Modeling Uncertainty in the Earth Sciences

Informationen zum Autor Jef Caers is currently an Assistant Professor of Petroleum Engineering at Stanford University. He is also Director of the Stanford Center for Reservoir Forecasting, an industrial affiliates program in reservoir characterization and modeling. He holds MS and PhD degrees in mining engineering from the Katholicke Universiteit Leuven, Belgium. Klappentext Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex Earth systems and the impact that it has on practical situations. The aim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Descriptions of concepts, philosophies, challenges, methodologies and workflows give the reader an understanding of the best way to make decisions under uncertainty for Earth Science problems.The book covers key issues such as: Spatial and time aspect; large complexity and dimensionality; computation power; costs of 'engineering' the Earth; uncertainty in the modeling and decision process. Focusing on reliable and practical methods this book provides an invaluable primer for the complex area of decision making with uncertainty in the Earth Sciences. Zusammenfassung Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex Earth systems and the impact that it has on practical situations. The aim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Inhaltsverzeichnis Preface xiAcknowledgements xvii1 Introduction 11.1 Example Application 11.1.1 Description 11.1.2 3D Modeling 31.2 Modeling Uncertainty 4Further Reading 82 Review on Statistical Analysis and Probability Theory 92.1 Introduction 92.2 Displaying Data with Graphs 102.2.1 Histograms 102.3 Describing Data with Numbers 132.3.1 Measuring the Center 132.3.2 Measuring the Spread 142.3.3 Standard Deviation and Variance 142.3.4 Properties of the Standard Deviation 152.3.5 Quantiles and the QQ Plot 152.4 Probability 162.4.1 Introduction 162.4.2 Sample Space, Event, Outcomes 172.4.3 Conditional Probability 182.4.4 Bayes' Rule 192.5 Random Variables 212.5.1 Discrete Random Variables 212.5.2 Continuous Random Variables 212.5.2.1 Probability Density Function (pdf) 212.5.2.2 Cumulative Distribution Function 222.5.3 Expectation and Variance 232.5.3.1 Expectation 232.5.3.2 Population Variance 242.5.4 Examples of Distribution Functions 242.5.4.1 The Gaussian (Normal) Random Variable and Distribution 242.5.4.2 Bernoulli Random Variable 252.5.4.3 Uniform Random Variable 262.5.4.4 A Poisson Random Variable 262.5.4.5 The Lognormal Distribution 272.5.5 The Empirical Distribution Function versus the Distribution Model 282.5.6 Constructing a Distribution Function from Data 292.5.7 Monte Carlo Simulation 302.5.8 Data Transformations 322.6 Bivariate Data Analysis 332.6.1 Introduction 332.6.2 Graphical Methods: Scatter plots 332.6.3 Data Summary: Correlation (Coefficient) 352.6.3.1 Definition 352.6.3.2 Properties of r 37Further Reading 373 Modeling Uncertainty: Concepts and Philosophies 393.1 What is Uncertainty? 393.2 Sources of Uncertainty 403.3 Deterministic Modeling 413.4 Models of Uncertainty 433.5 Model and Data Relationship 443.6 Bayesian View on Uncertainty 453.7 Model Verification and Falsification 483.8 Model Complexity 493.9 Talking about Uncertainty 503.10 Examples 513.10.1 Climate Modeling 513.10.1.1 Description 513.10.1.2 Creating Data Sets Using Models 513.10.1.3 Parameterization of Subgrid Variability 523.10.1.4 Model Complexity 523.10.2 Reservoir Modeling 523.10.2.1 Description 523.10.2.2 Creating Data Sets Using Models 533.10.2.3 Parameterizati...

Klappentext

Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex Earth systems and the impact that it has on practical situations. The aim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Descriptions of concepts, philosophies, challenges, methodologies and workflows give the reader an understanding of the best way to make decisions under uncertainty for Earth Science problems. The book covers key issues such as: Spatial and time aspect; large complexity and dimensionality; computation power; costs of 'engineering' the Earth; uncertainty in the modeling and decision process. Focusing on reliable and practical methods this book provides an invaluable primer for the complex area of decision making with uncertainty in the Earth Sciences.

Inhalt

Preface xi Acknowledgements xvii 1 Introduction 1 1.1 Example Application 1 1.1.1 Description 1 1.1.2 3D Modeling 3 1.2 Modeling Uncertainty 4 Further Reading 8 2 Review on Statistical Analysis and Probability Theory 9 2.1 Introduction 9 2.2 Displaying Data with Graphs 10 2.2.1 Histograms 10 2.3 Describing Data with Numbers 13 2.3.1 Measuring the Center 13 2.3.2 Measuring the Spread 14 2.3.3 Standard Deviation and Variance 14 2.3.4 Properties of the Standard Deviation 15 2.3.5 Quantiles and the QQ Plot 15 2.4 Probability 16 2.4.1 Introduction 16 2.4.2 Sample Space, Event, Outcomes 17 2.4.3 Conditional Probability 18 2.4.4 Bayes' Rule 19 2.5 Random Variables 21 2.5.1 Discrete Random Variables 21 2.5.2 Continuous Random Variables 21 2.5.2.1 Probability Density Function (pdf) 21 2.5.2.2 Cumulative Distribution Function 22 2.5.3 Expectation and Variance 23 2.5.3.1 Expectation 23 2.5.3.2 Population Variance 24 2.5.4 Examples of Distribution Functions 24 2.5.4.1 The Gaussian (Normal) Random Variable and Distribution 24 2.5.4.2 Bernoulli Random Variable 25 2.5.4.3 Uniform Random Variable 26 2.5.4.4 A Poisson Random Variable 26 2.5.4.5 The Lognormal Distribution 27 2.5.5 The Empirical Distribution Function versus the Distribution Model 28 2.5.6 Constructing a Distribution Function from Data 29 2.5.7 Monte Carlo Simulation 30 2.5.8 Data Transformations 32 2.6 Bivariate Data Analysis 33 2.6.1 Introduction 33 2.6.2 Graphical Methods: Scatter plots 33 2.6.3 Data Summary: Correlation (Coefficient) 35 2.6.3.1 Definition 35 2.6.3.2 Properties of r 37 Further Reading 37 3 Modeling Uncertainty: Concepts and Philosophies 39 3.1 What is Uncertainty? 39 3.2 Sources of Uncertainty 40 3.3 Deterministic Modeling 41 3.4 Models of Uncertainty 43 3.5 Model and Data Relationship 44 3.6 Bayesian View on Uncertainty 45 3.7 Model Verification and Falsification 48 3.8 Model Complexity 49 3.9 Talking about Uncertainty 50 3.10 Examples 51 3.10.1 Climate Modeling 51 3.10.1.1 Description 51 3.10.1.2 Creating Data Sets Using Models 51 3.10.1.3 Parameterization of Subgrid Variability 52 3.10.1.4 Model Complexity 52 3.10.2 Reservoir Modeling 52 3.10.2.1 Description 52 3.10.2.2 Creating Data Sets Using Models 53 3.10.2.3 Parameterization of Subgrid Variability 53 3.10.2.4 Model Complexity 54 Further Reading 54 4 Engineering the Earth: Making Decisions Under Uncertainty 55 4.1 Introduction 55 4.2 Making Decisions 57 4.2.1 Example Problem 57 4.2.2 The Language of Decision Making 59 4.2.3 Structuring the Decision 60 4.2.4 Modeling the Decision 61 4.2.4.1 Payoffs and Value Functions 62 4.2.4.2 Weighting 63 4.2.4.3 Trade-Offs 65 4.2.4.4 Sensitivity Analysis 67 4.3 Tools for Structuring Decision Problems 70 4.3.1 Decision Trees 70 4.3.2 Building Decision Trees 70 4.3.3 Solving Decision Trees 72 4.3.4 Sensitivity Analysis 76 Further Reading 76 5 Modeling Spatial Continuity 77 5.1 Introduction 77 5.2 The Variogram 79 5.2.1 Autocorrelation in 1D 79 5.2.2 Autocorrelation in 2D and 3D 82 5.2.3 The Variogram and Covariance Function 84 5.2.4 Variogram Analysis 86 5.2.4.1 Anisotropy 86 5.2.4.2 What is the Practical Meaning of a Variogram? 87 5.2.5 A Word on Variogram Modeling 87 5.3 The Boolean or Object Model 87 5.3.1…