11636nam 2200709 a 450 991087714230332120200520144314.01-283-17797-81-119-99871-91-119-99593-01-119-99592-29786613177971(CKB)2670000000112757(StDuBDS)AH21634310(SSID)ssj0000507242(PQKBManifestationID)11307665(PQKBTitleCode)TC0000507242(PQKBWorkID)10546555(PQKB)10113424(MiAaPQ)EBC819286(MiAaPQ)EBC712124(Au-PeEL)EBL712124(OCoLC)747314062(PPN)170229661(EXLCZ)99267000000011275720110330d2011 uy 0engur|||||||||||txtccrModeling uncertainty in the earth sciences /Jef Caers1st ed.Hoboken, N.J. Wiley20111 online resource (240 p.) Bibliographic Level Mode of Issuance: Monograph1-119-99262-1 1-119-99263-X Includes bibliographical references and index.Intro -- Modeling Uncertainty in the Earth Sciences -- Contents -- Preface -- Acknowledgements -- 1 Introduction -- 1.1 Example Application -- 1.1.1 Description -- 1.1.2 3D Modeling -- 1.2 Modeling Uncertainty -- Further Reading -- 2 Review on Statistical Analysis and Probability Theory -- 2.1 Introduction -- 2.2 Displaying Data with Graphs -- 2.2.1 Histograms -- 2.3 Describing Data with Numbers -- 2.3.1 Measuring the Center -- 2.3.2 Measuring the Spread -- 2.3.3 Standard Deviation and Variance -- 2.3.4 Properties of the Standard Deviation -- 2.3.5 Quantiles and the QQ Plot -- 2.4 Probability -- 2.4.1 Introduction -- 2.4.2 Sample Space, Event, Outcomes -- 2.4.3 Conditional Probability -- 2.4.4 Bayes' Rule -- 2.5 Random Variables -- 2.5.1 Discrete Random Variables -- 2.5.2 Continuous Random Variables -- 2.5.2.1 Probability Density Function (pdf) -- 2.5.2.2 Cumulative Distribution Function -- 2.5.3 Expectation and Variance -- 2.5.3.1 Expectation -- 2.5.3.2 Population Variance -- 2.5.4 Examples of Distribution Functions -- 2.5.4.1 The Gaussian (Normal) Random Variable and Distribution -- 2.5.4.2 Bernoulli Random Variable -- 2.5.4.3 Uniform Random Variable -- 2.5.4.4 A Poisson Random Variable -- 2.5.4.5 The Lognormal Distribution -- 2.5.5 The Empirical Distribution Function versus the Distribution Model -- 2.5.6 Constructing a Distribution Function from Data -- 2.5.7 Monte Carlo Simulation -- 2.5.8 Data Transformations -- 2.6 Bivariate Data Analysis -- 2.6.1 Introduction -- 2.6.2 Graphical Methods: Scatter plots -- 2.6.3 Data Summary: Correlation (Coefficient) -- 2.6.3.1 Definition -- 2.6.3.2 Properties of r -- Further Reading -- 3 Modeling Uncertainty: Concepts and Philosophies -- 3.1 What is Uncertainty? -- 3.2 Sources of Uncertainty -- 3.3 Deterministic Modeling -- 3.4 Models of Uncertainty -- 3.5 Model and Data Relationship.3.6 Bayesian View on Uncertainty -- 3.7 Model Verification and Falsification -- 3.8 Model Complexity -- 3.9 Talking about Uncertainty -- 3.10 Examples -- 3.10.1 Climate Modeling -- 3.10.1.1 Description -- 3.10.1.2 Creating Data Sets Using Models -- 3.10.1.3 Parameterization of Subgrid Variability -- 3.10.1.4 Model Complexity -- 3.10.2 Reservoir Modeling -- 3.10.2.1 Description -- 3.10.2.2 Creating Data Sets Using Models -- 3.10.2.3 Parameterization of Subgrid Variability -- 3.10.2.4 Model Complexity -- Further Reading -- 4 Engineering the Earth: Making Decisions Under Uncertainty -- 4.1 Introduction -- 4.2 Making Decisions -- 4.2.1 Example Problem -- 4.2.2 The Language of Decision Making -- 4.2.3 Structuring the Decision -- 4.2.4 Modeling the Decision -- 4.2.4.1 Payoffs and Value Functions -- 4.2.4.2 Weighting -- 4.2.4.3 Trade-Offs -- 4.2.4.4 Sensitivity Analysis -- 4.3 Tools for Structuring Decision Problems -- 4.3.1 Decision Trees -- 4.3.2 Building Decision Trees -- 4.3.3 Solving Decision Trees -- 4.3.4 Sensitivity Analysis -- Further Reading -- 5 Modeling Spatial Continuity -- 5.1 Introduction -- 5.2 The Variogram -- 5.2.1 Autocorrelation in 1D -- 5.2.2 Autocorrelation in 2D and 3D -- 5.2.3 The Variogram and Covariance Function -- 5.2.4 Variogram Analysis -- 5.2.4.1 Anisotropy -- 5.2.4.2 What is the Practical Meaning of a Variogram? -- 5.2.5 A Word on Variogram Modeling -- 5.3 The Boolean or Object Model -- 5.3.1 Motivation -- 5.3.2 Object Models -- 5.4 3D Training Image Models -- Further Reading -- 6 Modeling Spatial Uncertainty -- 6.1 Introduction -- 6.2 Object-Based Simulation -- 6.3 Training Image Methods -- 6.3.1 Principle of Sequential Simulation -- 6.3.2 Sequential Simulation Based on Training Images -- 6.3.3 Example of a 3D Earth Model -- 6.4 Variogram-Based Methods -- 6.4.1 Introduction -- 6.4.2 Linear Estimation.6.4.3 Inverse Square Distance -- 6.4.4 Ordinary Kriging -- 6.4.5 The Kriging Variance -- 6.4.6 Sequential Gaussian Simulation -- 6.4.6.1 Kriging to Create a Model of Uncertainty -- 6.4.6.2 Using Kriging to Perform (Sequential) Gaussian Simulation -- Further Reading -- 7 Constraining Spatial Models of Uncertainty with Data -- 7.1 Data Integration -- 7.2 Probability-Based Approaches -- 7.2.1 Introduction -- 7.2.2 Calibration of Information Content -- 7.2.3 Integrating Information Content -- 7.2.4 Application to Modeling Spatial Uncertainty -- 7.3 Variogram-Based Approaches -- 7.4 Inverse Modeling Approaches -- 7.4.1 Introduction -- 7.4.2 The Role of Bayes' Rule in Inverse Model Solutions -- 7.4.3 Sampling Methods -- 7.4.3.1 Rejection Sampling -- 7.4.3.2 Metropolis Sampler -- 7.4.4 Optimization Methods -- Further Reading -- 8 Modeling Structural Uncertainty -- 8.1 Introduction -- 8.2 Data for Structural Modeling in the Subsurface -- 8.3 Modeling a Geological Surface -- 8.4 Constructing a Structural Model -- 8.4.1 Geological Constraints and Consistency -- 8.4.2 Building the Structural Model -- 8.5 Gridding the Structural Model -- 8.5.1 Stratigraphic Grids -- 8.5.2 Grid Resolution -- 8.6 Modeling Surfaces through Thicknesses -- 8.7 Modeling Structural Uncertainty -- 8.7.1 Sources of Uncertainty -- 8.7.2 Models of Structural Uncertainty -- Further Reading -- 9 Visualizing Uncertainty -- 9.1 Introduction -- 9.2 The Concept of Distance -- 9.3 Visualizing Uncertainty -- 9.3.1 Distances, Metric Space and Multidimensional Scaling -- 9.3.2 Determining the Dimension of Projection -- 9.3.3 Kernels and Feature Space -- 9.3.4 Visualizing the Data-Model Relationship -- Further Reading -- 10 Modeling Response Uncertainty -- 10.1 Introduction -- 10.2 Surrogate Models and Ranking -- 10.3 Experimental Design and Response Surface Analysis -- 10.3.1 Introduction.10.3.2 The Design of Experiments -- 10.3.3 Response Surface Designs -- 10.3.4 Simple Illustrative Example -- 10.3.5 Limitations -- 10.4 Distance Methods for Modeling Response Uncertainty -- 10.4.1 Introduction -- 10.4.2 Earth Model Selection by Clustering -- 10.4.2.1 Introduction -- 10.4.2.2 k-Means Clustering -- 10.4.2.3 Clustering of Earth Models for Response Uncertainty Evaluation -- 10.4.3 Oil Reservoir Case Study -- 10.4.4 Sensitivity Analysis -- 10.4.5 Limitations -- Further Reading -- 11 Value of Information -- 11.1 Introduction -- 11.2 The Value of Information Problem -- 11.2.1 Introduction -- 11.2.2 Reliability versus Information Content -- 11.2.3 Summary of the VOI Methodology -- 11.2.3.1 Steps 1 and 2: VOI Decision Tree -- 11.2.3.2 Steps 3 and 4: Value of Perfect Information -- 11.2.3.3 Step 5: Value of Imperfect Information -- 11.2.4 Value of Information for Earth Modeling Problems -- 11.2.5 Earth Models -- 11.2.6 Value of Information Calculation -- 11.2.7 Example Case Study -- 11.2.7.1 Introduction -- 11.2.7.2 Earth Modeling -- 11.2.7.3 Decision Problem -- 11.2.7.4 The Possible Data Sources -- 11.2.7.5 Data Interpretation -- Further Reading -- 12 Example Case Study -- 12.1 Introduction -- 12.1.1 General Description -- 12.1.2 Contaminant Transport -- 12.1.3 Costs Involved -- 12.2 Solution -- 12.2.1 Solving the Decision Problem -- 12.2.2 Buying More Data -- 12.2.2.1 Buying Geological Information -- 12.2.2.2 Buying Geophysical Information -- 12.3 Sensitivity Analysis -- Index.'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.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. Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling 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 on how to make optimal 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 and invaluable primer for the complex areas of decision making with uncertainty in the Earth Sciences. First comprehensive book to present the uncertainties inherent in modeling for the Earth science community Full colour throughout Includes case study examples for greater clarity Geo-engineering focus Provides an accessible introduction to modeling uncertainty in the Earth Sciences Includes established tools as well as novel techniques developed by the author Companion website available with free software and examples Avoids complex mathematics for enhanced user-friendly approach Companion Website www.wiley.com/go/caers/modelingGeologyMathematical modelsEarth sciencesStatistical methodsThree-dimensional imaging in geologyUncertaintyGeologyMathematical models.Earth sciencesStatistical methods.Three-dimensional imaging in geology.Uncertainty.551.01/5195Caers Jef732927MiAaPQMiAaPQMiAaPQBOOK9910877142303321Modeling uncertainty in the earth sciences4186282UNINA