Page 124 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

Catchment Basin Analysis of Stream Sediment Anomalies 123

corrected uni-element residuals suggest enrichment due to anomalous sources, it is
intuitive to constrain the analysis of multi-element geochemical signatures by using only
a subset of samples with positive dilution-corrected residuals for at least one of the
elements under study (e.g., Carranza and Hale, 1997; Carranza, 2004a).
Analysis of multi-element geochemical signatures could be realised through a variety
of mathematical multivariate techniques, such as cluster analysis, correspondence
analysis, discriminant analysis, factor analysis, regression analysis, principal components
analysis (PCA), etc. Explanations of the fundamentals of such multivariate analytical
techniques can be found in textbooks (e.g., Davis, 2002) and explanations of applications
of such methods to analysis of multivariate geochemical data can be found in Howarth
and Sinding-Larsen (1983). For cases where there are few or no known occurrences of
mineral deposits of the type sought in a study area, PCA is a useful multivariate
analytical technique because it serves as an exploratory approach to discriminate
between background and anomalous multi-element signatures.
A brief explanation about PCA is given in Chapter 3. Because results of PCA tend to
be dominated by non-anomalous populations, recognition of anomalous multi-element
associations can be enhanced by using a subset of samples consisting of anomalous
dilution-corrected residuals of at least one of the elements under study. So, classification
of anomalous dilution-corrected uni-element residuals must be performed prior to PCA.
For the purpose of illustration using the stream sediment Cu and Zn data, an arbitrary
th
threshold representing the 70 percentile of positive dilution-corrected uni-element
residuals is used for uni-element anomaly classification. However, after the classification
of anomalous dilution-corrected uni-element residuals, there are still some problems that
must be overcome. Firstly, inspection of histograms or boxplots of data for a subset of
samples consisting of anomalous dilution-corrected residuals of at least one of the
elements under study can reveal the presence of multiple populations, outliers and
asymmetric empirical density distributions in the data. These factors undermine reliable
estimation of a covariance matrix or a correlation matrix, either of which is used as a
starting point of PCA. Secondly, logarithmic transformation of the data to alleviate the
effects of these factors is not feasible because negative dilution-corrected uni-element
residuals can be present in the data subset. A remedy to such problems is to perform a
simple rank-ordering approach. Thus, by considering 1 as lowest rank, descending ranks
(i.e., n to 1) are assigned to descending n values of dilution-corrected uni-element
residuals and averaging ranks in case of ties. A Spearman rank correlation matrix can
then be computed for the rank-transformed dilution-corrected uni-element residuals,
which can be used in PCA (e.g., George and Bonham-Carter, 1989; Carranza and Hale,
1997).
Table 5-III shows the results of PCA using the whole set of dilution-corrected Cu and
Zn residuals derived from multiple regression analysis of the stream sediment Cu and Zn
data and the results of PCA using a subset of samples with anomalous dilution-corrected
of either Cu or Zn residuals derived from multiple regression analysis of the stream
sediment Cu and Zn data. If all samples are used, then PC1 can be interpreted to
represent an anomalous inter-element association because the loadings on Cu and Zn are