Discriminatingfourtectonicsettings:Fivenewgeochemicaldiagramsforbasicandultrabasicvolcanicrocksbasedonlog–ratiotransformation
ofmajor-elementdata
SurendraPVerma1,?,MirnaGuevara1andSalilAgrawal2
1
CentrodeInvestigaci′onenEnerg′?a,UniversidadNacionalAut′onomadeM′exico,Priv.Xochicalcos/no.,
ColCentro,ApartadoPostal34,Temixco62580,Mexico.
2
DepartmentofGeology,UniversityofRajasthan,Jaipur302004,India.
?
e-mail:spv@cie.unam.mx
Wepresent?venewdiscriminantfunctiondiagramsbasedonanextensivedatabaserepresentativeofbasicandultrabasicrocksfromfourtectonicsettingsofislandarc,continentalrift,ocean-island,andmid-oceanridge.Thesediagramswereobtainedafterloge-transformationofconcentrationratiosofmajor-elements–atechniquerecommendedforacorrectstatisticaltreatmentofcomposi-tionaldata.Higher%successrates(overallvaluesfrom～83to97%)wereobtainedforproposingthesenewdiagramsascomparedtothose(～82to94%)obtainedfromthediscriminantanalysisoftherawmajor-elementconcentrationdata(i.e.,withouttheloge-transformationandwithouttakingratiosofthecompositionaldata,butusingexactlythesamedatabasetoprovideanunbi-asedcomparison),suggestingthatsuchadatatransformationconstitutesastatisticallycorrectandrecommendedtechnique.Thenewdiagramsalsoresultedinlessmis-classi?cationofbasicandultrabasicrocksfromknowntectonicsettingsthanthediagramsobtainedfromtherawdata.TheuseofthesehighlysuccessfulnewdiscriminantfunctiondiagramsisillustratedusingMiocenetoRecentbasicandultrabasicrocksfromthreeareasofMexicowithcomplexorcontroversialtec-tonicsettings(MexicanVolcanicBelt,LosTuxtlasvolcanic?eld,andEasternAlkalineProvince),aswellasolderrocksfromthreeareas(Deccan,Malani,andBastar)ofIndia.Additionally,themajor-elementdatafromtwo‘known’continentalarcsettingsareusedtoshowthattheyaresim-ilartothosefromtheislandarcsetting.ContinentalriftsettingisinferredforallMexicancasesandforonecratonicareaofIndia(Malani)andanIABsettingfortheBastarcraton.TheDeccan?oodbasaltprovinceofIndiaisusedtowarnagainstanindiscriminateuseofthosediscriminationdiagramsthatdonotexplicitlyincludethelikelysettingoftheareaunderevaluation.AnExceltemplateisalsoprovidedforaneasyapplicationofthesenewdiagramsfordiscriminatingthefoursettingsconsideredinthiswork.
1.Introduction
Contemporaneouslywiththedevelopmentofplatetectonicsandtherecognitionofspeci?ctectonicsettingssuchasislandarc,continentalrift,ocean-island,andmid-oceanridge,theideathatmag-masfromdi?erenttectonicsettingsmightbedistinguishableintheirchemistrywaspioneeredbyPearceandCann(1971,1973).Sincethen,numer-ousbivariateandternarytectonomagmaticdia-gramshaveappearedintheliterature(formoredetailssee,e.g.,Rollinson1993;Verma2000a,2006;Agrawaletal2004).Thesediagramspro-videadditionalevidence,complementarytothe
Keywords.Log-transformation;compositionalspace;discriminantfunctionanalysis;standardigneousnormandvolcanicrockclassi?cationsystemcomputerprogram;Mexico;India.J.EarthSyst.Sci.115,No.5,October2006,pp.485–528?PrintedinIndia.
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?eldevidence,andsuggestana?liationratherthananunequivocalcon?rmationofthetectonicenvironment.
Fromthestatisticalpointofview,probablyamajoradvanceintheproposalandfunctioningofdiscriminationdiagramscamewiththeintro-ductionofdiscriminantanalysis,inwhichalargenumberofvariablesareexaminedtoisolatethosethatmoste?ectivelyclassifythesamplesintheirprede?nedclassesorgroups.Asearlyas1965ChayesandVelde(1965)useddiscriminantfunc-tionstodistinguishbetweencircum-oceanicandocean-islandbasalticlavas.Later,Pearce(1976)used8major-elements(SiOCaO,Na2,TiO2,Al2O3,FeO,MgO,2O,andK2O)inatotalof358sam-plesofbasalticrocksand6classestoproposenewdiscriminantfunctiondiagrams.Thelinear?eldboundariesbetweenthegroupswere,however,drawnby‘eye’(Pearce1976,p.22),insteadofsomeobjectiveprocedure.Soonafterwards,YellurandNair(1978)usedPearce(1976)discriminantfunctionandotherdiagramstoinferthetectonicenvironmentofChitradurgametabasaltsinsouthIndia.
Theproblemof‘eye-?ttedboundaries’persistedintheproposalofmostdiscriminationdiagramsuntilAgrawal(1999)suggestedhowtoreplacetheseeye-?ttedboundariesbyprobability-basedsurfaceboundaries.Theotherprobleminthecre-ationofsuchdiscriminationdiagramswastheinadequacyofthedatasetusedtorepresentthepopulation,i.e.,thestatisticalsampleprobablywasnotrepresentativeofthepopulation.Forexample,only358sampleswereusedbyPearce(1976)torepresent6classes;manyotherdiagramsarebasedonsimilarorstillsmallerdatasets(e.g.,507sam-plesfrom5settingsbyMullen1983;35meanval-uesfromabout300analysisfor5classesbyButlerandWoronow1986).Thelackofrepresentativenessaswellastheuseof‘eye-?tted’boundariesmightbethereasonswhyArmstrong-AltrinandVerma(2005)foundthatmanytectonicsettingdiscrim-inationdiagramsproposedandusedforsedimen-taryrocksdonotworkproperly.
Boththeseshortcomingsofdiscriminationdia-grams(lackofrepresentativenessofthedatabaseanduseof‘eye-?tted’boundaries)wererecentlyovercomebyAgrawaletal(2004),whousedatotalof1159samplesofmostlybasicrocksfrom4tec-tonicsettings(islandarc,continentalrift,ocean-island,andmid-oceanridge)andperformedthediscriminantanalysistopropose5newdiscrimi-nantfunctiondiagrams,inwhichtheboundarieswereprobability-basedsurfaces(orlinesintwo-dimensions).
Anotherproblemattackedoraddressedbynoneoftheproposalsofdiscriminationdiagramsusing
lineardiscriminantanalysis,asoftoday,isthe‘closure’or‘constantsum’ofcompositionaldataincludingthemajor-elementsinrocks(e.g.,Chayes1960,1983;Skala1977,1979;Aitchison1986;Rey-ment1987;WoronowandLove1990;Rollinson1993;ReymentandSavazzi1999).OneoftherareexceptionsisButlerandWoronow(1986)whousedasmallsetof35TiOanalyses(basedonabout2,Zr,Y,andSraverage300individualanalyses)ofbasaltstoperformprincipalcomponentanaly-sis(butnotlineardiscriminantanalysis)oflog-centeredcomponents.
Asiswellknown,thecompositionaldataide-allysumto1(constantsumofparts)or100%(the‘closure’problempersistsevenifthecon-stituentsofanalysisdonotsumexactlyto100%).Thismakesthemstatisticallydependentofeachother,forexample,ifwesupposethattherockcompositionisrepresentedby10major-elementsoroxides(SiO2,TiO2,Al2O3,Feall2Otparts3,MnO,MgO,CaO,Na2O,K2O,andP2O5),aremutu-allydependentbecauseallofthemsumupideallyto1or100%.Now,ifweassumethatallpartsarenon-zero,andwe?xonepart(nomatterwhich?rstpartwechoose,anessentialpropertyoftheclosureorconstantsumisthatthisparthastobelessthanthewhole,i.e.,<1or<100%),thesecondpart(irrespectiveofwhichpartweimaginetobethesecond),althoughnottotallypredictable,hastobe<(1-?rstpart)or<(100%-?rstpart%)(i.e.,partlyprede?nedanddependent).Thethirdandlaterpartswillalsobepartlyde?ned,butwithinconsecutivelysmallerranges.The?nal(10th)partwillbetotallypredictable,de?ned,anddepen-dent.Theseinterdependencesarisingfromtheclo-sureproblemareanundesirablepropertyforanystatisticalanalysis,includingthefrequentlyusedbivariate‘Harker-type’andternarydiagramsfortheinterpretationofigneousrockchemistry(forthelatter,thesituationisevenworsebecauseoftherenormalization–to100–ofthethreepartsusedforconstructingthem;seeButler1979).Accord-ingtoAitchison(1986),thestudyofcompositionsisessentiallyconcernedwiththerelativemagni-tudesofthepartsratherthantheirabsolutevalues,whichleadstotheconclusionthatweshouldthinkintermsofratios(e.g.,Rollinson1993)andper-hapssomeadditionaltransformationoftheseratiodatainordertofreethesamplespace.Wemust,however,beawareofthedangerofspuriouscorre-lationsbetweencertainkindofratios(e.g.,Chayes1978;Butler1986).
Ourpresentworkisintendedtoaddresstheissueofclosureorconstantsum,whilecomplyingwiththeothertwoaspects–thestatisticalsamplerep-resentativeofthepopulationandanobjectivepro-cedurefordrawing?eldboundaries,toarriveata
Fivegeochemicaldiagramsforbasicandultrabasicrocks487
Figure1.Schematiclocationofbasic(andultrabasic)rocksamplesinthequadrant0–180?longitudeand0–90?Nlatitude(northernpartoftheeasternhemisphere:Asia,Europe,andpartofAfrica).Thesymbolsusedareshownasinset.Formeaningof#locationsrefertotable1,andfor#applicationlocations,table9.
statisticallysoundorvaliddiscriminantanalysisofmajor-elementdata.Wepresentasetof?ve,highlysuccessful,newdiscriminationdiagrams(usinglin-eardiscriminantanalysisofloge-transformationofmajor-elementratios).Weperformeddiscrimi-nantanalysisofactualmajor-elementconcentra-tiondatafromthenewextendeddatabaseandcomparedthesuccessrateswithourearlierworkwithasmallerdatabase,aswellaswiththoseobtainedfromtheloge-transformationofconcen-trationratiostoshowthattheloge-transformationisarecommended,statistically-correctprocedureforhandlingcompositionaldata.Wealsoincludesomespeci?cexamplesforillustrationpurposes.Finally,weprovideanMS-Exceltemplatetohelpinterestedpersonsinusingournewdiscriminantfunctiondiagrams.
2.Database
Wepreparedarepresentativedatabaseof10or11major-elements(dependingontheavailabilityofthetotalironasFe2O3andFeO)inmostlybasicrocks(ultrabasicrockswereincludedfromwher-everavailable)frommainly4tectonicsettings(?g-ures1–4;table1):islandarcbasicrocks(IAB),continentalriftbasicrocks(CRB),ocean-islandbasicrocks(OIB),andmid-oceanridgebasicrocks(MORB).AsinAgrawaletal(2004),wenotethatcontinentalarcisamissingsetbecausethemajor-elementcharacteristicsofbasicrocksfromthisset-tingareverysimilartothosefromtheislandarc;tosupportthisclaim,wewilluseexamplesfromthissettingtoshowthattherocksfromcontinen-talarcplotmainlyintheislandarc?eld.
Ourpresentdatabasecontainsatotalof2732samples(table2)asfollows:463samplesforIAB(namedgroup1),771samplesforCRB(group2),572samplesforOIB(group3),and926samplesforMORB(group4).Thetrainingsetconsistedof2332samples,whereasthetestingsetwasestablishedfromrandomlydrawn400samples,100fromeachtectonicsetting.Thepresentdata-basecontainsmoresamples(2732versus1159sam-ples;table2)thanourearlierstudy(Agrawaletal2004).
Therandomselectionofsamplesforthetest-ingsetwascarriedoutbyasimplecomputerprogram(inQUICKBASICwrittenbyoneofus–SAgrawal)forgeneratingrandomnumbers.Forexample,fortheIABgroupforwhichwehad463samplesandwewishedtorandomlyseparate100samples,100randomnumbersbetween1and463(thetotalnumberofsamplesinthisgroup)weregeneratedandthesamplescorrespondingtotheserandomnumberswereassignedtothetestinggroup.Similarly,fortheCRBgroup100randomnumbersweregeneratedbetween1and771(beingthetotalnumberofCRBsamplesinourdatabase)andsoontocompletethefoursettings.
ThecriteriaforchoosingthesamplesinourdatabasewerethesameasinAgrawaletal(2004),viz.,thetectonicsettingdescribedexplicitlyandunambiguouslybytheauthor(s),(SiO2)adjcontent≤52%(thesubscriptadjreferstotheadjusteddataasexplainedbelow),andagemostlyPiocenetoRecent(althoughsomeLateMiocenerockswere
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Figure2.Schematiclocationofbasic(andultrabasic)rocksamplesinthequadrant0–180?longitudeand0–90?Slatitude(southernpartoftheeasternhemisphere:Australia,NewZealand,partofAsia,andsouthernpartofAfrica).Thesymbolsusedareshownasinset.Formeaningof#locationsrefertotable1.
Figure3.Schematiclocationofbasic(andultrabasic)rocksamplesinthequadrant180–360?longitudeand0–90?Nlatitude(northernpartofthewesternhemisphere:northAmerica,centralAmerica,northernpartofsouthAmerica,andpartofAtlanticandPaci?cOceans).Thesymbolsusedareshownasinset.Formeaningof#locationsrefertotable1,andfor#applicationlocations,table9.
alsoincluded).Inclusionofsampleswith(SiO2)adjcontent≤52%alsomeansthatbasicaswellasultrabasicrocksfromalltectonicsettingswerepresentinourdatabasealthoughultrabasicrocksfromtheIABandMORBwerelessnumerousthanfromtheothertwosettings(CRBandOIB).Further,ourexperienceshowsthattheinclusionofafewadditionalsampleswith(SiO2)adjsome-whathigher(upto～53%),alongwiththebasicandultrabasicsamples,providesstatisticallysim-ilarresults.Thus,mostlybasicandultrabasicrocks,withouttheapplicationofanyothercri-teriaforprimitivemantle-derivedmagmas(seeVelasco-TapiaandVerma2001forasynthesis
Fivegeochemicaldiagramsforbasicandultrabasicrocks489
Figure4.Schematiclocationofbasicrocksamplesinthequadrant180–360?longitudeand0–90?Slatitude(southernpartofthewesternhemisphere:partofsouthAmerica,AtlanticandPaci?cOceans).Thesymbolsusedareshownasinset.Formeaningof#locationsrefertotable1,andfor#applicationlocations,table9.
ofsuchcriteria),werecompiledforthisstudy.Therefore,e?ectsofmagmaevolutionprocesses,suchasfractionalcrystallization,magmamixing,orassimilationcoupledoruncoupledwithfrac-tionalcrystallization,arealsotakenintoaccount,atleastindirectly,becauseourdatabaseincludesallultrabasicandbasicrocksamplesirrespectiveofwhethertheyareprimitiveorevolvedrocksintermsoftheseprocesses.Insummary,thelimitofabout52%(SiO2)adjwaschosensimplybecausewewantedtouseonlythebasicandultrabasicrocksinthiswork;ourfutureworkwillbedirectedtowardshandlingofmoredi?erentiatedintermediateandacidigneousrocks.
Speci?cally,foridentifyingultrabasicandbasicmagmasaccordingtotheIUGSSubcommissionontheSystematicsofIgneousRocks(LeBasetal1986),thevolcanicrockclassi?cationandTASdia-gramshouldbepreparedonananhydrous100-justedbasisafteraproperFe-adjustmentofthemajor-elementdata,i.e.,usingbothFe2O3andFeOvarietiesandnotsimplytotalFeasFe2Ot3orFeOt.TheSubcommissionrecommendedthateitheractually-analyzedFe2O3andFeOconcentra-tionsbeusedbeforetheadjustmentto100%,orwhenonlytotalFeisavailable,LeMaitre(1976)methodforFe2O3andFeOcalculationsshouldbeused.However,theuseofactuallymeasuredFe2O3andFeOconcentrationsinigneousrocksforrockclassi?cationmaynotbeappropriate,inspiteoftheSubcommission’srecommendations,becauseinevitable,extensivepost-eruptivechangesintheirvaluestakeplace,accordingtoMiddle-most(1989)who,infact,evaluatedthedi?er-entwaysforestimatingtheFe2O3/FeOratioand
proposedrock-typebasedvaluesforthedivisionoftotalFeintotheFe2O3andFeOvarieties.Andthissubdivisionisadi?culttaskwithoutusingasuitablecomputerprogram,suchasSINCLAS–standardigneousnormandvolcanicrockclassi?-cationsystem(Vermaetal2002).
Alldatawere,therefore,processedusingSIN-CLAScomputerprogramundertheoptionofMiddlemost(1989)foriron-oxidationratiocalcu-lationsand100-justmentonananhydrousbasis(Vermaetal2002);thiscomputerprogramprovideshighlyaccurateandconsistentresultsasdocumentedbyVermaetal(2003).ThedataprocessingbySINCLASisthusarequiredstepbecausewewishtoseparatethetotalFeintoitstwotypes–theFe2O3andFeOvarieties,andtochoosetheappropriatesamples(with(SiO2)adjcontent≤52%)inourdatabasebeforethetrans-formationofthedata.EvenforthesampleswithFe2O3andFeOindividuallyreported,wewishtostandardizethissubdivisionofironaccordingtosomestandardrecommendations(e.g.,Middle-most1989)by?rstcombiningthesepartsintototalFe2Ot3andthensubdividingitintoFe2O3andFeOvarieties.Thisisdonebecausealldatashouldbehandledinexactlythesamewayirre-spectiveofwhetherironwasreportedintheliter-t
atureastotalFe2Ot3ortotalFeOorasseparatevarieties.Thus,wenotethatthedataprocessingusingSINCLASwillbemandatoryforallappli-cationsbecause,inordertobeconsistentwiththeprocedureofthesenewdiscriminantfunctiondiagrams,allsamplesmustbeprocessedforthecalculationofFe2O3andFeOcontents,accordingtotheproposalofMiddlemost(1989),whichin