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The use of geochemical survey data for predictive geologic mapping at regional and continental scales Eric Grunsky Distinguished Lecturer International Association for Mathematical Geociences Servei dEstadistica Aplicada Universitat Autonoma de Barcelona Barcelona, Spain 09-June-2015

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Acknowledgements International Association for Mathematical Geosciences (IAMG) CoDaWork15

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Overview Introduction The nature and scale of geochemical surveys. Discovery and validation of structure (geochemical processes). Common issues in evaluating geochemical data. Evaluating geochemical data using multivariate methods. Kimberlite classification using lithogeochemistry. Predictive mapping of geochemical data using multivariate methods applied to multi-element geochemical survey data Regional mapping Predictive lithologic mapping using lake sediment geochemistry in northern Canada. Predictive geologic mapping in areas based on multi-element lake sediment geochemistry survey data an example from Nunavut Canada. Continental geochemical surveys What the US Soil Survey reveals about lithology, ecosystems and climate.

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Geochemical Surveys Geochemical surveys are conducted to provide baseline information for: Mineral exploration Geologic mapping Baseline values for environment/land use purposes

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Geochemical Survey Data Geochemical survey data are a rich source of information for geological, geochemical, environmental and climatic processes. More than 50 elements can be analyzed at sufficiently low detection limits. Geochemical data reflect processes that form or affect mineralogy. These data represent a multivariate data space over a two or three dimensional geographic space and time.

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Defining Scales of Geochemical Surveys Continental Scale > 1:500,000 & < 1:1,000,000 Mapping large crustal blocks/tectonic assemblages. Regional Scale - > 1:50,000 & < 1:500,000 Regional geological mapping Local/Camp Scale < 1:50,000 Exploration scale studies and detailed geologic mapping.

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Continental Scale > 1:500,000 & < 1:1,000,000 Mapping large crustal blocks/tectonic assemblages. USGS Soil Survey NGSA -National Geochemical Survey of Australia 1 site/1600km 2 1 site/5200km 2

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Regional scale of geochemical surveys 1:250,000 1 site/13km 2

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Structure in Data Structure in data are trends/patterns that can be described by linear and non-linear methods. Geochemical data reflect the structure of stoichiometry the ordered arrangement of elements according to atomic forces.

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The Closure Problem What is it? Geochemical analyses are typically reported as a part of a composition (weight %, ppm, ppb, g/t, mg/kg). All values are relative and sum to a constant (100%, 1000000 ppm,). If one value changes, then, by definition, all other values must change to maintain the constant sum. Thus, the variables (oxides, elements) are not independent.

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Closure Implications for Statistical Methods Statistical methods assume that the variables are independent. Since geochemical data variables are not independent, standard statistical methods are not valid. Statistical methods are based on values ranging from - to + whereas compositional data are constrained from 0 to a constant value [the simplex].

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Effects of Closure on Values & Ratios Ratios dont change! Adding CO2 To the composition changes the relative values but not the ratios.

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Correlation Coefficients Subcompositional Incoherence SiO2 TiO2 Al2O3 FeO MgO CaO SiO2 1.00 -0.66 -0.68 -0.23 0.64 -0.22 TiO2 1.00 0.44 0.09 -0.44 0.12 Al2O3 1.00 -0.40 -0.21 0.50 FeO 1.00 -0.55 -0.73 MgO 1.00 -0.11 CaO 1.00 SiO2 FeO MgO CaO SiO2 1.00 -0.64 0.66 0.04 FeO -0.63 -0.70 MgO 1.00 -0.09 CaO 1.00 Correlation Coefficients Based on 4 Elements - closed Correlation Coefficients Based on 6 Elements - closed Same data but different correlation coefficients

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Compositional Data Logratios Additive Logratio (alr) [Aitchison (1983)] y i = log(x i /x D ) (i = 1, , D-1) where x D = a compositional component of choice Centred Logratio (clr) [Aitchison (1983)] z i = log(x i /g(x D )) (i = 1, , D), where g(x D ) is the geometric mean of the composition Isometric Logratio (ilr) [Egozcue et al. (2003)] Combinations of elements that represent balances that result in an orthonormal space. ilr i = k [ln(g(x + )/g(x - ))] For 5+ part composition: (6/5) 1/2 ln(x 1 x 2 x 3 ) 1/3 (x 4 x 5 ) 1/2

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Olivine Crystal Structure Blue/Cyan Oxygen Green/Yellow Mg/Fe Magenta Si SiO4 tetrahedra with a Charge of -2, bind with Mg-Fe-Mn cations with charges of +2 Source: http://www.uwgb.edu/DutchS/petrolgy/Olivine-Structure.HTM Mg Fe Mn O O O O Si Al and Ti which have the same ionic charge as Si and can also substitute. Crystal defects can allow any other similar-sized cation enter the structure.

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Hawaii Olivines (Mg,Fe) 2 [SiO 4 ] Si is constant relative to Fe and Mg

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Geochemical Data Spaces Variable Space structure in the elements (stoichiometry) Statistics and Data visualization. Numerous graphical and statistical methods characterize and describe the variables. Geographic Space 2D or 3D (geospatial structure) Geographic representation of data using Geographic Information Systems (GIS) or Image Analysis Systems Geostatistical Analysis spatial processes.

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Investigating and Visualizing Structure in Geochemical Data Exploratory Approach (Process Discovery) Empirical investigate and characterize data. few assumptions. Scatter plot matrix, principal component analysis. Build models Modelled Approach (Process Validation) Create statistically distinct groups of geochemical data that represent classes that can be used to test and classify unknown samples or validate existing populations. Regression, discriminant analysis, neural networks. Forms the basis for predictive mapping. Test models

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The Challenges in Evaluating Geochemical Data Different - methods of digestion, limits of detection, instrumentation Level the data where appropriate Censoring- samples detection limit Remove or impute elements Missing values and zeros Delete elements or compute replacement values depending on objectives. Constant sum (closure) problem Application of ratios and logratios Spatial schemes & Geostatistical evaluation Adequate Spatial Sample Design

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Kimberlite Classification using Lithogeochemistry

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Local/Camp Scale < 1:50,000 Exploration scale studies and detailed geologic mapping. Star Kimberlite Fort a la Corne - Saskatchewan

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Kimberlite Classification using Lithogeochemistry Lithogeochemical sampling program of drill core from a series of kimberlite eruptions. Kimberlite mineralogy varies from olivine bearing magmas to fractionated magmas contaminated by crust. Kimberlites analyzed the following oxides/elements converted to cation values : Si, Ti, Al, Fe, Mg, Ca, Na, K, P, Rb, Nb, Zr, Th, V, Cr, Co, Ni, La, Er, Yb, Y, Ga

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Kimberlite Phases Classification - Visually-based Early Joli Fou Mid Joli FouLate Joli Fou Pense Cantuar

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Kimberlite Fractionation Trends [stoichiometric control]

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Kimberlites Logcentred PCA Process Discovery PC1-2 = 66% PC1-4 = 80% PC1-7 = 90% Overall variation [Grunsky & Kjarsgaard, 2008] Higher Grade Macrodiamonds Lower Grade Macrodiamonds Kimberlite Fractionation Crustal Contamination Mantle Contamination

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Kimberlite Suite Linear Discriminant Analysis Process Validation Classification based on PC1-7

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Kimberlite Suite Classification Accuracy Accuracy/Confusion Matrix

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Using logratio techniques with kimberlite lithogeochemistry: Describe geochemical trends related to kimberlite formation, contamination by deep mantle and near surface rocks. Classify, predict and identify phases of kimberlite that are relatively rich in diamonds. Methodology is currently being employed in mining activities

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Evaluating Geochemical Data Using Multivariate Methods and Predictive Mapping

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The Process of Predictive Mapping Process Discovery The use of empirical methods for identifying structure in data and forms the basis/justification to build or test models: Adjust data for censoring/missing values. Transform data to the centred logratio space. Discovery of processes through empirical analysis (principal component analysis, multidimensional scaling, cluster analysis). Determine suitable classes for predictive mapping (e.g. lithologic units). Tag classes to sample sites where available using GIS.

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The Process of Predictive Mapping Process Validation The use of modelled methods for process confirmation: Analysis of variance to determine which elements or principal components give maximum separation of the classes. Repeatedly sample the data for the generation of training sets and unknown observations (cross validation). Discriminant analysis to determine posterior probability or typicality from which a probability of class membership is assigned to each site. Other methods can be used (e.g. Random Forests). Spatial analysis to calculate semi-variograms and subsequent kriging (interpolation) to produce predictive maps for each class. Calculate accuracy of prediction for each class and overall accuracy.

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Predictive Lithologic Mapping and Mineralization Potential Using Lake Sediment Geochemistry in Northern Canada Eric Grunsky 1, David Corrigan 1, Ute Mueller 2 1 Geological Survey of Canada, Natural Resources Canada, Ottawa, Canada 2 School of Engineering, Edith Cowan University, Western Australia, Australia

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Melville Peninsula

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Melville Peninsula Geochemical Data 1631 re-analyzed lake sediment geochemical data Mix of ICP (aqua regia) & INA (complete) analyses. 46 elements -Ag, Al, As, Au, Ba, Bi, Br, Ca, Cd, Ce, Co, Cr, Cs, Cu, Eu, Fe, Ga, Hf, Hg, K, La, Lu, Mg, Mn, Mo, Na, Ni, P, Pb, Rb, S, Sb, Sc, Se, Sm, Sr, Ta, Tb, Te, Th, Tl, U, V, W, Yb, Zn Data corrected for censoring. Centred logratio applied to the data 8 lithologic units suitable for classification.( Akg, Agd, Agu, Amgn, APWs Ps1/2, Ps3, PHg) Although alr/ilr are suitable transformations for classification, PCs derived from clr offer some advantages

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Lake Sediment Sampling Sites Melville Peninsula Sample Site 8 lithologic units suitable for classification. ( Akg, Agd, Agu, Amgn, APWs Ps1/2, Ps3, PHg)

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Process Discovery (Empirical) PCA Biplot (clr) of Lake Sediment Geochemistry Screeplot 62% variability Under-sampled &/or Random Processes Geochemical /Physical Processes Biplot Agd/Amgn Ps/Hg Akg Coded by Underlying Lithology

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PC1 Till Blanket/Veneer/Felsenmeer

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PC2 Lithological Contrast Supracrustal - Granitoid Granitoid Supracrustal

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Analysis of Variance Testing lithologic separation (8 classes) using log-centred elements Moderate Decay for Group Separation More than 25 elements are required for high lithologic separation

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Analysis of Variance Testing lithologic separation (8 classes) using PCA Steep Decay for Group Separation Only 6 PCs are required for high lithologic separation PCs represent linear combinations of elements controlled by processes (stoichiometry &/or physical processes)

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Process Validation (Hypothesis Testing) Linear Discriminant Plot of Lake Sediment Geochemistry code by Lithology 87% of the discrimination is accounted for in LD1 & LD2. Note2: PHg is compositionally similar with Ps1/2 and Ps3. S-type granite? supracrustal K-rich granitoid granodiorite Note1: Significant overlap of classes!

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Accuracy of Lithological Classification based on Lake Sediment Geochemistry

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Variogram Map Identifying Anisotropy and Range Agd Ute Mueller Edith Cowan University

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Predictive Mapping Posterior Probabilities AguAgd Ps1/2Ps3 Akg PHg Posterior probability a forced fit into the class that has the shortest Mahalanobis distance to each class centroid.

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Predictive Mapping Typicality AguAgd Ps1/2Ps3 Akg PHg Typicality class membership based on Mahalanobis distance and the Chi-square distribution. A sample may not belong to any of the classes.

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Continental Scale Geochemical Mapping United States Soil Geochemistry Survey with Dave Smith, Larry Drew, Laurel Woodruff, Dave Sutphin USGS Laboratory Methods/Protocols 4 acid digestion ICP-MS/AES Instrument QA/QC protocols followed and documented. Low Density Sampling: 1 sample site\1,600 km 2 Sampling strategy based on Generalized Random Tessellation Survey Design (GRTS) 4857 sample sites x 3

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US Soil Survey Sample Sites Elements (43): Ag, Al, As, Ba, Be, Bi, C_Tot, Ca, Cd, Ce, Co, Cr, Cs, Cu, Fe, Ga, Hg, In, K, La, Li, Mg, Mn, Mo, Na, Nb, Ni, P, Pb, Rb, S, Sb, Sc, Se, Sn, Sr, Te, Th, Ti, Tl, U, V, W, Y, Zn

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Sampling the Soil Profile Unweathered mineral matter. Effects of groundwater, vegetation, oxidation. (not sampled) Oxidized, bioturbated and organic debris, extensive weathering of mineral matter. Top Layer = 0 to 5cm. Organic debris with little mineral matter. Progressive weathering of mineral matter up the profile. weathering

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Process Discovery

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Maps of PC1/PC2 [C Horizon] mafic feldspars/ carbonates felsic weathering/ organic mafic felsic feldspars/carbonates weathering/shales 0-5 cm layer A horizon C horizon Eolian Dunes

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Principal Component Analysis Biplot PC2/PC3 [A Horizon] A Horizon Mafic Feldspars Organic material/Shales/Weathering Carbonates PC3

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Difficulty in Identifying Processes In large continental scale surveys only coarse lithologic distinctions can be observed in principal component analysis biplots. It is difficult to identify specific processes due to the mixture of processes from many sources. Can we test existing models and validate the use of geochemistry for geology/crustal processes using models derived from other types of data?

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Soil Geochemistry for Characterization and Classification Can soil geochemistry be used to describe and classify geology, ecosystems and climate? The relative relationships of the data reveal information on surface lithologies, weathering, groundwater effects terrestrial ecosystems (soil moisture, vegetation). There are no continental-scale lithologic maps on which to predict lithology from soil geochemistry.

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Terrestrial Ecosystems / Surface Lithology / Climate Derived from A New Map of Standardized Terrestrial Ecosystems of the Conterminous United States (USGS Professional Paper 1768) Sayre et al. (2009). 1.Terrestrial Ecosystems - distribution of vegetation to climatic parameters (8 classes). 2.Thermotypes - thermoclimatic belts based on annual temperature thresholds / thermicity index thresholds (29 classes). 3.Ombrotypes - ombroclimatic belts - based on total positive precipitation and temperature (8 classes). 4.Surface lithologies (18 classes)

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Ecosystems/Climate/Lithology Humidity Thermal RegionsTerrestrial Ecosystems Surface Lithologies Initial resolution 1km resampled to 40km

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Process Validation

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Linear Discriminant Analysis Surface Lithology Eolian Dunes Significant overlap with other non carbonate residual material Predictive Accuracy 26% ilr transform C Horizon

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Predictive Maps of Surface Lithologies (posterior probability) [0-5 cm layer] Alluvium Colluvium Glacial Outwash Eolian Dunes Eolian Loess Glacial Lake Sediments Glacial Till - Loam Glacial Till - Clay Glacial Till - Coarse spatial coherence

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Predictive Maps of Surface Lithologies (posterior probability) [0-5 cm layer] Extrusive volcanicsCoastal Zone SedimentsSaline Lake Deposits Residual Ca Soils Residual Si Soils spatial coherence Surface Lithologies

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Summary A combined compositional and multivariate approach using geochemistry, enables the discovery of processes through the identification of structure (patterns/trends). These trends are defined through a combination of stoichiometric constraints on mineral formation and mixing of minerals by magmatic/metamorphic/sedimentary processes. In regional and continental scale studies it is difficult to identify specific lithologies/processes because of compositional overlap due to a lack of knowledge of the constituent mineralogy derived from these processes; followed by glacial action and/or subsequent weathering.

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Summary The establishment of training sets (specific lithologies, ecosystems, landforms, climate) can assist in the study and prediction in areas where there is a lack of information. Overlap between classes (lithologies) is expected and the use of posterior probabilities can identify the degree of distinctiveness and overlap. The results demonstrated from predictive mapping confirm the capacity of geochemical data to test new hypotheses from which new geological/geochemical process maps can be created. The results presented here confirm the value of using logratios in the evaluation of geochemical data.

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Comments/Questions/Further Discussion egrunsky@gmail.com