Handbook of Mathematical Geosciences: Fifty Years of IAMG

Handbook of Mathematical Geosciences: Fifty Years of IAMG

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This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.

Product Details

ISBN-13: 9783319789989
Publisher: Springer International Publishing
Publication date: 06/26/2018
Edition description: 1st ed. 2018
Pages: 914
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

B.S. Daya Sagar is a full Professor at the Systems Science and Informatics Unit (SSIU) at the Indian Statistical Institute in Bangalore, India. Dr. Sagar received his MSc and Ph.D. degrees in geoengineering and remote sensing from the Faculty of Engineering, Andhra University, Visakhapatnam, India, in 1991 and 1994 respectively. He is also first Head of the SSIU. Earlier, he worked at the College of Engineering, Andhra University, and Centre for Remote Imaging Sensing and Processing (CRISP), at the The National University of Singapore in various positions during 1992-2001. He served as Associate Professor and Researcher at the Faculty of Engineering & Technology (FET), Multimedia University, Malaysia, during 2001-2007. Since 2017, he has been a Visiting Professor at the University of Trento, Italy. His research interests include mathematical morphology, GISci, digital image processing, fractals and multifractals, their applications in extraction, analyses, and modelling of geophysical patterns. He has published over 85 papers in scientific journals, and has authored and/or guest edited 11 books and/or special theme issues for journals. He recently authored a book entitled "Mathematical Morphology in Geomorphology and GISci". He recently co-edited two special issues on "Filtering and Segmentation with Mathematical Morphology" for IEEE Journal of Selected Topics in Signal Processing and "Applied Earth Observation and Remote Sensing in India" for IEEE Journal of Selected Topics in Applied Earth Observation and Remote Sensing. He is an elected Fellow of Royal Geographical Society (1999), Indian Geophysical Union (2011), and was a member of the New York Academy of Science during 1995-1996. He received the Dr. Balakrishna Memorial Award from the Andhra Pradesh Academy of Sciences in 1995, the Krishnan Gold Medal from the Indian Geophysical Union in 2002, and the "Georges Matheron Award-2011 (with Lecturership)" of the International Association for Mathematical Geosciences. He is the Founding Chairman of Bangalore Section IEEE GRSS Chapter. He is on the Editorial Boards of Computers & Geosciences, and Frontiers: Environmental Informatics.

Qiuming Cheng did his Ph.D. in Earth Science under supervision of Dr. Frits Agterberg at the University of Ottawa in 1994. Dr. Cheng spent a year at the Geological Survey of Canada as a PDF under the supervision of Dr. Graeme Bonham-Carter, and soon became a faculty member at York University, Toronto, Canada in 1995 with cross appointments in the Department of Earth and Space Science and Engineering and the Department of Geography. He was promoted to associate professor in 1997 and to full professor in 2002. He was awarded a Changjiang Scholar Professorship in China by the China Ministry of Education where he has set up and leads the State Key Lab of Geological Processes and Mineral Resources (GPMR) located on both campuses of China University of Geosciences in Beijing and Wuhan. Currently, he holds a Thousand Talent National Special Professorship of China, serving as the founding director of the GPMR lab. Dr. Cheng has specialized in mathematical geosciences with a research focus on nonlinear mathematical modelling of earth processes and geoinformatics techniques for prediction of mineral resources. He has authored and coauthored more than 300 research articles. He has been awarded several prestigious awards including the Krumbein Medal, the highest award by the International Association for Mathematical Geosciences (IAMG). Dr. Cheng was an elected President of the International Association for Mathematical Geosciences (IAMG) during 2012-16. He is the president of International Union of Geological Sciences (IUGS) for the period between 2016 and 2020. Dr. Cheng is an international leader in the application of nonlinear mathematics and geoinformatics to the analysis, modelling and prediction of a wide range of geological processes and mineral resources quantitative assessment. Dr. Cheng’s primary research interest involves the interdisciplinary study of non-linear properties of the Earth’s systems, as well as quantitative assessment and prediction of natural resources and environmental impacts. His research on fractal density & local singularity analysis theory and geomathematical models has made a major impact in several geoscientific disciplines, including those concerned with ocean ridge heat flow, magmatic flare-up during continent crustal growth and formation of supercontinents, earthquakes, floods, hydrothermal mineralization, and prediction of deeply buried mineral deposits.

Frits Agterberg is a Dutch-born Canadian Mathematical Geologist who served at the Geological Survey of Canada in Ottawa. He attended Utrecht University in The Netherlands from 1954 to 1961. With other founding members, he was instrumental in establishing the International Association for Mathematical Geosciences (IAMG) in 1968. He received the IAMG's William Christian Krumbein Medal in 1978 and he was IAMG Distinguished Lecturer in 2004. In 2017 he was conferred with the Honorary Membership of the IAMG. He has authored or coauthored over 250 scientific papers and five books. He has served the IAMG in many ways, including being its President from 2004 to 2008. After defending his doctoral thesis on structural geology of the Italian Alps at Utrecht University and a one-year fellowship at the University of Wisconsin in Madison, he became "petrological statistician" in his first job at the Geological Survey of Canada (GSC) in 1962. He was asked to create the GSC Geomathematics Section in 1971. He retired from the GSC in 1996 but still has an office at their Ottawa headquarters. In 1968, he became associated with the University of Ottawa where he taught a "Statistics in geology" course for 25 years and has supervised six geomathematical PhD students. From 1978 to 1989, he directed the Quantitative Stratigraphy Project of the International Geological Correlation Program. From 1981 to 2001, Dr. Agterberg was a correspondent of the Royal Netherlands Academy of Arts and Sciences. During the past 20 years, primarily in collaboration with Qiuming Cheng, his colleagues and students at the China University of Geosciences in Wuhan and Beijing and at York University, Toronto, he has worked on applications of multifractals to study the spatial distribution of metals in rocks and ore bodies.

Table of Contents


B. S. Daya Sagar, Qiuming Cheng, Frits Agterberg

Part I Theory
1. Kriging, Splines, Conditional Simulation, Bayesian In-version and Ensemble Kalman Filtering Olivier Dubrule
1.1 Introduction
1.2 Deterministic Aspects of Geostatistics
1.3 Shastic Aspects of Geostatistics: Conditional Simulation
1.4 Geostatistical Inversion of Seismic Data
1.5 Kalman Filtering and Ensemble Kalman Filtering
1.6 Beyond the Formal Relationship between Geostatistics and Bayes
1.7 Conclusion

2. A Statistical Commentary on Mineral Prospectivity analysis Adrian Baddeley
2.1 Introduction
2.2 Example Data
2.3 Logistic Regression
2.4 Poisson Point Process Models
2.5 Monotone Regression
2.6 Nonparametric Curve Estimation
2.7 ROC curves
2.8 Recursive Partitioning
3. Testing joint conditional independence of categorical random variables with a standard log-likelihood ratio test Helmut Schaeben
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 Weightsof 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
3.9 Discussion and Conclusions

4. Modelling Compositional Data. The Sample Space Ap-proach Juan José Egozcue and Vera Pawlowsky-Glahn
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

5. Properties of Sums of Geological Random Variables
G.M. Kaufman
5.1 Introduction
5.2 Preliminaries
5.3 Thumbnail Case Studies
6. A Statistical Analysis of the Jacobian in Retrievals of Satellite Data Noel Cressie
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
6.5 ACOS Retrievals of the Atmospheric State from Japan’s GOSAT Satellite
6.6 Discussion

7. All Realizations All the Time
Clayton V. Deutsch
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

8. Binary Coefficients Redux Michael E. Hohn
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

9. Tracking Plurigaussian Simulations
M. Armstrong, A. Mondaini and S. Camargo
9.1 Introduction
9.2 Review of Complex Networks
9.3 Network Analysis of Google Citations of Plurigaus sian Simulations
9.4 Diffusion of the New Method into Industry9.5 Conclusions and Perspectives for Future Work

10. Mathematical Geosciences: Local Singularity Analysis of Nonlinear Earth Processes and Extreme Geo-Events Qiuming Cheng
10.1 Introduction
10.2 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 MG
10.5 Fractal density and singularity analysis of nonlinear geo-processes and extreme geo-events
10.6 Fractal Integral and fractal differential operations of nonlinear function
10.7 Earth dynamics processes and extreme events
10.8 Fractal density of continent rheology in phase transition zones and association with earthquakes
10.9 Discussion and Conclusions

Part II General Applications
11. Electrofacies in Reservoir Characterization
John Davis
11.1 Introduction
11.2 The Amal Field of Libya
11.3 Electrofacies Analysis
11.4 What Do Amal Electrofacies Mean?
11.5 Conclusions

12. Forecast of Shoreline Variations by Means of Median Sets Jean Serra12.1 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

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-Goya
13.1 Introduction13.2 Satellite Images
13.3 Derived Variables from Remote Sensing Data
13.4 Pre-processing
13.5 Spatial Interpolation
13.6 Spatio-Temporal Interpolation
13.7 Conclusions

14. Flint drinking water crisis: a first attempt to model geo-statistically the space-time distribution of water lead levels Pierre Goovaerts
14.1 Introduction
14.2 Materials and Methods
14.3 Results and Discussion
14.4 Conclusions

15. Statistical Parametric Mapping for Geoscience Applica-tions Sean A. McKenna
15.1 Introduction
15.2 Anomaly Detection with Statistical Parametric Mapping
15.3 Example Problems
15.4 Summary

16. Water chemistry: are new challenges possible from CoDA (Compositional Data Analysis) point of view? Antonella Buccianti
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?
16.3 Improving CoDA-Dendrogram: Checking for Vari ability, Resilience and Stability
16.4 Conclusions

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. Smith
17.1 Introduction
17.2 Methods
17.3 Results17.4 Discussion
17.5 Concluding Remarks
Part III Exploration and Resource Estimation
18. Quantifying the Impacts of Uncertainty
Peter Dowd
18.1 Introduction
18.2 Sources of In-Situ Uncertainty
18.3 Transfer Uncertainty
18.4 Consequences of In-Situ Uncertainty
18.5 Quantifying Epistemic Uncertainty
18.6 Quantifying the Effects of Transfer Uncertainty
18.7 Conclusion

19. Advances in Sensitivity Analysis of Uncertainty due to Sampling Density for Spatially Correlated Attributes Ricardo A. Olea
19.1 Introduction
19.2 Data
19.3 Traditional Uncertainty Assessment
19.4 Kriging
19.5 Shastic Simulation
19.6 Validation
19.7 Conclusions

20. Predicting Molybdenum Deposit Growth
John H. Schuenemeyer, Lawrence J. Drew and James D. Bliss
20.1 Introduction
20.2 Cutoff Grade as a Function of Deposit Grade
20.3 Deposit Growth as a Function of Cutoff Grade
20.4 An Example
20.5 Conclusions

21. General Framework of Quantitative Target Selections Guocheng Pan
21.1 Introduction
21.2 Randomness of Mineral Endowment
21.3 Fundamental Geo-Process Relations
21.4 Scarceness, Rareness, and Exceptionalness
21.5 Intrinsic Geological Unit
21.6 Economic Truncation and Translation
21.7 Information Synthesis
21.8 Prediction with Dynamic Control Samples

22. Solving the Wrong Resource Assessment Problems Pre-cisely Donald A. Singer
22.1 Introduction
22.2 Target Population
22.3 Examples of Mismatches in Assessments
22.4 How to Correct Type III Errors
22.5 Conclusions

23. Two ideas for analysis of multivariate geochemical survey data: proximity regression and principal component re-siduals
G.F. Bonham-Carter and E. C. Grunsky
23.1 Introduction
23.2 Method 1: Direct Prediction of Spatial Proximity
23.3 Method 2: Principal Component Residuals
23.4 ConclusionsReferences

24. Mathematical minerals: A history of petrophysical pe-trography John H. Doveton
24.1 Pioneering Computer Methods24.2 Mineralogy of Underdetermined Systems
24.3 Mineralogy of Overdetermined Systems
24.4 Optimization Methods
24.5 Clay Component Estimation
24.6 Normative Estimation by Geochemical Logs
24.7 Conclusion

25. Geostatistics for Seismic Characterization of Oil Reser-voirs Amílcar Soares and Leonado Azevedo
25.1 Integration of Geophysical Data for Reservoir Modeling and Characterization
25.2 Iterative Geostatistical Seismic Inversion Methodologies
25.3 Trace-by-Trace Geostatistical Seismic Inversion
25.4 Global Geostatistical Seismic Inversion Methodologies
25.5 Uncertainty and Risk Assessment at early stages of exploration25.6 Final Remarks

26. Statistical Modeling of Regional and Worldwide Size-Frequency Distributions of Metal Deposits Frits Agterberg
26.1 Introduction26.2 Modified Version of the Model of de Wijs Applied to Worldwide Metal Deposits
26.3 Theory and Applications of the Pareto-Lognormal Model
26.4 Upper Tail Pareto Distribution and its Connection to the Basic Lognormal Distribution
26.5 Prediction of Future Copper Resources
26.6 Concluding Remarks
Part IV Reviews
27. Bayesianism in the Geosciences
Jef Caers
27.1 Introduction
27.2 A Historical P
27.3 Science as Knowledge Derived from Facts, Data or Experience
27.4 The Role of Experiments – Data
27.5 Induction vs Deduction
27.6 Falsificationism
27.7 Paradigms
27.8 Bayesianism
27.9 Bayesianism for Subsurface Systems
27.10 Summary

28. Geological Objects and Physical Parameter Fields in the Subsurface: A Review Guillaume Caumon
28.1 Introduction
28.2 Motivations for Explicit Geological Parameterizations
28.3 Parameterizations for Physical Models
28.4 Geological Parameterizations28.5 Conclusions and Challenges

29. Fifty Years of Kriging
Jean-Paul Chilès and Nicolas Desassis29.1 Introduction
29.2 The Origins of Kriging
29.3 Development and Maturity: Trend, Neighborhood Selection
29.4 Iterative Use of Kriging to Handle Inequality Data
29.5 Nonstationary Covariance
29.6 Kriging for Large Data Sets
29.7 Iterative Algorithms for Solving the Kriging System
29.8 Conclusion

30. Multiple Point Statistics: A Review
Pejman Tahmasebi
30.1 Introduction
30.2 Two-Point based Shastic Simulation
30.3 Multiple Point Geostatistics (MPS)
30.4 Simulation Path
30.5 Current Multiple Point Geostatistical Algorithms
30.6 Current Challenges

31. When Should We Use Multiple-Point Geostatistics?
Gregoire Mariethoz
31.1 Under-Informed vs Over-Informed Models
31.2 MPS vs Covariance-Based Geostatistics
31.3 Examples for which MPS Works W
31.4 Conclusion

32. The Origins of the Multiple-Point Statistics (MPS) Algo-rithm R. Mohan Srivastava
32.1 Introduction
32.2 1970s
32.3 1980s
32.4 1990s
32.5 Concluding Thoughts

33. Predictive Geometallurgy: An Interdisciplinary Key Challenge for Mathematical Geosciences? K.G. van den Boogaart and R. Tolosana-Delgado
33.1 Introduction
33.2 Process Modelling
33.3 Ore Characterisation
33.4 Orebody Modelling
33.5 Decision Making
33.6 Conclusions References

34. Data Science for Geoscience: Leveraging Mathematical Geosciences with Semantics and Open Data Xiaogang Ma
34.1 Introduction
34.2 The Intelligent Stage of Mathematical Geosciences
34.3 Case Studies of Data Science in Geoscience
34.4 Concluding Remarks

35. Mathematical Morphology in Geosciences and GISci: An Illustrative Review B. S. Daya Sagar
35.1 Introduction
35.2 Terrestrial Pattern Retrieval
35.3 Terrestrial Pattern Analysis
35.4 Geomorphologic Modeling and Simulation
35.5 Geospatial Computing and Visualization
35.6 Conclusions

Part V Reminiscences
36. 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 Thiergärtner
36.1 The Birth of Mathematical Geology and the Origins of the IAMG
36.2 The Role of the Kansas Geological Survey in the origins of the IAMG
36.3 Name and Establishment of the Society
36.4 Foundation of IAMG Publications
36.5 Prague
36.6 Subsequent Events following Prague –
36.7 The Looming Gap

37. Forward and Inverse Models over 70 Years E. H. Timothy Whitten
37.1 Birth of IAMG in 1968
37.2 In the Beginning (one pre-1968 experience)
37.3 Inverse and Forward Geology Problems
37.4 Forward Models in Earth Sciences
37.5 Inverse Models in Earth Sciences
37.6 The Samples Analysed
37.7 The Black Swan Effect
37.8 Concluding Thoughts

38. From individual personal contacts 1962–1968 to my 50 years of service Václav Němec
38.1 Introduction
38.2 IAMG Foundation (Prague 1968)
38.3 Activities for the IAMG 1968 – 1993
38.4 Příbram – East - West Gate near the Iron Curtain
38.5 My own professional work
38.6 Two Separate Silver Anniversary Meetings of Mathematical Geologists in Prague (1993)
38.7 From the Silver to the Golden IAMG Jubilee
38.9 Conclusion

39. Andrey Borisovich Vistelius
Stephen Henley
39.1 Background
39.2 Scientific Achievements and Insights39.3 The International Association for Mathematical Geology
39.4 The "Father of Mathematical Geology"?
39.5 Legacy

40. Fifty Years’ Experience with Hidden Errors in Applying Classic Mathematical Geology Hannes Thiergärtner
40.1 Introduction and Definitions
40.2 Hidden errors and Case Study Examples
40.3 Conclusion and Suggestions

41. Mathematical Geology by Example: Teaching and Learning Perspectives James R. Carr
41.1 Introduction
41.2 Multivariate Analysis of Geochemical Data
41.3 Geostatistics and its Myriad Parameters
41.4 The Variogram as a Stand-Alone Data Analytical Tool

42. Linear Unmixing in the Geologic Sciences: More Than a Half of Century of Progress William E. Full
42.1 Introduction
42.2 History of Constant Sum HVA
42.3 Non-Constant Sum Data and Algorithms
42.4 Summary

43. Pearce Element Ratio Diagrams and Cumulate Rocks
James Nicholls
43.1 Introduction
43.2 Outline of a Cumulate Rock Paradigm
43.3 Pearce Element Ratio Patterns for Cumulate Rocks
43.4 Compositions of Units of the Skaergaard Intrusion
43.5 Melts of the Skaergaard Intrusion
43.6 Pearce Element Ratios, Cumulate Rocks, and September 11

44. Reflections on the Name of IAMG and of the Journal Donald E. Myers

45. Origin and Early Development of the IAMG
Frits Agterberg
45.1 Introduction
45.2 Pioneers of Mathematical Geology
45.3 Inputs from Mathematical Statisticians
45.4 Concluding Remarks

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