore not very practical
for data with moderate or even larger number of components. Although expert knowledge can
be used to select such log-ratios, a data-based approach can facilitate finding possible further
interesting geochemical markers by mutual considering specific geochemical behavior of
elements. Consequently, such an unsupervised approach can help to extract log-ratios (not
necessarily belonging to any of previously mentioned extreme cases, pairwise log-ratios
versus clr coordinates) able to recognize the geochemical signature.
For this purpose, in van den Boogaart and Tolosana-Delgado (2013) a compositional Q-mode
clustering was proposed. This clustering method is based on idea to obtain easily interpretable
orthonormal coordinates with respect to the Aitchison geometry, referred to as principal
balances (Pawlowsky-Glahn et al., 2011). It is essentially hierarchical clustering, where the
variation matrix plays the role of a measure of association between compositional parts. The
resulting graphical output, dendrogram, can be applied to define a sequential binary partition
of compositional parts into groups of parts (Egozcue and Pawlowsky-Glahn, 2005); each
horizontal link is used to set a new variable that expresses balance between the corresponding
groups of compositional parts. By denoting those on the left side of the link by plus sign and
parts on the right side by minus sign, the balance (orthonormal coordinate) is defined as
  
 
 , (7)
where g(x+) and g(x-) stand for the geometric mean of parts from the first and second group,
respectively; together coordinates are obtained by such a procedure. Their
interpretation can be enhanced by suppressing the normalization constant and changing the
base of logarithm. It is also worth to note that each balance aggregates all pairwise log-ratios
between both groups of parts (Fišerová and Hron, 2011), the fact that can be used to search
for simpler log-ratios responsible for the geochemical signature of the D/C boundary.
According to McKinley et al. (2016), the resulting clusters of compositional parts will contain
elements behaving proportionally throughout the dataset. Log-ratios between parts of two
different clusters should thus be similar to other log-ratios of the elements of the same
clusters. Therefore, as indicated above, one of these log-ratios or a balance of one cluster
against the other might be representative for many log-ratios, and consequently may represent
a process influencing many elements in the same way. Balances of elements within the cluster
will filter out these large-variability effects and focus on differences between elements
behaving similarly with respect to major processes.
As a default agglomerative clustering procedure the Ward method (Ward, 1963) is used in
Pawlowsky-Glahn et al. (2011) and van den Boogaart and Tolosana-Delgado (2013), where
those two clusters are fused which result in the least increase in the sum of the (squared)
distances from each observation to the centroid of cluster contained it. Consequently, this
methods leads to spherical, tightly bound clusters that might in general be intuitively
interpretable. Moreover, because the Ward criterion corresponds to minimizing the total
within-cluster variance, it seems be recommendable for clustering of variables (compositional
parts). On the other hand, as the variation matrix has all properties of quasimetics, it is
meaningful to consider also other clustering methods that might lead even to better
interpretable clusters. For example, smaller clusters might be geologically easily interpreted.
Large numbers of small, tightly bound clusters are obtained using complete linkage, therefore
being a candidate for such an alternative agglomerative clustering algorithm. By considering
all these aspects, the dendrogram output might help to reveal such coordinates (balances) that
contain log-ratios responsible for the geochemical signature of the D/C boundary, represented
by presence of HBE black shale and sandstone layer.
3. Results and discussion
Despite of strong limitations of univariate analysis of raw compositional data (Filzmoser et
al., 2009b; McKinley et al., 2016), summaries of elemental concentrations are popular starting
point of any geochemical study. According to Pawlowsky-Glahn and Egozcue (2002) and
Mateu-Figueras and Pawlowsky-Glahn (2008), geometric mean is used to compute mean
concentrations; for a raw impression about variability of elements, interquantile ranges (IQR)
are applied.
The mean concentrations of the elements in the composition (in the order of its geometric
mean) are as follow: Ca (geometric mean = 15.55 %; IQR = 21.57 %), Si (5.05 %; ),
Al (0.75 %; 2.69 %), Fe (0.70 %; ), K (0.29 %; 0.77 %), Ti (734.04 ppm; 2110.46
ppm), Mn (557.11 ppm;  ppm), Sr (208.40 ppm; 181.30 ppm), Zr (39.19 ppm; 84.14
ppm), Cr (28.39 ppm; 65.26 ppm), Rb (25.76 ppm; 81.29 ppm), Ni (22.19 ppm; 33.53 ppm),
Y (21.02 ppm; 18.99 ppm), Zn (15.50 ppm; 27.16 ppm), Cu (11.65 ppm; 16.21 ppm), and Pb
(8.58 ppm; 10.21 ppm). Taking the relative scale into account, the element concentrations
show a strong variance across the studied areas and sections. This largely reflects the
principal lithology where pure carbonate, shale, sandstone, and siliceous sediments represent
the ideal end members.
The Upper Devonian carbonate-dominated successions (layer 1) are generally characterized
by high concentrations of Ca (geometric mean: 22.60 %) and low concentrations of Al, Si, K,
Ti, Fe, Rb, and other elements. The highest concentrations of Ca were detected in the pelagic
successions of the Rhenish Massif, Carnic Alps and Montagne Noire. In contrast, coeval
strata of the NamurDinant Basin (Gendron-Celles, Les Ardennes sections) have relatively
lower Ca concentrations.
In the following HBE black shale and sandstone interval (layers 2 and 3), the element
composition at the majority of sections changes rapidly, consistently with the lithology
change. Compared to the underlying strata, the mean concentrations of Ca in the HBE shales
and sandstones are extremely low (geometric mean 3.58 %) while the mean concentrations of
typically terrigenous elements are much higher (Al = 4.62 %, K = 1.31 %, Fe = 3.16 %, Ti =
4500 ppm, Rb = 190 ppm, S = 15 cps). In addition, the HBE black shales (layer 2) have very
high mean concentrations of Zr (221 ppm), S (59 cps), Zn (51 ppm), Ni (114 ppm) and Pb
(95 ppm).
The lower Tournaisian carbonate successions (layer 4) have relatively high concentrations of
Ca (25.13 %) and relatively low concentrations of elements such as Al (0.39 %), K (0.16 %),
Fe (0.43 %), Ti (470 ppm) and Rb (15 ppm), which is similar to those of the upper Famennian
succession (layer 1).
The youngest strata of the LAS interval (layer 5) were reached only at several sections of the
Namur-Dinant Basin (Rivage), Rhenish Massif (Oese, Drewer), Montagne Noire (Puech de la
Suque), Pyrenees (Saubette) and Carnic Alps (Kronhofgraben). These sediments are shaly,
often siliceous and phosphatic. They have high mean concentrations of Al (2.69 %), Si (25.05
%), K (0.65 %), Fe (2.46 %), Ti (0.22 %), Rb (104 ppm) and low concentrations of Ca (3.69
%). Compared to the all underlying layers, they are markedly enriched in elements such as P
(11 cps), Cu (47 ppm), Zn (44 ppm) and Ni (85 ppm).
In order to reveal both overall and specific geochemical patterns, standard biplots of raw or
log-transformed data and compositional biplots were used at each stage of analysis and this
section presents those options which led to the most interesting results. Figure 1 shows a
standard biplot of raw data (left) and its compositional counterpart (right). In both plots, a
cluster of terrigenous elements (Al, Ti, Rb, K, Fe) stands in opposition to Ca along the first
principal component, which is interpreted as the effect of dilution of terrigenous input by
marine CaCO3 production. The first principal component (PC) in the biplot depicting raw data
explains 56.9 % of total variability indicating that the effect of CaCO3 dilution is the
dominant geochemical pattern in the whole dataset. The second PC in the standard biplot
shows the contents of such productivity- and redox- sensitive elements as S, P, and Mn, while
other productivity-sensitive elements (Zn, Cu) largely overlap with the terrigenous ones. The
effect of Ca dilution seems to override the subtle variations in element behaviors in the
standard biplot. On the other hand, the compositional biplot better differentiates between
samples from different locations (different provenance) particularly along the second
principal component, which represents the effects of provenance and marine productivity. In
addition, the typically detrital proxy elements (Al, Ti, Rb, K and Si) are more clearly
separated from productivity-sensitive elements (Zn, Pb and Cr) in the compositional biplot
than in the standard one. At the same time, the effect of Ca dilution is partly removed in the
compositional biplot as indicated by the fact the Ca and terrigenous elements are no more in
opposition (Figure 1).
Figure 1 Standard biplot of raw data (left) and clr biplot (right), with samples distributed according to its location.
The biplots showing the whole data set bring important information about the general data
structure. However, the clustered distribution of samples from different geographical settings
and, hence, different provenance (Figure 1) suggests that it is appropriate to analyze such data
clusters separately.
Log-transformation of the raw geochemical data reflects the relative scale of observations;
consequently, it should help to reveal further patterns, possibly hidden behind the raw data.
The Figure 2 shows the application of standard biplot on log-transformed data with the
distinct stratigraphic layers, from Upper Devonian carbonates to Lower Alum Shale,
indicated. As it will be shown later, such geochemical markers as element ratios are
instrumental in distinguishing these layers. The Figure 2, left, shows a standard biplot of log-
transformed data from the Oberrödinghausen section, Rhenish Massif, Germany with four of
the five layers (Uppermost Devonian /Famennian/ carbonates, the HBE black shale, HBE
sandstone, and Lower Carboniferous /Tournaisian/ carbonates) indicated. The layers group
together as distinct clusters; there is a general pattern of clustering of samples from the HBE
shales/sandstones and carbonates along the PC1 axis, which is interpreted as the dilution
effect of calcium carbonate (see above). In addition, samples representing the HBE black
shale event occur as distinct outlier observations due to the high concentrations of Pb, Zn, Ni
and Cu, typical productivity-sensitive elements. The overlaps between the HBE black shales
and HBE shales/sandstones in the area with negative PC1 scores and positive PC2 scores
suggests that the black shales and “normal” grey shales can be represented by very similar
geochemistry.
Similar patterns are shown for the Oese section, Rhenish Massif (Figure 2, right). The
carbonates are again well separated from the shales and sandstones and there are distinct
outliers representing the HBE black shales and Lower Alum Shales (negative scores on PC1
and PC2) suggesting high concentrations of productivity-sensitive elements such as Pb, Zn,
Cu, Ni and Y. This suggests that the black shales of the HBE and LAS interval share a similar
geochemical composition. Moreover, both the biplots show a distinct clustering of variables
(elements), in particular the terrigenous Al, Rb, Ti, K and Si, which is consistent with the
summary biplot of all observations (Figure 1) and their expected geochemical behavior (see
section 2.1).
Figure 2 Standard biplots of log-transformed data from locations Oberrödinghausen (left) and Oese (right), Rhenish Massif,
Germany.
An even better representation of sample clustering is shown in Figure 3 providing the D/C
boundary data from the Kronhofgraben section, Carnic Alps, Austria. This biplot of log-
transformed data clearly separates between the cherts and black cherty shales of the Lower
Alum Shale interval, enriched in Cu, Ni, Pb and Si (negative scores on PC1 and positive
scores on PC2) and black shales of the HBE black shale interval (negative scores on both PC1
and PC2). This is consistent with the dissimilar lithology patterns of the HBE and LAS layers
at the Kronhograben section, the former represented by typical black shales and the latter by
black cherts and cherty shales (Schönlaub et al., 1992).
Figure 3 Biplot of log-transformed data from location Kronhofgraben, Carnic Alps, Austria.
The applicability of raw data, which are somewhat inappropriate from purely methodological
perspective, and clr coordinates can be demonstrated on samples from the Rhenish Massif
(Oese, Oberrödinghausen and Drewer sections) (Figure 4). The raw-data biplot (Figure 4 left)
clearly separates the black shales enriched in Ni, Zn, Pb and Cu from the remainder of
samples. The latter samples mostly tend to align to a carbonate (Ca) fine-grained siliciclastic
(Al, Rb, K, Ti) component line, which again reflects the degree of carbonate dilution of the
siliciclastic detrital input. In the compositional biplot, this pattern is generally lost, while the
differences between individual localities are highlighted.
Figure 4 Biplot of raw data (left) and compositional biplot (right) for locations from Rhenish Massif (Oberrödinghausen,
Oese, Drewer sections).
Loadings in the raw-data biplot again show a distinct clustering of elements, depending
largely on the expected geochemical behavior. In the Rhenish Massif, this clustering is very
well visible in areas where the particular genetic element groups (see above) are represented
by typical lithologies (black shales) with relatively high concentrations of their nominal
elements (Zn, Pb, Ni and Cu, Figure 4, left). There is again the overwhelming negative
correlation between Ca on one hand and Al, Rb, K and Ti on the other hand. In the
compositional biplot, however, the effects of a strong association with Ca (dilution effect) are
strongly suppressed and elements show clustering into several, genetically related groups: Ca
and Sr associated with marine calcium carbonate; terrigenous elements associated with
detrital rock-forming minerals, mainly phyllosilicates (Al, Si, Rb, Ti, Rb), redox-sensitive
elements associated with sulphidic phases (Cu, Ni, S, P) and other redox-sensitive elements
(Mn, Fe).
We also tested these patterns in the Ardennes (Gendron Celles section), where the HBE s.l.
layer is not represented by the distinct shale/sandstone lithology and the section is carbonate-
dominated (Figure 5). In the raw-data biplot (Figure 5 left) the effect of carbonate dilution is
very strong as indicated by the alignment of samples along the PC1 axis as well as the
negative correlation between Ca and the remainder of elements (with the exception of Sr, Mn
a Zn). In the compositional biplot, the effect of Ca dilution is again suppressed but the
variables (elements) tend to group together according to their expected geochemical behavior
(Al+Ti+Rb vs. Si+Zr vs. Pb+Zn+Cr+Mn) despite their very low concentrations. As indicated
in the previous sections, this seems to be the effect of relative scale of compositions, captured
by their clr coordinates.
Figure 5 Biplot of raw data (left) and compostional biplot (right) for location Gendron Celles, Ardennes, Belgium.
Another source of information about the data structure is represented by dendrograms
resulting from Q-mode clustering, whose construction was described in Section 2.3. Instead
of the originally proposed Ward clustering method, the complete linkage shown here and
based on the variation matrix provides more reliable results. Groups of elements identified by
this method can facilitate finding log-ratios, which optimally describe the presence of the
Hangenberg event layers and thus provide a compositional alternative to the standard proxies
as Zr/Al, K/Al and Rb/K ratios (Kumpan et al., 2014b, 2015).
Figure 6 shows a dendrogram for the Kronhofgraben section as the output of the Q-mode
clustering. According to this method, several balance coordinates were defined; three of them,
which lead to best separation of groups, are shown in Figure 7. The last one (Figure 7, right),
which excludes Ca (based on the assumption that Ca is strongly related to the dilution effect),
was selected, to see whether it can affect the values of the resulting balance. For comparison,
Figure 8 shows values of standard Hangenberg event proxies Zr/Al, K/Al and Rb/K. The
proposed log-ratios are useful to differentiate individual groups of observations; e.g., the low
values of ln(g(Ca,Sr)/g(rest)), where g(rest) stands for geometric mean of all components
except Ca and Sr, and log-ratio between Ca and Sr mark the presence of HBE black shale and
the LAS layer. Element ratios such as Zr/Al and K/Al are capable of distinguishing between
the HBE black shales and LAS black cherts/ cherty shales, the former having much higher
Zr/Al and lower K/Al values as compared to the latter (Figure 8). Nevertheless, when
comparing Figures 7 and 8 we can see that the compositional variables (balances) better
distinguish four groups of observations; the changes are really dramatic a provide a clear
structure. Note that similar patterns could be also seen for some other balances, indicated by
the dendrogram of Q-mode clustering (Figure 6), but the presented ones seem to provide the
best performance.
Figure 6 Dendrogram of Q-mode clustering for location Kronhofgraben.
Figure 7 Proposed log-ratios, based on dendrogram of Q-mode clustering from location Kronhofgraben, which optimally
discriminate layers.
Figure 8 Standard ratios used for discrimination between layers applied on location Kronhofgraben.
Q-mode clustering can also help to find suitable proxies only for subsets of observations, for
example for similar lithologies (shales and sandstones). Figure 9 shows the resulting
dendrogram for Oese section, in which only the HBE black shale and sandstone and Lower
Alum Shales were taken into account.
Figure 9 Dendrogram of Q-mode clustering for location Oese and layers Hangenberg black shale, Hangenberg sandstone and
Lover Alum Shale.
According to this clustering, combined with geochemical knowledge, we selected first the
log-ratio between subcompositions formed by parts Ti, Al, K and Cr, Rb, respectively (Figure
10, upper left) and one additional balance that links the previous elements with Cu and Zn
from the same branch of the dendrogram (Figure 10, upper right). Both balances clearly
separate the Lower Alum Shale layer from the HBE black shales. This represents the
advantage of log-ratio approach, compared to standard proxies, whose values are displayed on
Figure 10 (lower row) and which do not distinguish between layers at all. This is a direct
consequence of the fact that Q-mode clustering supplements the preliminary geochemical
knowledge with further possible candidates (balances) to reveal better the D/C boundary.
Figure 10 Proposed log-ratios, based on Q mode clustering from location Oese, which optimally discriminate layers (upper
row) and standard ratios used for discrimination between layers (lower row ).
In general, statistical analysis of observations including elemental geochemistry of carbonate
and siliciclastic bed successions across the D/C boundary using both compositional and non-
compositional approaches has revealed several interesting features. Dimension reduction of
multivariate geochemical data through principal component analysis is nowadays a must for
any reasonable case study. In stratigraphy, statistical pre-treatment of geochemical data is also
a common approach prior to depicting of stratigraphic patterns of element concentrations
(Sedláček et al., 2013; Bábek et al., 2015). In the present paper, several approaches how to
process the input observations prior to PCA were presented. The work flow proceeds from the
raw compositions (which are often inappropriate due to the relative nature of compositional
data) to either log-transformation or clr coordinates that consider, or not, total abundances of
elements. Interestingly, raw-data biplots were found useful to depict the basic geochemical
patterns such as the dilution effect of Ca and enrichment of black shales with productivity-
sensitive elements (Cu, Zn, Ni, etc.). The possible reason is that these effects are
predominantly driven just by absolute concentrations (or cps signal) of components rather
than being inherently contained in their ratios. On the other hand, compositional biplots are
capable of filtering out these predominant geochemical trends (such as the Ca dilution effect)
and depicting subtle geochemical variations, which are obscured by the major trends.
Following the previous argumentation, depicting of compositional log-ratios in
vertical/horizontal logs, which is a common approach in stratigraphy, can be more appropriate
than depicting simple element ratios, because subtle geochemical trends can be obscured by
the predominant trends such as the Ca dilution. This applies, for example, for nodular
limestones (such as the Upper Devonian carbonates of the Rhenish Massif), in which
diagenetic Ca redistribution strongly affects the primary geochemical signal. Nevertheless,
analysis in the previous section has shown that even the dilution effect of Ca is desirably
suppressed, when sufficiently robust log-ratios are considered (Figure 7). Moreover, with Q-
mode clustering it is possible to cover both dimension reduction using PCA, performed in clr
coordinates, and D/C layer discrimination under one methodological framework.
5. Conclusions
Our recent experiments clearly indicate that the combination of raw/log-transformed data and
compositional analyses are capable of distinguishing D/C boundary sediment layers with
specific geochemical signature, in particular the HBE black shales and LAS shales. This is in
line with recent contributions from geochemistry (Montero-Serrano et al., 2010, Reimann et
al., 2012, Bábek et al., 2015, McKinley et al., 2016) showing that not just the standard
processing of geochemical data, represented mostly by log-transformation, but even the
compositional data analysis has some limitations that favour the use of the complementary
approach. It is unexceptionable that only the logratio methodology would be acceptable, if
exclusively relative information out of geochemical data were informative, but it rather seems
not to be the case in most practical situations. Consequently, neither the standard nor the
compositional approaches have prevalence, but it is advisable to use both of them to discern
predominant and subtle geochemical trends in large datasets. Using the fact that the standard
and compositional approaches have synergic effects is thus recommendable for future
developments, in sedimentology, and also in geochemistry in general. Nevertheless, one must
be aware of interpretational dangers by using the standard approaches (log-transformed or
even raw data) that do not occur with the logratio methodology; a deep understanding of the
underlying geological phenomena (being the case here) is a necessary presumption of their
possible use in geochemical practice.
Acknowledgements
Karel Hron gratefully acknowledges the support of the grant COST Action CRoNoS IC1408
and the grant IGA_PrF_2016_025 Mathematical Models of the Internal Grant Agency of the
Palacky University in Olomouc. This work was partly supported by the Czech Science
Foundation (GAČR) research project 14-18183S (O. Bábek). We thank to Tomáš Matys
Grygar (Institute of Inorganic Chemistry ASCR, v.v.i.,) for providing of EDXRF data
References
Aitchison, J., 1986. The Statistical Analysis of Compositional Data. Monographs on Statistics
and Applied Probability. Chapman & Hall Ltd., London (UK). (Reprinted in 2003 with
additional material by The Blackburn Press).
Aitchison, J., Barce-Vidal, C., Martín-Fernández, J.A. and Pawlowsky-Glahn, V., 2000.
Logratio analysis and compositional distance. Mathematical Geology 32:3, 271-275.
Aitchison, J., Greenacre, M., 2002. Biplots of compositional data. Journal of the Royal
Statistical Society: Series C (Applied Statistics) 51:4, 375-392.
Bábek, O., Grygar, T.M., Faměra, M., Hron, K., Nováková, T., Sedláček, J., 2015.
Geochemical background in polluted river sediments: how to separate the effects of
sediment provenance and grain size with statistical rigour? Catena 135, 240-253.
Bábek, O., Kumpan, T., Kalvoda, J., Matys and Grygar, T., 2016. Devonian/Carboniferous
boundary glacioeustatic fluctuations in a platform-to-basin direction: A geochemical
approach of sequence stratigraphy in pelagic settings. Sedimentary Geology, in print
Billheimer, D., Guttorp, P. and Fagan, W., 2001. Statistical interpretation of species
composition. Journal of the American Statistical Association, 96:456, 1205-1214.
Bout-Roumazeilles, V., Combourieu-Nebout, N., Desprat, S., Siani, G., Turon, J.-L. and
Essallami, L., 2013. Tracking atmospheric and riverine terrigenous supplies variability
during the last glacial and the Holocene in central Mediterranean. Clim. Past 9, 1065
1087.
Chayes, F., 1960. On correlation between variables of constant sum. Journal of Geophysical
Research 65 (12), 41854193.
Eaton, M. L., 1983. Multivariate statistics. A vector space approach. John Wiley & Sons, New
York (US).
Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G. and Barceló-Vidal, C., 2003.
Isometric logratio transformations for compositional data analysis. Mathematical
Geology, 35, 279-300.
Egozcue, J.J. and Pawlowsky-Glahn, V., 2005. Groups of parts and their balances in
compositional data analysis. Mathematical Geology 37 (7), 795-828.
Egozcue, J. J., 2009. Reply to “On the Harker Variation Diagrams” by J.A. Cortés.
Mathematical Geosciences 41, 829-834.
Filzmoser, P., Hron, K. and Reimann, C., 2009a. Principal component analysis for
compositional data with outliers. Environmetrics 20, 621-632.
Filzmoser, P., Hron, K., Reimann, C., 2009b. Univariate statistical analysis of environmental
(compositional) data: Problems and possibilities. Science of the Total Environment 407,
6100-6108.
Filzmoser, P. Hron, K. and Reimann, C., 2012. Interpretation of multivariate outliers for
compositional data. Computers & Geosciences 39, 77-85.
Fišerová, E. and Hron, K., 2011. On interpretation of orthonormal coordinates for
compositional data. Mathematical Geosciences 43, 455-468.
Fralick, P.W. and Kronberg, B.I., 1997. Geochemical discrimination of clastic sedimentary
rock sources. Sediment. Geol. 113, 111124.
Gabriel, K.R., 1971. The biplot graphical display of matrices with application to principal
component analysis. Biometrika 58, 453-467.
Haese, R.R., Petermann, H., Dittert, L. and Schulz, H.D., 1998 The early diagenesis of iron in
pelagic sediments: a multidisciplinary approach. Earth and Planetary Science Letters 157:
233 248.
Jones, A.F., Macklin, M.G. and Brewer, P.A., 2012. A geochemical record of flooding on the
upper River Severn, UK, during the last 3750 years. Geomorphology 179, 89105.
Kaiser, S.I., Becker, R.T., Steuber, T. and Aboussalam, S.Z., 2011. Climate-controlled mass
extinctions, facies, and sea-level changes around the DevonianCarboniferous boundary
in the eastern Anti-Atlas (SE Morocco). Palaeogeogr. Palaeoclimatol. Palaeoecol. 310,
340364.
Kumpan, T., Bábek, O., Kalvoda, J., Frýda, J. and Matys Grygar, T., 2014a. A high-
resolution, multiproxy stratigraphic analysis of the Devonian-Carboniferous boundary
sections in the Moravian Karst (Czech Republic) and a correlation with the Carnic Alps
(Austria). Geol. Mag. 151, 201215.
Kumpan, T., Bábek, O., Kalvoda, J., Matys Grygar, T. and Frýda, J., 2014b. Sea-level and
environmental changes around the DevonianCarboniferous boundary in the Namur
Dinant Basin (S Belgium, NE France): a multi-proxy stratigraphic analysis of carbonate
ramp archives and its use in regional and interregional correlations. Sediment. Geol. 311,
4359.
Kumpan, T., Bábek, O., Kalvoda, J., Matys Grygar, T., Frýda, J., Becker, R.T. and Hartenfels,
S., 2015. Petrophysical and geochemical signature of the Hangenberg Events: an
integrated stratigraphy of the Devonian-Carboniferous boundary interval in the Northern
Rhenish Massif (Avalonia, Germany). Bull. Geosci. 90, 667694.
Mateu-Figueras, G. and Pawlowsky-Glahn, V., 2008. A critical approach to probability laws in
geochemistry. Mathematical Geosciences 40:5, 489-502.
McKinley, J.M., Hron, K., Grunsky, E., Reimann, C., de Caritat, P., Filzmoser, P., van den
Boogaart, K.G. and Tolosana-Delgado, R., 2016. The single component geochemical
map: Fact or fiction. Journal of Geochemical Exploration 162, 16-28.
Montero-Serrano, J.C., Palarea-Albaladejo, J., Martín-Fernández, J. A., Martínez-Santana, M.
and Gutiérrez-Martín, J. V, 2010. Sedimentary chemofacies characterization by means of
multivariate analysis. Sedimentary Geology 228: 3-4, 218-228.
Pawlowsky-Glahn, V. and Egozcue, J.J., 2001. Geometric approach to statistical analysis on
the simplex. Stochastic Environmental Research and Risk Assessment (SERRA), 15:5,
384-398.
Pawlowsky-Glahn, V. and Egozcue, J.J., 2002. BLU estimators and compositional data.
Mathematical Geology 34:3, 259274.
Pawlowsky-Glahn, V. and Buccianti, A. (Eds.), 2011. Compositional Data Analysis, Theory
and Applications. Wiley, Chichester (UK) 378p.
Pawlowsky-Glahn, V., Egozcue, J.J. and Tolosana-Delgado, R., 2011. Principal balances. In
Egozcue, J.J., Tolosana-Delgado, R., Ortego, M. (Eds.) Proceedings of the 4th
International Compositional Analysis Workshop, Sant Feliu de Guixols, Girona, Spain.
Pawlowsky-Glahn, V., Egozcue, J.J. and Tolosana-Delgado, R., 2015a. Modeling and analysis
of compositional data. Wiley, Chichester (UK).
Pawlowsky-Glahn, V., Egozcue, J.J. and Lovell, D., 2015b. Tools for compositional data with
a total. Statistical Modelling 15:2, 175-190.
R Core Team, 2016. R: A language and environment for statistical computing. R Foundation
for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.
Reimann, C., Filzmoser, P., Fabian, K., Hron, K., Birke, M., Demetriades, A., Dinelli and E.,
Ladenberger, A., 2012. The concept of compositional data analysis in practice Total
major element concentrations in agricultural and grazing land soils in Europe. Science of
the Total Environment 426, 196-210.
Ross, D.J.K. and Bustin, R.M., 2009. Investigating the use of sedimentary geochemical
proxies for paleoenvironment interpretation of thermally mature organic-rich strata:
examples from the DevonianMississippian shales, Western Canadian Sedimentary
Basin. Chem. Geol. 260, 119.
Sageman, B.B. and Lyons, T.W., 2005. Geochemistry of fine-grained sediments and
sedimentary rocks. In: Mackenzie, F.T. (ed.) Sediments, Diagenesis, and Sedimentary
Rocks. Elsevier, Amsterdam, 115158.
Sedláček, J., Bábek, O., Matys Grygar, T., 2013. Trends and evolution of contamination in a
well-dated water reservoir sedimentary archive: the Brno Dam, Moravia, Czech Republic.
Environ. Earth Sci. 69, 25812593.
Schnetger, B., Brumsack, H.-J., Schale, H., Hinrichs, J. and Dittert, L., 2000. Geochemical
characteristics of deep-sea sediments from the Arabian Sea: a high-resolution study.
Deep-Sea Res. Part II 47, 27352768.
Schönlaub, H.P., Attrep, M., Boeckelmann, K., Dreesen, R., Feist, R., Fenninger, A., Hahn,
G., Klein, P., Korn, D., Kratz, R., Magaritz, M., Orth, C.J. and Schramm, J.-M., 1992.
The Devonian/Carboniferous boundary in the Carnic Alps (Austria) a multidisciplinary
approach. Abh. Geol. Bundesanst. 135, 5798.
Śliwiński, M.G., Whalen, M.T. and Day, J. 2010. Trace element variations in the Middle
Frasnian punctata zone (Late Devonian) in the Western Canada sedimentary basin
changes in oceanic bioproductivity and paleoredox spurred by a pulse of terrestrial
afforestation? Geol. Belg. 13, 459482.
Tribovillard, N., Algeo, T.J., Lyons, T. and Riboulleau, A., 2006. Trace metals as paleoredox
and paleoproductivity proxies: an update. Chem. Geol. 232, 1232.
van den Boogaart, K.G. and Tolosana-Delgado, R., 2013. Analyzing compositional data with
R. Springer, Heidelberg (Germany) 258p.
van den Boogaart, K. G., Tolosana-Delgado, R. and Bren, M., 2013. compositions:
Compositional Data Analysis. R package version 1.40-1. URL
http://www.stat.boogaart.de/compositions.
Vijver, M.G., Spijker, J., Vink, J.P.M. and Posthuma, L., 2008. Determining metal origins and
availability in fluvial deposits by analysis of geochemical baselines and solid-solution
partitioning measurements and modelling. Environ. Pollut. 156, 832839.
Ward, J.H., Jr., 1963. Hierarchical grouping to optimize an objective function. Journal of the
American Statistical Association 58, 236244.
Xia, Q., 2009. The geodesic problem in quasimetric spaces. Journal of Geometric Analysis
19:2, 452-479.
List of Figures
Figure 1 Standard biplot of raw data (left) and clr biplot (right), with samples distributed
according to its location.
Figure 2 Standard biplots of log-transformed data from locations Oberrödinghausen (left) and
Oese (right), Rhenish Massif, Germany.
Figure 3 Biplot of log-transformed data from location Kronhofgraben, Carnic Alps, Austria.
Figure 4 Biplot of raw data (left) and compositional biplot (right) for locations from Rhenish
Massif (Oberrödinghausen, Oese, Drewer.)
Figure 5 Biplot of raw data (left) and compostional biplot (right) for location Gendron Celles,
Ardennes, Belgium.
Figure 6 Dendrogram of Q-mode clustering for location Kronhofgraben.
Figure 7 Proposed log-ratios, based on dendrogram of Q-mode clustering from location
Kronhofgraben, which optimally discriminate layers.
Figure 8 Standard ratios used for discrimination between layers applied on location
Kranhofgraben.
Figure 9 Dendrogram of Q-mode clustering for location Oese and layers Hangenberg black
shale, Hangenberg sandstone and Lover alum shale.
Figure 10 Proposed log-ratios, based on Q mode clustering from location Oese, which
optimally discriminate layers (upper row) and standard ratios used for discrimination between
layers (lower row).
.
List of Equations
(1) Centred log-ratio coordinates.
(2) Geometric mean.
(3) Variation matrix.
(4) Non-negativity, identity of indiscernibles and symmetry of elements of the variation
matrix.
(5) Triangular inequality of elements of the variation matrix.
(6) Relation between elements of the variation matrix and variance of a logratio.
(7) Balance.
... Concentrations are compositional data, which carry exclusively relative information and require different treatment in statistical analysis (Kynčlová et al., 2017). Moreover, experiences show that use raw data can reveal interesting features (but it can be considered an incomplete and biased analysis) (Fačevicová et al., 2016). Combination with logratio alternatives of the standard statistical methods present considerable improvements (Boente et al., 2018), with centered logratio (clr) transformation most used in geochemical studies. ...
Article
Toxic metal enrichment in urban soils from natural and anthropogenic sources is a public health concern that challenges sustainable urban development. Active and legacy mining is likely a major contributor of localized metal pollution in resource-based economies, although other sources associated with industrial and transportation activities may also contribute in urban settings. In mining countries, such as Chile, with no soil quality regulation, public policies that seek to protect human health should assess metal distribution and pollution indexes to guide interventions, especially in urban green spaces. To assess the role of active and legacy mining waste sites within the urban and peri-urban areas, metal concentrations in the soils of urban parks were measured in this study, and four pollution indexes were calculated for four cities of Chile. Copiapó and Andacollo in northern Chile represented the cities with several active and legacy mining waste sites located within the urban area, while conurbation La Serena-Coquimbo and Gran Santiago represented the cities in mining districts that lacked major mining waste sites within their urban perimeters. A total of 82 (Copiapó), 30 (Andacollo), 26 (La Serena-Coquimbo), and 59 (Gran Santiago) composite surface soil samples were collected from the urban parks. Considering Canadian guidelines for residential/parkland soils, the value for Cu (63 mg/kg) was found to be exceeded in 99%, 50%, 100%, and 97% of samples collected from Copiapó, La Serena-Coquimbo, Andacollo, and Gran Santiago, respectively. The guidelines for lead (140 mg/kg) and zinc (250 mg/kg) were exceeded in less than 12% of samples collected from Copiapó and Gran Santiago. Arsenic was not mainly quantified (<10% quantification frequency, quantification limit = 36 mg/kg). The calculated modified pollution load, Nemerow, and soil quality indexes indicated that soils in the urban parks were more polluted in cities with urban mine wastes, however, the pollution load index ranked higher metal pollution in Gran Santiago. This study presented the first comparative study of metals in urban parks of Chile, highlighting a large proportion of parks with soil copper concentrations above the international guidelines, while showing higher median values in cities containing urban mine waste disposal sites.
... This presumption can be done first of all because the latter site classification is similar to that using the relative median contents of all major elements (r S = 0.870). Our present results also cannot be neglected, considering the findings of Fačevicova et al. [57] when studying the Devonian/Carboniferous boundary and comparing the results obtained by the standard approach with those obtained by the compositional approach and revealing that they have "synergic effects:" neither of them has prevalence and both can be further used in geochemical investigations. If so, the results of our research can be useful for future investigations of geochemical approaches based on intercorrelated major elements revealed using transformations that take into account the closure effect of data. ...
Article
Full-text available
This study of peri-urban minerogenic topsoil on glacigenic or post-glacial deposits shows the influence of the site-classification approach on the differentiated median background (DMB) values of major elements and the potentially harmful elements (PHEs) Ba, Cr, Cu, Mn, Ni, Pb and Zn. Composite samples from forests and meadows were taken in 25 sites, each of which had five sub-sites. A fraction of <2 mm was used to determine the organic matter by loss on ignition (LOI), grain size by laser diffraction and the elemental contents by X-ray fluorescence. The following five site-classification approaches are compared: geochemical (G), using relative median contents of Al, K, Ti; textural (T), according to mean percentages of clay-sized fraction (CLF) and silt fraction (SIF); lithological (L), based on soil parent material texture from the soil database; soil type (S), presented in the soil database; and parent material (P), generalising the underlying Quaternary deposits. Sites were classified into four level groups in which the DMB values were estimated after eliminating anomalies. The average ranks of three scores according to SIF, CLF, LOI, Al, K, Ti, Fe, Mg, Ca and S in the respective groups revealed the highest value for the G approach. It better eliminates the CLF and SIF influences on the median assessment indices of PHEs in sites.
... One of major principles of CoDA is to avoid work with element concentrations. The comparison of outputs of log-ratio methodology and empirical approach based on concentrations, presented in our work, could thus be considered principally incorrect by strict CoDA experts, but examples of such comparisons can also be found in literature Fačevicová et al., 2016;Zuzolo et al., 2018Zuzolo et al., , 2020. All data-treatment procedures, including construction of log-ratio coordinates, could benefit from testing in real case studies and comparisons with conventional methods to 1) be refined/approved for practical use and 2) persuade readers they could profit from replacing standard statistical tools implemented in common software for data plotting and processing by novel, advanced, and yet developing approaches and protocols. ...
Article
A compositional data analysis (CoDA) in fluvial sediments is performed to achieve separation of the geochemical signals (SGS) of grain size, anthropogenic contamination, and possible post-depositional alteration. The SGS is demonstrated and developed in the study of the sediments from the Skalka Reservoir (Czechia) and the floodplain of its tributary rivers, which have been impacted by pollution from the Chemical Factory Marktredwitz (Bavaria, Germany) brought through temporary sinks in the channels and floodplains to the reservoir. This paper compares CoDA tools with standard empirical approaches based on using deeper strata as uncontaminated or pre-industrial (examination of element concentration depth profiles), scatterplots with risk elements (mainly Zn in this study) as dependent variables and lithogenic reference elements as independent variables to construct background functions and to calculate local enrichment factors (LEF), and a principal component analysis performed on raw and geochemically normalised elemental concentrations. The utilised CoDA tools include classical and robust methods using the log-ratio approach that fully respects the mathematical specificity of the compositional data (data closure, or more generally scale invariance, and further related aspects like non-Gaussian distribution, and commonly polymodality) like the robust PCA with centred log-ratio (clr) transformation of concentrations; consequently, histograms of the raw and normalised concentrations and contamination scores were compared. The multivariate CoDA was considerably facilitated by a novel tool for understanding the grain-size control of sediment composition, i.e. a functional data analysis of particle size distributions (densities) based on Bayes spaces. Also, the robust correlation analysis was efficient using a (log-)ratio methodology. Several elements can be used for the geochemical normalisation and LEF calculations, of which Al, Fe, and Ti can definitely be recommended, while Cr, Mg, and even Si also produced comparable results. A more critical factor is a proper selection of the background functions. We demonstrated the limits of using some popular tools for the compositional data mining: the ordinary PCA failed or performed worse than LEF in the separation of grain-size and contamination signals. Some log-ratio methods performed well, in particular robust regression with selected (lithogenic elements at explaining side) and robust PCA with clr transformation. Even for apparently simple tasks, such as the separation of anthropogenic contamination signals, knowledgeable decisions during data preparation for the CoDA are still indispensable.
... Examples of compositional data are geochemical data where the chemical composition of soil samples is of interest, the composition of nutrients of food intake or the distribution of market shares. For further details and examples of compositional data see for example [1,2,3,4,5,6,7]. ...
Preprint
Full-text available
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is challenging as the application of standard multivariate analysis tools on the raw observations can lead to spurious results. Hence, it is appropriate to apply certain transformations prior further analysis. One popular multivariate data analysis tool is independent component analysis. Independent component analysis aims to find statistically independent components in the data and as such might be seen as an extension to principal component analysis. In this paper we examine an approach of how to apply independent component analysis on compositional data by respecting the nature of the former and demonstrate the usefulness of this procedure on a metabolomic data set.
... Robust regression (RR) should be preferred to the ordinary least-squares method in geochemical analyses, which has yet to be recognised for the environmental geochemistry of sediments (Matys Grygar and Popelka, 2016;Birch, 2017). Although robust statistics have already been established in the context of compositional data (Tolosana-Delgado and McKinley, 2016;Filzmoser et al., 2018), the implementation of robust approaches in sedimentary geochemistry is still rare (Fačevicová et al., 2016). ...
Article
The extraction of palaeoenvironmental (palaeoclimatic) signals from the chemical composition of siliciclastic sediments is valuable for the reconstruction of past environments, particularly in continental basins. Here we test novel weathering proxies, which are less sensitive to lithological control than the previously used raw element ratios K/Al, K/Ti, and K/Rb: (1) local enrichment factors of K/Al, Mg/Al, and K/Rb, i.e., the element ratios corrected for grain size- and matrix composition using local background functions (Al/Si, Fe, and Ca as explanatory variables) and ordinary regression and (2) robust regression residuals of those element ratios based on isometric log-ratio coordinates of the most relevant “lithogenic” elements (Ca, Fe, Rb, Si, Zr) in the chemical composition. Chemical weathering proxies can be obtained from departures of chemical composition of sedimentary profiles from relationships with other chemical elements, in particular those with grain-size control. The resulting weathering proxies were examined for the Miocene deposits from the Most Basin, the Czech Republic, which recorded one of the major warm episodes of the Cenozoic time – the Miocene Climatic Optimum. The performance of weathering proxies has been checked by (1) comparison of individual proposed proxies in one drill core HK930, (2) detailed analysis of orbital signals in the relevant compositional functions in HK930; and (3) lateral correlation of three cores HK930, DU7, and DO565 of the same basin. The novel proxies show lateral stability and orbital signatures of short eccentricity, obliquity, and precession, confirming their usefulness in palaeoenvironmental studies. Corrections for grain-size and carbonate contents should help to isolate climatic content from the weathering proxies, although in the studied sediments it weakened the precession component in the orbital signal, as grain-size proxies and other compositional data also carried orbital signals. We propose to consider these proxy ideas in palaeoclimatic reconstructions based on chemical weathering proxies.
... The Devonian-Carboniferous boundary transition is situated in the upper part of the Montagne Noire Griotte Group ("supragriottes" Boyer et al. 1968). It was studied for conodonts (Boyer et al. 1968;Girard 1994;Kaiser et al. 2009), ostracods Feist 1991, Casier et al. 2001), ammonoids (Korn and Feist 2007), sedimentology (Michel 1981, Casier et al. 2001) and geochemistry (Kaiser et al. 2008;Bábek et al. 2016;Fačevicová et al. 2016). The investigated topmost Wocklumeria limestone succession of the Montagne Noire Griotte Group (Beds PS85 to PS90) consists of bedded, nodular decimetre-thick micritic limestones with dominant cephalopods and filaments (pelagic bivalves), blind trilobites (Chaunoproetus) and predominantly Thuringian-type ostracods (Casier et al. 2001) that indicate a quiet off-shore environment below the photic zone. ...
Article
Sections with continuous sedimentation across the Devonian–Carboniferous (D-C) boundary in the Montagne Noire allow to build a virtual transect from shoreline to deep basin. Nearshore facies characterise the D-C boundary stratotype and neighbouring sections at La Serre in the Cabrières klippen domain, and offshore facies are present at the Col de Tribes and Puech de la Suque sections in the Mont Peyroux nappe domain. Both domains exhibit equivalents of the Hangenberg Black Shale (HBS). At La Serre, an initial regressive trend is indicated by the presence of oculated trilobites in the topmost pre-HBS Wocklumeria Limestones. Above the HBS level, regressive depositional conditions characterise oolitic deposits that comprise lithic erosional flows with an admixture of transported shallow-water biotas. Maximum regression is recognised with the deposition of coarse breccias and local features of emergence prior to the first appearance of Protognathodus kockeli. The oolites are superseded by the transgression of outer shelf deposits. In the nappe domain, the HBS is intercalated in outer ramp nodular limestones, and it exhibits detrital elements pointing to its regressive nature. The regressive trend culminates than reverses when post-HBS carbonate sedimentation resumes. Protognathodus kockeli appears in the post-HBS carbonates. Associated oculated trilobites indicate shallower bathymetric conditions then those of the pre-HBS Wocklumeria Limestones. Thereafter, replacement of sighted trilobites by blind ones and the protognathodid biofacies by facies dominated by siphonodellids indicate a deepening trend. The near- and offshore sites of the D-C transition permit correlation of short-term bathymetric fluctuations with faunal turnovers and entries of biostratigraphic markers.
... The Devonian-Carboniferous boundary transition is situated in the upper part of the Montagne Noire Griotte Group ("supragriottes" Boyer et al. 1968). It was studied for conodonts (Boyer et al. 1968;Girard 1994;Kaiser et al. 2009), ostracods (Lethiers and Feist 1991 (Michel 1981, Casier et al. 2001) and geochemistry (Kaiser et al. 2008;Bábek et al. 2016;Fačevicová et al. 2016). The investigated topmost Wocklumeria limestone succession of the Montagne Noire Griotte Group (Beds PS85 to PS90) consists of bedded, nodular decimetre-thick micritic limestones with dominant cephalopods and filaments (pelagic bivalves), blind trilobites (Chaunoproetus) and predominantly Thuringian-type ostracods (Casier et al. 2001) that indicate a quiet off-shore environment below the photic zone. ...
Poster
correlation of near- and offshore sections across the Devonian-Carboniferous boundary in the strato-type area (Montagne Noire, France)
... Recently, there have been several applications of compositional data analyses in the fields of geochemistry and hydrogeochemistry (Blake et al. 2016;Buccianti and Zuo 2016;Tolosana-Delgado and McKinley 2016). Fačevicová et al. (2016) reported a statistical characterization of the Devonian-Carboniferous boundary, in which results obtained by a log ratio method were compared with those obtained from a classical point of view, without any prior transformation. The paper proposed that using a combination of the two approaches brings more insights than using either of any of the two methods separately. ...
Article
Full-text available
The CO2-rich spring water (CSW) occurring naturally in three provinces, Kangwon (KW), Chungbuk (CB), and Gyeongbuk (GB) of South Korea was classified based on its hydrochemical properties using compositional data analysis. Additionally, the geochemical evolution pathways of various CSW were simulated via equilibrium phase modeling (EPM) incorporated in the PHREEQC code. Most of the CSW in the study areas grouped into the Ca–HCO3 water type, but some samples from the KW area were classified as Na–HCO3 water. Interaction with anorthite is likely to be more important than interaction with carbonate minerals for the hydrochemical properties of the CSW in the three areas, indicating that the CSW originated from interactions among magmatic CO2, deep groundwater, and bedrock-forming minerals. Based on the simulation results of PHREEQC EPM, the formation temperatures of the CSW within each area were estimated as 77.8 and 150 °C for the Ca–HCO3 and Na–HCO3 types of CSW, respectively, in the KW area; 138.9 °C for the CB CSW; and 93.0 °C for the GB CSW. Additionally, the mixing ratios between simulated carbonate water and shallow groundwater were adjusted to 1:9–9:1 for the CSW of the GB area and the Ca–HCO3-type CSW of the KW area, indicating that these CSWs were more affected by carbonate water than by shallow groundwater. On the other hand, mixing ratios of 1:9–5:5 and 1:9–3:7 were found for the Na–HCO3-type CSW of the KW area and for the CSW of the CB area, respectively, suggesting a relatively small contribution of carbonate water to these CSWs. This study proposes a systematic, but relatively simple, methodology to simulate the formation of carbonate water in deep environments and the geochemical evolution of CSW. Moreover, the proposed methodology could be applied to predict the behavior of CO2 after its geological storage and to estimate the stability and security of geologically stored CO2.
Chapter
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is challenging as the application of standard multivariate analysis tools on the raw observations can lead to spurious results. Hence, it is appropriate to apply certain transformations prior to further analysis. One popular multivariate data analysis tool is independent component analysis. Independent component analysis aims to find statistically independent components in the data and as such might be seen as an extension to principal component analysis. In this paper, we examine an approach of how to apply independent component analysis on compositional data by respecting the nature of the latter and demonstrate the usefulness of this procedure on a metabolomics dataset.
Chapter
Cluster analysis is an exploratory statistical technique to group observations or variables in data sets. The main goal of cluster analysis is to achieve highly homogeneous clusters, i.e. the observations (or compositional parts—in Q-mode clustering) within a cluster should be very similar to each other. On the other hand, different clusters should be dissimilar, because otherwise they should have been merged into one cluster. With cluster analysis one typically aims to find elliptically shaped partitions in the data, but also more special structures in the data are sometimes of interest. Cluster analysis again needs to be adapted in the context of compositional data. The use of the Aitchison distance or the clustering after representing the data in ilr coordinates is crucial. Moreover, for clustering of compositional parts in Q-mode clustering the variation matrix, either classically or robustly estimated, is taken. For clustering observations (compositions), no particular methodological peculiarities occur; basically, any orthonormal logratio coordinates serve well for this purpose. In this chapter, some of the most popular methods are described in more detail: hierarchical clustering with different linkage methods, the k-means algorithm, model-based clustering as well as fuzzy clustering. Finally, also some cluster validity measures for evaluating the quality of the clustering result are presented.
Article
Full-text available
Petrophysical (gamma-ray spectrometry, magnetic susceptibility) and geochemical (X-ray fluorescence spectrometry and inorganic carbon isotope geochemistry) methods are used for stratigraphic correlations and palaeoenvironmental interpretations of the Devonian-Carboniferous boundary interval in the northern part of the Rheinisches Schiefergebirge, Germany. Sections at Oese, Oberrodinghausen and Drewer were studied in the stratigraphic range from the Famennian Upper expansa Zone to the Tournaisian Lower crenulata Zone. The Famennian Wocklum Limestone reveals distinctive cyclicity in the limestone and shale arrangement, whose primary origin has been supported by correlation with K/Al ratio changes. Lower-order K/Al cyclicity follows bundles of alternating layers. On the other hand, Zr/Al cyclicity is rather independent on facies and K/Al and duration of Zr/Al cycles was estimated to be 370 ka, which is close to 405 ka eccentricity. Correlations of the curve patterns of Computed Gamma Ray, U/ThGRS, bulk magnetic susceptibility, K/Al, Zr/Al, S, and Mn proxies have been employed for regional correlation. Our dataset confirms previous palaeoenvironmental interpretations of the Hangenberg Events and additionally provides information on gradual decrease in a bottom oxygenation just prior the events. Peaks in redox and palaeoproductivity proxies (U/Th, Cu+Ni+Zn+Pb) occur in the Hangenberg Black Shale in all studied sections. Although sedimentation of the Hangenberg Black Shale took place during the deepening step, the enhanced palaeoproductivity and hypoxia to anoxia were the main cause of its deposition. An interregional correlation of the Devonian-Carboniferous intervals from the northern Rhenish Massif, Moravian Karst and Carnic Alps was carried out and underlines the potential for further chronostratigraphic definitions.
Article
The simplex plays an important role as sample space in many practical situations where compositional data, in the form of proportions of some whole, require interpretation. It is argued that the statistical analysis of such data has proved difficult because of a lack both of concepts of independence and of rich enough parametric classes of distributions in the simplex. A variety of independence hypotheses are introduced and interrelated, and new classes of transformed‐normal distributions in the simplex are provided as models within which the independence hypotheses can be tested through standard theory of parametric hypothesis testing. The new concepts and statistical methodology are illustrated by a number of applications.
Book
It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science. Key Features: • Reflects the state-of-the-art in compositional data analysis. • Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures. • Looks at advances in algebra and calculus on the simplex. • Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics. • Explores connections to correspondence analysis and the Dirichlet distribution. • Presents a summary of three available software packages for compositional data analysis. • Supported by an accompanying website featuring R code. Applied scientists working on compositional data analysis in any field of science, both in academia and professionals will benefit from this book, along with graduate students in any field of science working with compositional data.
Book
Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website. Complementing Pawlowsky-Glahn's earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.
Article
We investigated high-resolution stratigraphic distribution of selected major and trace elements and gamma-ray spectra of fourteen Devonian/Carboniferous (D/C) boundary sections of Europe constituting the late Palaeozoic Laurussia and Gondwana. The aim was to trace the geochemical signature of a marked forced and normal regressive interval which was associated with rapid progradation of siliciclastics into the marine carbonate systems (Rhenish Massif) and a prominent hiatus in shallow-water ramp settings (Namur–Dinant Basin). This interval represents the late Devonian Hangenberg event (HBE) sensu lato (middle praesulcata conodont zone) as defined by previous authors. This regressive interval (FSST to LST) correlates with thin shale layers (HBE shale) sandwiched between monotonous nodular calcilutite/calcisiltite successions at five pelagic sections of Moravia, Carnic Alps, Montagne Noire, and Pyrenees. In all sections with continuous D/C sedimentation (i.e., except those of the Namur–Dinant Basin), the HBE s.l. interval is accompanied by elevated percentages of detrital proxies (Al, K, Rb, Zr) and changes in their ratios (Zr/Rb, K/Al, Rb/K) which are normally interpreted as indicators of increased siliciclastic input, provenance, and grain size. Zr/Rb and other proxies are traceable even without apparent lithological evidence and can, therefore, facilitate stratigraphic correlation. Paleoredox and productivity proxies (U/Th and Ni/Rb enrichment factors) only rarely show elevated values in the Hangenberg black shale interval, indicating that the associated water dysoxia/anoxia was a local rather than global phenomenon. Global correlations based on the HBE black shales should therefore be dropped in favour of the HBE s.l. interval. Moreover, analysis of sedimentation rates in the upper expansa to kockeli zone interval using the published radiometric ages suggests that the HBE s.l. was a time of significant increase in the rate of siliciclastic supply into the ocean, even in the most distal pelagic sections. Consequently, the previous interpretation of the HBE black shale as a condensed succession deposited during rapid sea-level rise seems unlikely. We interpret the HBE s.l. (i.e., including the HBE black shale) as a marine record of glacioeustatic sea-level drop and increased aeolian transport in connection with late Devonian climatic cooling and glaciation. The set of geochemical markers related to the late Devonian sea-level fluctuation can be used for super-regional to global correlations from platform to basin settings. Moreover, they can facilitate current efforts to determine a new D/C boundary definition.
Article
Single component geochemical maps are the most basic representation of spatial elemental distributions and commonly used in environmental and exploration geochemistry. However, the compositional nature of geochemical data imposes several limitations on how the data should be presented. The problems relate to the constant sum problem (closure), and the inherently multivariate relative information conveyed by compositional data. Well known is, for instance, the tendency of all heavy metals to show lower values in soils with significant contributions of diluting elements (e.g., the quartz dilution effect); or the contrary effect, apparent enrichment in many elements due to removal of potassium during weathering. The validity of classical single component maps is thus investigated, and reasonable alternatives that honour the compositional character of geochemical concentrations are presented. The first recommended such method relies on knowledge-driven log-ratios, chosen to highlight certain geochemical relations or to filter known artefacts (e.g. dilution with SiO2 or volatiles). This is similar to the classical normalisation approach to a single element. The second approach uses the (so called) log-contrasts, that employ suitable statistical methods (such as classification techniques, regression analysis, principal component analysis, and clustering of variables) to extract potentially interesting geochemical summaries. The caution from this work is that if a compositional approach is not used, it becomes difficult to guarantee that any identified pattern, trend or anomaly is not an artefact of the constant sum constraint. In summary the authors recommend a chain of enquiry that involves searching for the appropriate statistical method that can answer the required geological or geochemical question whilst maintaining the integrity of the compositional nature of the data. The required log-ratio transformations should be applied followed by the chosen statistical method. Interpreting the results may require a closer working relationship between statisticians, data analysts and geochemists.
Article
Compositional data analysis usually deals with relative information between parts where the total (abundances, mass, amount, etc.) is unknown or uninformative. This article addresses the question of what to do when the total is known and is of interest. Tools used in this case are reviewed and analysed, in particular the relationship between the positive orthant of D-dimensional real space, the product space of the real line times the D-part simplex, and their Euclidean space structures. The first alternative corresponds to data analysis taking logarithms on each component, and the second one to treat a log-transformed total jointly with a composition describing the distribution of component amounts. Real data about total abundances of phytoplankton in an Australian river motivated the present study and are used for illustration.