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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. 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. Inhaltsverzeichnis 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 <...
