TY  - BOOK
AU  - Scheidt,Céline
AU  - Li,Lewis
AU  - Caers,Jef
TI  - Quantifying Uncertainty in Subsurface Systems
T2  - Geophysical Monograph Series
SN  - 9781119325871
AV  - QE33.2.S82 .S345 2018 
U1  - 553.0113 
PY  - 2018///
CY  - Newark
PB  - American Geophysical Union
KW  - Geology-Statistical methods
KW  - Geology-Mathematical models
KW  - Earth sciences-Statistical methods
KW  - Electronic books
N1  - Intro -- Title Page -- Copyright Page -- Contents -- Preface -- Authors -- Chapter 1 The Earth Resources Challenge -- 1.1. WHEN CHALLENGES BRING OPPORTUNITIES -- 1.2. PRODUCTION PLANNING AND DEVELOPMENT FOR AN OIL FIELD IN LIBYA -- 1.2.1. Reservoir Management from Discovery to Abandonment -- 1.2.2. Reservoir Modeling -- 1.2.3. The Challenge of Addressing Uncertainty -- 1.2.4. The Libya Case -- 1.3. DECISION MAKING UNDER UNCERTAINTY FOR GROUNDWATER MANAGEMENT IN DENMARK -- 1.3.1. Groundwater Management Challenges under Global Change -- 1.3.2. The Danish Case -- 1.4. MONITORING SHALLOW GEOTHERMAL SYSTEMS IN BELGIUM -- 1.4.1. The Use of Low-Enthalpy Geothermal Systems -- 1.4.2. Monitoring by Means of Geophysical Surveys -- 1.5. DESIGNING STRATEGIES FOR URANIUM REMEDIATION IN THE UNITED STATES -- 1.5.1. Global Environmental Challenges -- 1.5.2. Remediation: Decision Making Under Uncertainty -- 1.5.3. Remediation: Data and Modeling -- 1.5.4. Uranium Contamination in the United States -- 1.5.5. Assessing Remediation Efficacy -- 1.6. DEVELOPING SHALE PLAYS IN NORTH AMERICA -- 1.6.1. Introduction -- 1.6.2. What are Shales Reservoirs and How are They Produced? -- 1.6.3. Shale Development Using Data Science -- 1.7. SYNTHESIS: DATA-MODEL-PREDICTION-DECISION -- REFERENCES -- Chapter 2 Decision Making Under Uncertainty -- 2.1. INTRODUCTION -- 2.2. INTRODUCTORY EXAMPLE: THE THUMBTACK GAME -- 2.3. CHALLENGES IN THE DECISION-MAKING PROCESS -- 2.3.1. The Decision Analyst -- 2.3.2. Organizational Context -- 2.4. DECISION ANALYSIS AS A SCIENCE -- 2.4.1. Why Decision Analysis Is a Science -- 2.4.2. Basic Rules -- 2.4.3. Definitions -- 2.4.4. Objectives -- 2.4.5. Illustrative Example -- 2.5. GRAPHICAL TOOLS -- 2.5.1. Decision Trees -- 2.5.2. Influence Diagrams -- 2.6. VALUE OF INFORMATION -- 2.6.1. Introduction -- 2.6.2. Calculations -- REFERENCES; Chapter 3 Data Science for Uncertainty Quantification -- 3.1. INTRODUCTORY EXAMPLE -- 3.1.1. Description -- 3.1.2. Our Notation Convention -- 3.1.3. Variables -- 3.2. BASIC ALGEBRA -- 3.2.1. Matrix Algebra Notation -- 3.2.2. Eigenvalues and Eigenvectors -- 3.2.3. Spectral Decomposition -- 3.2.4. Quadratic Forms -- 3.2.5. Distances -- 3.3. BASICS OF UNIVARIATE AND MULTIVARIATE PROBABILITY THEORY AND STATISTICS -- 3.3.1. Univariate Transformations -- 3.3.2. Kernel Density Estimation -- 3.3.3. Properties of Multivariate Distributions -- 3.3.4. Characteristic Property -- 3.3.5. The Multivariate Normal Distribution -- 3.4. DECOMPOSITION OF DATA -- 3.4.1. Data Spaces -- 3.4.2. Cartesian Space of Size L: The Sample Size -- 3.4.3. Cartesian Space of Size N: Sample Dimension -- 3.4.4. Relationship Between Two Spaces -- 3.5. ORTHOGONAL COMPONENT ANALYSIS -- 3.5.1. Principal Component Analysis -- 3.5.2. Multidimensional Scaling -- 3.5.3. Canonical Correlation Analysis -- 3.6. FUNCTIONAL DATA ANALYSIS -- 3.6.1. Introduction -- 3.6.2. A Functional Basis -- 3.6.3. Functional PCA -- 3.7. REGRESSION AND CLASSIFICATION -- 3.7.1. Introduction -- 3.7.2. Multiple Linear Regression -- 3.7.3. Support Vector Machines -- 3.7.4. CART: Classification and Regression Trees -- 3.7.5. Gaussian Process Regression: Kriging -- 3.8. KERNEL METHODS -- 3.8.1. Introduction -- 3.8.2. Kernel-Based Mapping -- 3.8.3. Kernel PCA -- 3.9. CLUSTER ANALYSIS -- 3.9.1. k-Means -- 3.9.2. k-Medoids -- 3.9.3. Kernel Methods for Clustering -- 3.9.4. Choosing the Number of Clusters -- 3.9.5. Application -- 3.10 MONTE CARLO AND QUASI MONTE CARLO -- 3.10.1. Introduction -- 3.10.2. Sampling from Known Distributions -- 3.10.3. Variance Reduction Methods -- 3.11. SEQUENTIAL MC -- 3.11.1. Problem Formulation -- 3.11.2. Sequential Importance Resampling -- 3.12. MARKOV CHAIN MC -- 3.12.1. Motivation; 3.12.2. Random Walk -- 3.12.3. Gibbs Sampling -- 3.12.4. Metropolis-Hastings Sampler -- 3.12.5. Assessing Convergence -- 3.12.6. Approximate Bayesian Computation -- 3.12.7. Multichain McMC -- 3.13. THE BOOTSTRAP -- 3.13.1. Introduction -- 3.13.2. Nonparametric Bootstrap -- 3.13.3. Bootstrap with Correlated Data -- 3.13.4. Bootstrap Confidence Intervals and Hypothesis Testing -- REFERENCES -- Chapter 4 Sensitivity Analysis -- 4.1. INTRODUCTION -- 4.2. NOTATION AND APPLICATION EXAMPLE -- 4.3. SCREENING TECHNIQUES -- 4.3.1. OAT Method -- 4.3.2. Morris Method -- 4.4. GSA METHODS -- 4.4.1. SA Based on Linear Models -- 4.4.2. Variance-Based Methods/Measures of Importance -- 4.4.3. Generalized/Regionalized SA -- 4.4.4. Tree-Based SA -- 4.5. QUANTIFYING IMPACT OF STOCHASTICITY IN MODELS -- 4.6. SUMMARY -- REFERENCES -- Chapter 5 Bayesianism -- 5.1. INTRODUCTION -- 5.2. A HISTORICAL PERSPECTIVE -- 5.3. SCIENCE AS KNOWLEDGE DERIVED FROM FACTS, DATA, OR EXPERIENCE -- 5.4. THE ROLE OF EXPERIMENTS: DATA -- 5.5. INDUCTION VERSUS DEDUCTION -- 5.6. FALSIFICATIONISM -- 5.6.1. A Reaction to Induction -- 5.6.2. Falsificationism in Statistics -- 5.6.3. Limitations of Falsificationism -- 5.7. PARADIGMS -- 5.7.1. Thomas Kuhn -- 5.7.2. Is Probability Theory the Only Paradigm for UQ? -- 5.8. BAYESIANISM -- 5.8.1. Thomas Bayes -- 5.8.2. Rationality for Bayesianism -- 5.8.3. Objective Versus Subjective Probabilities -- 5.8.4. Bayes with Ad-Hoc Modifications -- 5.8.5. Criticism of Bayesianism -- 5.8.6. Deductive Testing of Inductive Bayesianism -- 5.9. BAYESIANISM IN GEOLOGICAL SCIENCES -- 5.9.1. Introduction -- 5.9.2. What Is the Nature of Geological Priors? -- 5.9.3. Moving Forward -- REFERENCES -- Chapter 6 Geological Priors and Inversion -- 6.1. INTRODUCTION -- 6.2. THE GENERAL DISCRETE INVERSE PROBLEM -- 6.2.1. Introduction; 6.2.2. Representation of Physical Variables in Probability Theory -- 6.2.3. Conjunction of Information -- 6.2.4. More Limited Formulations -- 6.3. PRIOR MODEL PARAMETERIZATION -- 6.3.1. The Prior Movie -- 6.3.2. Gridding -- 6.3.3. Process-Based Prior Model -- 6.3.4. Geostatistics -- 6.3.5. Non-Grid-Based Prior Movies -- 6.3.6. Dimension Reduction and Model Expansion from a Limited Prior Movie -- 6.4. DETERMINISTIC INVERSION -- 6.4.1. Linear Least Squares: General Formulation -- 6.4.2. Regularization -- 6.4.3. Resolution -- 6.4.4. Kalman Filter -- 6.4.5. Nonlinear Inversion -- 6.4.6. Conceptual Overview of Various Model Assumptions -- 6.4.7. Illustration of Deterministic Inversion -- 6.5. BAYESIAN INVERSION WITH GEOLOGICAL PRIORS -- 6.5.1. Inversion of Surface-Based Geological Structures -- 6.5.2. Inversion for Grid-Based Geological Structures -- 6.6. GEOLOGICAL PRIORS IN GEOPHYSICAL INVERSION -- 6.6.1. Introduction -- 6.6.2. Creating the Geophysical Image -- 6.6.3. Rock Physics: Linking the Image with Properties -- 6.6.4. Workflows and Role in UQ -- 6.7. GEOLOGICAL PRIORS IN ENSEMBLE FILTERING METHODS -- REFERENCES -- Chapter 7 Bayesian Evidential Learning -- 7.1. THE PREDICTION PROBLEM REVISITED -- 7.2. COMPONENTS OF STATISTICAL LEARNING -- 7.2.1. The Statistical Model -- 7.2.2. Generating the Training Set -- 7.2.3. Dimension Reduction and Feature Extraction -- 7.2.4. Regression Analysis -- 7.2.5. How Much Can We Trust the Statistical Model? -- 7.3. BAYESIAN EVIDENTIAL LEARNING IN PRACTICE -- 7.3.1. Predicting Dynamic from Dynamic -- 7.3.2. Predicting Static from Dynamic -- 7.3.3. Predicting Dynamic from Static -- 7.3.4. Predicting Static from Static -- 7.3.5. Summary -- REFERENCES -- Chapter 8 Quantifying Uncertainty in Subsurface Systems -- 8.1. INTRODUCTION -- 8.2. PRODUCTION PLANNING AND DEVELOPMENT FOR AN OIL FIELD IN LIBYA; 8.2.1. Three Decision Scenarios and a Strategy for UQ -- 8.2.2. The Prior -- 8.2.3. Uncertainty Quantification -- 8.2.4. Decision Making -- 8.3. DECISION MAKING UNDER UNCERTAINTY FOR GROUNDWATER MANAGEMENT IN DENMARK -- 8.3.1. A Strategy for UQ -- 8.3.2. Designing a Monte Carlo Study -- 8.3.3. Sensitivity Analysis -- 8.3.4. Uncertainty Reduction -- 8.3.5. Decision Model -- 8.4. MONITORING SHALLOW GEOTHERMAL SYSTEMS IN BELGIUM -- 8.4.1. A Strategy for UQ -- 8.4.2. Deterministic Prediction with Local Sensitivity Analysis -- 8.4.3. Bayesian Prediction with Global Sensitivity Analysis -- 8.5. DESIGNING URANIUM CONTAMINANT REMEDIATION IN THE UNITED STATES -- 8.5.1. A Strategy for UQ -- 8.5.2. Prior Distributions -- 8.5.3. Monte Carlo -- 8.5.4. Dimension Reduction on Data and Prediction Variables -- 8.5.5. Global Sensitivity Analysis -- 8.5.6. Correlation Analysis and UQ -- 8.6. DEVELOPING SHALE PLAYS IN NORTH AMERICA -- 8.6.1. Strategy for UQ -- 8.6.2. Data Preprocessing -- 8.6.3. SC1: Functional Spatial Regression -- 8.6.4. SC2: Functional Spatial Regression with Covariates -- REFERENCES -- Chapter 9 Software and Implementation -- 9.1. INTRODUCTION -- 9.2. MODEL GENERATION -- 9.2.1. Monte Carlo Sampling -- 9.2.2. The Need for Automation -- 9.3. FORWARD SIMULATION -- 9.3.1. The Need for Parallelism -- 9.3.2. Proxy Simulators -- 9.4. POST-PROCESSING -- 9.4.1. Companion Code Technologies -- 9.4.2. Deployment Considerations -- REFERENCES -- Chapter 10 Outlook -- 10.1. INTRODUCTION -- 10.2. SEVEN QUESTIONS -- 10.2.1. Bayes or Not Bayes? -- 10.2.2. How to Turn Geological Knowledge into Quantitative Numerical Models? -- 10.2.3. What Is a Proper Model Parameterization? -- 10.2.4. How to Establish a Realistic Prior Distribution? -- 10.2.5. What Combination of Data Is Needed and for What Purpose? -- 10.2.6. How to Deal with the Computational and Software Issues?; 10.2.7. What Educational Means Can We Design to Teach UQ?
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