Using Random Forests to distinguish gahnite ...

Journal of Geochemical Exploration 149 (2015) 74–86

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Using Random Forests to distinguish gahnite compositions as an exploration guide to Broken Hill-type Pb–Zn–Ag deposits in the Broken Hill domain, Australia Joshua J. O'Brien a, Paul G. Spry a,⁎, Dan Nettleton b, Ruo Xu b, Graham S. Teale c a b c

Department of Geological and Atmospheric Sciences, 253 Science I, Iowa State University, Ames, IA 50011-3212, USA Department of Statistics, Snedecor Hall, Iowa State University, Ames, IA 50011, USA Teale & Associates, P.O. Box 740, North Adelaide, South Australia 5006, Australia

a r t i c l e

i n f o

Article history: Received 22 September 2014 Accepted 21 November 2014 Available online 28 November 2014 Keywords: Random Forests Gahnite Broken Hill Statistics Exploration

a b s t r a c t Various studies have focused on evaluating variability in the major-trace element chemistry of minerals as exploration guides to metallic mineral deposits or diamond-bearing kimberlites. The chemistry of gahnite has previously been proposed as an exploration guide to Broken Hill-type Pb–Zn–Ag mineralization in the Broken Hill domain, Australia, with the development of a series of discrimination plots to compare the composition of gahnite from the supergiant Broken Hill deposit with those in occurrences of minor Broken Hill-type mineralization. Here, the performance of Random Forests, a relatively new statistical technique, is used to classify mineral chemistry using a database (n = 533) of gahnite compositions (i.e., Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd) from the Broken Hill deposit and 11 minor Broken Hill-type deposits in the Broken Hill domain. This statistical method has yet to be applied to geological problems involving mineral chemistry. Random Forests provide a framework for classification and decision making through a series of classification trees, which individually, resemble classification keys. Gahnite from the Broken Hill domain is classified here on the basis of the following schemes: 1. Random Forest 1 (RF1): gahnite in the Broken Hill deposit versus compositions of gahnite from other minor Broken Hill-type occurrences in the Broken Hill domain; 2. Random Forest 2 (RF2): gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type deposits containing N 0.25 million tonnes (Mt) of Pb–Zn–Ag mineralization versus gahnite in sulfide-free and sulfide-poor prospects containing b 0.25 Mt; and 3. Random Forest 3 (RF3): gahnite in sulfide-bearing quartz–gahnite lode rocks versus gahnite in sulfide-free samples. Misclassification rates, according to a ten-fold cross validation, of RF1, RF2, and RF3 are 1.6, 3.3, and 4.7% respectively. Results of this study suggest that Random Forests work well in classification problems involving mineral chemistry, and may prove useful in the exploration for Broken Hill-type and other types of metallic mineral deposits. © 2014 Elsevier B.V. All rights reserved.

1. Introduction The presence and composition of aluminous minerals and ferromagnesian silicates (e.g., garnet, tourmaline, biotite, chlorite, staurolite, cordierite, and amphibole) have long been used in the search for metamorphosed massive sulfide deposits (e.g., Bryndzia and Scott, 1987; Nesbitt, 1982, 1986a,b; Nesbitt and Kelly, 1980; Spry and Scott, 1986), and have led to mixed success with regard to finding new ore deposits. By contrast, mining companies have had considerable success in using the major and trace element compositions of in situ or detrital indicator minerals such as chromite, garnet, and Cr-diopside in the search for diamonds (e.g., Griffin and Ryan, 1995; Griffin et al., 1997; Quirt, 2004). Such success, along with the ability, since the early-1990s to collect large amounts of high precision trace element data via in situ laser

⁎ Corresponding author. E-mail address: [email protected] (P.G. Spry).

http://dx.doi.org/10.1016/j.gexplo.2014.11.010 0375-6742/© 2014 Elsevier B.V. All rights reserved.

ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) (e.g., Jackson et al., 1992; Sylvester, 2001, 2008) has led to a significant increase in the number of trace element studies of minerals (e.g., garnet, magnetite, chromite, gahnite), which can be used in the search for various types of ore deposits (e.g., Dupuis and Beaudoin, 2011; Heimann et al., 2011; O'Brien et al., in press). Trace element studies of garnet (Heimann et al., 2011; Spry et al., 2007), gahnite (e.g., Layton-Mathews et al., 2013; O'Brien et al., 2013, in press), and tourmaline (e.g., Griffin et al., 1996) have specifically been used to explore for metamorphosed massive sulfide deposits, including Broken Hill-type deposits. The chemistry of gahnite was evaluated as a guide to Broken Hilltype mineralization because blue quartz–gahnite rocks are spatially related to sulfides in the supergiant Broken Hill Pb–Zn–Ag deposit (Dewar, 1968; Forwood, 1968; Spry et al., 2003; Walters, 2001), and smaller Broken Hill-type deposits in the Broken Hill domain, New South Wales, Australia. Gahnite (AB2O4) contains Zn2 +, Fe2 +, Mg2 + , and minor amounts of Mn 2 + in the tetrahedral site (A), where Zn N (Fe + Mg), and Al3 + and trace Fe3 + in the octahedral

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site (B). An unpublished proprietary study by Broken Hill Proprietary Limited in the 1980s used the major element chemistry (i.e., Fe, Mg, Zn, Mn, and Al) of gahnite (n N 3000) from gahnitebearing rocks in the Broken Hill domain and elsewhere to develop discrimination diagrams to distinguish among metal-barren gahnite horizons, small prospects, and economic deposits (Walters, 2001). Also using major elements (Zn, Fe, and Mg) as components in a ternary diagram, Spry and Scott (1986) and Heimann et al. (2005) plotted compositions of gahnite from over one hundred locations worldwide, including Broken Hill-type deposits, and determined compositional fields for zinc-bearing spinels in marbles, S-poor rocks in Mg–Ca–Al alteration zones, metamorphosed massive sulfide deposits in altered Fe– Al metasedimentary and metavolcanic rocks, metabauxites, granitic pegmatites, unaltered and altered Fe–Al-rich metasedimentary and metavolcanic rocks, and Al-rich granulite. Although the major element chemistry of zincian spinels can be used to distinguish among geological host settings, Spry et al. (2003) showed, using bivariate and ternary plots, that the major element composition of gahnite in the Broken Hill deposit overlaps that for gahnite in minor Broken Hill-type deposits and sulfide-free gahnite lode rocks. As a consequence, O'Brien et al. (in press) used a combination of major and trace elements (e.g., Mn, V, Cr, Co, and Cd), which were obtained by electron probe and LA-ICP-MS analyses, to develop a series of bivariate plots (e.g., Co versus Ga; and Zn/Fe versus Co, Mn, and Ga; Fig. 1A–D) that characterize a compositional fingerprint of gahnite associated with high-grade Broken Hill-type mineralization in the Broken Hill domain. Gahnite in rocks with the highest ore grades (weight % Pb + Zn) from some minor Broken Hill-type deposits plots within the compositional field for gahnite from the Broken Hill deposit, and was considered by O'Brien et al. (in press) as deposits that should be considered for further exploration. The development of chemical fingerprints from graphical representation of data (e.g., bivariate, ternary plots) is complicated by the somewhat scattered nature of trace element datasets, which can be caused by various factors including changing physicochemical conditions (i.e., temperature, pressure, fO2, fS2, fH2O) during mineral growth, partitioning of elements between minerals, crystal-chemical controls of the major element chemistry of gahnite, the chemistry of precursor minerals consumed during mineral growth, and compositional zoning. Such scattering of data in bivariate plots is shown, for example, for the composition of magnetite (e.g., Dupuis and Beaudoin, 2011; Fig. 6), garnet (e.g., Heimann et al., 2011, Fig. 10), and gahnite (e.g., O'Brien et al., in press). Furthermore, two- and three-component projections only allow for characterization of mineral chemistry on the basis of selected elements, while ignoring others. Therefore, development of methods capable of classifying minerals on the basis of their complete chemical composition (major and trace elements) and resolving a signal in “noisy” datasets remains critical to improving data analysis and interpretation. Multivariate statistical techniques, such as principal component analysis, linear and quadratic discriminant function analyses, and correlation and regression trees offer promising ways to recognize signals within geochemical datasets because of their ability to characterize observational units on the basis of several variables (e.g., elements), and to resolve underlying structures within large datasets (see summaries of these methods in Davis (2002)) (Table 1). Although studies applying these techniques to the composition of minerals are limited in number, they are generally successful in distinguishing chemical signatures from large sets of data. Discriminant function analysis was tested by Clarke et al. (1989) on the composition (major, trace, and boron isotopes) of tourmaline as a way to distinguish compositions of tourmaline in mineralized rocks from those that were not spatially associated with known mineralization. This technique has also been used on lithogeochemical datasets, with applications including the definition of trace element halos surrounding known massive sulfide mineralization (e.g., Whitehead and Govett, 1974), correlation of volcanic tephra (i.e., Stokes et al., 1992),

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and the discrimination of geochemical signatures in sedimentary rocks to determine the provenance of sedimentary units (i.e., Roser and Korsch, 1988). A principal component analysis of the major-trace element composition of gahnite in the Broken Hill domain, Australia, by O'Brien et al. (in press) was able to distinguish among gahnite in different geological host settings (e.g., lode pegmatite and pegmatitic segregations, sillimanite gneiss, quartz lode rocks) (Fig. 2). However, despite this chemical distinction, principal component analysis showed overlap among the major-trace element compositions of gahnite in the Broken Hill deposit, gahnite in small Broken Hill-type deposits, and gahnite in relatively sulfide-free occurrences, which limited the potential of gahnite chemistry as an exploration guide to Broken Hill-type mineralization. Correlation and regression trees, multivariate adaptive regression splines, and nearest-neighbor analysis were able to distinguish compositions of chromite in kimberlites, lamproites, ultramafic lamprophyres, and crustal sources, and have been used in exploration for diamondbearing kimberlites (Griffin et al., 1997). Using correlation and regression trees on a database of apatite chemistry (major and trace), Belousova et al. (2002) were able to resolve compositional signatures of apatite in a variety of host rocks (e.g., granitoids, granite pegmatite, larvikite, iron ore deposits). Random Forest methodology, a relatively new statistical technique developed by Breiman (2001a), is an extension of classification and regression tree methodology (Breiman et al., 1984) that provides a framework for classification, prediction, and decision making by aggregating results from a randomly generated forest of classification or regression trees. Individual trees within a Random Forest comprise a series of hierarchical decision nodes, which resemble decision trees or classification keys, and are used to classify cases based on their attributes (Breiman et al., 1984). Despite application in the fields of ecology (e.g., De'Ath, 2007; Pal, 2005), neuroscience (e.g., Granitto et al., 2007), bacterial source tracking (e.g., Smith et al., 2010), and machine learning (e.g., Breiman, 2001a), Random Forests have rarely been used in the geosciences. Exceptions include, for example, studies to: estimate suspended sediment concentrations (Francke et al., 2008); provide a geological facies classification from wire-line logs (Gifford and Agah, 2010); predict gully erosion using remote sensing data (Kuhnert et al., 2010); distinguish rock units and zones of hydrothermal alteration in known ore fields (Cracknell et al., 2014); mapping of hyperspectral airborne visible/infrared imaging spectrometer data (Waske et al., 2009); and use in mineral prospectivity mapping (Carranza and Laborte, 2014; Rodriguez-Galiano et al., 2014). Random Forests were recently used by Cracknell and Reading (2013, 2014) to identify different lithologies and infer the location of geological contacts in the Broken Hill domain, Australia. However, Random Forests have yet to be applied to geological problems involving mineral chemistry, which may include the identification of chemical fingerprints for minerals in different geological settings (e.g., provenance studies), and uses in the exploration for metallic mineral deposits. Relative to other statistical methods, including principal component analysis, Random Forests are advantageous because of their ability to (Breiman, 2001a; Breiman and Cutler, 2004): 1. Find signals in “noisy” data bases; 2. accommodate many predictor variables (e.g., elements, deposit types); 3. efficiently handle large data bases; 4. use categorical data; and 5. run new data through previously generated forests to generate classifications or predictions. In this contribution, we evaluate the effectiveness of Random Forests for identifying Broken Hill-type Pb–Zn–Ag mineralization from the major-trace element chemistry (i.e., Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd) of gahnite. Specifically, Random Forests are applied to the dataset of O'Brien et al. (in press) to distinguish between the compositions of gahnite from the Broken Hill deposit and the compositions of gahnite in 11 minor Broken Hill-type deposits. Gahnite from the Broken Hill domain (n = 533) is classified here on the basis of the following schemes: 1. Random Forest 1 (RF1): a two-category classification of gahnite in the Broken Hill deposit versus compositions of gahnite from other minor Broken Hill-

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500

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A 5

400

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Ga, ppm

4 300

3

200 2 100

1

0

0 0

50

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250

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50

Co, ppm

100

150

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Co, ppm 6

6

D

5

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4

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Zn/Fe

C

3

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2

2

1

1

0

0 0

2000

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Mn, ppm

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Ga, ppm

Broken Hill (n = 95) Flying Doctor (n = 56) Globe (n = 26) Round Hill (n = 26) Potosi (n = 43) Zinc lode at the North mine (n = 71) Broken Hill deposit density ellipse (σ = 0.68) Fig. 1. Bivariate plots of gahnite compositions from Flying Doctor, Globe, Round Hill, Potosi, Zinc Lode at the North mine, and Broken Hill deposits: A. Ga (ppm) vs. Co (ppm), B. Zn/Fe vs. Co (ppm), C. Zn/Fe vs. Mn (ppm), D. Zn/Fe vs. Ga (ppm). A Compositional field for the Broken Hill deposit is defined as a density ellipse (σ = 0.68). Compositions of gahnite from other deposits are excluded due to the large dataset size and the overlap in gahnite composition among minor deposits (after O'Brien et al., in press).

type occurrences in the Broken Hill domain; 2. Random Forest 2 (RF2): a three-category classification of gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type deposits containing N 0.25 million tonnes (Mt) of Pb–Zn–Ag mineralization versus gahnite in sulfide-free and sulfide-poor prospects containing b 0.25 Mt; and 3. Random Forest 3 (RF3): a two-category classification of gahnite in sulfide-bearing quartz–gahnite lode rocks (samples containing N 1 vol.% sulfides) versus gahnite in sulfide-poor samples containing b 1 vol.% sulfides. The success of Random Forests in the classification of gahnite composition from the Broken Hill deposit versus that in minor deposits (RF1) will be compared to the results obtained from a linear discriminant analysis for the same classification scheme. 2. Regional geology Broken Hill-type Pb–Zn–Ag mineralization in the Broken Hill domain, including the supergiant Broken Hill deposit (280 Mt at 10% Pb,

8.5% Zn, and 148 g/t Ag), is spatially associated with a group of rocks known as “lode horizon” that include blue quartz–gahnite, quartz garnetite, garnetite, and lode pegmatite (Johnson and Klingner, 1975) (Fig. 3). Of these rock types, the first two are most commonly associated with the Broken Hill deposit. This deposit and hundreds of minor Broken Hill-type deposits, which range from sulfide-poor deposits to the 14 Mt Pinnacles Pb–Zn–Ag deposit, occur in the Willyama Supergroup (1710 to 1640 Ma), a sequence of Paleoproterozoic metasedimentary, metavolcanic, and metaintrusive rocks (Barnes, 1988; Parr and Plimer, 1993; Willis et al., 1983). Rocks in the Broken Hill domain were regionally metamorphosed to the granulite faces (740° to 800 °C and 5 to 6 kbar) and affected by four deformational events (denoted as D1, D2, D3 and D4) related to two metamorphic events, the Olarian (M1; D1, D2, D3, ~ 1600–1590 Ma) and Delamerian (M2) orogenies (D4 ~ 520– 458 Ma) (Forbes et al., 2005; Frost et al., 2005; Page and Laing, 1992; Page et al., 2005; Phillips, 1980). Information regarding the size, grade, and geology of the deposits studied here is in Table 2.

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Table 1 Minerals identified as exploration guides to a variety of ore deposit types. Mineral

Deposit type

Statistical analysis applied to mineral compositions

Reference

Apatite Chromite

Apatite-Fe Magmatic sulfide

Classification and regression trees None None Classification and regression trees, multivariate adaptive regression splines None None

Belousova et al. (2002) Pagé and Barnes (2009) Dare et al. (2012) Griffin and Ryan (1995) Griffin et al. (1997) Quirt (2004) Eppinger and Closs (1990)

None Principal component analysis Correlation matrices Correlation matrices None None None Cluster analysis None

Bau et al. (2003) O'Brien et al. (2013) Spry et al. (2007) Heimann et al. (2009, 2011) Griffin and Ryan (1995) Smith et al. (2004) Gaspar et al. (2008) Schmidt Mumm et al. (2012) Dupuis and Beaudoin (2011)

Factor analysis

Nadoll et al. (2012)

None None Linear and quadratic discriminant function analyses None

Singh (2007) Griffin et al. (1996) Clarke et al. (1989)

Diamond-bearing kimberlites Cr-diopside Fluorite

Muscovite Tourmaline

Diamond-bearing kimberlites Epithermal Au–Ag–Cu–Pb–Zn, Ba–Pb, and Au–Ag–Cu–Pb–Zn fissure veins, W–Be–Fe Skarn Mississippi Valley-type Broken Hill-type Broken Hill-type Broken Hill-type Diamond-bearing kimberlites Skarn Skarn IOCG IOCG, VMS, orogenic Ag, porphyry Cu–Mo, skarn, and Ni–Cu–platinum-group element Sediment hosted Cu–Ag, hydrothermal Cu–Pb–Zn Rare-metal bearing pegmatite Massive sulfide

Rutile

Porphyry Cu–Au

Gahnite Garnet

Hematite/Maghemite Magnetite

Gahnite is most abundant in blue quartz–gahnite lode rocks, which generally occur as 1–2 m wide, discontinuous horizons that are concordant to the primary bedding of their host (typically aluminous metasedimentary rocks), and outcrop intermittently (from centimeters to hundreds of meters in length) for over 330 km in the Broken Hill domain (e.g., Barnes, 1988; Barnes et al., 1983; Burton, 1994). The protolith of quartz–gahnite lode rocks is likely to have formed by the exhalation or inhalation of silica-saturated zinc-bearing fluids from submarine hydrothermal vents (Spry and Scott, 1986; Spry et al., 2000). Gahnite also occurs in aluminous metasedimentary rocks (i.e., pelitic– psammopelitic schists), lode pegmatite and pegmatitic segregations, massive sulfides, tourmalinite, iron formation, quartz–feldspar–garnet (Potosi) gneiss, and amphibolite (Barnes et al., 1983; Plimer, 1988; Segnit, 1961; Slack et al., 1993; Spry and Scott, 1986). Details on the mineralogy and origin of gahnite-bearing rocks are given in Johnson and Klingner (1975), Barnes et al. (1983), Plimer (1984), Jain (1999), and O'Brien et al. (in press). 3. Materials and methods 3.1. Sample collection Gahnite-bearing rocks were collected (Spry, 1978, 1984) from underground localities in the Broken Hill deposit (i.e., South East A lode, B lode, C lode, Western Longitudinal), surface outcrops at the Champion, Flying Doctor, Mutooroo, Round Hill, and Stirling Hill prospects, mine tailings from the Globe and Potosi prospects, and drill holes from 11:30, Flying Doctor, Henry George, and the Zinc Lode at the North mine (Fig. 3). 3.2. Analytical methods Major element compositions of gahnite (MgO, Al2O3, SiO2, TiO2, MnO, FeO, ZnO) were measured using a JEOL 8900 Electron Probe Microanalyzer at the University of Minnesota under the following operating conditions: accelerating voltage of 15 kV, a beam current of 20 nA, a spot size of 1–2 μm, and using gahnite (Zn, Al), pyrope (Si, Mg), hornblende (Ti), ilmenite (Fe), and spessartine (Mn) as mineral standards. The beam time for analysis was 20 s on peaks and 10 s on backgrounds.

Scott (2005)

Concentrations of 52 elements were measured at the Geological Survey of Canada (Ottawa) using a LA-ICP-MS, comprising a Photon Machines “Analyte 193” excimer (Ar–F) laser ablation system coupled to an Agilent 7700 Series ICP-MS, fitted with an additional second rotary interface pump that approximately doubles instrument sensitivity. Analyses were calibrated using an external standard, GSD-1G, a synthetic glass reference standard (USGS), and values of Al2O3 from EPMA analysis were used for internal standardization. GSD-1G was analyzed twice every 12–15 analyses of unknown samples to correct for instrument sensitivity drift. Analytical precision and accuracy were tested by analyzing reference material BCR-2G repeatedly throughout the day, under operating conditions identical to that used during routine gahnite analyses. 3.3. Data classification O'Brien et al. (in press) were able to distinguish the compositions of gahnite in lode pegmatite and pegmatitic segregations, and aluminous metasedimentary rocks from those in blue quartz–gahnite lode rocks using a principal component analysis and a scatter plot of Zn/Fe versus Ni + Cr + V. The current study extends the statistical part of O'Brien et al. (in press) study by attempting to distinguish the compositions of gahnite (n = 533) in sulfide-bearing rocks from those in sulfide-poor, and sulfide-free quartz–gahnite lode rocks. Prior to the creation of Random Forests, samples were classified on the basis of the following criteria: 1. Gahnite in the Broken Hill deposit (South East A lode, B lode, C lode, Western Longitudinal); 2. gahnite in minor Broken Hilltype occurrences (i.e., Champion, 11:30, Flying Doctor, Globe, Melbourne Rockwell, Mutooroo, Potosi, Round Hill, Stirling Hill, the Zinc Lode at the North mine); 3. gahnite in deposits known to contain more than 0.25 Mt of sulfide ore (i.e., Potosi (1.6 Mt), Flying Doctor (1.5 Mt), Henry George (1.3 Mt), and Zinc Lode at North mine (1.0 Mt)); 4. gahnite in relatively sulfide-poor and sulfide-free deposits that contain a known tonnage of less than 0.25 Mt of sulfides (i.e., 11:30 (0.20 Mt), Globe (~ 2685 t), Melbourne Rockwell (589 t), Round Hill (15 t), Stirling Hill (5 t), Mutooroo (no known tonnage), and Champion (no known tonnage)); and 5. the presence or absence of sulfides in gahnite rocks. Estimated sizes of the deposits studied here were obtained from Johnson and Klingner (1975) and unpublished

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6

(e.g., magnetite) and are referred to as “spinel elements” by Nadoll et al. (2012). Gahnite compositions (consisting of measurements of M = 11 variables: Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd) were transformed with CoDaPack version 2.01.13 to centered log ratio values as follows. Let xij be the ith observation of the jth variable, and let yij = ln(xij). Then the centered log ratio value for xij is

5 4

Sillimanite Gneiss

Component 2 (16.9 %)

3 2


 1 XM clr xi j ¼ yi j −yi where yi ¼ y : j¼1 i j M

1 0 -1

This centered log ratio transformation is equivalent to computing the natural log of the ratio xij divided by the geometric mean of xi1,…,xiM; this is a standard transformation for compositional data (Aitchison, 1986; Comas-Cufí and Thió-Henestrosa, 2011).

-2 -3

Melbourne Rockwell

-4 -5 -6

Lode Pegmatite and Pegmatitic Segregations -6

-5

-4

-3

-2

-1

0

1

4. Random Forest construction and classification

Broken Hill deposit 2

3

4

5

6

Component 1 (44 %)

Broken Hill (n = 95) Round Hill (n = 26) Henry George (n = 120) Zinc lode at the North mine (n = 77) Globe (n = 25) Flying Doctor (n = 56) Stirling Hill (n = 24) 11:30 (n = 40) Potosi (n = 43) Ten Two (n = 31) Champion (n = 13) Mutooroo (n = 54) Melbourne Rockwell (n = 16) Fig. 2. Score plot of the first two principal components, with the percentage of variance for each component noted in parentheses, using Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd contents of gahnite from the Broken Hill domain. Gahnite in lode pegmatite/pegmatitic segregations and sillimanite gneiss, and from the Broken Hill deposit and Melbourne Rockwell are circled (after O'Brien et al., in press).

reports of Perilya Limited. Although the Zinc Lode at the North mine is part of the Broken Hill deposit, it was classified here as a minor Broken Hill-type occurrence because of its distal location to the northern end of the line of lode, and because not all gahnite occurs in sulfides or blue quartz–gahnite lode rocks. Instead, much of the gahnite occurs in sillimanite gneisses surrounding massive sulfides. The presence or absence (i.e., b 1% volume) of sulfides was determined by petrographic studies and the hand sample mineralogy of each sample. 3.4. Pretreatment of compositional data Of the 52 elements measured here using LA-ICP-MS, Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd were selected for statistical analysis because they consistently occurred in concentrations above the limits of detection for LA-ICP-MS, which are on the order of 10s of parts per billion regardless of the diameter of the ablation spot. Details of the detection limits for all 52 elements are given in O'Brien et al. (in press) and not repeated here. Concentrations of these 11 elements appear to be unrelated to the presence of microinclusions of other mineral phases, which were identified as specific elemental peaks in time resolved element profiles during LA-ICP-MS analysis. Furthermore, these elements are shown to substitute into other members of the spinel group

Random Forests were created as described by Breiman (2001a) using the R (The R Core Team, 2012) package randomForest (Liaw and Wiener, 2002). The process of forest generation and classification in the context of our study begins with a dataset of n training cases. Each   training case is associated with a class label (e.g., clr xi j ¼ yi j −yi M

where yi ¼ M1 ∑ j¼1 yi j :, gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type occurrences) and a measurement for each of M predictor variables (in our study, a centered log-ratio value for Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd). Construction of an individual decision tree in the forest starts with a bootstrap sample of the n training cases. To produce a bootstrap sample, n draws are made from the n training cases, where any given case is selected with probability 1/n in each draw. A particular training case may appear once, multiple times, or not at all in any given bootstrap sample. The set of training cases that appears at least once in a particular bootstrap sample is referred to as “in bag” cases whereas those absent from the bootstrap sample are known as “out of bag” cases. Once a bootstrap sample of training cases is obtained, tree construction proceeds as illustrated in the schematic diagram of Fig. 4, which shows a partially completed classification tree for a two-category classification of gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type occurrences. The root node of the tree is assigned a subset of all M = 11 predictor variables that are randomly selected from the total M input variables (i.e., centered log-ratio values for Mg, Al, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, and Cd). The number of variables selected in subset M is set to be approximately the square root of the M (Breiman, 2002); therefore, three of eleven variables from the present study were randomly selected. The subset of M predictor variables is assessed for the best possible split of cases into two subnodes that will maximize the class purity of the cases within each subnode as measured by the Gini Index. A split is defined by a predictor variable and a value of that predictor variable. Cases with values of a predictor variable less than or equal to the split value go into the left subnode, whereas cases with values of a predictor variable greater than the split value go into the right subnode. Subnodes are evaluated on the basis of their homogeneity (Fig. 4). Pure subnodes (e.g., node 1; Fig. 4) contain compositions of gahnite that are all from one location (i.e., the Broken Hill deposit), whereas impure subnodes (e.g., nodes 2, 3, and 4; Fig. 4) contain gahnite from multiple locations (i.e., the Broken Hill deposit and minor Broken Hill-type occurrences). Impure subnodes are again split using the same process described for splitting the root node: a new set of three predictor variables is randomly selected from all 11 variables for each split, and the best split among the selected variables is determined. A tree is fully grown once each terminal node, or “leaf,” is pure. Each tree in the forest is grown using the same strategy but starting with a new bootstrap sample of cases from the training set. By software default, a Random Forest consists of 500 trees. Although any number of

J.J. O'Brien et al. / Journal of Geochemical Exploration 149 (2015) 74–86

141°30 0 E

141°20 0 E

141°10 0 E

79

31°35 0 S

31°35 0 S

ay

w gh

Mundi Mundi Plain er

ty Ci

Hi

lv

Si

31°45 0 S

31°45 0 S

12 Silverton 31°55 0 S

Broken Hill 4

11 31°55 0 S

9 7 8Menin

dee

3

y

Ro

ad

hwa

r Hig

ie Barr

6

10

2

1

5

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32°05 0 S

Torrowangee Group

1000 km

N

Paragon Group Sundown Group Broken Hill Group

Broken Hill

Thackaringa Group 0

5

32°15 0 S 141°10 0 E

10

15

20

Km

Gahnite Lode Rocks

141°20 0 E

32°15 0 S 141°30 0 E

Fig. 3. Geological map of the Broken Hill domain, showing outcrops of blue quartz–gahnite lode and the locations of study sites: 1. Pinnacles, 2. Henry George, 3. 11:30, 4. Stirling Hill, 5. Melbourne Rockwell, 6. the Broken Hill deposit — South East A lode, B lode, C lode, Western Longitudinal, 7. Zinc Lode at the North mine, 8. Potosi, 9. Round Hill, 10. Flying Doctor, 11. Globe, 12. Champion. Mutooroo is located in South Australia near the border with New South Wales and is not shown on the map.

trees can be generated to constitute a Random Forest, classification results are typically stable when 500 or more trees are used. To use a Random Forest to predict the class of a new case, the case is passed through each tree in the forest on the basis of predictor variable values (gahnite composition data in our study) until a terminal node is reached. The class of the training case or cases in the terminal node provides a vote for the class of the new case. The class that receives more votes than any other class, when considering the votes from all trees in the forest, is the predicted class for the new case. The accuracy of a classifier, like Random Forests, is often assessed through 10-fold cross-validation. As described by Hastie et al. (2009), 10-fold cross-validation provides an acceptable balance between bias

and variance when estimating the probability of misclassifying a new case. To carry out 10-fold cross-validation, the available cases are randomly partitioned into 10 sets of cases, where each set has approximate sample size n/10. The cases in each of the 10 sets are classified using the union of the other nine sets as the training set. The proportion of misclassified cases out of all cases is known as the misclassification rate. The misclassification rate provides an estimate of the probability of misclassifying a new case when using all cases as training data. To further reduce the variation associated with the 10-fold cross-validation estimate of the probability of misclassification, we conducted ten separate 10-fold cross-validations and, in the next subsection, report the average misclassification rate across the ten 10-fold cross-validations.

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Table 2 Summary of geological characteristics of Broken Hill-type deposits analyzed in the Broken Hill domain, Australia.1 Deposit

Grade, tonnage2, metallic minerals

Gangue minerals

Lode and country rocks

References

Broken Hill

280 Mt of 10.0% Pb, 8.5% Zn, 0.14% Cu and 148 g/t Ag: Gn–Sp–Ccp ± Asp ± Po ± Lo

Qz–Ghn–Grt ± Rhd ± Ms ± Sil ± Amp ± Ap ± Fsp

Qz–Grt and Qz–Ghn rocks envelope the orebodies in psammitic–psammopelitic–pelitic metasediments (Hores Gneiss) and locally a quartzofeldspathic gneiss (Potosi Gneiss).

Champion

Production and grade unknown; Sp–Py–Gn–Cer

Grt–Qz–Ghn ± Fsp

Johnson and Klingner (1975), Burton (1990, 1994), Webster (2006) Stevens et al. (2003)

11:30

0.2 Mt @ 1% Pb, 12% Zn, 7 g/t Ag; Sp ± Py–Po–Asp–Gn

Flying Doctor

1.5 Mt @ 4% Pb, 3% Zn, 44 g/t Ag; Gn–Sp–Asp–Po ± Ccp ± Py

Globe

2686 t produced, 502 kg Ag and 512 t Pb recorded; Cer–Gn–Sp ± Mlc ± Po 1.3 Mt @ 1% Pb, 8% Zn, 14 g/t Ag; Sp–Po–Py–Gn ± Apy

Henry George

Melbourne Rockwell

589 t carbonate hosted ore @ 50% Pb, 312 g/t Ag; Cer ± Az ± Mag ± Mlc Zinc Lode at North mine Past production 0.04 Mt @ 9.6% Zn, 4.6% Pb, 187 g/t Ag; reserves: 1 Mt @ 9.0% Pb, 7.0% Zn, 140 g/t Ag Potosi 1.6 Mt @ 3% Pb, 14% Zn, 77 g/t Ag; Cer–Sp–Gn–Ccp ± Mlc Round Hill

15 t @ unknown grade, records up to 2834 g/t Ag; Cer–Sp–Gn

Stirling Hill

5 t @ 35% Pb, 460 g/t Ag, 23 g/t Au; Gn–Sp

Qz–Ghn lode rocks in Sil–Gar–Bt-bearing pelitic to psammopelitic metasediments (Parnell Formation) Ghn–Qz–Grt–Bt ± Fsp Qz–Ghn–Grt lode rocks in psammite–psammopelitic metasediments (Broken Hill Group) Qz–Ghn ± Grt ± Bt ± Chl ± Ap Qz–Ghn-sulfide ± Grt lode rocks occur at 100 m below the surface, hosted in pelitic to psammopelitic metasediments Fsp–Qz ± Chl ± M s ± Grt ± Tur Qz–Ghn lode rocks in pelitic–psammitic metasediments (Purnamoota Subgroup) and in places the Potosi Gneiss Qz–Ghn–Fsp–Bt ± Grt Qz–Ghn lode rocks in pelitic to psammopelitic metasediments with minor pegmatitic segregations (Broken Hill Group) Ghn–Grt–Qz–Ap ± Ep ± Rdn Qz–Ghn lode horizon in Qz–Fsp–Bt ± Sil psammopelitic to pelitic metasediments (Allendale Metasediments) Qz–Grt–Ghn ± Sil ± Bt Po–Sp-bearing Grt–Qz lode rocks bounded by Grt–Sil-bearing psammites–psammopelites and pelitic metasediments Fsp–Ghn–Qz–Grt–Ms ± Bt ± Chl ± Ap Two sulfide lenses enveloped by Qz–Ghn rocks occur in a Grt + Sil-rich pelite in psammitic rocks (the Freyers Metasediments) Qz–Ghn ± Bt ± Fsp ± Grt Qz–Ghn ± Grt ± sulfide lode rock hosted within pelitic metasediments and Sil-gneiss (Purnamoota Subgroup) Grt–Qz–Ghn Qz–Grt–Ghn lode rocks occur adjacent to mafic-amphibolites in a sequence of Sil-rich pelitic to psammopelitic metasediments (Cues Formation)

Burton (1994), Teale et al. (2006) Burton (1994), Slack et al. (1993)

Burton (1994), Bartholomaeus (1987) Widdop (1983), Webster (2006) Buckley (2003), Burton (1994), Teale et al. (2006) Burton (1994)

Barnes (1988), Burton (1994)

1 Mineral abbreviations after Whitney and Evans (2010); Amp = amphibole, Ap = apatite, Asp = arsenopyrite, Az = azurite, Bt = biotite, BHT = Broken Hill-type, BIF = banded iron formation, Cer = cerussite, Ccp = chalcopyrite, Chl = chlorite, Fsp = feldspar, Ghn = gahnite, Gn = galena, Grt = garnet, Lo = löllingite, Mag = magnetite, Mlc = malachite, Ms = muscovite, Po = pyrrhotite, Py = pyrite, Rhd = rhodonite, Qz = quartz, Sil = sillimanite, Sp = sphalerite, Ttr = tetrahedrite, Tur = tourmaline. 2 Estimates of grades and tonnage supplied by Perilya Ltd for Zinc Lode at North mine, Henry George, 11:30, and Potosi.

5. Results 5.1. Random Forest 1 A two-category classification (RF1) of gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type occurrences had an average misclassification rate of 2.7% (with a standard deviation of 0.4 percentage points) across ten 10-fold cross-validations. Compositions of gahnite shown in Fig. 5 are grouped for each Broken Hill-type deposit, and are plotted against their average predicted response, over 10 rounds of 10-fold cross-validation, where a value of one represents the classification of a composition from the Broken Hill deposit (100% of the votes across trees in a forest for the Broken Hill deposit class), and zero represents classification of a composition from minor Broken Hill-type occurrences (received 0% of the votes across trees in a forest for the Broken Hill deposit class). With the exception of 13 compositions, most cases from the Broken Hill deposit were classified correctly (Table 3). One composition of gahnite from a minor Broken Hill-type occurrence (i.e., Henry George) was misclassified (i.e., had a predicted response N 0.50) as being from the Broken Hill deposit. Some compositions of gahnite from the 11:30, Flying Doctor, Henry George, Round Hill, Stirling Hill, and Zinc Lode at North mine received a larger proportion (e.g., N0.2) of votes for the Broken Hill deposit than predicted responses of gahnite from Champion, Globe, Melbourne Rockwell, Mutooroo, and Potosi, which are all below 0.2. Misclassified samples from the Broken Hill deposit and samples from minor Broken Hilltype occurrences with a response N 0.2 are labeled, with numbers

corresponding to Table 4, which lists their respective location, rock type, and assay values (weight % Pb; weight % Zn; Ag ppm) of its host rock. Although a Random Forest does not provide a prediction equation, the relative importance of any predictor can be assessed using the variable importance measure described by Breiman (2001b). For each tree in the forest, the out of bag cases are classified before and after randomly permuting the values of the predictor variable (whose importance is to be assessed) for the out of bag cases. The increase in misclassification rate caused by permutation serves as the measure of variable importance for the permuted variable. Using this approach, the centered log-ratios for Ni and Ga were identified as the two most important variables, whereas the centered log-ratio for Zn was least important. The relative importance of variables is as follows: Ni (0.182), Ga (0.158), Mn (0.091), Co (0.091), Fe (0.087), Mg (0.086), Cr (0.076), V (0.069), Cd (0.065), Al (0.054), and Zn (0.040). 5.2. Linear discriminant analysis The R function lda from the MASS R package (Venables and Ripley, 2002) was used to conduct a linear discriminant analysis of gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type deposits (the same classification as RF1). The average misclassification rate over ten 10-fold cross-validations was 11.6% (with a standard deviation of 0.3 percentage points) for linear discriminant analysis, more than four times the average misclassification rate for Random Forests. When linear discriminant analysis was applied to the entire training

J.J. O'Brien et al. / Journal of Geochemical Exploration 149 (2015) 74–86

Root Node

5.4. Random Forest 3 A two-category classification (RF3) of gahnite in rocks containing N 1 vol.% sulfides versus those in rocks containing only trace amounts of sulfide or no visible sulfides had a misclassification rate of 4.7% according to a ten-fold cross validation (Fig. 7). Misclassifications were confined to compositions of gahnite in rocks containing sulfides, which include those from the Broken Hill deposit, 11:30, Flying Doctor, Henry George, and the Zinc Lode at the North mine (Table 3). Compositions of gahnite in sulfide-poor rocks received an average predicted response ranging between 0.2 and 0.5, which include those from 11:30, Henry George, Mutooroo, Stirling Hill, and some from the main Broken Hill deposit and the Zinc Lode at the North mine.

Cobalt ≤ 50

> 50

Nickel

Vanadium ≤ 65

Node 1

≤5

> 65

>5

6. Discussion

1.0

1.0

1.0

1.0

0.5

0.5

0.5

0.5

0

Node 2

0

81

Node 3

0

Node 4

0

Gahnite in the Broken Hill deposit Gahnite in minor Broken Hill-type occurrences Fig. 4. An incomplete classification tree for a two-category classification of gahnite composition from the Broken Hill deposit versus gahnite in minor Broken Hill-type deposits modified after Breiman and Cutler (2004) and Smith et al. (2010). Note node 1 is homogenous (contains all gahnite compositions from the Broken Hill deposit); whereas nodes 2, 3, and 4 are heterogeneous in composition (contain gahnite from the Broken Hill deposit and minor Broken Hill-type occurrences).

dataset of 533 cases, the resulting linear discriminant rule for classifying cases as Broken Hill deposits was

0:67 Mg−1:30Fe þ 1:12Zn−0:96Al þ 0:20 V þ 0:48Cr−0:45Co þ 1:02Mn þ 0:08Ni þ 2:62Ga ≥ −7:34;

where Mg, Fe, Zn, Al, V, Cr, Co, Mn, Ni, and Ga represent the centered log-ratio values for the 11 elements.

5.3. Random Forest 2 A three-category classification (RF2) of gahnite in the Broken Hill deposit versus gahnite in minor Broken Hill-type deposits containing N 0.25 Mt sulfides versus gahnite in sulfide-poor and sulfide-free prospects containing b 0.25 Mt sulfides had a misclassification rate of 3.3% according to a ten-fold cross validation. Fig. 6 shows the probabilities for each of the three classes assigned by the Random Forest to all cases. Three compositions of gahnite from the Broken Hill deposit were misclassified as gahnite in minor Broken Hill type occurrences containing N 0.25 Mt, whereas two others were misclassified as being from sulfide-poor occurrences (Table 3). No compositions from the last two groups were misclassified as being from the Broken Hill deposit. Gahnite compositions from some sulfide-poor occurrences (i.e., Stirling Hill, Mutooroo, and Round Hill) were classified as having been derived from deposits that contain N 0.25 Mt, whereas three compositions from deposits containing N 0.25 Mt of sulfide mineralization (i.e., Potosi) were misclassified as gahnite in a sulfide-poor occurrence. Compositions from 11:30, Stirling Hill, and Round Hill received probabilities that ranged between 0.2 and 0.5 for the Broken Hill deposit.

Linear discriminant analysis was compared to Random Forests (i.e., RF1) because of its previous success in classifying mineral compositions (e.g., Clarke et al., 1989) and lithogeochemical datasets (e.g., El-Makky, 2011; Stokes et al., 1992). Linear discriminant analysis and Random Forests were used to distinguish compositions of gahnite in the Broken Hill deposit from those in minor Broken Hill-type occurrences, and yielded misclassification rates of 11.6 and 2.6%, respectively. Therefore, even though both techniques successfully classified compositions of gahnite, predictions by Random Forests were more accurate than linear discriminant analysis as indicated by the misclassification rates. According to misclassification rates determined by a 10-fold cross validation, Random Forests accurately classified gahnite chemistry for all three classification schemes: RF1, RF2, and RF3, which yielded misclassification rates of 2.6, 3.3, and 4.7%, respectively. Because compositions may be classified using previously grown forests, the success of these forests is crucial to their future application (Breiman, 2001a; Breiman and Cutler, 2004). Unlike principal component analysis (O'Brien et al., in press), RF1 was able to distinguish compositions of gahnite in the Broken Hill deposit from those in the minor Broken Hill-type occurrences (Fig. 5). One gahnite from minor Broken Hill-type occurrences (i.e., Henry George) was misclassified as being from the Broken Hill deposit. However, this sample occurs in a 1-m wide zone of high-grade sulfides (18.57 wt.% Zn; 14.05 wt.% Pb; 156 ppm Ag). Compositions from minor Broken Hill-type occurrences that have predicted responses between 0.2 and 0.5 (i.e., 11:30, Flying Doctor, Henry George, Round Hill, Stirling Hill, and Zinc Lode at North mine) are mostly from sulfidebearing rocks (e.g., Table 4) and deposits ~1 Mt in size (i.e., Flying Doctor, Henry George, the Zinc Lode at North mine). However, 11:30, Round Hill, and Stirling Hill are comparatively smaller, containing an estimated 0.2 Mt, 15 t, and 5 t of known sulfide ore, respectively. Compositions of gahnite from 11:30 received predicted responses between 0.2 and 0.5 and were associated with sulfides, whereas the assay values and the proximity of gahnite-bearing rocks to sulfides at the Round Hill and Stirling Hill deposits are unknown, because samples were collected from tailings piles surrounding historic mine workings rather than drill core. The composition of gahnite from the Henry George deposit was classified as being from the Broken Hill deposit, which suggests that the area surrounding the Henry George deposit may be a prospective target for further exploration. Compositions of gahnite from 11:30, Henry George, Round Hill, Stirling Hill, and the Zinc Lode at the North Mine received predicted responses ranging from 0.2 to 0.5, and although they were not classified as gahnite in the Broken Hill deposit, their elevated predicted response suggests that gahnite from these deposits may share compositional similarities with gahnite from the Broken Hill deposit. Additionally, compositions with predicted responses between 0.2 and 0.5 are mostly for gahnite associated with sulfides, which suggests that they should also be considered a target for future exploration.

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Random Forest 1: Deposits vs. averaged predicted response 1

Stirling Hill

1

2

1 2

2 3

Round Hill

3

Potosi 5 4

Zinc lode at North mine Mutooroo Melbourne Rockwell

6

Broken Hill

78 910

11 7 6 8 7

12,14 13

Henry George

13

13

13 15

16

13

Globe 17 18 19 20 20 18 20 22 21

Flying Doctor 11:30

23

Champion 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Averaged predicted response over 10 rounds Fig. 5. Predicted response of votes by Random Forests for compositions of gahnite from the Broken Hill deposit (1) versus minor Broken Hill-type occurrences (0). Predictions represent an average over ten 10-fold cross-validations. Numbers correspond to the deposits/prospects given in the caption of Fig. 3.

Results of RF1 show that compositions of gahnite from the Champion, Globe, Melbourne Rockwell, Mutooroo, and Potosi deposits received predicted responses b 0.2. Most of these deposits are small (i.e., Globe, Melbourne Rockwell) or the tonnages are unknown (i.e., Champion, Mutooroo). However, the Potosi deposit contains an estimated 1.6 Mt of sulfide ore. Low predicted responses of Potosi gahnite compositions may be due to the samples being collected from mine tailings adjacent to the Potosi pit, rather than being collected in situ (i.e., the spatial relationship to sulfides is unknown). Alternatively, low predicted responses for compositions of gahnite in the Potosi deposit may be related to how the deposit formed. According to Teale et al. (2006), highly deformed sulfides, along with quartz–gahnite rocks, occur in the Potosi shear zone, which suggests that sulfides were likely remobilized during prograde metamorphism. Although untested, gahnite associated with remobilized sulfides may have a different compositional signature than those

associated with non-mobilized sulfides, which may show low predicted responses. Samples were classified by RF2 to test whether or not gahnite in ore bodies N 0.25 Mt in size can be distinguished from sulfide-free Broken Hill-type occurrences, because in RF1, compositions of gahnite in both minor Broken Hill-type deposits (N 0.25 Mt) and some sulfide-free occurrences (e.g., Round Hill and Stirling Hill) received predicted responses ranging from 0.2 to 0.5. Additionally, in RF1, all compositions from the sulfide-free Champion, Melbourne Rockwell, and Mutooroo prospects, and the Potosi deposit, received predicted responses below 0.2. Therefore, RF2 was chosen to assess whether or not compositions of gahnite from sulfide deposits (N 0.25 Mt) can be distinguished from sulfide-free gahnite-bearing occurrences. Results of RF2 show that gahnite compositions from the Potosi deposit are mostly classified as being from minor Broken Hill-type deposits containing ~ 1 Mt of Pb–

Table 3 Summary of Random Forest 1, Random Forest 2, and Random Forest 3 statistical models. Deposit/rock type

(n)

RF1: number of misclassified

Percentages misclassified

RF2: number of misclassified

Percentages misclassified

RF3: number of misclassified

Percentages misclassified

Broken Hill Champion 11:30 Flying Doctor Globe Henry George Melbourne Rockwell Mutooroo Potosi Round Hill Stirling Hill Zinc Lode at the North mine Sulfide-bearing rocks Sulfide-free rocks

91 13 34 51 26 82 16 54 49 26 24 67 135 398

13 0 0 0 0 1 0 0 0 0 0 0 – –

14.3% 0.0% 0.0% 0.0% 0.0% 1.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% – –

5 0 0 2 1 1 0 1 4 2 2 2 – –

5.5% 0.0% 0.0% 3.9% 3.8% 1.2% 0.0% 1.9% 8.2% 7.7% 8.3% 3.0% – –

– – – – – – – – – – – – 26 0

– – – – – – – – – – – – 19.3% 0.0%

J.J. O'Brien et al. / Journal of Geochemical Exploration 149 (2015) 74–86

83

Table 4 Deposit, rock type, and ore grade (weight % Pb + Zn, Ag ppm) of compositions with a response N 0.20. Number

Sample ID

Deposit

Rock type

Wt.% Zn

Wt.% Pb

Ag ppm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

007-2-2 006-6-2 070-4-1 089-7-2 090-1-3 132-1-2 130-2-1 139-3-2 133-4-1 134-2-1 106-3-1 032-6-1 035-1-2 036A-2-1 033-1-1 029-2-1 073-5-1 099-3-1 095-2-2 099-2-1 040-1-2 044-5-1 044-5-1 039-1-2

Stirling Hill Stirling Hill Round Hill Zinc Lode at North mine Zinc Lode at North mine Broken Hill (C lode) Broken Hill (A lode) Broken Hill (C lode) Broken Hill (C lode) Broken Hill (B lode) Broken Hill (C lode) Henry George Henry George Henry George Henry George Henry George Flying Doctor Flying Doctor Flying Doctor Flying Doctor 11:30 11:30 11:30 11:30

Blue quartz–garnet–gahnite rock Quartz–gahnite–garnet rock Blue quartz–gahnite rock Sulfide-bearing quartz–gahnite rock Blue quartz–gahnite rock Quartz–garnet–gahnite rock Sulfide-bearing quartz–gahnite rock Sulfide-bearing quartz–gahnite rock Quartz–garnet–gahnite rock Quartz–garnet–gahnite–biotite rock Quartz–gahnite–garnet rock Sulfide-bearing biotite–garnet–gahnite rock Sulfide-bearing quartz–gahnite–muscovite rock Sulfide-bearing quartz–gahnite rock Sulfide bearing quartz–gahnite–biotite rock Quartz–garnet–gahnite rock Blue quartz–gahnite rock Blue quartz–gahnite rock Blue quartz–gahnite rock Blue quartz–gahnite rock Sulfide-bearing biotite–garnet–gahnite rock Quartz–biotite–garnet–gahnite rock Quartz–biotite–garnet–gahnite rock Quartz–biotite–garnet–gahnite rock

Unknown Unknown Unknown 4.72 0.82 Unknown Unknown Unknown Unknown Unknown Unknown 3.11 18.57 0.00 13.16 Unknown Unknown Unknown Unknown Unknown 0.19 2.92 2.92 18.60

Unknown Unknown Unknown 1.36 0.03 Unknown Unknown Unknown Unknown Unknown Unknown 0.00 14.05 0.31 2.50 Unknown Unknown Unknown Unknown Unknown 0.00 0.01 0.01 0.00

Unknown Unknown Unknown 135 17 Unknown Unknown Unknown Unknown Unknown Unknown 0 156 0 25 Unknown Unknown Unknown Unknown Unknown 0 5 5 0

and 0.5 include those from Broken Hill, 11:30, Henry George, Stirling Hill, Mutooroo, and the Zinc Lode at North mine. Although several sulfide-bearing rocks were misclassified, results suggest that Random Forests can be used to predict whether or not compositions of gahnite are spatially associated with the presence or absence of sulfides. The success of Random Forests may be critical to the use of gahnite compositions as exploration guides to sulfides elsewhere in the Broken Hill domain because compositions may be classified by forests grown in this study. RF1, RF2, and RF3 may be used by themselves or with each other, to recognize favorable targets for exploration on samples collected in situ, for targeted exploration, and on transported gahnite grains in the Broken Hill domain. Because gahnite is a resistate indicator mineral, it is mostly unaffected by weathering and may persist in surficial deposits (e.g., Averill, 2001; Morris et al., 1997; Spry and Teale, 2009)

Zn–Ag mineralization, with the exception of two compositions that are classified as sulfide-free occurrences. Compositions of gahnite from Round Hill and Stirling Hill are mostly classified as sulfide-free occurrences, with the exception of two and four compositions, respectively, which are misclassified as being from deposits containing N 0.25 Mt sulfides. As with RF1, the compositions of gahnite from 11:30, Flying Doctor, Henry George, Round Hill, Stirling Hill, and the Zinc Lode at the North mine received an average predicted response N 0.2 for the Broken Hill deposit, which further suggests compositional similarities between gahnite in these deposits and those in the supergiant Broken Hill deposit. Gahnite compositions can be classified on the basis of the presence or absence of sulfides using RF3. Compositions of gahnite in sulfidefree rocks that received an average predicted response between 0.2

Random Forest 2 Minor Broken Hill-type occurrences containing > 0.25 Mt

Broken Hill (n = 91) Champion (n = 13) 11:30 (n = 34) Flying Doctor (n = 51) Globe (n = 26) Henry George (n = 82) Melbourne Rockwell (n = 16) Mutooroo (n = 54) Potosi (n = 49) Round Hill (n = 26) Stirling Hill (n = 24) Zinc lode at the North mine (n = 67)

0.1

0.9

0.2

0.8

0.3

0.7

0.4

0.6

0.5

0.5

0.6

0.4

0.7

0.3

0.8

0.2

0.9

0.1

The Broken Hill deposit

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1 Deposits containing < 0.25 Mt

and Sulfide-free occurrences

Fig. 6. Triangular diagram of predicted response of votes by Random Forests for compositions of gahnite from the Broken Hill deposit, minor Broken Hill-type deposits containing N 0.25 Mt, and sulfide-free occurrences b 0.25 Mt. Predictions were generated using a 10-fold cross-validation.

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RF3: Sulfide-bearing and sulfide-free rocks vs. averaged predicted response Broken Hill (n = 91) Champion (n = 13) 11:30 (n = 34) Flying Doctor (n = 51) Globe (n = 26) Henry George (n = 82) Melbourne Rockwell (n = 16) Mutooroo (n = 54) Potosi (n = 49) Round Hill (n = 26) Stirling Hill (n = 24) Zinc lode at the North mine (n = 67)

Sulfide-bearing rocks

Sulfide-free rocks

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Averaged predicted response over 10 rounds Fig. 7. Predicted response of votes by Random Forests for compositions of gahnite from sulfide-bearing rocks (1) versus sulfide-free rocks (0). Predictions were generated using a 10-fold cross-validation.

such as in regolith (i.e., alluvial, colluvial, and aeolian) in the Broken Hill domain (e.g., Senior and Hill, 2002). Although the composition of detrital gahnite has yet to be obtained from the Broken Hill domain, the major-trace element chemistry of gahnite may serve to vector towards concealed Broken Hill-type mineralization covered by unconsolidated sediments. Successful classification of gahnite in the Broken Hill deposit from those in minor occurrences by Random Forests (RF1) suggests that this technique can be used to predict whether or not gahnite in gahnite-bearing rocks compositionally resembles gahnite in the Broken Hill deposit, and consequently, whether or not new areas are prospective for further exploration. Of the smaller Broken Hill prospects studied here, the composition of gahnite in the Henry George deposit most closely resembles those in the Broken Hill deposit, and therefore, should be considered a target for further exploration. Although compositions of gahnite in 11:30, Flying Doctor, Henry George, Round Hill, Stirling Hill, and the Zinc Lode at the North mine were not classified as being from the Broken Hill deposit, they show similarities to the Broken Hill deposit, and may also represent targets for further study using gahnite chemistry or other traditional exploration techniques. Random Forests created in this study should not be used indiscriminately to classify gahnite in other deposit types or ore fields. Although compositions of gahnite in other Broken Hill-type deposits from different domains (i.e., Broken Hill, South Africa) contain similar concentrations of trace elements, gahnite in sedimentary exhalative deposits and volcanogenic massive sulfide deposits is compositionally different (Layton-Matthews et al., 2013; O'Brien et al., 2013). Therefore, when used to fingerprint sulfide mineralization, Random Forests will likely be most successful when applied to exploration on a regional basis, and should constitute an affordable, nontraditional way to explore for metallic mineral deposits. 7. Conclusions 1. Random Forests and linear discriminant analysis differentiate the compositions of gahnite in the Broken Hill deposit from those in minor Broken Hill-type occurrences (RF1); although Random Forests

had a lower misclassification rate than linear discriminant analysis. Therefore, the Random Forest is considered to be the superior statistical technique of the two for the purposes of compositional discrimination in the Broken Hill domain. 2. Random Forests successfully classified gahnite in the following schemes: RF1 (gahnite from the Broken Hill deposit versus gahnite in minor Broken Hill-type deposits), RF2 (gahnite from the Broken Hill deposit versus gahnite in deposits ~ 1 Mt versus gahnite in sulfide-poor prospects), and RF3 (gahnite in sulfide-bearing rocks versus those in sulfide-poor rocks). This implies that this statistical technique, when applied to gahnite compositions, is useful as an exploration guide to Broken Hill-type mineralization in the Broken Hill domain, and has potential application for use of trace element compositions of other minerals (e.g., magnetite, chromite, garnet) in the exploration for ore deposits, in general. Now that that these three forests have been built, they can be used in the future for further gahnite studies involving the search for Broken Hill-type mineralization in the Broken Hill domain. 3. Compositions of gahnite from the Henry George deposit most closely resemble those from the Broken Hill deposit. Additionally, gahnite in 11:30, Flying Doctor, Henry George, Round Hill, Stirling Hill, and the Zinc Lode at the North mine overlaps in composition with those from Broken Hill deposit, and should be considered the most prospective deposits. Acknowledgments Funding for this project was provided by Perilya Limited, Society of Economic Geologists Hugh E. McKinstry Research Grant, and National Science Foundation Plant Genome Award0922746. We thank Ellery Frahm, Anette von der Handt, and Fred Davis from the Electron Microprobe Laboratory, University of Minnesota, for assistance with electron microprobe analyses, and Simon Jackson at the Geological Survey of Canada (Ottawa) for assistance with LA-ICP-MS analysis and reading a draft of this manuscript. The comments of John Carranza and an anonymous reviewer helped improve the manuscript.

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