Dunn Colin E. Biogeochemistry in Mineral Exploration

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Univariate statistics

Univariate statistical analysis explores e ach variable in a data set by examining

the range of values and the central tendency of the values. One of the simplest to

start with is the histogram, which is very easily a nd quickly plotted by, for example,

Excel. In order to comprehend the structure of a database, it is necessary to ex-

amine frequency distributions and cumulative frequencies, as well as some basic

statistics that include calculation of maximum, minimum, mean, standard deviation

and percentile values. Detailed accounts of cumulative frequencies and probability

plots are provided by Sinclair (1976) and as a computer programme by Stanley

(1988).

The median (50th percentile) of the data for each element provides a useful

estimation of ‘background’ concentrations – i.e., the normal levels found in a par-

ticular area or on a particular geological substrate. Table 10-I shows a typical set

of basic statistical parameters that were calculated from a suite of 455 samples of

Douglas-ﬁr outer bark during a survey in southern British Columbia. The software

programme SPSS was used to make these calculations.

The example in Table 10-I shows a selection of percentile values, with the 98th

percentile of the dataset as the highest percentile calculated. For the 455 samples in

this dataset, that repres ents only 9 samples with concentrations higher than the 98th

percentile (i.e., 2% of the 455 samples in the survey). For a dataset of this size the

98th percentile is an appropriate maximum percentile because of the smal l number of

samples that it represents. For larger datasets (>1000) the 99th percentile can be

of relevance. The software programme provides frequency distribution plots and

permits the calculation of any number of percentiles, depending on the degree of

interrogation of the dataset that is required and the precision of the analytical data.

If there is poor precision, then the subdivision into narrow percentile ranges becomes

meaningless. For data with good precision at low con centrations, it may sometimes

be of use to interrogate the data structure of values below the median in order to set

contour values for subsequent plotting of the data at, say, the 10th and 25th per-

centile values – or any preferred combination. It should be remembered that in

geochemistry in general, negative anomalies might often be of use in understanding

geochemical patterns, because zones of element depletion may point toward adjacent

zones of enrichment derived from the depletion. This remains true for biogeochemical

datasets.

An effective method of viewing data other than by absolute values is as a response

ratio, which is the ratio of the concentration in a sample to the background value for

each elem ent. This is especially useful for comparing concentrations among different

tissue types, different specie s or with other sample media. By this method all sets of

results from different media are levelled to a common baseline for inter-compa rison.

For example, a response ratio of unity indicates a sample concentration at the me-

dian (50th percentile) of the dataset. A response ratio of three indicates a concen-

tration of three times the median, regardless of the ab solute value.

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Data Handling and Analysis

TABLE 10-I

Univariate statistics calculated for a set of 455 Douglas-ﬁr outer bark samples. Concentrations in dry material determined by ICP-MS on a

nitric acid/aqua regia digestion. Values below detection expressed as half the detection limit (see table 7-III)

N Mean Standard

Deviation

Minimum Percentiles Maximum

50 70 80 90 95 98

Ag (ppb) 455 7.5 3.3 2 7 9 9.8 11 13 16 43

Al (%) 455 0.035 0.014 0.005 0.03 0.04 0.05 0.05 0.06 0.07 0.1

As (ppm) 455 1.4 0.76 0.4 1.3 1.5 1.8 2.3 2.9 3.5 7.6

Au (ppb) 455 0.26 0.5 0.1 0.2 0.3 0.3 0.4 0.5 0.9 9.2

B (ppm) 455 6.2 2.3 2 6 7 8 9 10 13 19

Ba (ppm) 455 107 51 22 100 127 144 168 195 258 336

Bi (ppm) 455 0.01 0.004 0.01 0.01 0.01 0.01 0.01 0.02 0.03 0.03

Ca (%) 455 0.77 0.23 0.28 0.74 0.88 0.96 1.08 1.192 1.298 1.7

Cd (ppm) 455 0.31 0.15 0.05 0.28 0.36 0.41 0.50 0.60 0.78 1.08

Co (ppm) 455 0.21 0.08 0.04 0.20 0.24 0.28 0.31 0.35 0.41 0.59

Cr (ppm) 455 2.97 0.8 1.70 2.90 3.20 3.50 4.00 4.40 4.99 8.4

Cs (ppm) 455 0.033 0.02 0.003 0.029 0.039 0.046 0.057 0.067 0.079 0.108

Cu (ppm) 455 8.0 1.4 4.2 7.9 8.7 9.0 9.8 10.4 11.2 13.0

Fe (%) 455 0.036 0.017 0.005 0.033 0.043 0.052 0.06 0.069 0.084 0.1

Ga (ppm) 455 0.1 0.04 0.05 0.1 0.1 0.1 0.1 0.2 0.2 0.3

Hg (ppb) 455 152 61 27 143 177 198 235 276 306 365

K (%) 455 0.093 0.03 0.03 0.09 0.1 0.11 0.13 0.15 0.179 0.25

La (ppm) 455 0.41 0.19 0.06 0.37 0.48 0.57 0.66 0.77 0.93 1.18

Mg (%) 455 0.028 0.008 0.011 0.027 0.031 0.034 0.038 0.042 0.049 0.074

Mn (ppm) 455 120 48 25 114 140 154 184 211 235 376

Mo (ppm) 455 0.10 0.04 0.02 0.09 0.11 0.12 0.14 0.16 0.19 0.29

Na (%) 455 0.003 0.002 0.001 0.003 0.004 0.005 0.006 0.007 0.008 0.021

Continued

333Biogeochemistry in Mineral Exploration

TABLE 10-I Continued

N Mean Standard

Deviation

Minimum Percentiles Maximum

50 70 80 90 95 98

Ni (ppm) 455 1.05 0.7 0.05 1 1.3 1.5 1.9 2.4 2.7 4.6

P (%) 455 0.031 0.007 0.017 0.031 0.035 0.037 0.041 0.044 0.047 0.058

Pb (ppm) 455 5.8 2.7 0.7 5.4 6.7 8.1 9.5 10.9 12.5 18.2

S (%) 455 0.04 0.02 0.01 0.04 0.05 0.05 0.07 0.082 0.1 0.15

Sb (ppm) 455 0.07 0.04 0.01 0.06 0.08 0.1 0.12 0.14 0.16 0.21

Sc (ppm) 455 0.17 0.06 0.05 0.2 0.2 0.2 0.2 0.3 0.3 0.4

Se (ppm) 455 0.16 0.06 0.05 0.2 0.2 0.2 0.2 0.22 0.3 0.4

Sr (ppm) 455 47 18 13 46 55 62 72 81 89 113

Te (ppm) 455 0.01 0.004 0.01 0.01 0.01 0.01 0.01 0.02 0.03 0.04

Th (ppm) 455 0.05 0.04 0.01 0.05 0.06 0.07 0.09 0.1 0.12 0.55

Ti (ppm) 455 20 10 3 18 24 28 34 41 49 58

Tl (ppm) 455 0.01 0.001 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02

U (ppm) 455 0.015 0.01 0.005 0.01 0.02 0.02 0.03 0.03 0.04 0.15

V (ppm) 455 1.5 0.6 1 1 2 2 2 3 3 3

W (ppm) 455 0.05 0 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.1

Zn (ppm) 455 39 12 12 39 45 50 55 61 69 77

334 Data Handling and Analysis

Bivariate statistics

Bivariate statistics are procedures used to describe the relationship between two

variables, examining primarily the extent to which they co-vary. ‘X–Y’ plots (‘scat-

terplots’) provide a rapid and simple view of the relationship between two variables,

and most software programmes (including Excel) permit rapid calculation and

insertion of a trend line along with its regression equation. Scatterplots should be

constructed when the relationship between two variables is of interest, because sta-

tistical summaries are not an adequate substitute for a visual appraisal of relationships.

Brooks (1982) shows how a regression line can be ﬁtted to a series of points on a

graph. He works through the mathematics of calculating a regression line for a plot

of Ni concentrations in plant ash as a function of the Ni content in the soil, and the

subsequent calculation of a reduced major axis. He shows, also, the calculations for

the Pearson product moment correlation coefﬁcient (r). This coefﬁcient quantiﬁes

how good the linear relationship is at equating, say, the Ni content of a plant with

respect to the Ni content of the underlying soil. Correlation coefﬁcient matrices

provide a quick evaluation of the relationships between each pair of elements

obtained from a multi-element analytical package. However, to determine the multi-

element relationship among all of the elements, a multivariate statistical technique

needs to be applied.

Multivariate analysis

Multivariate statistics are procedures used to describe the relationship between

three or more variables. In the case of geochemical data in general, the objective is to

elucidate ‘hidden’ (i.e., subtle and not apparent) relat ionships in a dataset, which may

assist in deﬁning spatially related associations derived from concealed mineralization.

In the case of biogeochemical datasets, a multivariate analysis can help to isolate

those elements, or that portion of an element content that can be ascribed to plant

nutrition from elements derived from a mineralized source. For example, Cu is an

essential element, so some of the Cu content of plant tissues is directly related to the

metabolic processes that result in Cu uptake and the health of the plant. However,

plants growing in the vicinity of a Cu deposit may absorb greater quantities of Cu,

and a part of that Cu concentration may be attributable to mineralization. A mul-

tivariate analysis may therefore indicate, for example, a Cu, Mo, B, Ca, K association

(i.e., a nutritional factor) separate from a Cu, Mo, Au, As, U association that is

derived from a concealed mineralized porphyry deposit. Factor analysis is a useful tool

for separating out these associations.

At the outset, it must be realized that a basic assumption of multivariate methods

is that the data are valid (i.e., the analytical precision is good). It should also be

realized that multi-element analytical data have variable precision, and so the appli-

cation of any multivariate statistical procedure should be entered into with caution.

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These methods do not use the same logic of statistical inference that dependence

methods do, and there are no robust measures that can overcome problems in the data.

So, multivariate methods are only as good as the input. When using statistical software

packages on a dataset, it is as well to ﬁrst test the default settings, and preferably

undertake a data analysis in two or more ways to see if the results are consistent. If

they are, there is a strong underlying structure in the data and the patterns are robust.

If not, it is advisable to discuss the methods with someone knowledgeable in these

techniques, because it is tempting to believe the output and rely on what may be false

assumptions.

Heydorn (2005) provides an up-to-date overview of exploratory multivariate

analysis of soil and plant multi-element data. He endorses the caveat in the previous

paragraph by stating that it is

absolutely necessary that proper mathematical and statistical techniques be applied to

scientiﬁc multivariate data to extract reliable information and to avoid drawing unjustiﬁed

conclusions.

In many respects plant systems are extra ordinarily complex, and with an ever-

increasing number of elements derived from the systematic chemical analysis of plant

tissues, it becomes a formidable task to establish the multi-element relationships that

occur within and among plants. Multivariate analysis is, therefore, becoming an

increasingly important tool in helping to sort out these interaction s and their sig-

nificance. From the perspective of biogeochemical exploration, the ultimate objective

is to isolate those factors that are simply a reﬂection of intra-plant processes from

those that are directly related to mineral deposits. Elements required for the ‘organic’

(plant) processes need isolating from the inorganic components that the geologist

seeks in the quest for deﬁning the location and extent of concealed mineralization.

There are several basic multivariate methods that are used in data analysis:



cluster analysis,



discriminant analysis (also referred to as Linear discriminant analysis),



factor analysis, and



principal components analysis (PCA – analogous to principal components analysis

is metric multidimensional scaling).

The ﬁrst two techniques seek groups of variables that can be extracted as separate

and significant entities from a seemingly homogeneous dataset. Factor analysis and

PCA are closely related, with factor analysis being the more complex and sometimes

the more difﬁcul t to interpret, although both PCA and factor analysis methods

commonly give similar results.

Most commercially available statistical analysis software programmes can perform

all these multivariate analyses, with adjustments that can be made for methods to

extract the desired output. The user can select the preferred technique. Rather than

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Data Handling and Analysis

elaborate on each technique, only factor analysis is described here, because in many

situations it provides the most useful and relevant information for biogeochemical

datasets.

The starting point for factor analysis is a spreadsheet of data (e.g., Excel) with

the data all in a numeric (rather than text) format. The spreadsheet is imported into

the statistical analysis software programme and ‘factor analysis’ is selected from the

drop-down menu. The range of elements (with any quantiﬁable ﬁeld parameters) to

be incorporated into the factor analysis is selected and the command ‘extract’ is

given. There is then a cho ice of methods that can be made, of whi ch the default is

usually ‘Principal Components’ and the defaul t matrix for analysis is the correlation

matrix. In factor analysis, vector ‘eigenvalues’ are calculated and for most purposes a

value of one is an appropriate cut-off level. The programme needs to know how

many iterations of calculations are required to generate the factor matrix. The

default value of 25 is usually adequate, but for large datasets a higher value may be

required to bring convergence to the dataset.

Factor analysis is used to explain variability among observed random variables in

terms of fewer unobserved random variables called factors. The observed variables

are linear combinations of the factors, plus error terms, and help to provide insight

to the structure of large amounts of data. The process of factor analysis can be

visualized as examining a dataset in n-dimensional space and inserting axes (typically

orthogonal) into the data matrix to optimize the ﬁt and thereby explain the variance

in the data. This generates coordinates (from 1 to +1) with loadings according to

the strength of correlation. The ﬁrst iteration extracts the factor that explains the

greatest propo rtion of the data variability, expressed as a percentage and represents

a list of coordinates in factor (or component) 1. Once this variability has been

extracted from the dataset, a new calculation is automatically generated to extract

the combination of elements that accounts for the next largest percentage of the data

variability. Commonly, about 7–10 factors will be extracted by this technique and

these usually account for 70–90% of the data variability. The sort of information

gleaned from this process may be isolation of elements related to plant structure (e.g.

Ca, K, Zn, Cu) from those related to plant nutrition (e.g., B, Mo, P), and perhaps

data related to mineralization (e.g., Au, As, Sb, Bi, Ag, Hg, U), a carbonate-rich

substrate (Ca, Sr, Ba, Mg), or maﬁc bedrock (Ni, Co, Cr, Mg). There is commonly,

too, a significant factor involving Fe and associated elements such as REE, Al, Hf,

Sc, Ti and Hg.

It should be appreciated that results from factor analysis should not be considered

as a deﬁnitive solution. The data that are entered are invariably of mixed quality with

respect to analytical precision, because the data for some elements are considerably

more precise than data for others. The uncertainty surrounding results from a factor

analysis becomes evident if the user generates several rotated factor solutions using

ﬁrst a complete array of elements, then extracting some of those elements and

re-calculating the factors for the remaining matrix. Commonly, there may be some

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Biogeochemistry in Mineral Exploration

changes in element associations, although some pervasive associations will reﬂect the

underlying robust components of the data structure.

Factor analysis provides another perspective on a dataset that can contribute

toward an unde rstanding of data structure and gives indications of associations that

may be relevant to a mineral exploration programme. Interpretations are subjective

and become based upon the intimate knowledge of a ﬁeld area with respect to the

natural environment, geology and mineralogical associations.

MAP PLOTS OF DATA DISTRIBUTIONS

A geologist needs maps – topographic, geological, geophysical and geochemical.

Data from a biogeochemical survey can be presented in many formats, which are

generic to the plotting of geochemical data from other exploration sampling media.

Proportional dots of different colours can be used to represent either different

species or different concentration levels of elements from a single species. Larger

datasets can be contoured and sample sites superimposed as symbols with or

without the data values (so-called ‘Post’ maps). The GIS packages discussed above

are ideal for undertaking these map plots. For the small operator who does not

have ready access to large and expensive GIS software programmes, a useful option

is the software package ‘Surfer’. A conc ise overview of the capabilities of this

programme can be viewed on website http://www.goldensoftware.com/produ cts/

surfer/surfer.shtml.

Surfer is a contouring and 3D surface mapping programme that runs with

Microsoft Windows. It converts data into contour, surface, wire-frame, vector,

image, shaded relief and post maps, and has a wide array of options for custom-

izing output. It is a rectangular grid-based contouring programme that requires

the generation of a grid ﬁle for many plotting operations. Gridding methods use

weighted average interpolation algorithms and various gridding methods can be

applied. In summary, the principal feat ures of the more common gridding methods

are as follows.



Kriging generates the best overall interpretation of most biogeochemical data sets.

The user should be alert to the fact that maps generated from kriged data will

extrapolate contours into areas with no data control. These areas should be

disregarded, since they invariably provide a false impression of the extrapolated

element concentrations.



Nearest Neighbour, Natural Neighbour, Minimum Curvature and Radial Basis

Functions all provide similar smoo th contour patterns to kriging.



Inverse Distance and Shepard’s Method tend to generate ‘bull’s eye’ patterns.

It is a useful exercise to experiment with each of the various gridding options to be

satisﬁed that the one selected is optimal for generating the output that the user ﬁnds

most meaningful for representing and interpreting the dataset.

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Data Handling and Analysis

UNUSUAL CONCENTRATIONS OF SELECTED ELEMENTS

The data received from a set of biogeochemical samples may sometimes yield

some anomalous results that can be attributed to either analytical errors or certain

environmental situations. The following examples are not exhaustive, but they rep-

resent problems that have been encountered from time to time, and are presented to

alert the user to possibl e explanations for unusual enrichments or depletions of

elements. There are many potential sources of these anomalies. A few to look out for

are the following.

Analytical artefacts

All elements high. Could be a weighing error.

All elements low. Could be a weighing error.

Extremely low levels of all elements in an isolated sample. Automated pipette failed to

enter the solution in the test tube (or the test tube was empty) with the result that no

material was aspirated into the analytical instrument.

Poor precision. Can result from the sample weight being too low. Typically, 1 g of dry

tissue or 0.25 g of ash would be a suitable amount. Lower sample weights commonly

result in a marked decrease in analytical precision.

Precision of Au determined by INAA (Repeat analysis).

a) If very ﬁne particles of Au (sub-micron) are distribut ed evenly throughout the

sample, excellent precision can be expected.

b) If larger particles of Au are present, during the ﬁrst count a Au particle may be in

one position with respect to the detector and in another position for the second count

resulting in either a lower or higher value being reco rded.

INAA – All data out by a factor of 5. Incorrect placement of the samples with respect

to the detector.

INAA – Reanalysis of material that has been irradiated previously: Isotopes of certain

elements (e.g., Co, Zn, Sc, etc.) created during the ﬁrst irradiation have not fully

decayed, resulting in elevated concentrations of these elements (whether subsequent

analysis by INAA or any other analytical technique).

ICP-ES – Data for an individual sample high by a factor of 2. The laborat ory may

have taken a smaller portion of a sample for analysis and failed to adjust for the

smaller sample weight. This situati on is only likely to occur if the laboratory has been

given insufﬁcient material for them to be able to analyze samples of consistent

weights. As a result, they may take only half the usual weight (i.e., 0.5 g of dry tissue),

and it has been known that a technician has forgotten to adjust the data for the

smaller sample weight.

Cobalt. Small amounts of Co contamination can come from the preparation of

tissues in mills with tungsten carbide surfaces, because the W particles are embedded

in a Co-based binding matrix.

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Mercury. Background concentrations in dry vegetation are usually 10–20 ppb. If

samples have been dried at a temperature over 100 1C, invariably some Hg will have

volatilized (Table 6-VI). Studies in the former Soviet Union have claimed that some

Hg remains in plant ash (as a carbide) but such claims have not been substantiated

by studies elsewhere, unless the Hg is structurally bound in a crystal lattice of a rock-

forming mineral (e.g., pyrite).

Nickel. On occasion, a miniscule fragment of the cutting blade used to mill the

samples becomes incorporated into a sample, resulting in a spurious spike in Ni data,

along with a slight increase in Fe, although, because of the relatively high

concentration of Fe in the plant tissue, Fe contamination is less evident.

Tungsten. Hard tissues that are milled in equipment with tungsten carbide

components may contain several ppm W in dry tissue.

Zirconium. Substantial enrichments in plant tissues will be recorded if samples are

ground in a ZrO mortar and pestle.

Sampling and sample preparation artefacts

Very high levels of gold, arsenic and antimony in ash: Samples may have been ashed in

equipment used for ﬁre assay. In one case, an analysis of over 200,000 ppb Au was

returned from a sample that was reduced to ash in a ﬁre-assay furnace.

One survey line yields high values and an adjacent line yields lower values: Check to see

if two samplers were collecting samples using different techniques.

Erratic bark analyses: Some inner bark might have been mixed-in with the outer bark

(i.e., check the techniques of the samplers) . Inner bark has lower concentrations than

outer bark of most commodity elements of interest to mineral exploration.

Erratic ash yields from the same sample medium may indicate that there is dust

contamination. However, samples that contain high concentrations of Fe commonly

have a high ash yield.

Erratic values for a particular element in twigs: This may indicate that there is a

mixture of old with new growth (e.g., 10 years of growth from one site an d only 3

years from another). As an example alder, for which old twig growth has relatively

high levels of Ba, REE and Fe, whereas new growth has relatively high levels of Mo

and Co. Sampling procedures of ﬁeld crews need to be veriﬁed.

Isolated sample with a different pattern of element concentrations would probably

indicate that the wrong species was collected.

Contamination of the natural environment

Lead: Lead anomalies near roadsides are likely to be related emissions of leaded

petroleum. Although unleaded petroleum is now widely used, Pb persists for many

years.

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Data Handling and Analysis

Vanadium and Nickel: Enrichments around oil-ﬁred power plants have been

recorded. Oils commonly contain V- and Ni-enriched porphyrins.

Zinc: Samples collected downstream from galvanized iron culverts or other

galvanized iron containers may give rise to elevated Zn levels in vegetation. Sampling

should be conducted upstream and upslope from potential sources of contamination.

High levels of lead and antimony: If these occur together at a single site, they could be

the result of someone having ﬁred a riﬂe at the tree. This has been known to occur.

See section on Hg in Chapter 9.

Species-speciﬁc enrichments

Arsenic – Douglas-ﬁr and western hemlock have an unusual ability to concentrate

As. Some ferns, too, can be highly enriched in As.

Barium – Douglas-ﬁr in western North America and the Brazil nut (Bertholletia

excelsa) in the Amazon can accumulate high levels of Ba.

Chromium – Hazelnuts (Corylus spp.) may be enriched in Cr.

Molybdenum – Alders are able to concentrate high levels of Mo.

Rare Earth Elements (REE) – Ferns can accumulate high levels of REE. Other

species may accumulate REE in certain environments, such as oxidized black shales.

Silver – Trunk wood of spruce and pine concentrates Ag.

Zinc – Birch and willow accumulate high concentrations of Zn.

Vascular plant species are known to hyperaccumulate about a dozen elements,

but few of the several hundred hyperaccumulator plant species are sufﬁciently com-

mon to be of general use in a biogeochemical exploration surveys.

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