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Paleo-depths reconstruction of the last 550,000 years based on the transfer function on recent and Quaternary
benthic foraminifers of the East Corsica margin
Maria-Angela Bassetti, Ricardo Jacinto, Charlie Morelle Angue Minto’o, Gwenael Jouet
To cite this version:
Maria-Angela Bassetti, Ricardo Jacinto, Charlie Morelle Angue Minto’o, Gwenael Jouet. Paleo-depths
reconstruction of the last 550,000 years based on the transfer function on recent and Quaternary
benthic foraminifers of the East Corsica margin. Comptes Rendus Géoscience, Elsevier, 2018, 350 (8),
pp.476-486. �10.1016/j.crte.2018.09.003�. �hal-02324724�
Stratigraphy, Sedimentology (Palaeoenvironment)
Paleo-depths reconstruction of the last 550,000 years based on the transfer function on recent and Quaternary benthic foraminifers of the East Corsica margin
Charlie Morelle Angue Minto’O
a,b,c,*, Ricardo Silva Jacinto
d, Maria-Angela Bassetti
a,b, Gwenael Jouet
daUniversite´ dePerpignanViaDomitia,CEFREM,UMR5110,52,avenuePaul-Alduy,66860Perpignan,France
bCNRS,CEFREMUMR5110,52,avenuePaul-Alduy,66860Perpignan,France
cE´colenormalesupe´rieure(ENS)deLibreville–De´partementdessciencesdelavieetdelaTerre,BP:17009,Libreville,Gabon
dIFREMER,CentreBretagne,Laboratoire‘‘Environnementsse´dimentaires’’,29280Plouzane´,France
1. Introduction
Sea level variation reconstructionrelated to climatic changes are carried out using numerous tools allowing directreadingofthepaleo-levelsrecordedbythebeach rocks, the marine terraces, the coral reefs or by the evaluationofthevariationsoftheicevolumesthroughthe foraminiferoxygenisotopesandsubmergedspeleothemin
coastal areas (Antonioli et al., 2001; Bard et al., 1996;
Chappell, 2002;Cutleretal.,2003; Rohlingetal.,2009;
Siddall et al., 2003). Those allowed quantifying the amplitudesrelatedtosealevelvariations.
Qualitative and quantitative methods based on the microfaunaassemblagedistributionsallowingtherecon- structionofthepaleo-depthsarealsousedtocharacterize sealevelfluctuations(Hayward,2004;Hohenegger,2005;
Milkeretal.,2011;Morigietal.,2005;RossiandHorton, 2009; SpezzaferriandTamburini,2007). Thesemethods arebasedonaverygoodknowledgeofthedistributionof living foraminifera and on the assumption that the ecologicalrequirementsofspecifictaxahavenotchanged overtime.Inthisstudy,weusethisprincipletoestablisha ARTICLE INFO
Articlehistory:
Received21September2018
Acceptedafterrevision24September2018 Availableonline23October2018
HandledbyVincentCourtillot
Keywords:
Benthicforaminifers East-Corsicabasin Paleo-depths Transferfunction
ABSTRACT
Inthisstudy,themodelH(i)=109.6103+C1F1(i)+C2F2(i)+...+C33F33(i)obtained fromdepthmodellingbasedon33recentbenthicforaminiferspeciesdistribution,has beenappliedtothefossilbenthicforaminifersfromtheboreholeGDEC-4-2drilledata waterdepthof491m,intheEast-Corsicabasin,covering thelast 550,000years.The obtainedvariationsofthepaleo-depthsshowamediumcorrelationwiththeoscillations oftherelativesealevelandalsowiththefluctuationsoftheoxygenisotopicratio(d18O G. bulloides and d18O C. pachyderma–C. wuellerstorfi). This newly developed transfer functionis accompaniedbyanerrormarginof86m,suggestingthatthismodelwill probablybemoresuitableforatimescaleoftheorderofamillionyearswheresealevel variationsarerecordedwithlargeramplitudes.Withoutconsideringtheseproblemsrelatedto amplitudes,italsoturnsoutthatthe‘‘eustatic’’signalofthemicrofaunaisaccompaniedbya
‘‘trophic’’signal,whichshouldnottobeneglected, especiallyatamillennial scaletime resolution.Thus,theapplicationofthismethodwouldrequiretakingintoaccountthebottom trophiceffectsstronglycontrollingthedistributionofbenthicforaminiferassemblages.
C 2018Acade´miedessciences.PublishedbyElsevierMassonSAS.Thisisanopenaccess articleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/
4.0/).
* Correspondingauthor.Universite´ dePerpignanViaDomitia,CEFREM, UMR5110,52,avenuePaul-Alduy,66860Perpignan,France.
E-mailaddresses:mintoocharly@yahoo.fr,
charlie.angue-mintoo@univ-perp.fr(C.M.AngueMinto’O).
ContentslistsavailableatScienceDirect
Comptes Rendus Geoscience
ww w . sci e nc e di r e ct . com
https://doi.org/10.1016/j.crte.2018.09.003
1631-0713/C 2018Acade´miedessciences.PublishedbyElsevierMassonSAS.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://
creativecommons.org/licenses/by-nc-nd/4.0/).
transferfunctioninwhichtherecentbenthicforaminifer assemblages of the East-Corsican margin are used for modelling the depths according to the formula:
Hm,j=ac,0+Zj,kac,k, where Hm,jis the modelled depth at eachsitej,Zj,kisthematrixcontainingthevaluesofthe principalcomponentsusedinthemodel.Eachline(j)is associatedwithasite;eachcolumnkisassociatedwithan used principal component. Both the scalar ac,0 and the vector ac,k are estimated by calibration based on least- squaresinterpolation.
The level of correlation observed between these modelled depths and the actual depths will allow the applicationofthis equationtofossilbenthicforaminifer assemblages.Comparisonwithothereustaticcurveswill allowdiscussingthismethodofsealevel reconstruction and evaluating the difficulties of using benthic assem- blagesastoolsofvariationsinthewatercolumn.
2. Studyarea
Located in the northern part of the Tyrrhenian Sea (Western Mediterranean), the East-Corsica margin is a continentalshelfregionvaryingfrom5to10kminwidth in thenorthernpartto25km in thesouthern one.The continentalshelfcharacterizingtheEast-Corsicamarginis narrow, with a shelf break situated around 110–120m (Gervais,2002;Gervaisetal.,2004).Thiscontinentalshelf is followed by a steep continental slope incised by numerousmeanderingcanyons(Gervais,2002).Thelatter open outintoa deepbasin, whichis characterizedby a depressionnamedCorsicanTrough.
3. Materialsandmethods
3.1. Micropaleontologicalandstableisotopeanalyses Beforeperformingmicropaleontologicalanalyses,sam- pleswerewashedandsieved(63
m
m)onthesedimentary fraction>150m
m.Therecentbenthicforaminifersofthe East-Corsicabasinwerestudiedin45surfacesamplesfrom theinterfacecorescollectedatdepthsrangingfrom7to 868m,and101benthicforaminifertaxawereidentified (AngueMinto’oetal.,2013).Theidentificationof84taxaof fossilbenthicforaminiferwaspossibleviatheanalysisof 291samplesfromtheGDEC-4boreholedrilledatawater depthof492mintheEast-Corsicamargincoveringthelast 550,000years(AngueMinto’oetal.,2016).Oxygenstableisotopemeasurementswereperformed onspecimensofplanktonicforaminiferaspeciesGlobige- rinabulloidesandG.ruber(white)fromthe250–315
m
m sizefraction,Neogloboquadrinapachyderma(dextral)from the200–250m
msizefraction,andontheepifaunalbenthic foraminifera Cibicides wuellerstorfi, Cibicidoides pachy- dermaandCibicidoideskullenbergifoundinthe>150m
m sizefraction(Toucanneetal.,2015).3.2. Speciesselectionandprincipalcomponentanalysis Inthisstudy,MatLabgenericfunctionsareusedforthe computations.WecallM0(i,j),theinitialmatrixofspecies
tobeconsiderintheanalysis.M0(i,j)consistsofrelative abundancesoftheallbenthic foraminifers(101species) identifiedinthesurfacesamples,whereiisthesiteandj thespecies.Withtheaimofobtainingqualitativeresults, thereductionofthenumberofspeciesofM0(i,j)ismadeby eliminating species with a median equal to0. Because PrincipalComponentAnalysis(PCA)isbasedoncorrela- tionanalysisandhencevariation quantifications,conse- quently,on101recentbenthicforaminifertaxaidentified, only33 taxawereretainedandarelistedinTable1.For these33 species, therelative abundance, at onesite, is alwayscalculatedusingthetotalnumberofindividualsper sitebased onthe101species.Thisallowedmaintaining independencebetween thefrequencies retained,i.e.the sumofthespeciesfrequenciespersitedoesnotequal1, and thedependent and untreatedvariableis ‘‘theother species’’
X33
j¼1
Mij1
whereMistheabundancematrixofsiteiandofspecies j. The analysis is based on the abundance matrix M expressingateachsitei(from1to***)theabundanceof each speciesj(from 1to33).Each valueofMis hence expressedbyMij.
Table1
Presentationofthe33benthicforaminifersderivedfromtheanalysisof theinterfacesamplesandhavingamediangreaterthan0.These33taxa wereselectedfortheprincipalcomponentanalysis.
Retainedspecies Ordernumber
Amphicorynascalaris 1
Buliminamarginata 2
Buliminacostata 3
Bigenerinanodosaria 4
Biloculinellalabiata 5
Bolivinaspathulata 6
Cibicideswuellerstorfi 7
Cibicideslobatulus 8
Cibicidessp. 9
Cyclogyracarinata 10
Cassidulinacarinata 11
Cassidulinacrassa 12
Cassidulinaminuta 13
Elphidiummacelum 14
Fissurinacucullata 15
Gyroidinaorbicularis 16
Gyroidinaaltiformis 17
Hoeglundinaelegans 18
Hyalineabalthica 19
Lenticulinasp. 20
Melonisbarleeanus 21
Pseudoclavulinacrustata 22
Quinqueloculinaduthiersi 23
Quinqueloculinaviennensis 24
Quinqueloculinaseminulum 25
Rosalinaglobularis 26
Spiroloculinaescavata 27
Sigmoilopsisschlumbergeri 28
Spiroplectinellasagitula 29
Textulariaagglutinans 30
Textulariatruncata 31
Valvulinariabradyana 32
Uvigerinamediterranea 33
PCAisbasedonthecovariancematrix(Mc)estimated onthebasisofthespeciesabundancematrixbysite:
Mc;kj¼covðMij;MikÞ
Mc,kjrepresentsthecorrelationbetweenspecieskandjfor theallsitesi:Mc,kj=Mc,jk.
TheeigenvaluesandeigenvectorsofthematrixMcare computedtoestablish,respectively,theweight(variance) associatedwitheachcomponentandthecoefficientsof the principal components. Thus, the matrix of the eigenvectors Cjk, and the coefficients of the principal componentsarecalculatedaswellasthediagonalmatrix of theeigenvalues Djk.The new matrixCjkverifies the followingequality:
Mc;kjCjk¼CjkDjk
Theprincipalcomponentsareobtainedbya‘‘rotation’’of the assembly matrix (Mij) along the principal vectors describedbythematrixofeigenvectorsorcoefficientsof thecomponents
Zik¼ MijCjk
ItisimportanttokeepinmindthatthematrixZikcontains thesameamountofinformationastheinitialabundance matrixMijfromwhichZikhasbeenderived.Theinforma- tion is organised in a new way, thecomponents being independent of one another. Hence, at each site i, Zik
providesthelocalvalueofcomponentk,whileMijprovides thelocalabundanceofspeciesj,thenumberofspeciesand ofcomponentsbeingthesame(33).
ThematrixCjkco-relatestheprincipalcomponentsand thespecies.Evenifitiscomputedfromthedata,itcontains anestimationofarelationthatissupposedtobevalidfor anyassemblage(notonlytheonesinthedata).Cjkisthe sameforallsites(observedornoted)andisthebaseofthe generalization.
Ateachnewsite,
Hk¼aZkþb¼ aCkjMjþb
We can evaluate the possibility of obtaining a model linkingthespeciesassemblagesandthedepthofthesites.
3.3. One-componentmodels
ForeachcomponentZk,onecandefineadepthmodelHk
obtainedbylinearregressionforthedepthH:
Hk¼aZkþb
wherethecoefficientsaandbareestimatedbytheleast squaresmethodforeachcomponent.ThusafunctionBk
canbedefined.Thisfunction givesthecorrelationlevel
(coefficient) obtained by regression (R) between the modelleddepthHkandthetruedepthH.
Bk¼RðHk;HÞ
3.4. Multi-componentmodels
For models consisting of several components, the methodappliedisthesame.Adepth modelis obtained bylinearregressionusingtheleastsquaresmethod.Here themostrepresentativecomponentofthevarianceisused.
Thus, a depth model Hncan bedefined,where n isthe number of components used (from the highest to the lowest):
Hn¼a0þXn
k1
aijZk
The performance of themodel Hn canbe associated withtheAnfunction,
An¼RðHn;HÞ
The value A6 will give the correlation level of a regression model based on the six most important componentsintermsofassemblagevariability.
3.5. Determinationofthefreedomfactor
Afreedomfactor(
l
n)ofamodelconsistingofprincipal componentsn withrespecttothepointsnumber (P)of calibration/validationisdefinedbythefollowingformula:l
n¼Pðnþ1Þ PAfreedomfactorisdefinedtoquantifytherobustnessof themodelsbasedonthenumberofitsnumberoffreedom degrees.Foramodelbasedonnprincipalcomponents,its freedom factor(Ln)is quantifiedbythenumber ofdata pointsusedforcalibration(P)andthenumberofdegreesof freedomoftheusedmodel(n+1,ifnPCsareused).
Ifthisfactorisclosetotheunit,themodelisrobustin termsofdegreesoffreedom.Ifthefactorisclosetozero, themodelisnotrobust,andtherearetoomanydegreesof freedomcomparedtothesizeofthedataavailableandthe basisofitsconstruction.Inourstudy,P=44.
Anperformanceindicatorofthemodelcouldbedefined asthe‘‘good’’compromisebetweenthecorrelationlevel anditsperformanceorfactoroffreedom.Thequalityofa model Hn described by the function Qn is defined as follows:
Qn¼RðHn;HÞ
l
n¼Anl
n3.6. Calibrationandvalidationofthemodels
Afterarankingbasedontheirdepths,the44sitesare dividedintotwogroups.Thefirstoneiscomposedofone
site outof twoand itis called‘‘calibration’’.Thisgroup includes variables with an index c. The second group consistsoftheothersitesanditiscalled‘‘validation’’.This validation group is characterized by variables with an index
v
.Thecoefficientsakarecalculatedbyregressionon thebasisofthefollowingsystemofequations:a0þZikak¼Hi
Themodelledvalueswillthenbe:
Hm;i¼a0þZi;kak
whereakrepresentstheregressioncoefficientsestimated by the least squares method and Zik represents the principalcomponentvaluekatsitei.Hiisthetruedepth atsiteiandHm,irepresentsthedepthmodelledatpoint i.Aswehave22sitesforcalibrationandvalidation,itis clearthatthenumberofcomponentsmustbewellbelow thisnumber(wetestedfromonetosixcomponents).The real model is based on calibrationdata (i.e.sites). The associatedcoefficientsarethusobtained:
ac;0þZc;kac;k¼Hc
Thecalibrationcoefficientsarethenusedforthevalidation datainordertoobtainthesimulateddataHm,v:
Hm;j¼ac;0þZjkac;k
4. Resultsanddiscussion
4.1. Principalcomponentanalysis(PCA)
TheresultsofthePCAshowthataveryimportantpart of the variance (>90%) is contained in the first five eigenvalues,orprincipalcomponents(Fig.1).Thecontri- butionofeachspeciestothetwomaincomponentscanbe visualizedbytherespectivecontributionsofeachspecies
(Fig.2). It maybenoted in Fig.2 that the speciesthat contribute the most to the expression of the first component are M. barleeanus (21) and U. mediterranea (33).This component is modulated (attenuated) by the presence of C. carinata (11), R. globularis (26), and Q. duthiersi (23). The second component, however, is expressedbythe‘‘competition’’betweenC.carinataand R.globularis(Fig.2).
4.2. Correlationbetweendepthsandprincipalcomponents Thecorrelationlevelsbetween thedepth ofthesites andtheprincipalcomponentsassociatedwiththeassem- blagesarepresentedinFig.3.ThefunctionBisrepresented bythebluebarsthatindicatethecorrelationlevelofeach componentwiththedepth.ThefunctionAisrepresented bytheredcurve.Thislatterindicatesthecorrelationlevel reachedbyregressionbetweenasetofNcomponentsand thedepth.Thus, thecomponent33,whichisthefirstin importance,istheonethatshowsthebestcorrelationwith thedepth.Thiscomponentaloneallowshavingacorrela- tionlevelhigherthan95%(Fig.3).Theothercomponents areindividuallyweaker.However, theyallowincreasing thetotalcorrelationtomorethan99%ifall33components areusedtoreproducethe44depths.
Thebestmodelisnotnecessarilytheonethatallows obtainingthe best correlationbetween true values and modelvalues estimatedon thesesame truevalues. The number of degrees of freedom associated with the calibrated models and thenumber of validation points must be taken into account, because the models are calibrated on thevalidation points. Thus, all modelsHk
havetwodegreesoffreedom:thecoefficientsaandb.The modelsHnhaven+1degreesoffreedom.Byabsurdity,a modelwhosenumberofdegreesoffreedomisequaltothe number of calibration/validation points will always presentacorrelationof100%.
TherepresentationofthefunctionQn(Fig.4)showsthat the use of a small number of components can be advantageousintermsofrobustnessofthechosenmodel.
Fig.1.Varianceassociatedwiththe33maincomponents.Themajorityofthevarianceiscontainedinthefirstfiveeigenvalues,orprincipalcomponents.
4.3. Evaluationofthemodels
Theevaluationismadeformodelsbuiltwithanumber ofvariablecomponents(between1and6).Themodelwith all the data (bluecurve) serves as a reference (Fig. 5).
Calibration1(cal1)andvalidation1(val1)areobtainedas described in the paragraph related to calibration and validationofmodels:thefirstsetisforcalibrationandthe secondsetforvalidation.Themodelscal.2andval.2are obtainedbyreversingtheuseofthesets(Fig.5).
Forcal.andval.1,weobtainacalibrationmodelthatis slightlyless efficientthan thereference one, while the validationisgenerallybetter(Fig.5).Thismeansthatthe validationsetiscloser,intermsofassemblages,towhat
can be explained by the depth. Overall, the correlation improves with the number of components used. This improvementis increasingforthereferenceandforthe calibration(Fig.5).Forthevalidationmodel,thetwominor contribution components (2 and 5) reduce the perfor- manceofthemodel.Whenwereversetheuseofsets,we fallbackonareverseresult,andmore‘‘classic’’.Calibra- tion,doneonlessdatathanthereference,ismoreefficient (butwithalowerfreedomfactor);validationislesswell thancalibrationandreference.
The choice seems to be made between 1, 4, or 6components,evenifitremainsconceivabletouseonly the useful components. Correlations are performance indicators. It is therefore important to visualize the Fig.2.Speciescontributiontothetwomaincomponents.
Fig.3. Correlationbetweenthedepthofthesitesandtheprincipalcomponents.ThebluebarsrepresentthefunctionBandtheredcurvecharacterizesthe functionA.
correlationspresentedinFigs.6and7,inwhichalossof linearitycanbeobservedfrom700mdepthwiththeerror marginsof43mandthus86min2
s
.4.4. Choiceofthefinalmodel
Principalcomponentanalysisallowsusto‘‘focus’’the variance of theassemblages on avery smallnumber of variables (components),whichis veryusefulin orderto reduce the number of freedom degrees of the models obtainedbyregression.
Outof33components(asmuchastheselectedspecies), wewillkeepfourcomponents(28,30,31and33),which means that the regression model is based on the estimationoffiveparameters.
Themodelobtainedmadeitpossibletohavea97.13%
correlationonallthesites.Thecalibratedmodelon22sites (performance of 96.85% in self-application) displays a correlationof 97.72% on the validation set. The perfor- manceofthechosenmodelisillustratedintheFig.8.
4.5. Thestructureofthemodel
ThestructureofthemodelispresentedinFig.9.Itcan benotedthatthefinalcontributiontoexplainingthedepth variability is very distinct from the distribution of the coefficientsassociatedwitheachspecies.Thisisbecause the relative abundance of each species has not been standardized.Thus,therearetwospeciesthatcontribute significantly: M. barleeanus and U. mediterranea.
M.barleeanusexplainsthevariationsofdepthatshallow depths and U. mediterraneaexplains the depth beyond 100m.
4.6. Applicationofthemodelandcomparisonwiththesemi- quantitativemethod
4.6.1. Numericalmodel
The application of the model H(i)=109.6103+C1 F1(i)+C2F2(i)+...+C33F33(i)(whereCicorrespondsto thecoefficientofspeciesiandFitoitsfrequency)onfossil benthicforaminifersspeciesallowedustoobtainthecurve ofpaleo-depthsvariation.Thereconstructedpaleo-depths range from 62286m to 2186m. In general, the variation ofthese paleo-depthscorrelates quitewellwith thevariationsofthesealevel(Fig.10).Aglobaltrendmarked byanincreaseindepthduring periodsofhighsealevelis observed.Interglacialsarecharacterizedbytheremoval(or melting)ofglaciersthatconducttoanincreaseinsealevel (Doraleetal.,2010)andthereforetoanincreaseinthewater level abovethe seabed.This could justifythis riseof the paleo-depthsduringthesewarmclimaticperiods.However, thesepaleo-depthvariationsarecharacterizedbyverylarge amplitudes.
Basedonthefactthatthesemodelledamplitudesare affectedby(1)localeffectsrelatedtothemorphologyof Fig.4.RepresentationofthefunctionQn.
Fig.5.Evaluationofthedifferentmodels:theonewithallthedata(blue curve)andthemodelscalibration(greencurves)andvalidation(orange curves).
thebasin,whichisshallowandsemi-marine(closetothe sources),(2)changesintrophicconditionsatthebottom stronglyinfluencingthevariationsofbenthicmicrofauna assemblages,(3)uncertainties related tothecalculation method and the bathymetry. Normalization from 0 to 120mwasthusmadeonthevaluesofpaleo-depthsand thesealevelvariationcurveobtainedwascomparedwith theeustaticcurveestablishedbyRohlingetal.(2009)and smoothedinthesameway(Fig.11).Thisresultsinafairly goodcorrelationbetweenthesetwocurves.
However,verylargetemporaloffsetsinamplitudeand intimeareobservedbetweenthetwointerglacialcurves:
between290and280,000years(15ka),200and180,000 years (15ka), 170 and 160,000 years (15ka), 125 and 100,000years(30ka)and between60 and30,000years (30ka,Fig.11).
Theseoffsetsthereforeappearduringperiodsofhigh sealevelthataregloballycharacterizedbyadecreasein the organic matter inputs related to the theoretical distance of the sources (Cortina et al., 2013) and by a decreasein theventilationattheseabottom(Toucanne etal.,2012).Theoffsetsresultfromanunderestimationof thedepthsthatcouldberelatedtothenon-integrationin themodel of thechanges in bottomtrophic conditions stronglyinfluencingthevariationsofbenthosforaminifer
assemblages(De Rijketal.,2000;Fontanieretal.,2002;
Gooday,2003;Jorissenetal.,1995;Mackensenetal.,1990;
Murray, 1991; Scho¨nfeld, 2002a; Scho¨nfeld, 2002b).
Indeed, U. mediterraneaand M. barleeanus are the two speciesofbenthicforaminifersthatstronglyinfluencethe calculationofpaleo-depth.Thisisillustratedbytheperfect correlation between the normalized eustatic variation curve and the variation in their cumulative abundance curve (Fig. 11). U. mediterranea and M. barleeanus are species related not only to the quality but also to the intensity of organic matter inputs to the bottom.
M. barleeanus is known as a species that develops in environmentswherethereistherefractoryorganicmatter (Fontanieretal., 2002;Lutzeand Coulbourn,1984)and U. mediterraneaadapts to environments withmoderate fluxesoflabileorganicmatter(LutzeandCoulbourn,1984;
Schmiedletal.,2000).
Based on this low correlationand theerror margins obtained (86m),andonthesignificantoffsetsobserved withtherelativesealevelvariationcurve(15and30ka),we cansaythatonatimescaleof100,000years,themethodis difficult toapply.Because atthistime scale,thevariation amplitudesofthesealevel(theorderofonehundredmeters) remain lower compared to the margin of error (86m) appliedtoourmodel.Thetransferfunctioncouldthereforebe Fig.6.Correlationformodelswiththeuseofonetosixmaincomponents(fromtoplefttobottomright).Calibrationset:cal.1.Reference(blue),calibration (green),andvalidation(red).
Fig.7.Correlationformodelswiththeuseofonetosixmaincomponents(fromtoplefttobottomright).Calibrationset:cal.2.Reference(blue),calibration (green)andvalidation(red).
Fig.8.Performanceoftheselectedmodel:correlationbetween‘‘true’’depthsandmodelleddepths.
Fig.9.Modelstructure:coefficientsandvarianceperspecies.
Fig.10.Characterizationofthepaleo-depthvariationduringthelast500,000years.Comparisonbetween:A,therelativesealevelvariationcurve(Rohling etal.,2009);B,thecurveofvariationofthemodelledpaleo-depths;CandD,curvesofchangesinoxygenisotopicratioofbenthic(Cibicideswuellerstofiand Cibicidespachyderma)andplanktonic(Globigerinabulloides)foraminifers.
moresuitableonamillion-yeartimescaleinwhichsealevel variationsare recordedwithlarger amplitudesandwhere isotopesaredifficulttouse.
5. Conclusion
Depth modelling using 33 species of recent benthic foraminifers in the East Corsicamargin was basedon a principalcomponentanalysis(PCA)thatallowsustoobtain the model H(i)=109.6103+C1F1(i)+C2F2(i)+...+ C33F33(i)withacorrelationof97.1%.Theapplicationof thismodelonfossilbenthicforaminifers conductstothe establishment of a paleo-depth variation curve with a marginoferrorof86m.Theresultingsea-levelvariation curveshowssignificantshiftsduringhighsealevels,which could partly be explained by the significant evolution of trophicconditionsduringinterglacialperiods.Thismarginof error and this offset can be indicators of the limit of application ofthis transferfunction on a scaleof 100,000 yearswherethesealevelvariationamplitudesareintheorder ofahundredmeters.Ontheotherhand,onamillion-year scalethatischaracterizedbyvariationwithlargeramplitudes,
thismodelcouldprovideaninterestingestimation.Inorderto reducethemarginoferrorandtoavoidasignificantsignal disturbance, it is necessary to take into account, in the function of transfer, the environmental parameters, in particulartheconcentrationandqualityoftheorganicmatter and other nutrients that largely affect the bathymetric distributionofbenthicforaminifers.
Thispaperisinvitedintheframeofthe2017Prizesof theFrenchAcademyofSciences(‘‘bourseLouis-Gentilde l’Acade´miedessciences’’).IlhasbeenreviewedbyPhilippe Janvier,DominiqueGibert,andVincentCourtillot.
Supplementarydataassociatedwiththisarticlecanbe found,in theonlineversion,at https://doi.org.10.1016/j.
crte.2018.09.003.
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