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.
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
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
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)
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.