Geoscience Reference
In-Depth Information
As an example consider a set of microprobe analyses on glass shards from
volcanic ash layers in a tephrochronology project. h e variables then
represent the
p
chemical elements and the objects are the
n
ash samples.
h e aim of the study is to correlate ash layers by means of their geochemical
i ngerprints.
Most multi-parameter methods simply try to overcome the main dii culty
associated with multivariate data sets, which relates to data visualization.
Whereas the character of univariate or bivariate data sets can easily be
explored by visual inspection of a 2D histogram or an
xy
plot (Chapter
3), the graphical display of a three variable data set requires a projection
of the 3D distribution of data points onto a two-dimensional display. It is
impossible to imagine or display a higher number of variables. One solution
to the problem of visualization of high-dimensional data sets is to reduce
the number of dimensions. A number of methods group together highly-
correlated variables contained within the data set and then explore the
reduced number of groups.
h e classic methods for reducing the number of dimensions are
principal
component analysis
(PCA) and
factor analysis
(FA). h ese methods seek the
directions of maximum variance in a data set and use these as new coordinate
axes. h e advantage of replacing the variables by new groups of variables is
that the groups are uncorrelated. Moreover, these groups can ot en assist in
the interpretation of a multivariate data set since they ot en contain valuable
information on the processes responsible for the distribution of the data
points. In a geochemical analysis of magmatic rocks the groups dei ned by
the method usually contain chemical elements with similar sized ions in
similar locations within the lattices of certain minerals. Examples include
Si
4+
and Al
3+
, and Fe
2+
and Mg
2+
, in silicates.
A second important suite of multivariate methods aims to group objects by
their similarity. As an example
cluster analysis
(CA) is ot en used to correlate
volcanic ash layers such as that used in the above example. Tephrochronology
attempts to correlate tephra by means of their geochemical i ngerprints.
When combined with a few radiometric age determinations from the key
ash layers this method allows correlation between dif erent sedimentary
sequences that contain these ash layers (e.g., Westgate 1998, Hermanns et
al. 2000). Cluster analysis is also used in the i eld of micropaleontology, for
example, to compare the pollen, foraminifera, or diatom content of dif erent
microfossil assemblages (e.g., Birks and Gordon 1985).
A third group of methods is concerned with the classii cation of
observations. Humans tend to want to classify the things around them,
