Page 79 - Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

78 Chapter 3

element data sets (Table 3-VI), nevertheless, indicate a Cu-Ni-Co association reflecting
lithologic control, a Mn-Zn-Co association reflecting metal scavenging chemical control
by Mn-oxides and an As-Ni-Cu association reflecting metallic mineralisation related to
certain lithologies (i.e., andesitic rather than dacitic). The presence of obvious and subtle
inter-element relationships in the case study data sets requires further application of
appropriate multivariate methods that allow quantification and mapping of such inter-
element relationships.

Analysis and mapping of multi-element associations
The multivariate methods most commonly employed in studying and quantifying
multi-element associations in exploration geochemical data include principal
components analysis (PCA), factor analysis (FA), cluster analysis (CA), regression
analysis (RA) and discriminant analysis (DA). PCA and FA are useful in studying inter-
element relationships hidden in multiple uni-element data sets. CA is useful for studying
inter-sample relationships, whilst RA and DA are useful for studying inter-element as
well as inter-sample associations. RA and DA require training data, i.e., samples
representative of processes of interest (e.g., from mineralised zones). Authoritative
explanations of multivariate methods applied to geochemical and geological data
analysis can be found in Howarth and Sinding-Larsen (1983) and Davis (2002). In this
case study, either PCA or FA is favourable for revealing inter-element relationships, a
few of which may reflect presence of mineralisation.
PCA and FA are very similar techniques so that they are often confused with each
other, but they have significant mathematical and conceptual differences. Howarth and
Sinding-Larsen (1983) and Reimann et al. (2002) provide clear discussions about the
similarities and dissimilarities between PCA and FA, which are summarised here. Both
methods start with either the correlation matrix or the covariance matrix of data for a
number (n) of variables. Both of them require transformation and/or standardisation of
the input data. The main difference between PCA and FA is related to the proportions of
the total variance of data for n variables accounted for in the analysis. The total variance
is composed of the common variance in all n variables and the specific variances of each
th
of the n variable. In PCA, principal components (or PCs) are determined, without any
statistical assumptions, to account for the maximum total variance of all input variables.
In FA, a number of common factors are defined, with assumption of a statistical model
with certain prerequisites, to account maximally for the common inter-correlation
between the input variables. Thus, on the one hand, PCA is variance-oriented and results
in a number of uncorrelated PCs (equal to n input variables) that altogether account for
st
the total variance of all input variables. The 1 PC accounts for the highest proportion of
the total variance (and thus represents the ‘most common’ variance) of the multivariate
th
data, whereas the n (or last) PC accounts for the least proportion of the total variance
(and thus represents the ‘most specific’ variance) of the multivariate data. On the other
hand, FA is correlation-oriented and results in a number (k) of uncorrelated common
factors (less than the n input variables) that together do not account for the total variance
of all input variables but altogether account for maximum common variance in all the