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ADE | Chapter 3-Quantitative Core-Log Analysis 91
3.5.1: Discussion of the statistical results and the bar diagram of minerals.
In comparison with massive pyrite deposits within the Broken Hill Block [e.g. Big
Hill cobaltian pyrite, Thackaringa Group (Plimer 1977)] the lack of pyrite within the
investigated samples of the Western Mineralisation suggests that the orebody is originally
sulphur-poor. Previous studies (Groombridge 2003; Kitchen 2001; Patchett 2003; Sproal
2001) showed that the galena and sphalerite samples of the Western Mineralisation were
highly enriched in Fe. This indicates a low sulphur system for formation of the orebody of
the Western Mineralisation. Plimer (1977, 2006a) claimed that the Broken Hill orebodies
have been unsaturated with S and the excess Pb and Zn have contributed to the
composition of silicate minerals such as gahnite, zincian garnet, zincian biotite, zincian
staurolite, zincian chlorite, zincian sericite, plumbian orthoclase, native lead, dyscrasite,
native silver, native lead, zincian manganese olivine, safflorite and löllingite. This study
also shows that the number of samples containing gahnite and green feldspar are relatively
substantial within the investigated samples of the Western Mineralisation. However, weak
acid digestion of sulphides for ICP-OES analysis would not have dissolved base metal-
bearing silicates and gahnite.
The low volume percentage and lack of arsenopyrite within the investigated
samples may be another reason for the deficiency of primary S in the Western
Mineralisation. Spry, Plimer and Teale (2008, p.232) suggested the chemical reaction (3.1)
as a possibility for formation of composite arsenopyrite-löllingite mineral3 in the -
Broken Hill deposit.
2FeAs + 2FeS + S = 4FeAsS (3.1)
2 2
The chemical reaction (3.1) shows that the generation of arsenopyrite during
metamorphism needs to consume S rather than production of S.
Despite the lack of pyrite and arsenopyrite (Table 3.5), chalcopyrite was presented
in a larger number of samples of the Western Mineralisation. This may indicate that the
dispersal of chalcopyrite (or minerals containing Cu) is controlled by different parameters.
Plimer (2006b) argued that in both the Olary and Broken Hill Domains, Cu was
remobilised during the Olarian Orogeny and participated at redox boundaries such as iron
3 Löllingite forms core and arsenopyrite forms rim of the composition mineral |
ADE | 92 Chapter 3-Quantitative Core-Log Analysis
formations or sulphide rocks. The spatial distribution of chalcopyrite and Cu will be
discussed in Chapters 6 to 8.
According to Table 3.6, the number of samples containing orange garnet,
hedenbergite, rhodonite and red garnet is very low within the total investigated samples. It
is possible that those silicate minerals were occurred naturally very low or they were
unstable over a long period and thus decomposed to other silicate minerals such as pink
garnet and gahnite.
Mineralogy of the investigated samples of the surface drill core shows:
1. An interdigitation of lode horizons (quartz-gahnite, quartz-garnet),
2. Replacement of metapsammite by quartz-gahnite and sulphides,
3. Replacement of metapelite by garnet rocks and ore types similar to C Lode
(quartz-gahnite-sphalerite-galena),
4. B Lode (quartz-hedenbergite-red garnet-sphalerite-galena), and
5. A Lode (quartz-orange garnet-rhodonite-galena-sphalerite).
The above observations suggest multiphase ore deposition in the Western
Mineralisation.
3.6 Evaluating the precision of the variation of galena+sphalerite against the
variation of Pb+Zn
The most important aspect of the quantitative core logging is how precisely the
variation of galena+sphalerite is correlated with the variation of Pb+Zn within the
investigated samples. The two important factors for determination of precision are
reliability and validity.
Reliability
Reliability refers to the reproducibility of the measurement in experimental studies
and the possible capacity for detecting agreements or internal consistency within
measurements. In fact, two data sets can show a high correlation coefficient but it is
possible they have little agreement and internal consistency in the variation of data. In this
study, reliability was measured by the following approaches (Garson 2010; Hopkins
2000a): |
ADE | Chapter 3-Quantitative Core-Log Analysis 93
1. Comparing the trend variation of mean and median concentrations for Pb+Zn and
galena+sphalerite within the corresponding drill cores (Section 3.6.1),
2. Comparing the COVs of Pb, Zn and Pb+Zn with the COVs of galena, sphalerite
and galena+sphalerite respectively within the corresponding drill cores (Section
3.6.1), and
3. Calculation of Spearman correlation coefficient4 and Cronbach’s alpha (UCLA:
ATS 2007; Yaffee 2003; Tables 3.9 and 3.10).
Validity
Validity refers to the amount of correlation between the value of the measurement
and its true value. In this study, the values of Pb+Zn are considered as true values and it
is important to know the extent of the correlation between the estimated values of
galena+sphalerite and the values of Pb+Zn. Also, the degree of validity was calculated by
the Pearson correlation coefficient5 (Hopkins 2000b) for logarithmic data (Table 3.8). But
as mentioned earlier a high PCC between Pb+Zn and galena+sphalerite does not mean that
the trend variation of Pb+Zn in drill cores is the same as the trend variation of
galena+sphalerite. A summary of statistical terms used in this section has outlined in Table
3.7.
4 SCC
5 PCC |
ADE | 94 Chapter 3-Quantitative Core-Log Analysis
Table 3.7: Different types of correlation coefficients and their statistical terms.
The correlation coefficients are normally reported as R= (a value between -1 and +1);
squaring the R value makes it easier to understand. The square of the correlation
coefficient multiplied by 100 [Equation (3.1)] describes the percentage of variation in one
variable in related to the variation of another variable.
R2 × 100 (3.1)
jk
Equation (3.1) is equal to percentage of variance in common between X and X . As a
j k
matter of routine it is the squared correlations that should be interpreted. This is because
the correlation coefficient shows the existence of more co-variation between two elements
than actually exists, and this problem gets worse as the correlation approaches zero.
Significance level indicates how likely the correlations reported may be due to chance in
the form of random sampling error. The significance level is important, if the data set is
very small. A significance level of 0.05 for a correlation coefficient means that there is
(1-0.05) or 95 % certainty of the possibility of being a true correlation coefficient and a
significance level of 0.01 for a correlation coefficient means that there is (1-0.01) or 99 %
certainty of the possibility of being a true correlation coefficient (Creative Research
Systems 1982).
There are both parametric and non-parametric statistical methods for measuring the
correlation coefficient. In parametric statistics it is supposed that the data set comes from
random data with normal distribution and that the parameters of the distribution can be
inferred by parametric statistics. In contrast, non-parametric statistics make no
assumptions about the randomness of the data and normal distribution and they are less
sensitive to outlier effects and skewed data.
PCC requires linearity of the relationship between the data and if the actual relationship
is non-linear, it may change the real degree of the correlation coefficient. Skewness of
distribution (pbarrett.net 2001) and outliers can affect linear relationships - this is the case
for most of the geochemical data. If the distribution of the data set is log-normal,
logarithmic data is preferable for the calculation of PCC (non-parametric method).
SCC is a non-parametric method that can also be used for calculation of the non-linear
correlation coefficient. Spearman’s approach is a form of rank order calculation based on
the median between all pairs of data in a scale that is also a type of measure of reliability
(Garson 2010).
Cronbach's alpha is not a statistical test but it is the most common form of reliability
coefficient or internal consistency based on the average correlation among the data set. It
is calculated in SPSS under the function of AnalysisScaleReliability Analysis.
In this study, the dialog of the Reliability Analysis was adjusted for the model of "Two-
Way Random Effects", consistency results and Cronbach's alpha. In the Two-Way
Random Effects model, both judges and measures effects are random.
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ADE | Chapter 3-Quantitative Core-Log Analysis 95
3.6.1 Comparison of the variation of Pb+Zn with variation of galena+sphalerite
Comparison of Figure 3.11 with Figure 3.3 shows that there are several similar
trend variations between galena and Pb and between sphalerite and Zn. However, in drill
core 4031 (Figure 3.11), the mean and median volume percentage of galena is very low,
although one would expect it to be higher in regard to its corresponding assay value (Pb) in
this drill core (Figure 3.3). This may have occurred due to the difficulty of visual
separation of galena from sphalerite and silicate minerals during the quantitative core
logging. This may especially be the case, when sphalerite appears as the major ore sulphide
mineral in a sample and its lustre masks the lustre of galena. This may be the general case
for the quantitative core logging of other polymetallic sulphide minerals as well and it is
the weakness of visual modal mineral mapping.
In this case, construction of a comparative bar diagram for variation of Pb+Zn and
galena+sphalerite is more reliable for the detection of possible human error. Especially, in
high grade sulphide mineralised samples, the concentration of Pb+Zn is supposed to be
high, but if it is considerably lower than expected, it may be a result of one or more of the
following mistakes in:
1. Reporting assay data,
2. Quantification of the ore sulphide minerals, or
3. Attributing the assay data to the wrong core sample.
Therefore, the comparison of bar diagrams of Pb+Zn and galena+sphalerite
(Figures 3.12 and 3.13) provides a more efficient tool for detection of potential mistakes at
the preliminary stage of data collection before data processing starts. This process
improves the degree of reliability of the important assay data (e.g. Pb and Zn in the
Western Mineralisation). Figure 3.13 shows many similarities in COVs of the following
pair variables:
1. Pb+Zn and galena+sphalerite,
2. Zn and sphalerite, and
3. Pb and galena. |
ADE | 98 Chapter 3-Quantitative Core-Log Analysis
3.6.2 Probability plot
The construction of a probability plot is a means of identification of the normal
distribution of a data set. The probability plots in Figure 3.14 were constructed for 1,219
samples containing Pb+Zn and galena+sphalerite. For construction of a probability plot,
the data set should be arranged in ascending order; the largest data will be plotted at a
lower percentage than 100 % and this makes it possible for some future data of Pb+Zn
concentrations and galena+sphalerite (vol. %) with larger values than the current largest
values to be located at a higher point in the order (Hart & Hart 2010). In Figure 3.14, the
estimated cumulative probabilities were calculated by the method of Median Rank
i0.3
(Benard) with the formula in which " n " is equal to the number of samples and "i"
n0.4
is equal to the rank-order of each value (i.e. i = 1 indicates the smallest value and i = n for
the largest). More details can be found in the "help" section of the Minitab software
(Minitab Inc. 2007).
Figure 3.14: (a) and (b) are related to the original data of Pb+Zn and galena+sphalerite. The
red curves show the experimental percentage of Pb+Zn concentrations and the volume
percentage of galena+sphalerite against their respective estimated values of cumulative
probability. The straight blue lines show the theoretical percentage of cumulative probability
for near-normal distribution of the variables. (c) and (d) are related to the logarithmic data of
Pb+Zn and galena+sphalerite. |
ADE | Chapter 3-Quantitative Core-Log Analysis 99
3.6.3 The results of correlation coefficients
In the Western Mineralisation, galena and sphalerite were observed only in 1,219
out of 1,849 samples containing Pb and Zn. This means that 6301 samples did not show
evidence of galena or sphalerite visually but they do have low assay values for Pb or Zn.
When considering this issue, PCC, SCC and alpha coefficients were calculated for the two
groups of 1,219 and 1,849 samples in order to evaluate the degree of reliability and validity
of the quantitative core log data.
In order to calculate correlation coefficient for 1,849 samples, a very small value of
0.000,1 was considered for the value of galena+sphalerite in 630 samples that do not have
any values for volume percentage of galena+sphalerite (Tables 3.8 to 3.10). Also, because
some volume percentages of galena+sphalerite are equal to one and the logarithm of one is
equal to zero, for calculation of PCC, the original data plus 0.000,1 were considered for
log-transformation (Table 3.8). According to Figures 3.14c and 3.14d, the logarithmic data
of Pb+Zn and galena+sphalerite show near-normal distributions and PCC can be applied to
the logarithmic data for evaluating the degree of validity between variation of Pb+Zn and
galena+sphalerite (Table 3.8).
Table 3.8: The results of PCC for logarithmic (data+0.000,1).
Minerals
Galena+Sphalerite Galena+Sphalerite
Elements
Pb+Zn 0.72* 0.45*
Number of samples 1219 1849
R2 % 51.8 20.2
*The significance level (2-tailed) is 0.01
Table 3.9: The results of SCC for the original data.
Minerals
Galena+Sphalerite Galena+Sphalerite
Elements
Pb+Zn 0.73* 0.78*
Number of samples 1219 1849
R2 % 53.3 60.1
*The significance level (2-tailed) is 0.01
1 1,819-1,219 |
ADE | 100 Chapter 3-Quantitative Core-Log Analysis
Table 3.10: The results of Cronbach’s alpha for the original data.
Cronbach's alpha Number of samples
0.814 1219
0.818 1849
3.6.4 Interpretation of the correlation coefficients
PCC
PCC in Table 3.8 shows a relatively high level of correlation (0.72) between the
variation of Pb+Zn and galena+sphalerite in 1,219 samples but when 1,849 samples are
considered the PCC shows a low level of correlation (0.45) between the pair values of
Pb+Zn and galena+sphalerite. The PCC result shows a strong validity between variations
of galena+sphalerite and Pb+Zn within the 1,219 investigated samples. In Table 3.8, the
result of R2 % for 1,219 samples means that the 51.8 % of variation of galena+sphalerite
can be estimated by the variation of Pb+Zn and the result of R2 % for 1,849 samples means
that only 20.2 % of variation of galena+sphalerite can be estimated by the variability of
Pb+Zn.
SCC
SCC in Table 3.9 shows a relatively high level of correlation (0.73) between the
variation of Pb+Zn and galena+sphalerite for 1,219 samples. Even when 1,849 samples are
considered the value of SCC increases from 0.73 to 0.78 between the pair values of Pb+Zn
and galena+sphalerite. This shows high internal consistency between the variation of
galena+sphalerite and Pb+Zn for two types of abundant samples.
Alpha coefficient
The alpha coefficient in Table 3.10 also shows a high level of internal consistency
or reliability between the variation of galena+sphalerite and Pb+Zn for two types of
abundant samples.
3.7 Exploration signature of lithologies in the Broken Hill Domain
In the Broken Hill Domain, garnet quartzite, garnetite, blue quartz-gahnite lode and
pegmatite show obvious spatial relationships with over 400 minor deposits of Broken Hill |
ADE | Chapter 3-Quantitative Core-Log Analysis 101
Type (BHT) deposits including the main Broken Hill orebody (Spry, Teale & Heimann
2003). Although, there are many competing ideas about the origin of these rock types in
the Broken Hill Domain of the Curnamona Province, these rock types are considered
widely as exploration guides to BHT deposits (Spry, Teale & Heimann 2003).
The question is whether it is possible to evaluate quantitatively the degree of relationship
of the lithologies of the Western Mineralisation with variation of Zn+Pb and whether the
rock types can be judged as major controlling factors of the mineralisation.
3.7.1 Statistical results for rock types of the Western Mineralisation
The results of SCCs of the investigated rock types with Pb+Zn and their descriptive
statistics are given in Table 3.11 and Figure 3.15 respectively. Table 3.11 shows at a
glance whether rock types vary with Pb+Zn perfectly, or nearly perfectly, and whether
positively or negatively.
Table 3.11: A summary of SCC results, significance levels (2-tailed) and abundance of rock
types.
Elements E l e m e n t s
Zn + Pb Zn + Pb
Rock types Rock types
Quartzite lode
- 0.04
Pegmatite
0.3**
Sig. (2-tailed) Sig. (2-tailed)
0.772 0.000
Number of Number of
56 339
samples samples
Metapsammite Blue quartz lode
- 0.13* -0.006
Sig. (2-tailed) Sig. (2-tailed)
0.033 0.880
Number of Number of
271 635
samples samples
Metapsammopelite Garnet quartzite
- 0.43** -0.29**
Sig. (2-tailed) Sig. (2-tailed)
0.000 0.000
Number of Number of
447 644
samples samples
Metapelite
- 0.53**
Sig. (2-tailed)
0.000
Number of
129
samples
Correlation is significant at the 0.05 level (2-tailed)
Correlation is significant at the 0.01 level (2-tailed) |
ADE | Chapter 3-Quantitative Core-Log Analysis 103
In Table 3.11, the variation of metapelite and metapsammopelite show a low
correlation with variation of Pb+Zn in opposite direction. It is not possible to compare
directly the SCC values of the rock types in Table 3.11 with each other because they were
calculated for different numbers of rock samples. The variations of the quartzite lode and
blue quartz lode are independent of the variation of Pb+Zn and there is no internal
relationship or consistency between them (Table 3.11).
3.7.2 Discussion of the correlation coefficient of the rock types with Pb+Zn
The results of SCC (Table 3.11) indicate that variations of the rock types within the
investigated samples have very low to low levels of relationship with the variation of
Pb+Zn. The results do not mean that the rock types are not suitable as an exploration guide
to the Western Mineralisation and variogram analysis for the rock types should be
calculated to understand the spatial relationship of the rock types with Pb and Zn. This will
be discussed in Chapters 6 and 8.
3.8 Summary
Descriptive statistics of assay data showed some similarities in the frequency
distribution of Zn-Pb, Fe-S, Bi-Sb and Ag-As-Cd. There are also some similarities in the
trend variation of mean and median concentrations of Pb-Ag and Zn-S in the bar diagram
of surface drill cores. Drill cores 4002 and 4031 contain high mean and median
concentrations of Zn, Pb and Ag. In the underground drill cores, there are some similar
trend variations among the mean and median values of Zn, Pb and S. The analysed samples
of drill cores 4062 and 4064 contain higher mean and median concentrations of Zn and Pb
relative to those within the analysed samples of the underground drill cores.
The mean and median concentrations of Zn, Pb and Fe within the surface drill cores
are less than those within the underground drill cores. In contrast, the mean and median
concentrations of As, Sb, Bi and S within the surface drill cores are more than those within
the underground drill cores. In the bar diagrams, drill cores with similar collar locations
(fanned drill holes) show significantly different mean and median concentration for some
elements. This suggests that spatial anisotropic parameters control the spatial distribution
and structural variation of the elements within the orebody. |
ADE | CHAPTER 4
The Relationship of Magnetic Pyrrhotite with the Orebody of
the Western Mineralisation
4.1 Introduction
The Western Mineralisation contains pyrrhotite. It is the only magnetic mineral in
the Western Mineralisation. There has been no quantitative mineralogical and statistical
approach on the magnetic properties and their variation within the Broken Hill orebodies.
A knowledge of the relationship between magnetic pyrrhotite and the orebody will be
useful for the development of the Western Mineralisation. It would be useful if a
geophysical interpretation could be integrated with geochemical information to improve
ore targeting.
One way in which geophysical methods could be incorporated would be via
aeromagnetic surveys, which are useful to outline an orebody’s magnetic properties (Clark
1997).The resulting aeromagnetic maps can also be applied to ore mineral tracking and
drill targeting at a scale suitable for exploration . However, a high-resolution aeromagnetic
survey has never been conducted over the Western Mineralisation owing to the proximity
of the City of Broken Hill and the large amount of magnetic noise above the Western
Mineralisation (e.g. steel structures, galvanised iron buildings, pipes, railway lines and
power lines).
Regional magnetic surveys in the Broken Hill area have shown the stratigraphic
distribution of magnetite-bearing amphibolite, felsic rocks and metasediments, minor thin
discontinuous banded iron formations comprising quartz-magnetite-spessartine-fluorapatite
and the Broken Hill orebody (Figure 4.1). Godber and Bishop (2006) recommended a
ground magnetic survey in order to understand the detailed magnetic properties of the
lithologies that contain magnetic minerals such as pyrrhotite and magnetite. The existing
drill cores provide an opportunity to conduct such a survey. |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 107
The data set was divided into two groups and they are productive samples
(galena+sphalerite ≥ 1 vol. %) and barren samples (galena+sphalerite = 0). Statistical tests
were performed in each group to examine the hypothesis whether the magnetic pyrrhotite
is enriched significantly in the productive units within the Western Mineralisation. The
correlation coefficient was calculated to determine the extent of the relationship between
the variations of volume percentage of pyrrhotite, its magnetic susceptibility and the
volume percentage of galena+sphalerite.
Contour plots and coefficient of variation (COV) and core logging models were
constructed in order to evaluate the variation of ore sulphide minerals present with the
variations of pyrrhotite abundance and its magnetic susceptibility. In view of the lack of
detailed magnetic surveys of the Western Mineralisation, this magnetic susceptibility
investigation and the quantification of pyrrhotite enable us to understand better the
subsurface pyrrhotite distribution, different types of pyrrhotite and magnetic variation
within the Western Mineralisation. The spatial distribution of magnetic susceptibility and
pyrrhotite are discussed in Chapters 6 and 8.
4.2 Characteristics of pyrrhotite
Pyrrhotite has a variable composition of Fe S that 0 ≤ x ≤ 0.13 (De Villiers and
(1-x)
Liles, 2010) and has monoclinic, hexagonal and orthorhombic polytypes. In nature,
pyrrhotite occurs in various superstructures (superlattice) that are represented by the axial
lengths of NiAs-type unit cell of "A" and "C" that they are equal to 3.44 Å1 and 5.70 Å
respectively. However, different structures of the pyrrhotite group are presented based on
Fe
"C" (Table 4.1). Pyrrhotite has a variable ratio (Table 4.1). The pure FeS iron rich
S
member of pyrrhotite is troilite (hexagonal). Arnold (1967) stated that natural pyrrhotite is
commonly a mixture of monocline and hexagonal polytypes.
1
Ångstrom |
ADE | 108 Chapter 4-The Relationship of Magnetic Pyrrhotite
Table 4.1: Atomic percentage of Fe in pyrrhotite polytypes ( from Carpenter & Bailey 1973;
Clark 1997; Kontny et al. 2000; Kruse & Ericsson 1988; Yund & Hall 1969).
Fe % , Superlattice
Crystal system Name
dimension
(Chemical formula)
2C pyrrhotite,
~ 50.0, (FeS) Hexagonal 3A, 2C
Troilite
4C pyrrhotite,
Magnetic pyrrhotite,
~ 46.67- (Fe S ) Monoclinic 2 3 A, 2A, 4C
7 8
Ferromagnetic
Weiss-type pyrrhotite
~ 47.37- (~Fe S ) Hexagonal 2A, 5C 5C pyrrhotite
9 10
~ 47.83- (~Fe S ) Pseudohexagonal 2A, 6C 6C pyrrhotite
11 12
11C pyrrhotite
~ 47.6- (~Fe S ) Orthorhombic 2A, 2B, 11C
10 11 (a mixture of 5C and 6C)
47.447.8 Orthorhombic 2A, 2B, nC
nC pyrrhotite
or Monoclinic
(Fe S Fe S ) 4.8n 6
9 10 11 12
Monocline pyrrhotite is the only ferromagnetic pyrrhotite with an approximate
crystallographic structure of Fe S (Zapletal 1992). It has a 4C superstructure. The
7 8
magnetic property of monocline pyrrhotite is related to cation vacancies in its crystal
structure. The vacancies decrease the overall crystal symmetry. Hence, the monoclinic
pyrrhotite commonly contains more defects than hexagonal forms and is therefore more
magnetic (Kontny et al. 2000). At temperatures above ~320° Celsius (Centigrade)
pyrrhotite loses its magnetism and, under suitable oxygen fugacities, may convert to
magnetite (Clark 1997; Rochette et al. 1990). The occurrences of pyrrhotite can be
considered as an important indicator of redox and temperature in metamorphic, magmatic
and diagenetic rocks (Rochette et al. 1990).
Hexagonal and other antiferromagnetic forms of pyrrhotite produce little magnetic
susceptibility in rocks (Dekkers 1988) and they cannot carry remnant magnetism (Zapletal
1992). However, monoclinic pyrrhotite is important mineral for identification of remnant
magnetisation and susceptibility anisotropy during geological times (Clark 1997) and it can |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 109
provide information regarding Palaeomagnetic characteristics, thermal evolution of the
ancient magnetisation and the genesis of pyrrhotite.
4.3 Pyrrhotite in the Broken Hill Domain
Scott, Both and Kissin (1977) and Bryndzia, Scott and Spry (1988) suggested that
hexagonal pyrrhotite in the Broken Hill orebody is a primary iron sulphide mineral formed
during high-grade metamorphism, whereas monoclinic pyrrhotite is a retrograde or post-
metamorphic product of primary hexagonal pyrrhotite. This indicates that crystallography
of pyrrhotite (changing from non-magnetic to magnetic pyrrhotite) was influenced by the
metamorphic evolution of the Broken Hill deposit.
Experimental studies of Scott, Both & Kissin (1977) showed that primary iron-rich
pyrrhotite formed at high temperature within metamorphic rocks of the Broken Hill
Domain and the Broken Hill orebodies. It is hexagonal pyrrhotite with exsolved troilite.
During cooling metamorphosed rocks, the primary pyrrhotite inverted to hexagonal
pyrrhotite + monoclinic pyrrhotite and further inverted during retrogression to monoclinic
pyrrhotite + pyrite (Scott, Both & Kissin 1977, p.1415; Figure 4.2).
In nature, the conversion of hexagonal pyrrhotite to monocline pyrrhotite requires
losing Fe and gaining S. Scott, Both and Kissin (1977) suggested that in the Broken Hill
deposit, the reaction of pyrrhotite and sphalerite during syn- to post- metamorphism events
resulted in releasing Fe and S from hexagonal pyrrhotite and sphalerite respectively.
During the chemical interaction and metamorphic evolution, the hexagonal pyrrhotite was
converted to monocline pyrrhotite while losing Fe and gaining S from sphalerite (Scott,
Both & Kissin 1977).
In the more advanced oxidation stages, the loss of iron from hexagonal pyrrhotite
may result in the occurrence of pyrite, marcasite and finally hematite or magnetite (Scott,
Both & Kissin 1977). Plimer (1977) stated that the presence of primary pyrite within
metapelites and metapsammites of several areas of the Broken Hill Domain (e.g. Stirling
Vale, Pyrite Hill and Thackaringa) indicates that pyrite is stable at the maximum
metamorphic grade of granulite facies and it did not convert to pyrrhotite. This suggests
that the primary pyrrhotite and troilite in the Broken Hill orebody formed because there |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 111
5. Pyrrhotite replacement by chlorite which has resulted in decomposition of
pyrrhotite to marcasite.
4.3.1 Evaluation of chemical properties of pyrrhotite among the Broken Hill
orebodies
There are several previous sets of EMPA analyses of pyrrhotite from the Western
Mineralisation and other Broken Hill orebodies (Table 4.2). There has been no study to
compare and contrast the chemical variation of pyrrhotite in the Broken Hill orebodies.
In this chapter, the data sets of others on pyrrhotite chemistry are used (Table 4.2). One
method was the visualisation of variation of the average atomic percent of Fe and S for
pyrrhotite samples from different orebodies (Figures 4.3 and 4.4). Another useful method
is correspondence analysis2 that categorises the orebodies based on major and minor
elements of pyrrhotite samples and visualise their inter-relationships on two-dimensional
maps (Figures 4.5 to 4.7). A three-dimensional model of association of different chemical
composition of pyrrhotite was interpreted by three correspondence maps2
Table 4.2: EMPA analyses of pyrrhotite from the Western Mineralisation and the Line of
Lode from CML7.
Reference Orebody Number of pyrrhotite samples and drill holes
Kitchen (2001) The Western Mineralisation 10 samples from 4001 and 4002
Patchett (2003) The Western Mineralisation 34 samples from 4003
47 samples from C Lode and 27 samples from
Sproal (2001) C Lode and 2 Lens
2 Lens
A and B Lodes, 1 Lens and 1 5 a n d 16 samples from A and B Lodes
Tully (2002) respectively, 5 samples from 1 Lens and 5
Kintore Pit
samples from Kintore Pit
Groombridge 2 and 3 Lenses 3 and 4 samples from 2 and 3 Lenses
(2003) respectively and 5 samples from south of 2 Lens
2 Lens South
4.3.1.1 Variation of Fe and S in pyrrhotite samples of the Broken Hill orebodies
In Figures 4.3 and 4.4, individual pyrrhotite samples were marked by red points and
the blue rhombic points represent the mean atomic percent of Fe and S. In Figure 4.3, some
pyrrhotite samples of B and C Lodes and the Western Mineralisation have atomic percent
2 See the explanations of Table 4.6 |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 113
4.3.1.2 Correspondence analysis for pyrrhotite samples of the Broken Hill orebodies
There are many references about mathematical theory and application of
correspondence analysis e.g. Adachi (2003), Benzercri (1992), Clausen (1998), Ender
(2010), Greenacre (1984, 2007), SAS Institute Inc. (1999), Social Research Update (1995),
Teil and Cheminee (1975), Valenchon (1982) and Van de Geer (1993a, 1993b) but the
major aim of correspondence analysis in this study is to show inter-relationship of
elements of pyrrhotite samples with the Broken Hill orebodies on two-dimensional
correspondence maps. Correspondence analysis is an exploratory method and non-
parametric technique that has no distribution assumptions, but it needs positive data values.
It is a geometric method to represent the inter-relationships of the rows and columns of a
two-way contingency table (Table 4.3) in a two-dimensional map (e.g. Figure 4.4) or a
low-dimensional space.
Table 4.3 shows categorical variables in a matrix format and in this Table, Fe and S
comprise the major average atomic percent of pyrrhotite and the other 8 elements
incorporate as minor element in atomic structure of pyrrhotite. There are significant
differences between average values of major and minor elements in Table 4.3. These
differences create difficulties for correspondence analysis because the variable with the
greatest variance will produce the highest influence on the outcome. One way for avoiding
this problem is performing correspondence analysis only with minor elements of pyrrhotite
(all elements of Table 4.3 without Fe and S) and another way is using standardisation that
the most universal method of standardisation is z-transformation.
Table 4.3: A contingency table of the average percentage of elements in pyrrhotite samples
within the Broken Hill orebodies.
Element
S Fe Cu Zn As Ag Cd Sb Pb Bi
Orebody
A Lode 52.38 47.3 0.008 0.011 0.085 0.006 0.009 0.007 0.005 0.18
B Lode 51.93 47.62 0.011 0.288 0.087 0.007 0.004 0.004 0.003 0.022
C Lode 52.79 46.75 0.0231 0.035 0.076 0.009 0.006 0.003 0.094 0.016
1 Lens 52.12 47.60 0.002 0.079 0.096 0.003 0.026 0.003 0.003 0.005
2 Lens 52.72 47.00 0.0535 0.074 0.089 0.011 0.004 0.003 0.001 0.007
3 Lens 52.97 46.58 0.0192 0.313 0.083 0.006 0.007 0.002 0.007 0.004
Western
52.27 47.32 0.0427 0.196 0.062 0.008 0.008 0.004 0.009 0.021
Mineralisation |
ADE | 114 Chapter 4-The Relationship of Magnetic Pyrrhotite
(x)
The z-transformation is calculated by subtraction of the mean value of each
column from each value (X) of the column and the resulting value of the column is divided
by the standard deviation (S) of the column [Equation. (4.1)].
x x
z
(4.1)
s
The z-transformation of values of Table 4.3 produces some negative values that
could not be analysed by correspondence analysis. It requires the addition of a minimum
constant value (e.g. 2) to all the values of Table 4.4 to change them to positive values
(Table 4.5). Although, with small changes of the constant value (e.g. addition of 4 instead
of 2 to values of Table 4.4), the relative distance of points3 will change inside a
correspondence map but the overall inter-relationships of the points will almost remain
comparable. In this case, if a great constant value is selected (e.g. 20 instead of 2), the
correspondence map will change significantly. Some statistical terms are broadly used in
correspondence analysis are explained in Table 4.6.
3 See the explanations of Table 4.6 |
ADE | 116 Chapter 4-The Relationship of Magnetic Pyrrhotite
Table 4.6: A summary of statistical terms used in correspondence analysis.
Points Demonstration of elements and orebodies of Table 4.3 in a correspondence map.
In Table 4.5, pyrrhotite samples collected from each orebody are associated with
Dimension 10 element concentrations. Therefore, each orebody can be defined by variation
of the 10 elements in a 10-dimensional space.
Scores show the coordinates of points in a correspondence map and each point is
Scores in
determined by a score in relation to the scale of each dimension of a
dimension
correspondence map.
V a r i a nce in correspondence analysis is called inertia. Inertia is "the weighted
Inertia sum of chi-square distance between each profile and the mean profile"
(Ender 2010, p. 1).
Mass is the marginal proportion of the row and column variables that is used to
weight the point profiles for calculation of point distance. So that the sum of all
Mass table entries is equal to 1.0 (StatSoft Electronic Statistics Textbook 2010) and
the row and column values are standardised for producing a correspondence
map. For example, in Table 4.5, each column total value will be divided by the
total of sum value for the columns, i.e., 140.
Determination of distances between the points provides all information about all
similarities among them. In correspondence analysis, the distances between
Chi-square
points are measured by chi-square method rather than the Euclidian distance.
method
The resulting distance matrix is used as entry data of the principal component
analysis1. The chi-square (Friendly 1995) is a weighted profile distance, where
the weight is the mass of the row or column values (Table 4.7).
T h e s u m of all the eigenvalues is named the total inertia or the total variance
The total inertia explained by the dimension. The total inertia is calculated by the total
chi-square value (29.952 in Table 4.7) divided by the total of the sum (140 in
Table 4.5).
The correspondence analysis is a method for decomposing the total inertia in
Correspondence
order to identify a lower-dimensional space for any given points. This analysis
analysis
makes easier interpretation of the internal relationships of the points.
Inertia of each dimension
Percentage of In Table 4.8, PPI is calculated by 100. For example,
Total inertia
proportional
the proportional inertia of the first dimension in Table 4.8 accounts for 37.82 %
inertia (PPI)
of the total inertia (21.39 %).
Visual presentation of the contribution of points to dimensions and contribution
of the dimensions to categorisation of the points and detection of their internal-
relationships. Each correspondence map accounts for part of the total variation
of the points within two dimensional spaces (Figures 4.5 and 4.7).
Correspondence
For measuring distances of row and column values, a symmetrical
map
normalisation was used in this study because the principal coordinate of row
and column values have slightly different scale. In a correspondence map,
relative distance of points from each other and the scores of points are
important parameters for interpretation (Section 4.3.1.3).
1 See the explanation of the principal component analysis in Section 5.7 |
ADE | 118 Chapter 4-The Relationship of Magnetic Pyrrhotite
4.3.1.3 Correspondence maps for pyrrhotite samples
Figures 4.5 to 4.7 display symmetrical plots of the elements of pyrrhotite samples
and the Broken Hill orebodies. Figure 4.5 shows 62.75 %5 of the total chemical variation
of pyrrhotite samples within the Broken Hill orebodies. In Figure 4.5, dimension 1
separates the plane from its zero value into two parts, positive and negative. C Lode, 2
Lens, S, Ag and Cu lie at the extreme end of the positive scale and 1 Lens, Fe and Cd are at
the extreme end of the negative scale of dimension 1.
Dimension 2 separates the plane from its zero value into two parts, positive and
negative. Bi, Sb and the Western Mineralisation lie at the extreme end of the negative scale
and 1 and 3 Lenses, As, Cd and S lie at the extreme end of the positive scale. Both the first
and second dimensions discriminates Fe-rich pyrrhotite from S-rich pyrrhotite.
Figure 4.5: Correspondence map in relation to dimensions 1 and 2 for pyrrhotite.
(* The Western Mineralisation)
In Figure 4.6, the correspondence map of dimensions 1 and 3 jointly accounts for
52.77 % of the total chemical variation of pyrrhotite within the Broken Hill orebodies.
Dimension 3 separates C Lode and Pb-rich pyrrhotite from Zn- rich pyrrhotite.
5 Calculated by PPI (dimension 1) + PPI (dimension 2) from Table 4.7 |
ADE | 120 Chapter 4-The Relationship of Magnetic Pyrrhotite
Together Figures 4.5 to 4.7 provide a three-dimensional model6 that shows
77.69 % 7 of total variation of pyrrhotite within the Broken Hill orebodies and their results
are outlined below:
A Lode contains Sb-rich pyrrhotite samples,
B Lode contains Fe-rich pyrrhotite samples,
C Lode contains Pb-rich pyrrhotite samples,
1 Lens contains Cd-rich pyrrhotite samples,
2 Lens contains Cu- and Ag-rich pyrrhotite samples,
3 Lens contains S-rich pyrrhotite samples, and
The Western Mineralisation contains Bi- and Sb-rich pyrrhotite samples.
4.4 Magnetic susceptibility measurements in the Western Mineralisation
In order to interpret the down-hole variation of magnetic susceptibility in
conjunction with variation of volume percentage of galena, sphalerite and pyrrhotite in the
Western Mineralisation, a total of 54 exploration drill cores were investigated. These
magnetic measurements were taken in CBH Resources’ core shed aiming to systematically
quantify the magnetic properties in 1,928 samples of the surface drill cores. The split cores
comprised the sulphide mineralised areas and their enclosing non-mineralised rocks. The
magnetic susceptibility is the intrinsic property that depends on the magnetic mineral
content and also on the size and orientation of magnetic particles present in a sample. The
magnetic susceptibility does not however depend on the strength of the geomagnetic field
in which lithologies occurred.
The hand held magnetic susceptibility metre model Digital Fugro GMS-2 (Figure
4.8) was used in this study. The GMS-2 is a high sensitivity portable instrument with a
detection range between 1×10-5 SI to 10 SI values and a resolution of 1×10-5 SI value.
Therefore, values less than 1 × 10-5 SI are outside the detection range of the GMS-2 and
are automatically assigned a value of 1 × 10-5 SI. The frequency of 760 Hz in this Model
indicates that this instrument is not susceptible to the effects of high conductivity in
some samples. When high magnetic susceptibility was shown, the instrument was
frequently zeroed to avoid drift. The magnetic survey took place in a temperature range of
about 10º-15° Celsius.
6 A combination of three correspondence maps in relation to dimensions 1, 2 and 3
7 Calculated by PPI (dimension 1) + PPI (dimension 2) + PPI (dimension 3) from Table 4.7 |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 121
Magnetic susceptibility has been measured to derive the range of magnetic degrees
for different rock types and the associated sulphide mineral assemblage exhibit at intervals
of one metre. The magnetic susceptibility measurements should show variation of the
magnetic properties and magnetic intensity from edge to the centre of the Western
Mineralisation. The following magnetic susceptibility values were measured in the
Western Mineralisation:
4.4.1 Average magnetic susceptibility (AMS)
Each 10 cm piece of one metre interval core sample was measured three times. The
AMS values of the core were determined for the one metre core sample. It was expressed
as AMS observed per metre and generally reflected lithological unit.
4.4.2 Maximum magnetic susceptibility (MMS)
Owing to the presence of disseminated pyrrhotite in each one metre interval core
sample, MMS was measured at one point in each one metre core sample. It was expressed
as MMS observed for a particular point in each sample.
Figure 4.8: A Magnetic Susceptibility Metre model Digital Fugro GMS-2. |
ADE | 122 Chapter 4-The Relationship of Magnetic Pyrrhotite
4.5 Descriptive statistics for magnetic susceptibility, pyrrhotite, Pb+Zn and
galena+sphalerite
In Table 4.9, maximum values of AMS and MMS are in the range of 10-3 SI8 (e.g.
5500 × 10-5 SI = 5.5 × 10-3 SI) and are associated with paramagnetic minerals such as
olivines, pyroxenes with positive susceptibility maximum of approximately 10-3 SI value
(Clark 1997). The maximum AMS value of 1500 × 10-5 was measured in drill core 4010 at
the depth of 256 m which contained 10 vol. % of pyrrhotite in a blue quartz lode. The
MMS values of samples were up to 5500 × 10-5 or 0.055 SI. As mentioned earlier, the
1,928 investigated samples of the Western Mineralisation were divided into two groups
(Table 4.10) and their statistical results are given in Table 4.11. Table 4.11 shows that the
mean values of pyrrhotite, AMS and MMS within productive samples are much greater
than the barren samples. This indicates that the mean volume percentage of magnetic
pyrrhotite is different between the two groups of samples in Table 4.10.
Statistical tests can then be used to test if the mean values of pyrrhotite and MMS
of barren and productive samples are indeed coming from two distinct distributions. The
differences of the two mean values of pyrrhotite and MMS between the barren and
productive samples may be significant or may be by chance. In statistics, when a result is
called significance, it is not possible to have occurred by chance. This issue can be
evaluated by further statistical tests.
4.5.1 Statistical tests
Depends on the distribution of data, statistical tests can be carried out by parametric
or non-parametric analysis. In parametric approach, data is supposed to come from a
normal distribution and parameters of the distribution can be inferred by parametric
statistics. In contrast, the non-parametric approach has no assumption about the
distribution and it is less sensitive to the effects of outliers.
8 International System of Units (metric system) |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 125
Figure 4.10: Probability graphs for logarithmic data of MMS, AMS, pyrrhotite and
galena+sphalerite. The red curves show the experimental logarithmic values of the variables
against their respective estimated percentage of cumulative probability and the straight blue
lines show the theoretical percentage of cumulative probability for near-normal distribution
of the variables.
Statistical tests give geologists a tool to make a quantitative assessment of
statistical significant differences of two sample groups. If there is a significant difference
between the two sample groups, it would confirm that the magnetic pyrrhotite or magnetic
property can be considered as a geophysical indicator for tracking galena and sphalerite in
the Western Mineralisation. The aim is to assess whether there is enough evidence to
accept the null hypothesis about two sample groups or to reject the null hypothesis
(alternative hypothesis).
4.5.1.1 Hypothesis of the non-parametric statistical tests
1. The null hypothesis is that the median values of AMS, MMS and pyrrhotite are the
same for both barren and productive samples, and
2. Alternative hypothesis is that the median values of AMS, MMS and pyrrhotite
differ between barren and productive samples. |
ADE | 126 Chapter 4-The Relationship of Magnetic Pyrrhotite
4.5.1.2 P value or significance level (1-tailed or 2-tailed)
1. If the P value of data < 0.01, it will indicate that the data provides statistically
significant evidence of a difference between the barren group and the productive
group with 99 % confidence level.
2. If the P value of data > 0.01, it will conclude that the data does not provide
statistically significant evidence of a difference between the barren group and the
productive groups with 99 % confidence level.
In this section, only the outcomes of the non-parametric statistical tests are
presented. A comprehensive description of the mechanism of the statistical tests for
independent groups is in the support section of the SPSS (SPSS Inc. 2009) software
package.
4.5.2 Wilcoxon Mann-Whitney U Test
In the case of independent groups, the Mann-Whitney U Test (Wilcoxon, 1945) is
the most widely-used significance test for comparing two independent samples based on
locations of the ranks and this test can evaluate whether two independent samples relate to
the same distribution (the null hypothesis) or not (the alternative hypothesis). In the Mann-
Whitney Test (Tables 4.12 and 4.13), significant values (2-tailed) and Mont Carlo Sig.9 are
less than 0.01. This indicates that AMS, MMS values and volume percentage of pyrrhotite
differ significantly between the two groups of productive and barren in the Western
Mineralisation (at the 99 % confidence level).
Table 4.12: The mean rank of AMS, MMS and pyrrhotite between the barren and the
productive groups using the Mann-Whitney Test.
Mann-Whitney Test Group N* Mean Rank Sum of Ranks
B a r r en 682 856.88 583533.5
AMS Productive 1246 1022.55 1274094.5
Barren 682 756.50 515174.5
MMS Productive 1246 1077.41 1342453.5
Barren 207 437.54 90571.5
Pyrrhotite Productive 790 515.10 406931.5
*Number of samples
9 Mont Carlo Significance |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 127
Table 4.13: The results of the Mann-Whitney Test.
Test Statistics AMS MMS Pyrrhotite
Mann-Whitney U 351312.5 282953.5 69043.5
Wilcoxon W 583533.5 515174.5 90571.5
Z -6.768 -12.228 -3.543
Asymp. Sig. (2-tailed)
0.000 0.000 0.000
Monte Carlo Lower Bound 0.000* 0.000* 0.000*
Sig. (2-tailed) 99 % confidence level 0.000 0.000 0.000
Upper Bound 0.000 0.000 0.001
* Based on 10,000 sampled tables with starting seed 2,000,000
4.5.3 Kolmogorov-Smirnov Z Test
The Kolmogorov-Smirnov Z test (Table 4.14) detects differences in both the
locations and shapes of the distributions. This test measures the maximum absolute
difference between the observed cumulative distribution functions in both groups. When
the differences are large enough to be significant, the two distributions are considered
different. In Table 4.14, the 99 % confidence level is smaller than 0.01 in the lower and
upper bound that indicate the two groups differ in either shape or location.
Table 4.14: Two-Sample Kolmogorov-Smirnov Frequencies Test.
Two-Sample
AMS MMS Pyrrhotite
Kolmogorov-Smirnov Test
Most Extreme Absolute Differences 0.147 0.295 0.157
Positive 0.000 0.000 0.010
Negative -0.147 -0.295 -0.157
Kolmogorov-Smirnov Z 3.095 6.196 2.006
Asymp. Sig. (2-tailed) 0.000 0.000 0.001
Monte Carlo Sig. (2-tailed) 0.000* 0.000* 0.000*
99 % confidence Lower Bound 0.000 0.000 0.000
level Upper Bound 0.000 0.000 0.000
* Based on 10,000 sampled tables with starting seed 2,000,000
4.5.4 Moses Test of Extreme Reactions
The Moses Test is used in experimental studies to assess whether the experimental
variable affects subjects in either a positive or a negative direction, creating a polarising
effect. The Moses Test compares extreme responses of one sample with another sample
obtained from a control group (in this study, barren group). If the probability associated |
ADE | 128 Chapter 4-The Relationship of Magnetic Pyrrhotite
with the Moses test is less than the desired significance level (in this study P < 0.01) then it
can be concluded that the two samples differ. In general, the Kolmogorov-Smirnov Z Test
check the middle of the distribution for differences in central tendency and do not take
account of the extreme low and high values. So it is possible when two different
distributions (e.g. one normal and another polarised at the two extreme) are compared with
each other and show similar central tendency that might not be found to be significantly
different by the Mann-Whitney U Test and the Kolmogorov-Smirnov Z Test, while the
Moses Test checks the tails of the distribution for differences in extreme tendencies (Table
4.15).
Table 4.15: Moses Extreme Reactions Test Frequencies at the 99 % confidence level.
Moses Test Group N
Barren (Control) 681
AMS Productive (Experimental) 1246
Barren (Control) 681
MMS Productive (Experimental) 1246
Barren (Control) 207
Pyrrhotite Productive (Experimental) 790
Test Statistics AMS MMS Pyrrhotite
Observed Control Group Span 1418 1661 827
Sig.(1-tailed) 0.000 0.000 0.000
Trimmed Control Group Span 1212 1487 771
Sig.(1-tailed) 0.000 0.000 0.000
Outliers Trimmed from each end 34 34 10
In Table 4.15, the barren group was defined as the control group. P values or Sig.10
(1-tailed) for AMS, MMS and pyrrhotite are below 0.01, thus indicating that the two
groups of barren and productive units differ significantly at 99 % confidence level. The
significance levels (1-tailed) in the trimmed group are the same as the observed group and
this confirms that even if the outlier samples are removed, these two groups of barren and
productive areas differ with respect to their AMS, MMS and pyrrhotite values. According
to the results of non-parametric statistical tests, there is enough evidence to suggest that
pyrrhotite abundance and AMS and MMS values are significantly different between
productive and barren samples in the Western Mineralisation.
4.6 Bar diagrams of magnetic susceptibility and pyrrhotite
In bar diagram of AMS (Figure 4.11), the drill cores 4028 and 4052 have higher
mean and median values relative to other drill cores and this indicates higher concentration
10 Significance level |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 129
of magnetic minerals in these drill cores. When considering HiP value, drill cores 4010 and
4028 show maximum AMS variation. In Figure 4.11, when considering HiP value, the
high variations of MMS are present within drill cores 4010, 4014 and 4031. Drill cores
4001, 4028, 4033 and 4052 reveal high mean and median values of MMS. The trends of
mean variations of AMS and MMS are roughly similar (Figure 4.11). In Figure 4.11, drill
cores 4028, 4033, 4045 and 4052 have high mean and median volume percentage of
pyrrhotite within the surface drill cores.
The greatest variation of pyrrhotite is present in drill core 4050 followed by drill
core 4030. The mean and median trend variations of pyrrhotite show similarity in a few
drill cores with AMS and MMS values. For example, the mean and median values of
AMS, MMS and pyrrhotite are high in drill cores 4028, 4033 and 4052 thus indicating an
increase of magnetic pyrrhotite abundance within the drill cores. It is evident from Figure
4.12 that every drill core shows distinct variation for AMS, MMS, specific gravity,
galena+sphalerite and Pb+Zn. There are significant similarities between the following
variations:
MMS and pyrrhotite, and
Pb+Zn and galena+sphalerite.
In Figure 4.12, there are several similar trends of COV for AMS, MMS, specific
gravity, galena+sphalerite and Pb+Zn in drill holes: 3231, 4010, 4011, 4012, 4015, 4026,
4028, 4031, 4032, 4037, 4038, 4039, 4040, 4052 and 4054. |
ADE | Chapter 4-The Relationship of Magnetic Pyrrhotite 133
4.7.1 Interpretation of the correlation coefficients
In Tables 4.16 and 4.17, the significance level (2-tailed) between AMS and
galena+sphalerite is more than 0.01 and it implies that there is less than (1- 0.01) or 99 %
certainty for chance of being a true correlation coefficient.
The non-parametric correlations in Tables 4.16 and 4.17 show 64.8 % and 50.7 %
correlation coefficients respectively between pyrrhotite (vol. %) and MMS (SI). In Tables
4.16 and 4.17, the result of correlation coefficient of MMS and pyrrhotite with
galena+sphalerite show values close to each other. For example, in the SCC (Table 4.16),
there is a 20.2 % correlation coefficient between MMS and galena+sphalerite versus
21.7 % correlation coefficient between pyrrhotite and galena+sphalerite. This indicates the
relationship of high magnetic pyrrhotite with the galena and sphalerite.
4.8 Appraisal of internal relationships among magnetic susceptibility, pyrrhotite,
galena+sphalerite and Pb+Zn relative to depth
There are major cases of internal relationships among variation of
galena+sphalerite, Pb+Zn, pyrrhotite, AMS, MMS, specific gravity relative to depth
among the 54 drill cores of the Western Mineralisation (Figures 4.13 to 4.17).
The results of observed internal relationships among the variables outline below:
1. The MMS values are anomalous in the presence of magnetic pyrrhotite and the trend of
intensity of AMS values is partially analogous with MMS signatures,
2. The down hole variation of MMS values, pyrrhotite abundance and specific gravity
values intensify within galena+sphalerite and Pb+Zn. It is unlikely that their marked
variations may be directly attributed to lithology variations,
3. The range of MMS values and volume percentage of pyrrhotite vary from 2×10-3 SI to
20×10-3 SI and from 3 to12 (vol. %) respectively within galena+sphalerite. The range
of specific gravity changes from 2 to 4, and
4. The MMS values and volume percentage of pyrrhotite display considerable fluctuation
in places where the sample contains rich sulphide ore. In more detail, the following |
ADE | 134 Chapter 4-The Relationship of Magnetic Pyrrhotite
compatibilities are shown among MMS values, pyrrhotite anomalies and
galena+sphalerite content.
4.1. In most core logs, the commencement and termination of the signals of MMS and
pyrrhotite anomalies roughly are consistent with the presence of sulphides (Figures
4.13 and 4.14),
4.2. In a few places, there is a partial shift or complete delay phase between the start
and termination of one anomaly of MMS against the presence of sulphide ore. For
example, in drill core 4014 (Figure 4.15), the anomaly of sulphide ore begins to
appear immediately after termination of the MMS and pyrrhotite anomalies. Drill
core 4005 (Figure 4.16) shows a delay phase and just part of the anomaly of MMS
and the presence of sulphide ore overlap each other, and
4.3. In some drill cores, for example, 4044 (Figure 4.17), there are some depths where
MMS anomalies are appeared in the absence of sulphide ore anomaly and vice
versa. The displacement and absence of sulphide ore (galena+sphalerite) against
MMS and pyrrhotite anomalies may be because pyrrhotite is ductile and during the
Olarian Orogeny may have been remobilised out of sulphide rocks into the
enclosing silicate rocks.
Textures in Figures 4.13 to 4.17 are associated to all sulphide minerals including
pyrrhotite. However, among the investigated samples of the Western Mineralisation,
pyrrhotite was present in various macroscopic textures such as stringer, disseminated,
brecciated, network, massive, crystalline and veinlets. Where adjacent to galena and
sphalerite, pyrrhotite is mostly disseminated, laminated and stringer, but further away from
galena and sphalerite the dominant textures are massive and network. Moreover, to some
extent the fine grained pyrrhotite reveals higher magnetic susceptibility and anisotropy
(changing of magnetic intensity at different directions) than pyrrhotite with massive and
network textures. The quantitative core log diagrams of this chapter have been provided in
supplementary files to this thesis. |
ADE | 140 Chapter 4-The Relationship of Magnetic Pyrrhotite
4.9 Contour plots
Contour plots are a useful tool for displaying anomalies. For example, contour plots
of galena+sphalerite and Pb+Zn in the parameter space of AMS and pyrrhotite (Figures
4.18a and 4.18b) show an anomaly of galena+sphalerite and Pb+Zn that appears between 2
to 12 volume percent of pyrrhotite and between 1×10-3 SI and 6×10-3 SI value of AMS.
In Figure 4.18a, another anomaly occurs between 12 and 19 volume percent of pyrrhotite
and measures that are higher than 4 ×10-3 SI values for AMS.
In Figure 4.18c, the major anomalies of galena+sphalerite appear between 2 and 15
volume percent of pyrrhotite and between 3×10-3 SI and 20×10-3 SI of MMS values. In
Figure 4.18d, the anomalies of Pb+Zn appear between volume percent of 4 and 12 of
pyrrhotite and for MMS between 4×10-3 SI to 16×10-3 SI. In Figure 4.18d, another anomaly
of Pb+Zn appears in the range of more than 35 volume percent pyrrhotite and the dominant
MMS is between 0.01×10-3 SI and 27×10-3 SI. This second anomaly occurs in a few
samples that are not covered by the major data set. |
ADE | 142 Chapter 4-The Relationship of Magnetic Pyrrhotite
4.10 Summary
This chapter investigated variation of magnetic pyrrhotite and its relationships with
galena and sphalerite and tried to understand whether magnetic susceptibility and
occurrences of pyrrhotite can be used as an exploration tool for tracking ore in the Western
Mineralisation. In order to interpret the down-hole variation of magnetic susceptibility in
conjunction with variation of galena (vol. %), sphalerite (vol. %) and pyrrhotite (vol. %), a
total 1,928 samples of 54 exploration drill cores were investigated. The data set was then
divided into two groups, productive and barren, based on the quantity of summation of
galena and sphalerite.
The outcomes of this study show that samples containing galena or sphalerite have
considerably more magnetic pyrrhotite than the samples without galena and sphalerite.
Thus, an understanding of the variation of pyrrhotite abundance and the geological
significance of its magnetic patterns provide a link between the mineralisation and the
geometrical configuration of the orebody.
Simple correspondence analysis performed in this study to show a picture of
internal relationships between chemical composition of pyrrhotite samples and the Broken
Hill orebodies. The result of 3D correspondence map shows that pyrrhotite samples of the
Western Mineralisation contain higher Bi and Sb in comparison with the other Broken Hill
orebodies.
Previous collected pyrrhotite samples from the Western Mineralisation shows
chemical formula of either magnetic pyrrhotite or non-magnetic pyrrhotite. The results of
the COVs show significant similarities between variations of pairs of MMS and pyrrhotite,
Pb+Zn and galena+sphalerite. The statistical tests of this chapter suggest that pyrrhotite
abundance, AMS and MMS values are significantly difference between productive and
barren samples of the Western Mineralisation.
The results of quantitative core logging suggest in most cases, the commencement
and termination of the signals of MMS and pyrrhotite anomalies in depth roughly is
consistent with the presence of sulphide ore anomalies. However, a partial shift or
complete delay between the start and termination of one anomaly of MMS against a
presence of galena+sphalerite are seen in some drill cores and in some cases, there are |
ADE | CHAPTER 5
Multi-Element Relationships: The Western Mineralisation
5.1 Introduction
Unlike geophysical data, geochemical data is stochastic in nature and multivariate
statistical analysis is in general used for their evaluation. Geochemical data often suffers
from several shortcomings, such as the detection limit problem, constrained data range
(Aitchison 1986; Le Maitre 1982), abnormal or multi-modal populations or strongly
skewed distributions (pbarrett.net 2001) and the presence of outliers (Filzmoser, Reimann
& Garrett 2005). Most classical statistics are based on assumptions that random variables
are following Gaussian distributions (Reimann & Filzmoser 2000), independent and
unconstrained in Euclidean real space. Multivariate statistical analysis can be used to
develop geochemical exploration models and identify mineral paragenesis and mineral
generations through:
1. The analysis of multi-element interactions,
2. The recognition of significant controlling factors,
3. The reduction of the geochemical dimensions,
4. The mass balance recognition, or
5. Statistical chemical equilibrium analysis
There are abundant publications regarding the geochemical characteristics and the
origin of the Broken Hill orebody based on interpretation of thermodynamic, sulphide
melting, isotopic data, element concentrations and geological observations (e.g. Frost,
Mavrogenes & Tomkins 2002; Mavrogenes et al. 2004; Phillips 1980; Phillips & Wall
1981; Ryall 1979; Spry, Plimer & Teale 2008; Stevens, Prins & Rozendaal 2005; Tomkins,
Pattison & Frost 2007). However, the application of multivariate statistical analyses in
relation to an orebody such as that at Broken Hill is still an area seriously under-
researched. In this chapter, there is a description of a variety of bivariate and multivariate
statistical analyses that were applied to detect and quantify the underlying structure of
geochemical variations of sulphide minerals. The methods are useful for identification of
the controlling chemical factors of sulphide ore formation in the framework of a multi-
influence elemental model. |
ADE | Chapter 5- Multi-Element Relationships 145
The detailed statistical analyses include:
1. Categorising chemical composition of galena and sphalerite samples of the
Broken Hill orebodies in order to identify the inter-relationship between the
orebodies and the chemical composition of the minerals,
2. Application of the compositional (closed) data analysis to make independent the
constrained geochemical data sets created from 10 element concentrations (Section
5.3.2),
3. Calculation of correlation coefficients for pairs of element concentrations,
4. Appraisal of multi-element relationships and the underlying structures, and
5. Evaluation of the biplot of the average atomic percentage of elements in the galena
and sphalerite samples in order to understand mineral generation.
The statistical analysis in this study was conducted by the following software programs:
1. Minitab software for performing simple correspondence analysis,
2. SPSS software for performing principal component analysis (PCA),
3. Matlab software (The MathWorks Inc. 2006) for programming of a 3D biplot, and
4. CoDaPack3D (Thió-Henestrosa 2008) a freeware module for conducting
compositional data analysis and construction of the 3D biplot.
5.2 The comparison of mineral chemistry of galena and sphalerite samples
Galena (PbS) and sphalerite (ZnS) are the major sulphide minerals of the
Broken Hill orebodies. The long term effect of deformation and metamorphism has caused
galena and sphalerite to show different percentages of major elements (Pb in galena, Zn in
sphalerite and S in both of them) and different minor substitution of Pb in sphalerite, Zn in
galena, and different traces of Fe, Ag, Sb, Bi, Cd, Cu, Zn, Mn, Co and As in samples
containing both minerals. In this section, the average atomic percentages of elements in
galena and sphalerite samples collected by Kitchen (2001), Sproal (2001), Tully (2002),
Groombridge (2003) and Patchett (2003) are compared (Tables 5.1 and 5.2). All these
samples were analysed by the CAMECA 50X electron microprobe at The University of
Melbourne. |
ADE | Chapter 5- Multi-Element Relationships 147
The results of comparison of the Western Mineralisation with the other Broken Hill
orebodies are outlined below using Tables 5.1 and 5.2:
1. The average atomic percentages of Bi, As, Fe, Sb and Zn in the galena samples of
the Western Mineralisation are at least 69.4, 9, 6.75, 2.75 and 1.6 times those of the
Broken Hill Lodes and Lenses respectively (Table 5.1),
2. The average atomic percentage of Pb in the sphalerite samples of the Western
Mineralisation is at least 1.59 times that of the Broken Hill Lodes and Lenses
(Table 5.2), and
3. The average atomic percentage of As in the sphalerite samples of the Broken Hill
Lodes and Lenses is at least 1.27 times that of the Western Mineralisation (Table
5.2).
5.2.1 Correspondence analysis for galena samples within the Broken Hill orebodies
The Broken Hill orebodies are categorised based on the major and minor elements
of galena and sphalerite samples using simple correspondence analysis. This method was
described earlier in Section 4.3.1.2. In this section similar procedures of correspondence
analysis were performed on the data of Tables 5.1 and 5.2. In the data sets of Tables 5.1
and 5.2, there are significant differences between the average values of major and minor
elements. This will produce significant differences between the variance of the major and
minor elements that consequently will affect greatly the result of correspondence analysis.
In order to solve this problem, the data sets of Tables 5.1 and 5.2 need to be standardised
using a z-transformation [Equation (4.1)].
During the z-transformation of data of Table 5.1, some negative values were
produced (Table 5.3) that could not be analysed by correspondence analysis, and therefore
a minimum constant value of 2 was added to all the data of Table 5.3 to change them to
positive values (Table 5.4). The reason for this was explained earlier in Section 4.3.1.2.
The result of decomposition of the data set of Table 5.4 into six dimensions (components)
is given in Table 5.5. In Table 5.4, galena samples collected from each orebody are
associated with 10 element concentrations in a 10-dimensional space. The correspondence
analysis decomposes the total variation of galena into a lower-dimensional space for the 10
element concentrations. This makes it easier to understand the internal relationships
between the Broken Hill orebodies and the different chemical compositions of galena. |
ADE | Chapter 5- Multi-Element Relationships 149
Table 5.5: The results of decomposition of Table 5.4 into six dimensions.
Proportion of Percentage of proportional Percentage of
Dimensions Inertia
inertia inertia (PPI) cumulative inertia
1 0.0751 0.4693 46.93 46.93
2 0.0458 0.2864 28.64 75.57
3 0.0194 0.1210 12.10 87.68
4 0.0154 0.0961 9.61 97.28
5 0.0043 0.0267 2.67 99.95
6 0.0001 0.0005 0.05 100.00
Total 0.16
5.2.2 Correspondence maps for galena samples
5.2.2.1 Interpretation of Figure 5.1
Figure 5.1 shows 75.57 % 1 of the total chemical variation of galena within the
Broken Hill orebodies.
Figure 5.1: Correspondence map in relation to dimensions 1 and 2 for galena.
(*The Western Mineralisation)
1 Dimension 1
In Figure 5.1, geochemical processes that can be inferred from dimension 1
separate the map at zero value into two parts, positive and negative. Pb- and Cd-rich
galena, A, B Lodes and 1 Lens lie on the positive scale of dimension 1 and the Western
Mineralisation (WestMin in map), C Lode, 3Lens, Bi-, Sb-, Fe-, Zn-, As- and S-rich galena
lie on the negative scale of dimension 1.
1 Calculated by PPI (dimension 1) + PPI (dimension 2) from Table 5.5 |
ADE | 150 Chapter 5- Multi-Element Relationships
2 Dimension 2
Dimension 2 separates 2, 3 Lenses (Pb Lenses) and Cu-, S- and Ag-rich galena
from the Western Mineralisation, B, C Lodes, 1 Lens and Pb-, Bi-, Fe-, Zn- and As- rich
galena samples.
3 Discriminator
Dimension 1 acts as a good discriminator of Cd- and Pb- rich galena from the
Western Mineralisation. Dimension 2 acts as a good separator of S-, Cu-, Ag-rich galena
from the Western mineralisation
5.2.2.2 Interpretation of Figure 5.2
In Figure 5.2, the correspondence map of dimensions 1 and 3 jointly accounts for
59.03%1 of the total chemical variation of galena samples.
4 Dimension 3
Dimension 3 is a good discriminator for separating C Lode, 2 Lens, Zn- and S-rich
galena from Ag-rich galena and A Lode.
Figure 5.2: Correspondence map in relation to dimensions 1 and 3 for galena.
5.2.2.3 Interpretation of Figure 5.3
In Figure 5.3, the correspondence map of dimensions 2 and 3 accounts for 40.74%
of the total chemical variation of galena.
1 Calculated by PPI (dimension 1) + PPI (dimension 3) from Table 5.5 |
ADE | Chapter 5- Multi-Element Relationships 151
Figure 5.3: Correspondence map in relation to dimensions 2 and 3 for galena.
5.2.2.4: Interpretation of a combination of Figures 5.1 to 5.3
Together Figures 5.1 to 5.3 provide a three-dimensional1 model that explains
87.68 %2 of the total chemical variation of galena within the Broken Hill orebodies and
their inter-relationships are outlined below:
A Lode contains Ag-rich galena samples,
B Lode contains Pb- and Cd-rich galena samples,
C Lode contains Zn-rich galena samples,
1 Lens contains Pb-rich galena samples,
2 Lens contains S-rich galena samples,
3 Lens contains Cu-rich galena samples, and
The Western Mineralisation contains Bi-, Fe-, As- and Sb-rich galena samples.
5.2.3: Correspondence analysis for sphalerite samples
The z-transformed values of Table 5.2 and the z-transformed values plus 2 for
sphalerite are given in Tables 5.6 and Table 5.7 respectively. The result of decomposition
of Table 5.7 into 6 dimensions is given in Table 5.8.
1A combination of three correspondence maps in relation to dimensions 1, 2 and 3
2 Calculated by PPI (dimension 1) + PPI (dimension 2) + PPI (dimension 3) from Table 5.5 |
ADE | Chapter 5- Multi-Element Relationships 153
Table 5.8: The results of decomposition of Table 5.7 into six dimensions.
Proportion of Percentage of
Dimensions Inertia PPI
inertia cumulative inertia
1 0.1029 0.5535 55.35 55.35
2 0.0404 0.2175 21.75 77.10
3 0.0235 0.1266 12.66 89.76
4 0.0116 0.0626 6.26 96.02
5 0.005 0.0271 2.71 98.73
6 0.0024 0.0127 1.27 100.00
Total 0.1859
5.2.4 Correspondence maps for sphalerite samples
5.2.4.1 Interpretation of Figure 5.4
Figure 5.4 shows 77.1 % of chemical variation of sphalerite samples within the
Broken Hill orebodies in relation to dimensions 1 and 2.
Dimension 1
In Figure 5.4, geochemical processes that can be inferred from dimension 1
separate Fe-, Sb- and S-rich sphalerite and 3 Lens at the extreme end of the negative scale
from A Lode, 1 Lens, Zn-, Ag-, Bi-, Cd-rich sphalerite at the extreme end of the positive
scale.
Dimension 2
Dimension 2, on the other hand, separates the Western Mineralisation and Pb-rich
sphalerite samples from 1 Lens and As-rich sphalerite samples.
Figure 5.4: Correspondence map in relation to dimensions 1 and 2 for sphalerite. |
ADE | Chapter 5- Multi-Element Relationships 155
Figure 5.6: Correspondence map in relation to dimensions 2 and 3 for sphalerite.
5.2.4.4 Interpretation of a combination of Figures 5.4 to 5.6
Together Figures 5.4 to 5.6 provide a three-dimensional model that explains
89.76 %1 of the total chemical variation of sphalerite within the orebody of the Broken Hill
deposit and their inter-relationships can be summarized as follows:
A Lode contains Ag-rich sphalerite samples,
B Lode contains Fe- and Sb-rich sphalerite samples,
C Lode contains As-rich sphalerite samples,
1 Lens contains Cd- , Bi- and Cu-rich sphalerite samples,
2 Lens contains Pb- and S-rich sphalerite samples,
3 Lens contains Sb- and Fe-rich sphalerite samples, and
The Western Mineralisation contains Pb-rich sphalerite samples.
There is a temptation in exploration to think that the "next" Broken Hill will be
identical to the main Broken Hill deposit on the Line of Lode. The result of
correspondence analysis for galena and sphalerite shows that such a view is not valid. The
chemical mineralogy of the Broken Hill Domain is similar to:
1 Calculated by PPI (dimension 1) + PPI (dimension 2) + PPI (dimension 3) from Table 5.8 |
ADE | 156 Chapter 5- Multi-Element Relationships
1. The Eastern Fold Belt of the Mount Isa Inlier where IOCG deposits (e.g. Ernest
Henry),
2. Iron formation Cu-Au deposits (e.g. Starra line, Osborne),
3. Co-As deposits (e.g. Mount Cobalt),
4. Pb-Ag-Zn deposits (e.g. Pegmont, Cannington), and
5. Mo-Re deposits (e.g. Merlin)
Another "Broken Hill" may not even have an abundance of gahnite and garnet
rocks. There may even be a Mount Isa-type Pb-Zn deposit at Broken Hill in the cover
rocks. What is known about the Broken Hill Domain is that it contains the largest Zn-Pb-
Ag deposit in the world, that there are thousands of minor deposits of different
commodities and that the area is a major metallogenic province. This suggests that the
Broken Hill Zn-Pb-Ag deposit is not an orphan.
5.3 Assay data used for multivariate statistical analysis
Some core samples (1,059) of the Western Mineralisation have equal assay data for
the concentration of the following ten elements: Zn, Pb, Cu, Fe, S, Ag, Cd, As, Sb and Bi.
The 1,059 samples have been cut from surface drill cores 4003 to 4032, 4040 and 4042.
Some of the element concentrations including Sb, As, Bi, Cd and Ag were measured based
on parts per million (ppm). Their values were converted to percentages so all assay values
have the same unit, hence simplifying the analysis. The data base has been provided in
supplementary file to this thesis.
5.3.1 Statistical distributions of assay values
The statistical distributions in terms of histograms of the raw data of the ten
elements are displayed in Figure 5.7 and their corresponding probability plots are given in
Figure 5.8. In Figure 5.7, all histograms except for Fe show strongly positive skewed
distributions that indicate that the proportion of a low concentration of elements is much
higher than that of a rich concentration of elements. The distribution of Bi and Sb show
that they have an approximately constant concentration value. It is clear from Figures 5.7
and 5.8 that the data for the element concentrations does not follow normal distributions.
They will have to be transformed to normal distributions first for effective bivariate
analysis. The reason for this has been explained in Table 3.7. |
ADE | Chapter 5- Multi-Element Relationships 159
5.3.2 Compositional data analysis
Compositional data is used in subjects such as geochemistry, petroleum chemistry
and environmental issues (Labus 2005). Compositional data is multivariate data defined as
a vector X with components of non-negative values X ,…, X that sum up to a constant,
1 D
usually 100 percent. As a consequence, elements of compositional data are not
independent. For example, if one of the elements is enriched, other elements must be
depleted to retain the geochemical mass balance (100%)1. Therefore, conventional
statistics applied to raw closed geochemical data may produce incorrect outcomes.
A sample space for D-part compositional data (e.g. D=10 for current data set), SD,
is called "Simplex" (Aitchison 1986). If D=3, a ternary diagram can show clearly the
different contributions of three elements for the closed data and if D=4, a tetrahedron
diagram can display the different contributions of four elements for the closed data (Figure
5.9). However, there is no satisfactory way to evaluate and demonstrate the contribution of
more than 4 elements in ternary and tetrahedron diagrams.
Figure 5.9: Contribution of 4 element concentrations within 1,059 samples of the
Western Mineralisation in a tetrahedron model.
1This problem is called closure effect (Filzmoser, Hron & Reimann 2009, p.627). |
ADE | 160 Chapter 5- Multi-Element Relationships
Aitchison (1986) introduced logarithms of ratios (log-ratio) to convert
compositional data into an unconstrained form in the real space RD. The transformed data
avoids the closure effect and the transformation is appropriate for elements that are
measured in percentages. The following three log-ratios are used for the transformation of
data into the real space (RD):
1. Additive log-ratio (alr) transformation: value of each element (x) is divided by the
value of a selected element (x ) before taking the logarithm i.e.:
D
xSD YRD1
x x x
Y alr (x) log 1 , log 2 ,...,log D1
x x x
D D D
2. Centred log-ratio (clr) transformation: value of each element (x) is divided by the
geometric mean (m ) of the data before taking the logarithm i.e.:
g
xSD YRD for i 1,..., D.
x x x x
Y clr (X) log log 1 ,log 2 ,...,log D
m m m m
g g g g
m D ΠD x
Where m is the geometrical mean defined as .
g g i1 i
3. Isometric log-ratio (ilr) transformation: the transformed vector is defined by
sequential binary partition that solves the problem of data collinearity resulting
from clr-transformation (Egozcue & Pawlowsky-Glahn 2005; Egozcue et al. 2003)
i.e.:
xSD YRD-1 for i 1,...,D-1
i i Πi x
Y ilr (x) log j1 j
i 1 x
i1 |
ADE | Chapter 5- Multi-Element Relationships 165
The results of Table 5.9 and 510 are outlined below.
1. Positive correlations range from 0.021(between Ag and S) to 0.955 (between Sb
and Bi),
2. Negative correlations change from -0.048 (between Ag and Cu) to -0.781(between
Sb and Zn),
3. Elements of Bi, Sb, As, Fe and Cu are negatively correlated with Pb, Zn, S, Ag and
Cd in this orebody,
4. The degree of correlation between Cu and other elements is generally very low,
5. There are strong positive correlations between Pb and Ag and between Zn and Cd,
6. Pb and Zn both have strong negative correlation with Fe, Sb and Bi,
7. Zn shows moderate positive correlation with S while Pb shows weak correlation
with S, and
8. Sb and Bi have strong positive correlations with each other and also with Fe, while
Sb and Bi both have strong negative correlations with S.
9. Table 5.10 shows that 60 % of the variability of the Zn concentration is negatively
correlated with the variation of Sb or Bi. According to Table 5.10, Sb and Bi are
negatively correlated with 40 % and 41 % of the variability of Pb respectively.
5.4.1 Interpretation of the PCC results
Silver and Cd contributed in the form of solid solution to the atomic structure of
galena and sphalerite respectively in the Western Mineralisation. Low correlation
coefficients of Cu with other elements indicate that enrichment or depletion of other
elements did not influence the degree of variability of Cu and vice versa. It is possible Cu
originated from a secondary geochemical process with a different source because the major
sulphide minerals of the orebody are galena and sphalerite. The low relationship of Cu
with Pb and Zn in the Western Mineralisation is similar to almost all of the Australian
sedimentary exhalative Pb-Zn-Ag deposits (McArthur River, Century, Hilton, George
Fisher and Cannington) that contain a Cu-content. However, the Mount Isa deposit in the
north of Australia has a spatial relationship with rich Cu-bearing sulphide minerals (Large
et al. 2005). |
ADE | 166 Chapter 5- Multi-Element Relationships
5.5 Linear multivariate regressions (LMR)
The LMR allows for prediction of the behaviour or variability of individual
elements such as Pb and Zn concentrations based on other elements as predictors.
Moreover, the LMR shows how well a predictor element can represent the variability of Pb
or Zn concentrations. The result of the LMR shows the most economical exploration model
for prediction of Pb and Zn concentrations by measuring the minimum number of predictor
elements. Thus, it is important to determine whether all of the predictor elements are
equally important to predict the variability of Pb or Zn and if not which of them has more
priority for the predication of the Pb and Zn concentrations. The method of LMR is also
used in exploration of gold (Bellehumeur & Jébrak 1993).
It is obvious that the number of predictor elements for Zn (or Pb) can increase if we
have access to more than 9 element concentrations associated with the Western
Mineralisation but as mentioned earlier only some of them may be considered as good
predictor elements of Pb and Zn. The resulting predictor elements of Pb and Zn can be
calculated by variogram analysis so as to understand whether the predictor elements are
suitable as "pathfinder" or "indicator" elements (Levinson 1974, pp.54-55; Peters 1987,
p.403) for tracking galena and sphalerite in the Western Mineralisation or similar Pb-Zn
sulphide orebodies. More details about pathfinder elements are given in Section 7.3 where
the spatial zonation of geochemical haloes is discussed for the Western Mineralisation.
In this study, a stepwise multiple regressions analysis using SPSS was carried out
to evaluate the contribution of all predictor variables for a prediction model of Pb or Zn
concentrations in the Western Mineralisation. In this process, the nine predictor elements
of Pb, Fe, S, Cd, Ag, Sb, Bi, As and Cu for Zn and the nine predictor elements of Zn, Fe,
S, Cd, Ag, Sb, Bi, As and Cu for Pb were added one by one to the regression model and
their accumulative effects on Pb and Zn predictions are calculated. Correlated elements
will make positive contributions to the regression model and they will be retained in the
model. The assessment can be done using a desired "Adjusted R Square". The aim is to
select a model with a higher Adjusted R Square and a lesser number of predictor elements.
Some of the statistical terms of the LMR are briefly described below:
1. The selected predictor elements may show correlation with Pb or Zn but they need
not necessarily have a strong correlation with the other predictor elements.
Otherwise, a strong correlation between some of the predictor elements may |
ADE | Chapter 5- Multi-Element Relationships 167
obscure the relative contributions of each predictor element to the success of the
model. This can be checked using the collinearity diagnostics section of SPSS. The
collinearity diagnostics measure the tolerance and Variance Inflation Factor (VIF)
value. The results are presented in the prediction models of Pb and Zn. A value less
than 0.01 for tolerance and more than 10 for VIF implies a strong correlation
between predictor elements, meaning they have the collinearity problem, and
2. The beta value represents the intensity of influence of each predictor element on the
variation of Pb and Zn. A large beta value indicates a higher impact of the predictor
element on variations of Pb and Zn. The beta value is defined in units of the
standard deviation. For example, a negative beta value of -0.274 of Fe for Pb
(Table 5.11) indicates that a positive change of one standard deviation in Fe will
result in a negative change of 0.274 standard deviations in Pb.
5.5.1 Results of LMR for Pb
A significant model with three predictor elements emerged in the third model
(Table 5.11) that is characterised by F , = 572.974 and p < 0.0005, where
713.787 438.092
713.787 and 438.092 in F (Fisher test) are sum of the squares for regression and residual
respectively. The Adjusted R Square is 0.619 and collinearity statistics are: Tolerance
(0.3 < X < 1) and VIF < 3.
Table 5.11: Significant predictor elements of Pb in the third model of LMR analysis.
Elements Beta p-value
Fe -0.275 p < 0.0005
Ag 0.410 p = 0.0005
Bi -0.245 p < 0.0005
Elements of Fe, Ag and Bi are part of the third prediction model for Pb with the
Adjusted R Square of 61.9 % indicating that the variability of Fe, Ag and Bi taken together
as an exploration model for Pb can predict 61.9 % of the variability (variance) of the Pb
concentration in the Western Mineralisation. |
ADE | 168 Chapter 5- Multi-Element Relationships
5.5.2 Interpretation of LMR results for Pb
The Adjusted R Square improved when more elements were added successfully to
the model. The final LMR model for Pb contains the following predictor elements in
decreasing order of their significant contributions: Fe, Ag, Bi, Zn, As, Cu, Cd, Ag and Sb.
Sulphur made little contribution to the prediction of Pb and therefore it was not included in
the final model. In comparison with the bivariate analysis (Table 5.9), the following
conclusions can be drawn based on LMR analysis of the Pb:
1. Iron and Bi concentrations have a negative impact (negative beta) on the variability
of the Pb concentration. The same conclusion was also reached based on Table 5.9,
and
2. Antimony concentrations did not appear in the third model as predictor elements
for Pb though it was in the last model but with little contribution (small beta). On
the contrary, Sb shows a strong negative correlation coefficient with Pb from the
bivariate analysis (Table 5.9).
From Table 5.1, the average atomic percentage of Fe, As, Bi and Sb in galena
samples of the Western Mineralisation is higher than the other Broken Hill orebodies. The
result of LMR analysis suggests Fe, Ag and Bi are appropriate predictor elements for the
prediction of Pb variation in the Western Mineralisation.
5.5.3 Results of LMR for Zn
For Zn concentration, the third model (Table 5.12) is characterised by
F , = 572.974 and p < 0.0005, adjusted R square of 0.816 and collinearity
1317.403 296.121
statistics: Tolerance (0.5 < X< 1) and VIF < 2.
Table 5.12: Significant predictor elements of Zn in the third model of LMR analysis.
Elements Beta p-value
Cd 0.487 p < 0.0005
Sb -0.578 p = 0.0005
Ag -0.134 p < 0.0005 |
ADE | Chapter 5- Multi-Element Relationships 169
Elements that contribute to the quality of the prediction model for Zn are (in
decreasing order of importance): Cd, Sb, Ag, Fe, As, Pb, Cu and Bi.
5.5.4 Interpretation of LMR results for Zn
A linear combination of the three elements Cd, Sb and Ag can provide a good
predictor model (81.6 %) for Zn concentration in the Western Mineralisation and similar
mineralisation.
1. The LMR model for Zn shows that Ag has a negative correlation (negative beta)
with Zn in contrast to the correlation coefficient in Table 5.9 where it shows a weak
positive correlation of Ag with Zn,
2. Bismuth has only a minor contribution to the final prediction model for Zn and
consequently this model suggests that Bi is not an appropriate predictor element for
tracking the variability of Zn concentration, while in Table 5.9, the Bi and Zn show
a strong negative correlation, and
3. Sulphur content is not recognised as a significant predictor in the final model (9)
for Zn and was thus removed from the model.
Based on these assessments, it can be concluded that LMR is more suitable for
identifying the major predictor elements for tracking ore minerals and Pearson correlation
coefficient should be used with care in geological interpretation.
5.6 Cluster analysis
Cluster analysis (Davis 1973; Hartigan 1975; Templ, Filzmoser & Reimann 2008)
is an investigative multivariate data analysis that can be used to classify geochemical
variables or samples. Cluster analysis can support the development of geochemical models
by identifying multi-element relationships or by clustering element concentrations based
on the amount of their percentage of similarities. Furthermore, it reduces the number of
variables that need to be considered in subsequent analysis and provides a visual
description of combined variables that is easier to understand than results obtained through
more traditional analysis such as PCA. |
ADE | 170 Chapter 5- Multi-Element Relationships
Cluster analysis needs to specify a final partitioning by selecting the number of
sub-clusters (user defined) and the problem is to select an optimum number of sub-clusters
for partitioning (Fraley & Raftery 1988). It is possible to group the elements into 1 to n7
clusters, a procedure that is called "hierarchical" clustering. Hierarchical clustering
provides n cluster solutions and the user should make a decision which model is the most
appropriate. The principal aim of cluster analysis in the Western Mineralisation is to divide
element concentrations into a number of groups to better understand the multivariate
behaviour and the structures of multi-element interactions. A good cluster analysis
attempts to classify the elements into groups with high levels of similarity while at the
same time the differences between the individual groups are kept as large as possible.
5.6.1 Distance measures for cluster analysis
Cluster analysis uses distance measures to quantify the similarity among the
element concentrations in a multivariate space based on the entered assayed samples. The
"distance" in cluster analysis is not the same as a geographical distance among samples and
the important issue is how best they can measure distance between the elements. Several
distance measures exist in this method such as Euclidean, Manhattan, Ward, Gower
(Gower 1966), Canberra (Lance & Williams 1966), the random forest proximity (Breiman
2001) and the correlation coefficient. The Euclidian is a straight-line distance in geometry
that is calculated by the root of the sum of the squares and the Manhattan is the sum of
linear distances.
More detail about distance measures and examples can be found in Arabie, Hubert
and De Soete (1996), Gordon (1999), Mark and Roger (1984) and Swan and Sandilands
(1995). However, there are no theoretical reasons to prefer one of the distances over the
other. In this thesis, the correlation coefficient of the elements was used as the distance
measure for quantifying the amount of similarity of 10 element concentrations.
5.6.2 Cluster algorithm
After selection of a distance measure (e.g. correlation distance) a cluster algorithm
should be selected in order to determine cluster membership for each element based on
their distance measures. The cluster algorithms can be "divisive" or "agglomerative".
A divisive method starts with all elements in one cluster and the cluster gradually splits the
7 Maximum n is equal to the number of variables (i.e. elements) |
ADE | Chapter 5- Multi-Element Relationships 171
smaller groups step by step. In contrast, in the agglomerative technique, at first each
element forms its own cluster and this process continues for "n" single element clusters and
then the number of clusters is reduced by joining the two closest elements and continues to
find another similar element for gradually joining the first two or two other elements. This
procedure will proceed until one large cluster is formed.
There are several algorithms for linking two clusters, such as average linkage,
complete linkage, single linkage, median linkage, centroid linkage and so on. In this study,
the agglomerative average linkage distance was selected for the calculation of the cluster
algorithm. The average linkage algorithm calculates the mean of all distances of two
elements between the elements of two sub-clusters and then combines two sub-clusters
with the minimum average distance into one new cluster.
5.6.3 Result of cluster analysis for the 1,059 clr-transformed data
Cluster analysis was calculated for the 1,059 clr-transformed data using the average
linkage algorithm and correlation coefficient distance (Figure 5.12).
Figure (5.12) shows the following three main groups for 10 elements:
1. Group 1 (red colour): Zn, Pb, S, Ag and Cd,
2. Group 2 (green colour): Cu, and
3. Group 3 (blue colour): Fe, As, Sb and Bi.
It is possible to define two main groups instead of three for the cluster algorithm in
Figure 5.12 and the percentage of similarity among the 10 elements does not change but
Cu will be considered as part of the group 3. The horizontal line in the dendrogram (Figure
5.12) represents the similarity level between two or more elements while the vertical line
indicates the distance level or differences. For example, the elements of Sb and Bi in group
3 shows the highest similarity level with 97.7 %, whereas all elements of the groups 1 and
2 reveal the lowest similarity (26.30 %) with all elements of the group 3.
Minor abundance of chalcopyrite, pyrrhotite, pyrite, gudmundite, tetrahedrite8 and
arsenopyrite in the Western Mineralisation may relate to the amount of dissimilarities of
Fe, Cu, As and S in Figure 5.12.
8 (Cu, Fe, Ag, Zn) Sb S
12 4 13 |
ADE | 172 Chapter 5- Multi-Element Relationships
Figure 5.12: Hierarchical horizontal cluster algorithm with three main groups for 1,059
clr-transformed data of each element.
According to Figure 5.12, there are a high percentage of similarities among the
following elements:
1. Zn-Cd with 89.4 %,
2. Pb-Ag with 89 %,
3. Fe-Sb-Bi with 83.4 %, and
4. S-Zn-Cd with 77 %.
Some of those similarities between the elements are seen in the sulphide minerals
of the Western Mineralisation e.g. sphalerite containing Cd and galena containing Ag.
5.7 Principal Component Analysis (PCA)
PCA is a non-spatial multivariate procedure that is most commonly applied with
the intention of recognising a small number of interesting sub-dimensional elements, which
may then be examined by spatial approaches, exploring for spatial patterns and
correlations. The aim of PCA is to reduce the complexity and dimensions of variables to a
smaller number of uncorrelated principal components (Anderson 1984; Johnson &
Wichern 1992; Rencher 1995). PCA helps to describe the greatest degree of variance for
the lowest amount of the uncorrelated variables. In geochemical study, the goal of PCA is
to facilitate the interpretation and explanation of the underlying data structure from large |
ADE | Chapter 5- Multi-Element Relationships 173
assay data. Moreover, PCA investigates the degree of continuity or clustering of samples
and identifies element concentrations whose significance is that they can be broken down
into some distinct groups.
5.7.1 Result of PCA
The 1,059 clr-transformed data of each element of the Western Mineralisation were
examined by a subprogram of the PCA and correlation matrix in SPSS 17. The correlation
matrix is preferred over the covariance method if the element concentrations are measured
by different scales (e.g. percentage and ppm) and need to be standardised. For solving this
problem, in the subprogram of PCA, the standardisation part of the program was selected.
In comparison to factor analysis, PCA deals with the total variation in the correlation
matrix rather than part of it and does not require showing if the PCA is appropriate for
structural detection of the data.
In Table 5.13, PC explains 51.6 % of the variance of ten element concentrations
1
and it is thus a relatively important PC, while the other PCs have less important roles in
describing the variation of ten element concentrations.
Table 5.13: Summary of PCs in the Western Mineralisation.
Percentage of Percentage of
PCs9 Eigenvalues proportional variance cumulative variance
(PPV) (PCV)
PC 5.1594 51.6 51.6
1
PC 1.5696 15.7 67.3
2
PC 1.2503 12.5 79.8
3
PC 0.9561 9.6 89.4
4
A combination of PC , PC , PC and PC provides sufficient detail about major
1 2 3 4
geochemical variation (89.4 %) in the Western Mineralisation, rather than studying ten
geochemical elements and their behaviours individually. It should be noted that additional
PCs, such as PC and PC , if used, should increase overall variance. The increment in the
5 6
variance will be case dependent but in general smaller and smaller contributions will be
expected, see Figure 5.13.
9 Principal Components |
ADE | 174 Chapter 5- Multi-Element Relationships
Figure 5.13: The scree plot of eigenvalues versus number of PCs.
Figure 5.13 represents the relative size of each eigenvalue in descending order
versus the number of the respective PC. It shows visually which of the 10 PCs accounted
for most of the variability in the Western Mineralisation. The first component shows
maximum variance and the successive components make an increasingly smaller
contribution to the total variance. According to the Figure, the first four eigenvalues
explain the major geochemical variations of the Western Mineralisation. It should be noted
that the remaining accumulated 11.6 % variances cannot be explained by the results of the
first four PCs and the remaining six PCs fulfil only a small portion of the accumulated
11.6 % variances. Hence, each of them contributes only minimally to the variation of the
element concentrations and cannot be interpreted meaningfully. Those PCs constitute
random variations or an unsystematic chemical process within the sulphide orebody of the
Western Mineralisation.
Spry, Plimer and Teal (2008) suggested that the Western Mineralisation is a
stratabound deposit formed by the replacement of sediments at the top of an upward-
coarsening sequence beneath an aquifer cap (Unit 4.6). If this were the case, sulphide
bearing ore must have pulsated numerous times between the deposition of C Lode and A
Lode and they can be interpreted as geochemical variations evident from the PCs of this
study (Table 5.13). The Western Mineralisation has also a variation in grade and zonation
and Plimer (2006b) argued that the intersection of F3 and F4 structures created dilation |
ADE | Chapter 5- Multi-Element Relationships 175
during the Olarian Orogeny. Plimer (2006b) also suggested that more ductile minerals such
as galena and pyrrhotite might have flowed into these dilation zones. The geochemical
variations evident from the PCs of this study can also be attributed to the dilation zones.
5.7.2 The amount of PC loadings
In Table 5.14, the PC loadings denote the degree of correlation between individual
element concentrations and the PCs (i.e. PC , PC , PC and PC ). Thus, elements with
1 2 3 4
higher PC loadings in each PC play more roles in geochemical variation of the PC and
have more potential for mineralisation. For example, in Table 5.14, Zn has maximum
positive PC loading in PC (0.857) in comparison with the weights of other elements in
1
PC and even the weights of Zn in PC , PC and PC .
1 2 3 4
Table 5.14: PC loadings10 of 10 elements for each PC (Table 5.13) of the Western
Mineralisation.
PCs loading
PC loading PC loading PC loading PC loading
1 2 3 4
Elements
Zn 0.857 0.346 - 0.224 - 0.063
Pb 0.697 - 0.584 0.056 0.071
Cu 0.029 0.221 0.929 0.057
Fe - 0.842 0.271 0.073 0.228
S 0.681 0.479 0.302 - 0.051
Ag 0.511 - 0.724 0.083 0.266
Cd 0.677 0.460 - 0.449 0.180
As - 0.549 - 0.147 - 0.055 - 0.810
Sb - 0.932 0.008 - 0.122 0.269
Bi - 0.936 0.010 - 0.106 0.238
This indicates a strong correlation of Zn with geochemical variation of PC . Therefore,
1
major sulphide mineralisation containing Zn (sphalerite) should occur during geochemical
variation evident from PC in the Western Mineralisation.
1
In regards to the sulphide mineralogy of the Western Mineralisation, the elements
with absolute PC loading values ≥ 0.4 in Table 5.14 are considered to have potential for
mineralisation or are considered to have a significant influence on the geochemical
variation of the PCs. According to the absolute PC loading values ≥ 0.4, the following
elements have major chemical contributions to each PC:
10 Weights of elements in each PC |
ADE | 176 Chapter 5- Multi-Element Relationships
1. PC : Bi, Sb, Zn, Fe, Pb, S, Cd, As and Ag,
1
2. PC : Ag, Pb, S and Cd,
2
3. PC : Cu and Cd, and
3
4. PC : As.
4
5.7.3 The sign of PC loadings of the elements
Interpretation of the PC loadings of the elements in Table 5.14 based on their signs
(i.e. negative or positive) depends on dominant sulphide minerals in the Western
Mineralisation. For example, the positive PC loadings of Zn and Pb in PC (with 51.6 %
1 1
contribution in the sulphide mineralisation; Table 5.13) should be interpreted as sulphide
mineralisation that is consistent with the dominant sulphide mineralogy (galena and
sphalerite) of the Western Mineralisation.
Elements with the positive PC loadings
1
In Table 5.14, the positive loadings of Zn, Pb, Cu, Ag, Cd and S indicate the
following possibilities:
1. These elements initially may tend to incorporated as a major constituent of the
mineral compositions of the Western Mineralisation (e.g. Pb in galena or Zn in
sphalerite),
2. These elements may be as mineral inclusions containing the elements inside other
major minerals (e.g. chalcopyrite in galena), or
3. These elements are incorporated into the atomic lattice of other minerals (solid
solution) as trace elements. This is most likely when the amount of an element
concentration is naturally very low to form an independent mineral. For example, the
average concentration of Cd is very low against the average concentrations of Zn and
Pb in the Western Mineralisation (Table 3.2).
The negative PC loadings of those elements are interpreted as dilution effects or
depletion or removal of those elements from sulphide bearing fluids during geochemical
variation evident from the PC. |
ADE | Chapter 5- Multi-Element Relationships 177
Elements with the negative PC loadings
1
In PC of Table 5.14, the semi-metallic elements of As, Bi and Sb and metallic
1
element of Fe have negative PC loadings indicating that these elements tend to be
incorporated in the atomic structure of other minerals (solid solution). In contrast, positive
weight values of the elements indicate that those elements trend to form independent
sulphide minerals (e.g. pyrite) and sulfosalt minerals (e.g. tetrahedrite) during geochemical
variations evident from the PCs.
5.7.4 Interpretation of PCs
PC
1
In Table 5.14, PC separates the elements of Zn, Pb, S, Ag and Cd with positive
1
PC loadings from the elements of Fe, As, Sb and Bi with negative PC loadings.
1 1
According to Table 5.13, major sphalerite and galena of the Western Mineralisation
occurred during the processes that can be inferred from the PC loadings of the elements.
1
PC
2
In Table 5.14, PC separates the elements of Zn, Cu, Fe, S and Cd with positive
2
PC loadings from the elements of Pb, Ag and As with negative PC loadings. PC has
2 2 2
week positive correlations with Fe and Cu and moderate positive correlation with S, Pb
and Zn.
PC
3
PC is characterised by highly distinct contrasts between Cu and Cd. Cu has the
3
significant positive loading (0.929 in Table 5.14) in PC that means a strong correlation
3
with the geochemical variation evident from PC .
3
PC
4
In Table 5.14, PC was affected dominantly by As content because As is the only
4
element with a highly negative PC loading that has a strong correlation with PC . In
4 4
contrast, the PC loading of S is very low which suggests S content was not effective in the
4
sulphide mineral formation during the geochemical variation evident from PC . This
4
suggests that the lack of S content should have been replaced by excess As. |
ADE | 178 Chapter 5- Multi-Element Relationships
5.7.5 Interpretation of elements within PCs
Zn
Maximum positive PC loading is associated with Zn and this element also has a
1
positive PC loading in contrast with a negative PC loading of Pb (Table 5.14). This is
2 2
consistent with a higher abundance of sphalerite relative to galena in the Western
Mineralisation.
Pb
Major Pb-rich sulphide minerals (such as galena) had to be produced during the
geochemical variation evident from PC . Pb shows smaller PC loading (0.697 in Table
1 1
5.14) relative to that of Zn (0.857 in Table 5.14) that means smaller potential for
mineralisation relative to Zn. PC loading of Pb is a negative value (-0.584 in Table 5.14)
2
that means the removal of Pb from sulphide mineralisation. According to Table 5.14, PC
3
and PC loadings of Pb are so small that this indicates no linear relationship with
4
geochemical variations evident from PC and PC . Therefore, major galena should be
3 4
produced during the processes that can be inferred from the loading of PC , but the amount
1
of galena is smaller than sphalerite in the Western Mineralisation.
S
Table 5.14 shows that the PC loading of S is reduced when comparing PC to PC .
1 3
This indicates the reduction of potential for sulphide mineralisation from PC to PC and
1 3
there is no linear correlation between S content and the geochemical variation of other
elements in PC .
4
Cu
Copper has a minimum PC loading (0.029 in Table 5.14) that suggests Cu
1
concentration is not correlated with PC . Accordingly, there is a lack of incorporation of
1
Cu during the formation of major galena and sphalerite minerals in the Western
Mineralisation. This result is consistent with the mineralogy of the Western Mineralisation
and Cu occurred there in the following form of minerals:
1. Chalcopyrite as major Cu-bearing sulphide mineral,
2. Incorporation of Cu in the atomic structure (solid solution) of sulphide minerals
(e.g. gudmundite, galena, sphalerite and pyrrhotite) and sulfosalt minerals (e.g.
tetrahedrite, tennantite and bournonite), and |
ADE | Chapter 5- Multi-Element Relationships 179
3. Appearance in form of inclusion in other sulphide minerals. Spry, Plimer & Teale
(2008, p.234) explained the presence of lamellar twins and inclusions of chalcopyrite
along the cleavage and twinplanes of galena samples within the Broken Hill orebodies
and they claimed that the inclusions of chalcopyrite have been generated from post-
peak modification to mineral assemblage involving galena and sphalerite.
Fe
Iron has a high negative PC loading (-0.842 in Table 5.14) which indicates a
1
strong negative correlation of Fe with the geochemical variation of PC . Iron in PC has
1 1
strongly concentrated in the atomic structure of major and minor sulphide minerals. This
result of PC is very consistent with the result of a high average atomic percentage of Fe
1
within the atomic structures of major sulphide minerals of the Western Mineralisation (see
the results of Fe concentration in Tables 5.1 and 3.2).
Cd and Ag
In Table 5.14, the PC loadings of Cd and Ag, being 0.677 and 0.511 respectively,
1
show a good positive correlation with PC that suggests the occurrence of minerals
1
containing Cd and Ag resulting from geochemical variation of PC . Cadmium also shows a
1
moderate positive correlation with geochemical variation of elements in PC . In contrast,
2
Ag reveals a strong negative correlation with PC . This indicates a removal of Ag
2
concentration during the geochemical variation evident from PC . In the Western
2
Mineralisation, Cd and Ag contributed mostly to the atomic structure of sphalerite and
galena respectively rather than forming major independent minerals. This may be because
of the low amount of Cd and Ag (Table 3.2).
Bi and Sb
In Table 5.14, Bi and Sb show strong negative correlations with PC and they are
1
incorporated significantly in the atomic lattice of galena (Table 5.1) and other sulphide
minerals of the Western Mineralisation.
As
Arsenic also has a moderate negative PC loading and high negative PC loading
1 4
(Table 5.14). This indicates that during the processes associated with PC and PC ,arsenic
1 4
may be highly concentrated in the atomic structure of sulphide minerals (e.g. galena; Table
5.1). Plimer (2006b) stated that it is possible that As, Mo, W and Au were added to
sulphide rocks during the Olarian Orogeny. |
ADE | 180 Chapter 5- Multi-Element Relationships
5.7.6 Maps of PC loadings
A map of PC loadings visualises distances between elements (points) in ratios to
the two dimensional space of two specific PCs. The maps of PC loadings help us to
understand the following issues:
1. Identification of the relative real distances of elements in different dimensional
spaces,
2. Evaluation of the probability of occurrence of mineral paragenesis, and
3. Identification of the potential mineralisation during the geochemical interaction of
the two PCs.
Similarity of the map of PC loadings to correspondence maps
They both aim to reduce dimensional spaces and chemical complexity. This helps
to better interpret the multi-influences of elements.
Differences between the map of PC loadings and correspondence maps
The map of PC loadings is used to show the relationship of one type of variable
(e.g. elements) within two PC spaces at one time; however, a correspondence map is used
to show the relationships between two different types of variable (e.g. the Broken Hill
orebodies with the elements of a mineral) simultaneously within two dimensional spaces.
Important factors for interpretation of the maps of PC loadings are:
1. The total variance of each map that indicates the degree of total mineralisation
during the effect of geochemical interaction between two PCs,
2. The magnitude value of PC loading for each element that indicates the degree of
potential for mineral formation of the element within the map in comparison with
the other elements, and
3. Distances of elements (points) from each pair of PCs in each map that reveal the
possible mineral paragenesis or occurrence of different minerals during the
geochemical interactions of the two PCs. |
ADE | Chapter 5- Multi-Element Relationships 181
5.7.6.1 Map of PC loadingand PC loading (Figure 5.14)
1 2
Chemical variation
PC loading and PC loading jointly account for 67.3 %11of the total geochemical
1 2
variation in the Western Mineralisation.
Position of important elements relative to PC loading scale
1
By dividing this map into two parts from the zero value of the PC loading scale,
1
the group of elements Fe, Bi, Sb and As lies at the extreme end of the negative scale of the
PC loading and the group of elements Pb, Zn, Cd, S and Ag lies at the extreme end of the
1
positive scale of the PC loading In this map, there is an intense polarization or divergence
1 .
between the two groups of elements on the negative and positive sides of the PC loading
1
scale. This is because of the relatively high distances between the two groups of elements.
PC loading as a chemical discriminator
1
In Figure 5.14, it is obvious that PC loading acts as a good geochemical
1
discriminator between the elements Zn-Pb-Ag-Cd-S and Bi-Sb-Fe-As in the Western
Mineralisation.
Figure 5.14: Map of PC loading, PC loading and the legend of 10 elements.
1 2
11 Calculated by PPV (PC ) + PPV (PC ) from Table 5.13
1 2 |
ADE | 182 Chapter 5- Multi-Element Relationships
Position of important elements in relation to PC loadingscale
2
If Figure 5.14 is divided into two parts from the zero value of the PC loading scale,
2
it shows distinct polarization between the group elements of Pb-Ag at the extreme end of
the negative scale of the PC loading and the group elements of S-Zn-Cd at the extreme
2
end of the positive scale of the PC loading. This result is very consistent with the chemical
2
composition of the sphalerite and galena samples collected from the Western
Mineralisation because the sphalerite samples (Table 5.2) contain a higher average atomic
percentage of Cd and S relative to the galena samples (Table 5.1). In contrast, the galena
samples (Table 5.1) contain more Ag relative to the sphalerite samples (Table 5.2).
The occurrence of arsenopyrite and löllingite12 can be associated with the
geochemical interaction between PC loading and PC loading. However, the abundance of
2 1
these minerals is very low in the Western Mineralisation because PC has only 15.7 %
2
contribution to sulphide mineralisation of the orebody.
5.7.6.2 Map of PC loading and PC loading (Figure 5.15)
1 3
Chemical variation
PC loadingand PC loading account for 64.1 %13 of the total geochemical
1 3
variation.
Position of important elements in relation to PC loadingscale
3
PC loading is characterised by significant loading of Cu, which is positioned at the
3
upper end of the positive scale of the PC loading and to a lesser extent Cd at the lower end
3
of negative scale of the PC loading.
3
Figure 5.15 also shows that the geochemical interaction between PC loading and
3
PC loading can produce arsenopyrite and löllingite. However, PC has only 12.5 %
1 3
contribution to sulphide mineralisation of the orebody.
12 FeAs
2
13 Calculated by PPV (PC ) + PPV (PC ) from Table 5.13
1 3 |
ADE | 184 Chapter 5- Multi-Element Relationships
5.7.6.4 Map of PC loading and PC loading (Figure 5.17)
2 3
Chemical variation
PC loading and PC loading only account for 28.2 %15 of the total geochemical
2 3
variation of the Western Mineralisation.
Figure 5.17: Map of PC loading and PC loading.
2 3
PC loading as a chemical discriminator
2
Based on this map, PC loading again separates the elements of Pb and Ag from the
2
elements of Zn, S and Cd. PC loading appears to act as a discriminator of Cu from other
3
elements.
5.7.6.5 Map of PC loading and PC loading (Figure 5.18)
2 4
Position of important elements in relation to PC scale
2
As shown in Figure 5.14 and 5.17, PC loading in Figure 5.18 also shows the
2
positive loading of Zn as opposed to the negative loading of Pb in relation to the PC
2
loading scale. This model highlights more enrichment of sphalerite relative to galena that is
very consistent with the Western Mineralisation.
15 Calculated by PPV (PC ) + PPV (PC ) from Table 5.13
2 3 |
ADE | Chapter 5- Multi-Element Relationships 185
Paragenesis
In Figure 5.18, the distance between Cu and the group elements of Fe, S, Sb, Zn,
Cd and Bi is small. This indicates that, during the geochemical interaction of PC loading
2
with PC loading, there was potential for occurrence of chalcopyrite, tetrahedrite and
4
gudmundite. However, they are minor minerals in the Western Mineralisation and this
conclusion is consistent with the present interpretation of this map. This is because the map
shows the elements have contributed only 25.3 % of the total chemical variation of the
Western Mineralisation and also that the elements show very weak loadings in this map
(i.e. low potential for occurrence of minerals with those elements).
Figure 5.18: Map of PC loading and PC loading.
2 4
5.7.6.6 Map of PC loading and PC loading (Figure 5.19)
3 4
Chemical variation
PC loading and PC loading account for 22.1%16 of the total geochemical variation
3 4
of the Western Mineralisation.
PC loading and PC loading as chemical discriminators
4 3
In this map, PC loadingseparates As from other elements and PC loading appears
4 3
to be a discriminator of Cu from other elements.
16 Calculated by PPV (PC ) + PPV (PC ) from Table 5.13
3 4 |
ADE | 186 Chapter 5- Multi-Element Relationships
Figure 5.19: Map of PC loading and PC loading.
3 4
5.7.7 Map of PC scores
A map of PC scores visualises the distribution of samples (observations) in ratios of
two dimensional spaces of specific PCs. The projections of samples in different maps that
resulted from two different PCs, constitute the possibility for evaluating the probability
distribution of samples based on the geochemical interaction of the two PCs (Figure 5.20).
The kth PC score of a sample is calculated by Equation (5.1):
10
PC score (PC loading Element concentration ) (5.1)
i k j k j
j1
In Equation (5.1), the PC score is calculated for the ith sample (i =1 to 1,059 in this
data set) and the kth PC (k =1 to 4), and j (j = 1 to 10) is the PC loading and element
concentration respectively listed in Table 5.14. For example, the PC score for PC is
1
calculated as:
PC score = 0.857 × Zn + 0.697 × Pb + 0.029 × Cu - 0.842 × Fe + 0.681 × S + 0.511 ×
i 1
Ag + 0.677 × Cd - 0.549 × As - 0.932 × Sb - 0.936×Bi |
ADE | 188 Chapter 5- Multi-Element Relationships
positive scale of PC score) from Pb- and Ag- rich sulphide samples (at the negative scale
2
of PC score). The distribution of samples in Figure 5.20d does not show a linear
2
relationship relative to PC score and PC score. This indicates that almost all of the
2 3
samples are independent from the two PCs. The data sets of PC scores have been provided
in supplementary file to this thesis.
5.7.8 Biplots of PC loadings and PC scores for 1,059 samples of the Western
Mineralisation
One of the most popular statistical approaches for the visualisation of
compositional data sets in geochemistry is seen in ternary diagrams. It can be used
effectively to evaluate the variability of three element concentrations or three oxide
elements. However, the technique has difficulty in handling more than three components
(Aitchison 1986), such as is the case in this study. For this reason, biplot diagrams are used
for this study instead of ternary diagrams. Biplots (Aitchison & Greenare 2002; Gabriel
1971; Greenacre 2010) can display samples (points), element concentrations (vectors) and
their degrees of correlation in a diagram. It is a very efficient tool to visualise multiple
element concentrations (more than 3 elements) and samples in a low dimensional space.
In a biplot, the lengths and directions of vectors are important for its interpretation.
The cosine of the angle between two vectors approximates the amount of correlation
between the two element concentrations. The length of a vector represents the standard
deviation of the element concentration. A short length of a vector for an element
concentration in a biplot indicates that the element is relatively constant in the data set,
whereas a long one indicates a greater relative variation of the element (Labus 2005). The
1,059 clr-transformed values of this chapter were used for the construction of biplots of 10
element concentrations and 1,059 samples in relation to for PC and PC loadings using
1 2
Minitab software (Figures. 5.21 and 5.22). |
ADE | 190 Chapter 5- Multi-Element Relationships
The distance between two vertices is approximately proportional to the variance of
their log-ratios, ln (X / X). The vertices of Fe, Sb, Bi and As are close to each other which
i j
indicates the geochemical variation of these elements are closely correlated. Figures 5.21
and 5.22 demonstrate the following four groups of correlated elements in association with
their PCs loadings:
1. Group 1: Zn, Cd and S have positive PC and PC loadings,
1 2
2. Group 2: Pb and Ag have positive PC loadings and negative PC loadings,
1 2
3. Group 3: Fe, As, Bi and Sb display clear negative PC loadings, and
1
4. Group 4: Cu shows a clear positive PC loading and very low correlation with other
2
elements.
5.8 Three-dimensional biplots for chemical composition of galena and sphalerite
samples of the Western Mineralisation
3D biplots can also be generated in relation to element concentrations and sample
distribution using the software packages of Matlab and CoDaPack3D for Excel. In these
software packages, it is possible to rotate orthogonally the whole biplot in space and
demonstrate the distribution of samples and elements within different angles. The spatial
rotation helps to separate different distributed samples within elements into suitable angles.
This helps to identify possible mineral generation, mineral alteration and remobilisation of
one or more elements.
For this investigation, 92 galena and 103 sphalerite samples from Kitchen (2001)
and Patchett (2003) were used. Kitchen’s samples were collected from drill cores 4001 and
4002 and Patchett’s samples were collected from drill core 4003. The galena and sphalerite
samples were analysed by measuring the atomic percentage of 11 elements using EMPA.
The measured elements in galena and sphalerite have been shown in Figures 5.23 and 5.25
respectively. The data sets of Kitchen and Patchett have been provided in a supplementary
file to this thesis.
5.8.1 Procedure for preparation of data for the CoDaPack3D
In the CodaPack3D, when introducing the geochemical data, the summation of the
atomic percentage of the elements should be 100. However, the summation does not
always reach 100 percent and calculation is required to find the remaining percentage |
ADE | Chapter 5- Multi-Element Relationships 191
value. That remaining value is calculated by the subtraction of the summation of other
percentage element concentrations from 100. The title row of each column in a standard
spreadsheet of CoDaPack3D was labelled according to the element concentrations and the
remaining percentage value. The atomic percentage of 11 element concentrations and the
remaining percentage value of each sample were inputted in columns of a standard
spreadsheet of CoDaPack3D. This program calculates the clr-transformation of the
constrained geochemical data automatically and generates a 3D biplot.
Current CoDaPack3D does not show visually the three axes of PC , PC and PC in
1 2 3
a 3D biplot (Figures 5.23a, 5.24a, 5.25a and 5.26a) but by programming in Matlab
software can show the PCs scales (Figures 5.23b, 5.24b, 5.25b and 5.26b). It should be
noted that a 3D biplot is not limited only to three PCs in a tetragonal model and a 3D biplot
can be defined and interpreted for more than three PCs, for example in a pentagonal or
hexagonal model.
5.8.2 Galena
Figures 5.23 and 5.24 show the same 3D biplot for galena but viewed from
different angles to give a sense of distance between vectors and show their real lengths.
Samples inside the red line of Figures 5.23a or 5.24a comprise a small number of galena
samples identified by the influence of chemical variation of Fe and Zn. Figures 5.23 and
5.24 show two types of galena generation containing Zn- and Fe-rich galena (samples
inside the red line) and Zn- and Fe-poor galena. The following observations can be drawn
from Figures 5.23 and 5.24 which are consistent with the results from previous analyses:
1. Strong positive correlation among Pb, Bi and S,
2. Strong positive correlation between Zn and Fe,
3. Strong negative correlation of Fe and Zn other eight elements,
4. Moderate positive correlation of Ag, Sb and As,
5. Moderate positive correlation of Co and Cd,
6. Strong negative correlation of Cd with Ag, Sb and As,
7. Strong negative correlation of Co with Ag, Sb and As, and
8. High atomic variation of Zn, Fe and Cd in galena samples. |
ADE | Chapter 5- Multi-Element Relationships 195
5.8.3 Sphalerite
The biplot of the sphalerite samples is given in Figures 5.25 and 5.26. They show
clearly two generations of sphalerite samples in the Western Mineralisation. One
generation of sphalerite samples was strongly affected by the chemical variation of Bi
(samples inside the red region) and they were enriched in Bi. The following observations
can be drawn from Figures 5.25 and 5.26:
1. Strong positive correlation among Zn, Cd, Fe and S,
2. Strong positive correlation among Pb, Co and Cu,
3. Strong positive correlation among Ag and Sb,
4. Strong negative correlation of Bi with the other 9 elements,
5. Strong negative correlation of Ag with Co, Pb and Cu,
6. Strong negative correlation of Sb with Co, Pb and Cu, and
7. High atomic variation of Bi in sphalerite samples.
Again, these observations agree well with the results from previous analyses.
Table 5.16: Summary of decomposition sphalerite samples into seven PCs based on variation
of eleven elements.
PCs PPV PCV
PC 29 29
1
PC 16 45
2
PC 15 60
3
PC 12 72
4
PC 11 83
5
PC 9 92
6
PC 7 99
7
According to Table 5.16, a combination of PC , PC and PC accounts for 60 % of
1 2 3
geochemical variation of sphalerite in the Western Mineralisation. |
ADE | 198 Chapter 5- Multi-Element Relationships
5.9 Summary
In this chapter, simple correspondence analysis was used to provide a picture of the
internal relationships between the chemical composition of the galena samples and the
Broken Hill orebodies and between the chemical composition of the sphalerite samples and
the Broken Hill orebodies. Bivariate and multivariate analyses were calculated for 1,059
assayed samples of each element concentration. In order to generate unconstrained data,
the compositional data of elements were transformed to a clr log-ratio. The clr transformed
data of the elements also showed normal distributions. The following conclusions can be
drawn from the analyses conducted in this chapter:
1. The results of 3D correspondence maps showed that galena samples of the Western
Mineralisation contain higher Bi, Fe, As and Sb, and sphalerite samples of the
Western Mineralisation contain higher Pb in comparison with the other Broken Hill
orebodies,
2. According to bivariate analysis, Zn showed a strong positive correlation with Cd
and high negative correlations with Fe, Sb and Bi. Lead showed a strong positive
correlation with Ag and high negative correlations with Fe, Sb and Bi,
3. Based on multiple linear regressions:
3.1 The three key predictor elements for Pb are Fe, Ag and Bi concentrations with
an Adjusted R Square value of 0.619,
3.2 The three key predictor elements for Zn are Cd, Sb and Ag concentrations with
an Adjusted R Square value of 0.816, and
3.3 This means that chemical variation of Pb and Zn in the Western Mineralisation
can be estimated by chemical variation of Fe, Ag, Bi, Sb and Cd.
4. The cluster algorithm grouped 10 elements based on their similarity. Three groups
were identified: group 1 shows high similarity among the elements of Zn, Pb, S, Ag
and Cd; group 2 contains Cu only; and group 3 shows high similarity among the
elements of Fe, As, Sb and Bi, |
ADE | Chapter 5- Multi-Element Relationships 199
5. PCA was used to reduce the chemical complexity of 10 elements (10 dimensional
spaces or 10 components) into four dimensional spaces or four PCs. The following
four PCs were derived:
5.1: PC : Bi, Sb, Zn, Fe, Pb, S, Cd, As and Ag,
1
5.2: PC : Ag, Pb, S and Cd,
2
5.3: PC : Cu and Cd, and
3
5.4: PC : As.
4
6. The four PCs were considered as major geochemical discriminators for the sulphide
mass of the Western Mineralisation: PC separated Zn and Pb from the other
1
elements, PC separated Zn from Pb, PC discriminated Cu from the other nine
2 3
elements and finally PC act as a good discriminator for As,
4
7. The biplot of PC and PC classified ten elements into the following groups
1 2
(Section 5.7.6):
7.1: Group-1: Zn, Cd and S,
7.2: Group-2: Pb and Ag,
7.3: Group-3: Fe, As, Bi and Sb, and
7.4: Group-4: Cu.
8. The 3D biplot of chemical composition of galena samples of the Western
Mineralisation showed two generations of Zn- and Fe- rich galena and Zn- and Fe-
poor galena samples, and
9. The 3D biplot of chemical composition of sphalerite samples of the Western
Mineralisation revealed two generations of Bi- rich and poor sphalerite samples. |
ADE | CHAPTER 6
Variogram Analysis for the Western Mineralisation
6.1 Introduction
Statistical analysis for variables which are spatially correlated uses geostatistics
rather than classical statistics. The technique uses a model (variogram) that describes the
spatial geological or geophysical continuity of the variables of mineralised zone. The
variogram model can be constructed provided there are sufficient samples available,
generally the case for a mining operation. The geostatistical approach enables the
quantification of structural and random variations of the variables in space, and more
importantly the approach retains the effects of significant anomalous samples and therefore
helps to identify the anomalous locations.
Combining variogram models with techniques, such as kriging or simulation,
geostatistics can then be used to generate the 3D block model for the orebody. Compared
with classical statistics, such as multivariate regression, the block model is a more effective
tool to visualise the continuity and distribution of grade variables in space. In general,
mining engineers’ main interests are to model only economic elements in the
mineralisation (e.g. Pb, Zn and Ag or combination of them) in order to estimate tonnage
and grade of future production. For example, at Broken Hill, uneconomic elements such as
Bi, As, Sb, Fe are usually not considered for any geostatistical analysis unless they are
treated as contaminant elements in the final product (for which the smelter may charge a
penalty).
In this chapter, 136 directional variogram and down-hole variogram models were
calculated for 43 variables (assays, minerals, rock types, magnetic susceptibility, specific
gravity and sulphide textures) measured in the Western Mineralisation. The software used
for these calculations is Geostatistics for Windows (Dowd & Xu 2006), a geostatistical
package developed at The University of Adelaide. The variogram models derived are then
used for the estimation of 43 block models using ordinary kriging. The specific objective
of this chapter is to determine variogram parameters of the 43 measured variables,
including the degree of spatial variability and grade continuity, the directional anisotropy
and the proportion of between the structural and random variations of the variables. |
ADE | 202 Chapter 6-Variogram Analysis
6.2.1 Variogram model-spherical scheme
In minerals applications, the variogram of grade values near the origin (i.e. zero
distance) in general appears to be a linear. It increases with distance and eventually reaches
a stable value (or fluctuating around a stable value) which is termed the sill value of the
variogram. The sill value, in stationary case, is also equal to the total variance. The
distance when the variogram reach the sill value is termed the range of the variogram. The
initial variogram value when h0 [Equation (6.1)] is termed the nugget variance.
The proportion of the nugget variance with the sill value is termed "nugget effect"
(Dowd 2006a, p.81), which together with the slope of the variogram are the two most
significant factors affecting the outcome of the kriging estimation. A variogram model
fitting this type of variogram behaviour is called the spherical model (see the red dashed
curve in Figure 6.1). Spherical model is the most popular variogram model used in
minerals application. In Figure 6.1, three structural components are fitted to achieve the
best-of-fit.
Figure 6.1: An experimental variogram ("+") and a fitted spherical model (red dashed curve)
for Zn concentration of the Western Mineralisation and its variogram parameters.
Formulae used for calculation of the three structural components and the ranges of
influence for a variogram model is given in Table 6.1. |
ADE | Chapter 6-Variogram Analysis 203
Table 6.1: Formulae for calculation of variogram models with three structural components.
γ(h)C C F(h,α )C F(h,α )C F(h,α ) for 0hα
0 1 1 2 2 3 3 1
γ(h)C C F(h,α )C F(h,α )C F(h,α ) for 0hα
0 1 1 2 2 3 3 1
γ(h)C C C F(h,α ) for α hα
0 1 2 2 1 2
γ(h)C C C C F(h,α ) for α hα
0 1 2 3 3 2 3
γ(h)C C C C for hα
0 1 2 3 3
3
3 h 1 h
F(h,a i) 2
α
2
α
i i
where C and a are the structural variance and the corresponding range for the
i i
ith structure and i=1, 2, 3 , C = The nugget variance , C , C , C = The
0 1 2 3
structural variance, C +C +C +C =Total variance or sill value of the
0 1 2 3
variogram, α ,α The range of influence, α The full range of influence
1 2 3
Nugget variance describes random variation of uncertain phenomena at small scale.
Sampling errors and geological discontinuity will also contribute to the value of nugget
variance. A high nugget effect is the case when the nugget variance is greater than 50 % of
the total variance1 (Dominy, Stephenson & Annels 2001). In this case, the application of
geostatistics will not have significant improvement in estimation over classical statistics. In
this application, the nugget effect for all 43 variables (element concentrations, minerals,
rocks and geophysical measurement) are significantly smaller than 50 %.
6.2.2 The range of influence
The range of influence is an indication of the extent of spatial correlations. The
maximum range is identified in a variogram model at the maximum distance when the
variogram value reaches the sill (e.g. a in Figure 6.1). The spatial correlation of the
3
concentration at a distance greater than the maximum range of the variogram model is
considered to be non-existence (Walter, Christensen & Simmelsgaard 2002).
1 Sill value |
ADE | 204 Chapter 6-Variogram Analysis
6.2.3 Advantages of application of geostatistics versus classic statistics
Compared with geostatistics, classical statistics assume spatial independence of
grade values i.e., any spatial correlation is disregarded. The variogram in this case is a
horizontal line (Figure 6.2a) which equals to the total variance of the variable. This type of
variogram model is termed the "pure nugget effect" (Carrasco 2010; Dominy, Stephenson
& Annels 2001) with zero range of correlation. In this case, the search neighbourhood
imposed in geostatistics for block estimation is irrelevant as no correlation is considered at
any scale (Vann, Jackson & Bertoli 2003). In geostatistics, the general appearance of the
variogram is shown in Figure 6.2b. The value of the variogram starts at a lower value and
it will increase gradually with distance until it reaches the sill value, which is the total
variance of the variable. The value of variogram smaller than the total variance indicates
that there is spatial correlation for the distance as variogram is indirectly proportional to
correlation.
Figure 6.2: The change of variance (the red line) versus distance in (a) classic statistics and
in (b) geostatistics.
6.2.4 Variogram calculations
A variogram is directional. In order to calculate variogram at different directions,
the following parameters should be defined:
1. The direction of variogram (azimuth and dip angles, or trend and plunge of the
directional line). The directions of variograms are defined by an azimuth angle that
is measured horizontally clockwise from north (0 to 360 degrees) and a dip angle
that |
ADE | Chapter 6-Variogram Analysis 205
is measured from the horizontal plane (-90 to 90 degrees) as positive (if the dipping
direction is in the positive elevation direction).
2. Conical search angle (0-90 degrees) and maximum search distance. In practice, it
is unlikely pairs of samples will be aligned exactly in the variogram direction. It is
then necessary to determine an approximate tolerance angle for capturing pairs of
samples in a particular direction. This tolerance angle help classify any pairs of
θ
samples within ± either side of a specified direction as being in that direction
2
(Figure 6.3). This angle is termed the angle of regularisation. Maximum search
distance will effectively turn the conical search into a truncated conical search
(Figure 6.3).
Figure 6.3: Conical search volume and effect of direction approximation in a cone.
3. Lag distance for variogram. In Figure 6.3, all sample locations falling within a slice
of width "dh" on the top of the cone are considered to be at a lag of "h" from
sample "X". |
ADE | 206 Chapter 6-Variogram Analysis
6.2.4.1 Down-hole variogram
Down-hole variograms refer to the variograms calculated along each drill hole. As
samples are aligned closely with each drill hole, the variograms calculated in general will
be the best candidates for identifying possible variogram structures. The down-hole
variogram also help derive a more reliable estimate for the nugget variance for the related
three-dimensional variogram model, which is in general difficult based on erratic three-
dimensional experimental variogram (Guibal 2001).
In order to work out variogram in a particular direction closely aligned with the
drill hole direction, drill holes are classified (projected) on cross-sections and directions on
the cross-sectional plane. The average of individual down-hole variograms is calculated for
each specified direction within each specified cross-section and then those directional
variograms are averaged over all cross-sections to determine the global average directional
variograms of the entire mineralised zone or some specified part of it (Dowd 2006b, p 32).
The drilling section of the Western Mineralisation is perpendicular to the strike of the
mineralisation. The alignment of drill cores along drilling section makes easier to calculate
directional variograms with minimum distance and angle approximations. The down-hole
variograms in this case are calculated based on cross-sections perpendicular to the strike
direction of the mineralisation (NNE-SSW).
6.2.4.2 Three-dimensional (3D) variograms in different directions
The ultimate purpose of variogram modelling is to construct the three dimensional
variogram structures that quantify the 3D spatial correlation. The full 3D variogram model
can be constructed based on directional variograms calculated along different directions.
The common representation for a 3D variogram model is using an ellipsoid with different
lengths of axes, representing different variogram ranges in the three main axes: major,
intermediate and minor. Major axis is the direction of longest range (maximum continuity)
in the direction and minor axis is the direction of the shortest range (minimum continuity).
In minerals applications, major axis normally coincides with the strike-plunge direction of
the orebody, intermediate axis with the down-dip direction and minor axis with the
cross-dip direction. This is also the case for the Western Mineralisation based on its 3D
variogram calculations. |
ADE | 210 Chapter 6-Variogram Analysis
Table 6.2: The approximate variogram model of Pb in raw data scale for the strike-plunge
direction resulted from the variogram model of the logarithms of the data.
σ2 C C C 22.910 213010 210010 2252.910 2
Logarithm , Pb 0 1 2
σ2 6.59 (%) 2
Raw data , Pb
C
0, Pb σ2
22.910 2
6.59 (%) 2 0.60 (%) 2
σ2 Raw data , Pb 252.910 2
Logarithm , Pb
C 13010 2
1, Pb σ2 6.59 (%) 2 3.40 (%) 2
σ2 Raw data , Pb 252.910 2
Logarithm , Pb
C 10010 2
2, Pb σ2 6.59 (%) 2 2.62 (%) 2
σ2 Raw data , Pb 252.910 2
Logarithm , Pb
6.3 The strike, plunge and dip of the orebody in the Western Mineralisation
The strike, plunge and dip of the orebody of the Western Mineralisation were
estimated for 3D visualisation of the sulphide sample locations (Figure 2.2), observations
of structural geology and variogram analysis. The primary estimated ranges were:
1. Strike direction of the orebody: between 5º and 25º from north,
2. Plunge of the orebody: between 15º and 35º from horizontal plane, and
3. Dip of the orebody: between 30° and 50° from horizontal plane.
Figure 6.7 shows an average intersection of the mineralisation zone in a couple of
dashed red planes in the Western Mineralisation which was simplified to depict the
possible strike, plunge and dip of the orebody. Therefore, the spatial outline of the orebody
is not a symmetrical plane. In Figure 6.7, plunge and dip are used as a term of structural
geology. In structural geology, plunge is used for lineation (e.g. fold hinges, mineral
lineations, cleavage and bedding intersections) and dip is used for planar features. Plunge
and dip in structural geology always have positive values. More accurate orientation angles
for the orebody of the Western Mineralisation (Figure 6.8) were determined based on
derived directional variogram models for the three perpendicular planes of strike-plunge,
down-dip and cross-dip (Figure 6.9). |
ADE | 212 Chapter 6-Variogram Analysis
On the strike-plunge plane, the variogram ranges construct the ellipse as shown in
Figure 6.9a. The major axis of the ellipse is the strike-direction of the orebody (azimuth
15°) and the minor axis is the dip-direction (285°). In the down-dip plane (Figure 6.9b), the
variogram model will have an ellipse with the major axis representing the strike-direction
of the 3D variogram model and the minor axis of the ellipse is in the intermediate axis.
The intermediate axis of the 3D variogram model in the down-dip direction is worked out
to be 40o. On the cross-dip plane (Figure 6.9c), the major axis of the ellipse is in the
intermediate axis direction of the ellipse and the minor axis represents the cross-dip
variogram range.
Figure 6.9: (a) shows a horizontal plane ellipse that is used for displaying the strike-direction
of the strike-plunge variogram and dip-direction of the down-dip variogram. (b) shows the
vertical plane ellipse for the dip angles of the down-dip (-40°) variogram and strike-direction
of the strike-plunge variogram and (c) displays the vertical plane ellipse for the dip angles of
the cross-dip (50°) and the down-dip (-40°) variograms.
It should be noted that a directional variogram model with an azimuth angle of X°
is identical to the variogram model with the azimuth angle of X°+180°, provided the sign
of the dip angle for the direction is also reversed.
6.4 The use of variogram ranges for the design of the optimal sampling grid
A simple application of the derived variogram ranges is in the design of the optimal
sampling grid which is cost effective. The optimal sampling grid derived based on the
variogram models from the Western Mineralisation can help the design of an optimal |
ADE | Chapter 6-Variogram Analysis 213
sampling grid for similar Zn-Pb-Ag type of mineralisation within the Broken Hill district
or in other areas. Once the full 3D variogram model is constructed, it is possible to
2
calculate the optimal distance between sampling drill holes. As a rule of thumb, of the
3
variogram range is usually considered an appropriate distance to capture the spatial grade
continuity of mineralisation (Flatman & Yfantis 1984, p.346). In practice, it is unlikely
variogram anisotropies will coincide exactly with the coordinate system (easting, northing
and elevation) used and the calculated sampling grid will have to be adjusted accordingly.
The optimal surface geochemical sample spacing for detecting anomalous concentration
and geochemical zonation in the Western Mineralisation are calculated and shown in
Tables 6.3 and 6.4.
Table 6.3: An appropriate surface geochemical sampling grid for Pb, S, Bi, Fe and Zn when
the real dip of orebody is not clear for the Western Mineralisation.
Elements
The full range of influence (metre)
Pb S Bi Fe Zn
The full range of influence at the
strike direction=15° 304.36 227.49 190.97 179.26 149.84
The full range of influence at the
strike direction=105° 151.27 39.31 130.19 84.30 104.09
The full range of influence at the
2
strike direction=15° ×
3 202.91 151.66 127.31 119.51 99.89
The full range of influence at the
2 100.85 26.21 86.79 56.20 69.39
strike direction=105° ×
3
Anisotropy ratios 2.01 5.79 1.47 2.13 1.44
As discussed above, the longer variogram range on the plane is in the strike-plunge
direction and the shorter range is in the cross-dip direction. |
ADE | 214 Chapter 6-Variogram Analysis
Table 6.4: An appropriate surface geochemical sampling grid for Cd, Cu, Sb, As and Ag
when the real dip of orebody is not clear for the Western Mineralisation.
Elements
The full range of influence (metre)
Cd Cu Sb As Ag
The full range of influence at the
strike direction=15° 115.92 100.85 79.00 51.98 33.58
The full range of influence at the
strike direction=105° 84.13 66.08 19.61 15.17 15.63
The full range of influence at the
2
strike direction=15° ×
3 77.28 67.23 52.67 34.65 22.39
The full range of influence at the
2 56.09 44.05 13.07 10.11 10.42
strike direction=105° ×
3
Anisotropy ratios 1.38 1.53 4.03 3.43 2.15
For example, in order to detect the extension of geochemical halo zoning for Zn in
the Western Mineralisation, the optimal surface sampling grid should be about 100 m
(99.89 m in Table 6.3) along the azimuth of 15° and 69 m (69.39 m in Table 6.3) along the
azimuth of 105° (Figure 6.10). Tables 6.3 show that S has the greatest variogram
anisotropy ratio. This indicates that spatial continuity of S concentration in the strike
direction of 105o is 5.75 times that of the strike direction of 15o in the Western
Mineralisation
Figure 6.10: A schematic geochemical sampling grid for detection of Zn concentration. |
ADE | Chapter 6-Variogram Analysis 215
It should be noted that different variogram anisotropies are detected for different
elements in the Western Mineralisation. An overall optimal sampling grid in this case will
be a compromise considering variograms for all elements, if the spatial variations for all
elements are to be appropriately quantified. If all ten elements are considered in this
example, the optimal sampling grid will be 10 m in the strike direction of 105° (the
minimum range for As in Table 6.4) and 22 m in the strike direction of 15° (the minimum
range for Ag in Table 6.4),
6.5 Comparison of variogram parameters of the Western Mineralisation with other
Pb and Zn deposits
One way to characterise the spatial structures and variations of mineralisation is
application of variogram parameters (range of influence, nugget effect and sill values)
derived for the elements concerned. Deposits with more irregular grade variations such as
gold or vein type deposits may have a large nugget effect and a short range of influence.
Relatively uniform deposits such as stratabound sedimentary Pb-Zn mineralisation are
characterised by very low nugget variance and a large variogram range. Figure 6.12
compares published variogram parameters from other types of lead and zinc sulphide
deposits such as Irish, Mississippi Valley-type deposits (MVT), sedimentary exhalative
deposits (Sedex) and vein-type Pb-Zn deposits with variogram parameters of the Western
Mineralisation. |
ADE | 216 Chapter 6-Variogram Analysis
C
Figure 6.12: The nugget effect ( 0 ) versus the full range of variogram for Zn and Pb
Sill
concentrations (modified from Wellmer 1998).
Figure 6.12 shows that the Western Mineralisation is a more continuous
mineralisation and has higher degree of spatial correlation relative to other lead and zinc
sulphide ore deposits. Therefore, the use of geostatistical analysis for the Western
Mineralisation is more appropriate technique in comparison with classic statistical
methods. In Figure 6.12, the Western Mineralisation has a long range of influence and the
nugget effect is only higher than the Mount Isa deposit in Australia. It should be noted that
relative nugget effect is also related to the composite length (size) of core samples. Smaller
nugget effect will be obtained for larger sample size (Guibal 2001).
6.6 Variogram anisotropy of different elements in the Western Mineralisation
Variogram anisotropy reveals different spatial variability of the elements in
different directions. The anisotropy can be represented by an ellipsoid where the major axis
is in the direction of the longest range and the minor axis is in the direction of the shortest
variogram range. In general, the longest variogram range coincides with the strike-plunge
direction of the orebody, the intermediate range with the down-dip direction and the
shortest variogram range with the cross-dip direction. However, this is not necessarily to
be always the case. In the following discussion, the variogram ellipsoids for different
elements are plotted using the following conventions (Figures 6.13 and 6.14): |
ADE | Chapter 6-Variogram Analysis 219
3. b > a > c: the longest range "b" is in the down-dip direction of the orebody and the
shortest range is in the cross-dip direction. Only the element of Sb is under this
category.
Anisotropy ratios can also be calculated for all the elements by Equation (6.3) in
Table 6.5. These ratios can help to analyse the spatial continuity of the elements. For this
exercise, the ratios are calculated for each ellipse of Figure 6.14 by dividing the major
radius of ellipse by its minor radius. For example, the anisotropy ratios of Zn (Figure 6.14)
are calculated in Table 6.5.
Table 6.5: Formula used for calculation of the anisotropy ratios and its results for Zn
concentration of the Western Mineralisation.
Max. radius of the ellipse
Anisotropy ratio of each ellipse (6.3)
Min. radius of the ellipse
a 149.8
At SD ellipse 1.4
b 109.7
a 149.8
At SC ellipse 5.5
c 27.2
b 109.7
At DC ellipse 4
c 27.2
The anisotropy ratios thus measure the ratios of the spatial correlation along the
major radius to the spatial correlation along the minor radius on the corresponding plane.
For instance, in the case of the SD ellipse, the anisotropy ratio of S is 4.6 indicating that
the extent of spatial correlation of S along the major radius with direction of 015° from
north and plunge of 25° is 4.6 times its minor radius with direction of 285° from north and
plunge of 40°. For the SC ellipse, the anisotropy ratios of Pb, Cu, Cd, S, Fe and Zn are
generally high. The highest value of 23 is observed for Pb. For the DC ellipse, the ratios
show high values for Pb, Cu, Cd and Zn. The highest value is 11.53 for Pb in this ellipse.
Bismuth, Sb, As and Ag have lower anisotropy ratios in comparison with those of the other
elements. |
ADE | 224 Chapter 6-Variogram Analysis
Table 6.6: Calculation of the anisotropic ratios 1 and 2 for Pb concentration.
a
15.9
1, Down-dip 0.52
a 30.5
1, Strike -plunge
a
150.7
2, Down-dip 0.49
The anisotropic ratio 1: a 304.3
2, Strike -plunge
a The first range of influence
1
a The second range of influence
2
a
3.3
1, Cross-dip 0.11
a 30.5
1, Strike -plunge
a
13
2, Cross-dip 0.04
The anisotropic ratio 2: a 304.3
2, Strike -plunge
a The first range of influence
1
a The second range of influence
2
6.10 Block Model
6.10.1 Orebody outline
The first step in the construction of block model is to define an orebody wireframe
(skin) which is then filled with blocks that divide up the orebody. The orebody skin
are constructed from orebody outlines defined on cross-sections based on drill hole
projection on the cross-sections. During the 3D wireframe construction process, the
Dijkstra algorithm method was selected in the Geostatistics for Windows as the algorithm
ensure the surface reconstructed is optimal in the sense that the surface area is minimised
(Xu & Dowd 2001).
6.10.2 Kriging parameters
Data search strategy and search parameters are also important for the successful
implementation of a kriging estimation regime. In this research, the largest variogram
range, together with the anisotropic parameters described above, are used to define the data
search neighbourhood for the kriging estimation. For example, 304 m is used to define the
search radius for the estimation of Pb as that is the largest range for the variogram for Pb.
For discrete block representation, 4×4×4 points are used. |
ADE | Chapter 6-Variogram Analysis 225
6.10.3 Block size determination
The use of appropriate block size is important for deriving a suitable block model
to be used. If the block size is too large, the resolution of orebody representation will be
too low, and to the contrary, if the block size is too small, the variation of estimated block
values will be greatly reduced (over-smoothed). The determination of a suitable block size,
however, is not an easy issue. From the geostatistical point of view, a suitable block size is
ultimately determined by the sample spacing. From the mining operation point of view, the
block size ideally should be identical to the actual selective mining unit to be used in the
mining operation. The actual spatial continuity of the grad values also plays a part in the
final decision. In the following section, it will try to find a suitable block size based only
on geostatistics.
Kriging variance in this case can be used as an effective tool to derive a suitable
block size. For smaller block size, correlations between samples and block will be lower
and the kriging variance is expected to be higher. A suitable block size can be found by
examining the variation of kriging variance against different block sizes. As a rule of
thumb, a suitable block size will be one that has the smallest possible size under the
condition that the kriging variance is reasonable compared with larger block sizes. The
results of kriging variances against different block size for three elements are given in
Table 6.7 and Figure 6.17 below. Based on these investigations, the block size of
20 × 20 × 10 m (or the volume of 4000 m3) is considered to be the most suitable.
Table 6.7: The selected discretisation grid, the corresponding volume and the mean value of
kriging variance for three elements of Pb, Zn and Bi.
Discretisation Volume The mean value of kriging variance
grid (m) (m3) Pb (%2) Zn(%2) Bi (ppm2)
5 ×5×10 250 3.49 8.11 951.11
10 ×10×10 1000 2.97 7.16 895.35
15 ×15×10 2250 2.72 6.36 847.79
20 ×20×10 4000 2.36 5.78 810.85
25 ×25×10 6250 2.31 5.32 780.7
30 ×30×10 9000 2.19 5 752.06
40 ×40×10 16000 2.1 4.52 714.48
50 ×50×10 25000 2.05 4.21 679.04 |
ADE | 226 Chapter 6-Variogram Analysis
Figure 6.17: Visualisation of the mean value of kriging variance estimation versus different
block volumes for Zn, Pb and Bi.
It is interesting to note that the average drilling spacing in the Western
Mineralisation is about 50 m and it is unusual for a block model with block size smaller
than half of the drilling spacing. This is only suitable for cases where the variogram shows
a low nugget effect and large correlation range i.e. mineralisation with high grade
continuity, such as the case for the Western Mineralisation. The block size of 20×20×10 m
is also suitable in this case for the identification of geochemical halo pattern, spatial
variation of minerals, rocks and geophysical features which will be discussed in Chapters 7
and 8. The 43 block model as defined will produce in total of 424 horizontal and vertical
cross-sections cutting through the orebody at different elevation and directions. Those
cross-sections will be examined in more detail in Chapters 7 and 8 for spatial variability of
all the 43 variables concerned.
6.10.4 Optimal number of samples for kriging estimation
In general, fewer number of samples used for kriging will produce higher kriging
(estimation) variance than greater number of samples, provided samples are all within the
correlation range to the point to be estimated. However large number of samples will
increase the computation cost and in some cases the improvement is negligible due to the
screen effect of kriging. In this context, the number of samples to be used for kriging can
be optimised. This can also be done by cross-validation. For this study, the cross-
validations for the elements are run using 10, 20, 30, 40, 50, 60 and 70 numbers of
samples. The average estimation errors for different cases are plotted against the number of |
ADE | 228 Chapter 6-Variogram Analysis
interpretation of geological, geochemical and geophysical data and will be used in the next
chapters for kriging estimations.
Ten elements were selected to evaluate their degree of similarity based on their
variogram parameters and their spatial anisotropic characteristics. The result showed that
the 10 elements can be classified in three similar groups, including:
1. Group 1: Zn, Pb, S, Fe, Cu, Cd and Bi,
2. Group 2: Ag and As, and
3. Group 3: Sb.
The variogram parameters for Pb and Zn in the Western Mineralisation were
compared with those of other similar significant Pb-Zn deposits and the result showed that
Pb and Zn concentrations in the orebody of the Western Mineralisation have a higher
degree of spatial correlation or greater degree of continuity. This indicates that application
of a spatial correlation tool, such as geostatistics rather than the classical statistics in this
case is a more appropriate choice for the modelling of the variables.
The variogram ranges of ten elements in the Western Mineralisation were also used
to derive the optimal sampling grid for this mineralisation, which is found to be 22 m in the
strike-plunge direction and 10 m in the cross-dip direction of the orebody. The analysis as
described has not been performed before at Broken Hill or similar types of deposits. The
study is the first to have comprehensive analyses of combined geological, geophysical and
geochemical characteristics for an unmined orebody.
Suitable variogram models for all 43 variables were calculated, modelled and cross-
validated to produce suitable models to be used in the kriging estimation. For a few
minerals, such as pyrite, arsenopyrite and red garnet, appropriate variogram models could
not be produced due to insufficient number of samples.
The kriging parameters for the linear estimation method chosen were also
optimised. The optimal numbers of samples to be used for kriging were found by
examining the kriging variance against the number of samples used. The optimal block size
to be used to construct the block model for the deposit was found to be 20×20×10 m,
which was calculated by examining the variation of kriging variance versus different block
sizes. |
ADE | CHAPTER 7
Spatial Geochemical Models for the Western Mineralisation
7.1 Introduction
The study of spatial models of mineral deposits based on archived data of drill core
from mine sites enables geologists to recognise and evaluate the scale of spatial correlation
of each type of mineralisation using geological, geochemical and geophysical information.
Thus, exploration guidelines for similar deposits can be developed on the base of existing
data and their quantitative statistical interpretation. In spatial geochemical models, element
concentrations are treated as spatial variables i.e. their variations are location dependent. A
spatial geochemical model of an orebody can present significant support to exploration
geochemistry when it is used for identification of the following issues:
1. Geometrical properties of geochemical haloes (e.g. distribution, size, orientation,
shape and dimension),
2. The spatial variability of geochemical haloes with depth in different cross-sections,
3. Separation of threshold1 level from background and anomalous concentrations, and
4. Identification of zonation sequence in different directions.
In this study, Western Mineralisation drill cores provide a valuable opportunity to
evaluate dispersion and zonation of the primary geochemical haloes and their geological
and geophysical associations for this type of Zn and Pb mineralisation. Since the spatial
geochemical model of the Western Mineralisation is derived directly from its mineralised
samples at different depths, it provides useful information for future geochemical survey.
This approach is widely used in mining operations for the estimation of in situ mineral
resource/reserve in relation to grade-tonnage of the orebody. However, it is still a rare
practice to use the spatial models for the appraisal of zonation patterns of the orebody.
More details concerning the geochemical halo zoning can be found in Beus and Grigorian
(1977), Chen, Huang and Liang (2008), Chen and Zhao (1998), Grigorian (1974),
Gundobin (1984), Huang and Zhang (1989), Kashirtseva (1967), Lawrie and Hinman
(1998), Liu and Xu (1995) and Walters (1998).
1 Minimum anomalous value |
ADE | 230 Chapter 7-Spatial Geochemical Models
The specific geochemical characteristics of the Western Mineralisation may be
controlled by its structural environment (dislocations, faults and fractures) and formation
of strike equivalent Broken Hill deposit. However, the different orebodies at the Broken
Hill deposit may be generated and controlled by different geological and geochemical
parameters with different scaling properties. For example, based on this study it is difficult
to define a universal zonation halo system valid for the entire Broken Hill deposit. The
main purposes of spatial geochemical modelling in this chapter are:
1. Construction of cross-sections for evaluating geochemical halo patterns of Pb, Zn,
As, Cu, Fe, S, Sb, Bi, Ag and Cd in different directions,
2. Separation of the concentration range of threshold values from its background and
anomalous levels in the orebody of the Western Mineralisation,
3. Quantitative comparison of the dimensional distribution patterns, orientation and
anisotropies of the 10 geochemical haloes in order to determine zonation sequence
of the orebody, and
4. Identification of pathfinder (indicator) elements associated with Pb and Zn ore of
the Western Mineralisation.
7.2 Construction of cross-sections for evaluating geochemical halo patterns
A zonation of a geochemical halo has a spatial nature and vectorial context that can
be defined by the three following parameters:
1. Dimension (space),
2. Direction, and
3. Element concentration.
The halo zonation can be a distinct spatial representation of the effects of the ore-
bearing solution (Beus & Grigorian 1977) plus any effects of secondary redistribution and
remobilisation (e.g. metamorphism and deformation). In order to study of the geochemical
haloes and the zonation patterns of the steeply dipping mineralised zone of the Western
Mineralisation, the following types of sections (Beus & Grigorian 1977) were constructed
inside the 3D block models of the 10 elements:
1. Transverse sections to show the variation of halo patterns in the horizontal
sections (Figure 7.1), |
ADE | Chapter 7-Spatial Geochemical Models 231
2. Longitudinal sections to show the variation of halo patterns in north-south vertical
sections along the strike of the mineralised zone (Figure 7.2), and
3. Axial sections2 to show the variation of halo patterns along east-west vertical
sections (Figure 7.3).
For identification of transverse zonation, the spatial models of the 10 element
concentrations of the Western Mineralisation were intersected by transverse (horizontal)
directions at an elevation of 10218 m close to the surface and an elevation of 9848 m next
to the bottom of the 3D mineralised sample locations and two cross-sections between them
at 10078 m and at 9958 m (Figure 7.1).
Figure 7.1: The position of four transverse (horizontal) sections (dashed red rectangles) and
locations of the mineralised drill core intersections.
For demonstrating of the longitudinal zonation, 3D block models of the 10 element
concentrations were cut vertically along north-south directions by two cross-sections at
east = 9357 m and east = 9467 m. In general, two longitudinal sections were mapped for
each of the spatial models (Figure 7.2).
2 Vertical zonation |
ADE | 234 Chapter 7-Spatial Geochemical Models
Ziaii 1997; Miesch 1981; Sinclair 1974, 1976; Stanley 1988; Stanley & Sinclair 1989),
fractal concentration-area method (Cheng 1999; Cheng, Agterberg & Ballantyne 1994;
Cheng, Agterberg & Bonham-Carter 1996; Cheng, Xu & Grunsky 2000), the multifractal
inverse distance weighted (Lima et al. 2003), the element concentration-distance method
(Li, Ma & Shi 2003) and finally, spatial statistical methods such as kriging, moving
average procedures and spatial factor analysis (Grunsky & Agterberg 1988).
The spatial methods (geostatistical framework) such as moving averages and
kriging have largely overtaken non-spatial methods because of consideration of sample
size, sample locations, the scale of structural relationship of intrinsic variables and the
degree of spatial continuity of mineralisation as well as their anisotropism.
For determination of local or regional threshold, the following situations can be
considered, depending on the number and location of samples within the mineralisation or
non-mineralisation area and their amount of concentrations:
1. The first situation arises in regional geochemical prospecting for detecting
secondary haloes (e.g. in soil and regolith). In this situation, most often the number
of samples representing the regional background concentration is greater than the
anomalous samples and recognition of a reliable regional anomalous grade is a very
difficult practice. The regional background levels are usually spread broadly over
an area and reflect regional geological processes with a wide-range of correlations.
In this case, it would be necessary to separate the regional threshold concentration
from a large number of background grades and to define this as maximum
deviation from the regional background contents, and
2. Unlike the above situation, when a large number of samples are extracted from a
mineralisation zone at different depths, the local threshold level should be separated
from a large number of local anomalous samples. In this case, the local threshold
level is deduced to be the minimum local anomalous content appearing in a
mineralisation zone and the local anomalous grades are confined to the mineralised
samples with a narrow-range of correlations. For this situation, the application of
the spatial statistical methods is more efficient.
For determination of local threshold in the Western Mineralisation, a similar
concept of concentration-area (Cheng, Agterberg & Ballantyne 1994) was integrated with a |
ADE | Chapter 7-Spatial Geochemical Models 235
3D kriged block model for each element. The combination of concentration-area and 3D
kriged block model provide a very powerful and robust technique for geochemical
anomaly separation and for minimising misclassification of threshold concentrations and
background levels.
7.3.1 Procedure of separating threshold from background in the Geostatistics for
Windows software
Figures 7.4 to 7.7 show 10 geochemical haloes of the Western Mineralisation in
different sections with a colour index distinguishing background level and threshold grade.
The method used for detection of threshold level relies on adjusting the colour index of the
Geostatistics for Windows software between minimum concentration (blue area) and a
relative maximum concentration (red area) for each of the 10 elements. In this method, the
relative maximum concentration of each element is changed manually in the colour index
until the red area becomes the largest area (Figures 7.4 to 7.7). In this situation, a slightly
increase or decrease of the relative maximum concentration causes an extreme reduction of
the red area. The largest red area for each of the 10 elements was obtained from
implementation of the above procedure at eight different cross-sections to identify the
commonest threshold level among them.
In colour indices of Figures 7.4 to 7.7, the minimum concentration of elements are
not zero except for Pb, Zn and Cu in the Western Mineralisation and this suggests the
elements will have larger dispersal haloes if geochemical sampling or the drilling network
spread is broader in the vicinity of the Western Mineralisation. Although the local
threshold level can be specified to the value of red colour of each element in Figures 7.4 to
7.7; however, because the regional threshold concentration is always lower than the local
threshold concentration, so a range of concentrations between green and red (in colour
index of Figures 7.4 to 7.7) were considered arbitrarily as the threshold concentrations
range for each element, rather than one specific concentration. |
ADE | 240 Chapter 7-Spatial Geochemical Models
The geochemical haloes in Figure 7.6 are characterised by an approximately 40°
dip toward the west. Figure 7.7 show that the geochemical haloes have a southward-dip of
about 25°. Although all the 10 geochemical haloes of the Western Mineralisation
are related to common geological features, geochemical environment, structure and
lithostratigraphy, they delineated various distinct intensifications and expansion dispersal
halo patterns with changes of depth and distance (Figures 7.4 to 7.7).
Antimony and Bi delineate maximum and most pronounced geochemical haloes in
all cross-sections. In addition, the orientation and distribution shape of Sb and Bi haloes
display a good conformity with the shape of Pb and Zn haloes. Therefore, they can be
considered as possible pathfinder elements for exploration of Pb and Zn in the Western
Mineralisation and similar types of mineralisation. Although there is a loose correlation
between lode horizon rocks (quartz-gahnite, quartz-garnet, plumbian orthoclase,
tourmalinite etc), such a correlation could not be determined in this statistical study. These
lode horizon rocks are commonly interpreted as proximal to sulphides and their presence
demonstrates a near miss. However, this may be flawed and the use of predictor elements
such as Sb and Bi may be more fruitful.
7.4 Quantitative comparison of the geometrical characteristics of the geochemical
halo patterns at different cross-sections of the Western Mineralisation
The geometrical dimensions of the 10 analysed elements within the Western
Mineralisation are distinctive and can be compared quantitatively with each other. For this
purpose, the maximum width and maximum length of each geochemical halo were
measured and their anisotropy ratios were calculated for each cross-section (Figures 7.4 to
7.7). The anisotropy ratio for each geochemical halo was calculated from the ratio of the
maximum length of the geochemical halo to its maximum width. The maximum length and
maximum width were measured in that part of the threshold ranges of each element that
was marked by colours in the range from green to red.
In Figures 7.4 to 7.7, a few geochemical haloes such as As and Ag display
discontinuous dispersal haloes in their images. In these cases, the maximum length of their
haloes was measured in exactly the same way as continuous geochemical haloes regardless
of the gaps in their haloes. This is mostly because the need to understand the maximum |
ADE | 242 Chapter 7-Spatial Geochemical Models
Table 7.1: Maximum lengths, maximum widths and anisotropy ratios on the transverse
sections at different elevations (Figures 7.4 and 7.5).
Elevations Transverse sections Length (m) Width (m) Anisotropy ratio
Sb 900 300 3.00
Bi 855 240 3.56
Pb 780 165 4.73
Zn 600 165 3.64
10218 m Cu 585 120 4.88
Cd 510 105 4.86
Fe 495 120 4.13
S 495 135 3.67
Ag 450 67.5 6.67
As 435 75 5.80
Sb 1050 375 2.80
Pb 990 180 5.50
Bi 960 300 3.20
S 840 180 4.67
10078 m Zn 840 180 4.67
Fe 840 135 6.22
Cu 750 135 5.56
As 660 135 4.89
Ag 615 135 4.56
Cd 585 150 3.90
Sb 990 360 2.75
Bi 975 285 3.42
Pb 945 165 5.73
Zn 855 180 4.75
9958 m Fe 780 165 4.73
Cd 765 142.5 5.37
Cu 765 135 5.67
S 750 165 4.55
As 630 120 5.25
Ag 630 105 6.00
Sb 840 300 2.80
Bi 795 255 3.12
Pb 735 195 3.77
Zn 360 157.5 2.29
9848 m Fe 315 142.5 2.21
Cu 315 120 2.63
S 300 135 2.22
Ag 255 78 3.27
As 240 45 5.33
Cd No halo No halo No halo |
ADE | Chapter 7-Spatial Geochemical Models 243
Table 7.2: The sequence of geochemical haloes based on their maximum lengths, maximum
widths and anisotropy ratios resulted from Table 7.1.
Elevation Maximum lengths
10218 m Sb > Bi > Pb > Zn > Cu > Cd > Fe = S > Ag > As
10078 m Sb > Pb > Bi > S = Zn = Fe > Cu > As > Ag > Cd
9958 m Sb > Bi > Pb > Zn > Fe > Cd = Cu > S > As = Ag
9848 m Sb > Bi > Pb > Zn > Fe = Cu > S > Ag > As
Elevation Maximum widths
10218 m Sb >Bi > Pb = Zn > S > Cu = Fe > Cd > As > Ag
10078 m Sb > Bi > Pb = Zn = S > Cd > Fe = Cu = As = Ag
9958 m Sb > Bi > Zn > Pb = Fe = S > Cd > Cu > As > Ag
9848 m Sb > Bi > Pb > Zn > Fe > S > Cu > Ag > As
Elevation Anisotropy ratios
10218 m Ag > As > Cu > Cd > Pb > Fe > S > Zn > Bi > Sb
10078 m Fe > Cu > Pb > As > S = Zn > Ag > Cd > Bi > Sb
9958 m Ag > Pb > Cu > Cd > As > Zn > Fe > S > Bi > Sb
9848 m As > Pb > Ag > Bi > Sb > Cu > Zn > S > Fe
Figure 7.8 shows the results of Tables 7.1 to 7.2.
Maximum length
According to Figures 7.8a, b, c, d, group (i) includes elements of Sb, Bi and Pb
with greater lengths than groups (ii) and (iii). Group (ii) consists of Zn, Cu, S and Fe with
greater lengths than group (iii) which contains As and Ag. Apart from Figure 7.8b, Cd can
be attributed to group (ii).
Maximum width
According to Figures 7.8e, f, g, h, elements of group (i) have greater widths and
wider distribution relative to the elements of group (ii).
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ADE | 244 Chapter 7-Spatial Geochemical Models
The anisotropy ratios
The anisotropy ratios in Figures 7.8i, j, k, l compare the amount of dispersion of
each element in two directions. In Figures 7.8i, j, k, l, Sb and Bi have relatively constant
anisotropy ratios at four elevations. The anisotropy ratio of Sb varies between 2.75 and 3
and for Bi between 3.12 and 3.56. Accordingly, Sb and Bi are showing very low
anisotropy ratios at all elevations and this highlights their greater dispersion within and
around the Western Mineralisation in all directions and depths relative to other elements.
At elevation 9848 m, Pb, Zn, Cu, S, Fe and Ag show a much lower anisotropy ratio relative
to other elevations. This is because the maximum lengths of geochemical haloes are highly
reduced at this depth while their maximum widths only vary a little.
Pathfinder elements
In Figures 7.8a, c, d, e, f, g, h, at all elevations, Sb and Bi display a greater length
and width relative to Pb and Zn. At elevation 10078 m (Figures 7.8b and 7.8f), Sb shows
higher length and width relative to Pb and Zn and Bi larger dispersion than Zn; however, in
Figure 7.8b, Bi shows shorter length relative to Pb.
According to Figures 7.8a to 7.8h, Sb and Bi can be considered as geochemical
pathfinders for the Western Mineralisation and similar Pb and Zn ores. By contrast, the
amount of length and width of other elements is between moderate and small and they
show shorter dispersion in comparison with haloes of Pb and Zn. This situation reduces
appreciably their effectiveness and the reliability of their applications as geochemical
pathfinders of the respective type of mineralisation. The threshold concentrations of Bi
within the mineralisation zone in the Western Mineralisation are estimated to be between 3
and 5 ppm and for Sb, a range between 5.23 and 10 ppm is suggested. Figures 7.8a to 7.8h
suggest that in lithogeochemical surveys of Pb and Zn mineralisation targets similar to the
Western Mineralisation, the priority should be given to detecting threshold content of Sb
and Bi or additive of Sb and Bi (Sb+ Bi) or composite (multiplicative) haloes (Sb × Bi) in
surface sampling. |
ADE | 246 Chapter 7-Spatial Geochemical Models
The composite and additive haloes intensify the extent of geochemical haloes and
present closer correlations with the structure of the mineralisation relative to monoelement
haloes. The application of multi-element haloes is more efficient in the mapping of weak
geochemical anomalies particularly, in superficial geochemical fingerprints (Beus &
Grigorian 1977). The multi-element haloes are more robust against random and analytical
sampling errors and improve the contrast of halo zoning reliability and the geochemical
interpretation (Beus & Grigorian 1977). Another important exploration guide for Western
Mineralisation type ore is Sb and Bi in the sequence of transverse zonation.
7.4.2 Geometrical characteristics of the axial zoning haloes
Table 7.3: Maximum lengths, maximum widths and anisotropy ratios on the E-W axial
sections at N = 2109 m and N = 1639 m (Figure 7.6).
Anisotropy
North E-W axial sections Length (m) Width (m)
ratio
Sb 630 330 1.91
Bi 630 240 2.63
Pb 615 135 4.56
Zn 525 135 3.89
Cu 480 105 4.57
2109 m S 465 135 3.44
Fe 465 120 3.88
Cd 435 105 4.14
Ag 345 105 3.29
As 330 90 3.67
Bi 600 240 2.50
Sb 570 300 1.90
Pb 555 180 3.08
Zn 420 150 2.80
S 360 150 2.40
1639 m Cu 315 105 3.00
Fe 315 135 2.33
As 195 60 3.25
Cd 180 60 3.00
Ag 180 90 2.00 |
ADE | Chapter 7-Spatial Geochemical Models 247
Table 7.4: The sequence of geochemical haloes based on maximum lengths, maximum widths
and anisotropy ratios resulted from Table 7.3.
North Maximum lengths
2109 m Sb = Bi > Pb > Zn > Cu > S = Fe > Cd > Ag > As
1639 m Bi > Sb > Pb > Zn > S > Cu = Fe > As > Cd > Ag
North Maximum widths
2109 m Sb > Bi > Pb = Zn = S > Fe > Cu = Cd =Ag > As
1639 m Sb > Bi > Pb > Zn = S > Fe > Cu > Ag > As = Cd
North Anisotropy ratios
2109 m Cu > Pb > Cd > Zn > Fe > As > S > Ag > Bi > Sb
1639 m As > Pb > Cu > Cd > Zn > Bi > S > Fe > Ag > Sb
Figure 7.9 show the results of Tables 7.3 and 7.4.
Maximum lengths
In Figures 7.9a and 7.9b, group (i) comprises Sb, Bi and Pb with greater lengths
than groups (ii) and (iii). Group (ii) contains Zn, Cu, S and Fe with greater lengths than
group (iii) which consists of As and Ag. Cadmium can be attributed to either group (ii) in
Figure 7.9a or group (iii) in Figure 7.9b.
Maximum widths
In Figures 7.9c and 7.9d, group (i) includes Sb and Bi with greater widths than
group (ii).
Anisotropy ratios
Figures 7.9e and 7.9f show that the anisotropy ratios of Sb and Bi are lower than
other elements. Hence, the anisotropic ratio of Sb is 1.90 and for Bi, the anisotropy ratios
vary between 2.50 and 2.63. This means distribution of Sb and Bi occurs more easily and
is larger than the other eight elements inside and around the mineralisation zone in the
Western Mineralisation.
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ADE | Chapter 7-Spatial Geochemical Models 249
7.4.3 Geometrical characteristics of the longitudinal zoning haloes
Table 7.5: Maximum lengths, maximum widths and anisotropy ratios on the N-S longitudinal
sections at E = 9467 m and E = 9357 m (Figure 7.7).
East N-S longitudinal sections Length (m) Width (m) Anisotropy ratio
Sb 1100 440 2.50
Bi 1100 360 3.06
Pb 1060 200 5.30
Zn 1000 200 5.00
9467 m S 840 220 3.82
Cu 840 140 6.00
Fe 840 200 4.20
Cd 680 160 4.25
As 660 100 6.60
Ag 660 100 6.60
Sb 1120 480 2.33
Bi 1080 340 3.18
Pb 1080 260 4.15
Zn 1000 200 5.00
9357 m Cu 960 140 6.86
Fe 940 220 4.27
S 940 280 3.36
Cd 880 120 7.33
As 640 100 6.40
Ag 600 100 6.00
Table 7.6: The sequence of geochemical haloes based on maximum lengths, maximum widths
and anisotropy ratios resulted from Table 7.5.
East Maximum lengths
9467 m Sb = Bi > Pb > Zn > S = Cu = Fe > Cd > As = Ag
9357 m Sb > Bi = Pb > Zn > Cu > Fe = S > Cd > As > Ag
East Maximum widths
9467 m Sb > Bi > S > Pb = Zn = Fe > Cd > Cu > As = Ag
9357 m Sb > Bi > S > Pb > Fe > Zn > Cu > Cd > As = Ag
East Anisotropy ratios
9467 m As = Ag > Cu > Pb > Zn > Cd > Fe > S > Bi > Sb
9357 m Cd > Cu > As > Ag > Zn > Fe > Pb > S > Bi > Sb
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ADE | 250 Chapter 7-Spatial Geochemical Models
Figure 7.10 shows the results of Tables 7.5 and 7.6.
Maximum lengths
In Figures 7.10a and 7.10b, group (i) includes Sb, Bi, Pb and Zn with greater
lengths relative to groups (ii) and (iii). Group (ii) contains Cu, S and Fe with greater
lengths than group (iii) which consists of As and Ag. Cadmium can be attributed to either
group (ii) in Figure 7.10a or group (iii) in Figure 7.10b.
Maximum widths
In Figures 7.10c and 7.10d, group (i) includes Sb and Bi with greater widths
relative to groups (ii) and (iii). Group (ii) encompasses Pb, Zn, Cu, S and Fe with greater
widths than group (iii) which consists of As and Ag. Cadmium can be attributed to either
group (ii) in Figure 7.10c or the group (iii) in Figure 7.10d.
Anisotropy ratios
The dispersal elements (Sb and Bi) show very low anisotropy ratios in comparison
with other dispersal elements (Figures 7.10e and 7.10f) thus, indicating that the elements’
distribution is widespread within the mineralisation zone. The anisotropy ratios of Sb range
between 2.33 and 2.5 and, for Bi, vary between 3.06 and 3.18. |
ADE | 252 Chapter 7-Spatial Geochemical Models
7.5 Evaluation of similarity levels among the geometrical patterns of haloes
Although the geometrical similarities of the geochemical haloes can be identified
visually in Figures 7.4 to 7.7, one of the useful quantitative methods for identification of
the similarity level is cluster analysis. The maximum lengths and widths of all geochemical
haloes within all corresponding sections were used as entry data for the cluster analysis
(Tables 7.1, 7.3 and 7.5). The cluster algorithm in Figure 7.11 classified the geochemical
haloes into a number of groups to ensure that the similarity of haloes based on maximum
length and maximum width inside each group is as greater as possible, while at the same
time within the groups, the differences are as large as possible. The method of average
linkage and correlation coefficient distance was used for amalgamation steps of the cluster
algorithm using Minitab software.
Figure 7.11 shows the amount of similarities among the spatial distribution of
geochemical haloes in the Western Mineralisation. For example, S and Fe show very
similar dispersal shape, orientation and dimension in 8 different cross-sections (Figures 7.4
to 7.7) and they show maximum similarity level in Figure 7.11 with 99.89 % as well.
Figure 7.11: The percent of similarity among 10 elements based on the maximum lengths
and the maximum widths of their geochemical haloes. |
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