Table Of ContentRichard J. Howarth
Dictionary of
Mathematical Geosciences
With Historical Notes
RichardJ.Howarth
DepartmentofEarthSciences
UniversityCollegeLondon
London,UnitedKingdom
ISBN978-3-319-57314-4 ISBN978-3-319-57315-1 (eBook)
DOI10.1007/978-3-319-57315-1
LibraryofCongressControlNumber:2017942721
#SpringerInternationalPublishingAG2017
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Introduction
Isitpossibleformathematical geologytoaccedetothetrue dignityofareally rationaland
scientificdiscipline,orshallitbenothingbutapurelymechanicalapplicationofcomputers?
(G.Matheron1967).
Many geologists become earth scientists because they are interested in rocks, minerals,
fossils,andthegreatoutdoors,anditisnotgenerallythoughtofasamathematicalbranch
of science. However, in recent years the interpretation of observational data, whether
structures in the field, geochemical determinations, mineralogical or fossil assemblage
compositions, stratigraphic correlation, the properties of geophysical or other time series
and their analysis, etc., have all become increasingly reliant on the use of statistical and
mathematicalmethods.Geophysicistswillgenerallyhavehadastrongbackgroundin,orat
least a good aptitude for, mathematics, but this is not necessarily the case with their
geological colleagues. In order to assist with this situation, this dictionary has been
compiledsoastoprovidesomeguidancetothemethodsandterminologyencounteredin
theliterature.
Allthewordswhichappearinboldintheexplanatorytextarethemselvesincludedas
topicselsewhere.Itisintendedtobeself-describingfromthemathematicalpointofview
andnopriorknowledgeisassumed.Forthisreason,someoftheentriesdealwithentirely
mathematicalorstatisticaltermsbecausetheyhavebeenusedinexplanationselsewhere.
It is intended as an aid for undergraduate and postgraduate earth science students, as
wellasprofessionalsintheacademicworldandindustry,whoneedaguidetoterminology
withpointerstotheappropriateliteraturefromwhichfurtherinformation,andexamplesof
use,canbefound.Itincludesmethodsusedingeology,geochemistry,palaeontology,and
geophysics. The field of “geostatistics” in its original sense, i.e. as applied to spatial
statistics and reserve estimation, is also included, but readers should be aware that the
International Association for Mathematical Geosciences has published a more specialist
glossary in this field (Olea et al. 1991). Since many aspects of early computing which
underpinned this growth have now themselves passed into history, some terms from this
fieldhavealsobeenincludedastheyoccurinthegeologicalliteratureofthe1960s–1980s
and may not be familiar to readers brought up in an era of laptops and tablets. I have
includednotesontheoriginofasmanyaspossibleofthetermsincludedinthisdictionary
asIhopeitwilladdtotheinterestforthereader.
Conventions used in biographical dates, etc. in this work: (?–1892) should be read as
“yearofbirthunknown”;(1904?–1942),“possiblybornin1904,diedin1942”;(?1520–?
1559), “born about 1520, died about 1559”; (1907–), “still alive or year of death not
recorded”; John [?Henry] Koonce, “second given name is possibly Henry”; ?A. Otsuka,
“givennameisunknown,butmaybeginwiththeletterA.”Bibliographiccitationssuchas
“Raphson(1668?)”meanthatthedateoftheoriginalworkisuncertain;and“(d’Alambert
1747 [1750])” mean that the date of publication was much later than submission to the
journal.
The history of mathematics websites maintained by Jeff Miller (New Port Richley,
Florida), and the Ancestry.com website were invaluable in preparing this work, and I am
immenselygrateful toAnnett Büttnerand D€orthe Mennecke-BuehleratSpringerDE and
particularlytotheirproofreadersatSPiGlobal(Chennai)fortheirhelpwiththemanuscript.
FritsAgterberg(Ottawa)andJohnMcArthur(London)arethankedfortheirinitialencour-
agementandsuggestions.
Readers are welcome to send the author suggested text (including references where
applicable)foradditionalentries,orimprovementstoexistingones,andtheirsubmissions
willbecreditedshouldanupdatededitionofthisworkbeproduced.
London,UK RichardJ.Howarth
Contents
A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611
U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669
Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
Acronyms, Abbreviations and Symbols
Acronyms
A/D Analogtodigitalconversion
AFMdiagram Alkalis-totalFeO-MgOdiagram(seeAFMdiagram)
AGC Automaticgaincontrol
AI Artificialintelligence
AIC Akaikeinformationcriterion
aln Additivelogisticnormaldistribution
alsn Additivelogisticskew-normaldistribution
AM Amplitudemodulation
ANN Artificialneuralnetwork
ANOVA Analysisofvariance
ARprocess Autoregressiveprocess
ARMAprocess Autoregressivemovingaverageprocess
ART Algebraicreconstructiontechnique
ASA Adaptivesimulatedannealing
BLUE Bestlinearunbiasedestimator
BME Bayesianmaximumentropy
BPT Backprojectiontomography
CAplot Concentration-areaplot
CAD Computer-aideddesignordrafting
CAI Computer-aidedorcomputer-assistedinstruction
CART Classificationandregressiontrees
CASC Correlationandscaling
CEP Circularerrorprobability
CICA Constrainedindependentcomponentanalysis
Unlessotherwiseindicated,forexplanationrefertotheirfulltitles.
CIPWnorm Cross,Iddings,Pirsson,Washingtonnorm(seeCIPWnorm)
CONOP Constrainedoptimisation
CPplot Cumulativeprobabilityplot
D/A Digital-to-analog
DBMS Databasemanagementsystem
DEM Digitalelevationmodel
DFT DiscreteFouriertransform
DPSS Discreteprolatespheroidalsequence
DSM Digitalsurfacemodel
DTM Digitalterrainmodel
EDA Exploratorydataanalysis
EDF Empiricaldiscriminantfunction
EMalgorithm Expectation-maximizationalgorithm
F Favorabilityfunction
FA Factoranalysis
FAP FORTRANassemblyprogram
FCM Fuzzyc-meansclustering
FFT FastFouriertransform
f-kanalysis Frequency-wavenumberanalysis
FM Frequencymodulation
FUNOP Fullnormalplot
FWT FastWalshtransform,fastwavelettransform
GA Geneticalgorithm
GIS Geographicinformationsystem
H Entropy,Hurstexponent
ICA Independentcomponentanalysis
IIRfilter Infiniteimpulseresponsefilter
IQR Interquartilerange
IRLS Iterativelyreweightedleastsquares(seeunderIWLS)
IWLS Iterativeweightedleastsquares
KEE Knowledgeengineeringenvironment
LAD Leastabsolutedeviation(seeunderLAV)
LAV Leastabsolutevalue
LMS Leastmeansquares,leastmediansquares
LOWESS Locallyweightedscatterplotsmoother
MA Movingaverage
MANOVA Multivariateanalysisofvariance
MAP Macroassemblyprogram
MCMC MarkovchainMonteCarlo
MDS Multidimensionalscaling
MED Minimumentropydeconvolution
MEM Maximumentropymethod
MESA Maximumentropyspectralanalysis
MFAdiagram MgO-totalFeO-alkalisdiagram(seeMFAdiagram)
ML Maximumlikelihood
MLA Machinelearningalgorithm
MLP Meanlaggedproduct
MTBF Meantimebetweenfailure
MV Multivariate
NLMalgorithm Nonlinearmappingalgorithm
ODE Ordinarydifferentialequation
OLS Ordinaryleastsquares
OOP Object-orientedprogramming
PCA Principalcomponentsanalysis
PDE Partialdifferentialequation
PDF Probabilitydensityfunction
P-PorPPplot Percent-percentplot
PSD Powerspectraldensity
PSO Particleswarmoptimization
QA Qualityassurance
QC Qualitycontrol
Q-Qplot Quantile-quantileplot
R Multiplecorrelationcoefficient
R/Sanalysis Rescaled-rangeanalysis
RBV Relativebiostratigraphicvalue
RDBMS Relationaldatabasemanagementsystem
REEdiagram Rareearthelementdiagram
RMAregression Reducedmajoraxisregression
RMS Rootmeansquare
RTLalgorithm Region-time-lengthalgorithm
SA Simulatedannealing
S-Amethod Spectrum-areamethod
SIRalgorithm Sampling-importance-resamplingalgorithm
SIRT Simultaneousiterativereconstructiontechnique
SNR Signal-to-noiseratio
SQC Statisticalqualitycontrol
SSA Singularspectrumanalysis
SVD Singularvaluedecomposition
TAS Totalalkalis-silicadiagram(seeTASdiagram)
UANOVA Unbalancedanalysisofvariance
URV Unitregionalvalue
URPV Unitregionalproductionvalue,seeURV
