Handbook of Mathematical Geosciences : : Fifty Years of IAMG.

• Author: Daya Sagar, B. S.
• TeilnehmendeR: Cheng, Qiuming.; Agterberg, Frits.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2018.; Ã2018.
• Year of Publication: 2018
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (911 pages)

Table of Contents

Intro -- Foreword -- Preface -- Contents -- Editors and Contributors -- Theory -- 1 Kriging, Splines, Conditional Simulation, Bayesian Inversion and Ensemble Kalman Filtering -- Abstract -- 1.1 Introduction -- 1.2 Deterministic Aspects of Geostatistics -- 1.2.1 Simple Stationary Kriging -- 1.2.2 Kriging with Intrinsic Random Functions of Order k -- 1.2.3 Kriging Extensions -- 1.2.3.1 Generalization of Kriging to the Interpolation of Average Values -- 1.2.3.2 Error CoKriging -- 1.2.3.3 Dual Kriging -- 1.2.4 Kriging and Splines -- 1.2.4.1 Interpolating Splines -- 1.2.4.2 Smoothing Splines -- 1.2.4.3 Kriging and Regularization-The Discrete Case -- 1.2.5 Kriging and Bayesian Inversion -- 1.2.5.1 Bayesian Linear Inversion -- 1.2.5.2 Kriging and Bayesian Inversion -- 1.2.6 Energy-Based Versus Probabilistic Estimates -- 1.2.7 Conclusion on Kriging -- 1.3 Stochastic Aspects of Geostatistics: Conditional Simulation -- 1.3.1 Method 1: "Smooth Plus Rough" or "Rough Plus Smooth" Algorithm -- 1.3.2 Method 2: Sequential Gaussian Simulation (SGS) -- 1.3.3 Spectrum and Conditional Simulation -- 1.4 Geostatistical Inversion of Seismic Data -- 1.4.1 Deterministic Seismic Inversion -- 1.4.2 Geostatistical Inversion (GI) -- 1.5 Kalman Filtering and Ensemble Kalman Filtering -- 1.5.1 Kalman Filtering (KF) -- 1.5.2 Constraining Reservoir Models by Production Data -- 1.5.3 Ensemble Kalman Filtering (EnKF) Versus Conditional Simulation -- 1.5.4 Ensemble Kalman Filtering and Its Relationship with CoKriging -- 1.6 Beyond the Formal Relationship Between Geostatistics and Bayes -- 1.6.1 Two Identical Formalisms but Different Assumptions -- 1.6.2 Model Falsifiability -- 1.6.3 Looking Ahead: Machine Learning and Falsifiability -- 1.7 Conclusion -- Acknowledgements -- References -- 2 A Statistical Commentary on Mineral Prospectivity Analysis -- 2.1 Introduction.

2.2 Example Data -- 2.3 Logistic Regression -- 2.3.1 Basics of Logistic Regression -- 2.3.2 Flexibility and Validity -- 2.3.3 Fitting Procedure and Implicit Assumptions -- 2.3.4 Pixel Size and Model Consistency -- 2.4 Poisson Point Process Models -- 2.4.1 Logistic Regression with Infinitesimal Pixels -- 2.4.2 Poisson Point Process -- 2.4.3 Fitting a Poisson Point Process Model -- 2.4.4 Murchison Example -- 2.4.5 Statistical Inference -- 2.4.6 Diagnostics -- 2.4.7 Rationale for Prediction -- 2.5 Monotone Regression -- 2.6 Nonparametric Curve Estimation -- 2.7 ROC Curves -- 2.8 Recursive Partitioning -- References -- 3 Testing Joint Conditional Independence of Categorical Random Variables with a Standard Log-Likelihood Ratio Test -- 3.1 Introduction -- 3.2 From Contingency Tables to Log-Linear Models -- 3.3 Independence, Conditional Independence of Random Variables -- 3.4 Logistic Regression, and Its Special Case of Weights-of-Evidence -- 3.5 Hammersley-Clifford Theorem -- 3.6 Testing Joint Conditional Independence of Categorical Random Variables -- 3.7 Conditional Distribution, Logistic Regression -- 3.8 Practical Applications -- 3.8.1 Practical Application with Fabricated Indicator Data -- 3.9 Discussion and Conclusions -- References -- 4 Modelling Compositional Data. The Sample Space Approach -- 4.1 Introduction -- 4.2 Scale Invariance, Key Principle of Compositions -- 4.3 The Simplex as Sample Space of Compositions -- 4.4 Perturbation, a Natural Shift Operation on Compositions -- 4.5 Conditions on Metrics for Compositions -- 4.6 Consequences of the Aitchison Geometry in the Sample Space of Compositional Data -- 4.7 Conclusions -- References -- 5 Properties of Sums of Geological Random Variables -- Abstract -- 5.1 Introduction -- 5.2 Preliminaries -- 5.2.1 Bounds -- 5.3 Thumbnail Case Studies -- 5.3.1 USGS Oil and Gas Resource Projections.

5.3.2 USGS Probabilistic Assessment of CO2 Storage Capacity -- 5.3.3 Cupolas and Oil and Gas Resource Assessment -- 5.4 Concluding Remarks -- References -- 6 A Statistical Analysis of the Jacobian in Retrievals of Satellite Data -- 6.1 Introduction -- 6.2 A Statistical Framework for Satellite Retrievals -- 6.3 The Jacobian Matrix and its Unit-Free Version -- 6.4 Statistical Significance Filter -- 6.4.1 Hypothesis Tests -- 6.4.2 Distribution Theory for the Robust Test Statistic -- 6.4.3 Multiple Hypothesis Tests Define the Statistical Significance Filter -- 6.5 ACOS Retrievals of the Atmospheric State from Japan's GOSAT Satellite -- 6.6 Discussion -- References -- 7 All Realizations All the Time -- Abstract -- 7.1 Introduction -- 7.2 Simulation -- 7.3 Decision Making -- 7.4 Geostatistical Simulation -- 7.5 Resource Decision Making -- 7.6 Alternatives to All Realizations -- 7.7 Concluding Remarks -- Acknowledgements -- References -- 8 Binary Coefficients Redux -- Abstract -- 8.1 Introduction -- 8.2 Empirical Comparisons and a Taxonomy -- 8.3 Effects of Rare and Endemic Taxa -- 8.4 Adjusting for Poor Sampling -- 8.5 Metric? Euclidean? -- 8.6 From Expected Values to Null Association -- 8.7 Illustrative Example -- 8.8 Discussion and Conclusions -- 8.9 Summary -- Acknowledgements -- References -- 9 Tracking Plurigaussian Simulations -- Abstract -- 9.1 Introduction -- 9.2 Review of Complex Networks -- 9.3 Network Analysis of Google Citations of Plurigaussian Simulations -- 9.3.1 Building a Citation Network -- 9.4 Diffusion of the New Method into Industry -- 9.4.1 Co-authors and Repeat Co-authors from Industry -- 9.4.2 Surveys of Academics and Consultants -- 9.5 Conclusions and Perspectives for Future Work -- 9.5.1 What Lessons Can Be Learned from the Study for Policy-Makers -- Acknowledgements -- Appendix 9.1 -- References.

10 Mathematical Geosciences: Local Singularity Analysis of Nonlinear Earth Processes and Extreme Geo-Events -- Abstract -- 10.1 Introduction -- 10.2 What Is Mathematical Geosciences or Geomathematics? -- 10.3 What Contributions Has MG Made to the Geosciences? -- 10.4 Frontiers of Earth Science and Opportunities of MG -- 10.5 Fractal Density and Singularity Analysis of Nonlinear Geo-Processes and Extreme Geo-Events -- 10.5.1 Fractal Density -- 10.5.2 Density-Scale Power-Law Model and Singularity -- 10.5.3 Multifractal Density -- 10.5.4 Fractal Density Structure and Clustering Distribution -- 10.6 Fractal Integral and Fractal Differential Operations of Nonlinear Functions -- 10.7 Earth Dynamic Processes and Extreme Events -- 10.7.1 Phase Transition -- 10.7.2 Self-organized Criticality -- 10.7.3 Multiplicative Cascade Processes -- 10.8 Fractal Density of Lithosphere Rheology in Phase Transition Zones and Association with Earthquakes -- 10.8.1 Rheology Constitutive Equation -- 10.8.2 Rheology and Phase Transition -- 10.8.3 Frequency-Depth Fractal Density Distribution and Singularity Analysis of Earthquakes -- 10.9 Discussion and Conclusions -- Acknowledgements -- References -- General Applications -- 11 Electrofacies in Reservoir Characterization -- Abstract -- 11.1 Introduction -- 11.2 The Amal Field of Libya -- 11.3 Electrofacies Analysis -- 11.3.1 Choice of Log Traces for Electrofacies Calculation -- 11.3.2 Standardization of Log Traces -- 11.3.3 Estimating the Number of Distinct Electrofacies -- 11.3.4 Assigning Well Log Intervals to Electrofacies -- 11.3.5 Converting the Electrofacies Classification into a Prediction Function -- 11.4 What Do Amal Electrofacies Mean? -- 11.4.1 Lithologic Description of Amal Electrofacies -- 11.5 Conclusions -- Acknowledgements -- References -- 12 Shoreline Extrapolations -- 12.1 Three Problems, One Theoretical Tool.

12.2 Median Set -- 12.3 Median and Average for Non Ordered Sets -- 12.4 Extrapolations via the Quench Function -- 12.5 Accretion and Homotopy -- 12.6 Conclusion -- References -- 13 An Introduction to the Spatio-Temporal Analysis of Satellite Remote Sensing Data for Geostatisticians -- 13.1 Introduction -- 13.2 Satellite Images -- 13.2.1 Access and Analysis of Satellite Images with R -- 13.3 Derived Variables from Remote Sensing Data -- 13.4 Pre-processing -- 13.5 Spatial Interpolation -- 13.6 Spatio-Temporal Interpolation -- 13.6.1 Geostatistical R Packages -- 13.7 Conclusions -- References -- 14 Flint Drinking Water Crisis: A First Attempt to Model Geostatistically the Space-Time Distribution of Water Lead Levels -- Abstract -- 14.1 Introduction -- 14.2 Materials and Methods -- 14.2.1 Datasets -- 14.2.2 Space-Time Kriging and Covariance Models -- 14.2.3 Accounting for Secondary Information -- 14.2.4 Cross-Validation -- 14.3 Results and Discussion -- 14.3.1 Spatial Distribution -- 14.3.2 Temporal Trend Modeling -- 14.3.3 Variography -- 14.3.4 Cross-Validation Analysis -- 14.4 Conclusions -- Acknowledgements -- References -- 15 Statistical Parametric Mapping for Geoscience Applications -- Abstract -- 15.1 Introduction -- 15.2 Anomaly Detection with Statistical Parametric Mapping -- 15.2.1 MultiGaussian Fields -- 15.2.2 Calculating the SPM -- 15.2.2.1 Conditional Differences -- 15.2.2.2 Isolated Regions of Activation -- 15.2.3 Localized Anomaly Detection -- 15.3 Example Problems -- 15.3.1 Anomaly Detection in Images -- 15.3.2 Ground Water Pumping -- 15.3.2.1 Problem Setup -- 15.3.2.2 Results -- 15.4 Summary -- Appendix: Conditional Differences -- References -- 16 Water Chemistry: Are New Challenges Possible from CoDA (Compositional Data Analysis) Point of View? -- Abstract -- 16.1 Water Chemistry Data as Compositional Data.

16.2 Isometric-Log Ratio Transformation: Is This the Key to Decipher the Dynamics of Geochemical Systems?.