3.4.Traceanalysis

3.4.1.Seismicamplitudeassociatedwithwedgemodels

Widess(1973)showsthatnormalincidentacousticamplitudesandwaveformsfromanisolatedthinbedchangewiththethicknessofthebeduntilthebedreachesacertainthickness.Atthelowerthicknesslimit,theamplitudeincreasesasthethicknessincreasesbecauseofconstructivewaveletinterferenceinthethinlayer.Themaximumamplitudeoccurswhenthethicknessreachesone-fourthofthepredominantwavelength(l/4),whichiscalledthetuningthickness.Asthelayerthickenstol/2,theamplitudedecreasesuntilitreachestheoriginalnon-interferingamplitudeofthelayerre?ectioncoef?cient.

WehaveobservedamplitudechangesassociatedwithvariationsingashydratesaturationsinGC955(ZhangandMcConnell,2010).Thus,traceanalysesintermsofgashydratesaturationandfreegasandreservoirlayerthicknessareanappropriatebasisfortheinterpretationofgashydrateinthearea.AmplitudeanalysiswithrespecttovariationofgashydratesaturationandlayerthicknesshaspreviouslybeenshownbyLeeetal.(2009),amongothers,usingamodi?edBiot-Gassmanntheory.Here,wefocusmoreoninterfaceresponsesatgashydrateandgasorwatercontactsusingrockphysicsmodelsbasedoneffectivemedia(Budiansky,1965;Hashin,1962;Hill,1963)andcontactmodeltheories(Mindlin,1949;Digby,1981;Walton,1987).

Toobservetheeffectonacousticamplitudesasaproductofreservoirthicknessesandsaturationsofgas-hydrate-,free-gas-andwater-bearingsandreservoirs,weevaluatedthreesandwedgemodels,“a”,“b”,and“c”,withvariousgashydrateandfreegassaturationlevels(Fig.8).TheresultsofthethreesandwedgemodelsaredepictedinFigure9.Inmodel“a”,thehighestampli-tudesoccurwithhighhydratesaturationsinhydrate-bearingsandswiththemaximumamplitudeoccurringatapproximatelyl/4.6,wherelistheacousticwavelength(e.g.75%hydratesaturationinFigure9a).Theamplitudesstarttodecreaseatl/4.6andsigni?-cantlydecreaseasthelayerthinsbelowapproximatelyl/9.2(Fig.9a).Whenhydratesaturationdeceases,acousticblankingandaphasereversalarepredictedtooccur(notethephaseofthewaveletintherangebetween50%and0%hydratesaturation,andweakamplituderesponseat25%hydratesaturationinFigure9a).FortheRickerwavelet,l/4.6istheapparentthickness(ortuningthickness)wherethepeakandtroughofaconvolvingwaveletstarttoseparate(KallweitandWood,1982).IncontrasttotheRicker

wavelet,thetuningthicknessisl/4fortheRayleighwaveletusedinWidess’experiments(Widess,1973).

Formodel“b”,Figure9bshowsthathighamplitudesstartwithlowfree-gassaturationsandthehighestamplitudeoccursatthetuningthicknessforagivengassaturation.Comparedwithamplitudesinwatersaturatedsandsabovethetuningthickness(0%gassaturationinFigure9b),theamplitudesat25%gassaturationcanbeclearlyrecognizedatapproximatelyl/9.2.Thephasedoesnotchangesigni?cantlyasthelayerthins.

Figure9c(model“c”)showtheacousticmodelresultsofagashydratelayerwithvariablesaturationsandthicknessthatisunderlainbyafree-gas-bearingzonewithuniformfree-gassatu-rationsof30%.Thestrongamplituderesponsecanbeseenattheinterfacebetweengashydrateandfreegas,thetypeofre?ectionthatcausesaBSR.Formodel“c”,inthecaseof50%gashydratesaturation,theamplitudeatthetopofathickgashydratelayerissigni?cantlyweakerthanatthebottomofthegashydratelayer(Fig.9c).Theweakamplitudecouldeasilybemissedbytheinter-preterasthetopofthethickhighlysaturatedgashydratesandsection.

Inmodel“a”,atthetuningthickness(l/4.6),thegashydratere?ectionisseenasarelativestrongwaveformpeakattheupperboundary(bluecolor)overarelativestrongwaveformtroughatthebase(redcolor)athighgashydratesaturations(e.g.75%hydratesaturationinFigure9a).Formodel“c”containingagashydrateintervalwith30%gassaturationbeneathit,theseismicwaveformresponsesforgashydratearefairlysimilarinallfourcases(Fig.9c).However,thewaveformtroughsatthebaseboundaryarestronglyaffectedbytheseismicresponsesofthefreegasbeneaththegashydratelayer,whichshowsconstanthighamplitudesasthethicknessofthelayervaries.Thus,peaktotroughratioisagoodindicatortoseparatehydrate-bearingsand(overwater)andhydrate-over-free-gas-bearingsand.

3.4.2.Spectraldecomposition

Asdiscussedabove,spectralanalyseswereperformedonthesixzoneswithhighamplitudeanomaliesasdelineatedinFigure2todetectthicklayersofgashydrate.Conventionalthicknessanalysisbypickinghorizonscannotbeusedifpeak-troughtimeseparationlessthanthetuningthickness(Partyka,2001).Thespectraldecompositionmethod,however,isavaluabletoolwhencombinedwiththeabilitytomapthinbeds(Partykaetal.,1999;Castagnaetal.,2003).Partyka(2001)describesarobustapproachtoseismicthicknessestimationforthinbedswhereinthicknessisderivedfromamplitudesatappropriatelylowdiscretefrequencies.Thistechniqueappearstobeespeciallyusefulforidentifyinggashydratedepositsanddeterminingtheirthicknessinthisstudy.ThefundamentalprinciplesofbedthicknessestimationarepresentedbyPartyka(2005,2001).Ingeneral,thethicknessofathinbedcanbederivedinthefrequencydomainbyspectraldecompositionofseismictracesandwaveletsderivedfromthesetraces.Are?ectivityserieshasaspectralexpressioninthefrequencydomainderivedfromthespectralsignatureoftheseismictracedividedbythespectralsignatureofthewavelet.Usually,re?ectivitiesconsistofaseriesofspikesintimedomain,buttheiramplitudespectrumisbroadbandinthefrequencydomain.Theamplitudedropstozeroifthereisnore?ectivitycoef?cientorequalstrengthcoef?cientsataninterfacecouplet.Intheproposedwedgemodels,thezeroorlowamplitude?eldsindicatetheperiodicityofamplitudebands.Thethicknessofthethinbedcanbeestimatedfromtheperiodicitiesandamplitudestrengthbecausethetwo-waytraveltimethroughthethinbedisinverselyproportionaltothebedthickness(Okaya,1995).

Figure10acontainsthefrequencyresponsesofthewedgemodel“a”inFigure9acontaining75%gashydratesaturation.Figure10b

Z.Zhangetal./MarineandPetroleumGeology34(2012)119e133127

amodel“a”

SeawaterSeafloor

Distance

Water-bearingsediments

Thickness(ms)

Water-bearingsediments

Hydrate-bearingsediments

25%hydrate

50%hydrate

BSR

75%hydrate

Hydrate-bearingsediments

Water-bearingsediments

Water-bearingsediments

SeawaterSeafloorWater-bearingsediments

bmodel“b”

Distance

Water-bearingsediments

free-gas-bearingsediments

25%freegas

50%freegas

75%freegas

Thickness(ms)

free-gas-bearingsediments

Water-bearingsediments

Water-bearingsediments

SeawaterSeafloorWater-bearingsediments

cmodel“c”

Distance

Water-bearingsediments

Hydrate-25%hydrateover-gas

-bearing30%freegassediments

50%hydrate30%freegas

75%hydrate30%freegas

Thickness(ms)

Hydrate-bearingsediments

Water-bearingsediments

free-gas-bearingsediments

Figure8.Acousticwedgemodelsforhydrate-bearingsediment(a),free-gas-bearingsediment(b),andhydrate-over-free-gas-bearingsediments(c).(a)isathree-layermodelofagashydrate-bearingsandlayerinclay.(b)isathree-layermodelofagas-bearingsandlayerinclay.(c)isahydrate-bearingsandlayerwithaclaycapandfreegasbelow.Thethicknessofwedgevariesfrom0to30ms.

showsthefrequencyresponsesofthemodel“c”inFigure9cwith75%gashydratesaturationwith30%freegassaturationbelow.TheamplitudespectrumforthemodelswascomputedfromaFouriertransformationofthesyntheticseismicdataproducedbyconvolvingthere?ectivityinthemodelswitha30HzRickerwavelet.Theseimagesshowtwouniformdistributionsofelongateorcircularfeaturesthatvaryinshapeandsize.The?eldsthathaveverylowamplitudestrengthsoramplitudestrengthsclosetozerocanbeseenbetweenthetwodistributionsinFigure10a.Thefrequencyatthe?eldscorrespondstothethicknessofthebedinthewedgemodel(frequencyisinverselyproportionaltothickness).Themaximumstrengthofspectralamplitudeoccursat30Hz,whichcorrespondstothedominantfrequencyofthewavelet.

Becausewearemostinterestedinthethickgashydratelayers,theamplitudesat12Hz(Fig.10)wereselectedtoestablishrelationshipswithgashydratesaturationsandthickness(Fig.11).Attherelativelylowerfrequency,thestrengthofspectralamplitudeisrelativelystableandthestrengthincreasesmoreslowlyasthebedthicknessincreases.Themaximumbedthicknesscorrespondingtothe12HzinFigure10aisapproximately45ms(Fig.11a).

Figure11ashowsthenormalizedrelativeFourieramplitudewithrespectto12Hzfrequencyforthevariablegashydratesatu-rationinthemodel“a”discussedintheprevioussection.ThediscreteFourieramplitudesincreasewithincreasinglayerthick-nessandhydratesaturation.NotethatastraightlinehasaFourieramplitudeof300inFigure11a.Theamplitudeofthewaveletforthehydratelayerscontaining50%gashydratesaturationorlesswouldbelessthan300(Fig.11a).Thus,weconsideredtheamplitudevalueof300asareferenceamplitude,withamplituderesponsesgreaterthan300beinginterpretedasthickhighlyconcentratedgas