D.R. Cohen 1 , D.B. Skillicorn 2 , S. Gatehouse 3 and I. Dalrymple 1
3
School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney,
NSW 2052, Australia.
2 School of Computing, Queen’s University, Kingston, Ontario K7L 3N6, Canada.
3
CSIRO Exploration and Mining, North Ryde, NSW 2121, Australia.
Abstract

The identification of weak geochemical signatures, derived from the effects of mineralisation on regolith samples, requires the appropriate combination of chemical analysis procedures and multivariate data processing methods capable of recognising those signatures. Existing multivariate data processing methods commonly assume that signatures related to the effects of mineralisation take the form of separated or outlying clusters or values. Trace element patterns are typically more subtle, including situations where geochemical signatures influenced by mineralisation may take the form of denser sub-clusters within larger clusters. A new approach to identifying such sub-clusters, involving the combination of singular value decomposition (SVD) and semi-discrete decomposition (SDD), has been investigated.
At the Mandamah porphyry Cu-Au deposit, deeply weathered mineralisation is covered by
50 m of alluvium. Partial geochemical extractions (potassium acetate, hydroxylamine.HCl, aqua regia and sodium pyrophosphate) were conducted on surface soil samples collected from grids over mineralised and non-mineralised areas. There were few discernible patterns in the raw partial extraction data related to the location of mineralisation, apart from sporadically elevated Ba and lower Ca, Mg and REE. K-means clustering of provided no interpretable patterns in the data. SVD-SDD processing of the partial extraction data, however, isolated clusters in which the majority of samples were located above or adjacent to the buried mineralisation. The results indicate the SVD-SDD technique may assist in discriminating mineralised from non-mineralised geochemical signatures.
Keywords – Partial extractions, multivariate, dispersion, anomaly.

Development of exploration methods to detect mineralisation buried by thick, transported cover has recently focussed on the use of partial geochemical extractions to enable recognition of subtle geochemical patterns associated with mineralisation. This includes separation of direct element dispersion and secondary geochemical effects in regolith from potentially highly variable background patterns related to differences in parent materials, regolith formation and subsequent geochemical processes. In cases where geochemical contrast between signatures related to mineralisation and background for individual elements is poor, various multivariate data analysis methods may be applied to numerically characterise subtle patterns associated with mineralisation.
Multivariate data processing have tended to focus on traditional parametric methods related to either population modelling or the geometry of variance in data, which appear ill-suited to partial extraction data. Anomalies have tended to be defined as individual datum or data clusters lying outside the main population (Garrett, 1989), however, such approaches progressively fail to detect anomalies as the numerical distance between the main population and anomalous data decreases.
Geochemical patterns are often recognised as observed stretching of data (sources of variance), for which principal components and factor analysis are commonly used in geochemical data processing
(Fig. 1a). Many such methods suffer significant bias if the data are not multivariate normal or there are multiple data clusters (Chork and Rousseeuw, 1992). Clustering is commonly used to define both patterns in the data and isolate anomalies. Approaches such as K-means clustering
(MacQueen, 1967; Kaski, 1997, Everitt et al.
, 2001), in which an arbitrary number of boundaries are generated between clusters in the data, and more recently use of methods such as neural networks (Benediktsson, 1990; Clare and Cohen, 2001), appear unable to detect clusters or anomalies defined by subtle variations in data densities within a cloud of points, especially if such clusters are not geometrically regular shapes.
This study involves the application of two matrix decomposition techniques, singular value decomposition (SVD) and semi-discrete decomposition (SDD), designed to identify clusters representing regions of increased density of data points (Fig. 1b). The underlying mathematical form or geometry of the data is not explicitly utilized nor accommodated when applying the techniques.
Visualisation of structures in high-dimensional data requires dimension reduction and SVD identifies subspaces that capture most of the variance in the data (Berry and Fierro, 1996; Dhillon et al ., 1998) and displays an ability to detect relative weak signatures (Wall et al.
, 2003). Singular value decomposition (SVD) is conceptually similar to principal components and factor analysis.

The original data matrix ( A ) of n samples by m variables is decomposed to a matrix of new orthogonal vectors ( V ), representing linear combinations of the original variables, a square matrix S whose diagonals containing the singular values, and a matrix of scores ( U ) for observations in the new orientation:
A = U . S . V T (1)
The product U .
S can be interpreted as the coordinates of each row of A as a point in a transformed space spanned by the rows of V . The transformed space has the property that the maximal possible variation occurs along the axis corresponding to the first row of V , the maximal remaining variation along the axis corresponding to the second row of V , and so on. In most cases, the majority of the
“noise” in a multivariate dataset may be eliminated by truncating Eqn. 1 to a k-dimensional space
( k < m ) while still providing a close approximation the original data matrix ( A ). The value for k can be selected using methods commonly used in factor analysis such as scree plots (Cattell, 1966).
There is a direct relationship between SVD and PCA where principal components are calculated from the covariance matrix (Wall et al.
, 2003).
Semi-discrete decomposition (SDD) originated in text indexing (Kolda and O’Leary, 1998) but has been shown to be a very effective anomaly detection method (McConnell and Skillicorn, 2001,
2003). SDD is superficially similar to SVD, as it decomposes the matrix A into forms that reveal features of its internal structure. The semidiscrete decomposition of A is:
A = X . D . Y (2)
Like SVD, a similar k can be chosen freely but unlike SVD k can be > m and values in X and Y are restricted to –1, 0 and +1. The diagonal values of D can be any scalars but like the singular values S of SVD are presented in decreasing order.
SDD processing proceeds as follows. If the first column of X (x n,1
) is multiplied by the first row of
Y (y
1,m
) the product (the level 1 clusters) has the same dimensions as A but comprises only the values –1, 0 or +1. If this product is further multiplied by the first diagonal element of D (d
1,1
), the resulting “stencil” will consist of rectilinearly aligned locations in the D matrix containing the values
 d
1,1
(representing a locally dense region in the matrix values or “bumps”) against a background of zeroes. The second stencil is produced by multiplying the second column of X by the second row of Y (providing the level 2 clusters) and then to form the second stencil by multiplying this product by the second diagonal element of D .
As an example, SDD processing of a simple matrix of integers values, A , for which k was set at 5, results in the following solution to Eqn. (2):

1 1 -8 8 1 1 1
-4 -4 -8 8 1 1 1
-4 -4 1 1 1 1 1
A
=
-1 0 1 1 0
-1 -1 1 0 0
0 -1 1 0 1
.
X
8 0 0 0 0
0 4 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
D
.
0 0 1 -1 0 0 0
1 1 0 0 0 0 0
0 0 0 0 1 1 1
1 1 0 0 0 0 0
0 0 1 1 0 0 0
Y
(3)
Observe that the diagonal elements of D represent the various heights of “bumps” (or
“depressions”) in
A . When the first column of X and the second column of Y are multiplied we obtain the first cluster level, which identifies the two +8 and the two –8 values as being bumps and the remainder of the data identified as part of the main plane of the data (0s). When the level 1 clusters values are multiplied by the first diagonal element of D (d
1,1
) and then subtracted from A, the result is the first level of residuals in which the –8 and +8 values have been levelled. The second residual is obtained by subtracting the product of the second column of X, the second row of
Y and d
2,2
from the first residual, and the result is the levelling of the block of –4s.
1 1 -8 8 1 1 1
-4 -4 -8 8 1 1 1
-4 -4 1 1 1 1 1
A
1 1 0 0 1 1 1
-4 -4 0 0 1 1 1
-4 -4 1 1 1 1 1
Residuals for level 1
1 1 0 0 1 1 1
0 0 0 0 1 1 1
0 0 1 1 1 1 1
Residuals for level 2
-
-
-
0 0 -1 1 0 0 0
0 0 -1 1 0 0 0
0 0 0 0 0 0 0 level 1 clusters
Template 1
0 0 0 0 0 0 0
-1 -1 0 0 0 0 0
-1 -1 0 0 0 0 0 level 2 clusters
Template 2
0 0 0 0 1 1 1
0 0 0 0 1 1 1
0 0 0 0 1 1 1 level 3 clusters
Template 3
.
8
d
1,1
.
4
d
2,2
.
1
d
3,3
=
=
=
1 1 0 0 1 1 1
-4 -4 0 0 1 1 1
-4 -4 1 1 1 1 1
Residuals for level 1
1 1 0 0 1 1 1
0 0 0 0 1 1 1
0 0 1 1 1 1 1
Residuals for level 2
1 1 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1 1 0 0 0
Residuals for level 3
(4.1)
(4.2)
(4.3)
In real data, the bumps would contain a range of values and the heights would be the average for the cluster of values falling within the bump. Also, log-transformation of highly skewed data is useful, but such preprocessing tends only to alter the order in which clusters are detected as the SDD proceeds from level to level, rather than a more dramatic change of data represented in the respective clusters.
As SDD expresses A as a sum of k stencils, the decomposition results in an hierarchical classification (or clustering) of the data with 3k possible clusters, although a significant number of such clusters may not contain any samples..

Sampling and Analysis
An extensive drilling program at the Mandamah Prospect, revealed two zones of sub-economic, porphyry-style mineralisation within a mixed volcanic sequence (Fig. 2). Drilling indicated that mineralisation contains significantly anomalous Cu, Au and Mo values. Zinc and Pb appear depleted in the core. There is up to 30 m of saprolite developed over mineralisation and host rocks.
The area displays topographic relief of <5 m and is mainly used for agriculture (mainly wheat). The saprolite is overlain by ~50 m of alluvial silts and fine sands. Mineral exploration has proven very difficult in areas where this regolith and landform setting is present in the Lachlan Fold Belt.
There is little visible variation in the characteristics of the alluvium, apart from erratic variations in the distribution of pedogenic carbonate (0 to ~2 %) in the upper 30 cm of the profile and some slight variation in the clay to quartz proportions. A zone of hard pan has formed by a desiccation layer (interpreted as tillage-base). There was no indication of either development of mottling or ferruginous duricrusts, which suggests the alluvium is post-Miocene. The alluvium has been divided into “older alluvium” and “recent alluvium” based on slight differences in regional radiometric K signature (indicative of very slightly lower clay contents) and the location of shallow current drainage channels. The extent to which the provenance of the alluvium might have changed over time is not known.
One hundred and forty near-surface (~25 cm depth) soil samples were collected from irregular grids of ~200 m spacing over three blocks, centred on a main east-west sampling traverse where sample spacings ranged from 6 to 100m. The northern and southern blocks contain mineralisation and the central block is not known to have mineralisation from current, albeit sparse, drilling. Samples were randomised and then subjected to a sequence of three partial digestions as set out in Table 1:
(a) K-acetate / acetic acid (exchangeable ions and carbonates)
(b) Hydroxylamine.HCl / HCl (poorly crystalline iron and manganese oxides)
(c) Aqua regia (more crystalline Fe oxides and in clay lattices) and a Na-pyrophosphate / NaOH (organics and easily dispersed colloids) digestion on a second subsample. Multielement analysis of the (re-randomised) digestion solutions was performed using a combination of ICP-AES and ICP-MS (Dalrymple et al.
, 2003).
Data Processing
Prior to data modelling, most variables were log-transformed to reduce skewness, and all variables were standardised. Some variables with significant detection limit or other data quality considerations were discarded. In addition, the REE generally formed a discrete cluster in SVD V-

space that was separated from other variables and these were also removed from the dataset, leaving
87 elements from the four partial extractions. The elements accepted for data processing are included in Table 2.
Raw data (plotted as percentiles) and all bivariate relationships within each partial extraction and between the same elements under different extractions were examined (with samples collected over mineralisation identified). K-means clustering was performed on all elements for each digestion, as well as selected elements related to the mineralisation, and the total dataset.
SVD-SDD processing then proceeded as follows:
(i) The standardised data matrix was decomposed using SVD. The matrix product U.S
was truncated to k=3 and retained for 3D display purposes.
(ii) The SVD was truncated from its original dimensionality (m=87) to k=15 and remultiplied to produce the matrix A k=15
. This matrix can be interpreted as a version of A where only some higher-order correlation information is retained and most of the “noise” removed.
(iii) The product A k=15
.
A
T k=15
(the truncated correlation matrix of the samples in A ) was calculated and the diagonal values set to zero.
(iv) This product matrix was then decomposed using SDD.
Exploratory Data Analysis
The partial extraction concentrations of elements directly associated with mineralisation, including
Cu, Mo, Zn and Au, displayed no obvious relationship to either the location of buried mineralisation, changes in lithology or minor variations in the composition of the alluvium indicated by the radiometrics (Figs. 3 to 5). The only two features that might tentatively be related to mineralisation are the prominent “rabbit-ears” patterns displayed by Ca, Mg and some REE surrounding mineralisation in both mineralised blocks and slightly elevated Ba contents above mineralisation in the northern block for the K-acetate extraction (Fig. 3). The Ca and Mg zonation was also evident in the other two extractions (hydroxymaine.HCl and aqua regia). High variability in the concentrations these elements was also observed in the unmineralised central block but depletion of Ca and Mg was not a strongly associated with depletion of REE.
Relative enrichment of Ba beyond the edges of mineralisation and lower concentrations over mineralisation were observed for the hydroxylamine.HCl and aqua regia extractions, but some elevated Ba values also occur well away from mineralisation in the northern, southern blocks and the central blocks. The variations in Ba are subtle as the range of values does not exceed two orders of magnitude in any of the digestions, e.g. the upper 20 th
percentile for Ba concentrations in the K-

acetate extraction is 20 – 65 ppm and the median is 10 ppm (Fig. 4). The distribution of Cu appears more influenced by the regolith type, with elevated Cu generally restricted to the “older alluvium” and no spatial relationship to mineralisation readily observed (Fig .5).
Some bivariate plots revealed interesting structures and patterns in the data (Fig. 6). The strongest linear correlation between variables were various REE pairings (as observed in most partial extraction datasets) and between Al and Fe for the hydroxymaine.HCl and aqua regia extractions
(reflecting the influence of variable quartz dilution and substitution of Al in the Fe-oxides). The general lack of correlation between Fe and other elements in the hydroxylamine.HCl extraction
(reflecting the contribution of poorly to moderately crystalline Fe-oxides) is unusual for the terrain studied. Many variable pairs displayed complex trends, including the distribution of samples collected above mineralisation within the total data spread. Over mineralisation most K-acetate extractable Ba values are elevated, but elevated values also occur away from mineralisation. Also the K-acetate Si versus Ca displays two opposing trends reflecting the interplay of Ca derived from carbonate dissolution and clay exchange. For aqua regia Al versus Fe the samples above mineralisation appear as a selvage on the upper side of the main linear correlation trend, suggesting a possible effect of mineralisation may be to deplete a fixed amount of Fe from samples over mineralisation.
Modelling
K-means clustering for separate extractions (Fig. 7) and for the total data set (transformed as required and standardised), resulted in three main clusters that appear to reflect variations in regolith and a small number of small clusters or isolated values that displayed no relationship to either the location of mineralisation or regolith type. Varying the number of pre-defined clusters between 6 and 12, merely resulted in further subdivision of the unique clusters or non-systematic splitting of the main clusters.
The main loadings for the SVD components (both positive and negative) are listed in Table 2 and the SVD component scores are plotted in Fig. 8. The first SVD component contains strong loadings for the B, Ba, Ca, Mg and Al in all digestions, with none of the transition elements directly associated with mineralisation displaying strong loading in any of the digestions. The second SVD component is mainly influenced by hydroxylamine.HCl extractable Fe and other elements that typically associate with secondary Fe-oxides, including Co, Cu, Mn and Ni, and is mirrored to an extent by the elements extracted by Na-pyrophosphate. The third SVD component is dominated by elements extracted by aqua regia, with nearly all elements displaying a moderate to strong loading.
The scores for the first three components, especially the first, appear more influenced by regolith type than the location of mineralisation, although such association is still very weak.

The first three SVD component scores for the complete Mandamah data (derived from the reduction in rank of A to 3), and coded according to SDD cluster for levels 1 (by shading) and 2 (by symbol) are plotted in Fig 9a. At the first SDD level, there is strong separation between the clusters in SVD component score space, with further spatial separation at level 2. The main separation between SDD clusters and sub-clusters occurs in the orientation of SVD component 1, which is dominated by the redistribution of carbonates and group 1 and 2 metals in clays. After outlining the limit of observations for samples from the different blocks, including samples overlying mineralisation, the central part of the SVD plot contains observations from all three blocks. A close relationship, however, emerges between the distribution of samples from clusters [–1,+1] and [0,+1], the northern block mineralisation and to a more limited extent southern block mineralisation.
Clustering within various SDD levels are plotted in Fig. 10. The level 1 clustering is spatially unrelated to the location of mineralisation, but the +1 cluster appears mostly restricted to the more recent regolith in the northern and southern blocks and a group in the middle of the central block. If level 1 is further subdivided at level 2, there is no further resolution of the structure of the data, although the [0,+1] cluster is mainly restricted to the northern block. The “anomaly detection” capabilities become more apparent when looking directly at the level 4 clusters, irrespective of the previous level clustering. The level 4 +1 cluster is mainly distributed in a nearly continuous zone across mineralisation on the northern block, another group of six samples above mineralisation in the southern block, and a few samples scatters across the central and outer parts of the northern block. This zone is not simply coincident with the weak K-acetate Ba anomalies that appear, at first pass, to best define mineralisation in the northern block. A number of non-coincident elevate Kacetate Ba values and SDD level 4 +1 cluster samples occur away from mineralisation.
Most applications of partial geochemical extractions to detect deeply buried mineralisation rely on some form of pattern recognition (Kelley et al.
, 2003), although this is commonly limited to a series of visual comparisons of individual variables with each other and with available geological, regolith and other field data to judge the effectiveness of a given extraction method. Such approaches may be successful where the strength of patterns related to mineralisation (geochemical contrast) greatly outweighs the influence of factors unrelated to mineralisation, but they may result in failure to detect weak signals related to mineralisation, especially if these signals are detectable only by the correlation among several variables.
The Mandamah data set displays a lack of distinct spatial patterns in the raw geochemical data that can be consistently related to the location of deeply buried mineralisation and which do not recur away from mineralisation. The raw data patterns appear most strongly influenced by compositional

variation in the regolith, including the effects of quartz-dilution in the hydroxylamine.HCl and aqua regia extractions and the clay versus carbonate partitioning of metals in the K-acetate and Napyrophosphate extractions (Dalrymple et al.
, 2003). The apparent redistribution of Ca, Mg and REE
(“rabbit-ears” effect) towards the edge of mineralisation in both northern and southern blocks, and slight increase in Ba contents over mineralisation in the northern block, may be explained in terms of electrochemical cells of the style predicted for oxidising sulphide mineralisation by the models of
Smee (1998) or Hamilton (1998). Such cells are unlikely to be currently active at Mandamah but their previous effects on trace element distributions within the alluvial cover may have been preserved after onset of aridity in the late Miocene (more research on this proposition is required).
The partial geochemical extraction data does exhibit significant multivariate data structure, as evident in a range of bivariate relationships and the retention of over 50% of total variance in the first three principal components. Traditional multivariate clustering methods applied to the
Mandamah data for clustering multivariate data (including K-means clustering) or isolating signals, however, did not provide a clearer definition of the location of mineralisation. The results of this modelling appeared most influenced by local variations in regolith composition.
The SVD-SDD processing also reveals significant multivariate structure in the data, including some separation between samples from the three blocks and confining of mineralised samples from the northern block to a small region of the SVD component space. SDD has produced both a significant refinement of the SVD structure, including the generation of a number of SDD clusters for which samples are mainly located in close proximity to mineralisation.
The SVD-SDD technique has demonstrated some capability to detect groupings in geochemical data related to geological and regolith factors, where direct assessment of raw data patterns and parametric clustering procedures such as K-means clustering does not. SVD-SDD and other novel approaches to data analysis may provide more efficient clustering of geochemical data, recognition of geochemical signatures where other methods appear less capable and this may be critical to the successful use of partial extractions to detect deeply buried mineralisation, especially in arid terrains.
Acknowledgments – This work was supported by Auriongold Ltd and CSIRO Exploration and
Mining.

BENEDIKTSSON, J.A., SWAIN, P.H. & ERSOY, O.K., 1990. Neural network approaches versus statistical methods in classification of multisource remote sensing data. IEEE Transactions on Geoscience and
Remote Sensing, 4 , 540–552.
BERRY, M.W. & FIERRO, R.D. 1996. Low rank orthogonal decomposition for information retrieval applications. Numerical Linear Algebra with Applications , 1 , 1–27.
CATTELL, R.B., 1966. The scree test for the number of factors. Multivariate Behavioral Research, 1 , 245–
76.
CHORK, C.Y. & ROUSSEEUW, P. J. 1992. Integrating a high-breakdown option into discriminant analysis in exploration geochemistry. Journal of Geochemical Exploration , 43 , 191–203.
CLARE A.P. & COHEN D.R., 2002. A comparison of unsupervised neural networks and k-means clustering in the analysis of multi-element stream sediment data. . Geochemistry: Exploration, Environment,
Analysis , 1 , 119–134.
DALRYMPLE, I., GATEHOUSE, S.G. & COHEN, D.R., 2002 . Evaluation of Selective Geochemical
Extractions in an Area of Deep Transported Regolith Cover, Mandamah, NSW . CSIRO Exploration and Mining Report 1007R.
DHILLON, S.I., MODHA, D.S. & SPANGLER, W.S., 1998. Visualizing class structure of multidimensional data. In: S. Weisberg (Ed.), Proceedings of the 30th Symposium on the Interface
Computing Science and Statistics , 30 , 488–493.
EVERITT S.E., LANDAU S. & LEESE M., 2001. Cluster Analysis . Arnold, London.
GARRETT, R.G., 1989. The chi-square plot: a tool for multivariate outlier recognition. Journal of
Geochemical Exploration.
, 32 , 319–341.
HAMILTON, S.M. 1998. Electrochemical mass-transport in overburden: a new model to account for the formation of selective leach geochemical anomalies in glacial terrain.
Journal of Geochemical
Exploration , 63 , 155–172.
KASKI, S. 1997. Data exploration using self-organizing maps. Acta Polytechnica Scandinavica,
Mathematics, Computing and Management in Engineering Series, 82 , 57 pp.
KELLEY, D.L., HALL, G.E.M., CLOSS, L.G., HAMILTON, I.C. & MCEWEN, R.M., 2003. The use of partial extraction geochemistry for copper exploration in northern Chile. Geochemistry: Exploration,
Environment, Analysis , 3 , 85–104.
KOLDA, T.G. & O’LEARY, D.P., 1998. A semidiscrete matrix decomposition for latent semantic indexing in information retrieval.
ACM Transactions on Information Systems, 16 , 322–346
MACQUEEN, J. 1967. Some methods for classification and analysis of multivariate observations. In: Le
Cam L. M. & Neyman J. (eds), Proceedings of the Fifth Berkeley Symposium on Mathematical
Statistics and Probability, Vol. 1 . Univ. of California Press, Berkeley, 281–297
McCONNELL, S. & SKILLICORN, D.B., 2001. Outlier Detection Using Semi-Discrete Decomposition.
Technical Report, Queen’s University. 15p.
McCONNELL, S. & SKILLICORN, D.B., 2002. Semidiscrete Decomposition: A bump hunting technique.
4 th Australasian Data Mining Workshop, Canberra, December 2002, 75–82.
SMEE, B.W., 1998. A new theory to explain the formation of soil geochemical responses over deeply covered gold mineralisation in arid environments. Journal of Geochemical Exploration , 61 , 149–172.
WALL, M.E., RECHTSTEINER, A. & ROCHA, L.M., 2003. Singular value decomposition and principal component analysis.
In: D.P. Berrar, W. Dubitzky and M. Granzow, (eds.) A Practical Approach to
Microarray Data Analysis . Kluwer. 91–109.

Figure Captions
Figure 1. Multivariate pattern recognition defined by (a) variance structure or stretching in data and (b) variations in density of data within a geometrically irregular data cloud.
Figure 2. Geological map of the Mandamah prospect showing sampling locations, the positions of mineralisation defined by drilling, and cross-sections through mineralised zones in the nrothern and southern blocks.
Figure 3. Potassium acetate extractable element contents in surface soils from the main traverses over the northern, central and southern blocks.
Figure 4. Distribution of percentiles for K-acetate, hydroxylamine.HCl and aqua regia extractable Ba contents of surface soil samples from the three sampling blocks over the Mandamah prospect, and relationship of percentile cuts to raw Ba data distributions.
Figure 5. Distribution of percentiles for K-acetate, hydroxylamine.HCl and aqua regia extractable Cu contents of surface soil samples from the three sampling blocks over the Mandamah prospect, and relationship of percentile cuts to raw Cu data distributions.
Figure 6. Examples of complex bivarite patterns for selected element pairs (data have been transfored and standardised).
Figure 7 Distribution of K-means clusters (k = 8) for standardised K-acetate, hydroxylamine.HCl and aqua regia extraction data from the three sampling blocks over the Mandamah prospect. Small clusters were defined as containing less than 10 observations, though many just contain single samples.
Figure 8. Plot of singular value decompositions scores (converted to percentiles) for total Mandamah selective extraction dataset (K-acetate, hydroxylamine.HCl, aqua regia and Na-pyrophosphate).
The SVD V-matrix was reduced to rank = 3.
Figure 9. X-Y-Z plot of SVD component scores with (a) SDD coded for level 1 (by shading) and level 2
(by symbol) and (b) general regions in SVD-space occupied by samples from the three sampling blocks with the [-1,+1] and [0,+1] clusters shown.
Figure 10. Plot of SDD clusters for (a) level 1 (b) level 1 further subdivided into level 2 and (c) level 4 with location of elevated K-acetate Ba concentrations.

Table 1. Partial extractions procedures.
Code Name Reagent Temp.
Sequence
1 KAC Potassium acetate
2 CHX Hydroxylamine.HCl
0.05M K OAc / pH 3.75 H OAc
0.1M NH
2
OH.HCl / 1M HCl
25

C
100

C
100

C 3 AQR Aqua regia
Batch
- SPF Sodium pyrophosphate 0.1M Na
4
P
2
O
7
.10H
2
O / pH 11 NaOH 0
(2 g sample in 20 mL reagent; vortexing every hour)

C
Time
6 hours
1 hour
3 hours
6 hours

Table 2. Summary of elements displaying strong (>|0.1|) positive (+) or negative (–) loadings in the three SVD components for the A matrix reduced to rank = 3.
SVD Digestion Element
Cpt.
Ag Al As Au B Ba Ca Co Cr Cu Fe Hg Mg Mn Mo Ni Pb Se Ti U V Zn
1
2
3
KAC
CHX
AQR
SPF
KAC
CHX
AQR
SPF
KAC
CHX
AQR
SPF
+ + + + + + + +
+ + + + + + + +
+ + + + + +
+ + + + + + + +
+ -
+ + + + + + + + + + +
+
+ + + + + + + -
-
-
+ + + + + + + + + + + + + + +

X
3 c pt
2
(
V
2 ) c pt
3
(
V
)
3
U
1
= v
1,1
X i
+v 1,2
X j
+v 1,3
X k cpt
1 (
V
1
)
X
3
X
2
(a)
X
1
X
2
(b)
X
1

Figure 2
6217000 mN
6216000
6215000
6214000
200 m
536000
Northern
Block
Central
Block
Monzodiorite
Subvolcanic diorites
Andesitic lavas
& volcaniclastics
Ultramafics
Fault
Mineralised zone
Sampling location
536200 536400
50 m
30 m
2
0
6
m
@ 0
0.
3
7
.5
%
1
g/
Cu t Au
Alluvium
Lower Saprolite
Andesite
Sericite-chlorite-magnetite alteration
Sericite-pyrite alteration
537400 537600
536600 mE
Northern Block
Section
200 m
0 m
537800 mE
50 m
200 m
Southern
Block
50m @ 0.8 g/t Au
0.5 % Cu
Alluvium
Lower Saprolite
Andesite
Monzodiorite / diorite
Ultramafic volcanics
Volcaniclastics
29m @ 0.3 g/t Au
0.2 % Cu
Southern Block
Section
0 m
537000 mE

Figure 3
10,000 ppm
1,000
100
Mg
Ca
10
Ce
Ba
Mg
Ca
Ce
1
Mo
Ba
Mo
Mg
Ca
Ce
Ba
Mo
0.1
0.01
andesite
Cu mineral n diorite andesite
Cu monzon .
mineral n
Cu andesite

Northern
Block
Central
Block
Southern
Block
Figure 4
Projected mineralisation
Fault
Recent alluvium
“Older” alluvium
Ba (ppm)
1000
100
10
200 m
> 90 th percentile
80 - 90
20 - 80
10 - 20
< 10
1
KAC
CHX
AQR maximum
90 th % ile
80 th % ile median
20 th % ile
10 th % ile minimum

Northern
Block
Central
Block
Southern
Block
Figure 5
Projected mineralisation
Fault
Recent alluvium
“Older” alluvium
Cu (ppm)
100
10
1
CHX AQR
0.1
200 m
> 90 th percentile
80 - 90
20 - 80
10 - 20
< 10
0.01
KAC

3
Potassium acetate
Ba
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2
Ca
3
3
Potassium acetate
Si
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2
Ca
3
1
0
3
Aqua regia
Al
2
-1
-2
-3
-3 -2 -1 0 1 2
Fe
3
Alluvium overlying mineralisation
Alluvium overlying background
Figure 6.

Figure 7
Northern
Block
Central
Block
Southern
Block
Projected mineralisation
Fault
Recent alluvium
“Older” alluvium
200 m
main clusters
small clusters

Northern
Block
Central
Block
Figure 8.
Southern
Block
Projected mineralisation
Fault
Recent alluvium
“Older” alluvium
200 m
> 90 th percentile
80 - 90
20 - 80
10 - 20
< 10

Figure 9.
(a)
(b)
0.3
0.0
-0.1
0.2
0.1
-0.2
-0.3
0.2
0.1
-0.1
scores
-0.2
-0.3
0.3
-0.2
0.0
-0.1
scores
0.1
0.2
Component 2
-0.3
SDD Level 1 -1
SDD Level 2 -1 0 +1 symbol
0
-1 0 +1
1
-1 0 +1
0.3
0.0
-0.1
0.2
0.1
-0.2
-0.3
0.2
0.1
-0.1
scores
-0.2
-0.3
0.3
-0.2
0.0
-0.1
scores
0.1
0.2
Component 2
-0.3
SDD Level 1,2 -1,+1 0,+1 symbol
Northern block samples
(over mineralisation)
Central block samples
Southern block samples
(over mineralisation)

(a) (b) (c)
Northern
Block
Central
Block
Figure 10
Southern
Block
Projected mineralisation
Fault
Recent alluvium
“Older” alluvium
Level 1 % data
-1 22
0 51
+1 27
Level 1
-1
0
+1
Level 2
0
+1
-1
0
+1
-1
0
% data
14
9
3
36
12
12
14
200 m
Level 4
+1
% data
23
>90 th % ile for KAC Ba