Handbook of Mathematical Geosciences

Handbook of Mathematical Geosciences

Fifty Years of IAMG

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Springer Nature Switzerland AG






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ForewordPreface IntroductionB. S. Daya Sagar, Qiuming Cheng, Frits Agterberg Part I Theory1. Kriging, Splines, Conditional Simulation, Bayesian In-version and Ensemble Kalman Filtering Olivier Dubrule1.1 Introduction1.2 Deterministic Aspects of Geostatistics1.3 Stochastic Aspects of Geostatistics: Conditional Simulation1.4 Geostatistical Inversion of Seismic Data1.5 Kalman Filtering and Ensemble Kalman Filtering1.6 Beyond the Formal Relationship between Geostatistics and Bayes 1.7 ConclusionReferences 2. A Statistical Commentary on Mineral Prospectivity analysis Adrian Baddeley2.1 Introduction2.2 Example Data2.3 Logistic Regression2.4 Poisson Point Process Models2.5 Monotone Regression2.6 Nonparametric Curve Estimation2.7 ROC curves2.8 Recursive PartitioningReferences3. Testing joint conditional independence of categorical random variables with a standard log-likelihood ratio test Helmut Schaeben3.1 Introduction3.2 From Contingency Tables to Log-Linear Models3.3 Independence, Conditional Independence of Random variables3.4 Logistic Regression, and its Special Case of Weightsof Evidence3.5 Hammersley-Clifford Theorem3.6 Testing Joint Conditional Independence of Categorical Random Variables3.7 Conditional Distribution, Logistic Regression3.8 Practical Applications3.9 Discussion and ConclusionsReferences 4. Modelling Compositional Data. The Sample Space Ap-proach Juan Jose Egozcue and Vera Pawlowsky-Glahn4.1 Introduction4.2 Scale Invariance, Key Principle of Compositions4.3 The Simplex as Sample Space of Compositions4.4 Perturbation, a Natural Shift Operation on Compositions4.5 Conditions on Metrics for Compositions4.6 Consequences of the Aitchison Geometry in the Sample Space of Compositional Data4.7 ConclusionsReferences 5. Properties of Sums of Geological Random Variables G.M. Kaufman5.1 Introduction5.2 Preliminaries5.3 Thumbnail Case StudiesReferences6. A Statistical Analysis of the Jacobian in Retrievals of Satellite Data Noel Cressie6.1 Introduction6.2 A Statistical Framework for Satellite Retrievals6.3 The Jacobian Matrix and its Unit-Free Version6.4 Statistical Significance Filter6.5 ACOS Retrievals of the Atmospheric State from Japan's GOSAT Satellite6.6 DiscussionReferences 7. All Realizations All the Time Clayton V. Deutsch7.1 Introduction7.2 Simulation7.3 Decision Making7.4 Geostatistical Simulation7.5 Resource Decision Making7.6 Alternatives to All Realizations7.7 Concluding RemarksReferences 8. Binary Coefficients Redux Michael E. Hohn8.1 Introduction8.2 Empirical Comparisons and a Taxonomy8.3 Effects of Rare and Endemic Taxa8.4 Adjusting for Poor Sampling 8.5 Metric? Euclidean?8.6 From Expected Values to Null Association8.7 Illustrative Example8.8 Discussion and Conclusions8.9 SummaryReferences 9. Tracking Plurigaussian Simulations M. Armstrong, A. Mondaini and S. Camargo9.1 Introduction9.2 Review of Complex Networks9.3 Network Analysis of Google Citations of Plurigaus sian Simulations9.4 Diffusion of the New Method into Industry9.5 Conclusions and Perspectives for Future WorkReferences 10. Mathematical Geosciences: Local Singularity Analysis of Nonlinear Earth Processes and Extreme Geo-Events Qiuming Cheng10.1 Introduction10.2 What is Mathematical Geosciences or Geomathemat ics?10.3 What contributions has MG made to geosciences?10.4 Frontiers of Earth science and opportunity of MG10.5 Fractal density and singularity analysis of nonlinear geo-processes and extreme geo-events 10.6 Fractal Integral and fractal differential operations of nonlinear function10.7 Earth dynamics processes and extreme events10.8 Fractal density of continent rheology in phase transition zones and association with earthquakes 10.9 Discussion and Conclusions References Part II General Applications11. Electrofacies in Reservoir Characterization John Davis11.1 Introduction11.2 The Amal Field of Libya11.3 Electrofacies Analysis11.4 What Do Amal Electrofacies Mean?11.5 ConclusionsReferences 12. Forecast of Shoreline Variations by Means of Median Sets Jean Serra12.1 Three problems, One Theoretical Tool12.2 Median Set12.3 Median and Average for Non-Ordered Sets12.4 Extrapolations via the Quench Function12.5 Accretion and Homotopy12.6 ConclusionReferences 13. An Introduction to the Spatio-Temporal Analysis of Sat-ellite Remote Sensing Data for Geostatisticians A. F. Militino, M. D. Ugarte, and U. Perez-Goya13.1 Introduction13.2 Satellite Images13.3 Derived Variables from Remote Sensing Data13.4 Pre-processing13.5 Spatial Interpolation13.6 Spatio-Temporal Interpolation13.7 ConclusionsReferences 14. Flint drinking water crisis: a first attempt to model geo-statistically the space-time distribution of water lead levels Pierre Goovaerts14.1 Introduction14.2 Materials and Methods14.3 Results and Discussion14.4 ConclusionsReferences 15. Statistical Parametric Mapping for Geoscience Applica-tions Sean A. McKenna15.1 Introduction15.2 Anomaly Detection with Statistical Parametric Mapping15.3 Example Problems15.4 Summary References 16. Water chemistry: are new challenges possible from CoDA (Compositional Data Analysis) point of view? Antonella Buccianti16.1 Water Chemistry Data as Compositional Data16.2 Isometric-Log Ratio Transformation: Is this the Key to Decipher the Dynamics of Geochemical Systems?16.3 Improving CoDA-Dendrogram: Checking for Vari ability, Resilience and Stability16.4 ConclusionsReferences 17. Analysis of the United States Portion of the North Ameri-can Soil Geochemical Landscapes Project - A Composi-tional Framework Approach E. C. Grunsky, L. J. Drew, and D. B. Smith17.1 Introduction17.2 Methods17.3 Results17.4 Discussion17.5 Concluding RemarksReferencesPart III Exploration and Resource Estimation18. Quantifying the Impacts of Uncertainty Peter Dowd18.1 Introduction18.2 Sources of In-Situ Uncertainty18.3 Transfer Uncertainty18.4 Consequences of In-Situ Uncertainty18.5 Quantifying Epistemic Uncertainty18.6 Quantifying the Effects of Transfer Uncertainty18.7 ConclusionReferences 19. Advances in Sensitivity Analysis of Uncertainty due to Sampling Density for Spatially Correlated Attributes Ricardo A. Olea19.1 Introduction19.2 Data19.3 Traditional Uncertainty Assessment19.4 Kriging19.5 Stochastic Simulation19.6 Validation19.7 ConclusionsReferences 20. Predicting Molybdenum Deposit Growth John H. Schuenemeyer, Lawrence J. Drew and James D. Bliss20.1 Introduction20.2 Cutoff Grade as a Function of Deposit Grade20.3 Deposit Growth as a Function of Cutoff Grade20.4 An Example20.5 ConclusionsReferences 21. General Framework of Quantitative Target Selections Guocheng Pan21.1 Introduction21.2 Randomness of Mineral Endowment21.3 Fundamental Geo-Process Relations21.4 Scarceness, Rareness, and Exceptionalness21.5 Intrinsic Geological Unit21.6 Economic Truncation and Translation21.7 Information Synthesis21.8 Prediction with Dynamic Control SamplesReferences 22. Solving the Wrong Resource Assessment Problems Pre-cisely Donald A. Singer22.1 Introduction22.2 Target Population22.3 Examples of Mismatches in Assessments22.4 How to Correct Type III Errors22.5 ConclusionsReferences 23. Two ideas for analysis of multivariate geochemical survey data: proximity regression and principal component re-siduals G.F. Bonham-Carter and E. C. Grunsky23.1 Introduction23.2 Method 1: Direct Prediction of Spatial Proximity23.3 Method 2: Principal Component Residuals23.4 ConclusionsReferences 24. Mathematical minerals: A history of petrophysical pe-trography John H. Doveton24.1 Pioneering Computer Methods24.2 Mineralogy of Underdetermined Systems 24.3 Mineralogy of Overdetermined Systems24.4 Optimization Methods24.5 Clay Component Estimation 24.6 Normative Estimation by Geochemical Logs24.7 ConclusionReferences 25. Geostatistics for Seismic Characterization of Oil Reser-voirs Amilcar Soares and Leonado Azevedo25.1 Integration of Geophysical Data for Reservoir Modeling and Characterization25.2 Iterative Geostatistical Seismic Inversion Methodologies25.3 Trace-by-Trace Geostatistical Seismic Inversion 25.4 Global Geostatistical Seismic Inversion Methodologies25.5 Uncertainty and Risk Assessment at early stages of exploration25.6 Final RemarksReferences 26. Statistical Modeling of Regional and Worldwide Size-Frequency Distributions of Metal Deposits Frits Agterberg26.1 Introduction26.2 Modified Version of the Model of de Wijs Applied to Worldwide Metal Deposits26.3 Theory and Applications of the Pareto-Lognormal Model26.4 Upper Tail Pareto Distribution and its Connection to the Basic Lognormal Distribution26.5 Prediction of Future Copper Resources26.6 Concluding RemarksReferencesPart IV Reviews27. Bayesianism in the Geosciences Jef Caers27.1 Introduction27.2 A Historical P27.3 Science as Knowledge Derived from Facts, Data or Experience27.4 The Role of Experiments - Data 27.5 Induction vs Deduction27.6 Falsificationism27.7 Paradigms27.8 Bayesianism27.9 Bayesianism for Subsurface Systems27.10 SummaryReferences 28. Geological Objects and Physical Parameter Fields in the Subsurface: A Review Guillaume Caumon28.1 Introduction28.2 Motivations for Explicit Geological Parameterizations28.3 Parameterizations for Physical Models28.4 Geological Parameterizations28.5 Conclusions and ChallengesReferences 29. Fifty Years of Kriging Jean-Paul Chiles and Nicolas Desassis29.1 Introduction29.2 The Origins of Kriging29.3 Development and Maturity: Trend, Neighborhood Selection29.4 Iterative Use of Kriging to Handle Inequality Data29.5 Nonstationary Covariance29.6 Kriging for Large Data Sets29.7 Iterative Algorithms for Solving the Kriging System29.8 ConclusionReferences 30. Multiple Point Statistics: A Review Pejman Tahmasebi30.1 Introduction30.2 Two-Point based Stochastic Simulation30.3 Multiple Point Geostatistics (MPS)30.4 Simulation Path30.5 Current Multiple Point Geostatistical Algorithms30.6 Current ChallengesReferences 31. When Should We Use Multiple-Point Geostatistics? Gregoire Mariethoz31.1 Under-Informed vs Over-Informed Models31.2 MPS vs Covariance-Based Geostatistics31.3 Examples for which MPS Works W31.4 ConclusionReferences 32. The Origins of the Multiple-Point Statistics (MPS) Algo-rithm R. Mohan Srivastava32.1 Introduction32.2 1970s 32.3 1980s32.4 1990s32.5 Concluding ThoughtsReferences 33. Predictive Geometallurgy: An Interdisciplinary Key Challenge for Mathematical Geosciences? K.G. van den Boogaart and R. Tolosana-Delgado33.1 Introduction33.2 Process Modelling33.3 Ore Characterisation33.4 Orebody Modelling33.5 Decision Making33.6 Conclusions References 34. Data Science for Geoscience: Leveraging Mathematical Geosciences with Semantics and Open Data Xiaogang Ma34.1 Introduction34.2 The Intelligent Stage of Mathematical Geosciences34.3 Case Studies of Data Science in Geoscience34.4 Concluding RemarksReferences 35. Mathematical Morphology in Geosciences and GISci: An Illustrative Review B. S. Daya Sagar35.1 Introduction 35.2 Terrestrial Pattern Retrieval35.3 Terrestrial Pattern Analysis35.4 Geomorphologic Modeling and Simulation35.5 Geospatial Computing and Visualization35.6 ConclusionsReferences Part V Reminiscences36. IAMG: Recollections from the Early Years John Cubitt and Stephen Henley, with contributions from T. Victor (Vic) Loudon, EHT (Tim) Whitten, John Gower, Dan-iel (Dan) Merriam, Thomas (Tom) Jones, and Hannes Thiergartner36.1 The Birth of Mathematical Geology and the Origins of the IAMG36.2 The Role of the Kansas Geological Survey in the origins of the IAMG36.3 Name and Establishment of the Society36.4 Foundation of IAMG Publications36.5 Prague36.6 Subsequent Events following Prague - 36.7 The Looming Gap References 37. Forward and Inverse Models over 70 Years E. H. Timothy Whitten 37.1 Birth of IAMG in 196837.2 In the Beginning (one pre-1968 experience)37.3 Inverse and Forward Geology Problems37.4 Forward Models in Earth Sciences37.5 Inverse Models in Earth Sciences37.6 The Samples Analysed37.7 The Black Swan Effect37.8 Concluding ThoughtsReferences 38. From individual personal contacts 1962-1968 to my 50 years of service Vaclav Nemec 38.1 Introduction38.2 IAMG Foundation (Prague 1968)38.3 Activities for the IAMG 1968 - 199338.4 Pribram - East - West Gate near the Iron Curtain38.5 My own professional work38.6 Two Separate Silver Anniversary Meetings of Mathematical Geologists in Prague (1993)38.7 From the Silver to the Golden IAMG Jubilee 38.9 ConclusionReferences 39. Andrey Borisovich Vistelius Stephen Henley39.1 Background39.2 Scientific Achievements and Insights39.3 The International Association for Mathematical Geology39.4 The "Father of Mathematical Geology"? 39.5 LegacyReferences 40. Fifty Years' Experience with Hidden Errors in Applying Classic Mathematical Geology Hannes Thiergartner40.1 Introduction and Definitions40.2 Hidden errors and Case Study Examples40.3 Conclusion and SuggestionsReferences 41. Mathematical Geology by Example: Teaching and Learning Perspectives James R. Carr41.1 Introduction41.2 Multivariate Analysis of Geochemical Data41.3 Geostatistics and its Myriad Parameters41.4 The Variogram as a Stand-Alone Data Analytical ToolReferences 42. Linear Unmixing in the Geologic Sciences: More Than a Half of Century of Progress William E. Full42.1 Introduction42.2 History of Constant Sum HVA42.3 Non-Constant Sum Data and Algorithms42.4 SummaryReferences 43. Pearce Element Ratio Diagrams and Cumulate Rocks James Nicholls43.1 Introduction43.2 Outline of a Cumulate Rock Paradigm43.3 Pearce Element Ratio Patterns for Cumulate Rocks43.4 Compositions of Units of the Skaergaard Intrusion43.5 Melts of the Skaergaard Intrusion43.6 Pearce Element Ratios, Cumulate Rocks, and September 11References 44. Reflections on the Name of IAMG and of the Journal Donald E. Myers 45. Origin and Early Development of the IAMG Frits Agterberg45.1 Introduction45.2 Pioneers of Mathematical Geology45.3 Inputs from Mathematical Statisticians45.4 Concluding RemarksReferences
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