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  Information Theory and the Analysis of Uncertainties in a Spatial Geological Context

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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 ;-)

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  Information Theory and the Analysis of Uncertainties in a Spatial Geological Context

  1. 1. Information Theory and the Analysis of Uncertainties in a Spatial Geological Context Florian Wellmann, Mark Lindsay and Mark Jessell Centre for Exploration Targeting (CET) PICO presentation — EGU 2014 May 9, 2014
  2. 2. Structural Geological Models and Uncertainties Section view of a structural geological model Model created during a mapping course by one team of students... Yellow lines: surface contacts White lines: faults (From: Courrioux et al., 34th IGC, Brisbane, 2012)
  3. 3. 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)
  4. 4. Stochastic Geological Modelling Stochastic modelling approach Primary Observations Realisation 1 Realisation n Realisation 3 Realisation 2 Model 1 Model n Model 3 Model 2 c (Jessell et al., submitted) Generate multiple structural geological models with a stochastic approach
  5. 5. So how to analyse all those generated models? Our approach taken here: Calculate probabilities for geological units in discrete regions (cells) of the model;
  6. 6. So how to analyse all those generated models? Our approach taken here: Calculate probabilities for geological units in discrete regions (cells) of the model; Determine information entropy for each cell as a measure of uncertainty;
  7. 7. So how to analyse all those generated models? Our approach taken here: Calculate probabilities for geological units in discrete regions (cells) of the model; Determine information entropy for each cell as a measure of uncertainty; Evaluate conditional entropy to determine how knowledge at one location could reduce uncertainties elsewhere.
  8. 8. Application to Gippsland Basin model We apply the concept here to a kinematic structural model of the Gippsland Basin, SE Australia: We assume that parameters related to the geological history are uncertain and generate multiple realisations.
  9. 9. Analysis of a 2-D slice of the model As an example, consider uncertainties in a E-W slice through the model: Information entropy shows high uncertainties in basin: 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 entropy(bits)
  10. 10. Analysis of a 2-D slice of the model As an example, consider uncertainties in a E-W slice through the model: Conditional entropy to determine potential uncertainty reduction (e.g. during drilling):
  11. 11. Overview of Presentation “PICO madness” Geological uncertainties Brief overview: important concepts of Information Theory Stochastic geo- logical modelling Application to a kinematic struc- tural model of the Gippsland Basin
  12. 12. 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 information theory to evaluate uncertainties in a spatial context:
  13. 13. 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 information theory to evaluate uncertainties in a spatial context: 1 Information entropy as a measure of uncertainty at one spatial location, and
  14. 14. 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 information theory to evaluate uncertainties in a spatial context: 1 Information entropy as a measure of uncertainty at one spatial location, and 2 Conditional entropy to determine how knowledge at one location could reduce uncertainties at another location. Finally,
  15. 15. 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 information theory to evaluate uncertainties in a spatial context: 1 Information entropy as a measure of uncertainty at one spatial location, and 2 Conditional entropy to determine how knowledge at one location could reduce uncertainties at another location. Finally, 3 Multivariate conditional entropy is applied to evaluate how gathering successive information, e.g. while drilling, reduces uncertainty.
  16. 16. 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 information theory to evaluate uncertainties in a spatial context: 1 Information entropy as a measure of uncertainty at one spatial location, and 2 Conditional entropy to determine how knowledge at one location could reduce uncertainties at another location. Finally, 3 Multivariate conditional entropy is applied to evaluate how gathering successive information, e.g. while drilling, reduces uncertainty. In this subsection, we provide a brief and intuitive introduction into these concepts.
  17. 17. Back to overview . Information theory and the coin flip Coin flip example Simple example for the interpretation of information entropy: For a fair coin, p(head) = p(tail) = 0.5: the uncertainty is highest as no outcome is preferred (•)
  18. 18. Back to overview . Information theory and the coin flip Coin flip example Simple example for the interpretation of information entropy: For a fair coin, p(head) = p(tail) = 0.5: the uncertainty is highest as no outcome is preferred (•) If the coin is unfair (and we know it), uncertainty is reduced (•)
  19. 19. Back to overview . Information theory and the coin flip Coin flip example Simple example for the interpretation of information entropy: For a fair coin, p(head) = p(tail) = 0.5: the uncertainty is highest as no outcome is preferred (•) If the coin is unfair (and we know it), uncertainty is reduced (•) For a double-headed coin, outcome is known, no uncertainty remains (•)
  20. 20. Back to overview . Conditional entropy and uncertainty reduction Sharing information about a coin toss Now we assume a related experiment: we ask someone who observed the coin toss about the outcome. What is the remaining uncertainty about the 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
  21. 21. Back to overview . Conditional entropy and uncertainty reduction Sharing information about a coin toss Now we assume a related experiment: we ask someone who observed the coin toss about the outcome. What is the remaining uncertainty about the 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...
  22. 22. Back to overview . Conditional entropy and uncertainty reduction Sharing information about a coin toss Now we assume a related experiment: we ask someone who observed the coin toss about the outcome. What is the remaining uncertainty about the 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!
  23. 23. Back to overview . Interpretation in a spatial context Interpretation in a spatial context: Calculate probabilities for geological units in discrete regions (cells) of the model;
  24. 24. Back to overview . Interpretation in a spatial context Interpretation in a spatial context: Calculate probabilities for geological units in discrete regions (cells) of the model; Determine information entropy for each cell as a measure of uncertainty;
  25. 25. Back to overview . Interpretation in a spatial context Interpretation in a spatial context: Calculate probabilities for geological units in discrete regions (cells) of the model; Determine information entropy for each cell as a measure of uncertainty; Evaluate conditional entropy to determine how knowledge at one location could reduce uncertainties elsewhere.
  26. 26. Back to overview . Conclusion More information For more information, see: The landmark paper by Claude Shannon (1948); As a good extended theoretic overview: Cover and Thomas: Elements of Information Theory; Our paper in Entropy (open access); The wikipedia page for Information theory.
  27. 27. Back to overview . Conclusion More information For more information, see: The landmark paper by Claude Shannon (1948); As a good extended theoretic overview: Cover and Thomas: Elements of Information Theory; Our paper in Entropy (open access); The wikipedia page for Information theory. Next ... Continue with the next section: the overview of Geological uncertainties Or go back to the Overview
  28. 28. Back to overview . Uncertainties in 3-D Geological Modelling Types of uncertainty Mann (1993): Error, bias, imprecision B´ardossy and Fodor (2001): Sampling and observation error
  29. 29. Back to overview . Uncertainties in 3-D Geological Modelling Types of uncertainty Mann (1993): Error, bias, imprecision Inherent randomness B´ardossy and Fodor (2001): Sampling and observation error Variability and propagation error
  30. 30. Back to overview . Uncertainties in 3-D Geological Modelling Types of uncertainty Mann (1993): Error, bias, imprecision Inherent randomness Incomplete knowledge B´ardossy and Fodor (2001): Sampling and observation error Variability and propagation error Conceptual and model uncertainty
  31. 31. 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)
  32. 32. 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)
  33. 33. 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)
  34. 34. 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)
  35. 35. 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)
  36. 36. 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)
  37. 37. 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)
  38. 38. 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)
  39. 39. 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)
  40. 40. 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)
  41. 41. 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)
  42. 42. 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)
  43. 43. Back to overview . Next... Conclusion Uncertainties in structural geological models can be significant! In practice, creating several models for the same region is not feasible - we therefore attempt to simulate the effect of uncertainties with stochastic methods (see next section).
  44. 44. Back to overview . Next... Conclusion Uncertainties in structural geological models can be significant! In practice, creating several models for the same region is not feasible - we therefore attempt to simulate the effect of uncertainties with stochastic methods (see next section). Next ... Continue with the next section: Stochastic Modelling for structural models Or go back to the Overview
  45. 45. 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 c ologies per voxel 6 (Jessell et al., submitted) Start with geological parameters (observations or aspects of geological history)
  46. 46. 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 c ologies per voxel 6 (Jessell et al., submitted) Start with geological parameters (observations or aspects of geological history) Assign probability distributions to observations
  47. 47. 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 c ologies per voxel 6 (Jessell et al., submitted) Start with geological parameters (observations or aspects of geological history) Assign probability distributions to observations Randomly generate new parameter sets
  48. 48. 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 c ologies per voxel 6 (Jessell et al., submitted) Start with geological parameters (observations or aspects of geological history) Assign probability distributions to observations Randomly generate new parameter sets Create models for all sets
  49. 49. Back to overview . 3-D Modelling Methods Different methods to create 3-D models Several methods exist to generate 3-D geological models. Most suitable for stochastic structural modelling are: Implicit modelling method SKUA% Earthvision% Geomodeller% Noddy% Explicit( Implicit( Kinema/c/( Mechanical( Geophysical( Inversion( VPmg% Kine3D% Vulcan%(old)%
  50. 50. Back to overview . 3-D Modelling Methods Different methods to create 3-D models Several methods exist to generate 3-D geological models. Most suitable for stochastic structural modelling are: Implicit modelling method Kinematic/ mechanical modelling methods SKUA% Earthvision% Geomodeller% Noddy% Explicit( Implicit( Kinema/c/( Mechanical( Geophysical( Inversion( VPmg% Kine3D% Vulcan%(old)%
  51. 51. Back to overview . 3-D Modelling Methods Different methods to create 3-D models Several methods exist to generate 3-D geological models. Most suitable for stochastic structural modelling are: Implicit modelling method Kinematic/ mechanical modelling methods We use in the application in this presentation a kinematic modelling approach. SKUA% Earthvision% Geomodeller% Noddy% Explicit( Implicit( Kinema/c/( Mechanical( Geophysical( Inversion( VPmg% Kine3D% Vulcan%(old)%
  52. 52. Back to overview . Next... For more information, please see: on stochastic structural geological modelling, e.g.: Jessell et al., 2010 Lindsay et al., 2012 Wellmann et al., 2010 For implicit geological modelling, e.g. Calcagno et al., 2008 For kinematic modelling and Noddy: Jessell, 2001.
  53. 53. Back to overview . Next... For more information, please see: on stochastic structural geological modelling, e.g.: Jessell et al., 2010 Lindsay et al., 2012 Wellmann et al., 2010 For implicit geological modelling, e.g. Calcagno et al., 2008 For kinematic modelling and Noddy: Jessell, 2001. Next ... Continue with the next section: Application to a kinematic structural model of the Gippsland Basin Or go back to the Overview
  54. 54. Back to overview . Example model: Gippsland Basin, SE Australia The Gippsland Basin is a sedimentary basin, located in SE Australia: ( Lindsay et al., 2013)
  55. 55. Back to overview . Example model: Gippsland Basin, SE Australia Kinematic model reflects main geological events leading to the formation of the basin: 6580 70 FoldUnconformity Unconformity Unconformity Fault Fault Fault Unconformity Tectonic EvolutionTectonic Evolution Kinematicmodel Noddy FINAL MODEL!F AL DEL! 90 Jessell(1981) For more information, see also poster on Thursday, Session SSS11.1/ESSI3.6 B190, or the Abstract
  56. 56. 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 the Graben structure.
  57. 57. 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 Parameters of geological history:
  58. 58. 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 Parameters of geological history: Fault positions and dip angle (•)
  59. 59. 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 2 3 Parameters of geological history: Fault positions and dip angle (•) Age relationship (order) of faults (•)
  60. 60. 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 2 3 Parameters of geological history: Fault positions and dip angle (•) Age relationship (order) of faults (•) Unit thickness (•)
  61. 61. 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 2 3 Parameters of geological history: Fault positions and dip angle (•) Age relationship (order) of faults (•) Unit thickness (•) Position of unconformity (•)
  62. 62. Back to overview . Multiple model realisations These are samples of the set of randomly generated models: 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z 0 20 40 60 80 X 0 20 40 Z
  63. 63. Back to overview . Analysis of unit probabilities Visualising probabilities for different units provides an insight into specific outcomes, but is not suitable to represent spatial uncertainty for the entire model: 0 20 40 60 80 0 10 20 30 40 Probability of unit 15 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 40 60 80 0 10 20 30 40 Probability of unit 12 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 40 60 80 0 10 20 30 40 Probability of unit 11 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 40 60 80 0 10 20 30 40 Probability of unit 14 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
  64. 64. 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 entropy(bits) 1 1 Uncertainties are highest in the deep parts of the basin; Entropy is calculated for each cell based on estimated unit probabilities with Shannon’s equation: H(X) = − n i=1 pi (X) log2 pi (X)
  65. 65. 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 entropy(bits) 1 2 1 Uncertainties are highest in the deep parts of the basin; 2 At shallow depth, only uncertainty due to depth of unconformity; Entropy is calculated for each cell based on estimated unit probabilities with Shannon’s equation: H(X) = − n i=1 pi (X) log2 pi (X)
  66. 66. 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 entropy(bits) 1 2 3 3 1 Uncertainties are highest in the deep parts of the basin; 2 At shallow depth, only uncertainty due to depth of unconformity; 3 In shoulders uncertainty due to stratigraphic layer thickness. Entropy is calculated for each cell based on estimated unit probabilities with Shannon’s equation: H(X) = − n i=1 pi (X) log2 pi (X)
  67. 67. Back to overview . Potential uncertainty reduction Uncertainty reduction After analysing uncertainties, the logical next question is how these uncertainties can be reduced with additional information?
  68. 68. Back to overview . Potential uncertainty reduction Uncertainty reduction After analysing uncertainties, the logical next question is how these uncertainties can be reduced with additional information? We use here (multivariate) conditional entropy to evaluate how uncertainty at a position X2 is reduced when knowing the outcome at another (or multiple other) position(s) X1: H(X2|X1) = n i=1 pi (xi )H(X2|X1 = i)
  69. 69. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): First approach: drilling into area of highest uncertainty: Conditional entropy of each cell given information at subsequent locations along a line (“drillhole”): uncertainty in the model is reduced with new knowledge.
  70. 70. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): First approach: drilling into area of highest uncertainty: Conditional entropy of each cell given information at subsequent locations along a line (“drillhole”): uncertainty in the model is reduced with new knowledge.
  71. 71. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): First approach: drilling into area of highest uncertainty: Conditional entropy of each cell given information at subsequent locations along a line (“drillhole”): uncertainty in the model is reduced with new knowledge.
  72. 72. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): First approach: drilling into area of highest uncertainty: Conditional entropy of each cell given information at subsequent locations along a line (“drillhole”): uncertainty in the model is reduced with new knowledge.
  73. 73. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): If we gather instead information on the sholder, something interesting happens...
  74. 74. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): If we gather instead information on the sholder, something interesting happens...
  75. 75. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): If we gather instead information on the sholder, something interesting happens...
  76. 76. Back to overview . Uncertainty reduction with additional information Gathering subsequent information at one location (“drilling”): If we gather instead information on the sholder, something interesting happens...
  77. 77. 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 information can be expected to reduce uncertainties.
  78. 78. Back to overview . Kinematic block model 3-D view of the base model We now briefly evaluate uncertainties in a N-S slice that shows the folding pattern. As additional parameters, fold wavelength and amplitude are considered uncertain. E-WN-S
  79. 79. Back to overview . Information entropy in a N-S slice Visualisation of information entropy 0 20 40 60 80 100 120 X 0 20 40 Y 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 entropy(bits) 1 1 Uncertainties are highest at a depth where several thin stratigraphic units are possible;
  80. 80. Back to overview . Information entropy in a N-S slice Visualisation of information entropy 0 20 40 60 80 100 120 X 0 20 40 Y 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 entropy(bits) 1 2 1 Uncertainties are highest at a depth where several thin stratigraphic units are possible; 2 Uncertainties generally increase towards the right (South), as folding patterns are anchored at left where more data exists.
  81. 81. Back to overview . Uncertainty reduction with additional information Evaluation of uncertainty reduction with conditional entropy A comparison of conditional entropies for gathering information at different locations shows again where we can expect to reduce the uncertainty:
  82. 82. Back to overview . Conclusion and Outlook Conclusion Measures from information theory provide a suitable framework to visualise uncertainties and evaluate uncertainty reduction in a geospatial setting.
  83. 83. Back to overview . Conclusion and Outlook Conclusion Measures from information theory provide a suitable framework to visualise uncertainties and evaluate uncertainty reduction in a geospatial setting. The analysis provides insights into the underlying model structure that can lead to, sometimes counter-intuitive, insights.
  84. 84. Back to overview . Conclusion and Outlook Conclusion Measures from information theory provide a suitable framework to visualise uncertainties and evaluate uncertainty reduction in a geospatial setting. The analysis provides insights into the underlying model structure that can lead to, sometimes counter-intuitive, insights. Outlook Future work will focus on methods to determine the overall reduction of uncertainty and more detailed analyses of uncertainty correlations.
  85. 85. Back to overview . Conclusion and Outlook Conclusion Measures from information theory provide a suitable framework to visualise uncertainties and evaluate uncertainty reduction in a geospatial setting. The analysis provides insights into the underlying model structure that can lead to, sometimes counter-intuitive, insights. Outlook Future work will focus on methods to determine the overall reduction of uncertainty and more detailed analyses of uncertainty correlations. In addition, we are working on algorithmic efficiency as computation time becomes critical for large multivariate evaluations.
  86. 86. Back to overview . More information Thank you for your attention!
  87. 87. 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: Wellmann and Regenauer-Lieb, 2012 in Tectonophysics; Wellmann, 2013 in Entropy (open access);
  88. 88. 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: Wellmann and Regenauer-Lieb, 2012 in Tectonophysics; Wellmann, 2013 in Entropy (open access); The software to create the kinematic model realisations, pynoddy, is available online on github!
  89. 89. 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: Wellmann and Regenauer-Lieb, 2012 in Tectonophysics; Wellmann, 2013 in Entropy (open access); The software to create the kinematic model realisations, pynoddy, is available online on github! Also, come and visit us at our poster on Thursday B190 at Session SSS11.1/ESSI3.6, or see the Abstract

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