Shallow-water-records-of-astronomical-forcing-and-

GEOLOGY,May2011491ABSTRACTThetranslationofclimatesignalsintosedimentsisacomplexandpoorlyunderstoodprocess,andonethatislikelytobeinherentlynonlinear.Agreatdealofdebateconcernsthemismatchbetweentheamplitudespectrumofastronomicalinsolationforcingandtheampli-tudespectrumofclimaticsignalsderivedfromgeologicalarchives.Manyancientshallow-watersuccessions,suchasperitidalcarbon-ates,arewidelysuggestedtoshowevidenceforeccentricity-bandforcing,despiteeccentricityhavinganegligibleeffectoninsolation.Instead,eccentricitymanifestsitselfprimarilyastheamplitudemod-ulatorofprecession,whichdominatestheinsolationsignalatlowtomidlatitudes.Theappearanceanddominanceofeccentricity-bandfrequenciesinstratigraphicdatacanarise,however,withouttheneedtoappealtocomplexnonlinearitiesintheclimatesystemordeposi-tionalenvironment.Instead,eccentricityfrequencieswillappearasaconsequenceofsignal-drivennondepositionthatresultsinarecti-ficationoftheprecession-dominatedinsolationsignal.Furthermore,itcanbeshownthatthisrectificationeffectiscapableofinducingasignal-drivenmodulationofcyclethickness(i.e.,afrequencymod-ulation)thatcanleadtoasimilarrangeofcyclebundlingpatternsdocumentedfromancientshallow-watersuccessions.Numericalexperimentsusinganastronomicalinsolationsolutionasaninputsignalemphasizehoweccentricitycandominateclimaterecordsthathaveundergoneonlypartialrectification,andthatarestrati-graphicallycompleteatastronomicaltimescalesofresolution.Theseexperiments,supportedbygeologicalobservations,thusdescribeaviablemechanismcapableofexplainingtheeccentricityparadoxinancientshallow-watersuccessions,andalsoemphasizehowmeasuresofstratigraphiccompletenessatastronomicaltimescalesfurnishnoclueastothelikelyfidelityoftheactualclimateforcingrecordsortheirspectra.INTRODUCTIONTherepetitionoffaciesinancientshallow-watersuccessions,inparticularshallow-watercarbonates,isfrequentlyattributedtocyclicchangesinrelativesealevel,whichinturninfluencethetypeoffaciesdeposited.Constraintsonthetimescaleofthesefaciesrepetitionsaresometimessupportiveofanastronomicalcontroloneustasy,suggestingthatanastronomicallycontrolledclimatesignalhasbecometranslatedintoasea-levelsignal,perhapsthroughglobalicevolumemediationorviathethermalexpansionandcontractionofseawater(e.g.,Goldham-meretal.,1990;Pretoetal.,2001;Cozzietal.,2005).Thesensitivityofshallow-watersedimentationtochangesinsealevelmeansthatcyclesarecommonlydelineatedbysubaerialexposuresurfacesordiagenetichardgroundsindicativeofnondepositionand/orerosion(KoerschnerandRead,1989;Goldhammeretal.,1990;Sadler,1994;Strasseretal.,1999).Bycompilingsedimentation-ratedatafrommostlyQuater-naryshallow-watercarbonateenvironments,Sadler(1994)wasabletodemonstratethathiatusesassociatedwithastronomicallycontrolledsea-leveloscillationsaccountfor80%–90%ofthetotaldurationofacompletecycle.One-dimensionalforwardmodelingworkofCambrianshallow-watercarbonatecyclesbyKoerschnerandRead(1989)simi-larlysuggestedthatbetween60and90%ofthedurationofacompletecycleisaccountedforbyperiodsofemergence.Proofofanastronomicalcontrolonthedepositionofshallow-watercarbonates,orindeedanyfacies,requirestheaccurateandstatisticallyobjectiverecognitionoftemporallyregularfaciesoscillationswithfre-quenciesthatpertaintotheastronomicalmodel.Atlowtomidlatitudes,astronomicallycontrolledinsolationchangesaredominatedby~20k.y.(19k.y.and23k.y.)precession(e.g.,Laskaretal.,2004),withlittleornoappreciableforcingfromeither~41k.y.obliquityforcingor~100and~400k.y.eccentricityforcing.Paradoxically,however,eccentric-ityforcinginparticularappearsasadominantsignalcomponentinanumberofstudiesthathavedocumentedastronomicalforcinginancientshallow-waterenvironments(e.g.,ReinhardtandRicken,2000;Pretoetal.,2001;Cozzietal.,2005;KempandCoe,2007).Althoughboththe100k.y.short-termand~400k.y.long-termeccentricitysignalshaveonlyasmallaffectonaverageannualinsolation,thesesignalsareresponsibleformodulatingthestrength(i.e.,amplitude)ofprecession,andhaveimportanteffectsonseasonality.Basicsignalprocessingthe-orydictates,however,thatinanamplitude-modulated(AM)signal,novarianceiscontributedtothespectrumatthefrequencyofthemodulat-ingsignal(fm).Rather,powerisconcentratedatthefrequencyofthemodulated(carrier)signal(fc)itself,andatsidebandsoneithersideofthecarrierfrequencyequaltofc–fmandfc+fm(e.g.,Weedon,2003).Theparadoxofhigheccentricity-bandamplitudesinancientclimaterecordsisparticularlywellknownfromtheQuaternary(e.g.,MaslinandRidgwell,2005,andreferencestherein;Bergeretal.,2006).Explanationsforthepresenceofeccentricityoftenappealtononlinearamplificationeffectsinherentintheclimatesystem.Ithasalsobeensuggestedthatnon-linearprocessesoperatingwithineithertheclimatesystemorthedeposi-tionalsystemcanresultintherectificationofanAMsignal(RipepeandFischer,1991;Weedon,2003).Asanexample,foraninputsignalthatisamplitudemodulatedsymmetricallyaboutthemeanvalueofthecar-rier,anonlinearfunctionappliedtothissignalthatamplifieshighvaluesandsuppresseslowvaluesresultsinarectifiedoutputsignalwheretheAMenvelopesoneachsideofthesignalarenolongersymmetrical.