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?.