Geology, Chemostratigraphy, and Alteration Geochemistry of the Rosemont Cu-Mo-Ag Skarn Deposit,...
35
HBM Presented at TGDG, Toronto, ON | January 31, 2017 Geology, Chemostratigraphy, and Alteration Geochemistry of the Rosemont Cu-Mo-Ag Skarn Deposit, Southern Arizona by Juan Carlos Ordóñez-Calderón Sergio Gelcich
-
Upload
juan-carlos-ordonez-calderon-phd-pgeo -
Category
Data & Analytics
-
view
328 -
download
2
Transcript of Geology, Chemostratigraphy, and Alteration Geochemistry of the Rosemont Cu-Mo-Ag Skarn Deposit,...
HBM
Presented at TGDG, Toronto, ON | January 31, 2017
Geology, Chemostratigraphy, and Alteration
Geochemistry of the Rosemont Cu-Mo-Ag Skarn Deposit,
Southern Arizona by
Juan Carlos Ordóñez-Calderón
Sergio Gelcich
Contents
PRESENTATION | 2
Rosemont Geology and Mineralization
Part 1. Unsupervised Data Analysis: Compositional Data Analysis
for Lithogeochemistry and Chemostratigraphy
Part 2. Supervised Data Analysis: Predictive Models of Skarn
Alteration Facies
Conclusions
Acknowledgments
References
Rosemont Geology and Mineralization
PRESENTATION | 3
Regional geological context
Backbone Footwall Block
Graben Block Lower Plate
Upper Plate
Rosemont Geology and Mineralization
PRESENTATION | 4
Structural domains
Rosemont Geology and Mineralization
PRESENTATION | 5
Stratigraphy
Meso-cenozoic sequence
Paleozoic sequence
Precambrian Basement
Part 1. Unsupervised Data Analysis
PRESENTATION | 6
Compositional Data Analysis for
Lithogeochemistry and Chemostratigraphy Motivation for Compositional Data Analysis
What is compositional data (CoDa)
Motivation 1: Spurious correlations
Motivation 2: Problem with distances; a synthetic example
Exploratory Data Analysis
Cluster analysis on compositional variables
Principal component analysis
Mapping the Geochemical Space
Different sample spaces
Mapping in the simplex
Lithogeochemical model
Relationships between grades and lithogeochemistry
Mapping the Geospace
Geospatial distribution of lithogeochemical classes
Simplified chemostratigraphy
Motivation for Compositional Data Analysis
What is compositional data (CoDa)
PRESENTATION | 7
Compositional Data (CoDa) are vectors of positive components that
sum to a constant (e.g., 1, 100, 1 million, 1 billion, etc).
Those vectors represent parts of a whole which only carry relative
information.
Examples of compositional data include geochemical and
mineralogical data.
Standard multivariate statistical methods are not directly applicable
to compositional data in their raw form.
John Aitchison (1986)
Motivation for Compositional Data Analysis
Motivation 1: Spurious correlations
PRESENTATION | 8
Al
0 2000 6000 10000
020000
60000
02000
6000
10000
Ti
0 20000 60000 0 50000 150000
050000
150000
Fe
Al
0.00 0.02 0.04 0.06 0.08
0.0
0.2
0.4
0.6
0.8
0.0
00.0
20.0
40.0
60.0
8
Ti
0.0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1.0
0.2
0.4
0.6
0.8
1.0
Fe
Closed 3-part subcomposition scatter plot matrix Full composition scatter plot matrix
Karl Pearson (1897); Felix Chayes (1960); John Aitchison (1986)
Motivation for Compositional Data Analysis
Motivation 2: Problems with distances; a synthetic example
PRESENTATION | 9
-2 -1 0 1 2
-2-1
01
2
Compositional Data : Centred log ratios
clrAl2O3
Clr
SiO
20 20 40 60 80 100
02
04
06
08
01
00
Compositional Data : Raw Scale
x= Al2O3 (%)
y=
SiO
2 (
%)
1
2 3 3
2
1
Al2O3 SiO2 samp1 19.49 80.51 samp2 5.54 94.46 samp3 1.40 98.60
Al2O3 SiO2
samp1 + mass addition 19.49 (80.51+251.96) = samp2 + mass addition 19.49 ((80.51+251.96)+1040.48) =
Closure Al2O3 SiO2
Altered samp2 5.54 94.46 Altered samp3 1.40 98.60
Raw Geochemical Data Centered Log Ratio Transformation
𝑐𝑙𝑟 𝑥 = ln𝑥𝑖
𝑔𝑚(𝑥) 𝑖 = 1, … . , D
Exploratory Data Analysis
Variation Matrix
PRESENTATION | 10
Al Ca Ce Co Cr Hf La Mg Nb Ni P Sc Ta Th Ti V Y Zr
Al 0 5.78 0.23 0.93 1.54 0.71 0.43 2.92 0.13 1.58 1.24 0.38 0.35 0.26 0.22 0.84 0.73 0.82
Ca 5.78 0 4.82 4.16 2.26 3.73 4.02 2.01 5.09 2.40 3.65 4.34 4.37 5.75 5.54 3.68 3.17 3.80
Ce 0.23 4.82 0 0.70 1.15 0.61 0.10 2.43 0.18 1.22 1.00 0.31 0.30 0.29 0.32 0.61 0.41 0.73
Co 0.93 4.16 0.70 0 1.01 0.77 0.74 1.95 0.69 1.02 1.16 0.68 0.84 1.22 0.79 0.44 0.81 0.83
Cr 1.54 2.26 1.15 1.01 0 0.99 0.85 1.26 1.21 0.26 0.87 0.88 1.00 1.73 1.35 0.68 0.62 1.06
Hf 0.71 3.73 0.61 0.77 0.99 0 0.61 1.82 0.50 1.06 1.16 0.65 0.59 0.87 0.69 0.78 0.66 0.12
La 0.43 4.02 0.10 0.74 0.85 0.61 0 2.16 0.34 0.96 0.75 0.29 0.29 0.48 0.53 0.51 0.21 0.77
Mg 2.92 2.01 2.43 1.95 1.26 1.82 2.16 0 2.50 1.23 2.25 2.32 2.30 2.92 2.70 2.02 1.90 1.74
Nb 0.13 5.09 0.18 0.69 1.21 0.50 0.34 2.50 0 1.26 1.11 0.30 0.23 0.31 0.17 0.65 0.53 0.62
Ni 1.58 2.40 1.22 1.02 0.26 1.06 0.96 1.23 1.26 0 1.00 0.93 1.13 1.82 1.31 0.84 0.73 1.10
P 1.24 3.65 1.00 1.16 0.87 1.16 0.75 2.25 1.11 1.00 0 0.84 0.93 1.52 1.23 0.72 0.70 1.31
Sc 0.38 4.34 0.31 0.68 0.88 0.65 0.29 2.32 0.30 0.93 0.84 0 0.17 0.64 0.34 0.46 0.34 0.90
Ta 0.35 4.37 0.30 0.84 1.00 0.59 0.29 2.30 0.23 1.13 0.93 0.17 0 0.51 0.46 0.64 0.36 0.86
Th 0.26 5.75 0.29 1.22 1.73 0.87 0.48 2.92 0.31 1.82 1.52 0.64 0.51 0 0.47 1.13 0.77 0.99
Ti 0.22 5.54 0.32 0.79 1.35 0.69 0.53 2.70 0.17 1.31 1.23 0.34 0.46 0.47 0 0.74 0.74 0.77
V 0.84 3.68 0.61 0.44 0.68 0.78 0.51 2.02 0.65 0.84 0.72 0.46 0.64 1.13 0.74 0 0.53 0.87
Y 0.73 3.17 0.41 0.81 0.62 0.66 0.21 1.90 0.53 0.73 0.70 0.34 0.36 0.77 0.74 0.53 0 0.87
Zr 0.82 3.80 0.73 0.83 1.06 0.12 0.77 1.74 0.62 1.10 1.31 0.90 0.86 0.99 0.77 0.87 0.87 0
Variation Matrix
𝑡𝑖𝑗 = var lnxi
xj The variance of the logratio of parts i and j
Exploratory Data Analysis
Cluster analysis on compositional variables
PRESENTATION | 11
N scatter plots= D(D − 1)/2 N scatter plots = 820
Exploratory Data Analysis
Cluster analysis on compositional variables
PRESENTATION | 12
N scatter plots= D(D − 1)/2 N scatter plots = 153
Exploratory Data Analysis
Principal Component Analysis
PRESENTATION | 13
PC biplot on 18 variables
Cluster dendrogram on 18 variables
Mapping the Geochemical Space
Different sample spaces
PRESENTATION | 14
3D-Simplex
ilr-balances; 3D Real space
Raw data; 3D space
𝑏𝑖 = 𝑟 ∗ 𝑠
𝑟 + 𝑠 ln
𝑔𝑚(𝑐+)
𝑔𝑚(𝑐−)
𝑔𝑚 = 𝑥𝑖
𝑛
𝑖=1
1/𝑛
= 𝑥1𝑥2 …𝑥𝑛𝑛
Mapping the Geochemical Space
Mapping in the Simplex
PRESENTATION | 15
Cluster dendrogram on 18 variables
Effective geochemical mapping relies on good
understanding of the geometry of the
geochemical space; as much as geological
mapping relies in understanding the structural
geometry of the geospace.
Mapping the Geochemical Space
PRESENTATION | 16
Centered data Non centered data
Mapping in the Simplex
Centering operation
𝑐𝑒𝑛𝑡𝑒𝑟𝑒𝑑(𝑋) = 𝐶 1
𝑔𝑚(𝑥1),
1
𝑔𝑚(𝑥2),
1
𝑔𝑚(𝑥3)
Mapping the Geochemical Space
Lithogeochemical model
PRESENTATION | 17
SC = ZrHfThTiAlNbScTaYLaCeCrNiPCoV Lm= Ca Dol= Mg
Lithogeochemical Classes
Siliciclastic-Crystalline
Siliciclastic-Limestone
Siliciclastic-Dolostone
Limestone-Siliciclastic
Dolostone-Siliciclastic
Limestone
Dolostone
Mapping the Geochemical Space
PRESENTATION | 18
Copper (ppm) Box Plot 2D Simplex
Relationships between grades and the lithogeochemistry
Mapping the Geospace
PRESENTATION | 19
Geospatial distribution of lithogeochemical classes
Predictive Model in the Geospace
PRESENTATION | 20
Simplified chemostratigraphy
Upper plate arkose
Part 2. Supervised Data Analysis
PRESENTATION | 21
Predictive Models of Skarn Alteration Facies
Exploratory Data Analysis on Quantitative Mineralogy
Cluster analysis on variables vs. principal component analysis
Basic Concepts of Predictive Modelling
Model bias versus model variance; a synthetic example
Choosing the Best Predictive Model for Skarn Classification
Cross-validation: Training and test set accuracy
Rationale behind tree-based methods
The confusion matrix; assessing the predictive models by class
Quality of geological core logging by class
Predictive Models in the Geospace
Mapping the random forest predictive skarn model
Spatial relationships between skarn facies and porphyries
Exploratory Data Analysis
PRESENTATION | 22
Cluster Dendrogram
Ep
ido
te
K-f
eld
sp
ar
Pla
gio
cla
se
Am
ph
ibo
le
Serp
en
tin
e
Calc
ite
Do
lom
ite
Garn
et
Pyro
xen
e
Wo
llas
ton
ite
Vesu
via
nit
e
020
40
60
80
100
12
0
Qu
art
z
Calcic skarn
gnpxwovs
Magnesian skarn
SpAm
Epidote skarn
Ep
Cluster analysis on variables vs. principal component analysis
-20 -10 0 10 20
-20
-10
010
20
Form Biplot
Principal Component 1
-0.5 0.0 0.5
-0.5
0.0
0.5
o
oo
o
o
o
o
oo
oo
o
ooo
o
oo
o
o
oo
o
o
o
o
o
o
o
oo
o
o ooo
o
o
o
o
o
o
oo
o
o
o
o
o
o
o
o
o
o
o
o
o
ooooo
o
o
o
o
o o
oo
o
o
ooo
o
ooo
oooo
o
oo
o
o
oo
o
o
oo
oooo
ooo o o
oo
oo
o
o
o
o
o
o
o
o
oo
o
o
oo
o
oo
oo
o
o
o
o oo
o
o
o
o
o
ooo
o
o
o
o
oo
o o
oo
o
o oo
o
o
o
o
o
o
oo
o
o
oo
o
oo
o
o
o
o
oo
o
o
o
ooo
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
ooo
o
o
o oo
o
o
o
o
o
o
o
o
oo
o
o
o
o
o
o
o
o
o o
o
o
o
o
ooo
o
oo
o
o
oo
o
o
o
o
o
o
o
o
o
oo
o
o
o
o
o
o o
o
o
o
o
o oo
o
o ooo
o o
o
o
o
o
o
o o
o
o
o
ooo
o
o
o
o
oo
oo
o
o
o
o
o oo
o
o
o
o
o
o
o
o
o
o
o
o
oo
o
o
oo
o
o
oo
oo
o
o
o
o
o
o
o
o
o
o o
o
o
o
o
o
o
oo
o
o
oo
o o
oo
o
ooo oo
oo
o
o
o
o
o
o
o
o
o
o
oo
o
o
o
ooo
oo
o
o
o
o
o
o
ooo
o
o
o
o
o
o
o
oo o
o
o
o
oo
o
o
o
o o
oooo
o
o
o
o
o
o
o
o
o
o
o
o o
oo
o
o
o
o
o
o
oooo
o
ooo
o
o
o oo oo
oooo
o o
ooo
o
oo
o
o
oo
o oo
o
o
o
ooo
o
o
o
oo
ooo o o
o
o
o
o
o
o
o
o
o
oo
oo
o
oo
oo
oo
o
o
o
o
o
ooo
ooo
o
o
oooo
o
o
o
oo
oo
o
o
oo
o
o
oo
o
o
oo
o
o
o
o
ooo
o
o
o
o
oo
o
o
ooo
o
o
o
o
o o
o
o
o
o
o
o
o
oooo o ooo
oo
oo
o
o
o
o
o
oo
oo
o
o
oo
oooooo
o
oo
oo
ooo
o
oo
o
o
o
ooo
o
o
oo
oo
oo
oo
oooo
oo
o o
o
oo
o
o
ooo
o
o
o
o
o
o
o
o
oo
oo
o
oo
o
o
o
o
o o
o
o
o
oo
o
o o
o
oo
o o
o
o
o
o o
o
oo
o
oo
oo
o o
o
oo
o
o
o
o
o o
o
oo
o
o
o
oo
o
o
o
oo o o
o
ooooo
oo
o
oo o
o
o
o
o
o
o
o
oo
o
o
o
oo
o
oooo
o
oo
ooo
o
o
o
o
o
oo
oo
o
o
o
oo
o
o
o
o
oo
oo oo o
o
o
o
o
o
o
o
o
o
oo
ooo
ooooo
o
o
o
oo
o
o
o
o
oo
o
o
o
o
o
oo
o
oo
o
ooo
o
oo
o
o
o
o
o
ooo
o
oo
o
o
o
o
o
oo
oo
o
oo
oo o
o
o
o
oo
o
o
o
o o oo o
oo
o
o
oo
o
o
oo o
o
o
o
WollastoniteVesuvianite
Garnet
Calcite
DolomitePyroxene
SerpentineAmphibole
K-feldspar
Plagioclase
Quartz
Epidote
Pri
ncip
al C
om
po
nen
t 2
400 samples with mineralogy
>30,000 samples with geochemistry
Basic Concepts of Predictive Modelling
Model bias versus model variance; a synthetic example
PRESENTATION | 23
0.0 0.2 0.4 0.6 0.8 1.0
-6-5
-4-3
-2-1
0
Training Data
Predictor Variable x
Response V
ari
able
y
0.0 0.2 0.4 0.6 0.8 1.0
-6-5
-4-3
-2-1
0
Test Data
Predictor Variable x
Response V
ari
able
y
RSE1= 0.15 RSE2= 0.26 (↑73%)
Basic Concepts of Predictive Modelling
PRESENTATION | 24
0.0 0.2 0.4 0.6 0.8 1.0
-6-5
-4-3
-2-1
0
Training Data
Predictor Variable x
Response V
ari
able
y
0.0 0.2 0.4 0.6 0.8 1.0
-6-5
-4-3
-2-1
0
Test Data
Predictor Variable x
Response V
ari
able
y0.0 0.2 0.4 0.6 0.8 1.0
-6-5
-4-3
-2-1
0
Training Data
Predictor Variable x
Response V
ari
able
y0.0 0.2 0.4 0.6 0.8 1.0
-6-5
-4-3
-2-1
0
Test Data
Predictor Variable x
Response V
ari
able
y
RSE1= 0.15 RSE2= 0.26 (↑73%)
RSE1= 0.46 (↑207%) RSE2= 0.31 (↑20%) I.E = 0.27
Key concepts • Bias • Variance • Overfitting • Irreducible Error (I.E)
Optimum balance between bias and variance
Model bias versus model variance; a synthetic example
Choosing the Best Predictive Model
Cross-validation: Training and test set accuracy
PRESENTATION | 25
Support vector machines (SVM)
Quadratic discriminant analysis (QDA)
Linear discriminant analysis (LDA)
Classification and regression trees
(CART)
Random forests (RF)
Training set
90%
Test set
10%
10-fold cross-validation
Choosing the Best Predictive Model
PRESENTATION | 26
Cross-validation: Training and test set accuracy
Support vector machines (SVM)
Quadratic discriminant analysis (QDA)
Linear discriminant analysis (LDA)
Classification and regression trees
(CART)
Random forests (RF)
Choosing the Best Predictive Model
PRESENTATION | 27
Rationale behind tree-based methods
Choosing the Best Predictive Model
The confusion matrix; assessing the predictive models by class
PRESENTATION | 28
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 79% 7% 5% 9% 100%
Serpentine-Amphibole 10% 70% 5% 15% 100%
Epidote 15% 2% 72% 11% 100%
Least Altered 7% 5% 4% 84% 100%
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 86% 17% 26% 9%
Serpentine-Amphibole 5% 72% 9% 7%
Epidote 2% 1% 47% 2%
Least Altered 7% 10% 18% 82%
100% 100% 100% 100%
True Classes
Pre
dic
ted
Cla
ss
es
True Classes
Pre
dic
ted
Cla
ss
es
Random Forest (nt= 500, m=15) Confusion Matrix Test Set Precision
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 79% 7% 5% 9% 100%
Serpentine-Amphibole 10% 70% 5% 15% 100%
Epidote 15% 2% 72% 11% 100%
Least Altered 7% 5% 4% 84% 100%
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 86% 17% 26% 9%
Serpentine-Amphibole 5% 72% 9% 7%
Epidote 2% 1% 47% 2%
Least Altered 7% 10% 18% 82%
100% 100% 100% 100%
True Classes
Pre
dic
ted
Cla
ss
es
True Classes
Pre
dic
ted
Cla
ss
es
Random Forest (nt= 500, m=15) Confusion Matrix Test Set True Class Prediction Rate
Choosing the Best Predictive Model
Quality of geological core logging by class
PRESENTATION | 29
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 66% 13% 7% 14% 100%
Serpentine-Amphibole 13% 57% 3% 26% 100%
Epidote 13% 0% 37% 50% 100%
Least Altered 20% 12% 5% 63% 100%
Unknown 32% 15% 12% 41% 100%
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 58% 25% 27% 12%
Serpentine-Amphibole 4% 34% 4% 7%
Epidote 2% 0% 19% 6%
Least Altered 16% 21% 16% 50%
Unknown 20% 20% 33% 25%
100% 100% 100% 100%
True Classes
Pre
dic
ted
Cla
ss
es
True Classes
Pre
dic
ted
Cla
ss
es
Geologist Visual Core Logging Confusion Matrix True Class Prediction Rate
Geologist Visual Core Logging Confusion Matrix True Class Prediction Rate
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 66% 13% 7% 14% 100%
Serpentine-Amphibole 13% 57% 3% 26% 100%
Epidote 13% 0% 37% 50% 100%
Least Altered 20% 12% 5% 63% 100%
Unknown 32% 15% 12% 41% 100%
Garnet-Pyroxene-Wollastonite-Vesuvianite Serpentine-Amphibole Epidote Least Altered
Garnet-Pyroxene-Wollastonite-Vesuvianite 58% 25% 27% 12%
Serpentine-Amphibole 4% 34% 4% 7%
Epidote 2% 0% 19% 6%
Least Altered 16% 21% 16% 50%
Unknown 20% 20% 33% 25%
100% 100% 100% 100%
True Classes
Pre
dic
ted
Cla
ss
es
True Classes
Pre
dic
ted
Cla
ss
es
Predictive Model in the Geospace
Mapping the random forest predictive skarn model
PRESENTATION | 30
Skarn Class Garnet-Pyroxene-Wollastonite-Vesuvianite
Serpentine-Amphibole
Epidote
Least Altered
Predictive Model in the Geospace
PRESENTATION | 31
Garnet-Pyroxene-Wollastonite-Vesuvianite
Skarn Class
Serpentine-Amphibole
Epidote
Porphyries
Low angle fault
Backbone fault
Spatial relationships between skarn facies and porphyries
Acknowledgments
PRESENTATION | 32
References
PRESENTATION | 33
Aitchison, J., 1986. The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. London, Chapman &
Hall, 416 pp.
Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V., (eds) 2006. Compositional Data Analysis in the Geosciences: From Theory to
Practice. Geological Society, London, Special Publications, 264 pp.
Chayes, F., 1960. On Correlation Between Variables of Constant Sum. Journal of Geophysical Research, 65 (12), 4185-4193.
Chayes, F., 1971. Ratio Correlation, University of Chicago Press, Chicago, IL, 99 pp.
Egozcue, J.J., Pawlowsky-Glahn, V., 2005. Groups of Parts and Their Balances in Compositional Data Analysis. Mathematical Geology,
37(7), 795-828.
Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barceló-Vidal, C., 2003. Isometric Logratio Transformations for Compositional
Data Analysis. Mathematical Geology, 35 (3), 279-300.
Hastie, T., Tibshirani, R., Friedman, J., 2009. The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Ed.
Springer, 745 pp.
James, G., Witten, D., Hastie, T., Tibshirani, R., 2015. An Introduction to Statistical Learning: with Applications in R. Springer, 426 pp.
Kuhn, M., Johnson, K., 2013. Applied Predictive Modeling. Springer, 600 pp.
Martín-Fernández, J.A., Barceló-Vidal, C., Pawlowsky-Glahn, V., 1998. A Critical Approach to Non-parametric Classification of
Compositional Data. In: Rizzi, A., Vichi, M., Bock, H., (eds). Advances in Data Science and Classification. Proceedings of the 6th
Conference of the International Federation of Classification Societies (IFCS-98), Rome, July 21-24, 1998. Springer, 49-56.
Pawlowsky-Glahn, V., Buccianti, A., (eds) 2011. Compositional Data Analysis: Theory and Applications. John Wiley & Sons, Ltd., 378 pp.
Pawlowsky-Glahn, V., Egozcue, J.J., Tolosana-Delgado, R., (eds) 2015. Modeling and Analysis of Compositional Data. John Wiley &
Sons, Ltd., 247 pp.
Pearson, K., 1897. Mathematical Contributions to the Theory of Evolution. On a form of Spurious correlation Which May Arise When
Indices Are Used in the Measurement of Organs. Proceedings of the Royal Society of London, LX, 489-502.
R Core Team 2017. R: A Language and Environment for Statistical Computing. R Foundation for Statistical. Computing, Vienna, Austria,
https://www.r-project.org/
van den Boogaart, K.G., Tolosana-Delgado, R., (eds) 2013. Analyzing Compositional Data with R. Springer, 258 pp.
Tolosana-Delgado, R., Otero, N., Pawlowsky-Glahn, V., 2005. Some Basic Concepts of Compositional Geometry. Mathematical Geology,
37 (7), 673-680.
Software
PRESENTATION | 34
R packages for statistical computing
Adler, D., Murdoch, D., 2017. R Package “rgl”, Version 0.97.0. 3D Visualization Using OpenGL, 143 pp.
Breiman, L., Cutler, A., Liaw, A., Wiener, M., 2015. R Package “randomForest”, Version 4.6-12. Breiman and Cutler's Random Forests for
Classification and Regression, 29 pp.
Meyer, D., Dimitriadou, E., Hornik, K., Weingessel, A., Leisch, F., Chang, C-C., Lin, C-C., 2015. R Package “e1071”, Version 1.6-7. Misc
Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien, 62 pp.
R Core Team 2017. R: A Language and Environment for Statistical Computing. R Foundation for Statistical. Computing, Vienna, Austria,
https://www.r-project.org/
Ripley, B., 2016. R Package “tree”, Version 1.0-37. Classification and Regression Trees, 19 pp.
Ripley, B., Venables, B., Bates, D.M., Hornik, K., Gebhardt, A., Firth, D., 2016. R Package “MASS”, Version 7.3-45. Support Functions and
Datasets for Venables and Ripley's MASS, 169 pp.
van den Boogaart, K.G., Tolosana-Delgado, R., Bren, M., 2015. R Package “compositions”, Version 1.40-1. Compositional Data Analysis,
264 pp.
3D modeling software
Leapfrog Geo, Version 4.0.
Data visualization
Adler, D., Murdoch, D., 2017. R Package “rgl”, Version 0.97.0. 3D Visualization Using OpenGL, 143 pp.
ioGAS, Reflex, Version 6.2.1
For more information contact:
Juan Carlos Ordóñez-Calderón, Geochemist
416.564.4174 | [email protected]
For investor inquiries, please contact:
Candace Brûlé, Director, Investor Relations
416.814.4387 | [email protected]
