Handbook of Mathematical Geosciences

B. S. Daya Sagar • Qiuming ChengFrits AgterbergEditors

Handbook of MathematicalGeosciencesFifty Years of IAMG

EditorsB. S. Daya SagarSystems Science and Informatics UnitIndian Statistical Institute–BangaloreCentre

BengaluruIndia

Qiuming ChengState Key Lab of Geological Processesand Mineral Resources

China University of GeosciencesBeijingChina

Frits AgterbergGeological Survey of CanadaOttawa, ONCanada

ISBN 978-3-319-78998-9 ISBN 978-3-319-78999-6 (eBook)https://doi.org/10.1007/978-3-319-78999-6

Library of Congress Control Number: 2018937688

© The Editor(s) (if applicable) and The Author(s) 2018. This book is an open access publication.Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adap-tation, distribution and reproduction in any medium or format, as long as you give appropriate credit tothe original author(s) and the source, provide a link to the Creative Commons license and indicate ifchanges were made.The images or other third party material in this book are included in the book’s Creative Commonslicense, unless indicated otherwise in a credit line to the material. If material is not included in the book’sCreative Commons license and your intended use is not permitted by statutory regulation or exceeds thepermitted use, you will need to obtain permission directly from the copyright holder.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publi-cation does not imply, even in the absence of a specific statement, that such names are exempt from therelevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made. The publisher remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.

Cover illustration: Presidents of the International Association for Mathematical Geosciences (IAMG).From Left to Right and Top to Bottom: First Row: IAMG Logo, William Christian Krumbein (First PastPresident), Andrei B. Vistelius (1968–1972), Richard A. Reyment (1972–1976), Daniel F. Merriam(1976–1980), Second Row: E. H. Timothy Whitten (1980–1984), John C. Davis (1984–1989),Richard B. McCammon (1989–1992), Michael Ed. Hohn (1992–1996), Ricardo A. Olea (1996–2000),Third Row: Graeme Bonham-Carter (2000–2004), Frits P. Agterberg (2004–2008), Vera Pawlowsky-Glahn (2008–2012), Qiuming Cheng (2012–2016), Jennifer McKinley (2016–2020).

Printed on acid-free paper

This Springer imprint is published by the registered company Springer International Publishing AGpart of Springer NatureThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Dedicated toDaniel F. Merriam and Richard A. Reyment(Fathers of the IAMG)

Foreword

The International Association for Mathematical Geosciences (IAMG) was foundedduring the 23rd International Geological Congress in Prague, August 1968. Withinthe Earth Sciences, the IAMG has played a prominent role during the past 50 yearsby living up to its mandate to promote, worldwide, the advancement of mathe-matics, statistics, and informatics in the geosciences. Under its auspices there havebeen and continue to be important developments in applications of mathematics,statistics and computer science in the Earth Sciences. To give two examples: IAMGmembers Georges Matheron and Jean Serra developed geostatistics and mathe-matical morphology resulting in methods that are now widely applied in otherbranches of science and engineering; John Aitchison invented methods to cir-cumvent the problem of spurious correlations that often arise in compositional dataanalysis of petrological and geochemical data. IAMG members later followed up ondeveloping this topic now used in other fields of science and in the social sciencesas well. During the first 30 years of its existence, IAMG stood as the abbreviation ofInternational Association for Mathematical Geology, but its current name wasadopted to widen its scope and provide a home to scientists who are not onlygeologists but who perform research in other fields of science and engineering.From the beginning, prominent mathematical statisticians including John Tukey,Geoffrey Watson, and Franklin Graybill played a prominent part within the IAMGby providing advice and collaborating in research projects.

In addition to organizing or co-sponsoring international conferences, workshops,and lecture series, the IAMG established three successful scientific journals:Mathematical Geosciences, Computers & Geosciences, and Natural ResourcesResearch (formerly: Nonrenewable Resources). In total, five types of IAMG awardswere created to honor William Christian Krumbein (1902–1979), AndrewBorisovich Vistelius (1915–1995), John Cedric Griffiths (1912–1992), FelixChayes (1916–1993), and Georges Matheron (1930–2000), who were pioneers inmathematical geology. The book in front of us “Handbook of MathematicalGeosciences: Fifty Years of IAMG” published to celebrate the Golden Anniversaryof the IAMG contains 45 chapters prepared by IAMG award winners, foundingmembers, and distinguished lecturers. It covers new theoretical developments,

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applications, reviews of subfields of the mathematical geosciences, and historicalinformation on the IAMG, especially in its early years.

Bill Krumbein, as a geologist, first started using a digital computer in 1958, andgradually more mathematical geologists began working with digital computers inthe 1960s. This involved the development of computer programs written inFORTRAN or ALGOL to use existing statistical techniques such as analysis ofvariance, multiple regression, multivariate statistical techniques, and time seriesanalysis that had been developed during the first half of the twentieth century. Also,new methods including trend surface analysis and geostatistical ore reserve esti-mation techniques were developed specifically for solving geoscience problems.Dan Merriam established the “Kansas Geological Survey Computer Contributions.”In this series, 50 computer programs were published between 1966 and 1970.During this time period, Dick Reyment worked closely with Dan to establish theIAMG.

Computers brought about further important changes that were rapidly adoptedby mathematical geologists including geographic information systems (GIS),exploratory data analysis, the fast Fourier transform, mathematical morphology,fractals, and nonlinear models. Even more recently, our world has entered the “BigData” era, with the production of data with unprecedented speed and in largequantities. The new knowledge obtained through digital analysis and the novelmethods of data mining are greatly benefitting human decision making. People’slife, working, and thinking are being subjected to drastic changes. “Big Data”resulted in the emergence of “Data Science” which, to some extent, is affecting allfields of science both in how scientific research is being conducted using digitaldata and by facilitating the use of scientific methods to study the digital data.

Nowadays, geosciences and geological research are mainly characterized bythe following words: “Systematic,” “Comprehensive,” “Quantitative,” “Three-dimensional,” “New-model,” “Green,” “Intelligent,” and “Beneficial to People.” Inthis regard, Mathematical Geosciences and the IAMG play an increasinglyimportant role, prompting the advancement of the geosciences in the future. Earthscience and geological studies are data-intensive. If we want to solve geologicalproblems and use the results in a meaningful way, we have to obtain and work withmany different kinds of data obtained by using sound geological concepts andmethods borrowed from physics, chemistry, and remote sensing. Geoscienceexperts in the latter fields of science make invaluable contributions to our under-standing of the Earth and the geological processes that took place millions of yearago. In all these endeavors, mathematics plays a significant role. This is where theIAMG is exceedingly helpful. Geology is characterized by the four “Deeps”: Itsdata and processes are deep in the Earth, deep under the sea, deep in outer space,and deep in time. It is not easy to obtain comprehensive geological data sets inpractice. Data collection can be very expensive. Much attention is to be paid tocosts and benefits.

Earth scientists should always do their best to define target populations fromwhich truly representative samples are to be drawn. Geological samples almostnever fully comprise the entire population of study because of differences in space

viii Foreword

and time. There is no “overall data completeness” or “comprehensive data” ingeological science and practice. Other methods of data collection have to bedeveloped and used in order to make the random samples fit the target populationsas closely as possible so that information loss because of spatial restrictions isminimized.

The ultimate purpose of Earth Science is to promote progress and developmentof human society: The products of the Earth’s evolution over millions of years areto be used to our advantage, and we have to guard against the negative effects of thedifferent types of disasters that can be associated with geological processes.Geological data have particular characteristic features that reflect time and cause oforigin, spatial environments, and genesis. They can manifest different outcomesreflecting spatial and temporal conditions. When faced with geological data, oneshould not only know the “What?” but also the “Why?” and the “How?” for thedata: What they truly mean and how they are to be used. One should not onlyestablish “correlations” but also “causality” and spatiotemporal relations. Geologydiffers from most other areas in the Big Data era in that the focus is on the “What?”only and on correlations without causality and the “Why.”

The laws of physics and chemistry have not changed through geologic time. Thisfact underlies the principle of actualism already understood by geologists in thenineteenth century. Some early geologists already surmised that the ice ages ofwhich the effects can be clearly seen on the surface of the Earth were caused byminor systematic fluctuations in amount of radiation received from the sun. A fullexplanation of this periodicity was provided in the theory of Milankovitch. Thistheory currently is used to estimate ages of stage boundaries in the geologictimescale during the past 65 million years with a precision that is better thanprecisions provided by geochronological dating methods.

The age of the Earth is about 4.5 billion years, and it is in its middle age. Taking90 years as expectation of human age, for example, this means that one year in ourlife is approximately equivalent to 50 million years in the past of the Earth. Thus,the factor of difference is about 4,500,000,000/90 = 50,000,000. The followingexamples illustrate the change of perspective needed to understand geologicalprocesses. Earthquakes with a magnitude greater than 8.0 earthquakes on theGutenberg–Richter scale occur about once a year. Consequently, about 50 millionsuch earthquakes probably have occurred over the last 50 million years. The speedof tectonic plates is of the order of 1–10 cm/year. Thus, plates have moved 500–5000 km per 50 million years. It explains why oceans are opening and closing overgeologic time.

Early in the nineteenth century, it became known that most coal deposits orig-inated during the Carboniferous. More recently, Earth scientists have developedtheories about the genesis of ore and hydrocarbon deposits that help to make newdiscoveries. Recognition of importance of bio-factors has aided in the under-standing of various geological processes including ore and hydrocarbon formation,as well as distribution of pollutants in the ecosystem. Increasingly, mathematics andstatistics are fruitfully employed in the discovery process as abundantly exemplifiedin many of the chapters in this Handbook. All of the preceding considerations

Foreword ix

illustrate the complexity and particularities of geological data as well as theirusefulness and importance. Fully comprehensive geological data collection, theireffective computer-based treatment, rational analysis, and translation into digitalknowledge, all depend on the guidance provided by powerful theory based onmathematics with applications of efficient methods.

Initially, most IAMG members were located within the USA or Europe. Theseregions continue to have relatively many members, but China and other Asiancountries now also constitute a large regional group. In 1990, a workshop wasorganized at the China University of Geosciences in Wuhan at which the partici-pants included Richard McCammon, IAMG President at the time as well as fourfuture IAMG Presidents. Now, the IAMG’s China Section holds annual meetingsattended by hundreds of mathematical geoscientists. Increasingly, it became feltthat mathematical geoscience is making an indispensable contribution in China toaid in the prediction of occurrences of mineral resources, especially in thenon-traditional regions such as deep Earth and in covered regions and the assess-ment of hazards such as earthquakes and landslides. As society develops from itsindustrialization to post-industrialization stage, environmental and ecologicalapplications become increasingly important to establish and reduce the effects ofregional patterns of pollution. Other anticipated areas of applications are urbanspace utilization and agricultural products under the new concepts of green andlow-carbon development.

Beijing, China Pengda ZhaoAcademician of the Chinese Academy of Sciences,

China University of GeosciencesOttawa, CanadaFebruary 2018

Frits AgterbergGeological Survey of Canada

x Foreword

Preface

The International Association of Mathematical Geosciences (IAMG) was formed in1968, and the year 2018 is marked as its Golden Anniversary. The “Handbook ofMathematical Geosciences: Fifty Years of IAMG” released during the IAMGConference held at Olomouc and Prague (Czech Republic), September 2–8, 2018,motivates readers including professional geomathematicians, and undergraduateand postgraduate students to learn about the fifty years of contributions byaward-winning mathematical geoscientists. This book that showcases the successof the IAMG celebrating its fifty years of existence is a compilation of 45 chapters.Compiled by academics, scientists, and engineers who are the recipients of IAMG’saccolades such as the Krumbein Medal/Chayes Prize/Vistelius Award/GriffithsAward/Matheron Lectureship/Distinguished Lectureship/Honorary Membership aswell as IAMG Founding Members, this Handbook covers 45 chapters on topicssuch as mathematical geosciences, mathematical morphology, geostatistics, fractalsand multifractals, spatial statistics, multipoint geostatistics, compositional dataanalysis, informatics, geocomputation, numerical methods, and chaos theory in thegeosciences categorized broadly into theory, general applications, exploration andresource estimation, reviews, and reminiscences. Unique features of this bookinclude the following:

• Contributions by award-winning mathematical geoscientists of interest toacademics/researchers/students engaged in applications of mathematics, statis-tics, computers, and informatics.

• A unique fusion of geology, hydrology, mining engineering, geoengineering,and applications of quantitative techniques and methodology in the aforemen-tioned fields.

• Historical perspectives on how the IAMG evolved during the past fifty years.• Past, present, and future demands for mathematical geosciences in academics,

industry, and the professions.• Pathbreaking mathematical frameworks/approaches/methodologies/algorithms

to deal with varied aspects usually encountered by geoscientists.

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The first ten chapters are categorized as theoretical, followed by seven chapters(from 11 to 17) in the general applications part. Chapters 18–26 and 27–35 are,respectively, categorized as exploration and resources estimation, and reviews. Thelast ten chapters (from 36 to 45) are categorized as reminiscences. What followsincludes a brief summary for each of the chapters of the Handbook.

Chapter 1 by Dubrule reviews relationships between Bayesian methods, geo-statistics, and ensemble Kalman filtering which are well discussed and reviewed.The author rightly mentions that (i) inversion techniques are not discussed and(ii) fast-growing machine learning algorithms are challenging the geostatistical andBayesian formalisms.

In Chap. 2, Baddeley compares and contrasts various statistical methods–such aslogistic regression, Poisson point process models, maximum entropy, monotoneregression, nonparametric survey estimates, recursive partitioning, and receiveroperating characteristic curves–for predicting the occurrence of mineral deposits.

Chapter 3 by Schaeben is concerned with testing joint conditional independenceof categorical random variables with a newly proposed standard likelihood ratiotest. How it resolves limitations obvious with “omnibus” and “new omnibus” testsis explained with a strong theoretical basis invoking the Hammersley–Cliffordtheorem.

The sample space approach for modeling compositional data is explained inChap. 4 by Egozcue and Pawlowsky-Glahn. Interestingly, perturbation betweenelements and its opposite, i.e., difference perturbation, appear to be Matheron–Serra’s morphological dilations and erosions or Minkowski additions and sub-tractions. Repeated perturbations and their inverted versions (difference perturba-tions) seem to be multiscale morphological dilations and erosions.

Possible methods required to refocus and streamline expert geological judgmentinputs along with analytical methods are reviewed by Kaufman in Chap. 5.

Remotely sensed satellite data acquisition via various sensing mechanisms posechallenges particularly in developing filters meant for feature extraction or retrieval.Many developed filters yield promising results, but could not be generalized due tovaried complexities involved in sensing mechanisms leading to the acquisition ofdifferent types of satellite images. For instance, filters that work fine for satelliteimages acquired via optical sensing mechanisms would not yield appropriate resultsfor those images acquired via microwave sensing mechanisms. Besides, satelliteimages now available are with a large number of channels at high spatial/temporal/spectral resolutions making the ability to map features with high degree of precisionmore challenging. However, due to availability of filters that cannot be generalizedfor images acquired by different mechanisms, there is a need for the development offilters with strong theoretical basis. Cressie contributes rich content in Chap. 6, andthe ideas provided in this chapter are of fundamental importance.

Deutsch in his Chap. 7 provides convincing arguments/discussions that arelogical and powerful on why the ensemble of realizations needs to be consideredinstead of one single realization for proper planning, decision making, and uncer-tainty assessment.

xii Preface

In the past forty years, how criteria and arguments are employed in comparingbinary coefficients in multivariate statistical analysis is reviewed in Chap. 8 byHohn.

Armstrong, Mondaini, and Camargo provide a sociological study based onGoogle retrievals in Chap. 9. How research in geosciences diffuses within academiaand into industry is studied in this chapter, whereby the research idea employed isplurigaussian simulation invented in France. This study is someway related to“scientometrics.” The obvious choice to carry out this type of study is complexnetwork based analysis, small-world network analysis (due to Duncan Watts andSteven Strogatz). Such ideas in social network analysis were predominantlydeveloped by Barabasi and his group.

In the first part of Chap. 10, Cheng gave an excellent overview chronologicallyon how mathematical geosciences or geomathematics evolved in the last fifty yearsby also providing (i) historical connections between the mathematics and thegeosciences, and (ii) a new definition of mathematical geosciences. An introductionto fractal density and singularity analysis and related subjects to solve geologicalproblems discussing geological principles with case studies related to earthquakes isprovided in the second part of this chapter. Cheng demonstrated the application ofhis original concept of fractal density and the local singularity to model the clus-tering frequency of earthquakes of the Pacific subduction zones. Much strongersingularity is discovered via the clustering frequency of earthquakes in the colderand older western boundaries of Pacific plates than that of the hotter and youngereastern boundaries of the Pacific plates.

Use of electrofacies in reservoir characterization is provided with demonstrationon a giant clastic oil reservoir, the Amal field of Libya, in Chap. 11 by Davis.

In Chap. 12, morphological medians and weighted morphological medians areemployed by Serra in a new elegant approach demonstrated on shoreline extrap-olations. Quench stripe generation, based on these novel two types of mediansprovides the main basis in predicting the locations of the shorelines.

A comprehensive review of geostatistical methods to analyze remote-sensingdata is presented in Chap. 13 by Militino, Ugarte, and P´erez-Goya. This reviewhighlights the importance of geostatistics in processing and analysis of remotelysensed satellite data available in multiple spatial/temporal/spectral resolutionsacquired via a host of different sensing mechanisms.

Chapter 14 by Goovaerts contains an interesting first application of space–timegeostatistics to assess lead levels recorded in drinking water of public distributionsystem in Flint, Michigan.

Statistical Parametric Mapping (SPM)—popular in medical imaging science toevaluate differences between individual pairs of images or average images—appliedon examples drawn from environmental and geoscience contexts is reviewed inChap. 15 by McKenna. Extending the application of SPM to the hundreds ofchannels of hyperspectral remotely sensed satellite data would provide new insightsinto remote-sensing scientists.

Preface xiii

In the interesting Chap. 16, Buccianti shows how compositional data analysishas a role in dealing with water chemistry. The author puts Illya Prigogine’s ideasand concepts (including dissipative structures, dynamical systems, open and closedsystems that respectively draw energy from external sources and from within,self-organized criticality, universal power laws, time irreversibility) into a newperspective. It reminds the reader of the popular book on Chaos: Man’s NewDialogue with Nature by Illya Prigogine and Isabelle Stengers.

Chapter 17 by Grunsky, Drew, and Smith is the outcome of a major projectconcerned with soil geochemical analyses in the USA via principal componentanalysis and compositional framework approach. The material is presented withmany maps, tabular data, and supplementary information.

Work carried out across three decades by Dowd and his group on the quan-tification of uncertainty in mineral/energy/environmental applications via variousapproaches is reviewed with a focus on mineral and energy resources, and envi-ronmental applications in Chap. 18.

Olea in Chap. 19 explains uncertainty, geostatistics, and kriging methods on thebasis of a coal seam example. Three ad hoc methods, namely distance analysis,kriging, and stochastic simulation, are employed for evaluation of their usage forpredicting changes in uncertainty due to changes in spatially correlated samples.Also included is a demonstration of the efficacy of these methods on real data forthe Anderson coal bed. It is inferred that the stochastic simulation-based approachoutperforms distance and kriging-based methods.

The topic in relation to predicting molybdenum deposit growth as a function ofcutoff grade via a nonlinear model constructed by using data from several depositsis addressed in Chap. 20 by Schuenemeyer, Drew, and Bliss. Predicting molyb-denum deposit growth cutoff grades is decided on the basis of a prior model derivedby plotting cutoff grade as a function of deposit grade.

Chapter 21 by Pan provides a discussion with focus on several aspects of mineralresources, mineral resource estimation, and associated features with moreinformation on how/why details provided in this chapter are of fundamentalimportance.

Mineral resource assessment problems and involved three types of errors arediscussed in Chap. 22 by Singer. Also presented in this chapter are possible ways toavoid these errors. The chapter is written in a way that can be understood bynon-mathematicians or non-statisticians.

In Chap. 23 by Bonham-Carter and Grunsky, two exploratory multivariatemethods, namely proximity regression and residual principal component analysis,are applied to analyze geochemical survey data. The first method is useful inmaking predictions of spatial proximity to geological features, whereas the secondmethod is a recommended way for partitioning geochemical elements into clusters.

Chapter 24 by Doveton is concerned with an approach to compositional dataanalysis that is significantly different from the Aitchison/Pawlowsky-Glahn/Egozcue approach to CoData problem-solving.

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Two parts of Chap. 25 by Soares and Azevedo, respectively, provide the(i) state of the art in recent geostatistical seismic inversion methods and theirapplications to evaluate reservoir properties, and (ii) seismic inversion-basedmethodology to assess uncertainty and risks at early stage of exploration.

In Chap. 26, Agterberg provides rich information-related studies to understandthe differences in the degree of heterogeneities in the spatial distribution of metaldeposits between the regional level and global level. It is interesting to see that deWijs’ work formed the basis for this new version of the model that provides aframework for explaining difference between regional and worldwide distributions.The de Wijs model has also been used elsewhere in the iterated bisection process tocompute multifractal spectra that provide a host of dimensions such as topologicaldimension, capacity dimension, and information dimension. A host of suchdimensions is of immense use to understand not only spatial but also temporaldistribution patterns.

Chapter 27 by Caers provides views on why philosophical principles arerequired to be translated into workable practices.

Various approaches involving spatial statistics, geological variables, geometryand topology of geological objects to develop coherent Earth models are welldocumented as an excellent review in Chap. 28 by Caumon.

Origins of kriging, its success, and its new application domains across the lastfive decades, and the role of IAMG journals popularizing this technique by pub-lishing in English are explained in Chap. 29 by Chilès and Desassis.

Recent advances in Multiple-Point Statistics (MPS)—that is important andsignificant in handling complex and realistic phenomena of relevance to the Earthsciences—are thoroughly reviewed in Chap. 30 by Tahmasebi.

Mariethoz provides interesting views on the conceptual differences between theconcurrent approaches of Minimum Point Statistics and Covariance-BasedGeostatistics in Chap. 31 with an illustrated example.

Srivastava provides information on the origin of Multiple-Point Statistics(MPS) algorithms along with many personal reminiscences in Chap. 32.

Chapter 33 by van den Boogaart and Tolosana-Delgado contains useful newproposals. This chapter provides state of the art and mathematical building blocksfor solutions in predictive geometallurgy—i.e., the understanding of geometallurgy.The chapter further explores possible links between geometallurgical problems andrelevant techniques taken from mathematical geosciences. From the insights pro-vided into this chapter, the next generation of mathematical geoscientists andexperts in geoinformatics would surely benefit.

Chapter 34 by Ma provides possible links between mathematical geosciencesand Data Science. Many learning techniques such as artificial intelligence, activelearning, machine learning and intelligence, and deep learning approaches togethernow play a much bigger role in pattern discovery from massive data sets—pre-dictive geosciences. The journey from toy models developed by nonlinear physi-cists to predictive models has posed several newer challenges. Data Science wouldbring under one umbrella the powerful theories, algorithms available under differentnames in different disciplines.

Preface xv

Daya Sagar reviews potential applications of nonlinear mathematical morpho-logical transformations to deal with a host of challenges encountered in geosciencesand Geographical Information Science (GISci) with a large number of excellentcase studies shown illustratively in Chap. 35.

Many recollections by IAMG members from the old days are provided inChap. 36 by Cubitt and Henley, with contributions provided by T. Victor(Vic) Loudon, EHT (Tim) Whitten, John Gower, Daniel (Dan) Merriam, Thomas(Tom) Jones, and Hannes Thiergärtner. Also provided in this chapter is informationon those pioneering scientists who were instrumental in forming and shaping theIAMG. The chapter is immensely useful for young generation mathematical geo-scientists in order to know and appreciate the hard work of peers and scientists ofearlier generations.

How the applications of forward and inverse models in particular in Earthscience-related problems evolved over a period of 70 years is lucidly explained insimplest possible language by Whitten in Chap. 37. Besides this, how otherapproaches in particular applications of scaling theories or fractal geometry andtheory of chaos, in other words nonlinear approaches—that have already shownsignificant success in modeling and characterization of various phenomena andprocesses of relevance to the Earth sciences—can be foreseen in the next 50 yearsto give a scope for further research.

Václav Němec’s professional and personal reminiscences are chronologicallyprovided in Chap. 38 by Němec, along with details on the IAMG’s formation andpersonal early development.

Chap. 39 by Henley provides a rounded view of the life and works, and aglimpse of the legacy of Andrey Vistelius, first President of the IAMG.

Many theoretical sound techniques, algorithms, and software tools developedhave shown promising results in certain application-specific domains but withlimited utility in terms of generalization. Thiergärtner’s interesting and genuineviews, opinions, and recommendations in Chap. 40 are thought provoking.

Application of kriging, inverse distance methods, and the variogram in multi-variate data analysis, spatial estimation, and in texture-based classification areshown with simple illustrations by Carr in Chap. 41.

Full in Chap. 42 provides a review of the development and applications of alinear unmixing method fairly extensively used by geologists during the past 50years.

Chapter 43 on Pearce Element Ratios provides insight into the evolution of meltsin volcanic systems along with many personal memories and (from the point ofview of compositional data analysis) a somewhat antiquated method of approach.An excellent review with extensive Skaergaard applications is provided in thischapter by Nicholls.

Myers in Chap. 44 gives a helpful set of reflections by a mathematician whoadopted geostatistics as a principal field of research and has made many importantcontributions to the field along with personal reminiscences on IAMG and theJournal of Mathematical Geosciences.

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Agterberg in his Chap. 45 provides a holistic view on the beginnings of IAMGand about the academics/scientists/engineers who were instrumental in shaping theIAMG and making it a most successful association promoting worldwide theadvancement of mathematics, statistics, and informatics in the geosciences. Thischapter enlightens and motivates the young generation mathematical geoscientists.

Bangalore, India B. S. Daya SagarBeijing, China Qiuming ChengOttawa, Canada Frits Agterberg

Preface xvii

Contents

Part I Theory

1 Kriging, Splines, Conditional Simulation, Bayesian Inversionand Ensemble Kalman Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Olivier Dubrule

2 A Statistical Commentary on Mineral Prospectivity Analysis . . . . . 25Adrian Baddeley

3 Testing Joint Conditional Independence of Categorical RandomVariables with a Standard Log-Likelihood Ratio Test . . . . . . . . . . 67Helmut Schaeben

4 Modelling Compositional Data. The Sample Space Approach . . . . . 81Juan José Egozcue and Vera Pawlowsky-Glahn

5 Properties of Sums of Geological Random Variables . . . . . . . . . . . 105G. M. Kaufman

6 A Statistical Analysis of the Jacobian in Retrievalsof Satellite Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Noel Cressie

7 All Realizations All the Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Clayton V. Deutsch

8 Binary Coefficients Redux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Michael E. Hohn

9 Tracking Plurigaussian Simulations . . . . . . . . . . . . . . . . . . . . . . . . 161M. Armstrong, A. Mondaini and S. Camargo

10 Mathematical Geosciences: Local Singularity Analysisof Nonlinear Earth Processes and Extreme Geo-Events . . . . . . . . . 179Qiuming Cheng

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Part II General Applications

11 Electrofacies in Reservoir Characterization . . . . . . . . . . . . . . . . . . 211John C. Davis

12 Shoreline Extrapolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225Jean Serra

13 An Introduction to the Spatio-Temporal Analysis of SatelliteRemote Sensing Data for Geostatisticians . . . . . . . . . . . . . . . . . . . . 239A. F. Militino, M. D. Ugarte and U. Pérez-Goya

14 Flint Drinking Water Crisis: A First Attempt to ModelGeostatistically the Space-Time Distribution of WaterLead Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255Pierre Goovaerts

15 Statistical Parametric Mapping for Geoscience Applications . . . . . . 277Sean A. McKenna

16 Water Chemistry: Are New Challenges Possible from CoDA(Compositional Data Analysis) Point of View? . . . . . . . . . . . . . . . . 299Antonella Buccianti

17 Analysis of the United States Portion of the North American SoilGeochemical Landscapes Project—A Compositional FrameworkApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313E. C. Grunsky, L. J. Drew and D. B. Smith

Part III Exploration and Resource Estimation

18 Quantifying the Impacts of Uncertainty . . . . . . . . . . . . . . . . . . . . . 349Peter Dowd

19 Advances in Sensitivity Analysis of Uncertainty to Changes inSampling Density When Modeling Spatially CorrelatedAttributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375Ricardo A. Olea

20 Predicting Molybdenum Deposit Growth . . . . . . . . . . . . . . . . . . . . 395John H. Schuenemeyer, Lawrence J. Drew and James D. Bliss

21 General Framework of Quantitative Target Selections . . . . . . . . . . 411Guocheng Pan

22 Solving the Wrong Resource Assessment Problems Precisely . . . . . 437Donald A. Singer

xx Contents

23 Two Ideas for Analysis of Multivariate GeochemicalSurvey Data: Proximity Regression and PrincipalComponent Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447G. F. Bonham-Carter and E. C. Grunsky

24 Mathematical Minerals: A History of PetrophysicalPetrography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467John H. Doveton

25 Geostatistics for Seismic Characterization of Oil Reservoirs . . . . . . 483Amílcar Soares and Leonardo Azevedo

26 Statistical Modeling of Regional and Worldwide Size-FrequencyDistributions of Metal Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505Frits Agterberg

Part IV Reviews

27 Bayesianism in the Geosciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527Jef Caers

28 Geological Objects and Physical Parameter Fieldsin the Subsurface: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567Guillaume Caumon

29 Fifty Years of Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589Jean-Paul Chilès and Nicolas Desassis

30 Multiple Point Statistics: A Review . . . . . . . . . . . . . . . . . . . . . . . . . 613Pejman Tahmasebi

31 When Should We Use Multiple-Point Geostatistics? . . . . . . . . . . . . 645Gregoire Mariethoz

32 The Origins of the Multiple-Point Statistics (MPS) Algorithm . . . . 655R. Mohan Srivastava

33 Predictive Geometallurgy: An Interdisciplinary Key Challengefor Mathematical Geosciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673K. G. van den Boogaart and R. Tolosana-Delgado

34 Data Science for Geoscience: Leveraging MathematicalGeosciences with Semantics and Open Data . . . . . . . . . . . . . . . . . . 687Xiaogang Ma

35 Mathematical Morphology in Geosciences and GISci:An Illustrative Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703B. S. Daya Sagar

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Part V Reminiscences

36 IAMG: Recollections from the Early Years . . . . . . . . . . . . . . . . . . 743John Cubitt and Stephen Henley

37 Forward and Inverse Models Over 70 Years . . . . . . . . . . . . . . . . . 765E. H. Timothy Whitten

38 From Individual Personal Contacts 1962–1968 to My 50Years of Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777Václav Němec

39 Andrey Borisovich VISTELIUS . . . . . . . . . . . . . . . . . . . . . . . . . . . 793Stephen Henley

40 Fifty Years’ Experience with Hidden Errors in ApplyingClassical Mathematical Geology . . . . . . . . . . . . . . . . . . . . . . . . . . . 813Hannes Thiergärtner

41 Mathematical Geology by Example: Teaching and LearningPerspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831James R. Carr

42 Linear Unmixing in the Geologic Sciences: More ThanA Half-Century of Progress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849William E. Full

43 Pearce Element Ratio Diagrams and Cumulate Rocks . . . . . . . . . . 875J. Nicholls

44 Reflections on the Name of IAMG and of the Journal . . . . . . . . . . 897Donald E. Myers

45 Origin and Early Development of the IAMG . . . . . . . . . . . . . . . . . 901Frits Agterberg

xxii Contents

Editors and Contributors

About the Editors

B. S. Daya Sagar is a Full Professor of the SystemsScience and Informatics Unit (SSIU) at the IndianStatistical Institute. He received his M.Sc. andPh.D. degrees in Geoengineering and Remote Sensingfrom the Faculty of Engineering, Andhra University,Visakhapatnam, India, in 1991 and 1994, respectively.He is also first Head of the SSIU. Earlier, he worked inthe College of Engineering, Andhra University, Centrefor Remote Imaging, Sensing and Processing (CRISP),and the National University of Singapore in variouspositions during 1992–2001. He served as AssociateProfessor and Researcher in the Faculty of Engineeringand Technology (FET), Multimedia University,Malaysia, during 2001–2007. Since 2017, he has beena Visiting Professor at the University of Trento, Trento,Italy. His research interests include mathematical mor-phology, GISci, digital image processing, fractals andmultifractals, their applications in extraction, analyses,and modeling of geophysical patterns. He has publishedover 85 papers in journals and has authored and/or guestedited 11 books and/or special theme issues for journals.He recently authored a book entitled MathematicalMorphology in Geomorphology and GISci, CRC Press:Boca Raton, 2013, p. 546. He recently co-edited twospecial issues on “Filtering and Segmentation withMathematical Morphology” for IEEE Journal ofSelected Topics in Signal Processing (v. 6, no. 7,p. 737–886, 2012), and “Applied Earth Observation andRemote Sensing in India” for IEEE Journal of Selected

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Topics in Applied Earth Observation and RemoteSensing (v. 10, no. 12, p. 5149–5328, 2017). He is anelected Fellow of Royal Geographical Society (1999),Indian Geophysical Union (2011), and was a Member ofNew York Academy of Sciences during 1995–1996. Hereceived the Dr. Balakrishna Memorial Award fromAndhra Pradesh Academy of Sciences in 1995, theKrishnan Gold Medal from Indian Geophysical Unionin 2002, and the “Georges Matheron Award-2011(with Lecturership)” of the International Associationfor Mathematical Geosciences. He is the FoundingChairman of Bangalore Section IEEE GRSS Chapter.He is on the Editorial Boards of Computers andGeosciences, and Frontiers: Environmental Informatics.

Qiuming Cheng did his Ph.D. degree in Earth Scienceunder supervision of Dr. Frits Agterberg at theUniversity of Ottawa in 1994. He spent a year atthe Geological Survey of Canada as a PDF under thesupervision of Dr. Graeme Bonham-Carter and soonbecame a Faculty Member at York University, Toronto,Canada, in 1995 with cross-appointments in theDepartment of Earth and Space Science and Engi-neering and the Department of Geography. He waspromoted to associate professor in 1997 and fullprofessor in 2002. He was awarded a ChangjiangScholar Professorship in China by the China’s Ministryof Education where he has set up and leads the StateKey Lab of Geological Processes and MineralResources (GPMR) located on both campuses ofChina University of Geosciences in Beijing andWuhan. Currently, he holds a Thousand TalentNational Special Professorship of China, serving asthe Founding Director of the GPMR laboratory. He hasspecialized in mathematical geoscience with researchfocus on nonlinear mathematical modeling of Earthprocesses and geoinformatics techniques for predictionof mineral resources. He has authored and co-authoredmore than 300 research articles. He has been awardedseveral prestigious awards including the KrumbeinMedal, the highest award by the InternationalAssociation for Mathematical Geosciences (IAMG).He was an elected President of the InternationalAssociation for Mathematical Geosciences (IAMG)during 2012–16. He is the President of International

xxiv Editors and Contributors

Union of Geological Sciences (IUGS) for the periodbetween 2016 and 2020. He is an international leader inthe application of nonlinear mathematics and geoinfor-matics to the analysis, modeling, and prediction of awide range of geological processes and mineralresources quantitative assessment. His primary researchinterest involves the interdisciplinary study of nonlinearproperties of the Earth’s systems, as well as quantitativeassessment and prediction of natural resources andenvironmental impacts. His research on fractal densityand local singularity analysis theory and geomathemat-ical models has made major impacts in several geosci-entific disciplines, including those concerned withocean ridge heat flow, magmatic flare-up duringcontinent crustal growth and formation of superconti-nents, earthquakes, floods, hydrothermal mineraliza-tion, and prediction of deeply buried mineral deposits.

Frits Agterberg is a Dutch-born Canadian Mathe-matical Geologist who served at the Geological Surveyof Canada in Ottawa. He attended Utrecht Univer-sity in the Netherlands from 1954 to 1961. Withother founding members, he was instrumental inestablishing the International Association for Mathe-matical Geosciences (IAMG) in 1968. He received theIAMG’s William Christian Krumbein Medal in 1978,and he was IAMG Distinguished Lecturer in 2004. In2017, he was conferred with the Honorary Membershipof the IAMG. He has authored or co-authored over 250scientific papers and 5 books. He has served the IAMGin many ways, including being its President from2004 to 2008. After defending his doctoral thesis onstructural geology of the Italian Alps at UtrechtUniversity and a one-year fellowship at the Universityof Wisconsin in Madison, he became “petrologicalstatistician” in his first job at the Geological Survey ofCanada (GSC) in 1962. He was asked to create the GSCGeomathematics Section in 1971. He retired from theGSC in 1996 but still has an office at their Ottawaheadquarters. In 1968, he became associated with theUniversity of Ottawa where he taught a “statistics ingeology” course for 25 years and has supervised six

Editors and Contributors xxv

geomathematical Ph.D. students. From 1978 to 1989,he directed the Quantitative Stratigraphy Project of theInternational Geological Correlation Program. From1981 to 2001, he was a Correspondent of the RoyalNetherlands Academy of Arts and Sciences. During thepast 20 years, primarily in collaboration with QiumingCheng, his colleagues, and students at the ChinaUniversity of Geosciences in Wuhan and Beijing andat York University, Toronto, he has worked onapplications of multifractals to study the spatial distri-bution of metals in rocks and orebodies.

Contributors

Frits Agterberg Geological Survey of Canada, Ottawa, ON, Canada

M. Armstrong Escola de Matemática Aplicada, Fundação Getulio Vargas, Rio deJaneiro, Brazil; MINES Paristech, PSL Research University, CERNA – Centre forIndustrial Economy, i3, CNRS UMR 9217, Paris, France

Leonardo Azevedo CERENA, Instituto Superior Técnico, Universidade deLisboa, Lisbon, Portugal

Adrian Baddeley Department of Mathematics and Statistics, Curtin University,Perth, WA, Australia

James D. Bliss Southwest Statistical Consulting, LLC, Cortez, CO, USA

G. F. Bonham-Carter Merrickville, ON, Canada

Antonella Buccianti Department of Earth Sciences, University of Florence,Florence, Italy; CNR-IGG, Unit of Florence, Florence, Italy

Jef Caers Stanford University, Stanford, USA

S. Camargo Escola de Matemática Aplicada, Fundação Getulio Vargas, Rio deJaneiro, Brazil

James R. Carr Department of Geological Sciences and Engineering, Universityof Nevada, Reno, Reno, NV, USA

Guillaume Caumon GeoRessources-ENSG, Université de Lorraine – CNRS–CREGU, Vandoeuvre-lès-Nancy, France

Qiuming Cheng State Key Lab of Geological Processes and Mineral Resources,China University of Geosciences, Beijing, China

Jean-Paul Chilès Centre of Geosciences, Mines ParisTech, Fontainebleau, France

xxvi Editors and Contributors

Noel Cressie Distinguished Professor, National Institute for Applied StatisticsResearch Australia (NIASRA), School of Mathematics and Applied Statistics,University of Wollongong, Wollongong, Australia

John Cubitt Holt, Wrexham, UK

John C. Davis Heinemann Oil GmbH, Baldwin City, KS, USA

B. S. Daya Sagar Systems Science and Informatics Unit, Indian StatisticalInstitute-Bangalore Centre, Bengaluru, India

Nicolas Desassis Centre of Geosciences, Mines ParisTech, Fontainebleau, France

Clayton V. Deutsch University of Alberta, Edmonton, Canada

John H. Doveton Kansas Geological Survey, Lawrence, KS, USA

Peter Dowd, FREng, FTSE The University of Adelaide, Adelaide, Australia

L. J. Drew United States Geological Survey, Reston, VA, USA

Lawrence J. Drew Southwest Statistical Consulting, LLC, Cortez, CO, USA

Olivier Dubrule Imperial College London, London, UK

Juan José Egozcue Department of Civil and Environmental Engineering,Universidad Politécnica de Cataluña, Barcelona, Spain

William E. Full GXStat, LLC, Wichita, KS, USA

Pierre Goovaerts BioMedware, Inc, Jerome, MI, USA

E. C. Grunsky Department of Earth and Environmental Sciences, University ofWaterloo, Waterloo, ON, Canada; China University of Geosciences, Beijing, China

Stephen Henley Resources Computing International Limited, Matlock,Derbyshire, UK

Michael E. Hohn West Virginia Geological and Economic Survey, Morgantown,USA

G. M. Kaufman Management Emeritus, E62-437, Sloan School of ManagementMIT, Cambridge, MA, USA

Xiaogang Ma Department of Computer Science, University of Idaho, Moscow,ID, USA

Gregoire Mariethoz Institute of Earth Surface Dynamics (IDYST), University ofLausanne, Lausanne, Switzerland

Sean A. McKenna IBM Research, Dublin, Ireland

A. F. Militino Department of Statistics and O.R., Public University of Navarra(Spain), Pamplona, Spain; InaMat (Institute for Advanced Materials), Pamplona,Spain

Editors and Contributors xxvii

R. Mohan Srivastava TriStar Gold Inc., Toronto, ON, Canada

A. Mondaini Department of Physics, UERJ, Rio de Janeiro, Brazil

Donald E. Myers Department of Mathematics, University of Arizona, Tucson,AZ, USA

J. Nicholls Department of Geoscience, University of Calgary, Calgary, AB,Canada

Václav Němec Praha 10 - Strašnice, Czech Republic

Ricardo A. Olea U.S. Geological Survey, Reston, VA, USA

Guocheng Pan China Hanking Holdings, Shenyang, Liaoning, People’s Republicof China

Vera Pawlowsky-Glahn Department of Computer Science, Applied Mathematicsand Statistics, University of Girona, Girona, Spain

U. Pérez-Goya Department of Statistics and O.R., Public University of Navarra(Spain), Pamplona, Spain

Jean Serra Ecole des Mines de Paris, Paris, France

Helmut Schaeben Geophysics and Geoinformatics, TU Bergakademie Freiberg,Freiberg, Germany

John H. Schuenemeyer Southwest Statistical Consulting, LLC, Cortez, CO, USA

Donald A. Singer Cupertino, CA, USA

D. B. Smith United States Geological Survey, Denver, CO, USA

Amílcar Soares CERENA, Instituto Superior Técnico, Universidade de Lisboa,Lisbon, Portugal

Pejman Tahmasebi Department of Petroleum Engineering, University ofWyoming, Laramie, WY, USA

Hannes Thiergärtner Department of Geosciences, Free University of Berlin,Berlin, Germany

R. Tolosana-Delgado Helmholtz Institute Freiberg for Resource Technology,Freiberg, Germany

M. D. Ugarte Department of Statistics and O.R., Public University of Navarra(Spain), Pamplona, Spain; InaMat (Institute for Advanced Materials), Pamplona,Spain

K. G. van den Boogaart Helmholtz Institute Freiberg for Resource Technology,Freiberg, Germany

E. H. Timothy Whitten Riverside, Widecombe-in-the-Moor, Devon, UK

xxviii Editors and Contributors