  information theory and the analysis of uncertainties in a spatial geological context
DESCRIPTION
PICO presentation at EGU 2014 about the use of measures from information theory to visualise uncertainty in kinematic structural models - and to estimate where additional data would help reduce uncertainties. Some nice counter-intuitive results ;-)TRANSCRIPT
Information Theory and the Analysis of Uncertainties ina Spatial Geological Context
Florian Wellmann, Mark Lindsay and Mark Jessell
Centre for Exploration Targeting (CET)
PICO presentation — EGU 2014
May 9, 2014
Structural Geological Models and Uncertainties
Section view of a structural geological model
Model created during a mapping course by one team of students...
...and results from multiple teams!
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Structural Geological Models and Uncertainties
Section view of a structural geological model
Model created during a mapping course by one team of students......and results from multiple teams!
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Stochastic Geological Modelling
Stochastic modelling approach
Primary Observations
Realisation 1
Realisation n
Realisation 3
Realisation 2
Model 1
Model n
Model 3
Model 2
a
b
d e
c
Prin
cipa
l Com
pone
nt 2
Principal Component 10
0
0.40.30.2
0.4
-0.1-0.2-0.3-0.4
-0.3
-0.4
-0.2
-0.1
0.1
0.3
0.2
0.1
0.5
-0.5
0.5-0.5
Initialmodel
Model spaceboundary
2 Lithologies per voxel 6
Gravity misfit
-2.5 mgal 1.5
Figure 2
(Jessell et al., submitted)
Generate multiple structuralgeological models with astochastic approach
So how to analyse all those generated models?
Our approach taken here:
Calculate probabilitiesfor geological units indiscrete regions (cells) ofthe model;
Determine informationentropy for each cell asa measure ofuncertainty;
Evaluate conditionalentropy to determinehow knowledge at onelocation could reduceuncertainties elsewhere.
So how to analyse all those generated models?
Our approach taken here:
Calculate probabilitiesfor geological units indiscrete regions (cells) ofthe model;
Determine informationentropy for each cell asa measure ofuncertainty;
Evaluate conditionalentropy to determinehow knowledge at onelocation could reduceuncertainties elsewhere.
So how to analyse all those generated models?
Our approach taken here:
Calculate probabilitiesfor geological units indiscrete regions (cells) ofthe model;
Determine informationentropy for each cell asa measure ofuncertainty;
Evaluate conditionalentropy to determinehow knowledge at onelocation could reduceuncertainties elsewhere.
Application to Gippsland Basin model
We apply the concept here to a kinematic structural model of theGippsland Basin, SE Australia:
We assume that parameters related to the geological history areuncertain and generate multiple realisations.
Analysis of a 2-D slice of the model
As an example, consider uncertainties in a E-W slice through themodel:
Information entropy shows high uncertainties in basin:
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40
Y
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1.00
1.25
1.50
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2.00
2.25
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entr
opy
(bits)
Analysis of a 2-D slice of the model
As an example, consider uncertainties in a E-W slice through themodel:
Conditional entropy to determine potential uncertainty reduction (e.g.during drilling):
Overview of Presentation
I “PICO madness”
I Geologicaluncertainties
Brief overview:important concepts ofI Information Theory
I Stochastic geo-logical modelling
I Application toa kinematic struc-tural model of theGippsland Basin
Back to overview.
Information theoretic concepts - intuitive introduction
Concepts from information theory used in this work
In the work presented here, we apply basic measures from informationtheory to evaluate uncertainties in a spatial context:
1 Information entropy as a measure of uncertainty at one spatiallocation, and
2 Conditional entropy to determine how knowledge at one locationcould reduce uncertainties at another location. Finally,
3 Multivariate conditional entropy is applied to evaluate howgathering successive information, e.g. while drilling, reducesuncertainty.
In this subsection, we provide a brief and intuitive introduction into theseconcepts.
Back to overview.
Information theoretic concepts - intuitive introduction
Concepts from information theory used in this work
In the work presented here, we apply basic measures from informationtheory to evaluate uncertainties in a spatial context:
1 Information entropy as a measure of uncertainty at one spatiallocation, and
2 Conditional entropy to determine how knowledge at one locationcould reduce uncertainties at another location. Finally,
3 Multivariate conditional entropy is applied to evaluate howgathering successive information, e.g. while drilling, reducesuncertainty.
In this subsection, we provide a brief and intuitive introduction into theseconcepts.
Back to overview.
Information theoretic concepts - intuitive introduction
Concepts from information theory used in this work
In the work presented here, we apply basic measures from informationtheory to evaluate uncertainties in a spatial context:
1 Information entropy as a measure of uncertainty at one spatiallocation, and
2 Conditional entropy to determine how knowledge at one locationcould reduce uncertainties at another location. Finally,
3 Multivariate conditional entropy is applied to evaluate howgathering successive information, e.g. while drilling, reducesuncertainty.
In this subsection, we provide a brief and intuitive introduction into theseconcepts.
Back to overview.
Information theoretic concepts - intuitive introduction
Concepts from information theory used in this work
In the work presented here, we apply basic measures from informationtheory to evaluate uncertainties in a spatial context:
1 Information entropy as a measure of uncertainty at one spatiallocation, and
2 Conditional entropy to determine how knowledge at one locationcould reduce uncertainties at another location. Finally,
3 Multivariate conditional entropy is applied to evaluate howgathering successive information, e.g. while drilling, reducesuncertainty.
In this subsection, we provide a brief and intuitive introduction into theseconcepts.
Back to overview.
Information theoretic concepts - intuitive introduction
Concepts from information theory used in this work
In the work presented here, we apply basic measures from informationtheory to evaluate uncertainties in a spatial context:
1 Information entropy as a measure of uncertainty at one spatiallocation, and
2 Conditional entropy to determine how knowledge at one locationcould reduce uncertainties at another location. Finally,
3 Multivariate conditional entropy is applied to evaluate howgathering successive information, e.g. while drilling, reducesuncertainty.
In this subsection, we provide a brief and intuitive introduction into theseconcepts.
Back to overview.
Information theory and the coin flip
Coin flip example
Simple example for the interpretationof information entropy:
For a fair coin, p(head) =p(tail) = 0.5: the uncertaintyis highest as no outcome ispreferred (•)
If the coin is unfair (and weknow it), uncertainty isreduced (•)For a double-headed coin,outcome is known, nouncertainty remains (•)
Back to overview.
Information theory and the coin flip
Coin flip example
Simple example for the interpretationof information entropy:
For a fair coin, p(head) =p(tail) = 0.5: the uncertaintyis highest as no outcome ispreferred (•)If the coin is unfair (and weknow it), uncertainty isreduced (•)
For a double-headed coin,outcome is known, nouncertainty remains (•)
Back to overview.
Information theory and the coin flip
Coin flip example
Simple example for the interpretationof information entropy:
For a fair coin, p(head) =p(tail) = 0.5: the uncertaintyis highest as no outcome ispreferred (•)If the coin is unfair (and weknow it), uncertainty isreduced (•)For a double-headed coin,outcome is known, nouncertainty remains (•)
Back to overview.
Conditional entropy and uncertainty reduction
Sharing information about a coin toss
Now we assume a related experiment: we ask someone who observedthe coin toss about the outcome. What is the remaining uncertainty aboutthe outcome?
Case 1: We ask a good friend
H(X ) = 1 H(Y |X ) = 0
Friend
100%
Always tells us the right result, no remaining uncertainty
Back to overview.
Conditional entropy and uncertainty reduction
Sharing information about a coin toss
Now we assume a related experiment: we ask someone who observedthe coin toss about the outcome. What is the remaining uncertainty aboutthe outcome?
Case 2: We ask someone who might be a friend
H(X ) = 1 H(Y |X ) = 0.47
“Friend”
90%
Might tell us the outcome mostly correctly, but uncertainties remain...
Back to overview.
Conditional entropy and uncertainty reduction
Sharing information about a coin toss
Now we assume a related experiment: we ask someone who observedthe coin toss about the outcome. What is the remaining uncertainty aboutthe outcome?
Case 3: We ask someone who may not be a friend at all...
H(X ) = 1 H(Y |X ) = 1
Friend
0%
We can not rely at all on the reply, the uncertainty is not reduced at all!
Back to overview.
Interpretation in a spatial context
Interpretation in a spatialcontext:
Calculate probabilitiesfor geological units indiscrete regions (cells) ofthe model;
Determine informationentropy for each cell asa measure ofuncertainty;
Evaluate conditionalentropy to determinehow knowledge at onelocation could reduceuncertainties elsewhere.
Back to overview.
Interpretation in a spatial context
Interpretation in a spatialcontext:
Calculate probabilitiesfor geological units indiscrete regions (cells) ofthe model;
Determine informationentropy for each cell asa measure ofuncertainty;
Evaluate conditionalentropy to determinehow knowledge at onelocation could reduceuncertainties elsewhere.
Back to overview.
Interpretation in a spatial context
Interpretation in a spatialcontext:
Calculate probabilitiesfor geological units indiscrete regions (cells) ofthe model;
Determine informationentropy for each cell asa measure ofuncertainty;
Evaluate conditionalentropy to determinehow knowledge at onelocation could reduceuncertainties elsewhere.
Back to overview.
Conclusion
More information
For more information, see:
The I landmark paper by Claude Shannon (1948);
As a good I extended theoretic overview: Cover and Thomas:Elements of Information Theory;
I Our paper in Entropy (open access);
The I wikipedia page for Information theory.
Next ...
Continue with the next section: the overview of I Geologicaluncertainties
Or go back to the I Overview
Back to overview.
Conclusion
More information
For more information, see:
The I landmark paper by Claude Shannon (1948);
As a good I extended theoretic overview: Cover and Thomas:Elements of Information Theory;
I Our paper in Entropy (open access);
The I wikipedia page for Information theory.
Next ...
Continue with the next section: the overview of I Geologicaluncertainties
Or go back to the I Overview
Back to overview.
Uncertainties in 3-D Geological Modelling
Types of uncertainty
Mann (1993):
Error, bias, imprecision
Inherent randomness
Incomplete knowledge
Bardossy and Fodor (2001):
Sampling andobservation error
Variability andpropagation error
Conceptual and modeluncertainty
Back to overview.
Uncertainties in 3-D Geological Modelling
Types of uncertainty
Mann (1993):
Error, bias, imprecision
Inherent randomness
Incomplete knowledge
Bardossy and Fodor (2001):
Sampling andobservation error
Variability andpropagation error
Conceptual and modeluncertainty
Back to overview.
Uncertainties in 3-D Geological Modelling
Types of uncertainty
Mann (1993):
Error, bias, imprecision
Inherent randomness
Incomplete knowledge
Bardossy and Fodor (2001):
Sampling andobservation error
Variability andpropagation error
Conceptual and modeluncertainty
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Geological Uncertainties are real
Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students
Yellow lines: surface contacts White lines: faults
(From: Courrioux et al., 34th IGC, Brisbane, 2012)
Back to overview.
Next...
Conclusion
Uncertainties in structural geological models can be significant!
In practice, creating several models for the same region is notfeasible - we therefore attempt to simulate the effect ofuncertainties with stochastic methods (see next section).
Next ...
Continue with the next section: I Stochastic Modelling forstructural models
Or go back to the I Overview
Back to overview.
Next...
Conclusion
Uncertainties in structural geological models can be significant!
In practice, creating several models for the same region is notfeasible - we therefore attempt to simulate the effect ofuncertainties with stochastic methods (see next section).
Next ...
Continue with the next section: I Stochastic Modelling forstructural models
Or go back to the I Overview
Back to overview.
Stochastic Geological Modelling
Stochastic modelling approach
Primary Observations
Realisation 1
Realisation n
Realisation 3
Realisation 2
Model 1
Model n
Model 3
Model 2
a
b
d e
c
Prin
cipa
l Com
pone
nt 2
Principal Component 10
0
0.40.30.2
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0.1
0.3
0.2
0.1
0.5
-0.5
0.5-0.5
Initialmodel
Model spaceboundary
2 Lithologies per voxel 6
Gravity misfit
-2.5 mgal 1.5
Figure 2
(Jessell et al., submitted)
Start with geologicalparameters (observations oraspects of geological history)
Assign probabilitydistributions to observations
Randomly generate newparameter sets
Create models for all sets
Back to overview.
Stochastic Geological Modelling
Stochastic modelling approach
Primary Observations
Realisation 1
Realisation n
Realisation 3
Realisation 2
Model 1
Model n
Model 3
Model 2
a
b
d e
c
Prin
cipa
l Com
pone
nt 2
Principal Component 10
0
0.40.30.2
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-0.1-0.2-0.3-0.4
-0.3
-0.4
-0.2
-0.1
0.1
0.3
0.2
0.1
0.5
-0.5
0.5-0.5
Initialmodel
Model spaceboundary
2 Lithologies per voxel 6
Gravity misfit
-2.5 mgal 1.5
Figure 2
(Jessell et al., submitted)
Start with geologicalparameters (observations oraspects of geological history)
Assign probabilitydistributions to observations
Randomly generate newparameter sets
Create models for all sets
Back to overview.
Stochastic Geological Modelling
Stochastic modelling approach
Primary Observations
Realisation 1
Realisation n
Realisation 3
Realisation 2
Model 1
Model n
Model 3
Model 2
a
b
d e
c
Prin
cipa
l Com
pone
nt 2
Principal Component 10
0
0.40.30.2
0.4
-0.1-0.2-0.3-0.4
-0.3
-0.4
-0.2
-0.1
0.1
0.3
0.2
0.1
0.5
-0.5
0.5-0.5
Initialmodel
Model spaceboundary
2 Lithologies per voxel 6
Gravity misfit
-2.5 mgal 1.5
Figure 2
(Jessell et al., submitted)
Start with geologicalparameters (observations oraspects of geological history)
Assign probabilitydistributions to observations
Randomly generate newparameter sets
Create models for all sets
Back to overview.
Stochastic Geological Modelling
Stochastic modelling approach
Primary Observations
Realisation 1
Realisation n
Realisation 3
Realisation 2
Model 1
Model n
Model 3
Model 2
a
b
d e
c
Prin
cipa
l Com
pone
nt 2
Principal Component 10
0
0.40.30.2
0.4
-0.1-0.2-0.3-0.4
-0.3
-0.4
-0.2
-0.1
0.1
0.3
0.2
0.1
0.5
-0.5
0.5-0.5
Initialmodel
Model spaceboundary
2 Lithologies per voxel 6
Gravity misfit
-2.5 mgal 1.5
Figure 2
(Jessell et al., submitted)
Start with geologicalparameters (observations oraspects of geological history)
Assign probabilitydistributions to observations
Randomly generate newparameter sets
Create models for all sets
Back to overview.
3-D Modelling Methods
Different methods to create 3-D models
Several methods exist to generate 3-D geological models. Most suitablefor stochastic structural modelling are:
Implicit modellingmethod
Kinematic/ mechanicalmodelling methods
We use in the I applicationin this presentation akinematic modellingapproach.
SKUA%Earthvision% Geomodeller%
Noddy%
Explicit(
Implicit(
Kinema/c/(Mechanical(
Geophysical(Inversion(
VPmg%
Kine3D%
Vulcan%(old)%
Back to overview.
3-D Modelling Methods
Different methods to create 3-D models
Several methods exist to generate 3-D geological models. Most suitablefor stochastic structural modelling are:
Implicit modellingmethod
Kinematic/ mechanicalmodelling methods
We use in the I applicationin this presentation akinematic modellingapproach.
SKUA%Earthvision% Geomodeller%
Noddy%
Explicit(
Implicit(
Kinema/c/(Mechanical(
Geophysical(Inversion(
VPmg%
Kine3D%
Vulcan%(old)%
Back to overview.
3-D Modelling Methods
Different methods to create 3-D models
Several methods exist to generate 3-D geological models. Most suitablefor stochastic structural modelling are:
Implicit modellingmethod
Kinematic/ mechanicalmodelling methods
We use in the I applicationin this presentation akinematic modellingapproach.
SKUA%Earthvision% Geomodeller%
Noddy%
Explicit(
Implicit(
Kinema/c/(Mechanical(
Geophysical(Inversion(
VPmg%
Kine3D%
Vulcan%(old)%
Back to overview.
Next...
For more information, please see:
on stochastic structural geological modelling, e.g.:
I Jessell et al., 2010I Lindsay et al., 2012I Wellmann et al., 2010
For implicit geological modelling, e.g. I Calcagno et al., 2008
For kinematic modelling and Noddy: I Jessell, 2001.
Next ...
Continue with the next section: I Application to a kinematicstructural model of the Gippsland Basin
Or go back to the I Overview
Back to overview.
Next...
For more information, please see:
on stochastic structural geological modelling, e.g.:
I Jessell et al., 2010I Lindsay et al., 2012I Wellmann et al., 2010
For implicit geological modelling, e.g. I Calcagno et al., 2008
For kinematic modelling and Noddy: I Jessell, 2001.
Next ...
Continue with the next section: I Application to a kinematicstructural model of the Gippsland Basin
Or go back to the I Overview
Back to overview.
Example model: Gippsland Basin, SE Australia
The Gippsland Basin is a sedimentary basin, located in SE Australia:
(I Lindsay et al., 2013)
Back to overview.
Example model: Gippsland Basin, SE Australia
Kinematic model reflects main geological events leading to the formationof the basin:
658070
FoldUnconformity Unconformity Unconformity Fault Fault Fault Unconformity
Tectonic EvolutionTectonic Evolution
Kine
mat
ic m
odel
Nodd
y FINAL MODEL!F AL DEL!
90
Jess
ell (
1981
)
For more information, see also poster on Thursday, Session SSS11.1/ESSI3.6 B190, or the I Abstract
Back to overview.
Kinematic block model
3-D view of the base model
E-WN-S
In a first step, we evaluate uncertainties in an E-W slice through theGraben structure.
Back to overview.
Model slice and uncertainties
Slice in E-W direction and considered uncertainties
The parameterisation of the geological events contains uncertainties,and we consider here as uncertain:
0 20 40 60 80
X
0
20
40
Z
1
23
Parameters of geologicalhistory:
Fault positions and dipangle (•)Age relationship(order) of faults (•)Unit thickness (•)Position ofunconformity (•)
Back to overview.
Model slice and uncertainties
Slice in E-W direction and considered uncertainties
The parameterisation of the geological events contains uncertainties,and we consider here as uncertain:
0 20 40 60 80
X
0
20
40
Z
1
23
Parameters of geologicalhistory:
Fault positions and dipangle (•)
Age relationship(order) of faults (•)Unit thickness (•)Position ofunconformity (•)
Back to overview.
Model slice and uncertainties
Slice in E-W direction and considered uncertainties
The parameterisation of the geological events contains uncertainties,and we consider here as uncertain:
0 20 40 60 80
X
0
20
40
Z
1
23
Parameters of geologicalhistory:
Fault positions and dipangle (•)Age relationship(order) of faults (•)
Unit thickness (•)Position ofunconformity (•)
Back to overview.
Model slice and uncertainties
Slice in E-W direction and considered uncertainties
The parameterisation of the geological events contains uncertainties,and we consider here as uncertain:
0 20 40 60 80
X
0
20
40
Z
1
23
Parameters of geologicalhistory:
Fault positions and dipangle (•)Age relationship(order) of faults (•)Unit thickness (•)
Position ofunconformity (•)
Back to overview.
Model slice and uncertainties
Slice in E-W direction and considered uncertainties
The parameterisation of the geological events contains uncertainties,and we consider here as uncertain:
0 20 40 60 80
X
0
20
40
Z
1
23
Parameters of geologicalhistory:
Fault positions and dipangle (•)Age relationship(order) of faults (•)Unit thickness (•)Position ofunconformity (•)
Back to overview.
Multiple model realisations
These are samples of the set of randomly generated models:
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Back to overview.
Analysis of unit probabilities
Visualising probabilities for different units provides an insight intospecific outcomes, but is not suitable to represent spatial uncertaintyfor the entire model:
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Probability of unit 15
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Probability of unit 12
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Probability of unit 11
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Probability of unit 14
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Back to overview.
Analysis of information entropy
Visualisation of information entropy
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Y
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opy
(bits)
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1 Uncertainties are highest in thedeep parts of the basin;
2 At shallow depth, onlyuncertainty due to depth ofunconformity;
3 In shoulders uncertainty due tostratigraphic layer thickness.
Entropy is calculated for each cell based on estimated unit probabilitieswith Shannon’s equation:
H(X ) = −n∑
i=1
pi (X ) log2 pi (X )
Back to overview.
Analysis of information entropy
Visualisation of information entropy
0 20 40 60 80
X
0
20
40
Y
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
entr
opy
(bits)
1
2
33
1 Uncertainties are highest in thedeep parts of the basin;
2 At shallow depth, onlyuncertainty due to depth ofunconformity;
3 In shoulders uncertainty due tostratigraphic layer thickness.
Entropy is calculated for each cell based on estimated unit probabilitieswith Shannon’s equation:
H(X ) = −n∑
i=1
pi (X ) log2 pi (X )
Back to overview.
Analysis of information entropy
Visualisation of information entropy
0 20 40 60 80
X
0
20
40
Y
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
entr
opy
(bits)
1
2
33
1 Uncertainties are highest in thedeep parts of the basin;
2 At shallow depth, onlyuncertainty due to depth ofunconformity;
3 In shoulders uncertainty due tostratigraphic layer thickness.
Entropy is calculated for each cell based on estimated unit probabilitieswith Shannon’s equation:
H(X ) = −n∑
i=1
pi (X ) log2 pi (X )
Back to overview.
Potential uncertainty reduction
Uncertainty reduction
After analysing uncertainties, the logical next question is how theseuncertainties can be reduced with additional information?
We use here (multivariate) conditional entropy to evaluate howuncertainty at a position X2 is reduced when knowing the outcome atanother (or multiple other) position(s) X1:
H(X2|X1) =n∑
i=1
pi (xi )H(X2|X1 = i)
Back to overview.
Potential uncertainty reduction
Uncertainty reduction
After analysing uncertainties, the logical next question is how theseuncertainties can be reduced with additional information?
We use here (multivariate) conditional entropy to evaluate howuncertainty at a position X2 is reduced when knowing the outcome atanother (or multiple other) position(s) X1:
H(X2|X1) =n∑
i=1
pi (xi )H(X2|X1 = i)
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Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
First approach: drilling intoarea of highest uncertainty:Conditional entropy of eachcell given information atsubsequent locations along aline (“drillhole”):uncertainty in the model isreduced with newknowledge.
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
First approach: drilling intoarea of highest uncertainty:Conditional entropy of eachcell given information atsubsequent locations along aline (“drillhole”):uncertainty in the model isreduced with newknowledge.
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
First approach: drilling intoarea of highest uncertainty:Conditional entropy of eachcell given information atsubsequent locations along aline (“drillhole”):uncertainty in the model isreduced with newknowledge.
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
First approach: drilling intoarea of highest uncertainty:Conditional entropy of eachcell given information atsubsequent locations along aline (“drillhole”):uncertainty in the model isreduced with newknowledge.
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
If we gather insteadinformation on the sholder,something interestinghappens...
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
If we gather insteadinformation on the sholder,something interestinghappens...
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
If we gather insteadinformation on the sholder,something interestinghappens...
Back to overview.
Uncertainty reduction with additional information
Gathering subsequent information at one location (“drilling”):
If we gather insteadinformation on the sholder,something interestinghappens...
Back to overview.
Comparison of ”drillhole” positions
Comparison of remaining uncertainty for different drillhole positions
The difference is clearly visible when we compare both results:uncertainty in Graben reduced more when drilling on side!
This analysis can give us an insight ino where additional informationcan be expected to reduce uncertainties.
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Kinematic block model
3-D view of the base model
We now briefly evaluate uncertainties in a N-S slice that shows thefolding pattern. As additional parameters, fold wavelength andamplitude are considered uncertain.
E-WN-S
Back to overview.
Information entropy in a N-S slice
Visualisation of information entropy
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1 Uncertainties are highest at adepth where several thinstratigraphic units are possible;
2 Uncertainties generally increasetowards the right (South), asfolding patterns are anchored atleft where more data exists.
Back to overview.
Information entropy in a N-S slice
Visualisation of information entropy
0 20 40 60 80 100 120
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1 Uncertainties are highest at adepth where several thinstratigraphic units are possible;
2 Uncertainties generally increasetowards the right (South), asfolding patterns are anchored atleft where more data exists.
Back to overview.
Uncertainty reduction with additional information
Evaluation of uncertainty reduction with conditional entropy
A comparison of conditional entropies for gathering information atdifferent locations shows again where we can expect to reduce theuncertainty:
Back to overview.
Conclusion and Outlook
Conclusion
Measures from information theory provide a suitable framework tovisualise uncertainties and evaluate uncertainty reduction in ageospatial setting.
The analysis provides insights into the underlying model structurethat can lead to, sometimes counter-intuitive, insights.
Outlook
Future work will focus on methods to determine the overallreduction of uncertainty and more detailed analyses of uncertaintycorrelations.
In addition, we are working on algorithmic efficiency as computationtime becomes critical for large multivariate evaluations.
Back to overview.
Conclusion and Outlook
Conclusion
Measures from information theory provide a suitable framework tovisualise uncertainties and evaluate uncertainty reduction in ageospatial setting.
The analysis provides insights into the underlying model structurethat can lead to, sometimes counter-intuitive, insights.
Outlook
Future work will focus on methods to determine the overallreduction of uncertainty and more detailed analyses of uncertaintycorrelations.
In addition, we are working on algorithmic efficiency as computationtime becomes critical for large multivariate evaluations.
Back to overview.
Conclusion and Outlook
Conclusion
Measures from information theory provide a suitable framework tovisualise uncertainties and evaluate uncertainty reduction in ageospatial setting.
The analysis provides insights into the underlying model structurethat can lead to, sometimes counter-intuitive, insights.
Outlook
Future work will focus on methods to determine the overallreduction of uncertainty and more detailed analyses of uncertaintycorrelations.
In addition, we are working on algorithmic efficiency as computationtime becomes critical for large multivariate evaluations.
Back to overview.
Conclusion and Outlook
Conclusion
Measures from information theory provide a suitable framework tovisualise uncertainties and evaluate uncertainty reduction in ageospatial setting.
The analysis provides insights into the underlying model structurethat can lead to, sometimes counter-intuitive, insights.
Outlook
Future work will focus on methods to determine the overallreduction of uncertainty and more detailed analyses of uncertaintycorrelations.
In addition, we are working on algorithmic efficiency as computationtime becomes critical for large multivariate evaluations.
Back to overview.
More information
Thank you for your attention!
More information
If you are interested, please have a look at our publications on this topic:
I Wellmann and Regenauer-Lieb, 2012 in Tectonophysics;
I Wellmann, 2013 in Entropy (open access);
The software to create the kinematic model realisations, I pynoddy, isavailable online on github!Also, come and visit us at our poster on Thursday B190 at SessionSSS11.1/ESSI3.6, or see the I Abstract
Back to overview.
More information
Thank you for your attention!
More information
If you are interested, please have a look at our publications on this topic:
I Wellmann and Regenauer-Lieb, 2012 in Tectonophysics;
I Wellmann, 2013 in Entropy (open access);
The software to create the kinematic model realisations, I pynoddy, isavailable online on github!Also, come and visit us at our poster on Thursday B190 at SessionSSS11.1/ESSI3.6, or see the I Abstract
Back to overview.
More information
Thank you for your attention!
More information
If you are interested, please have a look at our publications on this topic:
I Wellmann and Regenauer-Lieb, 2012 in Tectonophysics;
I Wellmann, 2013 in Entropy (open access);
The software to create the kinematic model realisations, I pynoddy, isavailable online on github!
Also, come and visit us at our poster on Thursday B190 at SessionSSS11.1/ESSI3.6, or see the I Abstract
Back to overview.
More information
Thank you for your attention!
More information
If you are interested, please have a look at our publications on this topic:
I Wellmann and Regenauer-Lieb, 2012 in Tectonophysics;
I Wellmann, 2013 in Entropy (open access);
The software to create the kinematic model realisations, I pynoddy, isavailable online on github!Also, come and visit us at our poster on Thursday B190 at SessionSSS11.1/ESSI3.6, or see the I Abstract