Transcript The use of geochemical survey data for predictive geologic mapping

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 d’Estadistica Aplicada
Universitat Autonoma de Barcelona
Barcelona, Spain
09-June-2015
Acknowledgements
• International Association for Mathematical
Geosciences (IAMG)
• CoDaWork15
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.
Geochemical Surveys
Geochemical surveys are conducted to provide
baseline information for:
• Mineral exploration
• Geologic mapping
• Baseline values for environment/land use purposes
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.
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.
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/1600km2
1 site/5200km2
Regional scale of geochemical surveys
1:250,000
1 site/13km2
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.
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.
“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”].
Effects of Closure on Values & Ratios
Adding CO2
To the composition
changes the relative
values but not the
ratios.
Ratios don’t change!
Correlation Coefficients
Subcompositional Incoherence
Correlation Coefficients Based on 6 Elements - closed
SiO2
TiO2
Al2O3
FeO
MgO
CaO
SiO2 TiO2 Al2O3 FeO
MgO
CaO
1.00 -0.66 -0.68 -0.23 0.64 -0.22
1.00 0.44 0.09 -0.44 0.12
1.00 -0.40 -0.21 0.50
1.00 -0.55 -0.73
1.00 -0.11
1.00
Correlation Coefficients Based on 4 Elements - closed
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
Same data but different correlation coefficients
Compositional Data – Logratios
Additive Logratio (alr) [Aitchison (1983)]
yi = log(xi/xD) (i = 1, …, D-1)
where xD = a compositional component of choice
Centred Logratio (clr) [Aitchison (1983)]
zi = log(xi/g(xD)) (i = 1, …, D),
where g(xD) 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.
ilri = k [ln(g(x+)/g(x-))]
For 5+ part composition:
(6/5)1/2 ln(x1 x2 x3)1/3
(x4 x5)1/2
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
Al and Ti which have the Si
same ionic charge as Si
and can also substitute.
Mn O
O O Mg
Fe O
Crystal defects can allow
any other similar-sized
cation enter the structure.
Source: http://www.uwgb.edu/DutchS/petrolgy/Olivine-Structure.HTM
Hawaii Olivines
(Mg,Fe)2 [SiO4]
Si is constant relative to Fe and Mg
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.
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
The Challenges in Evaluating
Geochemical Data
Different  methods of digestion,
 limits of detection,

instrumentation
Censoringsamples < | > detection limit
Missing values and zeros
Constant sum (closure)
problem
Adequate Spatial Sample
Design
Level the data where
appropriate
Remove or impute
elements
Delete elements or compute
replacement values depending
on objectives.
Application of ratios and
logratios
Spatial schemes &
Geostatistical evaluation
Kimberlite Classification
using Lithogeochemistry
Local/Camp Scale < 1:50,000
Exploration scale studies and detailed geologic
mapping.
Star Kimberlite – Fort a la Corne - Saskatchewan
A
A
B
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
Kimberlite Phases
Classification - Visually-based
Early Joli Fou
Mid Joli Fou
Pense
Late Joli Fou
Cantuar
Kimberlite Fractionation Trends
[stoichiometric control]
Kimberlites – Logcentred PCA
Process Discovery
Kimberlite Suite Log-centred PCA
0.5
Crustal
K
Rb
ContaminationNa
Lower Grade
Al
Macrodiamonds
Higher Grade
Macrodiamonds
0.3
eJF
mJF
lJF
Pense
Cantuar
Yb
Si
Ni
Mg
Fe Cr
Co
Mantle
Contamination
-0.5
-0.3
-0.1
C2
0.1
Ga
-0.6
-0.4
Ca
V
-0.2
Er
Y
Kimberlite
FractionationZr
Ti
P Th
La
Nb
0.0 0.1 0.2 0.3 0.4 0.5
C1
[Grunsky & Kjarsgaard, 2008]
PC1-2 = 66%
PC1-4 = 80%
PC1-7 = 90%
Overall variation
Kimberlite Suite
Linear Discriminant Analysis
Process Validation
Classification
based
onGaPC1-7
Kimberlite Suite Logratio
- Divisor:
[PC's 1-7]
eJF
mJf
lJf
Pense Cantuar
4
Phases -
0
mJF
eJF
-2
Pense
Cantuar
-4
2nd ld
2
lJF
-4
-2
0
2
1st ld
4
6
8
Kimberlite Suite
Classification Accuracy
Accuracy/Confusion Matrix
eJF
mJF
lJF
Pense
Cantuar
eJF
90.90
0.00
0.00
0.00
3.45
mJF
0.00
96.78
3.58
2.50
10.35
lJF
0.00
0.00
85.71
0.00
0.00
Pense
0.00
2.58
10.71
97.50
0.00
Cantuar
9.10
0.65
0.00
0.00
86.21
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
Evaluating Geochemical Data
Using Multivariate Methods
and Predictive Mapping
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.
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.
Predictive Lithologic Mapping and
Mineralization Potential Using Lake
Sediment Geochemistry in Northern
Canada
Eric Grunsky1, David Corrigan1, Ute Mueller2
1Geological Survey of Canada, Natural Resources Canada, Ottawa, Canada
2 School of Engineering, Edith Cowan University, Western Australia, Australia
Melville Peninsula
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, PC’s derived from clr offer some
advantages …
Lake Sediment Sampling Sites
Melville Peninsula
·Sample Site
8 lithologic units suitable for classification.
(Akg, Agd, Agu, Amgn, APWs Ps1/2, Ps3, PHg)
Process Discovery (Empirical)
PCA Biplot (clr) of
Lake Sediment Geochemistry
Screeplot
Biplot
Geochemical
/Physical
Processes
Agd/Amgn
Akg
Under-sampled &/or
Random Processes
Ps/Hg
l1 + … l5 =62% variability
Coded by Underlying Lithology
PC1 – Till Blanket/Veneer/Felsenmeer
PC2 – Lithological Contrast
Supracrustal - Granitoid
Granitoid
Supracrustal
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
Analysis of Variance – Testing lithologic
separation (8 classes)
using PCA
Steep Decay for Group Separation
Only 6 PC’s are required for high lithologic separation
PC’s represent linear combinations of elements controlled by
processes (stoichiometry &/or physical processes)
Process Validation (Hypothesis Testing)
Linear Discriminant Plot of Lake Sediment
Geochemistry code by Lithology
granodiorite
supracrustal
Note1: Significant
overlap of classes!
K-rich granitoid
Note2: PHg is
compositionally
similar with Ps1/2 and
Ps3. S-type granite?
87% of the discrimination is accounted for in LD1 & LD2.
Accuracy of Lithological Classification based on
Lake Sediment Geochemistry
Linear Discriminant Analysis Accuracy (%)
Agd
Agu
Akg Amgn APWs
Prior Probabilites
0.14
0.21
0.2
0.1
0.04
Agd
82.05
1.10
2.56
9.52
4.76
Agu
6.97 55.53 14.18
1.68
1.92
Akg
3.28
9.60 75.76
6.06
4.29
Amgn
29.02
3.11 23.32 39.90
4.66
APWs
11.27 16.90 21.13
5.63 42.25
PHg
0.00 15.07
6.85
0.00
0.00
Ps1/2
1.40 17.89
0.70
0.00
0.00
Ps3
0.00 17.79
0.34
0.00
0.00
Overall Accuracy 60.60
PHg Ps1/2
0.04
0.14
0.00
0.00
0.72 13.70
0.00
0.76
0.00
0.00
0.00
0.00
31.51 17.81
4.56 57.19
4.03 21.81
Ps3
0.15
0.00
5.29
0.25
0.00
2.82
28.77
18.25
56.04
Variogram Map
Identifying Anisotropy and Range
Agd
Ute Mueller – Edith Cowan University
Predictive Mapping
Posterior Probabilities
Agd
Agu
Akg
Ps1/2
Ps3
PHg
Posterior probability – a forced fit into the class that has
the shortest Mahalanobis distance to each class centroid.
Predictive Mapping
Typicality
Agd
Agu
Akg
Ps1/2
Ps3
PHg
Typicality – class membership based on Mahalanobis
distance and the Chi-square distribution. A sample may not belong
to any of the classes.
Continental Scale Geochemical Mapping
United States Soil Geochemistry Survey
with Dave Smith, Larry Drew, Laurel Woodruff, Dave Sutphin
USGS
Low Density Sampling:
• 1 sample site\1,600 km2
• Sampling strategy based on
Generalized Random
Tessellation Survey Design
(GRTS)
• 4857 sample sites x 3
Laboratory Methods/Protocols
• 4 acid digestion
• ICP-MS/AES Instrument
• QA/QC protocols followed and
documented.
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
Sampling the Soil Profile
Top Layer = 0 to 5cm. Organic debris with
little mineral matter.
Oxidized, bioturbated and organic debris,
extensive weathering of mineral matter.
weathering
Effects of groundwater, vegetation, oxidation.
(not sampled)
Unweathered mineral matter.
Progressive weathering of mineral matter up the profile.
Process Discovery
Maps of PC1/PC2
[C Horizon]
mafic
feldspars/
carbonates
felsic
weathering/shales
Eolian Dunes
mafic
felsic
feldspars/carbonates
weathering/
organic
0-5 cm layer
A horizon
C horizon
Principal Component Analysis
Biplot PC2/PC3 [A Horizon]
A Horizon
Organic material/Shales/Weathering
Mafic
Carbonates
Feldspars
PC3
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?
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.
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)
Ecosystems/Climate/Lithology
Terrestrial Ecosystems
Thermal Regions
Humidity
Surface Lithologies
Initial resolution 1km – resampled to 40km
Process Validation
Linear Discriminant Analysis
Surface Lithology – Eolian Dunes
Predictive Accuracy 26%
Significant overlap with other non
carbonate residual material
C Horizon
ilr transform
Predictive Maps of Surface Lithologies
(posterior probability) [0-5 cm layer]
spatial coherence
Alluvium
Eolian Dunes
Colluvium
Eolian Loess
Glacial Outwash
Glacial Lake Sediments
Glacial Till - Loam
Glacial Till - Clay
Glacial Till - Coarse
Predictive Maps of Surface Lithologies
(posterior probability) [0-5 cm layer]
Extrusive volcanics
Residual Si Soils
Coastal Zone Sediments
Saline Lake Deposits
Residual Ca Soils
Surface Lithologies
spatial coherence
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.
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.
Comments/Questions/Further Discussion
[email protected]