Carranza E. Geochemical anomaly and mineral prospectivity mapping in GIS
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130 Chapter 5
samples with censored values for As are not excluded as in the exploratory data analysis
in Chapter 3. That is because the censored values are needed to estimate local
background uni-element concentrations for samples with uni-element concentrations
below detection limits. Data for subset A pertain to stream sediment sample sites (n=38)
underlain by Aroroy Diorite, whereas data for subset B pertain to stream sediment
sample sites (n=97) underlain by dacitic/andesitic volcano-sedimentary rocks (Fig. 5-7).
The multiple regression analysis performed on each of the two subsets of the data is
forced through the origin (i.e., setting b
o
=0) so that the problem of matrix singularity is
avoided and equation (5.4) is determinate. In addition, because the uni-element data are
log
e
-transformed, the regression coefficients (b
j
) of j (=1,2,…,m) independent variables
(lithologic units represented as areal proportions in individual sample catchment basins)
are usually positive and readily interpretable as the geometric mean of uni-element
concentrations in individual lithologic units. Likewise, because the uni-element data are
log
e
-transformed, the M
j
values for the j (=1,2,…,m) lithologic units (represented by their
areas in individual sample catchment basins) are interpreted as the weighted geometric
mean uni-element concentrations in individual lithologic units.
The estimates of regression coefficients and M
j
values for the lithologic units in data
subset A are given in Tables 5-IV and 5-V, respectively. Note that the sample catchment
basins for stream sediment data subset A are underlain by at least one of the three
lithologic units listed in either Table 5-IV or 5-V. The regression coefficients of
lithologic units in data subset A show that the Aroroy Diorite has the lowest geometric
means of concentrations of most elements compared to the Mandaon and Sambulawan
Formations, whilst the Mandaon Formation has the highest geometric means of
concentrations of most elements, particularly As, compared to Aroroy Diorite and
Sambulawan Formation. Likewise, the M
j
values of lithologic units in data subset A
show that the Aroroy Diorite has the lowest geometric means of concentrations of most
elements compared to the Mandaon and Sambulawan Formations, whilst the Mandaon
Formation has the highest geometric means of concentrations of most elements,
particularly As, compared to Aroroy Diorite and Sambulawan Formation. However, for
TABLE 5-IV
Regression coefficients of lithologic units (represented as areal proportions in sample catchment
basins) for subset A of log
e
-transformed uni-element stream sediment data (n=38) at sampling sites
underlain by Aroroy Diorite (see Fig. 5-7), Aroroy district (Philippines).
Regression coefficients of lithologic units (data subset A; n=38)
Mandaon Formation Aroroy Diorite Sambulawan Formation
Cu 4.882 3.623 4.447
Zn 4.394 3.888 3.614
Ni 3.024 1.951 3.730
Co 2.628 2.422 3.775
Mn 6.983 6.185 6.066
As 1.319 -1.115 0.084
Catchment Basin Analysis of Stream Sediment Anomalies 131
the Mandaon and Sambulawan Formations, most of the regression coefficients are higher
than the corresponding M
j
values; whilst for the Aroroy Diorite, the regression
coefficients and M
j
values are more or less similar.
The estimates of regression coefficients and the M
j
values for the lithologic units in
data subset B are given in Tables 5-VI and 5-VII, respectively. Note that the sample
catchment basins for stream sediment data subset B are underlain by at least one of the
six lithologic units listed in either Table 5-VI or 5-VII. The regression coefficients of
lithologic units in data subset B show that the alluvial deposits have the lowest geometric
means of concentrations of most elements, followed by the Nabongsoran Andesite,
compared to the other lithologic units. In contrast, the estimated M
j
values of lithologic
units in data subset B suggest that the Nabongsoran Andesite and the alluvial deposits
have more or less similar geometric mean uni-element concentrations as the other
TABLE 5-V
Values of M
j
(calculated according to equation (5.5)) for lithologic units (represented by their
areas in sample catchment basins) based on subset A of log
e
-transformed uni-element stream
sediment data (n=38) at sampling sites underlain by Aroroy Diorite (see Fig. 5-7), Aroroy district
(Philippines).
M
j
values of lithologic units (data subset A; n=38)
Mandaon Formation Aroroy Diorite Sambulawan Formation
Cu 4.387 3.711 3.787
Zn 3.992 3.452 3.436
Ni 2.617 2.065 3.436
Co 2.635 2.512 2.833
Mn 6.659 6.210 6.107
As 0.441 -0.983 -0.669
TABLE 5-VI
Regression coefficients of lithologic units (represented as areal proportions in sample catchment
basins) for subset B of log
e
-transformed uni-element stream sediment data (n=97) at sampling sites
underlain by dacitic/andesitic volcano-sedimentary rocks (see Fig. 5-7), Aroroy district
(Philippines).
Regression coefficients of lithologic units (data subset B; n=97)
Mandaon
Formation
Aroroy
Diorite
Sambulawan
Formation
Lanang
Formation
Nabongsoran
Andesite
Alluvial
deposits
Cu 4.262 4.176 4.089 4.028 2.203 -4.911
Zn 4.051 3.699 3.593 4.218 4.218 2.140
Ni 2.537 2.684 2.619 2.466 1.497 -5.320
Co 2.905 2.607 3.065 2.798 2.629 0.678
Mn 6.663 6.407 6.093 6.794 6.785 7.267
As 1.511 -2.209 -0.303 0.864 -3.604 2.994
132 Chapter 5
lithologic units. The regression coefficients and M
j
values are more or less similar for the
Aroroy Diorite and Mandaon, Sambulawan and Lanang Formations. Among the
lithologic units, excluding the alluvial deposits, the Mandaon Formation seems to be the
most enriched in As.
There is either agreement or disagreement between the regression coefficients and
the M
j
values, depending on the element and lithologic unit examined (Tables 5-IV to 5-
VII). In view of the inconsistencies between the regression coefficients and the M
j
values, it is instructive to analyse the results further in order to determine whether to use
the regression coefficients or the M
j
values for reliable estimates of local uni-element
background per sample catchment basin. A plausible explanation for the inconsistencies
between the regression coefficients and M
j
values can be deduced by plotting (b
j
– M
j
)
against the percentage of individual lithologic units in the total area covered by the
sample catchment basins (Fig. 5-8) (cf. Bonham-Carter et al., 1987). Based on data
subset A, there are large differences (i.e.,⏐ b
j
– M
j
⏐> 0.5) between the regression
coefficients and M
j
values if lithologic units occupy less than 7% of the total area
covered by the sample catchment basins (Fig. 5-8A). Based on data subset B, there are
large differences (i.e., ⏐ b
j
– M
j
⏐> 0.5) between the regression coefficients and M
j
values if lithologic units occupy less than 5% of the total area occupied by the sample
catchment basins (Fig. 5-8B). From Figs. 5-8A and 5-8B, it is evident that the results for
data subset A show that the regression coefficients are mostly overestimated and that the
results for data subset B show that the regression coefficients are mostly underestimated
if lithologic units occupy, on average, less than 6% of the total area covered by the
sample catchment basins. In particular, regression coefficients of the independent
variables with respect to As – the pathfinder element for mineral deposits of interest in
this case study – are usually either overestimated or underestimated. The plots in Fig. 5-8
indicate that estimates of the regression coefficients are highly sensitive to variations in
areal proportions of lithologic units in sample catchment basins, whilst the M
j
values
TABLE 5-VII
Values of M
j
(calculated according to equation (5.5)) for lithologic units (represented by their
areas in sample catchment basins) based on subset B of log
e
-transformed uni-element stream
sediment data (n=97) at sampling sites underlain by dacitic/andesitic volcano-sedimentary rocks
(see Fig. 5-7), Aroroy district (Philippines).
M
j
values of lithologic units (data subset B; n=97)
Mandaon
Formation
Aroroy
Diorite
Sambulawan
Formation
Lanang
Formation
Nabongsoran
Andesite
Alluvial
deposits
Cu 4.248 4.175 4.074 4.103 3.534 3.045
Zn 4.054 3.722 3.677 4.230 4.217 3.989
Ni 2.498 2.452 2.523 2.454 2.140 1.609
Co 2.873 2.655 3.003 2.838 2.834 2.565
Mn 6.669 6.376 6.267 6.816 6.834 6.846
As 1.127 -0.405 -0.050 0.937 -0.456 1.099
Catchment Basin Analysis of Stream Sediment Anomalies 133
seem to represent more stable estimates of average uni-element concentrations in
individual lithologic units. Therefore, the M
j
values and equation (5.7) are used further in
this case study to estimate local uni-element background concentrations due to lithology
in individual sample catchment basins.
Derivation and standardisation of uni-element residuals
In order to recognise uni-element anomalies, the estimated values of
i
Y
′
, which
represent local uni-element background concentrations due to lithology in individual
sample catchment basins, are subtracted from the corresponding measured uni-element
concentrations in stream sediment samples. This means empirically-derived uni-element
concentrations due to background sources (e.g., lithology) must be removed from
measured uni-element concentrations in order to leave geochemical residuals, from
which the contributions or effects of anomalous factors (e.g., mineralisation) may be
recognised. Because there are two subsets of data from which local uni-element
background concentrations due to lithology were estimated, then there are also two
subsets of geochemical residuals. It is important that uni-element residuals per subset are
standardised prior to analysis of anomalies, via downstream dilution correction, so that
dilution-corrected uni-element residuals and thus uni-element anomalies from both
subsets are comparable and can be analysed as one data set.
To standardise the dilution-corrected uni-element residuals per subset, the median
and inter-quantile range (IQR) are determined and equation (3.10) (see Chapter 3) is
Fig. 5-8. Plots of b
j
– M
j
, the difference between regression estimates (b
j
) of geometric means o
f
uni-element contents of stream sediment and weighted estimates (M
j
) of geometric means of uni-
element contents of stream sediment, versus percent area occupied by individual lithologic units in
sample catchment basins, Aroroy district (Philippines). Results from analysis of (A) data subset A
and (B) data subset B. Abbreviations in the plots refer to lithologic units (see Fig. 3-9): MF =
Mandaon Formation; AD = Aroroy Diorite; SF = Sambulawan Formation; LF = Lanang
Formation; NA = Nabongsoran Andesite; AL = alluvial deposits. Lengths of rectangular boxes
indicate for which lithologic units the differences between values of b
j
and M
j
are large (i.e., ⏐b
j
–
M
j
⏐> 0.5, as indicated by the dashed horizontal lines in the plots).
134 Chapter 5
applied. Equation (3.10) is used in this case instead of equation (3.11) because (a) the
MAD (median of absolute deviations of data values from the data median) is less
resistant to outliers than the IQR and (b) it can be expected theoretically that the
geochemical residuals consist mainly of outliers. For example, Bonham-Carter and
Goodfellow (1984) found that uni-element residuals lack spatial autocorrelation,
meaning that geochemical residuals in a data (sub)set have large deviations from their
central tendency. In addition, Table 5-VIII shows the results of standardisation based on
robust statistics (median, IQR), as used in equation (3.10) for exploratory data analysis
(EDA), compared to results of standardisation based on classical statistics (mean,
standard deviation), as used in equation (3.9) for confirmatory data analysis (CDA).
On the one hand, depending on the element examined in data subset A, the EDA-
based standardisation results in a 0-25% increase in number of positive residuals and in a
0-18% decrease in the number of negative residuals. In addition, depending on the
element examined in data subset B, the EDA-based standardisation results in either a 0-
11% increase or a 0-11% decrease in the number of positive residuals and in either a 0-
10% decrease or a 0-10% increase in the number of negative residuals. Moreover,
depending on the element examined in the whole data set, the EDA-based
TABLE 5-VIII
Changes in numbers (and percentages) of positive and negative uni-element residuals in data
subsets A and B, Aroroy district (Philippines), after standardisation by using robust statistics in
equation (3.10) for exploratory data analysis (EDA) and using classical statistics in equation (3.9)
for confirmatory data analysis (CDA).
No. of residuals
No. of EDA-standardised
residuals*
No. of CDA-standardised
residuals*
Positive Negative Positive Negative Positive Negative
Data subset A (n=38)
Cu 19 19 19 (0) 19 (0) 15 (–21) 23 (+21)
Zn 16 22 20 (+25) 18 (–18) 14 (–13) 24 (+9)
Ni 21 17 19 (0) 19 (0) 18 (–13) 20 (+18)
Co 19 19 19 (0) 19 (0) 17 (–11) 21 (+11)
Mn 17 21 19 (+12) 19 (–10) 14 (–18) 24 (+14)
As 13 25 13 (0) 25 (0) 10 (–23) 28 (+12)
Data subset B (n=97)
Cu 45 52 50 (+11) 47 (–10) 41 (–9) 56 (+8)
Zn 49 48 49 (0) 48 (0) 39 (–20) 58 (+21)
Ni 55 42 49 (–11) 49 (+10) 41 (–25) 56 (+33)
Co 50 47 50 (0) 47 (0) 48 (–4) 51 (+13)
Mn 52 45 49 (–6) 48 (+7) 46 (–12) 51 (+14)
As 53 44 49 (–8) 48 (+10) 17 (–68) 80 (+82)
*Values in italics represent increase in number of either positive or negative residuals. Values in
bold represent decrease in number of either positive or negative residuals. Values in parentheses
indicate percentage increase (+) or decrease (–) in number of positive or negative residuals
resulting from standardisation.
Catchment Basin Analysis of Stream Sediment Anomalies 135
standardisation results in a median 0% increase/decrease in number of positive residuals
and in a median 0% increase/decrease in number of negative residuals.
On the other hand, depending on the element examined in data subset A, the CDA-
based standardisation results in an 11-23% decrease in number of positive residuals and
in a 9-21% increase in the number of negative residuals. In addition, depending on the
element examined in data subset B, the CDA-based standardisation results in a 4-68%
decrease in the number of positive residuals and in an 8-82% increase in the number of
negative residuals. Moreover, depending on the element examined in the whole data set,
the CDA-based standardisation results in a median 16% decrease in number of positive
residuals and in a median 14% increase in number of negative residuals.
Results of the CDA-based standardisation are therefore deleterious in the synthesis of
uni-element residuals derived from different ‘homogenous’ subsets of uni-element
geochemical data aimed at performing conjunctive modeling of anomalies. Therefore,
the EDA-based standardisation according to equation (3.10) is applied to uni-element
residuals in subsets A and B. Fig. 5-9 shows the spatial distributions of the whole set of
measured As values and the synthesised set of standardised As residuals in subsets A and
Fig. 5-9. Spatial distributions, based on percentile (%le) classification, of As in stream sediments
represented as sample catchment polygons, Aroroy district (Philippines). (A) Measured (or raw)
As data. (B) Standardised As residuals after removing from the measured As data the estimated
uni-element background As contents due to lithology in individual sample catchment basins.
Triangles represent locations of epithermal Au deposit occurrences, whilst thin black lines
represent lithologic contacts (see Fig. 3-9).
136 Chapter 5
B. In contrast to the spatial distributions of the measured As values (Fig. 5-9A), the
spatial distributions of the standardised As residuals show not only enrichment of As
along the north-northwest trend of the epithermal Au deposit occurrences but also
enrichment of As in the eastern parts of the area underlain by the Aroroy Diorite (Fig. 5-
9B). These results demonstrate the value of estimating and then removing local
background uni-element contents attributable to lithology from measured uni-element
concentrations in stream sediments. The standardised uni-element residuals are then
further subjected to downstream dilution correction to identify significant anomalies.
Correction for downstream dilution and classification of anomalies
Equation (5.9) is applied to the standardised uni-element residuals in order to correct
for downstream dilution. Note that the standardised geochemical residuals are the values
used for the term
ii
YY
′
− in equation (5.9). The dilution-corrected uni-element residuals
are then subjected to fractal analysis via the concentration-area method (Cheng et al.,
1994) demonstrated in Chapter 4. In this analysis, negative dilution-corrected uni-
element residuals cannot be considered in a log-log graph of the concentration-area
relation. This is not a concern, however, because negative dilution-corrected uni-element
residuals can already be considered to represent background populations and thus
excluded in the analysis, leaving high background to anomalous populations to be
recognised from the positive dilution-corrected uni-element residuals.
Fig. 5-10A shows that the log-log graph of the concentration-area model for positive
dilution-corrected As residuals follows power-law relations indicating multifractal
patterns in the data. Three straight lines satisfactorily fit the concentration-area plots,
indicating the presence of three populations that can be separated by threshold values at
the breaks in slopes of the straight lines. These three populations, from lowest to highest
values, are considered to represent high background, low anomaly and high anomaly of
As. The three recognised thresholds, plus a threshold for the highest negative or zero
dilution-corrected As residual to represent upper limit of background, are used to display
the spatial distributions of the background and anomalous populations of dilution-
corrected As residuals (Fig. 5-10B).
The spatial distributions of the classified dilution-corrected As residuals (Fig. 5-10B)
show a series of anomalies that follow the north-northwest trend of the epithermal Au
deposit occurrences and indicate some low anomalies in the eastern sections of the area
underlain by the Aroroy Diorite. These latter anomalies cannot be readily considered as
significant or not without considering other uni-element anomalies. Fractal analysis via
the concentration-area method was also applied to separate background and anomalies in
the dilution-corrected residuals of Cu, Zn, Ni, Co and Mn, so that analysis of multi-
element anomalies can be performed.
Modeling of multi-element anomalies via principal components analysis
Principal components analysis is performed on a subset of samples (n=93 out of the
total 135) with anomalous dilution-corrected residuals for at least one of the elements
Catchment Basin Analysis of Stream Sediment Anomalies 137
under study. Prior to PCA, descending ranks of n to 1 (i.e., considering 1 as the lowest
rank) are assigned to descending n values of dilution-corrected uni-element residuals and
tied ranks are averaged. A Spearman rank correlation matrix is computed for rank-
transformed dilution-corrected uni-element residuals, and is used in the PCA (e.g.,
George and Bonham-Carter, 1989; Carranza and Hale, 1997). Table 5-IX shows the
results of the PCA.
The PC1, accounting for about 34% of the total variance, plausibly represents a Co-
Zn-Mn multi-element association reflecting metal-scavenging by Mn-oxides in the
drainage environments in most parts of the area; Cu, Ni and As have antipathetic, weak
sympathetic and very weak sympathetic relations, respectively, with this multi-element
association. The PC2, accounting for about 22% of the total variance, represents a Ni-
Cu-As association having an antipathetic relation with Mn and thus plausibly reflects an
anomalous multi-element association. The association between Cu and As in PC2
plausibly reflects enrichment of these elements in stream sediments due to weathering
and erosion of anomalous sources containing sulphide (chalcopyritic and arsenopyritic)
Fig. 5-10. (A) Log-log plot of concentration-area fractal model of positive dilution-corrected As
residuals, Aroroy district (Philippines), showing two thresholds (dots) that separate high (H)
anomaly, low (L) anomaly and high background populations in the data. (B) Spatial distributions
of high background and anomalous populations of dilution-corrected As residuals based on
thresholds recognised in the concentration-area plot. Background class pertains to negative
dilution-corrected As residuals, which are not represented in the log-log plot of the concentration-
area relation. Triangles in the map represent locations of epithermal Au deposit occurrences,
whilst thin black lines represent lithologic contacts (see Fig. 3-9).
138 Chapter 5
minerals, which generally characterise the mineralogy of epithermal Au deposits. The
association of Ni with Cu and As in PC2 can be due to the dacitic/andesitic rocks that
hosts the epithermal Au deposits in the area. The PC3, accounting for about 17% of the
total variance, is dominated by As and is plausibly an anomalous pathfinder signature for
epithermal Au deposits. The PC4, accounting for about 14% of the total variance,
represents an antipathetic relation between an As-Mn-Cu association and a Co-Ni
association; the former is possibly due to metal-scavenging by Mn-oxides in some parts
of the area whilst the latter is possibly due to lithologies with slightly more mafic
compositions that are not represented in the analysis because they are not mappable at
the scale of the lithologic map shown in Fig. 3-9. The last two PCs, together accounting
for about 13% of the total variance, are not easily interpretable in terms of geological
significance.
The presence of two anomalous multi-element associations in the subset of samples
with anomalous dilution-corrected residuals for at least one of the elements under study
is possibly due to differences in mobility of As, Cu and Ni in the surficial environments.
Thus, the scores of PC2 and PC3 (computed according to equation (5.10)) are analysed
further to determine if they represent significant anomalies. Because loading on As in
PC3 is negative, the PC3 scores are negated (i.e., multiple by -1) so that high negated
PC3 scores represent As anomalies. The PC2 and negated PC3 scores are separately
portrayed, using the sample catchment basins, as discrete geochemical surfaces, which
are then subjected to the concentration-area fractal method for separation of background
and anomaly (see also Chapter 4). On the one hand, the spatial distributions of the PC2
scores, representing a multi-element Ni-Cu-As association, show a northwest-trending
zone of low to high anomalies roughly following the north-northwest trend of the
epithermal Au deposit occurrences (Fig. 5-11A). The low to high anomalies of the PC2
scores seem to decay from the southeastern parts to the northwestern parts of the area.
On the other hand, the spatial distributions of the negated PC3 scores, representing an
As-dominated multi-element association, show a north-northwest-trending zone of low
to very high anomalies closely following the north-northwest trend of the epithermal Au
TABLE 5-IX
Principal components of rank-transformed dilution-corrected uni-element residuals for samples
(n=93) with anomalous dilution-corrected uni-element residuals for at least one of the elements
under study, Aroroy district (Philippines).
Cu Zn Ni Co Mn As
% of
Variance
Cum. % o
f
variance
PC1 -0.193 0.722 0.514 0.817 0.700 0.251 34.05 34.05
PC2 0.710 0.050 0.731 -0.037 -0.455 0.298 22.29 56.34
PC3 0.436 0.416 -0.048 -0.121 0.147 -0.780 16.82 73.16
PC4 0.378 0.225 -0.357 -0.365 0.387 0.483 13.95 87.11
PC5 0.345 -0.482 -0.090 0.352 0.270 -0.063 9.33 96.44
PC6 0.085 0.143 -0.254 0.243 -0.242 0.056 3.55 99.99
Catchment Basin Analysis of Stream Sediment Anomalies 139
deposit occurrences. There is also a north-trending zone of low to high anomalies of
negated PC3 scores in the eastern parts of the area where epithermal Au deposits are not
known to occur.
The apparent similarity and difference between the spatial distributions of anomalous
PC2 and negated PC3 scores may be explained as follows. On the one hand, the low and
high anomalies of PC2 scores along a zone roughly following the trend of the epithermal
Au deposits plausibly represent weathered materials derived from mineralised outcrops,
which have been transported downstream and farther away from the deposits. On the
other hand, the low, high and very high anomalies of negated PC3 scores along a zone
closely following the trend of the epithermal Au deposits plausibly represent weathered
materials derived from mineralised outcrops, which have been transported downstream
but not farther away from the deposits. Thus, anomalies of either PC2 scores or negated
PC3 scores are both significant, although anomalies PC2 are possibly related to
‘allochthonous’ mineralisation whilst anomalies of negated PC3 scores are possibly
related to ‘autochthonous’ mineralisation.
Fig. 5-11. Spatial distributions of element associations in stream sediment sample catchment
basins, Aroroy district (Philippines), determined via principal components analysis (see Table 5-
IX) and then classified via concentration-area fractal analysis. (A) Multi-element Ni-Cu-As
association represented by PC2 scores. (B) As-dominated multi-element association represented
by negated PC3 scores. L = low; H = high; VH = very high. Triangles represent locations o
f
epithermal Au deposits, whilst thin black lines represent lithologic contacts (see Fig. 3-9).