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seismic Interpretation

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Common techniques forquantitative seismic interpretation Until a few decadesago, it would be lheirseveral-meters-long papersections I 4 - Thereareno facts,only interpretations. lriedrith Niet:sche - 4.1 Introduction Conventionalseismicinterpretation implies picking and trackinglaterallyconsistent seismic reflectorsfor the purpose of mapping geologic structures,stratigraphyand reservoir architecture. Theultimategoalis to detecthydrocarbon accumulations, delin- eatetheir extent,andcalculatetheir volumes.Conventionalseismicinterpretationis an art that requiresskill and thoroughexperiencein geology and geophysics. Traditionally,seismicinterpretationhasbeenessentiallyqualitative.The geometrical expressionof seismicreflectorsis thoroughly mappedin spaceandtraveltime,but litfle emphasis is put on the physicalunderstanding of seismicamplitudevariations.In the last few decades,however,seismicinterpretershaveput increasingemphasison more quantitativetechniquesfbr seismic interpretation,as thesecan validate hydrocarbon anomaliesand give additional information during prospectevaluation and reservoir characterization. The most important of thesetechniquesinclude post-stackamplitucle analysis (bright-spot anddim-spotanalysis), offset-dependent amplitudeanalysis (AVO analysis), acousticandelasticimpedance inversion,andforwardseismicmodeling. Thesetechniques,if usedproperly, open up new doors for the seismic interpreter. The seismicamplitudes, representing primarilycontrasts in elasticproperties between individual layers,containinformation aboutlithology, porosity,pore-fluidtype andsat- uration,aswell asporepressure- information thatcannotbe gainedfiom conventional seismic interpretalion. - 4.2 Qualitativeseismicamplitude interpretation common for seismic interpretersto roll out with seismicdatadown the hallway, go down 168
I 169 - 4,2 Qualitative seismic amplitude interpretation on their knees,and use their coloredpencilsto interpretthe horizonsof interestrn order to map geologic bodies. Little attention was paid to amplitude variations and their interpretations. In the early 1970sthe so-called"brighrspot" techniqueproved successful in areas of theGulf of Mexico,wherebrightamplitudes would coincidewith gas-filled sands.However, experiencewould show that this techniquedid not always work. Some of the bright spotsthat were interpretedas gas sands,and subsequently drilled, were fbund to be volcanic intrusionsor other lithologies with high impedance contrastcomparedwith embeddingshales.Thesetailures were also relatedto lack of waveletphase analysis, ashardvolcanicintrusions wouldcause opposite polarityto low- impedancegas sands.Moreover, experienceshowedthat gas-filled sandssometimes could cause"dim spots,"not "bright spots,"if the sandshadhigh impedancecompared with surrounding shales. With the introductionof 3D seismicdata,the utilizationof amplitudesin seismic interpretation became much more important. Brown (see Brown et ul., l98l) was one of the pioneersin 3D seismicinterpretation of lithofaciesfiom amplitudes. The generationoftime slicesandhorizon slicesrevealed3D geologicpatternsthathadbeen impossibleto discoverfrom geometricinterpretationof the wiggle tracesin 2D stack sections.Today,the further advancein seismictechnology has provided us with 3D visualization toolswheretheinterpreter canstepinto a virtual-realityworld of seismic wiggles and amplitudes,and tracethesespatially (3D) and temporally (4D) in a way that onecould only dreamof a few decadesago.Certainly,the leapfiom the rolled-out papersectionsdown the hallways to the virtual-reality imagesin visualization"caves" is a giant leapwith greatbusiness implicationsfor the oil industry.In this sectionwe reviewthequalitativeaspects of seismicamplitudeinterpretation,beforewe dig into the morequantitative androck-physics-based techniques suchasAVO analysis, impedance inversion,andseismicmodeling,in fbllowing sections. 4.2.1 Wavelet phase andpolarity The very first issueto resolve when interpreting seismic amplitudesis what kind of wavelct we have.Essentialquestionsto ask are the fbllowing. What is the defined polarityin our case?Are we dealingwith a zero-phase or a minimum-phase wavelet? Is there a phaseshift in the data?These are not straightfbrwardquestionsto answet, becausethe phaseof the wavelet can changeboth laterally and vertically. However, therearea f'ewpitfalls to be avoided. First, we want to make surewhat the definedstandardis when processingthe data. There exist two standards. The American standarddefinesa black peak asa "hard" or "positive"event,anda white troughasa "soft" or a "negative"event.On a near-ofl.set stacksectiona "hard" eventwill correspondto an increasein acousticimpedancewith depth,whereasa "soft" eventwill correspondto a decrease in acousticimpedancewith depth. According to the Europeanstandard,a black peak is a "soft" event,whereasa
170 Gommon techniques forquantitative seismic interpretation T white trough is a "hard" event.One way to checkthe polarity of marine datais to look at the sea-floorreflector.This reflectorshouldbea strongpositivereflectorrepresenting the boundarybetweenwater and sediment. Data polarity ' Americanpolarity:An increase in impedance givespositiveamplitude.normally displayedasblackpeak(wiggle r.race) or red intensitylcolor displayt. . European (or Australian)polarity:An increase in impedance givesnegal.ive ampli- tude,normally displayedas white rrough(wiggle trace)or blue intensity(color display). (Adaptedfrom Brown.200la, 2001b) For optimal quantitativeseismicinterpretations,we shouldensurethat our dataare zero-phase. Then, the seismicpick shouldbe on the crestof the waveformconespond- ing with the peak amplitudesthat we desirefor quanrirativeuse(Brown, l99g). with today's advancedseismic interpretationtools involving the use of interactivework- stations,there exist various techniquesfbr horizon picking that allow efficient inter- pretationof largeamountsof seismicdata.Thesetechniques includemanualpicking, interpolation,autotracking, voxel tracking,and surfaceslicing (seeDorn (199g) fbr detaileddescriptions). For extraction of seismic horizon slices,autopickedor voxel-trackedhorizons are very common. The obvious advantageof autotracking is the speedand efficiency. Furthermore,autopicking ensuresthat the peak amplitude is picked along a horizon. However,one pitfall is the assumptionthat seismichorizonsare locally continuous and consistent.A lateral change in polarity within an event will not be recognized during autotracking.Also, in areasof poor signal-to-noise ratio or wherea singleevent splits into a doublet, the autopicking may fail to track the corect horizon. Not only will important reservoirparameters be neglected,but the geometriesandvolumesmay alsobe significantly off if we do not regardlateralphaseshifts.It is important that the interpreter realizesthis andreviewsthe seismicpicksfor qualitycontrol. Sand/shale cross-overs withdepth Simplerock physicsmodelingcan assistthe initial phaseof qualitativeseismicinrer- pretation,when we are uncertainabout what polarity to expectfor diff'erentlithology boundaries. In asiliciclastic environment, mostseismic reflectors will beassociated with sand-shaleboundaries.Hence,the polarity will be relatedto the contrastin impedance betweensandand shale.This contrastwill vary with depth (Chapter2). Usually, rela- tively sott sandsare fbund at relatively shallow depthswhere the sandsare unconsol- idated.At greaterdepths,the sandsbecomeconsolidatedand cemented.whereasthe 4.2.2
rmpe0ance 1 t 171 - 4.2 Qualitative seismic amplitude interpretati0n Sand versus shale impedance depth trends andseismic polarity (schematic) Sand-shale cross-over DeDth Figure 4'1 Schematic depth trends of sand andshale impeclances. Thedepth trends canvaryfiom basin to basin, andthere canbemorethanonecross-over. Localdepth trends should beestablished fordifferent basins. shalesaremainly affectedby mechanicalcompaction.Hence,cementedsandstones are normally found to be relatively hardeventson the seismic.Therewill be a correspond- ing cross-overin acousticimpedanceof sandsandshalesaswe go fiom shallowandsoft sandsto the deepand hard sandstones (seeFigure 4.1). However,the depth trendscan bemuch morecomplexthanshownin Figure4.1 (Chapter2, seeFigures2.34 and,2.35'). Shallow sandscan be relatively hard comparedwith surroundingshales,whereasdeep cementedsandstones can be relatively soft comparedwith surounding shales.There is no rule of thumb fbr what polarity to expectfbr sandsand shales.However, using rock physicsmodeling constrainedby local geologicknowledge,one can improve the understandingof expectedpolarity of seismicreflectors. "Hard" venius "soft"events During seismicinterpretation of a prospect or a provenreser"yoir sand.the following questionshouldbe one of the first to be asked:what type of eventdo we expect, a "hard" or a "soft"? [n otherwords.shouldwe pick a positivepeak,or a negative trough?lfwe havegoodwell control,thisissue canbesolvedby generating synthetic seismograms andcorrelating these with realseismicdata.If we haveno well control, we may have to guess.However. a reasonableguesscan be made basedon rock physicsmodeling.Below we havelisted some"rules of thumb" on what type of reflectorwe expectl-ordifferent geologic scenarios.
172 Common techniques forquantitative seismic interpretation T I ii ji Typical "hard"events . Veryshallowsandsat normalpressure embedded in pelagicshales . Cementedsandstone with brinesaluration . Carbonate rocksembedded in siliciclastics ' Mixecllithologies (heterolithics) like shatysands, marls.volcanic ashdeposits Typical "soft"events . Pelagic shale ' S.hallow, unconsolidated sands(anyporefluid) embedded in normallycompacted shales ' Hydrocarbon accumularions in clean.unconsolidated or poorlyconsolidated sancls . Overpressured zones Some pitfalls inconventional interpretation ' Make sureyou know the polarityof the data.Rememberthereare two different standards, the US standard andthe European standard. which areopposire. ' A hard eventcan changeto a soft laterally(i.e.. lateralphaseshifi; if thereare l:jloloCic. petrographic or pore-fluidchanges. Seismicaurotracking will norderecr these. ' A dim seismicreflector or intervalmay be significant. especially in the zoneof sand/shale impedancecross-over. AVO analysisshouldbe underraken to reveal potentialhydrocarbon accumulations. 4.2.3 Frequency andscaleeffects Seismic resolution Verticalseismicresolution isdefinedastheminimum separation between two interfaces such that we can identify two interfacesratherthan one (SherifTand Geldhart, 199-5). A stratigraphic layercanberesolvedin seismicdataif thelayerthickness is largerthan a quarterof a wavelength.The wavelengthis given by: - t / / f ( 4 . 1 ) where v is the interval velocity of the layer, and.l is the frequency of the seis- mic wave. lf the wavelet has a peak frequency of 30 Hz, and the layer velocity is 3000 m/s, then the dominantwavelengthis 100m. In this case,a layer of 25 m can be resolved.Below this thickness, we can still gain importantinfbrmationvia quan- titativeanalysisof the interference amplitude.A bed only ),/30 in thicknessmay be detectable, althoughitsthicknesscannotbedeterminedfiom thewaveshape(Sheriffand Geldhart.199-5).
173 4.2 Qualitative seismic amplitude interpretation E Layer tiickness Figure 4,2 Seismic amplitude asafunction of layer thickness fbragiven wavelength. The horizontal resolutionof unmigratedseismicdatacan be definedby the Fresnel zone. Approximately, the Fresnel zone is defined by a circle of radius, R, around a rellection point: n - Jgz G.2) where z is the reflector clepth.Roughly, the Fresnelzone is the zone from which all reflectedcontributionshave a phasedifl-erence of lessthan z radians.For a depth of 3 km andvelocity of 3 km/s, the Fresnelzoneradiuswill be 300-470 m for fiequencies ranging fiom 50 to 20 Hz. When the size of the reflector is somewhatsmaller than the Fresnelzone,the responseis essentiallythat of a diffractionpoint. Using pre- stack migration we can collapsethe difliactions to be smaller than the Fresnelzone, thusincreasing the lateralseismicresolution(SheriffandGeldhart,1995).Depending on the migration aperture,the lateral resolution after migration is of the order of a wavelength.However,the migrationonly collapses the Fresnelzonein the direction of the migration, so if it is only performed along inlines of a 3D survey,the lateral resolutionwill still be limiteclby the Fresnelzone in the cross-linedirection.The lateral resolution is also restrictedby the lateral sampling which is governedby the spacingbetweenindividual CDP gathers,usually 12.5or 18 metersin 3D seismic clata. For typical surf'ace seismicwavelengths(-50-100 m), lateralsamplingis not the limitinglactor. Interference and tuning effects A thin-layeredreservoir can causewhat is called eventtuning, which is interf'erence betweenthe seismicpulserepresenting the top of the reservoirandthe seismicpulse representingthe baseof the reservoir.This happensif the layer thicknessis lessthan a quarterof a wavelength (Widess,1973).Figure4.2 showsthe efTective seismicampli- tude as a function of layer thickness for a given wavelength, where a given layer hashigher impedancethan the surroundingsediments.We observethat the amplitude
174 Gommon techniques forquantitative seismic interpretation - increasesand becomeslarger than the real reflectivity when the layer thickness is between a half and a quarter of a wavelength.This is when we have constructive interferencebetween the top and the base of the layer. The rlaximum constructive interferenceoccurswhen the bed thicknessis equal to ),14, and this is often referred to as the tuning thickness.Furthermore,we observethat the amplitucledecreases and approacheszero for layer thicknessesbetweenone-quarterof a wavelengthand zero thickness.We refer to this as destructiveinterferencebetween the top and the base. Trough-to-peak time measurements give approximatelythe correctgrossthicknesses for thicknesses largerthana quarterof a wavelength,but no information fbr thicknesses lessthana quarterof a wavelength. The thickness of an individualthin-bedunit canbe extractedfrom amplitude measurements if the unit is thinner than about ),/4 (Sheriff and Geldhart,1995).When the layer thicknessequals)./8, Widess(1973)found that the compositeresponseapproximatedthe derivativeof the original signal.He referred to this thicknessas the theoretical threshold of resolution. The amplitude-thickness curveis almostlinearbelow ),/8 with decreasing amplitudeasthe layergetsthinner, but thecompositeresponse staysthe same. 4.2.4 Amplitude andreflectivity strength "Bright spots" and "dim spots" The first use of amplitude information as hydrocarbon indicators was in the early 1970swhen it was fbund that bright-spotamplitudeanomaliescould be associated with hydrocarbon traps (Hammond, 1974).This discovery increasedinterest in the physical propertiesof rocks and how amplitudeschangedwith difTerenttypesof rocks and pore fluids (Gardner et al., 1914').In a relatively soft sand,the presenceof gas and/orlight oil will increasethe compressibilityof the rock dramatically,the veloc- ity will drop accordingly, andthe amplitudewill decrease to a negative"bright spot." However, if the sand is relatively hard (comparedwith cap-rock),the sand saturated with brine may inducea "brighlspot" anomaly,while a gas-filledsandmay be trans- parent,causinga so-calleddim spot,that is, a very weak reflector.It is very important beforestartingto interpretseismicdatato find out what changein amplitudewe expect for different pore fluids, and whether hydrocarbonswill causea relative dimrning or brighteningcomparedwith brinesaturation. Brown (1999)states that"themostimpnr- tant seismicproperty of a reservoir is whether it is bright spot regime or tlim sltot regime." One obviousproblem in the identificationof dim spotsis thatthey areclim- they are hardto see.This issuecanbe dealtwith by investigating limited-range stacksections. A very weak near-offsetreflectormay havea correspondingstrongf'ar-oflsetreflector. However,some sands,althoughthey are significant,producea weak positivenear- offset reflection as well as a weak negativefar-offset reflection. Only a quantitative analysis of thechangein near-to far-offsetamplitude,a gradientanalysis, will be able
175 T 4.2 Qualitative seismic amplitude interpretation to reveal the sand with any considerabledegreeof confidence.This is explained in Section4.3. Pitfalls:False"bright spots" During seismicexplorationof hydrocarbons. "brighrspots"areusuallythefirsttype of DHI (direct hydrocarbonindicators)one looks for. However.therehave been severalcaseswherebright-spotanomalieshavebeendrilled.and turnedout not lo be hydrocarbons. Somecommon"falsebright spors"include: . Volcanicintrusionsand volcanicashlayers . Highly cementedsands. oftencalcitecementin thin pinch-outzones . Low-porosityheterolithicsands . Overpressured sandsor shales . Coal beds . Top of saltdiapirs Only the lastthreeon the list abovewill causethe samepolarityasa gassand.The firstthreewill causeso-called"hard-kick" amplitudes. Therefore.if oneknowsthe polariryof thedataoneshouldbeablelo discriminare hydrocarbon-associated bright spotsfrom the "hard-kick" anomalies. AVO analysisshouldpermit discrimination of hydrocarbons from coal,saltor overpressured sands/shales. A very common seismicamplitudeattributeusedamongseismicinterpreters is rellectionintensity,which is root-mean-square amplitudescalculated over a given lime window. This anributedoes not distinguishbetweennegativeand positive amplitudes; thereforegeologicinterpretation ol this attributeshouldbe madewith greatcaution. "Flat spots" Flat spotsoccur at the reflectiveboundarybetweendifferentfluids,eithergas-oil, gas- warer,or warer-oil contacts.Thesecanbe easyto detectin areaswherethebackground stratigraphyis tilted, sothe flat spotwill stick out. However,if the stratigraphyis more or less flat, the fluid-related flat spot can be difficult to discover.Then, quantitative methodslike AVO analysiscanhelp to discriminatethe fluid-relatedflat spotfrom the flarlying lithostratigraphy. One should be awareof severalpitfalls when using flat spotsas hydrocarbonindi- cators.Flat spots can be relatedto diageneticeventsthat are depth-dependent. The boundarybetweenopal-A and opal-CT represents an impedanceincreasein the same way as fbr a fluid contact, and dry wells have been drilled on diageneticflat spots. Clinoforms can appearas flat featureseven if the larger-scalestratigraphyis tilted. Other"false" flat spotsincludevolcanicsills,paleo-contacts, sheet-flood deposits and flat basesof lobesandchannels. t l
176 Common techniques forquantitative seismic interpretation - Pitfalls: False "flatspots" One of fhe bestDHIs ro look for is a flat spot,the contactbetweengasand water, gasand oil, or oil and water.However.thereareothercauses that can give riseto flatspots: . Oceanbottommultiples . Flat stratigraphy. The bases of sandlobesespecially tendto be flat. . Opal-A to opal-CTdiagenetic boundary . Paleo-contacts, eitherrelatedto diagenesis or residualhydrocarbon saturation . Volcanicsills Rigorousflat-spotanalysisshouldincludedetailedrock physicsanalysis.and for- ward seismicmodeling,aswell asAVO analysisof realdata(seeSection4.3.8). t I lt il i, Lithology, porosity and fluid ambiguities The ultimategoalin seismicexplorationis to discoveranddelineate hydrocarbon reser- voirs. Seismicamplitudemapsfrom 3D seismicdataare oftenqualitarlvel.finterpreted in termsof lithologyandfluids.However,rigorousrockphysicsmodelingandanalysis of availablewell-log data is requiredto discriminatefluid effectsquantitatively trom lithology effects(ChaptersI and 2). The "bright-spot"analysismethodhasofien beenunsuccessful becauselithology effectsratherthanfluid eff-ects setup thebright spot.The consequence is the drilling of dry holes.In orderto reveal"pitfall" amplitudeanomaliesit is essential to investigatethe rock physicspropertiesfiom well-log data.However,in newfrontier areaswell-1ogdata are sparse or lacking.This requiresrock physicsmodelingconstrained by reasonable geologicassumptions and/orknowledgeabout local compactionaland depositional trends. A common way to extractporosityfrom seismicdatais to do acousticimpedance inversion.Increasing porositycanimply reducedacousticimpedance, andby extract- ing empiricalporosity-impedance trendsfrom well-logdata,onecanestimate porosity from the invertedimpedance.However,this methodology suffersfrom severalambi- guities.Firstly, a clay-rich shalecanhavevery high porosities,evenif the permeability is closeto zero.Hence,a high-porosity zoneidentifiedby this technique may be shale. Moreover, the porosity may be constantwhile fluid saturationvaries,and one sin-rple impedance-porosity modelmay not be adequate fbr seismicporositymapping. In addition to lithology-fluid ambiguities,lithology-porosity ambiguities,and porosity-fluid ambiguities,we may have lithology-lithology ambiguitiesand fluid- fluid ambiguities.Sandand shalecan havethe sameacousticimpedance, causingno reflectivity on a near-offsetseismic section.This has beenreported in severalareas of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that fluvial channelsor turbidite channelsare dim on seismicamplitudemaps,and the
:fff!;"{riii;iiiffr ,)) )))))t)))l)))))))))f )) t))) D,D ))), )D,D D))D rr,D )r>), i)P,?),,?l? ), l?? )?i)i) p iriiiiiiii iiiii r)ii)i) ii l r l l l l i i l r l l l l l i l , Plate1,1 SeismicP-P amplitudemapovera submarine fan.The amplitudes aresensitive to lithofaciesand porefluids,but therelationvariesacrosstheimagebecause ofthe interplayofsedimentologicanddiagenetic influences. Blue indicateslow amplitudes, yellow andredhigh amplitudes. 2.9 lilllWi7", 4120 4140 41 60 41 B0 5 4200 o o 4220 4240 4260 4280 4300 VP rho*l/p Distance Plate1,30 Top left, logspenetrating a sandyturbiditesequence; top right,normal-incidence synthetics with a 50 Hz Rickerwavelet.Bottom: increasing watersaturation S* from l1a/c Lo907c(oil API 35,GOR 200) increases densityand Vp(left),giving both amplitudeandtraveltimechanges (right). 2.92 2.94 2.96 2.98 3 3.02 o E F 25 20 15 1 0 rn0
177 r 4.2 Qualitative seismic amplitude interpretation interpretationis usually that the channel is shale-filled.However, a clean sand fill- ing in the channelcan be transparentas well. A geological assessment of geometries indicating differential compactionabovethe channelmay revealthe presenceof sand. More advancedgeophysicaltechniquessuch as offset-dependent reflectivity analysis may alsorevealthe sands.During conventionalinterpretation,one shouldinterprettop reservoirhorizonsfrom limited-rangestacksections,avoiding the pitfall of missing a dim sandon a near-or full-stackseismicsection. Facies interpretation Lithology influence on amplitudescan often be recognizedby the pattern of ampli- tudes as observedon horizon slices and by understandinghow different lithologies occurwithin a depositional system.By relatinglithologiesto depositional systems we often refer to theseas lithofaciesor f-acies. The link betweenamplitudecharacteristics and depositionalpatternsmakesit easierto distinguishlithofaciesvariationsand fluid changes in amplitudemaps. Traditionalseismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon seismictraveltimes. The traditionalmethodologyconsisted of purelyvisualinspection of geometricpatterns in theseismicreflections (e.g.,Mitchum etal., 1977;Weimerand Link, l99l ). Brown et al. (1981),by recognizing buriedriverchannels from amplitude information, were amongstthe first to interpret depositionalfacies from 3D seismic amplitudes.More recentand increasinglyquantitativework includesthat of Ryseth et al. (.1998)who used acousticimpedanceinversionsto guide the interpretationof sand channels,and Zeng et al. (1996) who used forward modeling to improve the understanding of shallow marine faciesfrom seismicamplitudes.Neri (1997) used neuralnetworksto mapfaciesfrom seismicpulseshape. Reliablequantitativelithofacies predictionfiom seismicamplitudesdependson establishingalink betweenrock physics propertiesand sedimentaryfacies.Sections2.4 and2.5 demonstratedhow such links might be established.The casestudiesin Chapter5 show how theselinks allow us to predict litholacies from seismicamplitudes. Stratigraphic interpretation The subsurfaceis by nature a layered medium, where different lithologies or f'acies havebeensuperimposedduring geologic deposition.Seismic stratigraphicinterpreta- tion seeksto mapgeologicstratigraphyfrom geometricexpression of seismicreflections in traveltime and space.Stratigraphicboundariescan be definedby dilferent litholo- gies (taciesboundaries) or by time (time boundaries). Theseoften coincide,but not always. Examples where facies boundariesand time boundariesdo not coincide are erosional surfacescutting acrosslithostratigraphy,or the prograding fiont of a delta almost perpendicularto the lithologic surf'aces within the delta. Thereareseveralpittalls when interpretingstratigraphyfiom traveltimeinfbrmation. First, the interpretationis basedon layer boundariesor interf'aces, that is, the contrasts a
178 T Gommon techniques forquantitative seismic interpretation between diff'erentstrata or layers, and not the propertiesof the layers themselves. Two layers with different lithology can have the same seismic properties;hence, a lithostratigraphicboundary may not be observed.Second' a seismic reflection may occurwithout a lithologychange(e.g.,Hardage,1985).For instance, a hiatuswith no deposition within a shaleintervalcangivea strongseismicsignature because theshales above and below the hiatus have difTerentcharacteristics.Similarily, amalgamated sandscanyield internal stratigraphywithin sandyintervals,reflectingdifferent texture of sancls fiom difl-erentdepositionalevents.Third, seismicresolutioncanbe a pitfall in seismicinterpretation, especiallywhen interpretingstratigraphic onlapsor downlaps. Theseareessential characteristics in seismicinterpretation,astheycangiveinformation about the coastaldevelopmentrelated to relative sealevel changes(e.g.,Vail er ai., I977). However,pseudo-onlaps can occur if the thicknessof individual layersreduces beneath the seismicresolution. The layercanstill exist,evenif the seismicexpression yieldsan onlap. Pittalls Thereareseveral pitfallsin conventional seismicstratigraphic interpretation thatcan be avoidedif we usecomplementary quantitative techniques: . lmportantlithostratigraphic boundaries betweenlayerswith very weak contrasts in seismicpropefiiescan easilybe missed.However.if differentlithologiesare transparent in post-stack seismic data.theyarenormallyvisiblein pre-stack seismic dara.AVO analysisis a useful tool to revealsandswith impedances similar to cappingshales {seeSection 4.31. . It iscommonlybelieved thatseismic events aretimeboundaries. andnotnecessarily lithostratigraphic boundaries. For instance.a hiatuswithin a shalemay causea strongseismicreflectionif the shaleabovethe hiatusis lesscompactedthan the onc below.evenif the lithologyis the same.Rock physicsdiagnostics of well-log datamay revealnonlithologicseismicevents(seeChapter2). . Because of limited seismicresolution,falseseismiconlapscan occur.The layer maystill existbeneath resolution. Impedance inversion canimprovetheresolution. and revealsubtlesrrailgraphic featuresnot observedin the original seismicdata (seeSection 4.4). Quantitative interpretationof amplituclescan add information about stratigraphic patterns,and help us avoid someof the pitfalls mentionedabove.First, relating lithol- ogy to seismicproperties(Chapter2) canhelp us understandthe natureof reflections, and improve the geologic understandingof the seismicstratigraphy.Gutierrez (2001) showedhow stratigraphy-guidedrock physics analysisof well-log data improved the sequence stratigraphicinterpretationof a fluvial systemin Colombia using impedance inversionof 3D seismicdata.Conductingimpedanceinversionof the seismicdatawill
179 - 4,2 Qualitative seismic amplitude interpretation give us layer propertiesfrom interfhceproperties,and an impedancecross-section can reveal stratigraphicfeaturesnot observedon the original seismic section.Impedance inversion has the potential to guide the stratigraphicinterpretation,becauseit is less oscillatorythantheoriginalseismicdata,it is morereadilycorrelated to well-log data, and it tendsto averageout random noise,therebyimproving the detectabilityof later- ally weakreflections (Glucketa.,1997).Moreover, frequency-band-limited impedance inversioncanimprove on the stratigraphicresolution,andthe seismicinterpretationcan be signilicantlymodified if theinversionresultsareincludedin theinterpretationproce- dure.For brief explanationsof differenttypesof impedanceinversions,seeSection4.4. Forwardseismicmodelingis alsoan excellenttool to studythe seismicsignatures of geologicstratigraphy (seeSection4.5). Layer thickness and net-to-gross from seismic amplitude As mentioned in the previous section, we can extract layer thicknessfrom seismic amplitudes. As depictedin Figure4.2,the relationship is only linearfor thin layersin pinch-outzonesor in sheet-likedeposits,sooneshouldavoidcorrelatinglayerthickness to seismicamplitudesin areaswherethe top andbaseof sandsareresolvedasseparate reflectorsin the seismicdata. Meckel and Nath (.1911)found that, for sandsembeddedin shale,the amplitude would dependon the net sandpresent,given that the thicknessof the entire sequence is less than ).14. Brown (1996) extendedthis principle to include beds thicker than the tuning thickness,assumingthat individualsandlayersare below tuning and that the entire interval of interbeddedsandshasa uniform layering. Brown introducedthe "composite amplitude" defined as the absolutevalue summationof the top reflection amplitude and the basereflectionamplitudeof a reservoirinterval.The summationof the absolutevaluesof the top and the baseemphasizesthe eff'ectof the reservoirand reducesthe effect of the embeddingmaterial. Zeng et al. (.1996) studiedthe influenceof reservoir thickness on seismicsignaland introduced what they referred to as effectivereflectionstrength,applicableto layers thinnerthanthe tunins thickness: o . - 2 " - Z ' n . , ' Zrr (4.3) whereZ. is the sandstone impedance, 216is the average shaleimpedance and/zis the layerthickness. A morecommonwayto extractlayerthickness from seismicamplitudes is by linear regressionof relative amplitude versusnet sandthicknessas observedat wells thatareavailable.A recentcasestudyshowingtheapplicationto seismicreservoir mappingwasprovidedby Hill andHalvatis(2001). Vernik et al. (2002) demonstratedhow to estimate net-to-grossfiom P- and S- impedances fbr a turbidite system. From acoustic impedance (AI) versus shear impedance (SI) cross-plots,the net-to-grosscan be calculated with the fbllowing fbrmulas:
r 180 Common techniques forquantitative seismic interpretation E Vrung dZ N I G : A Z where V."n,lis the oil-sand fraction given bv; Kano S I - b A I - c e a t - a o where b is the averageslopeof the andz7tiiretherespective intercepts (4.-5) shaleslope(06)andoil-sandslope(b1),whereas ae in theAI-SI cross-plor. I Zrr. (44) calculationof reservoir thickness from seismicamplitude shouldbe doneonly in areaswhere sandsare expectedto be thinnerthan the tuning thickness.that is a quarterof a wavelength. andwherewell-logdatashowevidence of goodcorrelation belweennet sandlhicknessandrelativeamplirude. It canbedifficultto discriminate layerrhickness changes from lirhologyandfluid changes. In relativelysoftsands, theimpactof increasing porosityandhydrocarbon saturation tendslo increase the seismicamplitude,andthereforeworks in the same "direction"to Iayerthickness. However.in relativelyhardsands. increasing porosity and hydrocarbonsaturationLendto decrease the relaliveamplitudeand therefore work in the opposite"direction"to layerthickness. ilouo anatysis In 1984, 12 years afler the bright-spot technology became a commercial tool fbr hydrocarbon prediction, ostrander published a break-through paper in Geophl-sics (ostrander,1984).He showedthat the presence of gas in a sandcappedby a shale would causean amplitudevariationwith ofTset in pre-stackseismicdata.He alsofound thatthischangewasrelatedto thereduced Poisson's ratiocaused by thepresence ofgas. Then,theyearafter,Shuey(1985)confirmedmathematically via approximations of the Zoeppritzequations thatPoisson'sratio wasthe elasticconstantmost directlyrelated to the off.set-dependent reflectivity fbr incident anglesup to 30". AVo technology,a commercial tool for the oil industry,was born. The AVO techniquebecamevery popularin the oil industry,asonecould physicaly explaintheseismicamplitudes in termsof rockproperties. Now, bright-spot anomalies couldbe investigated beforestack,to seeif theyalsohadAVo anomalies (Figure4.3). The techniqueproved successfulin certainareasof the world, but in many casesit was not successful.The techniquesufI'eredfrom ambiguitiescausedby lithology efTects,
181 4.3 AVO analysis I Stacksection CDP locqtion . *{bu Target harizon Geolog ic interpretation Shale Sondstone with gos Aryle ol inc,d?nca Figure 4.3 Schematic illustration of theprinciples inAVOanalysis. tuning effects,and overburdeneft'ects.Even processingand acquisition effectscould causefalseAVO anomalies. But in manyo1'thefailures,it wasnot the techniqueitself thatfailed,but theuseof thetechnique thatwasincorrect.Lack of shear-wave velocity informationandtheuseof toosimplegeologicmodelswerecommonreasons fbr failure. Processingtechniquesthat aff'ectednear-ofTset tracesin CDP gathers in a difl-erent way from far-offset tracescould also createtalse AVO anomalies.Nevertheless,in the last decadewe have observeda revival of the AVO technique.This is due to the improvementof 3D seismictechnology, betterpre-processing routines, rnorefrequent shear-wavelogging andimprovedunderstanding of rock physicsproperties,largerdata capacity,more fbcus on cross-disciplinaryaspectsof AVO, and lastbut not least,mclre awareness amongthe usersof the potentialpitfalls. The techniqueprovidesthe seismic interpreterwith more data,but also new physical dimensionsthat add infbrmation to the conventionalinterpretationof seismicfacies,stratigraphyand geomorphology. In this section we describethe practical aspectsof AVO technology, the poten- tial of this technique as a direct hydrocarbon indicator, and the pitfalls associated with this technique. Without going into the theoretical details of wave theory, we addressissuesrelatedto acquisition.processing and interpretation of AVO data.For an excellent overview of the history of AVO and the theory behind this technology, we refer the readerto Castagna(1993). We expectthe luture application of AVO to CDPgather af interest CDPgather Time AVOresponseat targethorizon 0,1 -0 -0, -0
182 Common techniques forquantitative seismic interpretation - expandon today'scommonAVO cross-plotanalysisandhencewe includeoverviewsof important contributionsfrom the literature,include tuning, attenuationand anisotropy effectson AVO. Finally,we elaborateon probabilisticAVO analysisconstrainedby rock physicsmodels.Thesecomprisethemethodologies appliedin casestudiesl, 3 and4 in Chapter5. 4.3.1 Thereflection coefficient Analysis of AVO, or amplitude variation with ofTset,seeksto extractrock parameters by analyzingseismicamplitudeasa function of offset,or more corectly asa function of reflection angle.The reflection coefficient for plane elastic wavesas a lunction of reflectionangleat a singleinterfaceisdescribedby thecomplicatedZoeppritzequations (Zoeppritz,l9l9). For analysisof P-wavereflections, a well-knownapproximationis givenby Aki andRichards( 1980),assumingweaklayercontrasts: R ( 0 , ) - ; ( r , , A p I A Y p , A V s - -17,-vi) T + 2*r4 W +p'lt K (4.6) (4.1) where: sin01 I t - - Y P I L p : p z - p r L V p : V p z - V p t A V s - V s : - V s r e : ( 0 r l u ) 1 2 = e t Pr) l2 + vPt)12 + vst)12 P : ( . P z I Vp : (.Vpz V5: (V52 In the fbrmulasabove,p is the ray parameter, 01 is the angleof incidence, and02 is the transmissionangle; Vp1and Vp2arethe P-wavevelocitiesaboveand below a given interface,respectively. Similarly,V51and V5r arethe S-wavevelocities,while py and p2 aredensitiesaboveand below this interface(Figure 4.4). The approximationgiven by Aki and Richardscanbe further approximated(Shuey, r985): R(01;:, R(o) + G sin29+ F(tan2e- sin2o; where R(o):;(T.T) G::^+-'#(+.'+) :R(o) -+(:.'#) #+
183 4.3 AVO analvsis n Medium 1 (Vp1, V51, p1) Medium 2 (Vn, Vsz, Pi PS{t) Figure4'4 Reflections andtransmissions at a singleinterfacebetweentwo elastichalf-space rr-redia firr an incidentplaneP-wave.PP(i).Therewill be botha reflected p-wave,pp(r). anda transmittecl P-wave,PP(t).Notethattherearewavemocleconversions at thereflectionpoint occurrrngar nonzeroincidence angles.In additionto theP-waves, a reflectedS-wave,pS(r),anda transrnitted S-wave,PS(t),will beprodr.rced. and _ t a y P 1 r / / v D This form can be interpretedin terms of difierent angular ranges!where R(0) is the normal-incidence reflection coefficient, G describes thevariationat intermecliate offsets and is often referredto asthe AVO gradient,whereasF dominatesthe far ofTsets. near critical angle.Normally, the rangeof anglesavailablefor AVO analysisis lessthan 30-40.. Therefbre,we only needto considerthe two first terms,valid fbr anslesless than.l0 tShuey. I985,1: R ( P ) = R ( 0 ) + G s i n 2 d (4.8) The zero-oft'set reflectivity,R(0), is controlledby the contrastin acousticimpedance acrossan interface.The gradient,G, is more complex in terms of rock properties,but fiom the expressiongiven abovewe seethat not only the contrastsin Vp and density afrect the gradient, but also vs. The importanceof the vplvs ratio (or equivalently the Poisson'sratio) on the ofTset-dependent reflectivity was first indicatedby Koefoed (1955).ostrander(1984) showedthat a gas-filledfbrmation would havea very low Poisson's ratio comparedwith the Poisson's ratiosin the surrounding nongaseous fbr- mations.This would causea significantincreasein positiveamplitudeversusangle at the bottomof the gaslayer,anda significantincrease in negativeamplitudeversus angleat the top of the gaslayer. Theeffectofanisotropy Velocity anisotropyoughtto be takeninto accountwhen analyzingtheamplitudevaria- tionwith offset(AVO) response of gassands encased in shales. Althoughit is generally PP(r) 4.3.2 * d
184 - Common techniques forquantitative seismic interpretation thought that the anisotropyis weak (10-20%) in most geological settings(Thomsen, 1986), some eff'ectsof anisotropy on AVO have been shown to be dramatic using shale/sand models(Wright, 1987).In somecases, the signof the AVO slopeor rateof changeof amplitudewith ofliet canbe reversedbecauseof anisotropyin the overlying shales (Kim et al.,1993 Blangy,1994). The elasticstiffnesstensorC in transversely isotropic(TI) mediacanbe expressed in compactform asfbllows: C - C l (c11- 2C66) C r : 0 0 0 I (Ctt - 2Coo) C t r C r : 0 0 0 - Cn) Cr: 0 C n 0 C:: 0 0 C++ 0 0 0 0 0 0 0 0 0 0 0 0 C++ 0 0 Cr,o whereC6,6, : t(Crt (4e) andwherethe 3-axis(z-axis)lies alongthe axisof symmetry. Theabove6 x 6 matrixis symmetric, andhasfiveindependent components, Crr, Crr, Cr, C++,and C66.For weak anisotropy, Thomsen(1986)expressed threeanisotropic parameters, t, y and6, asa function of the five elasticcomponents,where C l - C r a , - - 2Cr Cor, C++ 2C++ ( C r : * C + + ) 2 - ( . C y - C a l z 2C.3(Cy C++) The constants canbe seento describethe fiactional differenceofthe P-wavevelocities in the verticalandhorizontaldirections: yP(90')- vp(0') (4.l3) Vp(o') and thereforebestdescribeswhat is usually referredto as"P-wave anisotropy." In the samemanner,the constanty canbe seento describethe fiactional difference of SH-wavevelocitiesbetweenverticalandhorizontaldirections,which is equivalent to the differencebetweenthe vertical and horizontal polarizationsof the horizontally propagating S-waves: (4.10) (4. rr) (4.12)
185 r 4.3 AVO analysis V s H ( 9 0 1 - V s v ( 9 0 )7sH(90") - Vss(0') (4.14) T - Vsv(90') Vsn(0') The physicalmeaningof 6 is not as clearas s and y, but 6 is the most important parameterfbr normal moveout velocity and reflectionamplitude' Under the plane wave assumption,Daley and Hron (1911) derived theoreticalfbr- mulas for reflection and transmissioncoefficientsin Tl media.The P-P reflectivity in the equationcan be decomposedinto isotropic and anisotropicterms asfollows: Rpp(0): Rrpp(O) * R'rpp(0) (4.1s) Assumingweak anisotropyanclsmalloffsets,Banik ( 1987)showedthatthe anisotropic term canbe simply expressed asfbllows: sin2e Repp(d)- - Ad Blangy (lgg4) showedthe effectof a transverselyisotropicshaleoverlying anisotropic gas sand on offset-dependentreflectivity, for the three different types of gas sands. He found that hard gas sandsoverlain by a soft TI shaleexhibited a larger decrease in positive amplitude with offset than if the shalehad been isotropic. Similarly, soft gassan4soverlain by a relatively hard TI shaleexhibited a largerincreasein negative amplitude with offset than if the shalehad beenisotropic. Furthermore,it is possible fbr a soft isotropic water sand to exhibit an "unexpectedly" Iarge AVO eff'ectif the overlyingshaleis sufficientlyanisotropic' TheeffectoftuningonAVO As mentioned in the previous section,seismicinterf'erence or eventtuning can occur asclosely spacedreflectorsinterferewith eachother.The relativechangein traveltime betweenthe reflectorsdecreases with increasedtraveltime and off.set.The traveltime hyperbolasof the closely spacedreflectorswill thereforebecomeevencloserat larger ofTsets.In f-act,the amplitudes may interfere at large ofTsetseven if they do not at small offsets.The effectof tuning on AVO hasbeendemonstrated by Juhlin andYoung ( 1993),Lin andPhair( 1993),BakkeandUrsin(1998),andDong (1998),amongothers. JuhlinandYoung(1993)showedthatthin layersembedded in a homogeneous rock can producea significantly different AVO responsefiom that of a simple interfaceof the samelithology. They showedthat,for weakcontrastsin elasticpropertiesacrossthe layer boundaries,the AVO responseof a thin bed may be approximatedby modeling it as an interferencephenomenonbetweenplane P-wavesfiom a thin layer' ln this casethin-bed tuning affectsthe AVO responseof a high-velocity layer embeddedin a homogeneousrock more than it affectsthe responseof a low-velocity layer. (4.I6) 4.3.3 l
186 Common techniques forquantitative seismic interpretation Lin andPhair( 1993)suggested thefollowing expression for theamplitudevariation with angle(AVA) response of a thin layer: Rr(0): rr.roA?'(0) cosd' R(6) where a.re is the dominant frequencyof the wavelet, Af (0) is the two-way traveltirne at normal incidencefiom the top to the baseof the thin layer,andR (0) is the reflection coefficientfiom the top interface. Bakkeand Ursin ( 1998)extended the work by Lin andPhairby introducingtuning correctionfactorsfbr a generalseismicwaveletas a functionof offset.If the seismic response fiom the top of a thick layeris: (4.11) (4.l8) theseismic (4.19) ( 4 ) t d(t, t') : R(t')p(r) where R(,1') is the primary reflection as a function of ofTset.t',andp(0 is pulseasa flnction of time /, thenthe response from a thin layeris tl(r, y) f(.y)AI(0)C(t")p'(t) wherep'(r) is the time derivativeof the pulse,A7"(0)is the traveltimethicknessof the thin layer at zero offset,and C (-v)is the offiet-dependentAVO tuning factor given by (4.20) where 7(0) and Z(-r')are the traveltimes atzero ofliet and at a given nonzerooffset, respectively. The root-mean-square velocity VBy5,is definedalong a ray path: c(.v):ffi[' .##"] t l ' t t ) t ' r s , . l v t t | t V R M S - J d t 0 For small velocity contrasts(Vnvs - y), the last term in equation(4.20) can be ignored,and the AVO tuning f'actorcanbe approximatedas r(0) C(r') :v ----:-- (4.22 r(,r') For large contrastin elasticproperties,one ought to include contributionsfiom P- wave multiples and convertedshearwaves.The locally convertedshearwave is ofien neglectedin ray-tracingmodeling when reproductionof the AVO responseof potential hydrocarbonreservoirsis attempted.Primaries-onlyray-tracemodeling in which the Zoeppritz equationsdescribethe reflectionamplitudesis most common.But primaries- only Zoeppritz modeling can be very misleading,becausethe locally convertedshear wavesoften have a first-order eff-ecton the seismicresponse(Simmons and Backus, 1994).lnterferencebetweenthe convertedwavesand the primary reflectionsfiom the
(1) Primaries 187 I 4,3 AVO analysis (2) Single-leg a (3)Double-leg (4)Reverberations Figure 4.5 Converted S-waves andmultiples thatmustbeincluded in AVOmodeling whenwehave thinlayers. causing these nrodes tointerfere withtheprimaries. (l) Primary reflections; (2)single-leg shear waves; (3)double-leg shear wave; and(4)primary reverberations. (After Simmons andBackus, 1994.) 7ps: transmitted S-wave converted fiomP-wave, Rsp: reflected P-wave converted fiomS-wave. etc. baseof thelayersbecomesincreasinglyimportantasthelayerthicknesses decrease. This often producesa seismogramthat is different fiom one producedunderthe primaries- only Zoeppritzassumption. In thiscase,oneshouldusefull elasticmodelingincluding the convertedwave modesand the intrabedmultiples.Martinez (1993) showedthat surface-related multiplesandP-to-SV-modeconvertedwavescaninterf-ere with primary pre-stackamplitudesandcauselargedistortionsin theAVO responses. Figure4.5 shows the ray imagesof convertedS-wavesand multiples within a layer. Structuralcomplexity, overburden and wave propagation effects onAVO Structuralcomplexity and heterogeneities at the targetlevel aswell as in the overbur- den can have a greatimpact on the wave propagation.Theseeffectsinclude focusing and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed and surf'acemultiples, P-wave to vertically polarized S-wavemode conversions,and anelasticattenuation.The offset-dependent reflectivity should be correctedfor these wave propagationeffects,via robustprocessingtechniques(seeSection4.3.6). Alter- natively, theseefTectsshould be included in the AVO modeling (see Sections4.3.7 and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor overburdeneffectsaswell ascertainacquisitioneffects(seeSectiona.3.5) by normal- izing a targethorizon amplitude to a referencehorizon amplitude.However, in more recentyearsthere have been severalmore extensivecontributionsin the literatureon amplitude-preserved imaging in complexareasandAVO correctionsdueto overburden effects,someof which we will summarizebelow. R$ 4.3.4
188 Common techniques forquantitative seismic interpretation - AVO in structurally complex areas TheZoeppritzequations assume a singleinterf-ace between two semi-infinite layerswith infinitelateralextent.In continuouslysubsidingbasinswith relativelyflat stratigraphy (suchasTertiarysediments in theNorth Sea),the useof Zoeppritzequations shouldbe valid.However,complexreservoirgeologydue to thin beds,verticalheterogeneities, faultingandtilting will violatetheZoeppritzassumptions. Resnicketat. (1987)discuss the efl'ectsof geologic dip on AVO signatures,whereasMacleod and Martin (1988) discusstheeff-ects of reflectorcurvature.Structuralcomplexity canbe accountedfor by doing pre-stack depthmigration(PSDM). However,one shouldbe awarethatseveral PSDM routinesobtain reliablestructuralimageswithout preservingthe amplitudes. Grubb et ul. (2001) examined the sensitivity both in structureand amplitr-rde related to velocity uncertainties in PSDM migratedimages.They performedan amplitude- preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO signatures they evaluated both the uncertaintyin AVO cross-plots and uncertaintyof AVO attributevaluesalonggivenstructuralhorizons. AVO effects due to scattering attenuation in heterogeneous overburden Widmaier etztl.. (1996)showedhow to correcta targetAVO response fbr athinly layered overburden. A thin-bedded overburden will generate velocityanisotropy andtransmis- sion lossesdueto scatteringattenuation,andtheseeflectsshouldbe takeninto account whenanalyzinga targetseismicreflector. They combinedthegeneralized O'Doherty- Anstey formula (Shapiroet ul., 1994a)with amplitude-preservingmigration/inversion algorithms and AVO analysisto compensatefor the influence of thin-beddedlayers on traveltimesand amplitudesof seismic data. In particr-rlar, they demonstratedhow the estimation of zero-offsetamplitude and AVO gradient can be improved by cor- recting fbr scatteringattenuationdue to thin-bed efl'ects.Sick er at. (2003) extendecl Widmaier's work andprovideda methodof compensatingfor the scatteringattenuation eflects of randomly distributed heterogeneities above a target reflector.The general- ized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent, time- harmoniceffectivetransmissivity T for scalarwaves(P-wavesin acousticI D medium or SH-wavesin elasticlD medium)andis givenby Tt II u Tue ('' l t)|ift l AL (4.23) where.fis the frequencyandn andp arethe angle-andfiequency-dependent scattering attenuationandphaseshift coefficients,respectively.The angleg is the initial angleof an incident plane wave at the top surfaceof a thinly layeredcompositestack;L is the thickness of the thinly layeredstack;ft denotes the transmissivity fbr a homogeneous isotropic ref-erence medium thatcausesa phaseshifi. Hence,the equationaboverepre- sentsthe relativeamplitudeandphasedistortionscausedby the thin layerswith regard to the reference medium.Neglectingthe quantityZowhich describes the transmission
189 4.3 AVoanalysis - responsefor a homogeneousisotropicreferencemedium (thatis, a pttrephaseshift), a phase-reduced transmissivityis defined: f ( f) o " @tf'o)+tP(l a))r (4.24) For a P-wave in an acoustic lD medium, the scatteringattenuation,cv,and the phase coefficient, B,were derivedfrom Shapiroet al. (1994b)by Widmaieret al. (1996): a(.f ,0) : | tr'oot.f' (4.25) cos2o V,f I l6n:a2f2 cos2u and r f'o2 l- B ( f . ( ) ) - " | - V r c o s eL gnz n: 7'z r 4 ) 6 r V ; + t 6 n ) 0 2 . t 2 c o r 2 e where the statisticalparametersof the referencemedium include spatial correlation lengtha, standarddeviationo, and meanvelocity Vs. The medium is modeledas a 1D random medium with fluctuating P-wave velocities that are characterizedby an exponential correlation function. The transmissivity (absolutevalue) of the P-wave decreases with increasing angleof incidence. If the uncorrected seismicamplitude(i.e.,the analyticalP-waveparticledisplace- ment) is definedaccordingto ray theory by: I U(S,G,/) : Rc-W(r - rv) v where U is the seismic trace, S denotesthe source,G denotesthe receiver,t is the varying traveltime along the ray path,Rs is the reflection coefficient at the reflection point M, y is the spherical divergencefactor, W is the soutce wavelet, and ry is the traveltime fbr the ray between sourceS, via reflection point M, and back to the receiverG. A reflectorbeneatha thin-beddedoverburdenwill havethe following compensated seismicamplitude: ur(s,G,t): fr*(t)*R. I w1r- ,r; v where thetwo-way, time-reduced transmissivity isgivenby; 4*(r) : irtrc(r)x Zsrvr(r) (4 )R (4 )q The superscriptT of Ur(S, G, r) indicatesthat thin-bedeffectshavebeenaccounted fbr. Moreover,equation(4.28)indicatesthatthesourcewavelet,W(0, is convolvedwith the transienttransmissivity both for the downgoing (i5p1) and the upgoing raypaths (f n4c)betweensource(S), reflectionpoint (M), and receiver(G). (4 )1
190 Common techniques forquantitative seismic interpretation - In conclusion,equation(4.28) representsthe angle-dependent time shift causedby transverse isotropic velocity behaviorof the thinly layeredoverburden.Furthermore,it describes thedecrease of theAVO response resultingfrom multiple scatteringadditional to the amplitudedecayrelatedto sphericaldivergence. Widmaier eI ai. ( I 995)presented similar lbrmulationsfor elasticP-waveAVO, where theelasticcorrectionformula dependsnot only on variancesandcovariances of P-wave velocity,but also on S-wavevelocity and density,and their correlationand cross- correlationfunctions. Ursin andStovas(2002)furtherextendedon theO'Doherty-Anstey fbrmula andcal- culatedscatteringattenuationfbr a thin-bedded,viscoelasticmedium. They found that in the seismicfrequencyrange,the intrinsic attenuationdominatesover the scattering attenuation. AVO and intrinsic attenuation (absorption) Intrinsic attenuation,alsoreferredto asanelasticabsorption,is causedby the fact that even homogeneoussedimentaryrocks are not perf'ectlyelastic.This effect can com- plicatetheAVO response (e.g.,Martinez, 1993).Intrinsic attenuation canbe described in terms of a transt'ertunction Gt.o, t) fbr a plane wave of angular frequency or and propagation time r (Luh, 1993): G@, i : exp(at 12Qe* i(at lr Q) ln atI tos) (4.30) where Q" is the effectivequality f'actorof the overburdenalong the wave propagation path and areis an angularreferencefrequency. Luh demonstratedhow to correct for horizontal, vertical and ofTset-dependent wavelet attenuation.He suggestedan approximate,"rule of thumb" equation to cal- culatethe relativechangein AVo gradient,6G, due to absorptionin the overburden: f t t 3G ry :-' Q" (4.31) wherei is the peak frequencyof the wavelet,and z is the zero-offsettwo-way travel time at the studiedreflector. Carcione et al. (1998) showedthat the presenceof intrinsic attenuationaffectsthe P-wavereflectioncoefficientnearthe critical angleandbeyondit. They alsofound that the combined effect of attenuationand anisotropyaff'ectsthe reflection coefficientsat non-normalincidence,but thattheintrinsic attenuationin somecasescanactuallycom- pensate the anisotropiceffects.In mostcases, however,anisotropiceffectsaredominant over attenuationeffects.Carcione(1999) furthermoreshowedthat the unconsolidated sedimentsnearthe seabottom in offshoreenvironmentscanbe highly attenuating,and that thesewaveswill for any incidenceanglehave a vector attenuationperpendicular
191 4,3 AVO analysis r 4.3.5 to the sea-floorinterf'ace. This vector attenuationwill afl'ectAVO responses of deeper reflectors. Acquisition etfects onAVO The most important acquisition eff-ects on AVO measurements include sourcedirec- tivity, and sourceand receivercoupling (Martinez,J993). ln particular,acquisition footprint is a largeproblemfbr 3D AVO (Castagna,2001). Inegular'Eoverage at the surfacewill causeunevenillumination of the subsurface. Theseeffectscanbecorrected for usinginverseoperations.Difl'erentmethodsfor this havebeenpresentedin the liter- ature(e.g.,Gassaway et a.,1986;Krail andShin,1990;CheminguiandBiondi, 2002). Chiburis' ( 1993)methodfor normalizationof targetamplitudeswith a referenceampli- tude provided a fast and simple way of corecting for certain data collection factors including sourceand receivercharacteristics and instrumentation. Pre-processing ofseismic data forAVO analysis AVO processingshouldpreserveor restorerelativetraceamplitudeswithin CMP gath- ers.This implies two goals:(1) reflectionsmust be correctlypositionedin the sub- surface;and (2) data quality should be sufficient to ensurethat reflection amplitudes contain infbrmation aboutreflectioncoefficients. AVO processing Even though the unique goal in AVO processingis to preservethe true relative amplitudes,thereis no uniqueprocessing sequence. lt dependson the complexity of the geology.whetherit is landor marineseismicdata.andwhetherthedatawill be used to extract regression-based AVO attributesor more sophisticatedelastic inversionattributes. Cambois(200l) definesAVO processing asany processing sequence thatmakes the datacompatiblewith Shuey'sequation,if that is the model usedfor the AVO inversion.Camboisemphasizes thatthis canbe a very complicated task' Factorsthatchangetheamplitudesof seismictracescanbegroupedinto Eartheffects, acquisition-relatedeffects, and noise (Dey-Sarkar and Suatek, 1993). Earth effects include sphericaldivergence,absorption,transmissionlosses,interbedmultiples, con- verted phases,tuning, anisotropy,and structure.Acquisition-relatedeft-ectsinclude sourceand receiver arrays and receiversensitivity.Noise can be ambient or source- generated. coherent or random.Processing attempts to compensate for or removethese effects,but can in the processchangeor distort relative trace amplitudes.This is an important trade-offwe needto considerin pre-processing for AVO. We thereforeneed 4.3.6
192 r Common techniques forquantitative seismic interpretation to select a basic butrobust processing scheme (e.g., ostrander, 1984; chiburis,l9g4; Fouquet, f990;Castagna andBackus, 1993; Yilma42001). Common pre-processingstepsbeforeAVO analysis Spiking deconvolution and wavelet processing In AVO analysis we normallywantzero-phase data.However,theoriginalseismicpulse is causal,usuallysomesortof minimum phasewaveletwith noise.Deconvolutionis defined as convolving the seismic trace with an inversefilter in order to extract the impulse responsefrom the seismic trace. This procedurewill restorehigh frequen- cies and thereforeimprove the vertical resolutionand recognitionof events.One can make two-sided,non-causalfilters, or shapingfilters, to producea zero-phasewavelet (e.g.,Leinbach,1995;Berkhout,1977). The waveletshapecan vary vertically (with rime), larerally(spatially),and with offset. The vertical variationscan be handledwith deterministicQ-cornpensation (see Section4.3.4).However,AVO analysisis normally carriedout within a limited time window where one can assumestationarity.Lateral changesin the wavelet shapecan be handledwith surface-consistent amplitudebalancing(e.g.,Camboisand Magesan, 1997).Offset-dependent variationsare often more complicatedto correct for, an4 are attributedto both ofl.set-dependent absorption(seeSection4.3.4), tuning efl'ects(see Section 4.3.3),andNMo stretching. NMo stretching actslikea low-pass, mixed-phase, nonstationaryfilter, andtheeff'ects arevery difficult to eliminatefully (Cambois,2001). Dong (1999) examined how AVO detectability of lithology and fluids was afl'ected by tuning and NMo stretching,and suggesteda procedurefor removing the tuning and stretchingeffectsin order to improve AVO detectability.Cambois recommendecl picking the reflectionsof interestprior to NMo corrections,and flattening them for AVO analysis. Spherical divergence correction Spherical divergence,or geometrical spreading,causesthe intensity and energy of sphericalwaves to decreaseinversely as the squareof the distancefiom the source (Newman, 1973).For a comprehensive reviewon ofTset-dependent geometricalspread- ing, seethe studyby Ursin ( 1990). Surface-consistentamplitude balancing Sourceand receivereff'ectsas well as water depth variation can produce large devi- ations in amplitude that do not coffespondto target reflector properties.Commonly, statisticalamplitude balancingis carried out both fbr time and offset. However. this procedure can have a dramatic efl'ect on the AVO parameters.It easily contributes to interceptleakageand consequentlyerroneousgradientestimates(Cambois,2000). Cambois (2001) suggestedmodeling the expectedaverageamplituclevariation with
't 193 4.3AVO analvsis n off.setfbllowing Shuey'sequation,and then using this behavior as a ret'erence for the statistical amplitudebalancing. Multiple removal One of the most deterioratingeff-ects on pre-stackamplitudesis the presenceof multi- ples.Thereareseveralmethodsof filtering awaymultiple energy,but not all of theseare adequatefor AVo pre-processing. The methodknown asfft multiple filtering, donein the frequency-wavenumberdomain,is very efficientat removing multiples,but the dip in the.l-lrdomain is very similar fbr near-offsetprimary energyandnear-offsetmultiple energy.Hence,primary energycaneasilybe removedfrom neartracesandnot from far traces,resultingin an ar-tificialAVO effect.More robustdemultiple techniquesinclude linear and parabolic Radon transform multiple removal (Hampson, l9g6: Herrmann et a1.,2000). NMO (normal moveout) correction A potential problem during AVO analysisis error in the velocity moveout conection (Spratt, 1987).When extractingAVO attributes,one assumes that primarieshavebeen completelyflattenedto a constanttraveltime.This israrely thecase,astherewill always be residualmoveout.The reasonfor residualmoveoutis almostalwaysassociated with erroneousvelocity picking, andgreatef'fortsshouklbeput into optimizing theestimated velocityfield (e.g.,Adler, 1999;Le Meur andMagneron,2000).However,anisorropy andnonhyperbolicmoveoutsdueto complexoverburclen may alsocausemisalignments betweennearandfar off.sets (anexcellentpracticalexampleon AVO andnonhyperbolic moveoutwas publishedby Ross,1997).Ursin and Ekren (1994)presented a method for analyzing AVO eff-ects in the off.setdomain using time windows. This technique reducesmoveoutelrorsandcreatesimprovedestimatesof AVO parameters. Oneshoulcl be awareof AVO anomalieswith polarity shifts(classIIp, seedefinition below) during NMO corrections,asthesecaneasilybemisinterpretedasresidualmoveouts(Ratcliffe and Adler, 2000). DMO correction DMO (dip moveout) processinggenerates common-reflection-pointgathers.It moves the reflection observedon an off'settrace to the location of the coincident source- receivertrace that would have the samereflecting point. Therefore,it involves shift- ing both time and location. As a result, the reflection moveout no longer depends on dip, reflection-point smear of dipping reflections is eliminated, and eventswith various dips have the same sracking velocity (Sheriff and Geldhart, 1995). Shang et al. (1993) published a rechnique on how to extract reliable AVA (ampli- tude variation with angle) gathers in the presenceof dip, using partial pre-stack misration.
194 Common techniques forquantitative seismic interpretation - Pre-stack migration Pre-stackmigration might bethoughtto be unnecessary in areaswherethe sedimentary sectionis relatively flat, but it is an importantcomponentof all AVO processing. Pre-stackmigration should be used on data for AVO analysiswheneverpossible, because it will collapsethe diffractionsat the targetdepthto be smallerthanthe Fresnel zoneandthereforeincrease the lateralresolution(seeSection4.2.3;Berkhout,1985; Mosher et at., 1996).Normally, pre-stacktime migration (PSTM) is preferredto pre- stackdepthmigration (PSDM), because the former tendsto preserveamplitudesbetter. However, in areaswith highly structuredgeology, PSDM will be the most accurate tool (Cambois,2001).An amplitude-preserving PSDM routineshouldthenbe applied (Bleistein, 1987;Schleicher et ctl.,l993;Hanitzsch, 1997). Migration fbr AVO analysiscan be implementedin many different ways. Resnick et aL.(1987) and Allen and Peddy (1993) among othershave recommended Kirch- hoff migration togetherwith AVO analysis.An alternativeapproachis to apply wave- equation-based migration algorithms.Mosher et al. (.1996) deriveda waveequationfbr common-angletime migration and used inversescatteringtheory (seealso Weglein, 1992'7for integration of migrationandAVO analysis (i.e.,migration-inversion). Mosher et at. (1996) usecla finite-differenceapproachfbr the pre-stackmigrations and illus- tratedthe value of pre-stackmigration fbr improving the stratigraphicresolution,data quality, and location accuracyof AVO targets. Example ofpre-processing scheme forAVO anatysis of a2lseismic line (Yilmaz, 2001.) (I ) Pre-stack signal processing (source signature processing. geometric scaling, spikingdeconvolution andspecffalwhitening). (2t Sortto CMP anddo sparse intervalvelocityanalysis. (3) NMO usingvelocityfieldfrom step2. (4) DemultipleusingdiscreteRadontransform. (5) Sort to common-offsetand do DMO correction. (6) Zero-offsetFK time migration. (7) Sort datato common-reflection-point (CRP) and do inverseNMO using the velocityfield from step2. (8) Detailedvelocityanalysisassociated with the migrateddala' (9) NMO correclionusingvelocityfield from step8. ( l0) StackCRPgathers to obtainimageof pre-stack migrated data.Removeresidual multiplesrevealed by lhe stacking. (l l) Unmigrate usingsamevelocityfieldasin step6. ( l2; Post-stack spikingdeconvolution. (13) Remigrateusingmigrationvelocityfield from step8.
195 4.3 AVO analysis E Some pitfalls inAVO interpretation due t0processing etfects . Waveletphase. The phaseof a seismicsectioncanbe significantlyalteredduring processing. lf rhephase of a sectionis notestablished by theinterpreter. thenAVO anomaliesthat would be interpretedas indicativeof decreasing impedance,for example.canbeproducedat interfaces wheretheimpedance increases (e.g.,Allen andPeddy.I993). . Multiple filtering. Not all demultiple techniquesare adequatelor AVO pre- processing. Multiple filtering,donein thefrequency-wavenumber domain,is very efficientar removing multiples.but the dip in the/-k domain is very similar for near-offsetprimary energyandnear-offsetmultiple energy.Hence,primary energy can easlly be removed from the near-offsettraces.resulting in an artificial AVO effect. . NMO correction. A potentialproblemduringAVO analysis is errorsin thevelocity moveoutcorrection(Spran.1987).When extractingAVO attributes. oneassumes that primarieshave beencompletelyflattenedto a constanttraveltime.This is rarelythecase.astherewill alwaysbe residualmoveout.Ursin andEkren(1994) presenteda method for analyzing AVO effects in rhe offset domain using time windows.This technique reducesmoveoulerrorsandcreates improvedestimates of AVO paramerers. NMO stretchis anotherproblem in AVO analysis.Because the amount of normal moveout varieswith arrival time. frequenciesare lowered at large offsets compared with short offsets. Large offsets, where the stretching effect is significant.shouldbe muted beforeAVO analysis.Swan (1991),Dong (1998)and Dong ( 1999)examinethe eft'ectof NMO stretchon offset-dependenl reflectivity. . AGC amplirude conection. Automatic gain control must be avoided in pre- processing of pre-stack databeforedoing AVO analysis. Pre-processing for elastic impedance inversion Severalof the pre-processingstepsnecessary for AVO analysisare not requiredwhen preparingdatafor elasticimpedanceinversion(seeSection4.4for detailson themethod- ology). First of all, the elasticimpedanceapproachallows for waveletvariationswith offset(Cambois,2000).NMO stretchcorrectionscanbe skipped,because eachlimited- rangesub-stack(in which the waveletcanbe assumedto be stationary)is matchedto its associated syntheticseismogram, andthis will removethewaveletvariationswith angle. It is, however,desirableto obtain similar bandwidth fbr eachinvertedsub-stackcube, since theseshould be comparable.Furthermore,the data used for elastic impedance inversionarecalibratedto well logs before stack,which meansthat averageamplitude variations with offset are automatically accountedfor. Hence, the complicated pro- cedureof reliable amplitude correctionsbecomesmuch less labor-intensivethan for
196 Common techniques forquantitative seismic interpretation - 4.3.7 u 1 0 2 0 3 0 4 0 5 0 6 0 Angle ofincidence (degree) Figure4,6 AVO curvesfbr differenthalf'-space models(i.e.,two layers oneintertace). FaciesIV is cap-rock. Inputrockphysics propertie represent meanvalues for eachfacies. standard AVO analysis. Finally,residualNMO andmultiplesstill mustbeaccounted fbr (Cambois,2001).Misalignmentsdo not causeinterceptleakageasfbr standard AVO analysis, but near-andfar-anglereflections muststill be in phase. AVO modeling andseismic detectability AVO analysisis normally carriedout in a deterministicway to predictlithology and fluidsfrom seismicdata(e.g.,SmithandGidlow, 1987;RutherfordandWilliams, 1989; Hilterman, 1990;Castagna andSmith, 1994;Castagna et al., 1998). Forward modeling of AVO responsesis normally the best way to start an AVO analysis,as a feasibility study before pre-processing,inversion and interpretationof real pre-stackdata.We show an example in Figure 4.6 where we do AVO modeling of difTerentlithofacies defined in Section 2.5. The figure shows the AVO curves for different half-spacemodels,where a silty shaleis takenasthe cap-rock with difTerent underlying lithofacies.For eachfacies,Vp, Vs, and p are extractedfrom well-log data and usedin the modeling.We observea cleansand/pure shaleambiguity (faciesIIb andfaciesV) at nearof1iets,whereascleansandsand shalesare distinguishableat far offsets.This exampledepictshow AVO is necessary to discriminatedifferentlithofacies in this case. I
-T I 197 - 4.3 AVO analysis V Hydrocarlon tr€ild Cemenled {el brino 0 Ceme|rbd w/ hydruca]ton Unconsolidaled w/ brine Unconsolidtlsd w/ hydrocarbon Figure 4.7 Schcgatic AVOcurves firrcemented sandstone andunconsolidated sands capped by shlle.frll brine-saturated andoil-saturated cases. Figure 4.7 shclwsanotherexample,where we considertwo typesof clean sands, cementedandunconsolidated,with brine versushydrocarbonsaturation.We seethat a cementedsanclstone with hydrocarbonsaturationcan have similar AVO responseto a brine-saturated. unconsolidatedsand. The examplesin Figures4.6 and 4.7 indicate how important it is to understandthe localgeologyduring AVO analysis.lt is necessary to know whattypeof sandis expected for a given prospect,and how much one expectsthe sandsto changelocally owing to textural changes,before interpretingfluid content.It is thereforeequally important to coniluctrealisticlithology substitutions in additionto fluid substitutionduring AVO rnodelingstudies.The examplesin Figures4.6 and 4.7 alsodemonstrate the impor- tanceof the link betweenrock physicsand geology (Chapter2) during AVO analysis. Whenis AVOanalysisthe appropriate technique? It is well known that AVO analysisdoes not always work. Owing to the many caseswhere AVO hasbeenappliedwithoul success, the techniquehasreceiveda bad reputationas an unreliabletool. However.part ol the AVO analysisis to find out if the techniqueis appropriatein the first place.It will work only if lhe rock physicsand ffuid characleristics of the targetreservoirareexpectedto give a good AVO response. This mustbeclarifiedbeforetheAVO analysis of realdata.Without a properfeasibility study.one can easily misinterpretAVO signatures in the real data.A good feasibilitystudycould includeboth simple reflectivitymodelingand moreadvanced forward seismicmodeling(seeSection4.51.Both thesetechniques shouldbe foundedon a thoroughunderstanding of localgeologyandpetrophysical properties. Realisticlithologysubstitution is asimportantasfluid substitution during thisexercise. CemellHion trend I I
198 Gommon techniques forquantitative seismic interpretation I 4.3.8 Often, one will find that there is a certain depth interval where AVO will work, often referredto as the "AVO window." Outside this, AVO will not work well. That is why analysis of rack physics depth trends should be an integral part of AVO analysis(seeSections2.6 and 4.3.16). However. the "AVO window" is also constrained by dataquality.With increasingdepth,absorptionof primary energy reduces the signal-to-noise ratio.higherfrequencies aregraduallymoreattenualed thanlower frequencies. the geologyusuallybecomesmorecomplexcausingmore complexwavepropagations, andtheanglerangereduces for agivenstreamer length. All thesefactorsmakeAVO lessapplicablewith increasing depth. Deterministic AVO analysis ofGDP gathers After simple half--space AVO modeling,the next stepin AVO analysisshouldbe deter- ministic AVO analysisof selectedCDP (common-depth-point)gathers,preferably at well locations where syntheticgatherscan be generatedand comparedwith the real CDP gathers. In this section,we showanexampleof how themethodcanbeappliedto discriminate lithofacies in realseismicdata,by analyzingCDP gathers atwell locations in a deterministic way. Figure 4.8 showsthe real and syntheticCDP gathersat three adjacent well locationsin a North Seafield (thewell logsareshownin Figure5.1,case study l). The figurealsoincludesthe pickedamplitudesat a top targethorizonsuper- imposed on exact Zoeppritz calculatedreflectivity curves derived fiom the well-log data. In Well 2, the reservoirsandsareunconsolidated, representoil-saturatedsands,and arecappedby silty shales.According to the saturationcurvesderivedfiom deepresis- tivity measurements, the oil saturationin the reservoirvaries from 20-807o, with an averageof about 60Va.The sonic and density logs are found to measurethe mud filtrate invaded zone (0-l0o/o oil). Hence, we do fluid substitution to calculate the seismicpropertiesof the reservoir from the Biot-Gassmann theory assuminga uni- form saturationmodel (the processof fluid substitution is describedin Chapter l). Before we do the fluid substitution, we need to know the acoustic properties of the oil and the mud filtrate. These are calculatedfrom Batzle and Wang's relations (seeChapter l). For this case,the input parametersfor the fluid substitutionare as fbllows. oilGoR Oil relative density Mud-filtrate density Pore pressure atreservoir level Temperature atreservoir level 64 UI 32APT 1.09g/cm3 20 MPa 77.2',C
-v i 199 4.3 AVO analysis - Well 3 0 323 726 1210 1694 2177 CDP ] OFF t Relleclvity Rel ectivity 0 100 0 050 0 050 0 - weill i'. - r -r;r! . 1 ' ' , . P B 0.r00 0.050 Well3 : 0 1 0 0; : I I 0.050 ! : '. 0 i : : 0 0 5 0 i n n q n I ' - I l'o" .. 0 r00 l 0 150 Angle 0 1 14 21 28 34 (deq) Anqle 0 8 l5 22 29 (deg) Angle 0 1 14 20 26 32 (deg) Figure4.8 RealCDP gathers(upper),syntheticCDP gathers(middle),andAVO curvesfor Wells I 3 (lower).
200 Common techniques lorquantitative seismic interpretation I The correspondingAVO responseshowsa negativezero-ofTset reflectivity and a neg- ativeAVO gradient.In Well l, we havea water-saturated cementedsandbelow a silty shale.The correspondingAVO responsein this well showsa strongpositivezero-ofl.set reflectivity and a relatively strong negativegradient.Finally, in Well 3 we observea strongpositivezero-offsetreflectivity anda moderatenegativegradient,corresponding to interbeddedsand/shale faciescappedby silty shales.Hence,we observethreedistinct AVO responsesin the three different wells. The changesare relatedto both Iithology and pore-fluid variations within the turbidite system.For more detailed information aboutthis system,seecasestudy I in Chapter5. Avsethet al. (2000)demonstratedthe etlect of cementationon the AVO responsein real CDP gathersaroundtwo wells, one where the reservoirsandsare friable, and the other where the reservoir sandsare cemented.They found that if the textural eflects of the sandswere ignored,the correspondingchangesin AVO responsecould be inter- pretedas pore-fluidchanges, just as depictedin the reflectivitymodelingexamplein Figure4.7. lmpodance0f AVOanalysisof individualCDPgathers Investigations of CDP gathersare importanlin order ro confirm AVO anomalies seenin weightedstacksect.ions (Shuey:s intercepr andgradient,SmithandGidlow's fluid factor.etc.).The weightedstackscan containanomaliesnot relatedto true offset-dependent amplitudevariations. 4.3.9 Estimation ofAVO parameters Estimating intercept and gradient The next stepin an AVO analysisshouldbe to extractAVO attributesanddo multivari- ate analysisof these.Severaldifferent AVO attributescan be extracted,mappedand analyzed.The two most importantonesarezero-offsetreflectivity (R(0)) andAVO gra- dient(G) basedon Shuey'sapproximation. Theseseismicpararneters canbe extracted, via a least-squares seismicinversion,for eachsamplein a CDP gatherovera selected portionof a 3D seismicvolume. For a given NMO-conected CDP gather, R(/,,r), it is assumed that for each time sample, /, the reflectivity data can be expressedas Shuey's formula (equation (4.8)): R(r, r) : R(/,0) + c(/) sin2g(r, -r) (4 7 ) where 0(r, x) is the incident angle correspondingto the data sample recorded at (t.r).
201 - 4.3 AVO analysis For a layeredEarth,the relationshipbetweenofliet (r) andangle(0) is givenapprox- imatelyby: r VrNr (4.33) sin0(r,x) I k3+x2fvi^)tt2 where VrNr is the interval velocity and Vnr,,rs is the averageroot-mean-square veloc- ity, as calculated from an input velocity profile (fbr example obtained from sonic log). For any given valueof zero-offsettime, /e,we assumethatR is measuredat N offsets (xi, i:1, A/).Hence,we canrewritethe definingequationfbr this time as(Hampson andRussell.1995): t t 2 YRMS R(.rr) R(xz) sin2o(4 xr) sin2g(r,,rz) Inmor-l I c u r I (4.34) N equationsin the two equationis obtainedbY R(r,r,) I sin2g(r, ,rr,') This matrix equationis in the form of b: Ac and represents unknowns,R(/, 0) and G(r).The least-squares solutionto this solvingthe so-called"normal equation": c: (ArA)-1(ATb) (4.3s) usthe least-squares solutionfbr R(0) andG at time t. Inversion for elastic Parameters Going beyond the estimationof interceptand gradient,one can invert pre-stackseis- mic amplitudesfor elasticparameters, including Vp, V5anddensity.This is commonly ref'erredto asAVO inversion,and can be performedvia nonlinearmethods(e'g.,Dahl ancl Ursin. 19921 Bulandetal., 1996;GouveiaandScales,1998)or linearizedinversion methods(e.g.,Smith and Gidlow, 1987;Loertzerand Berkhout,1993).Gouveiaand Scales( 1998)clefined a Bayesiannonlinearmodelandestimated, via a nonlinearcon- jugate gradient method, the maximum a-posteriori(MAP) distributionsof the elastic parameters.However, the nonlinearity of the inversion problem makestheir method very compurerintensive.LoertzerandBerkhout ( 1993)performedlinearizedBayesian inversion basedon single interfacetheory on a sample-by-samplebasis.Buland and Omre (2003) extendedthe work of Loertzer and Berkhout and developeda linearized BayesianAVO inversion method where the wavelet is accountedfor by convolution. The inversionis perfbrmedsimultaneously fbr all timesin a giventime window,which ^
202 r Common techniques forquantitative seismic interpretation makes it possibleto obtain temporal correlation betweenmodel parametersclose in time. Furthermore,they solved the AVO inversion problem via Gaussianpriors and obtainedan explicit analyticalform for the posteriordensity,providing a computation- ally fastestimationof the elasticparameters. Pittalls ofAVO inversion . A linearapproximation of theZoeppntzequations is commonlyusedin thecalcu- lationof R(01andG. The two-termShueyapproximationis known lo be accurate for anglesof incidenceup to approximately 30'. Make surethatthe datainverted do not exceedthis range,so the approximalionis valid' . The Zoeppritzequations areonly valid fbr singleinterfaces. lnversionalgorithms thatarebasedon theseequations will not be valid lor thin-bedded geology. . The linear AVO inversionis sensitiveto uncharacteristic amplitudescausedby noise(includingmultiples.) or processing and acquisirioneffects.A few outlying valuespresent in thepre-stack amplitudes areenoughto causeerroneous estimates of R(0) and G. Mosr commercialsoftwarepackagesfor eslimationof R(0) and C applyrobusr estimarion techniques (e.g.,Walden.199l) to limit thedamage ol' outlying amPlitudes. . Another potential problem during sample-by-sample AVO inversionis errors in the moveoutcorrection(Spratt, 1987l. Ursin and Ekren (1994) presented a method for analyzingAVO eflects in the offset domain using time windows. This techniquereducesmoveouterrorsand createsimprovedestimates oi AVO parameters. 4,3.10AVO cross-Plot analysis A very helpful way to interpretAVO attributesis to makecross-plotsof intercept(R(0)) versusgradient(G).Theseplotsarea veryhelpfulandintuitiveway of presenting AVO data,and can give a better understandingof the rock propertiesthan by analyzingthe standardAVO curves. AVO classes RutherfordandWilliams ( 1989)suggested a classification schemeof AVO responses fbr 6iflerent typesof gassanils(seeFigure 4.9). They definedthreeAVO classes based on wherethe top of the gassandswill be locatedin an R(0) versusG cross-plot. The cross-plotis split up into fbur quadrants. In a cross-plotwith R(0) along.r-axisand C along,v-axis, the I stquadrantis whereR(0) andG arebothpositivevalues(upperright quadrant). The2ndis whereR(0)is negative andG is positive(upperleft quadrant). The 3rd is whereborhR(0) andG arenegative(lower left quadrant).Finally,the4th quadrant is where R(0) is positive and G is negative(lower right quadrant).The AVO classes
203 I- 4.3 AVoanalysis Tabfe 4.1AVO classes, after Ruthe(brd and Williams (1989)' extendecl b1'Castagnaand Smith (1994),and Rossand Kinman( 1995) Class RelativeimPedance Quadrant R(0) G AVO product High-impedance sand No or low contrast Low impedance Low impedance 4th ,lth 3rd 3rd 2nd Negative Negative Positive Positive Negative class lll t a t -- Ictass tt t.. ' r O D 1 I cra.i rrp I crass r [ - Figure 4,9 Ruthertbrd andwilliamsAVOclasses, originally defined forgassands (classes I, ll and III),along withtheadded clnsses IV (Castagna andSmith. 1994) andIIp(Ross andKinman' 1995)' Figure isaclapted fiomCastagna etal.(1998)' must not be confused with the quadrantnumbers.Class I plots in the 4th quadrant with positiveR(0) and negativegradients.Theserepresenthard eventswith relatively high impedanceand low vp/vs ratio comparedwith the cap-rock.class II represents sandswith weak interceptbut strong negatjvegradient.Thesecan be hard to seeon the seismic data, becausethey often yield dim spots on stackedsections'Class III is the AVO categorythat is normally associatedwith bright spots'These plot in the 3rd quadrantin R(0)-G cross-plots,and are associated with soft sandssaturatedwith hydrocarbons (seePlate4.l0). Rossand Kinman (1995) distinguished betweena classIIp and classII anomaly' ClassIIp hasa weak but positive interceptand a negativegradient,causinga polarity changewith oflset. This classwill disappearon full stacksections.class II hasa weak but negativeinterceptand negativegraclient,henceno polarity change.This classmay be observedasa negativeamplitudeon a full-ofliet stack' Castagnaand Swan (1997) extendeclthe classificationschemeof Rutherford and Williams to incluclea 4th class,plotting in the 2n<1 quadrant.Thesearerelatively rare' but occur when soft sandswith gas are cappedby relatively stiff shalescharacter- ized by Vp/Vs ratios slightly higher than in the sands(i'e" very compactedor silty shales).
204 Gommon techniques forquantitative seismic interpretation : Summary ofAVO classes ' AVOclassI represents relativelyhardsands with hydrocarbons. Thesesands tendl"o plotalongthe background trendin intercept-gradient cross-plots. Moreover,very hardsandscan have little sensitivityto fluids.so theremay not be an associated flat spot.Hence.thesesandscan be hardto discoverlrom seismicdata. . AVo classII. representing transparent sandswith hydrocarbons, oftenshowup as dim spotsorweaknegativereflectorson theseismic. However. becauseof relatively largegradients. they shouldshow up as anomaliesin an Rt0)-c cross-plot.and plot off the backgroundtrend. ' AVO classIII is the"classical"AVO anomalywith negative intercept andnegative gradient.This class represents relativelysoft sandswirh high fluid sensitivity, locatedfar awayfrom the background trend.Hence,theyshouldbe easyro derect on seismic data. ' AVO classIV aresands with negative intercept butpositivegradient. Thereflection coefficientbecomeslessnegaLive with increasing offset,andamplitudedecreases versusoffset.eventhoughLhese sandsmay be bright spots(castagnaand Swan. 1997).ClasslV anomalies arerelativelyrare,but occurwhen soft sandswith gas arecappedby relativelystiffcap-rockshales characterized by vplvs ratiosslightly higherthanin thesands (i.e..verycompacted or siltyshales). The AVo classes were originally definedfor gassands.However.todaythe AVo classsystemis usedfor descriptiveclassification of observedanomaliesthal are not necessarily gassands.An AVO classIl that is drilled can turn out to be brine sands.It does not mean that the AVo anomaly was not a class ll anomaly.we therefbresuggestapplyingtheclassification only asdescriptive termsfor observed AVo anomalies, without aulomaticallyinferringthat we are dealingwith gas sands. AVO trends and the effects of porosity, lithology and compaction When we plot R(0) andG ascross-plots,we can analyzethetrendsthatoccurin termsof changes in rock physicsproperties, includingfluid trends, porositytrendsandlithology trends,as thesewill have differentdirectionsin the cross-plot(Figure4.1l). Using rock physicsmodelsand then calculatingthe corresponding interceptand gradients, we can study various"What lf" scenarios,and then comparethe modeledtrendswith the inverteddata. Brine-saturatedsandsinterbeddedwith shales,situatedwithin a limited depthrange andat a particularlocality, normally follow a well-defined"backgroundtrend" in AVO cross-plot (Castagnaand Swan, 1991). A common and recommendedapproach in qualitativeAVO cross-plotanalysisis to recognizethe "background" trend and then look fbr datapoints that deviatefrom this trend.
205 r 4,3 AVO analysis FigUre 4.11Difl'erent trends occurring in anintercept gradient cross-plot' (Adapted fiomSimm etal.,2O0O.) Castagnaet at. (1998) presentedan excellentoverview and a fiamework for AVO gradientand interceptinterpretation.The top of the sandswill normally plot in the 4th quadrant,with positiveR(0) andnegativeG. The baseof the sandswill normally plot in the 2ndquadrant,with negativeR(0) andpositiveG. The top andbaseof sands,together with shale-shaleintertaces,will createa nice trend or ellipse with centerin the origin of the R(O)-G coordinatesystem.This trend will rotate with contrastin Vp/V5 ratio betweena shalycap-rockancla sandyreservoir(Castagna et al., 1998;Sams' 1998)' We can extractthe relationshipbetweenVplVs tatio and the slopeof the background trencl(a6)by clividingthe gradient,G, by the intercept,R(0): G R(0) Assuming the density contrastbetween shaleand wet sandto be zero, we can study how changinE VplVs ratio affectsthe backgroundtrend.The densitycontrastbetween sandandshaleat a givendepthis normallyrelativelysmallcompared with the velocity contrasts (Fosteret a.,1991).Thenthe backgroundslopeis givenby: . ^ l - ( V s r * Y s 2 ) A Y s l u h - I " L t Y nt V p : t A V p l (4..r7) where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir, respectively;Vs1and V52are the correspondingS-wavevelocities,whereasAVp and AV5 arethe velocity differencesbetweenreservoiranclcap-rock.If the Vp/V5 ratio is 2 in the cap-rock and 2 in the reservoir,the slopeof the backgroundtrend is - l, that is a 45' slopediagonalto the gradientand interceptaxes.Figure 4'12 showsdifferent lines correspondingto varying Vp/V5 ratio in the reservoirand the cap-rock. The rotation of the line denoting the backgroundtrend will be an implicit function of rock physics propertiessuch as clay content and porosity.Increasingclay content (4.36)
VplVs=2.5 incaP-rock 206 Common techniques forquantitative seismic interpretation - 0 B(0) -0.5L -0.5 Figure4,12 BackgroundtrendsinAVOcross-plotsasafunctionofvaryingVplV<ralioincap-rock andreservoir. (Weassume nodensity contrast.) Notice thataVplVsratioof 1.5in thereservoir can have diff'erent locations in theAVOcross-plot depending onthecap-rock VplV5ratio. Ifthe Vp/V5 ratioof thecap-rock is2.5,thesand will exhibit AVOclass ll to III behavior (lefi),whereas if the cap-rock Vp/V5 ratiois2.0, thesand will exhibit class I toIIpbehavior (right). at a reservoirlevel will causea counter-clockwise rotation,as the Vp/V5 ratio will increase.Increasing porosity related to less compaction will also cause a counter- clockwise rotation, as less-compactedsedimentstend to have relatively high VplVg ratio. However,increasingporosityrelatedto lessclay contentor improved sortingwill normally causea clockwise rotation, as clean sandstend to have lower Vp/V5 ratio than shaly sands.Hence,it can be a pitfall to relateporosity to AVO responsewithout identifying the causeof the porosity change. Thebackground trendwill change with depth,buttheway it changes canbecomplex. Intrinsicattenuation, discussed in Section4.3.4(Luh, 1993),will afI-ect thebackground trendasa function of depth,but correctionshouldbe madefbr this beforerock physics analysisof the AVO cross-plot(seeSection4.3.6).Nevertheless, the rotationdue to depth trends in the elastic contrastsbetweensandsand shalesis not straightforward, because theVplVs in the cap-rockas well as the reservoirwill decrease with depth. Thesetwo efTects will counteracteachother in termsof rotationaldirection. asseenin Figure4.12.Thus,therotationwith depthmustbeanalyzed locally.Also, thecontrasts betweencap-rock and reservoir will changeas a function of lithology, clay content, sorting,and diagenesis,all geologic factorsthat can be unrelatedto depth.That being said,we shouldnot includetoo largeadepthintervalwhenwe extractbackgroundtrends (Castagna and Swan, 1997).That would causeseveralslopesto be superimposed and resultin a lessdefinedbackgroundtrend.For instance,note that the top of a soft sand will plot in the 3rd quadrant, while thebaseof a softsandwill plot in the I st quadrant, giving a backgroundtrendrotatedin the oppositedirectionto the trendfor hard sands. VplVs=2.Q incaP-rock
T 207 r 4.3 AVO analysis Fluid effects and AVO anomalies As mentionedabove,deviationsfiom thebackgroundtrendmay be indicativeof hydro- carbons,or somelocal lithology or diagenesiseffectwith anomalouselasticproperties (Castagnaet at., 1998).Fosteret al. (1991)mathematicallyderivedhydrocarbontrends that would be nearly parallel to the backgroundtrend,but would not passthrough the origin in R(0) versusG cross-plots.For both hard and soft sandswe expectthe top of hydrocarbon-filleclrocks to plot to the left of the backgroundtrend, with lower R(0) and G valuescomparedwith the brine-saturated case.However,Castagnaet al. (1998) fbund that,in particular,gas-saturated sandscould exhibit a variety of AVO behaviors. As lisredin Table4.1. AVO classIII anomalies(Rutherfordand Williams, 1989), representingsoft sandswith gas,will fall in the 3rd quadrant(the lower left quadrant) and havenegativeR(0) and G. Theseanomaliesarethe easiestto detectfiom seismic data(seeSection 4.3.1l). Harclsandswith gas,representing AVO classI anomalies,will plot in the4th quadrant (lower right) and have positive R(0) and negativeG. Consequently,thesesandstend to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented), they will not show a large changein seismicresponsewhen we go from brine to gas (cf. Chapterl). This type of AVO anomalywill not showup asananomalyin a product stack. In fact, they can plot on top of the background trend of some softer, brine- saturatedsands.Hence,very stifTsandswith hydrocarbonscanbe hardto discriminate with AVO analysis. AVO classII anomalies,representingsandssaturatedwith hydrocarbonsthat have very weak zero-offsetcontrastcomparedwith the cap-rock, can show great overlap with thebackground trend,especially if thesandsarerelativelydeep.However,classII type oil sandscanoccurvery shallow,causingdim spotsthatstickout comparedwith a bright backgroundresponse (i.e.,when heterolithicsand brine-saturated sandsare relatively stifTcomparedwith overlying shales).However,becausethey are dim they areeasyto miss in near-or full-stack seismicsections,andAVO analysiscantherefore be a very helpful tool in areaswith classII anomalies. Castagnaand Swan (199'l) discovereda diff'erenttype of AVO responsefor some gas sands,which they ref-erredto as class IV AVO anomalies(see Table 4.l), or a "false negative."They found that in some rare cases,gas sandscould have negative R(0) and positive G, henceplotting in the 2nd quadrant(upper left quadrant).They showedthatthis may occur if the gas-sandshear-wave velocity is lower thanthat of the overlyingformation.The mostlikely geologicscenario for suchanAVO anomalyis in unconsolidatedsandswith relativelylarge VplVs ratio(Fosteret crl.,1997).That means that if the cap-rockis a shale,it must be a relativelystiff and rigid shale,normally a very silt-rich shale.This AVO responsecanconfusethe interpreter.First, the gradients of sandsplotting in the 2nd quadranttend to be relatively small, and lesssensitiveto fluid type thanthe gradientsfor sandsplotting in the 3rd quadrant.Second,theseAVO anomalieswill actually showup asdim spotsin a gradientstack.However,they should a
208 Common techniques forquantitative seismic interpretation - standout in an R(0)-G cross-plot,with lower R(0) valuesthan the backgroundtrend. Seismically, they shouldstandout asnegative bright spots. Pitfalls . Differentrockphysicstrencls in AVO cross-plots canbeambiguous. Theinterpreta- tion of AVO trendsshouldbebasedon locallyconstrained rock physicsmodeling. not on naiverulesof thumb. . Trendswithin individualclustersthatdo not projectthroughtheorigin on an AVO cross-plol. cannot always be interpretedas a hydrocarbonindicatoror unusual lithology.Sams(1998) showedthat it is possiblefortrends to have largeoffsets from the origin evenwhen no hydrocarbons are presentand the lithology is not unusual.Only where the rocks on eitherside of the reflectingsurfacehave the sameVp/V5 ratio will the lrends(not to be confusedwith backgroundlrendsas shownin Figure4. l2.l projectthroughthe origin. Samsshowedan exampleof a brinesandthatappeared moreanomalous thana Iessporoushydrocarbon-bearing sand. . Residualgassaturation can causesimilar AVO effectsro high saturations of gas or light oil. Three-termAVO wherereliableestimates of densityareoblained.or attenuation attributes. can potentiallydiscriminateresidualgas saturations from commercialamountsof hydrocarbons (seeSections 4.3.12 and4.3.|5 for further discussions). Noise trends A cross-plot betweenR(0) andG will alsoincludea noisetrend,because of thecorre- lation betweenR(0) and G. BecauseR(0) and G areobtainedfrom least-square fitting, there is a negativecorrelation betweenR(0) and G. Larger interceptsare correlated with smallerslopesfbr a givendataset.Hence,uncorrelated randomnoisewill show an oval, correlateddistributionin the cross-plotas seenin Figure 4.13 (Cambois, 2000). Furthermore,Cambois (2001) formulatedthe influenceof noise on R(0), G and a range-limitedstack(i.e.,sub-stack)in termsof approximateequationsof standard deviations: 3 dR(o) : ;o, /, ^ / ; 'JV-) o f t - - - " t i - ^ ) z stn-0n," t; (I/t(l)) o C : V f . r ^ sln-umrx (4.38) (4.3e) (4.40)
209 - 4.3 AVO analysis -0.1 ir.} * , rl "t; -0.15 -0"1 -0.05 0 I (0) 0.05 0.1 0.15 Figure4,13 Randomnoisehasa ttendin rR(0) versusG (afterCambois,2000) and o,,- Ji .o, (4.41) whered " is the standard deviationof thefull-stackresponse, o, is thestandard deviation of the sub-stack.and n is the number of sub-stacks of the full fold data.As we see,the stack reducesthe noise in proportion to the squareroot of the fold. These equations indicate that the intercept is less robust than a half-fold sub-stack,but more robust than a third-fold sub-stack.The gradientis much more unreliable,sincethe standard deviationof the gradientis inverselyproportionalto the sinesquaredof the maximum angle of incidence. Eventually, the intercept uncertaintyrelated to noise is more or lessinsensitiveto the maximum incidenceangle,whereasthe gradientuncertaintywill decreasewith increasingaperture(Cambois,2001). Simm era/. (2000)claimedthatwhile rock propertyinfbrmation is containedin AVO cross-plots,it is not usually detectablein terms of distinct trends,owing to the effect of noise.The fact that the slopeestimationis more uncertainthan the interceptduring a least-squareinversion makesthe AVO gradientmore uncertainthan the zero-offset reflectivity (e.g.,Houck, 2002).Hence,the extensionof a trendparallelto the gradient axisis an indicationof the amountof noisein thedata. I A -,:'i.;.d-f,*t 'i;l? 4 , , r
210 Common techniques forquantitative seismic interpretation I Fluid versus noise trends In areaswhere fluid changesin sandscauselarge impedancechanges,we tend to seea right-to-left lateralshift along the interceptdirection.This direction is almostopposite tothenoisedirection.which ispredominantJy in thevertical/gradient direction. In thesecasesthereshould be a fair chanceof discriminating hydrocarbon- saturated sandsfrom brine-saturated sands, evenin relativelynoisydata. Simm er al. (2000) furthermore stressedthat one should create AVO cross-plots aroundhorizons,notfrom time windows.Horizon cross-plotclearlytargetsthereservoir of interestand helps determinethe noise trend while revealingthe more subtle AVO responses. Moreover,only samplesof the maximum amplitudesshouldbe included. Samplingpartsof the wavefbrmsotherthan the maxima will infill the areabetween separate clusters,and a lot of sampleswith no physical significancewould scatter aroundthe origin in an R(0) G cross-plot. However,picking only peaksand troughs raisesa delicatequestion:what about transparent sandswith low or no impedance contrastwith overlyingshales'l Theseare significantreflections with very smallR(0) valuesthat could be missedif we invertthe waveformonly at absolutemaxima (in commercialsoftwarepackages tbr AVO inversion, theabsolute maximaarecommonly definedfiom R(0) sections). Anotherissueis shale shaleinterfaces. Theseareusually very weak reflectionsthat would be locatedcloseto the origin in an AVO cross-plot, but they are still important for assessment of a local backgroundtrend. Therearealsoothertypesof noiseaff-ecting the AVO cross-plotdata,suchasresidual moveout.It is essential to try to reducethenoisetrendin thedatabeforeanalyzingthe cross-plot in termsof rockphysicsproperties. A goodpre-processing scheme isessential in orderto achievethis (seeSection4.3.6). Cambois(2000)is doubtful thatAVO cross-plotscanbe usedquantitatively,because of the noiseeffect.With that in mind, it shouldstill be possibleto separate the real rock physicstrendsfiom the noise trends.One way to distinguishthe noise trend is to cross-plota limited numberof samplesfrom the samehorizonfrom a seismic section.The extensionof the trend along the gradientaxis indicatesthe amount of noisein the data (Simm et al., 2000).Another way to investigate noiseversusrock physics trends is to plot the anomaly cluster seenin the AVO cross-plot as color- codedsamples ontotheseismicsection. If theclusteris mainly dueto randomnoise,it shouldbe scattered randomlyaroundin a seismicsection.However,if the anomaly conesponds with a geologic structure and closure, it may representhydrocarbons (seePlate4.10). Finally, we claim that via statistical rock physicswe can estimatethe most likely fluid and lithology fiom AVO cross-plots even in the presence of somenoise.This is ref'erredto as probabilistic AVO analysis,and was first introducedby Avseth er a/. (1998b).This methodworks by estimatingprobabilitydistributionfunctionsof R(0)
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Seismic Interpretation.pdf

  • 1. Common techniques forquantitative seismic interpretation Until a few decadesago, it would be lheirseveral-meters-long papersections I 4 - Thereareno facts,only interpretations. lriedrith Niet:sche - 4.1 Introduction Conventionalseismicinterpretation implies picking and trackinglaterallyconsistent seismic reflectorsfor the purpose of mapping geologic structures,stratigraphyand reservoir architecture. Theultimategoalis to detecthydrocarbon accumulations, delin- eatetheir extent,andcalculatetheir volumes.Conventionalseismicinterpretationis an art that requiresskill and thoroughexperiencein geology and geophysics. Traditionally,seismicinterpretationhasbeenessentiallyqualitative.The geometrical expressionof seismicreflectorsis thoroughly mappedin spaceandtraveltime,but litfle emphasis is put on the physicalunderstanding of seismicamplitudevariations.In the last few decades,however,seismicinterpretershaveput increasingemphasison more quantitativetechniquesfbr seismic interpretation,as thesecan validate hydrocarbon anomaliesand give additional information during prospectevaluation and reservoir characterization. The most important of thesetechniquesinclude post-stackamplitucle analysis (bright-spot anddim-spotanalysis), offset-dependent amplitudeanalysis (AVO analysis), acousticandelasticimpedance inversion,andforwardseismicmodeling. Thesetechniques,if usedproperly, open up new doors for the seismic interpreter. The seismicamplitudes, representing primarilycontrasts in elasticproperties between individual layers,containinformation aboutlithology, porosity,pore-fluidtype andsat- uration,aswell asporepressure- information thatcannotbe gainedfiom conventional seismic interpretalion. - 4.2 Qualitativeseismicamplitude interpretation common for seismic interpretersto roll out with seismicdatadown the hallway, go down 168
  • 2. I 169 - 4,2 Qualitative seismic amplitude interpretation on their knees,and use their coloredpencilsto interpretthe horizonsof interestrn order to map geologic bodies. Little attention was paid to amplitude variations and their interpretations. In the early 1970sthe so-called"brighrspot" techniqueproved successful in areas of theGulf of Mexico,wherebrightamplitudes would coincidewith gas-filled sands.However, experiencewould show that this techniquedid not always work. Some of the bright spotsthat were interpretedas gas sands,and subsequently drilled, were fbund to be volcanic intrusionsor other lithologies with high impedance contrastcomparedwith embeddingshales.Thesetailures were also relatedto lack of waveletphase analysis, ashardvolcanicintrusions wouldcause opposite polarityto low- impedancegas sands.Moreover, experienceshowedthat gas-filled sandssometimes could cause"dim spots,"not "bright spots,"if the sandshadhigh impedancecompared with surrounding shales. With the introductionof 3D seismicdata,the utilizationof amplitudesin seismic interpretation became much more important. Brown (see Brown et ul., l98l) was one of the pioneersin 3D seismicinterpretation of lithofaciesfiom amplitudes. The generationoftime slicesandhorizon slicesrevealed3D geologicpatternsthathadbeen impossibleto discoverfrom geometricinterpretationof the wiggle tracesin 2D stack sections.Today,the further advancein seismictechnology has provided us with 3D visualization toolswheretheinterpreter canstepinto a virtual-realityworld of seismic wiggles and amplitudes,and tracethesespatially (3D) and temporally (4D) in a way that onecould only dreamof a few decadesago.Certainly,the leapfiom the rolled-out papersectionsdown the hallways to the virtual-reality imagesin visualization"caves" is a giant leapwith greatbusiness implicationsfor the oil industry.In this sectionwe reviewthequalitativeaspects of seismicamplitudeinterpretation,beforewe dig into the morequantitative androck-physics-based techniques suchasAVO analysis, impedance inversion,andseismicmodeling,in fbllowing sections. 4.2.1 Wavelet phase andpolarity The very first issueto resolve when interpreting seismic amplitudesis what kind of wavelct we have.Essentialquestionsto ask are the fbllowing. What is the defined polarityin our case?Are we dealingwith a zero-phase or a minimum-phase wavelet? Is there a phaseshift in the data?These are not straightfbrwardquestionsto answet, becausethe phaseof the wavelet can changeboth laterally and vertically. However, therearea f'ewpitfalls to be avoided. First, we want to make surewhat the definedstandardis when processingthe data. There exist two standards. The American standarddefinesa black peak asa "hard" or "positive"event,anda white troughasa "soft" or a "negative"event.On a near-ofl.set stacksectiona "hard" eventwill correspondto an increasein acousticimpedancewith depth,whereasa "soft" eventwill correspondto a decrease in acousticimpedancewith depth. According to the Europeanstandard,a black peak is a "soft" event,whereasa
  • 3. 170 Gommon techniques forquantitative seismic interpretation T white trough is a "hard" event.One way to checkthe polarity of marine datais to look at the sea-floorreflector.This reflectorshouldbea strongpositivereflectorrepresenting the boundarybetweenwater and sediment. Data polarity ' Americanpolarity:An increase in impedance givespositiveamplitude.normally displayedasblackpeak(wiggle r.race) or red intensitylcolor displayt. . European (or Australian)polarity:An increase in impedance givesnegal.ive ampli- tude,normally displayedas white rrough(wiggle trace)or blue intensity(color display). (Adaptedfrom Brown.200la, 2001b) For optimal quantitativeseismicinterpretations,we shouldensurethat our dataare zero-phase. Then, the seismicpick shouldbe on the crestof the waveformconespond- ing with the peak amplitudesthat we desirefor quanrirativeuse(Brown, l99g). with today's advancedseismic interpretationtools involving the use of interactivework- stations,there exist various techniquesfbr horizon picking that allow efficient inter- pretationof largeamountsof seismicdata.Thesetechniques includemanualpicking, interpolation,autotracking, voxel tracking,and surfaceslicing (seeDorn (199g) fbr detaileddescriptions). For extraction of seismic horizon slices,autopickedor voxel-trackedhorizons are very common. The obvious advantageof autotracking is the speedand efficiency. Furthermore,autopicking ensuresthat the peak amplitude is picked along a horizon. However,one pitfall is the assumptionthat seismichorizonsare locally continuous and consistent.A lateral change in polarity within an event will not be recognized during autotracking.Also, in areasof poor signal-to-noise ratio or wherea singleevent splits into a doublet, the autopicking may fail to track the corect horizon. Not only will important reservoirparameters be neglected,but the geometriesandvolumesmay alsobe significantly off if we do not regardlateralphaseshifts.It is important that the interpreter realizesthis andreviewsthe seismicpicksfor qualitycontrol. Sand/shale cross-overs withdepth Simplerock physicsmodelingcan assistthe initial phaseof qualitativeseismicinrer- pretation,when we are uncertainabout what polarity to expectfor diff'erentlithology boundaries. In asiliciclastic environment, mostseismic reflectors will beassociated with sand-shaleboundaries.Hence,the polarity will be relatedto the contrastin impedance betweensandand shale.This contrastwill vary with depth (Chapter2). Usually, rela- tively sott sandsare fbund at relatively shallow depthswhere the sandsare unconsol- idated.At greaterdepths,the sandsbecomeconsolidatedand cemented.whereasthe 4.2.2
  • 4. rmpe0ance 1 t 171 - 4.2 Qualitative seismic amplitude interpretati0n Sand versus shale impedance depth trends andseismic polarity (schematic) Sand-shale cross-over DeDth Figure 4'1 Schematic depth trends of sand andshale impeclances. Thedepth trends canvaryfiom basin to basin, andthere canbemorethanonecross-over. Localdepth trends should beestablished fordifferent basins. shalesaremainly affectedby mechanicalcompaction.Hence,cementedsandstones are normally found to be relatively hardeventson the seismic.Therewill be a correspond- ing cross-overin acousticimpedanceof sandsandshalesaswe go fiom shallowandsoft sandsto the deepand hard sandstones (seeFigure 4.1). However,the depth trendscan bemuch morecomplexthanshownin Figure4.1 (Chapter2, seeFigures2.34 and,2.35'). Shallow sandscan be relatively hard comparedwith surroundingshales,whereasdeep cementedsandstones can be relatively soft comparedwith surounding shales.There is no rule of thumb fbr what polarity to expectfbr sandsand shales.However, using rock physicsmodeling constrainedby local geologicknowledge,one can improve the understandingof expectedpolarity of seismicreflectors. "Hard" venius "soft"events During seismicinterpretation of a prospect or a provenreser"yoir sand.the following questionshouldbe one of the first to be asked:what type of eventdo we expect, a "hard" or a "soft"? [n otherwords.shouldwe pick a positivepeak,or a negative trough?lfwe havegoodwell control,thisissue canbesolvedby generating synthetic seismograms andcorrelating these with realseismicdata.If we haveno well control, we may have to guess.However. a reasonableguesscan be made basedon rock physicsmodeling.Below we havelisted some"rules of thumb" on what type of reflectorwe expectl-ordifferent geologic scenarios.
  • 5. 172 Common techniques forquantitative seismic interpretation T I ii ji Typical "hard"events . Veryshallowsandsat normalpressure embedded in pelagicshales . Cementedsandstone with brinesaluration . Carbonate rocksembedded in siliciclastics ' Mixecllithologies (heterolithics) like shatysands, marls.volcanic ashdeposits Typical "soft"events . Pelagic shale ' S.hallow, unconsolidated sands(anyporefluid) embedded in normallycompacted shales ' Hydrocarbon accumularions in clean.unconsolidated or poorlyconsolidated sancls . Overpressured zones Some pitfalls inconventional interpretation ' Make sureyou know the polarityof the data.Rememberthereare two different standards, the US standard andthe European standard. which areopposire. ' A hard eventcan changeto a soft laterally(i.e.. lateralphaseshifi; if thereare l:jloloCic. petrographic or pore-fluidchanges. Seismicaurotracking will norderecr these. ' A dim seismicreflector or intervalmay be significant. especially in the zoneof sand/shale impedancecross-over. AVO analysisshouldbe underraken to reveal potentialhydrocarbon accumulations. 4.2.3 Frequency andscaleeffects Seismic resolution Verticalseismicresolution isdefinedastheminimum separation between two interfaces such that we can identify two interfacesratherthan one (SherifTand Geldhart, 199-5). A stratigraphic layercanberesolvedin seismicdataif thelayerthickness is largerthan a quarterof a wavelength.The wavelengthis given by: - t / / f ( 4 . 1 ) where v is the interval velocity of the layer, and.l is the frequency of the seis- mic wave. lf the wavelet has a peak frequency of 30 Hz, and the layer velocity is 3000 m/s, then the dominantwavelengthis 100m. In this case,a layer of 25 m can be resolved.Below this thickness, we can still gain importantinfbrmationvia quan- titativeanalysisof the interference amplitude.A bed only ),/30 in thicknessmay be detectable, althoughitsthicknesscannotbedeterminedfiom thewaveshape(Sheriffand Geldhart.199-5).
  • 6. 173 4.2 Qualitative seismic amplitude interpretation E Layer tiickness Figure 4,2 Seismic amplitude asafunction of layer thickness fbragiven wavelength. The horizontal resolutionof unmigratedseismicdatacan be definedby the Fresnel zone. Approximately, the Fresnel zone is defined by a circle of radius, R, around a rellection point: n - Jgz G.2) where z is the reflector clepth.Roughly, the Fresnelzone is the zone from which all reflectedcontributionshave a phasedifl-erence of lessthan z radians.For a depth of 3 km andvelocity of 3 km/s, the Fresnelzoneradiuswill be 300-470 m for fiequencies ranging fiom 50 to 20 Hz. When the size of the reflector is somewhatsmaller than the Fresnelzone,the responseis essentiallythat of a diffractionpoint. Using pre- stack migration we can collapsethe difliactions to be smaller than the Fresnelzone, thusincreasing the lateralseismicresolution(SheriffandGeldhart,1995).Depending on the migration aperture,the lateral resolution after migration is of the order of a wavelength.However,the migrationonly collapses the Fresnelzonein the direction of the migration, so if it is only performed along inlines of a 3D survey,the lateral resolutionwill still be limiteclby the Fresnelzone in the cross-linedirection.The lateral resolution is also restrictedby the lateral sampling which is governedby the spacingbetweenindividual CDP gathers,usually 12.5or 18 metersin 3D seismic clata. For typical surf'ace seismicwavelengths(-50-100 m), lateralsamplingis not the limitinglactor. Interference and tuning effects A thin-layeredreservoir can causewhat is called eventtuning, which is interf'erence betweenthe seismicpulserepresenting the top of the reservoirandthe seismicpulse representingthe baseof the reservoir.This happensif the layer thicknessis lessthan a quarterof a wavelength (Widess,1973).Figure4.2 showsthe efTective seismicampli- tude as a function of layer thickness for a given wavelength, where a given layer hashigher impedancethan the surroundingsediments.We observethat the amplitude
  • 7. 174 Gommon techniques forquantitative seismic interpretation - increasesand becomeslarger than the real reflectivity when the layer thickness is between a half and a quarter of a wavelength.This is when we have constructive interferencebetween the top and the base of the layer. The rlaximum constructive interferenceoccurswhen the bed thicknessis equal to ),14, and this is often referred to as the tuning thickness.Furthermore,we observethat the amplitucledecreases and approacheszero for layer thicknessesbetweenone-quarterof a wavelengthand zero thickness.We refer to this as destructiveinterferencebetween the top and the base. Trough-to-peak time measurements give approximatelythe correctgrossthicknesses for thicknesses largerthana quarterof a wavelength,but no information fbr thicknesses lessthana quarterof a wavelength. The thickness of an individualthin-bedunit canbe extractedfrom amplitude measurements if the unit is thinner than about ),/4 (Sheriff and Geldhart,1995).When the layer thicknessequals)./8, Widess(1973)found that the compositeresponseapproximatedthe derivativeof the original signal.He referred to this thicknessas the theoretical threshold of resolution. The amplitude-thickness curveis almostlinearbelow ),/8 with decreasing amplitudeasthe layergetsthinner, but thecompositeresponse staysthe same. 4.2.4 Amplitude andreflectivity strength "Bright spots" and "dim spots" The first use of amplitude information as hydrocarbon indicators was in the early 1970swhen it was fbund that bright-spotamplitudeanomaliescould be associated with hydrocarbon traps (Hammond, 1974).This discovery increasedinterest in the physical propertiesof rocks and how amplitudeschangedwith difTerenttypesof rocks and pore fluids (Gardner et al., 1914').In a relatively soft sand,the presenceof gas and/orlight oil will increasethe compressibilityof the rock dramatically,the veloc- ity will drop accordingly, andthe amplitudewill decrease to a negative"bright spot." However, if the sand is relatively hard (comparedwith cap-rock),the sand saturated with brine may inducea "brighlspot" anomaly,while a gas-filledsandmay be trans- parent,causinga so-calleddim spot,that is, a very weak reflector.It is very important beforestartingto interpretseismicdatato find out what changein amplitudewe expect for different pore fluids, and whether hydrocarbonswill causea relative dimrning or brighteningcomparedwith brinesaturation. Brown (1999)states that"themostimpnr- tant seismicproperty of a reservoir is whether it is bright spot regime or tlim sltot regime." One obviousproblem in the identificationof dim spotsis thatthey areclim- they are hardto see.This issuecanbe dealtwith by investigating limited-range stacksections. A very weak near-offsetreflectormay havea correspondingstrongf'ar-oflsetreflector. However,some sands,althoughthey are significant,producea weak positivenear- offset reflection as well as a weak negativefar-offset reflection. Only a quantitative analysis of thechangein near-to far-offsetamplitude,a gradientanalysis, will be able
  • 8. 175 T 4.2 Qualitative seismic amplitude interpretation to reveal the sand with any considerabledegreeof confidence.This is explained in Section4.3. Pitfalls:False"bright spots" During seismicexplorationof hydrocarbons. "brighrspots"areusuallythefirsttype of DHI (direct hydrocarbonindicators)one looks for. However.therehave been severalcaseswherebright-spotanomalieshavebeendrilled.and turnedout not lo be hydrocarbons. Somecommon"falsebright spors"include: . Volcanicintrusionsand volcanicashlayers . Highly cementedsands. oftencalcitecementin thin pinch-outzones . Low-porosityheterolithicsands . Overpressured sandsor shales . Coal beds . Top of saltdiapirs Only the lastthreeon the list abovewill causethe samepolarityasa gassand.The firstthreewill causeso-called"hard-kick" amplitudes. Therefore.if oneknowsthe polariryof thedataoneshouldbeablelo discriminare hydrocarbon-associated bright spotsfrom the "hard-kick" anomalies. AVO analysisshouldpermit discrimination of hydrocarbons from coal,saltor overpressured sands/shales. A very common seismicamplitudeattributeusedamongseismicinterpreters is rellectionintensity,which is root-mean-square amplitudescalculated over a given lime window. This anributedoes not distinguishbetweennegativeand positive amplitudes; thereforegeologicinterpretation ol this attributeshouldbe madewith greatcaution. "Flat spots" Flat spotsoccur at the reflectiveboundarybetweendifferentfluids,eithergas-oil, gas- warer,or warer-oil contacts.Thesecanbe easyto detectin areaswherethebackground stratigraphyis tilted, sothe flat spotwill stick out. However,if the stratigraphyis more or less flat, the fluid-related flat spot can be difficult to discover.Then, quantitative methodslike AVO analysiscanhelp to discriminatethe fluid-relatedflat spotfrom the flarlying lithostratigraphy. One should be awareof severalpitfalls when using flat spotsas hydrocarbonindi- cators.Flat spots can be relatedto diageneticeventsthat are depth-dependent. The boundarybetweenopal-A and opal-CT represents an impedanceincreasein the same way as fbr a fluid contact, and dry wells have been drilled on diageneticflat spots. Clinoforms can appearas flat featureseven if the larger-scalestratigraphyis tilted. Other"false" flat spotsincludevolcanicsills,paleo-contacts, sheet-flood deposits and flat basesof lobesandchannels. t l
  • 9. 176 Common techniques forquantitative seismic interpretation - Pitfalls: False "flatspots" One of fhe bestDHIs ro look for is a flat spot,the contactbetweengasand water, gasand oil, or oil and water.However.thereareothercauses that can give riseto flatspots: . Oceanbottommultiples . Flat stratigraphy. The bases of sandlobesespecially tendto be flat. . Opal-A to opal-CTdiagenetic boundary . Paleo-contacts, eitherrelatedto diagenesis or residualhydrocarbon saturation . Volcanicsills Rigorousflat-spotanalysisshouldincludedetailedrock physicsanalysis.and for- ward seismicmodeling,aswell asAVO analysisof realdata(seeSection4.3.8). t I lt il i, Lithology, porosity and fluid ambiguities The ultimategoalin seismicexplorationis to discoveranddelineate hydrocarbon reser- voirs. Seismicamplitudemapsfrom 3D seismicdataare oftenqualitarlvel.finterpreted in termsof lithologyandfluids.However,rigorousrockphysicsmodelingandanalysis of availablewell-log data is requiredto discriminatefluid effectsquantitatively trom lithology effects(ChaptersI and 2). The "bright-spot"analysismethodhasofien beenunsuccessful becauselithology effectsratherthanfluid eff-ects setup thebright spot.The consequence is the drilling of dry holes.In orderto reveal"pitfall" amplitudeanomaliesit is essential to investigatethe rock physicspropertiesfiom well-log data.However,in newfrontier areaswell-1ogdata are sparse or lacking.This requiresrock physicsmodelingconstrained by reasonable geologicassumptions and/orknowledgeabout local compactionaland depositional trends. A common way to extractporosityfrom seismicdatais to do acousticimpedance inversion.Increasing porositycanimply reducedacousticimpedance, andby extract- ing empiricalporosity-impedance trendsfrom well-logdata,onecanestimate porosity from the invertedimpedance.However,this methodology suffersfrom severalambi- guities.Firstly, a clay-rich shalecanhavevery high porosities,evenif the permeability is closeto zero.Hence,a high-porosity zoneidentifiedby this technique may be shale. Moreover, the porosity may be constantwhile fluid saturationvaries,and one sin-rple impedance-porosity modelmay not be adequate fbr seismicporositymapping. In addition to lithology-fluid ambiguities,lithology-porosity ambiguities,and porosity-fluid ambiguities,we may have lithology-lithology ambiguitiesand fluid- fluid ambiguities.Sandand shalecan havethe sameacousticimpedance, causingno reflectivity on a near-offsetseismic section.This has beenreported in severalareas of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that fluvial channelsor turbidite channelsare dim on seismicamplitudemaps,and the
  • 10. :fff!;"{riii;iiiffr ,)) )))))t)))l)))))))))f )) t))) D,D ))), )D,D D))D rr,D )r>), i)P,?),,?l? ), l?? )?i)i) p iriiiiiiii iiiii r)ii)i) ii l r l l l l i i l r l l l l l i l , Plate1,1 SeismicP-P amplitudemapovera submarine fan.The amplitudes aresensitive to lithofaciesand porefluids,but therelationvariesacrosstheimagebecause ofthe interplayofsedimentologicanddiagenetic influences. Blue indicateslow amplitudes, yellow andredhigh amplitudes. 2.9 lilllWi7", 4120 4140 41 60 41 B0 5 4200 o o 4220 4240 4260 4280 4300 VP rho*l/p Distance Plate1,30 Top left, logspenetrating a sandyturbiditesequence; top right,normal-incidence synthetics with a 50 Hz Rickerwavelet.Bottom: increasing watersaturation S* from l1a/c Lo907c(oil API 35,GOR 200) increases densityand Vp(left),giving both amplitudeandtraveltimechanges (right). 2.92 2.94 2.96 2.98 3 3.02 o E F 25 20 15 1 0 rn0
  • 11. 177 r 4.2 Qualitative seismic amplitude interpretation interpretationis usually that the channel is shale-filled.However, a clean sand fill- ing in the channelcan be transparentas well. A geological assessment of geometries indicating differential compactionabovethe channelmay revealthe presenceof sand. More advancedgeophysicaltechniquessuch as offset-dependent reflectivity analysis may alsorevealthe sands.During conventionalinterpretation,one shouldinterprettop reservoirhorizonsfrom limited-rangestacksections,avoiding the pitfall of missing a dim sandon a near-or full-stackseismicsection. Facies interpretation Lithology influence on amplitudescan often be recognizedby the pattern of ampli- tudes as observedon horizon slices and by understandinghow different lithologies occurwithin a depositional system.By relatinglithologiesto depositional systems we often refer to theseas lithofaciesor f-acies. The link betweenamplitudecharacteristics and depositionalpatternsmakesit easierto distinguishlithofaciesvariationsand fluid changes in amplitudemaps. Traditionalseismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon seismictraveltimes. The traditionalmethodologyconsisted of purelyvisualinspection of geometricpatterns in theseismicreflections (e.g.,Mitchum etal., 1977;Weimerand Link, l99l ). Brown et al. (1981),by recognizing buriedriverchannels from amplitude information, were amongstthe first to interpret depositionalfacies from 3D seismic amplitudes.More recentand increasinglyquantitativework includesthat of Ryseth et al. (.1998)who used acousticimpedanceinversionsto guide the interpretationof sand channels,and Zeng et al. (1996) who used forward modeling to improve the understanding of shallow marine faciesfrom seismicamplitudes.Neri (1997) used neuralnetworksto mapfaciesfrom seismicpulseshape. Reliablequantitativelithofacies predictionfiom seismicamplitudesdependson establishingalink betweenrock physics propertiesand sedimentaryfacies.Sections2.4 and2.5 demonstratedhow such links might be established.The casestudiesin Chapter5 show how theselinks allow us to predict litholacies from seismicamplitudes. Stratigraphic interpretation The subsurfaceis by nature a layered medium, where different lithologies or f'acies havebeensuperimposedduring geologic deposition.Seismic stratigraphicinterpreta- tion seeksto mapgeologicstratigraphyfrom geometricexpression of seismicreflections in traveltime and space.Stratigraphicboundariescan be definedby dilferent litholo- gies (taciesboundaries) or by time (time boundaries). Theseoften coincide,but not always. Examples where facies boundariesand time boundariesdo not coincide are erosional surfacescutting acrosslithostratigraphy,or the prograding fiont of a delta almost perpendicularto the lithologic surf'aces within the delta. Thereareseveralpittalls when interpretingstratigraphyfiom traveltimeinfbrmation. First, the interpretationis basedon layer boundariesor interf'aces, that is, the contrasts a
  • 12. 178 T Gommon techniques forquantitative seismic interpretation between diff'erentstrata or layers, and not the propertiesof the layers themselves. Two layers with different lithology can have the same seismic properties;hence, a lithostratigraphicboundary may not be observed.Second' a seismic reflection may occurwithout a lithologychange(e.g.,Hardage,1985).For instance, a hiatuswith no deposition within a shaleintervalcangivea strongseismicsignature because theshales above and below the hiatus have difTerentcharacteristics.Similarily, amalgamated sandscanyield internal stratigraphywithin sandyintervals,reflectingdifferent texture of sancls fiom difl-erentdepositionalevents.Third, seismicresolutioncanbe a pitfall in seismicinterpretation, especiallywhen interpretingstratigraphic onlapsor downlaps. Theseareessential characteristics in seismicinterpretation,astheycangiveinformation about the coastaldevelopmentrelated to relative sealevel changes(e.g.,Vail er ai., I977). However,pseudo-onlaps can occur if the thicknessof individual layersreduces beneath the seismicresolution. The layercanstill exist,evenif the seismicexpression yieldsan onlap. Pittalls Thereareseveral pitfallsin conventional seismicstratigraphic interpretation thatcan be avoidedif we usecomplementary quantitative techniques: . lmportantlithostratigraphic boundaries betweenlayerswith very weak contrasts in seismicpropefiiescan easilybe missed.However.if differentlithologiesare transparent in post-stack seismic data.theyarenormallyvisiblein pre-stack seismic dara.AVO analysisis a useful tool to revealsandswith impedances similar to cappingshales {seeSection 4.31. . It iscommonlybelieved thatseismic events aretimeboundaries. andnotnecessarily lithostratigraphic boundaries. For instance.a hiatuswithin a shalemay causea strongseismicreflectionif the shaleabovethe hiatusis lesscompactedthan the onc below.evenif the lithologyis the same.Rock physicsdiagnostics of well-log datamay revealnonlithologicseismicevents(seeChapter2). . Because of limited seismicresolution,falseseismiconlapscan occur.The layer maystill existbeneath resolution. Impedance inversion canimprovetheresolution. and revealsubtlesrrailgraphic featuresnot observedin the original seismicdata (seeSection 4.4). Quantitative interpretationof amplituclescan add information about stratigraphic patterns,and help us avoid someof the pitfalls mentionedabove.First, relating lithol- ogy to seismicproperties(Chapter2) canhelp us understandthe natureof reflections, and improve the geologic understandingof the seismicstratigraphy.Gutierrez (2001) showedhow stratigraphy-guidedrock physics analysisof well-log data improved the sequence stratigraphicinterpretationof a fluvial systemin Colombia using impedance inversionof 3D seismicdata.Conductingimpedanceinversionof the seismicdatawill
  • 13. 179 - 4,2 Qualitative seismic amplitude interpretation give us layer propertiesfrom interfhceproperties,and an impedancecross-section can reveal stratigraphicfeaturesnot observedon the original seismic section.Impedance inversion has the potential to guide the stratigraphicinterpretation,becauseit is less oscillatorythantheoriginalseismicdata,it is morereadilycorrelated to well-log data, and it tendsto averageout random noise,therebyimproving the detectabilityof later- ally weakreflections (Glucketa.,1997).Moreover, frequency-band-limited impedance inversioncanimprove on the stratigraphicresolution,andthe seismicinterpretationcan be signilicantlymodified if theinversionresultsareincludedin theinterpretationproce- dure.For brief explanationsof differenttypesof impedanceinversions,seeSection4.4. Forwardseismicmodelingis alsoan excellenttool to studythe seismicsignatures of geologicstratigraphy (seeSection4.5). Layer thickness and net-to-gross from seismic amplitude As mentioned in the previous section, we can extract layer thicknessfrom seismic amplitudes. As depictedin Figure4.2,the relationship is only linearfor thin layersin pinch-outzonesor in sheet-likedeposits,sooneshouldavoidcorrelatinglayerthickness to seismicamplitudesin areaswherethe top andbaseof sandsareresolvedasseparate reflectorsin the seismicdata. Meckel and Nath (.1911)found that, for sandsembeddedin shale,the amplitude would dependon the net sandpresent,given that the thicknessof the entire sequence is less than ).14. Brown (1996) extendedthis principle to include beds thicker than the tuning thickness,assumingthat individualsandlayersare below tuning and that the entire interval of interbeddedsandshasa uniform layering. Brown introducedthe "composite amplitude" defined as the absolutevalue summationof the top reflection amplitude and the basereflectionamplitudeof a reservoirinterval.The summationof the absolutevaluesof the top and the baseemphasizesthe eff'ectof the reservoirand reducesthe effect of the embeddingmaterial. Zeng et al. (.1996) studiedthe influenceof reservoir thickness on seismicsignaland introduced what they referred to as effectivereflectionstrength,applicableto layers thinnerthanthe tunins thickness: o . - 2 " - Z ' n . , ' Zrr (4.3) whereZ. is the sandstone impedance, 216is the average shaleimpedance and/zis the layerthickness. A morecommonwayto extractlayerthickness from seismicamplitudes is by linear regressionof relative amplitude versusnet sandthicknessas observedat wells thatareavailable.A recentcasestudyshowingtheapplicationto seismicreservoir mappingwasprovidedby Hill andHalvatis(2001). Vernik et al. (2002) demonstratedhow to estimate net-to-grossfiom P- and S- impedances fbr a turbidite system. From acoustic impedance (AI) versus shear impedance (SI) cross-plots,the net-to-grosscan be calculated with the fbllowing fbrmulas:
  • 14. r 180 Common techniques forquantitative seismic interpretation E Vrung dZ N I G : A Z where V."n,lis the oil-sand fraction given bv; Kano S I - b A I - c e a t - a o where b is the averageslopeof the andz7tiiretherespective intercepts (4.-5) shaleslope(06)andoil-sandslope(b1),whereas ae in theAI-SI cross-plor. I Zrr. (44) calculationof reservoir thickness from seismicamplitude shouldbe doneonly in areaswhere sandsare expectedto be thinnerthan the tuning thickness.that is a quarterof a wavelength. andwherewell-logdatashowevidence of goodcorrelation belweennet sandlhicknessandrelativeamplirude. It canbedifficultto discriminate layerrhickness changes from lirhologyandfluid changes. In relativelysoftsands, theimpactof increasing porosityandhydrocarbon saturation tendslo increase the seismicamplitude,andthereforeworks in the same "direction"to Iayerthickness. However.in relativelyhardsands. increasing porosity and hydrocarbonsaturationLendto decrease the relaliveamplitudeand therefore work in the opposite"direction"to layerthickness. ilouo anatysis In 1984, 12 years afler the bright-spot technology became a commercial tool fbr hydrocarbon prediction, ostrander published a break-through paper in Geophl-sics (ostrander,1984).He showedthat the presence of gas in a sandcappedby a shale would causean amplitudevariationwith ofTset in pre-stackseismicdata.He alsofound thatthischangewasrelatedto thereduced Poisson's ratiocaused by thepresence ofgas. Then,theyearafter,Shuey(1985)confirmedmathematically via approximations of the Zoeppritzequations thatPoisson'sratio wasthe elasticconstantmost directlyrelated to the off.set-dependent reflectivity fbr incident anglesup to 30". AVo technology,a commercial tool for the oil industry,was born. The AVO techniquebecamevery popularin the oil industry,asonecould physicaly explaintheseismicamplitudes in termsof rockproperties. Now, bright-spot anomalies couldbe investigated beforestack,to seeif theyalsohadAVo anomalies (Figure4.3). The techniqueproved successfulin certainareasof the world, but in many casesit was not successful.The techniquesufI'eredfrom ambiguitiescausedby lithology efTects,
  • 15. 181 4.3 AVO analysis I Stacksection CDP locqtion . *{bu Target harizon Geolog ic interpretation Shale Sondstone with gos Aryle ol inc,d?nca Figure 4.3 Schematic illustration of theprinciples inAVOanalysis. tuning effects,and overburdeneft'ects.Even processingand acquisition effectscould causefalseAVO anomalies. But in manyo1'thefailures,it wasnot the techniqueitself thatfailed,but theuseof thetechnique thatwasincorrect.Lack of shear-wave velocity informationandtheuseof toosimplegeologicmodelswerecommonreasons fbr failure. Processingtechniquesthat aff'ectednear-ofTset tracesin CDP gathers in a difl-erent way from far-offset tracescould also createtalse AVO anomalies.Nevertheless,in the last decadewe have observeda revival of the AVO technique.This is due to the improvementof 3D seismictechnology, betterpre-processing routines, rnorefrequent shear-wavelogging andimprovedunderstanding of rock physicsproperties,largerdata capacity,more fbcus on cross-disciplinaryaspectsof AVO, and lastbut not least,mclre awareness amongthe usersof the potentialpitfalls. The techniqueprovidesthe seismic interpreterwith more data,but also new physical dimensionsthat add infbrmation to the conventionalinterpretationof seismicfacies,stratigraphyand geomorphology. In this section we describethe practical aspectsof AVO technology, the poten- tial of this technique as a direct hydrocarbon indicator, and the pitfalls associated with this technique. Without going into the theoretical details of wave theory, we addressissuesrelatedto acquisition.processing and interpretation of AVO data.For an excellent overview of the history of AVO and the theory behind this technology, we refer the readerto Castagna(1993). We expectthe luture application of AVO to CDPgather af interest CDPgather Time AVOresponseat targethorizon 0,1 -0 -0, -0
  • 16. 182 Common techniques forquantitative seismic interpretation - expandon today'scommonAVO cross-plotanalysisandhencewe includeoverviewsof important contributionsfrom the literature,include tuning, attenuationand anisotropy effectson AVO. Finally,we elaborateon probabilisticAVO analysisconstrainedby rock physicsmodels.Thesecomprisethemethodologies appliedin casestudiesl, 3 and4 in Chapter5. 4.3.1 Thereflection coefficient Analysis of AVO, or amplitude variation with ofTset,seeksto extractrock parameters by analyzingseismicamplitudeasa function of offset,or more corectly asa function of reflection angle.The reflection coefficient for plane elastic wavesas a lunction of reflectionangleat a singleinterfaceisdescribedby thecomplicatedZoeppritzequations (Zoeppritz,l9l9). For analysisof P-wavereflections, a well-knownapproximationis givenby Aki andRichards( 1980),assumingweaklayercontrasts: R ( 0 , ) - ; ( r , , A p I A Y p , A V s - -17,-vi) T + 2*r4 W +p'lt K (4.6) (4.1) where: sin01 I t - - Y P I L p : p z - p r L V p : V p z - V p t A V s - V s : - V s r e : ( 0 r l u ) 1 2 = e t Pr) l2 + vPt)12 + vst)12 P : ( . P z I Vp : (.Vpz V5: (V52 In the fbrmulasabove,p is the ray parameter, 01 is the angleof incidence, and02 is the transmissionangle; Vp1and Vp2arethe P-wavevelocitiesaboveand below a given interface,respectively. Similarly,V51and V5r arethe S-wavevelocities,while py and p2 aredensitiesaboveand below this interface(Figure 4.4). The approximationgiven by Aki and Richardscanbe further approximated(Shuey, r985): R(01;:, R(o) + G sin29+ F(tan2e- sin2o; where R(o):;(T.T) G::^+-'#(+.'+) :R(o) -+(:.'#) #+
  • 17. 183 4.3 AVO analvsis n Medium 1 (Vp1, V51, p1) Medium 2 (Vn, Vsz, Pi PS{t) Figure4'4 Reflections andtransmissions at a singleinterfacebetweentwo elastichalf-space rr-redia firr an incidentplaneP-wave.PP(i).Therewill be botha reflected p-wave,pp(r). anda transmittecl P-wave,PP(t).Notethattherearewavemocleconversions at thereflectionpoint occurrrngar nonzeroincidence angles.In additionto theP-waves, a reflectedS-wave,pS(r),anda transrnitted S-wave,PS(t),will beprodr.rced. and _ t a y P 1 r / / v D This form can be interpretedin terms of difierent angular ranges!where R(0) is the normal-incidence reflection coefficient, G describes thevariationat intermecliate offsets and is often referredto asthe AVO gradient,whereasF dominatesthe far ofTsets. near critical angle.Normally, the rangeof anglesavailablefor AVO analysisis lessthan 30-40.. Therefbre,we only needto considerthe two first terms,valid fbr anslesless than.l0 tShuey. I985,1: R ( P ) = R ( 0 ) + G s i n 2 d (4.8) The zero-oft'set reflectivity,R(0), is controlledby the contrastin acousticimpedance acrossan interface.The gradient,G, is more complex in terms of rock properties,but fiom the expressiongiven abovewe seethat not only the contrastsin Vp and density afrect the gradient, but also vs. The importanceof the vplvs ratio (or equivalently the Poisson'sratio) on the ofTset-dependent reflectivity was first indicatedby Koefoed (1955).ostrander(1984) showedthat a gas-filledfbrmation would havea very low Poisson's ratio comparedwith the Poisson's ratiosin the surrounding nongaseous fbr- mations.This would causea significantincreasein positiveamplitudeversusangle at the bottomof the gaslayer,anda significantincrease in negativeamplitudeversus angleat the top of the gaslayer. Theeffectofanisotropy Velocity anisotropyoughtto be takeninto accountwhen analyzingtheamplitudevaria- tionwith offset(AVO) response of gassands encased in shales. Althoughit is generally PP(r) 4.3.2 * d
  • 18. 184 - Common techniques forquantitative seismic interpretation thought that the anisotropyis weak (10-20%) in most geological settings(Thomsen, 1986), some eff'ectsof anisotropy on AVO have been shown to be dramatic using shale/sand models(Wright, 1987).In somecases, the signof the AVO slopeor rateof changeof amplitudewith ofliet canbe reversedbecauseof anisotropyin the overlying shales (Kim et al.,1993 Blangy,1994). The elasticstiffnesstensorC in transversely isotropic(TI) mediacanbe expressed in compactform asfbllows: C - C l (c11- 2C66) C r : 0 0 0 I (Ctt - 2Coo) C t r C r : 0 0 0 - Cn) Cr: 0 C n 0 C:: 0 0 C++ 0 0 0 0 0 0 0 0 0 0 0 0 C++ 0 0 Cr,o whereC6,6, : t(Crt (4e) andwherethe 3-axis(z-axis)lies alongthe axisof symmetry. Theabove6 x 6 matrixis symmetric, andhasfiveindependent components, Crr, Crr, Cr, C++,and C66.For weak anisotropy, Thomsen(1986)expressed threeanisotropic parameters, t, y and6, asa function of the five elasticcomponents,where C l - C r a , - - 2Cr Cor, C++ 2C++ ( C r : * C + + ) 2 - ( . C y - C a l z 2C.3(Cy C++) The constants canbe seento describethe fiactional differenceofthe P-wavevelocities in the verticalandhorizontaldirections: yP(90')- vp(0') (4.l3) Vp(o') and thereforebestdescribeswhat is usually referredto as"P-wave anisotropy." In the samemanner,the constanty canbe seento describethe fiactional difference of SH-wavevelocitiesbetweenverticalandhorizontaldirections,which is equivalent to the differencebetweenthe vertical and horizontal polarizationsof the horizontally propagating S-waves: (4.10) (4. rr) (4.12)
  • 19. 185 r 4.3 AVO analysis V s H ( 9 0 1 - V s v ( 9 0 )7sH(90") - Vss(0') (4.14) T - Vsv(90') Vsn(0') The physicalmeaningof 6 is not as clearas s and y, but 6 is the most important parameterfbr normal moveout velocity and reflectionamplitude' Under the plane wave assumption,Daley and Hron (1911) derived theoreticalfbr- mulas for reflection and transmissioncoefficientsin Tl media.The P-P reflectivity in the equationcan be decomposedinto isotropic and anisotropicterms asfollows: Rpp(0): Rrpp(O) * R'rpp(0) (4.1s) Assumingweak anisotropyanclsmalloffsets,Banik ( 1987)showedthatthe anisotropic term canbe simply expressed asfbllows: sin2e Repp(d)- - Ad Blangy (lgg4) showedthe effectof a transverselyisotropicshaleoverlying anisotropic gas sand on offset-dependentreflectivity, for the three different types of gas sands. He found that hard gas sandsoverlain by a soft TI shaleexhibited a larger decrease in positive amplitude with offset than if the shalehad been isotropic. Similarly, soft gassan4soverlain by a relatively hard TI shaleexhibited a largerincreasein negative amplitude with offset than if the shalehad beenisotropic. Furthermore,it is possible fbr a soft isotropic water sand to exhibit an "unexpectedly" Iarge AVO eff'ectif the overlyingshaleis sufficientlyanisotropic' TheeffectoftuningonAVO As mentioned in the previous section,seismicinterf'erence or eventtuning can occur asclosely spacedreflectorsinterferewith eachother.The relativechangein traveltime betweenthe reflectorsdecreases with increasedtraveltime and off.set.The traveltime hyperbolasof the closely spacedreflectorswill thereforebecomeevencloserat larger ofTsets.In f-act,the amplitudes may interfere at large ofTsetseven if they do not at small offsets.The effectof tuning on AVO hasbeendemonstrated by Juhlin andYoung ( 1993),Lin andPhair( 1993),BakkeandUrsin(1998),andDong (1998),amongothers. JuhlinandYoung(1993)showedthatthin layersembedded in a homogeneous rock can producea significantly different AVO responsefiom that of a simple interfaceof the samelithology. They showedthat,for weakcontrastsin elasticpropertiesacrossthe layer boundaries,the AVO responseof a thin bed may be approximatedby modeling it as an interferencephenomenonbetweenplane P-wavesfiom a thin layer' ln this casethin-bed tuning affectsthe AVO responseof a high-velocity layer embeddedin a homogeneousrock more than it affectsthe responseof a low-velocity layer. (4.I6) 4.3.3 l
  • 20. 186 Common techniques forquantitative seismic interpretation Lin andPhair( 1993)suggested thefollowing expression for theamplitudevariation with angle(AVA) response of a thin layer: Rr(0): rr.roA?'(0) cosd' R(6) where a.re is the dominant frequencyof the wavelet, Af (0) is the two-way traveltirne at normal incidencefiom the top to the baseof the thin layer,andR (0) is the reflection coefficientfiom the top interface. Bakkeand Ursin ( 1998)extended the work by Lin andPhairby introducingtuning correctionfactorsfbr a generalseismicwaveletas a functionof offset.If the seismic response fiom the top of a thick layeris: (4.11) (4.l8) theseismic (4.19) ( 4 ) t d(t, t') : R(t')p(r) where R(,1') is the primary reflection as a function of ofTset.t',andp(0 is pulseasa flnction of time /, thenthe response from a thin layeris tl(r, y) f(.y)AI(0)C(t")p'(t) wherep'(r) is the time derivativeof the pulse,A7"(0)is the traveltimethicknessof the thin layer at zero offset,and C (-v)is the offiet-dependentAVO tuning factor given by (4.20) where 7(0) and Z(-r')are the traveltimes atzero ofliet and at a given nonzerooffset, respectively. The root-mean-square velocity VBy5,is definedalong a ray path: c(.v):ffi[' .##"] t l ' t t ) t ' r s , . l v t t | t V R M S - J d t 0 For small velocity contrasts(Vnvs - y), the last term in equation(4.20) can be ignored,and the AVO tuning f'actorcanbe approximatedas r(0) C(r') :v ----:-- (4.22 r(,r') For large contrastin elasticproperties,one ought to include contributionsfiom P- wave multiples and convertedshearwaves.The locally convertedshearwave is ofien neglectedin ray-tracingmodeling when reproductionof the AVO responseof potential hydrocarbonreservoirsis attempted.Primaries-onlyray-tracemodeling in which the Zoeppritz equationsdescribethe reflectionamplitudesis most common.But primaries- only Zoeppritz modeling can be very misleading,becausethe locally convertedshear wavesoften have a first-order eff-ecton the seismicresponse(Simmons and Backus, 1994).lnterferencebetweenthe convertedwavesand the primary reflectionsfiom the
  • 21. (1) Primaries 187 I 4,3 AVO analysis (2) Single-leg a (3)Double-leg (4)Reverberations Figure 4.5 Converted S-waves andmultiples thatmustbeincluded in AVOmodeling whenwehave thinlayers. causing these nrodes tointerfere withtheprimaries. (l) Primary reflections; (2)single-leg shear waves; (3)double-leg shear wave; and(4)primary reverberations. (After Simmons andBackus, 1994.) 7ps: transmitted S-wave converted fiomP-wave, Rsp: reflected P-wave converted fiomS-wave. etc. baseof thelayersbecomesincreasinglyimportantasthelayerthicknesses decrease. This often producesa seismogramthat is different fiom one producedunderthe primaries- only Zoeppritzassumption. In thiscase,oneshouldusefull elasticmodelingincluding the convertedwave modesand the intrabedmultiples.Martinez (1993) showedthat surface-related multiplesandP-to-SV-modeconvertedwavescaninterf-ere with primary pre-stackamplitudesandcauselargedistortionsin theAVO responses. Figure4.5 shows the ray imagesof convertedS-wavesand multiples within a layer. Structuralcomplexity, overburden and wave propagation effects onAVO Structuralcomplexity and heterogeneities at the targetlevel aswell as in the overbur- den can have a greatimpact on the wave propagation.Theseeffectsinclude focusing and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed and surf'acemultiples, P-wave to vertically polarized S-wavemode conversions,and anelasticattenuation.The offset-dependent reflectivity should be correctedfor these wave propagationeffects,via robustprocessingtechniques(seeSection4.3.6). Alter- natively, theseefTectsshould be included in the AVO modeling (see Sections4.3.7 and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor overburdeneffectsaswell ascertainacquisitioneffects(seeSectiona.3.5) by normal- izing a targethorizon amplitude to a referencehorizon amplitude.However, in more recentyearsthere have been severalmore extensivecontributionsin the literatureon amplitude-preserved imaging in complexareasandAVO correctionsdueto overburden effects,someof which we will summarizebelow. R$ 4.3.4
  • 22. 188 Common techniques forquantitative seismic interpretation - AVO in structurally complex areas TheZoeppritzequations assume a singleinterf-ace between two semi-infinite layerswith infinitelateralextent.In continuouslysubsidingbasinswith relativelyflat stratigraphy (suchasTertiarysediments in theNorth Sea),the useof Zoeppritzequations shouldbe valid.However,complexreservoirgeologydue to thin beds,verticalheterogeneities, faultingandtilting will violatetheZoeppritzassumptions. Resnicketat. (1987)discuss the efl'ectsof geologic dip on AVO signatures,whereasMacleod and Martin (1988) discusstheeff-ects of reflectorcurvature.Structuralcomplexity canbe accountedfor by doing pre-stack depthmigration(PSDM). However,one shouldbe awarethatseveral PSDM routinesobtain reliablestructuralimageswithout preservingthe amplitudes. Grubb et ul. (2001) examined the sensitivity both in structureand amplitr-rde related to velocity uncertainties in PSDM migratedimages.They performedan amplitude- preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO signatures they evaluated both the uncertaintyin AVO cross-plots and uncertaintyof AVO attributevaluesalonggivenstructuralhorizons. AVO effects due to scattering attenuation in heterogeneous overburden Widmaier etztl.. (1996)showedhow to correcta targetAVO response fbr athinly layered overburden. A thin-bedded overburden will generate velocityanisotropy andtransmis- sion lossesdueto scatteringattenuation,andtheseeflectsshouldbe takeninto account whenanalyzinga targetseismicreflector. They combinedthegeneralized O'Doherty- Anstey formula (Shapiroet ul., 1994a)with amplitude-preservingmigration/inversion algorithms and AVO analysisto compensatefor the influence of thin-beddedlayers on traveltimesand amplitudesof seismic data. In particr-rlar, they demonstratedhow the estimation of zero-offsetamplitude and AVO gradient can be improved by cor- recting fbr scatteringattenuationdue to thin-bed efl'ects.Sick er at. (2003) extendecl Widmaier's work andprovideda methodof compensatingfor the scatteringattenuation eflects of randomly distributed heterogeneities above a target reflector.The general- ized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent, time- harmoniceffectivetransmissivity T for scalarwaves(P-wavesin acousticI D medium or SH-wavesin elasticlD medium)andis givenby Tt II u Tue ('' l t)|ift l AL (4.23) where.fis the frequencyandn andp arethe angle-andfiequency-dependent scattering attenuationandphaseshift coefficients,respectively.The angleg is the initial angleof an incident plane wave at the top surfaceof a thinly layeredcompositestack;L is the thickness of the thinly layeredstack;ft denotes the transmissivity fbr a homogeneous isotropic ref-erence medium thatcausesa phaseshifi. Hence,the equationaboverepre- sentsthe relativeamplitudeandphasedistortionscausedby the thin layerswith regard to the reference medium.Neglectingthe quantityZowhich describes the transmission
  • 23. 189 4.3 AVoanalysis - responsefor a homogeneousisotropicreferencemedium (thatis, a pttrephaseshift), a phase-reduced transmissivityis defined: f ( f) o " @tf'o)+tP(l a))r (4.24) For a P-wave in an acoustic lD medium, the scatteringattenuation,cv,and the phase coefficient, B,were derivedfrom Shapiroet al. (1994b)by Widmaieret al. (1996): a(.f ,0) : | tr'oot.f' (4.25) cos2o V,f I l6n:a2f2 cos2u and r f'o2 l- B ( f . ( ) ) - " | - V r c o s eL gnz n: 7'z r 4 ) 6 r V ; + t 6 n ) 0 2 . t 2 c o r 2 e where the statisticalparametersof the referencemedium include spatial correlation lengtha, standarddeviationo, and meanvelocity Vs. The medium is modeledas a 1D random medium with fluctuating P-wave velocities that are characterizedby an exponential correlation function. The transmissivity (absolutevalue) of the P-wave decreases with increasing angleof incidence. If the uncorrected seismicamplitude(i.e.,the analyticalP-waveparticledisplace- ment) is definedaccordingto ray theory by: I U(S,G,/) : Rc-W(r - rv) v where U is the seismic trace, S denotesthe source,G denotesthe receiver,t is the varying traveltime along the ray path,Rs is the reflection coefficient at the reflection point M, y is the spherical divergencefactor, W is the soutce wavelet, and ry is the traveltime fbr the ray between sourceS, via reflection point M, and back to the receiverG. A reflectorbeneatha thin-beddedoverburdenwill havethe following compensated seismicamplitude: ur(s,G,t): fr*(t)*R. I w1r- ,r; v where thetwo-way, time-reduced transmissivity isgivenby; 4*(r) : irtrc(r)x Zsrvr(r) (4 )R (4 )q The superscriptT of Ur(S, G, r) indicatesthat thin-bedeffectshavebeenaccounted fbr. Moreover,equation(4.28)indicatesthatthesourcewavelet,W(0, is convolvedwith the transienttransmissivity both for the downgoing (i5p1) and the upgoing raypaths (f n4c)betweensource(S), reflectionpoint (M), and receiver(G). (4 )1
  • 24. 190 Common techniques forquantitative seismic interpretation - In conclusion,equation(4.28) representsthe angle-dependent time shift causedby transverse isotropic velocity behaviorof the thinly layeredoverburden.Furthermore,it describes thedecrease of theAVO response resultingfrom multiple scatteringadditional to the amplitudedecayrelatedto sphericaldivergence. Widmaier eI ai. ( I 995)presented similar lbrmulationsfor elasticP-waveAVO, where theelasticcorrectionformula dependsnot only on variancesandcovariances of P-wave velocity,but also on S-wavevelocity and density,and their correlationand cross- correlationfunctions. Ursin andStovas(2002)furtherextendedon theO'Doherty-Anstey fbrmula andcal- culatedscatteringattenuationfbr a thin-bedded,viscoelasticmedium. They found that in the seismicfrequencyrange,the intrinsic attenuationdominatesover the scattering attenuation. AVO and intrinsic attenuation (absorption) Intrinsic attenuation,alsoreferredto asanelasticabsorption,is causedby the fact that even homogeneoussedimentaryrocks are not perf'ectlyelastic.This effect can com- plicatetheAVO response (e.g.,Martinez, 1993).Intrinsic attenuation canbe described in terms of a transt'ertunction Gt.o, t) fbr a plane wave of angular frequency or and propagation time r (Luh, 1993): G@, i : exp(at 12Qe* i(at lr Q) ln atI tos) (4.30) where Q" is the effectivequality f'actorof the overburdenalong the wave propagation path and areis an angularreferencefrequency. Luh demonstratedhow to correct for horizontal, vertical and ofTset-dependent wavelet attenuation.He suggestedan approximate,"rule of thumb" equation to cal- culatethe relativechangein AVo gradient,6G, due to absorptionin the overburden: f t t 3G ry :-' Q" (4.31) wherei is the peak frequencyof the wavelet,and z is the zero-offsettwo-way travel time at the studiedreflector. Carcione et al. (1998) showedthat the presenceof intrinsic attenuationaffectsthe P-wavereflectioncoefficientnearthe critical angleandbeyondit. They alsofound that the combined effect of attenuationand anisotropyaff'ectsthe reflection coefficientsat non-normalincidence,but thattheintrinsic attenuationin somecasescanactuallycom- pensate the anisotropiceffects.In mostcases, however,anisotropiceffectsaredominant over attenuationeffects.Carcione(1999) furthermoreshowedthat the unconsolidated sedimentsnearthe seabottom in offshoreenvironmentscanbe highly attenuating,and that thesewaveswill for any incidenceanglehave a vector attenuationperpendicular
  • 25. 191 4,3 AVO analysis r 4.3.5 to the sea-floorinterf'ace. This vector attenuationwill afl'ectAVO responses of deeper reflectors. Acquisition etfects onAVO The most important acquisition eff-ects on AVO measurements include sourcedirec- tivity, and sourceand receivercoupling (Martinez,J993). ln particular,acquisition footprint is a largeproblemfbr 3D AVO (Castagna,2001). Inegular'Eoverage at the surfacewill causeunevenillumination of the subsurface. Theseeffectscanbecorrected for usinginverseoperations.Difl'erentmethodsfor this havebeenpresentedin the liter- ature(e.g.,Gassaway et a.,1986;Krail andShin,1990;CheminguiandBiondi, 2002). Chiburis' ( 1993)methodfor normalizationof targetamplitudeswith a referenceampli- tude provided a fast and simple way of corecting for certain data collection factors including sourceand receivercharacteristics and instrumentation. Pre-processing ofseismic data forAVO analysis AVO processingshouldpreserveor restorerelativetraceamplitudeswithin CMP gath- ers.This implies two goals:(1) reflectionsmust be correctlypositionedin the sub- surface;and (2) data quality should be sufficient to ensurethat reflection amplitudes contain infbrmation aboutreflectioncoefficients. AVO processing Even though the unique goal in AVO processingis to preservethe true relative amplitudes,thereis no uniqueprocessing sequence. lt dependson the complexity of the geology.whetherit is landor marineseismicdata.andwhetherthedatawill be used to extract regression-based AVO attributesor more sophisticatedelastic inversionattributes. Cambois(200l) definesAVO processing asany processing sequence thatmakes the datacompatiblewith Shuey'sequation,if that is the model usedfor the AVO inversion.Camboisemphasizes thatthis canbe a very complicated task' Factorsthatchangetheamplitudesof seismictracescanbegroupedinto Eartheffects, acquisition-relatedeffects, and noise (Dey-Sarkar and Suatek, 1993). Earth effects include sphericaldivergence,absorption,transmissionlosses,interbedmultiples, con- verted phases,tuning, anisotropy,and structure.Acquisition-relatedeft-ectsinclude sourceand receiver arrays and receiversensitivity.Noise can be ambient or source- generated. coherent or random.Processing attempts to compensate for or removethese effects,but can in the processchangeor distort relative trace amplitudes.This is an important trade-offwe needto considerin pre-processing for AVO. We thereforeneed 4.3.6
  • 26. 192 r Common techniques forquantitative seismic interpretation to select a basic butrobust processing scheme (e.g., ostrander, 1984; chiburis,l9g4; Fouquet, f990;Castagna andBackus, 1993; Yilma42001). Common pre-processingstepsbeforeAVO analysis Spiking deconvolution and wavelet processing In AVO analysis we normallywantzero-phase data.However,theoriginalseismicpulse is causal,usuallysomesortof minimum phasewaveletwith noise.Deconvolutionis defined as convolving the seismic trace with an inversefilter in order to extract the impulse responsefrom the seismic trace. This procedurewill restorehigh frequen- cies and thereforeimprove the vertical resolutionand recognitionof events.One can make two-sided,non-causalfilters, or shapingfilters, to producea zero-phasewavelet (e.g.,Leinbach,1995;Berkhout,1977). The waveletshapecan vary vertically (with rime), larerally(spatially),and with offset. The vertical variationscan be handledwith deterministicQ-cornpensation (see Section4.3.4).However,AVO analysisis normally carriedout within a limited time window where one can assumestationarity.Lateral changesin the wavelet shapecan be handledwith surface-consistent amplitudebalancing(e.g.,Camboisand Magesan, 1997).Offset-dependent variationsare often more complicatedto correct for, an4 are attributedto both ofl.set-dependent absorption(seeSection4.3.4), tuning efl'ects(see Section 4.3.3),andNMo stretching. NMo stretching actslikea low-pass, mixed-phase, nonstationaryfilter, andtheeff'ects arevery difficult to eliminatefully (Cambois,2001). Dong (1999) examined how AVO detectability of lithology and fluids was afl'ected by tuning and NMo stretching,and suggesteda procedurefor removing the tuning and stretchingeffectsin order to improve AVO detectability.Cambois recommendecl picking the reflectionsof interestprior to NMo corrections,and flattening them for AVO analysis. Spherical divergence correction Spherical divergence,or geometrical spreading,causesthe intensity and energy of sphericalwaves to decreaseinversely as the squareof the distancefiom the source (Newman, 1973).For a comprehensive reviewon ofTset-dependent geometricalspread- ing, seethe studyby Ursin ( 1990). Surface-consistentamplitude balancing Sourceand receivereff'ectsas well as water depth variation can produce large devi- ations in amplitude that do not coffespondto target reflector properties.Commonly, statisticalamplitude balancingis carried out both fbr time and offset. However. this procedure can have a dramatic efl'ect on the AVO parameters.It easily contributes to interceptleakageand consequentlyerroneousgradientestimates(Cambois,2000). Cambois (2001) suggestedmodeling the expectedaverageamplituclevariation with
  • 27. 't 193 4.3AVO analvsis n off.setfbllowing Shuey'sequation,and then using this behavior as a ret'erence for the statistical amplitudebalancing. Multiple removal One of the most deterioratingeff-ects on pre-stackamplitudesis the presenceof multi- ples.Thereareseveralmethodsof filtering awaymultiple energy,but not all of theseare adequatefor AVo pre-processing. The methodknown asfft multiple filtering, donein the frequency-wavenumberdomain,is very efficientat removing multiples,but the dip in the.l-lrdomain is very similar fbr near-offsetprimary energyandnear-offsetmultiple energy.Hence,primary energycaneasilybe removedfrom neartracesandnot from far traces,resultingin an ar-tificialAVO effect.More robustdemultiple techniquesinclude linear and parabolic Radon transform multiple removal (Hampson, l9g6: Herrmann et a1.,2000). NMO (normal moveout) correction A potential problem during AVO analysisis error in the velocity moveout conection (Spratt, 1987).When extractingAVO attributes,one assumes that primarieshavebeen completelyflattenedto a constanttraveltime.This israrely thecase,astherewill always be residualmoveout.The reasonfor residualmoveoutis almostalwaysassociated with erroneousvelocity picking, andgreatef'fortsshouklbeput into optimizing theestimated velocityfield (e.g.,Adler, 1999;Le Meur andMagneron,2000).However,anisorropy andnonhyperbolicmoveoutsdueto complexoverburclen may alsocausemisalignments betweennearandfar off.sets (anexcellentpracticalexampleon AVO andnonhyperbolic moveoutwas publishedby Ross,1997).Ursin and Ekren (1994)presented a method for analyzing AVO eff-ects in the off.setdomain using time windows. This technique reducesmoveoutelrorsandcreatesimprovedestimatesof AVO parameters. Oneshoulcl be awareof AVO anomalieswith polarity shifts(classIIp, seedefinition below) during NMO corrections,asthesecaneasilybemisinterpretedasresidualmoveouts(Ratcliffe and Adler, 2000). DMO correction DMO (dip moveout) processinggenerates common-reflection-pointgathers.It moves the reflection observedon an off'settrace to the location of the coincident source- receivertrace that would have the samereflecting point. Therefore,it involves shift- ing both time and location. As a result, the reflection moveout no longer depends on dip, reflection-point smear of dipping reflections is eliminated, and eventswith various dips have the same sracking velocity (Sheriff and Geldhart, 1995). Shang et al. (1993) published a rechnique on how to extract reliable AVA (ampli- tude variation with angle) gathers in the presenceof dip, using partial pre-stack misration.
  • 28. 194 Common techniques forquantitative seismic interpretation - Pre-stack migration Pre-stackmigration might bethoughtto be unnecessary in areaswherethe sedimentary sectionis relatively flat, but it is an importantcomponentof all AVO processing. Pre-stackmigration should be used on data for AVO analysiswheneverpossible, because it will collapsethe diffractionsat the targetdepthto be smallerthanthe Fresnel zoneandthereforeincrease the lateralresolution(seeSection4.2.3;Berkhout,1985; Mosher et at., 1996).Normally, pre-stacktime migration (PSTM) is preferredto pre- stackdepthmigration (PSDM), because the former tendsto preserveamplitudesbetter. However, in areaswith highly structuredgeology, PSDM will be the most accurate tool (Cambois,2001).An amplitude-preserving PSDM routineshouldthenbe applied (Bleistein, 1987;Schleicher et ctl.,l993;Hanitzsch, 1997). Migration fbr AVO analysiscan be implementedin many different ways. Resnick et aL.(1987) and Allen and Peddy (1993) among othershave recommended Kirch- hoff migration togetherwith AVO analysis.An alternativeapproachis to apply wave- equation-based migration algorithms.Mosher et al. (.1996) deriveda waveequationfbr common-angletime migration and used inversescatteringtheory (seealso Weglein, 1992'7for integration of migrationandAVO analysis (i.e.,migration-inversion). Mosher et at. (1996) usecla finite-differenceapproachfbr the pre-stackmigrations and illus- tratedthe value of pre-stackmigration fbr improving the stratigraphicresolution,data quality, and location accuracyof AVO targets. Example ofpre-processing scheme forAVO anatysis of a2lseismic line (Yilmaz, 2001.) (I ) Pre-stack signal processing (source signature processing. geometric scaling, spikingdeconvolution andspecffalwhitening). (2t Sortto CMP anddo sparse intervalvelocityanalysis. (3) NMO usingvelocityfieldfrom step2. (4) DemultipleusingdiscreteRadontransform. (5) Sort to common-offsetand do DMO correction. (6) Zero-offsetFK time migration. (7) Sort datato common-reflection-point (CRP) and do inverseNMO using the velocityfield from step2. (8) Detailedvelocityanalysisassociated with the migrateddala' (9) NMO correclionusingvelocityfield from step8. ( l0) StackCRPgathers to obtainimageof pre-stack migrated data.Removeresidual multiplesrevealed by lhe stacking. (l l) Unmigrate usingsamevelocityfieldasin step6. ( l2; Post-stack spikingdeconvolution. (13) Remigrateusingmigrationvelocityfield from step8.
  • 29. 195 4.3 AVO analysis E Some pitfalls inAVO interpretation due t0processing etfects . Waveletphase. The phaseof a seismicsectioncanbe significantlyalteredduring processing. lf rhephase of a sectionis notestablished by theinterpreter. thenAVO anomaliesthat would be interpretedas indicativeof decreasing impedance,for example.canbeproducedat interfaces wheretheimpedance increases (e.g.,Allen andPeddy.I993). . Multiple filtering. Not all demultiple techniquesare adequatelor AVO pre- processing. Multiple filtering,donein thefrequency-wavenumber domain,is very efficientar removing multiples.but the dip in the/-k domain is very similar for near-offsetprimary energyandnear-offsetmultiple energy.Hence,primary energy can easlly be removed from the near-offsettraces.resulting in an artificial AVO effect. . NMO correction. A potentialproblemduringAVO analysis is errorsin thevelocity moveoutcorrection(Spran.1987).When extractingAVO attributes. oneassumes that primarieshave beencompletelyflattenedto a constanttraveltime.This is rarelythecase.astherewill alwaysbe residualmoveout.Ursin andEkren(1994) presenteda method for analyzing AVO effects in rhe offset domain using time windows.This technique reducesmoveoulerrorsandcreates improvedestimates of AVO paramerers. NMO stretchis anotherproblem in AVO analysis.Because the amount of normal moveout varieswith arrival time. frequenciesare lowered at large offsets compared with short offsets. Large offsets, where the stretching effect is significant.shouldbe muted beforeAVO analysis.Swan (1991),Dong (1998)and Dong ( 1999)examinethe eft'ectof NMO stretchon offset-dependenl reflectivity. . AGC amplirude conection. Automatic gain control must be avoided in pre- processing of pre-stack databeforedoing AVO analysis. Pre-processing for elastic impedance inversion Severalof the pre-processingstepsnecessary for AVO analysisare not requiredwhen preparingdatafor elasticimpedanceinversion(seeSection4.4for detailson themethod- ology). First of all, the elasticimpedanceapproachallows for waveletvariationswith offset(Cambois,2000).NMO stretchcorrectionscanbe skipped,because eachlimited- rangesub-stack(in which the waveletcanbe assumedto be stationary)is matchedto its associated syntheticseismogram, andthis will removethewaveletvariationswith angle. It is, however,desirableto obtain similar bandwidth fbr eachinvertedsub-stackcube, since theseshould be comparable.Furthermore,the data used for elastic impedance inversionarecalibratedto well logs before stack,which meansthat averageamplitude variations with offset are automatically accountedfor. Hence, the complicated pro- cedureof reliable amplitude correctionsbecomesmuch less labor-intensivethan for
  • 30. 196 Common techniques forquantitative seismic interpretation - 4.3.7 u 1 0 2 0 3 0 4 0 5 0 6 0 Angle ofincidence (degree) Figure4,6 AVO curvesfbr differenthalf'-space models(i.e.,two layers oneintertace). FaciesIV is cap-rock. Inputrockphysics propertie represent meanvalues for eachfacies. standard AVO analysis. Finally,residualNMO andmultiplesstill mustbeaccounted fbr (Cambois,2001).Misalignmentsdo not causeinterceptleakageasfbr standard AVO analysis, but near-andfar-anglereflections muststill be in phase. AVO modeling andseismic detectability AVO analysisis normally carriedout in a deterministicway to predictlithology and fluidsfrom seismicdata(e.g.,SmithandGidlow, 1987;RutherfordandWilliams, 1989; Hilterman, 1990;Castagna andSmith, 1994;Castagna et al., 1998). Forward modeling of AVO responsesis normally the best way to start an AVO analysis,as a feasibility study before pre-processing,inversion and interpretationof real pre-stackdata.We show an example in Figure 4.6 where we do AVO modeling of difTerentlithofacies defined in Section 2.5. The figure shows the AVO curves for different half-spacemodels,where a silty shaleis takenasthe cap-rock with difTerent underlying lithofacies.For eachfacies,Vp, Vs, and p are extractedfrom well-log data and usedin the modeling.We observea cleansand/pure shaleambiguity (faciesIIb andfaciesV) at nearof1iets,whereascleansandsand shalesare distinguishableat far offsets.This exampledepictshow AVO is necessary to discriminatedifferentlithofacies in this case. I
  • 31. -T I 197 - 4.3 AVO analysis V Hydrocarlon tr€ild Cemenled {el brino 0 Ceme|rbd w/ hydruca]ton Unconsolidaled w/ brine Unconsolidtlsd w/ hydrocarbon Figure 4.7 Schcgatic AVOcurves firrcemented sandstone andunconsolidated sands capped by shlle.frll brine-saturated andoil-saturated cases. Figure 4.7 shclwsanotherexample,where we considertwo typesof clean sands, cementedandunconsolidated,with brine versushydrocarbonsaturation.We seethat a cementedsanclstone with hydrocarbonsaturationcan have similar AVO responseto a brine-saturated. unconsolidatedsand. The examplesin Figures4.6 and 4.7 indicate how important it is to understandthe localgeologyduring AVO analysis.lt is necessary to know whattypeof sandis expected for a given prospect,and how much one expectsthe sandsto changelocally owing to textural changes,before interpretingfluid content.It is thereforeequally important to coniluctrealisticlithology substitutions in additionto fluid substitutionduring AVO rnodelingstudies.The examplesin Figures4.6 and 4.7 alsodemonstrate the impor- tanceof the link betweenrock physicsand geology (Chapter2) during AVO analysis. Whenis AVOanalysisthe appropriate technique? It is well known that AVO analysisdoes not always work. Owing to the many caseswhere AVO hasbeenappliedwithoul success, the techniquehasreceiveda bad reputationas an unreliabletool. However.part ol the AVO analysisis to find out if the techniqueis appropriatein the first place.It will work only if lhe rock physicsand ffuid characleristics of the targetreservoirareexpectedto give a good AVO response. This mustbeclarifiedbeforetheAVO analysis of realdata.Without a properfeasibility study.one can easily misinterpretAVO signatures in the real data.A good feasibilitystudycould includeboth simple reflectivitymodelingand moreadvanced forward seismicmodeling(seeSection4.51.Both thesetechniques shouldbe foundedon a thoroughunderstanding of localgeologyandpetrophysical properties. Realisticlithologysubstitution is asimportantasfluid substitution during thisexercise. CemellHion trend I I
  • 32. 198 Gommon techniques forquantitative seismic interpretation I 4.3.8 Often, one will find that there is a certain depth interval where AVO will work, often referredto as the "AVO window." Outside this, AVO will not work well. That is why analysis of rack physics depth trends should be an integral part of AVO analysis(seeSections2.6 and 4.3.16). However. the "AVO window" is also constrained by dataquality.With increasingdepth,absorptionof primary energy reduces the signal-to-noise ratio.higherfrequencies aregraduallymoreattenualed thanlower frequencies. the geologyusuallybecomesmorecomplexcausingmore complexwavepropagations, andtheanglerangereduces for agivenstreamer length. All thesefactorsmakeAVO lessapplicablewith increasing depth. Deterministic AVO analysis ofGDP gathers After simple half--space AVO modeling,the next stepin AVO analysisshouldbe deter- ministic AVO analysisof selectedCDP (common-depth-point)gathers,preferably at well locations where syntheticgatherscan be generatedand comparedwith the real CDP gathers. In this section,we showanexampleof how themethodcanbeappliedto discriminate lithofacies in realseismicdata,by analyzingCDP gathers atwell locations in a deterministic way. Figure 4.8 showsthe real and syntheticCDP gathersat three adjacent well locationsin a North Seafield (thewell logsareshownin Figure5.1,case study l). The figurealsoincludesthe pickedamplitudesat a top targethorizonsuper- imposed on exact Zoeppritz calculatedreflectivity curves derived fiom the well-log data. In Well 2, the reservoirsandsareunconsolidated, representoil-saturatedsands,and arecappedby silty shales.According to the saturationcurvesderivedfiom deepresis- tivity measurements, the oil saturationin the reservoirvaries from 20-807o, with an averageof about 60Va.The sonic and density logs are found to measurethe mud filtrate invaded zone (0-l0o/o oil). Hence, we do fluid substitution to calculate the seismicpropertiesof the reservoir from the Biot-Gassmann theory assuminga uni- form saturationmodel (the processof fluid substitution is describedin Chapter l). Before we do the fluid substitution, we need to know the acoustic properties of the oil and the mud filtrate. These are calculatedfrom Batzle and Wang's relations (seeChapter l). For this case,the input parametersfor the fluid substitutionare as fbllows. oilGoR Oil relative density Mud-filtrate density Pore pressure atreservoir level Temperature atreservoir level 64 UI 32APT 1.09g/cm3 20 MPa 77.2',C
  • 33. -v i 199 4.3 AVO analysis - Well 3 0 323 726 1210 1694 2177 CDP ] OFF t Relleclvity Rel ectivity 0 100 0 050 0 050 0 - weill i'. - r -r;r! . 1 ' ' , . P B 0.r00 0.050 Well3 : 0 1 0 0; : I I 0.050 ! : '. 0 i : : 0 0 5 0 i n n q n I ' - I l'o" .. 0 r00 l 0 150 Angle 0 1 14 21 28 34 (deq) Anqle 0 8 l5 22 29 (deg) Angle 0 1 14 20 26 32 (deg) Figure4.8 RealCDP gathers(upper),syntheticCDP gathers(middle),andAVO curvesfor Wells I 3 (lower).
  • 34. 200 Common techniques lorquantitative seismic interpretation I The correspondingAVO responseshowsa negativezero-ofTset reflectivity and a neg- ativeAVO gradient.In Well l, we havea water-saturated cementedsandbelow a silty shale.The correspondingAVO responsein this well showsa strongpositivezero-ofl.set reflectivity and a relatively strong negativegradient.Finally, in Well 3 we observea strongpositivezero-offsetreflectivity anda moderatenegativegradient,corresponding to interbeddedsand/shale faciescappedby silty shales.Hence,we observethreedistinct AVO responsesin the three different wells. The changesare relatedto both Iithology and pore-fluid variations within the turbidite system.For more detailed information aboutthis system,seecasestudy I in Chapter5. Avsethet al. (2000)demonstratedthe etlect of cementationon the AVO responsein real CDP gathersaroundtwo wells, one where the reservoirsandsare friable, and the other where the reservoir sandsare cemented.They found that if the textural eflects of the sandswere ignored,the correspondingchangesin AVO responsecould be inter- pretedas pore-fluidchanges, just as depictedin the reflectivitymodelingexamplein Figure4.7. lmpodance0f AVOanalysisof individualCDPgathers Investigations of CDP gathersare importanlin order ro confirm AVO anomalies seenin weightedstacksect.ions (Shuey:s intercepr andgradient,SmithandGidlow's fluid factor.etc.).The weightedstackscan containanomaliesnot relatedto true offset-dependent amplitudevariations. 4.3.9 Estimation ofAVO parameters Estimating intercept and gradient The next stepin an AVO analysisshouldbe to extractAVO attributesanddo multivari- ate analysisof these.Severaldifferent AVO attributescan be extracted,mappedand analyzed.The two most importantonesarezero-offsetreflectivity (R(0)) andAVO gra- dient(G) basedon Shuey'sapproximation. Theseseismicpararneters canbe extracted, via a least-squares seismicinversion,for eachsamplein a CDP gatherovera selected portionof a 3D seismicvolume. For a given NMO-conected CDP gather, R(/,,r), it is assumed that for each time sample, /, the reflectivity data can be expressedas Shuey's formula (equation (4.8)): R(r, r) : R(/,0) + c(/) sin2g(r, -r) (4 7 ) where 0(r, x) is the incident angle correspondingto the data sample recorded at (t.r).
  • 35. 201 - 4.3 AVO analysis For a layeredEarth,the relationshipbetweenofliet (r) andangle(0) is givenapprox- imatelyby: r VrNr (4.33) sin0(r,x) I k3+x2fvi^)tt2 where VrNr is the interval velocity and Vnr,,rs is the averageroot-mean-square veloc- ity, as calculated from an input velocity profile (fbr example obtained from sonic log). For any given valueof zero-offsettime, /e,we assumethatR is measuredat N offsets (xi, i:1, A/).Hence,we canrewritethe definingequationfbr this time as(Hampson andRussell.1995): t t 2 YRMS R(.rr) R(xz) sin2o(4 xr) sin2g(r,,rz) Inmor-l I c u r I (4.34) N equationsin the two equationis obtainedbY R(r,r,) I sin2g(r, ,rr,') This matrix equationis in the form of b: Ac and represents unknowns,R(/, 0) and G(r).The least-squares solutionto this solvingthe so-called"normal equation": c: (ArA)-1(ATb) (4.3s) usthe least-squares solutionfbr R(0) andG at time t. Inversion for elastic Parameters Going beyond the estimationof interceptand gradient,one can invert pre-stackseis- mic amplitudesfor elasticparameters, including Vp, V5anddensity.This is commonly ref'erredto asAVO inversion,and can be performedvia nonlinearmethods(e'g.,Dahl ancl Ursin. 19921 Bulandetal., 1996;GouveiaandScales,1998)or linearizedinversion methods(e.g.,Smith and Gidlow, 1987;Loertzerand Berkhout,1993).Gouveiaand Scales( 1998)clefined a Bayesiannonlinearmodelandestimated, via a nonlinearcon- jugate gradient method, the maximum a-posteriori(MAP) distributionsof the elastic parameters.However, the nonlinearity of the inversion problem makestheir method very compurerintensive.LoertzerandBerkhout ( 1993)performedlinearizedBayesian inversion basedon single interfacetheory on a sample-by-samplebasis.Buland and Omre (2003) extendedthe work of Loertzer and Berkhout and developeda linearized BayesianAVO inversion method where the wavelet is accountedfor by convolution. The inversionis perfbrmedsimultaneously fbr all timesin a giventime window,which ^
  • 36. 202 r Common techniques forquantitative seismic interpretation makes it possibleto obtain temporal correlation betweenmodel parametersclose in time. Furthermore,they solved the AVO inversion problem via Gaussianpriors and obtainedan explicit analyticalform for the posteriordensity,providing a computation- ally fastestimationof the elasticparameters. Pittalls ofAVO inversion . A linearapproximation of theZoeppntzequations is commonlyusedin thecalcu- lationof R(01andG. The two-termShueyapproximationis known lo be accurate for anglesof incidenceup to approximately 30'. Make surethatthe datainverted do not exceedthis range,so the approximalionis valid' . The Zoeppritzequations areonly valid fbr singleinterfaces. lnversionalgorithms thatarebasedon theseequations will not be valid lor thin-bedded geology. . The linear AVO inversionis sensitiveto uncharacteristic amplitudescausedby noise(includingmultiples.) or processing and acquisirioneffects.A few outlying valuespresent in thepre-stack amplitudes areenoughto causeerroneous estimates of R(0) and G. Mosr commercialsoftwarepackagesfor eslimationof R(0) and C applyrobusr estimarion techniques (e.g.,Walden.199l) to limit thedamage ol' outlying amPlitudes. . Another potential problem during sample-by-sample AVO inversionis errors in the moveoutcorrection(Spratt, 1987l. Ursin and Ekren (1994) presented a method for analyzingAVO eflects in the offset domain using time windows. This techniquereducesmoveouterrorsand createsimprovedestimates oi AVO parameters. 4,3.10AVO cross-Plot analysis A very helpful way to interpretAVO attributesis to makecross-plotsof intercept(R(0)) versusgradient(G).Theseplotsarea veryhelpfulandintuitiveway of presenting AVO data,and can give a better understandingof the rock propertiesthan by analyzingthe standardAVO curves. AVO classes RutherfordandWilliams ( 1989)suggested a classification schemeof AVO responses fbr 6iflerent typesof gassanils(seeFigure 4.9). They definedthreeAVO classes based on wherethe top of the gassandswill be locatedin an R(0) versusG cross-plot. The cross-plotis split up into fbur quadrants. In a cross-plotwith R(0) along.r-axisand C along,v-axis, the I stquadrantis whereR(0) andG arebothpositivevalues(upperright quadrant). The2ndis whereR(0)is negative andG is positive(upperleft quadrant). The 3rd is whereborhR(0) andG arenegative(lower left quadrant).Finally,the4th quadrant is where R(0) is positive and G is negative(lower right quadrant).The AVO classes
  • 37. 203 I- 4.3 AVoanalysis Tabfe 4.1AVO classes, after Ruthe(brd and Williams (1989)' extendecl b1'Castagnaand Smith (1994),and Rossand Kinman( 1995) Class RelativeimPedance Quadrant R(0) G AVO product High-impedance sand No or low contrast Low impedance Low impedance 4th ,lth 3rd 3rd 2nd Negative Negative Positive Positive Negative class lll t a t -- Ictass tt t.. ' r O D 1 I cra.i rrp I crass r [ - Figure 4,9 Ruthertbrd andwilliamsAVOclasses, originally defined forgassands (classes I, ll and III),along withtheadded clnsses IV (Castagna andSmith. 1994) andIIp(Ross andKinman' 1995)' Figure isaclapted fiomCastagna etal.(1998)' must not be confused with the quadrantnumbers.Class I plots in the 4th quadrant with positiveR(0) and negativegradients.Theserepresenthard eventswith relatively high impedanceand low vp/vs ratio comparedwith the cap-rock.class II represents sandswith weak interceptbut strong negatjvegradient.Thesecan be hard to seeon the seismic data, becausethey often yield dim spots on stackedsections'Class III is the AVO categorythat is normally associatedwith bright spots'These plot in the 3rd quadrantin R(0)-G cross-plots,and are associated with soft sandssaturatedwith hydrocarbons (seePlate4.l0). Rossand Kinman (1995) distinguished betweena classIIp and classII anomaly' ClassIIp hasa weak but positive interceptand a negativegradient,causinga polarity changewith oflset. This classwill disappearon full stacksections.class II hasa weak but negativeinterceptand negativegraclient,henceno polarity change.This classmay be observedasa negativeamplitudeon a full-ofliet stack' Castagnaand Swan (1997) extendeclthe classificationschemeof Rutherford and Williams to incluclea 4th class,plotting in the 2n<1 quadrant.Thesearerelatively rare' but occur when soft sandswith gas are cappedby relatively stiff shalescharacter- ized by Vp/Vs ratios slightly higher than in the sands(i'e" very compactedor silty shales).
  • 38. 204 Gommon techniques forquantitative seismic interpretation : Summary ofAVO classes ' AVOclassI represents relativelyhardsands with hydrocarbons. Thesesands tendl"o plotalongthe background trendin intercept-gradient cross-plots. Moreover,very hardsandscan have little sensitivityto fluids.so theremay not be an associated flat spot.Hence.thesesandscan be hardto discoverlrom seismicdata. . AVo classII. representing transparent sandswith hydrocarbons, oftenshowup as dim spotsorweaknegativereflectorson theseismic. However. becauseof relatively largegradients. they shouldshow up as anomaliesin an Rt0)-c cross-plot.and plot off the backgroundtrend. ' AVO classIII is the"classical"AVO anomalywith negative intercept andnegative gradient.This class represents relativelysoft sandswirh high fluid sensitivity, locatedfar awayfrom the background trend.Hence,theyshouldbe easyro derect on seismic data. ' AVO classIV aresands with negative intercept butpositivegradient. Thereflection coefficientbecomeslessnegaLive with increasing offset,andamplitudedecreases versusoffset.eventhoughLhese sandsmay be bright spots(castagnaand Swan. 1997).ClasslV anomalies arerelativelyrare,but occurwhen soft sandswith gas arecappedby relativelystiffcap-rockshales characterized by vplvs ratiosslightly higherthanin thesands (i.e..verycompacted or siltyshales). The AVo classes were originally definedfor gassands.However.todaythe AVo classsystemis usedfor descriptiveclassification of observedanomaliesthal are not necessarily gassands.An AVO classIl that is drilled can turn out to be brine sands.It does not mean that the AVo anomaly was not a class ll anomaly.we therefbresuggestapplyingtheclassification only asdescriptive termsfor observed AVo anomalies, without aulomaticallyinferringthat we are dealingwith gas sands. AVO trends and the effects of porosity, lithology and compaction When we plot R(0) andG ascross-plots,we can analyzethetrendsthatoccurin termsof changes in rock physicsproperties, includingfluid trends, porositytrendsandlithology trends,as thesewill have differentdirectionsin the cross-plot(Figure4.1l). Using rock physicsmodelsand then calculatingthe corresponding interceptand gradients, we can study various"What lf" scenarios,and then comparethe modeledtrendswith the inverteddata. Brine-saturatedsandsinterbeddedwith shales,situatedwithin a limited depthrange andat a particularlocality, normally follow a well-defined"backgroundtrend" in AVO cross-plot (Castagnaand Swan, 1991). A common and recommendedapproach in qualitativeAVO cross-plotanalysisis to recognizethe "background" trend and then look fbr datapoints that deviatefrom this trend.
  • 39. 205 r 4,3 AVO analysis FigUre 4.11Difl'erent trends occurring in anintercept gradient cross-plot' (Adapted fiomSimm etal.,2O0O.) Castagnaet at. (1998) presentedan excellentoverview and a fiamework for AVO gradientand interceptinterpretation.The top of the sandswill normally plot in the 4th quadrant,with positiveR(0) andnegativeG. The baseof the sandswill normally plot in the 2ndquadrant,with negativeR(0) andpositiveG. The top andbaseof sands,together with shale-shaleintertaces,will createa nice trend or ellipse with centerin the origin of the R(O)-G coordinatesystem.This trend will rotate with contrastin Vp/V5 ratio betweena shalycap-rockancla sandyreservoir(Castagna et al., 1998;Sams' 1998)' We can extractthe relationshipbetweenVplVs tatio and the slopeof the background trencl(a6)by clividingthe gradient,G, by the intercept,R(0): G R(0) Assuming the density contrastbetween shaleand wet sandto be zero, we can study how changinE VplVs ratio affectsthe backgroundtrend.The densitycontrastbetween sandandshaleat a givendepthis normallyrelativelysmallcompared with the velocity contrasts (Fosteret a.,1991).Thenthe backgroundslopeis givenby: . ^ l - ( V s r * Y s 2 ) A Y s l u h - I " L t Y nt V p : t A V p l (4..r7) where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir, respectively;Vs1and V52are the correspondingS-wavevelocities,whereasAVp and AV5 arethe velocity differencesbetweenreservoiranclcap-rock.If the Vp/V5 ratio is 2 in the cap-rock and 2 in the reservoir,the slopeof the backgroundtrend is - l, that is a 45' slopediagonalto the gradientand interceptaxes.Figure 4'12 showsdifferent lines correspondingto varying Vp/V5 ratio in the reservoirand the cap-rock. The rotation of the line denoting the backgroundtrend will be an implicit function of rock physics propertiessuch as clay content and porosity.Increasingclay content (4.36)
  • 40. VplVs=2.5 incaP-rock 206 Common techniques forquantitative seismic interpretation - 0 B(0) -0.5L -0.5 Figure4,12 BackgroundtrendsinAVOcross-plotsasafunctionofvaryingVplV<ralioincap-rock andreservoir. (Weassume nodensity contrast.) Notice thataVplVsratioof 1.5in thereservoir can have diff'erent locations in theAVOcross-plot depending onthecap-rock VplV5ratio. Ifthe Vp/V5 ratioof thecap-rock is2.5,thesand will exhibit AVOclass ll to III behavior (lefi),whereas if the cap-rock Vp/V5 ratiois2.0, thesand will exhibit class I toIIpbehavior (right). at a reservoirlevel will causea counter-clockwise rotation,as the Vp/V5 ratio will increase.Increasing porosity related to less compaction will also cause a counter- clockwise rotation, as less-compactedsedimentstend to have relatively high VplVg ratio. However,increasingporosityrelatedto lessclay contentor improved sortingwill normally causea clockwise rotation, as clean sandstend to have lower Vp/V5 ratio than shaly sands.Hence,it can be a pitfall to relateporosity to AVO responsewithout identifying the causeof the porosity change. Thebackground trendwill change with depth,buttheway it changes canbecomplex. Intrinsicattenuation, discussed in Section4.3.4(Luh, 1993),will afI-ect thebackground trendasa function of depth,but correctionshouldbe madefbr this beforerock physics analysisof the AVO cross-plot(seeSection4.3.6).Nevertheless, the rotationdue to depth trends in the elastic contrastsbetweensandsand shalesis not straightforward, because theVplVs in the cap-rockas well as the reservoirwill decrease with depth. Thesetwo efTects will counteracteachother in termsof rotationaldirection. asseenin Figure4.12.Thus,therotationwith depthmustbeanalyzed locally.Also, thecontrasts betweencap-rock and reservoir will changeas a function of lithology, clay content, sorting,and diagenesis,all geologic factorsthat can be unrelatedto depth.That being said,we shouldnot includetoo largeadepthintervalwhenwe extractbackgroundtrends (Castagna and Swan, 1997).That would causeseveralslopesto be superimposed and resultin a lessdefinedbackgroundtrend.For instance,note that the top of a soft sand will plot in the 3rd quadrant, while thebaseof a softsandwill plot in the I st quadrant, giving a backgroundtrendrotatedin the oppositedirectionto the trendfor hard sands. VplVs=2.Q incaP-rock
  • 41. T 207 r 4.3 AVO analysis Fluid effects and AVO anomalies As mentionedabove,deviationsfiom thebackgroundtrendmay be indicativeof hydro- carbons,or somelocal lithology or diagenesiseffectwith anomalouselasticproperties (Castagnaet at., 1998).Fosteret al. (1991)mathematicallyderivedhydrocarbontrends that would be nearly parallel to the backgroundtrend,but would not passthrough the origin in R(0) versusG cross-plots.For both hard and soft sandswe expectthe top of hydrocarbon-filleclrocks to plot to the left of the backgroundtrend, with lower R(0) and G valuescomparedwith the brine-saturated case.However,Castagnaet al. (1998) fbund that,in particular,gas-saturated sandscould exhibit a variety of AVO behaviors. As lisredin Table4.1. AVO classIII anomalies(Rutherfordand Williams, 1989), representingsoft sandswith gas,will fall in the 3rd quadrant(the lower left quadrant) and havenegativeR(0) and G. Theseanomaliesarethe easiestto detectfiom seismic data(seeSection 4.3.1l). Harclsandswith gas,representing AVO classI anomalies,will plot in the4th quadrant (lower right) and have positive R(0) and negativeG. Consequently,thesesandstend to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented), they will not show a large changein seismicresponsewhen we go from brine to gas (cf. Chapterl). This type of AVO anomalywill not showup asananomalyin a product stack. In fact, they can plot on top of the background trend of some softer, brine- saturatedsands.Hence,very stifTsandswith hydrocarbonscanbe hardto discriminate with AVO analysis. AVO classII anomalies,representingsandssaturatedwith hydrocarbonsthat have very weak zero-offsetcontrastcomparedwith the cap-rock, can show great overlap with thebackground trend,especially if thesandsarerelativelydeep.However,classII type oil sandscanoccurvery shallow,causingdim spotsthatstickout comparedwith a bright backgroundresponse (i.e.,when heterolithicsand brine-saturated sandsare relatively stifTcomparedwith overlying shales).However,becausethey are dim they areeasyto miss in near-or full-stack seismicsections,andAVO analysiscantherefore be a very helpful tool in areaswith classII anomalies. Castagnaand Swan (199'l) discovereda diff'erenttype of AVO responsefor some gas sands,which they ref-erredto as class IV AVO anomalies(see Table 4.l), or a "false negative."They found that in some rare cases,gas sandscould have negative R(0) and positive G, henceplotting in the 2nd quadrant(upper left quadrant).They showedthatthis may occur if the gas-sandshear-wave velocity is lower thanthat of the overlyingformation.The mostlikely geologicscenario for suchanAVO anomalyis in unconsolidatedsandswith relativelylarge VplVs ratio(Fosteret crl.,1997).That means that if the cap-rockis a shale,it must be a relativelystiff and rigid shale,normally a very silt-rich shale.This AVO responsecanconfusethe interpreter.First, the gradients of sandsplotting in the 2nd quadranttend to be relatively small, and lesssensitiveto fluid type thanthe gradientsfor sandsplotting in the 3rd quadrant.Second,theseAVO anomalieswill actually showup asdim spotsin a gradientstack.However,they should a
  • 42. 208 Common techniques forquantitative seismic interpretation - standout in an R(0)-G cross-plot,with lower R(0) valuesthan the backgroundtrend. Seismically, they shouldstandout asnegative bright spots. Pitfalls . Differentrockphysicstrencls in AVO cross-plots canbeambiguous. Theinterpreta- tion of AVO trendsshouldbebasedon locallyconstrained rock physicsmodeling. not on naiverulesof thumb. . Trendswithin individualclustersthatdo not projectthroughtheorigin on an AVO cross-plol. cannot always be interpretedas a hydrocarbonindicatoror unusual lithology.Sams(1998) showedthat it is possiblefortrends to have largeoffsets from the origin evenwhen no hydrocarbons are presentand the lithology is not unusual.Only where the rocks on eitherside of the reflectingsurfacehave the sameVp/V5 ratio will the lrends(not to be confusedwith backgroundlrendsas shownin Figure4. l2.l projectthroughthe origin. Samsshowedan exampleof a brinesandthatappeared moreanomalous thana Iessporoushydrocarbon-bearing sand. . Residualgassaturation can causesimilar AVO effectsro high saturations of gas or light oil. Three-termAVO wherereliableestimates of densityareoblained.or attenuation attributes. can potentiallydiscriminateresidualgas saturations from commercialamountsof hydrocarbons (seeSections 4.3.12 and4.3.|5 for further discussions). Noise trends A cross-plot betweenR(0) andG will alsoincludea noisetrend,because of thecorre- lation betweenR(0) and G. BecauseR(0) and G areobtainedfrom least-square fitting, there is a negativecorrelation betweenR(0) and G. Larger interceptsare correlated with smallerslopesfbr a givendataset.Hence,uncorrelated randomnoisewill show an oval, correlateddistributionin the cross-plotas seenin Figure 4.13 (Cambois, 2000). Furthermore,Cambois (2001) formulatedthe influenceof noise on R(0), G and a range-limitedstack(i.e.,sub-stack)in termsof approximateequationsof standard deviations: 3 dR(o) : ;o, /, ^ / ; 'JV-) o f t - - - " t i - ^ ) z stn-0n," t; (I/t(l)) o C : V f . r ^ sln-umrx (4.38) (4.3e) (4.40)
  • 43. 209 - 4.3 AVO analysis -0.1 ir.} * , rl "t; -0.15 -0"1 -0.05 0 I (0) 0.05 0.1 0.15 Figure4,13 Randomnoisehasa ttendin rR(0) versusG (afterCambois,2000) and o,,- Ji .o, (4.41) whered " is the standard deviationof thefull-stackresponse, o, is thestandard deviation of the sub-stack.and n is the number of sub-stacks of the full fold data.As we see,the stack reducesthe noise in proportion to the squareroot of the fold. These equations indicate that the intercept is less robust than a half-fold sub-stack,but more robust than a third-fold sub-stack.The gradientis much more unreliable,sincethe standard deviationof the gradientis inverselyproportionalto the sinesquaredof the maximum angle of incidence. Eventually, the intercept uncertaintyrelated to noise is more or lessinsensitiveto the maximum incidenceangle,whereasthe gradientuncertaintywill decreasewith increasingaperture(Cambois,2001). Simm era/. (2000)claimedthatwhile rock propertyinfbrmation is containedin AVO cross-plots,it is not usually detectablein terms of distinct trends,owing to the effect of noise.The fact that the slopeestimationis more uncertainthan the interceptduring a least-squareinversion makesthe AVO gradientmore uncertainthan the zero-offset reflectivity (e.g.,Houck, 2002).Hence,the extensionof a trendparallelto the gradient axisis an indicationof the amountof noisein thedata. I A -,:'i.;.d-f,*t 'i;l? 4 , , r
  • 44. 210 Common techniques forquantitative seismic interpretation I Fluid versus noise trends In areaswhere fluid changesin sandscauselarge impedancechanges,we tend to seea right-to-left lateralshift along the interceptdirection.This direction is almostopposite tothenoisedirection.which ispredominantJy in thevertical/gradient direction. In thesecasesthereshould be a fair chanceof discriminating hydrocarbon- saturated sandsfrom brine-saturated sands, evenin relativelynoisydata. Simm er al. (2000) furthermore stressedthat one should create AVO cross-plots aroundhorizons,notfrom time windows.Horizon cross-plotclearlytargetsthereservoir of interestand helps determinethe noise trend while revealingthe more subtle AVO responses. Moreover,only samplesof the maximum amplitudesshouldbe included. Samplingpartsof the wavefbrmsotherthan the maxima will infill the areabetween separate clusters,and a lot of sampleswith no physical significancewould scatter aroundthe origin in an R(0) G cross-plot. However,picking only peaksand troughs raisesa delicatequestion:what about transparent sandswith low or no impedance contrastwith overlyingshales'l Theseare significantreflections with very smallR(0) valuesthat could be missedif we invertthe waveformonly at absolutemaxima (in commercialsoftwarepackages tbr AVO inversion, theabsolute maximaarecommonly definedfiom R(0) sections). Anotherissueis shale shaleinterfaces. Theseareusually very weak reflectionsthat would be locatedcloseto the origin in an AVO cross-plot, but they are still important for assessment of a local backgroundtrend. Therearealsoothertypesof noiseaff-ecting the AVO cross-plotdata,suchasresidual moveout.It is essential to try to reducethenoisetrendin thedatabeforeanalyzingthe cross-plot in termsof rockphysicsproperties. A goodpre-processing scheme isessential in orderto achievethis (seeSection4.3.6). Cambois(2000)is doubtful thatAVO cross-plotscanbe usedquantitatively,because of the noiseeffect.With that in mind, it shouldstill be possibleto separate the real rock physicstrendsfiom the noise trends.One way to distinguishthe noise trend is to cross-plota limited numberof samplesfrom the samehorizonfrom a seismic section.The extensionof the trend along the gradientaxis indicatesthe amount of noisein the data (Simm et al., 2000).Another way to investigate noiseversusrock physics trends is to plot the anomaly cluster seenin the AVO cross-plot as color- codedsamples ontotheseismicsection. If theclusteris mainly dueto randomnoise,it shouldbe scattered randomlyaroundin a seismicsection.However,if the anomaly conesponds with a geologic structure and closure, it may representhydrocarbons (seePlate4.10). Finally, we claim that via statistical rock physicswe can estimatethe most likely fluid and lithology fiom AVO cross-plots even in the presence of somenoise.This is ref'erredto as probabilistic AVO analysis,and was first introducedby Avseth er a/. (1998b).This methodworks by estimatingprobabilitydistributionfunctionsof R(0)