Table Of ContentQuantitative Geology and Geostatistics
Frits Agterberg
Geomathematics:
Theoretical
Foundations,
Applications and
Future
Developments
Geomathematics: Theoretical Foundations,
Applications and Future Developments
Quantitative Geology and Geostatistics
VOLUME 18
For furthervolumes:
http://www.springer.com/series/6466
Frits Agterberg
Geomathematics: Theoretical
Foundations, Applications
and Future Developments
FritsAgterberg
MinistryofNaturalResourcesCanada,
GeologicalSurveyofCanada(NRCan-GSC)
Ottawa,ON,Canada
ISSN0924-1973
ISBN978-3-319-06873-2 ISBN978-3-319-06874-9(eBook)
DOI10.1007/978-3-319-06874-9
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To Codien
Foreword
Our world has entered the “Big Data” era, in which new data are produced with
unprecedentedspeedandinlargequantities.Thenewknowledgeobtainedthrough
digital analysis and the novel methods of data mining are greatly benefitting the
processofhumandecision-making.Thearrivalofthisneweraisgraduallychang-
ingpeople’slife,workandthinking.Inthefieldofscience,“BigData”hasledto
the emergence of “Data Science” which will affect, to some extent, all fields of
science, by performing scientific research by using digital data and by using
scientificmethodstostudydigitaldata.
Earth Science and geological work are data-intensive. It is no exaggeration to
say that different kinds of geological data have to be obtained and aggregated by
different means, if we want to solve geological problems and use the results. No
geological problem can be solved correctly and effectively without the in-depth
studyofavarietyofgeologicalinputs.Geologicaldataarecharacterizedbythefour
“deeps”:theyaredeepintheEarth,deepunderthesea,deepinouterspaceanddeep
intime.Consequently,itisnoteasytoobtainusefulgeologicaldatainpractice,and
data collection can be expensive. Much attention has to be paid to costs and
benefits.
EarthScientistsshouldalwaysdotheir besttodefine “populations”andensure
that truly representative samples are collected from these target populations.
Because they differ from place to place, geological samples can never fully
comprise the entire population of study; there is no “overall data completeness”
or“comprehensivedata”ingeologicalscienceandpractice.Becauseofthis,other
methods of approach have to be developed in order to make random sampling
results fit the target populations as closely as possible, so that information loss
becauseofrestrictedsamplingaccessisminimized.
Ultimately, the purposeofEarth Science is topromotethe progress and devel-
opment of human society: it explores the course, procedures, and products of the
Earth’sevolution,inordertomakeuseoftheadvantagesofandguardagainstthe
disadvantagesthattheEarth’sevolutionbringstous.Geologicaldatahavesignif-
icantcharacteristicsreflectingtimeoforigin,spaceandgenesis.Theycanmanifest
different outcomes of genetic processes depending on space and time conditions.
vii
viii Foreword
Therefore,whenfacedwithgeologicaldata,oneshouldnotonlyknowthe“what?”
but also the “why?” and “how?” about what the data truly mean and how they
should be used. One should not only establish “correlations” but also “causality”
and“spatiotemporalrelations”.Inthis,geologydiffersfromsomeotherareasinthe
BigDataerawherethefocusisonthe“what?”andcorrelationswithoutthe“why?”
andcausality.
All of the preceding considerations aim toillustrate the complexity and partic-
ularities of geological data as well as their usefulness and importance. Fully
comprehensive geological data collection, their effective treatment, rational anal-
ysisandtranslationinto“digital” knowledge,alldependonguidanceprovidedby
powerful theory and applications of efficient methods. Mathematical geosciences
preciselyprovidethepowerfultoolsneededtorealizetheseaims.Intheearlydays,
monographs in mathematical geoscience were published under the name of “sta-
tistical analysis of geological data” or by using similar titles. However, in the
information age and Big Data era, we prefer the word “geomathematical” for
increasedemphasisandclarification.
ThebookinfrontofusisanewmasterpiecebyCanadianscholarF.Agterberg:
Geomathematics: Theoretical Foundations, Applications and Future Develop-
ments. It follows Geomathematics: Mathematical Background and Geo-science
Applications,anothermasterpiece ofhis publishedin1974.There are12chapters
inthisnewbookanditcontainsalargenumberofcase-historystudiestoillustrate
theapplicationofmathematicalmethodsinresearchingbasicgeologicalproblems
in stratigraphy, tectonics, igneous petrology and geochronology, in order to solve
practicalproblemssuchasthedescriptionandcharacterizationofvarioustypesof
oredepositsandthepredictionandevaluationofmineralresources.
Honoringthecomplexityandcharacteristicfeaturesofgeologicaldata,thisbook
illustrates the application of geomathematical methods in detail. Although it also
discussestheprocessingoftraditionallystructureddata,thisbookfocussesmoreon
theprocessingofunstructureddatasuchasthatariseintheanalysisandprocessing
of various geological map and image data. Besides introduction of theory and
methodsofclassicalprobabilitycalculusandstatistics,thisbookextensivelycovers
non-linear process theory as applied to the geosciences. The book fully describes
the latest developments and achievements of mathematical geosciences over the
past decade. Inhis last chapter,the author suggestsanumber oftopics forfurther
development of the mathematical geosciences showing his deep interest in
nonlinear process simulation and applications in future geological research. The
solutionofthesenewproblemswillundoubtedlyraisetheresearchlevelingeology
andopenupnewavenuesofapproachinthemathematicalgeosciences.
Professor Agterberg’s ideas, theories, methods and practical applications of
geomathematics have significant impact on the development of mathematical
geosciencesworldwide.DuringhistenureasPresidentoftheInternationalAssoci-
ation for Mathematical Geosciences (IAMG), he paid much attention to and
promoted the development of mathematical geosciences in all countries. Espe-
cially, as an old friend of the Chinese people, F. Agterberg has offered valuable
concernandhelpinthedevelopmentofthemathematicalgeosciencesinChina.Itis
Foreword ix
mygreathonour towrite the foreword for this book, andI would like totake this
opportunitytoextendmywarmcongratulationstoF.Agterbergforthepublication
of this book. I also thank him sincerely for his personal contributions to the
developmentofthemathematicalgeosciencesinChina.
ChinaUniversityofGeosciences PengdaZhao
AcademicianoftheChineseAcademyofSciences
8thMarch2014
