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I 4 Common techniques quantitative for interpretation seismic - Thereare no facts,only interpretations. lriedrith Niet:sche - 4.1 Introduction Conventionalseismicinterpretationimplies picking and tracking laterally consistent seismic reflectors for the purpose of mapping geologic structures,stratigraphy and reservoirarchitecture. The ultimategoal is to detecthydrocarbonaccumulations, delin- eatetheir extent, and calculatetheir volumes.Conventionalseismic interpretationis an art that requires skill and thorough experiencein geology and geophysics. Traditionally, seismicinterpretationhasbeenessentiallyqualitative.The geometrical expressionof seismic reflectorsis thoroughly mapped in spaceand traveltime,but litfle emphasis put on the physicalunderstanding seismicamplitudevariations.In the is of last few decades,however, seismic interpretershave put increasingemphasison more quantitative techniques fbr seismic interpretation,as these can validate hydrocarbon anomalies and give additional information during prospect evaluation and reservoir The most important of thesetechniquesinclude post-stackamplitucle characterization. (bright-spot analysis anddim-spotanalysis), offset-dependentamplitudeanalysis(AVO acousticand elasticimpedance analysis), inversion,and forward seismicmodeling. These techniques,if used properly, open up new doors for the seismic interpreter. The seismicamplitudes, representingprimarily contrasts elasticproperties in between individual layers,contain information about lithology, porosity,pore-fluid type and sat- uration, as well as pore pressure- information that cannot be gained fiom conventional i s e i s m i cn t e r p r e t a l i o n . - 4.2 Qualitativeseismicamplitude interpretation Until a few decades ago, it would be common for seismic interpreters to roll out ng l h e i r s e v e r a l - m e t e r s - l op a p e rs e c t i o n s with seismic data down the hallway, go down 168 169 4,2 Qualitative interpretation amplitude seismic - on their knees,and use their colored pencils to interpretthe horizons of interestrn order to map geologic bodies. Little attention was paid to amplitude variations and their interpretations. the early 1970sthe so-called"brighrspot" techniqueproved In successful areas the Gulf of Mexico, wherebright amplitudes in of would coincidewith gas-filled sands.However, experiencewould show that this technique did not always work. Some of the bright spots that were interpreted as gas sands,and subsequently drilled, were fbund to be volcanic intrusions or other lithologies with high impedance contrast compared with embedding shales.These tailures were also related to lack of waveletphase analysis, hardvolcanicintrusions as would cause opposite polarityto low- impedance gas sands.Moreover, experienceshowed that gas-filled sands sometimes could cause"dim spots," not "bright spots," if the sandshad high impedancecompared with surroundingshales. With the introductionof 3D seismicdata, the utilization of amplitudesin seismic interpretation became much more important. Brown (see Brown et ul., l98l) was one of the pioneersin 3D seismicinterpretation lithofaciesfiom amplitudes. of The generationoftime slicesand horizon slicesrevealed3D geologic patternsthat had been impossible to discover from geometric interpretationof the wiggle tracesin 2D stack sections.Today, the further advance in seismic technology has provided us with 3D visualization can stepinto a virtual-realityworld of seismic tools where the interpreter wiggles and amplitudes, and trace these spatially (3D) and temporally (4D) in a way that one could only dream of a few decadesago. Certainly, the leap fiom the rolled-out paper sectionsdown the hallways to the virtual-reality imagesin visualization "caves" is a giant leap with greatbusiness implicationsfor the oil industry.In this sectionwe review the qualitative aspects seismicamplitude interpretation,before we dig into the of and rock-physics-based more quantitative impedance suchasAVO analysis, techniques inversion,and seismicmodeling,in fbllowing sections. phase polarity 4.2.1 Wavelet and The very first issue to resolve when interpreting seismic amplitudes is what kind of wavelct we have. Essentialquestionsto ask are the fbllowing. What is the defined I polarity in our case?Are we dealingwith a zero-phase a minimum-phase or wavelet? Is there a phase shift in the data? These are not straightfbrward questions to answet, becausethe phase of the wavelet can change both laterally and vertically. However, there are a f'ew pitfalls to be avoided. First, we want to make sure what the defined standardis when processingthe data. There exist two standards. The American standarddefinesa black peak as a "hard" or "positive" event,and a white trough as a "soft" or a "negative"event.On a near-ofl.set stack section a "hard" event will correspondto an increasein acousticimpedancewith depth, whereasa "soft" event will correspondto a decrease acousticimpedancewith in depth. According to the European standard,a black peak is a "soft" event, whereas a 170 techniques quantitative Gommon for interpretation seismic T white trough is a "hard" event. One way to check the polarity of marine data is to look at the sea-floorreflector.This reflector should be a strongpositive reflector representing the boundary between water and sediment. polarity Data ' American polarity: An increase impedance in gives positiveamplitude.normally displayedas black peak (wiggle r.race) red intensitylcolor displayt. or . European Australian)polarity:An increase impedance (or in givesnegal.ive ampli- tude, normally displayedas white rrough (wiggle trace) or blue intensity(color display). (Adaptedfrom Brown. 200la, 2001b) For optimal quantitative seismic interpretations,we should ensurethat our data are zero-phase. Then, the seismicpick should be on the crest of the waveform conespond- ing with the peak amplitudes that we desire for quanrirativeuse (Brown, l99g). with today's advanced seismic interpretation tools involving the use of interactive work- stations,there exist various techniquesfbr horizon picking that allow efficient inter- pretationof large amountsof seismicdata.Thesetechniques include manualpicking, interpolation,autotracking,voxel tracking, and surfaceslicing (see Dorn (199g) fbr detaileddescriptions). For extraction of seismic horizon slices, autopicked or voxel-tracked horizons are very common. The obvious advantageof autotracking is the speed and efficiency. Furthermore, autopicking ensuresthat the peak amplitude is picked along a horizon. However,one pitfall is the assumptionthat seismichorizons are 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 where a single event splits into a doublet, the autopicking may fail to track the corect horizon. Not only will important reservoirparameters neglected,but the geometriesand volumes may be also be significantly off if we do not regard lateral phaseshifts. It is important that the interpreterrealizesthis and reviewsthe seismicpicks for quality control. 4.2.2 Sand/shale cross-overs depth with Simple rock physicsmodeling can assistthe initial phaseof qualitativeseismicinrer- pretation, when we are uncertain about what polarity to expect for diff'erentlithology boundaries. a siliciclastic In environment, most seismic reflectorswill be associated with sand-shaleboundaries.Hence, the polarity will be related to the contrastin impedance between sand and shale.This contrastwill vary with depth (Chapter 2). Usually, rela- tively sott sandsare fbund at relatively shallow depths where the sandsare unconsol- idated. At greater depths, the sandsbecome consolidatedand cemented.whereas the 171 4.2 Qualitative seismic amplitude interpretati0n - versus Sand impedance trends shale depth polarity andseismic (schematic) rmpe0ance 1 t Sand-shale cross-over DeDth Figure Schematic 4'1 depthtrends sand shale of and impeclances. depth The trends varyfiom can basin basin, there be morethanonecross-over. to and can Localdepthtrendsshould established be for different basins. shalesare mainly affectedby mechanicalcompaction.Hence, cementedsandstones are normally found to be relatively hard eventson the seismic.There will be a correspond- ing cross-overin acousticimpedanceof sandsand shalesas we go fiom shallow and soft sandsto the deep and hard sandstones (seeFigure 4.1). However, the depth trends can be much more complex than shown in Figure 4.1 (Chapter2, seeFigures 2.34 and,2.35'). Shallow sandscan be relatively hard comparedwith surroundingshales,whereasdeep cementedsandstones can be relatively soft compared with surounding shales.There is no rule of thumb fbr what polarity to expect fbr sandsand shales.However, using rock physics modeling constrainedby local geologic knowledge, one can improve the understandingof expectedpolarity of seismic reflectors. venius "Hard" "soft"events During seismicinterpretation a prospect a provenreser"yoir of or sand.the following questionshould be one of the first to be asked:what type of event do we expect, a "hard" or a "soft"? [n other words. should we pick a positivepeak, or a negative trough?lfwe havegood well control,this issuecan be solvedby generating synthetic seismograms correlating and thesewith realseismicdata.If we haveno well control, we may have to guess. However. a reasonableguess can be made based on rock physics modeling. Below we have listed some "rules of thumb" on what type of reflector we expect l-ordifferent geologic scenarios. 172 techniques quantitative Common for seismic interpretation T Typical "hard"events . Very shallow sandsat normal pressureembedded pelagicshales in . Cementedsandstone with brine saluration . Carbonate rocks embedded siliciclastics in ' M i x e c ll i t h o l o g i e s h e t e r o l i t h i c s i)k e s h a t ys a n d s m a r l s .v o l c a n i c s h ( l , a deposits Typical "soft" events . Pelagic shale ' S.hallow, sands(any pore fluid) embedded normally compacted unconsolidated in shales ' Hydrocarbonaccumularions clean.unconsolidated poorly consolidated in or sancls . Overpressured zones pitfalls conventional Some in interpretation ' Make sure you know the polarity of the data. Rememberthere are two different standards, US standard the and the European standard. which are opposire. ' A hard event can changeto a soft laterally (i.e.. lateralphaseshifi; I if there are ii petrographic pore-fluidchanges. or Seismicaurotracking will nor derecr l:jloloCic. these. ' A d i m s e i s m i cr e f l e c t o r r i n t e r v a lm a y b e s i g n i f i c a n te s p e c i a l l yn o . i t h e z o n eo f ji sand/shale impedancecross-over. AVO analysisshould be underraken reveal to potentialhydrocarbon accumulations. 4.2.3 Frequency scaleeffects and Seismic resolution Verticalseismicresolution definedas theminimum separation is between two interfaces such that we can identify two interfacesrather than one (SherifTand Geldhart, 199-5). A stratigraphiclayer can be resolvedin seismicdataif the layer thickness largerthan is a quarter of a wavelength.The wavelength is 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 dominant wavelengthis 100 m. In this case,a layer of 25 m can be resolved.Below this thickness, can still gain important infbrmation via quan- we titative analysisof the interference amplitude.A bed only ),/30 in thicknessmay be detectable,althoughits thicknesscannotbe determinedfiom the wave shape(Sheriff and Geldhart.199-5). 173 interpretation amplitude seismic 4.2 Qualitative E tiickness Layer 4,2 Figure Seismic thickness a given amplitude a function layer as of fbr wavelength. The horizontal resolution of unmigrated seismic data can be defined by the Fresnel zone. Approximately, the Fresnel zone is defined by a circle of radius, R, around a p rellection oint: n - Jgz G.2) where z is the reflector clepth.Roughly, the Fresnel zone is the zone from which all reflected contributions have a phase difl-erence less than z radians. For a depth of of 3 km and velocity of 3 km/s, the Fresnelzone radius will be 300-470 m for fiequencies ranging fiom 50 to 20 Hz. When the size of the reflector is somewhat smaller than the Fresnel zone, the responseis essentiallythat of a diffraction point. Using pre- stack migration we can collapse the difliactions to be smaller than the Fresnel zone, thus increasing lateralseismicresolution(Sheriff and Geldhart,1995).Depending the on the migration aperture, the lateral resolution after migration is of the order of a wavelength.However,the migration only collapses the Fresnelzone in the direction of the migration, so if it is only performed along inlines of a 3D survey, the lateral resolution will still be limitecl by the Fresnelzone in the cross-linedirection. The lateral resolution is also restricted by the lateral sampling which is governed by the spacing between individual CDP gathers,usually 12.5 or 18 meters in 3D seismic For typical surf'ace clata. seismic wavelengths(-50-100 m), lateral sampling is not the l i m i t i n gl a c t o r . Interference and tuning effects A thin-layered reservoir can cause what is called event tuning, which is interf'erence betweenthe seismicpulse representing top of the reservoirand the seismicpulse the representingthe baseof the reservoir.This happensif the layer thicknessis less than a quarterof a wavelength (Widess,1973).Figure 4.2 showsthe efTective seismicampli- tude as a function of layer thickness for a given wavelength, where a given layer has higher impedancethan the surrounding sediments.We observethat the amplitude 174 techniques quantitative Gommon for seismic interpretation - increasesand becomes larger than the real reflectivity when the layer thickness is between a half and a quarter of a wavelength. This is when we have constructive interference between the top and the base of the layer. The rlaximum constructive interferenceoccurs when the bed thickness is equal to ),14, and this is often referred to as the tuning thickness.Furthermore, we observethat the amplitucledecreases and approacheszero for layer thicknessesbetween one-quarterof a wavelength and zero thickness. We refer to this as destructive interferencebetween the top and the base. Trough-to-peak time measurements give approximatelythe correctgrossthicknesses for thicknesses larger than a quarterof a wavelength,but no information fbr thicknesses lessthan a quarterof a wavelength. The thickness an individualthin-bedunit can be of extractedfrom amplitude measurements the unit is thinner than about ),/4 (Sheriff if and Geldhart,1995).When the layer thicknessequals)./8, Widess(1973) found that the composite responseapproximatedthe derivative of the original signal. He referred to this thickness as the theoretical threshold of resolution. The amplitude-thickness curve is almost linear below ),/8 with decreasing amplitudeas the layer gets thinner, but the compositeresponse staysthe same. 4.2.4 Amplitude reflectivity and 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-spotamplitude anomaliescould be associated with hydrocarbon traps (Hammond, 1974). This discovery increased interest in the physical propertiesof rocks and how amplitudeschangedwith difTerenttypes of rocks and pore fluids (Gardner et al., 1914').In a relatively soft sand, the presenceof gas and/or light oil will increasethe compressibilityof the rock dramatically,the veloc- ity will drop accordingly, and the amplitudewill decrease a negative"bright spot." to However, if the sand is relatively hard (compared with cap-rock), the sand saturated with brine may induce a "brighlspot" anomaly,while a gas-filledsandmay be trans- parent, causing a so-calleddim spot, that is, a very weak reflector.It is very important before startingto interpret seismicdata to find out what changein amplitude we expect for different pore fluids, and whether hydrocarbonswill cause a relative dimrning or brighteningcomparedwith brine saturation. Brown (1999)states that "the most impnr- tant seismic property of a reservoir is whether it is bright spot regime or tlim sltot regime." One obvious problem in the identification of dim spotsis that they are clim - they are hard to see.This issuecan be dealt with by investigating limited-range stack sections. A very weak near-offsetreflector may have a correspondingstrong f'ar-oflsetreflector. However,some sands,although they are significant,produce a weak positive near- offset reflection as well as a weak negative far-offset reflection. Only a quantitative analysis the changein near-to far-offsetamplitude,a gradientanalysis, of will be able 175 interpretation amplitude seismic 4.2 Qualitative T to reveal the sand with any considerabledegree of confidence. This is explained in Section4.3. Pitfalls:False"bright spots" "brighr spots"are usuallythe first type During seismicexplorationof hydrocarbons. of DHI (direct hydrocarbonindicators)one looks for. However.there have been severalcaseswhere bright-spotanomalieshavebeendrilled. and turned out not lo be hydrocarbons. Some common "false bright spors"include: . Volcanicintrusionsand volcanicash layers . Highly cementedsands. often calcitecementin thin pinch-outzones . Low-porosityheterolithicsands . Overpressuredsandsor shales . Coal beds . Top of salt diapirs Only the last threeon the list abovewill causethe samepolarity as a gas sand.The first three will causeso-called"hard-kick" amplitudes.Therefore.if one knows the polariryof the dataone shouldbe able lo discriminarehydrocarbon-associated bright spots from the "hard-kick" anomalies. AVO analysisshould permit discrimination of hydrocarbons from coal, salt or overpressuredsands/shales. A very common seismicamplitude attributeusedamong seismicinterpreters is rellectionintensity,which is root-mean-square amplitudescalculatedover a given lime window. This anribute does not distinguish between negativeand positive thereforegeologic interpretation this attributeshould be made with amplitudes; ol greatcaution. "Flat spots" Flat spotsoccur at the reflectiveboundary betweendifferent fluids, either gas-oil, gas- warer,or warer-oil contacts.Thesecan be easyto detectin areaswhere the background stratigraphyis tilted, so the flat spot will stick out. However, if the stratigraphyis more or less flat, the fluid-related flat spot can be difficult to discover. Then, quantitative methods like AVO analysiscan help to discriminate the fluid-related flat spot from the fl arlying lithostratigraphy. One should be aware of severalpitfalls when using flat spots as hydrocarbon indi- cators. Flat spots can be related to diagenetic events that are depth-dependent. The boundary between opal-A and opal-CT represents impedance increasein the same an way as fbr a fluid contact, and dry wells have been drilled on diagenetic flat spots. Clinoforms can appear as flat features even if the larger-scalestratigraphy is tilted. sheet-flood Other "false" flat spotsinclude volcanicsills, paleo-contacts, deposits and flat basesof lobesand channels. tl 176 techniques quantitative Common for interpretation seismic - False Pitfalls: "flatspots" One of f he best DHIs ro look for is a flat spot, the contactbetweengas and water, gas and oil, or oil and water.However.there are other causes that can give rise to flat spots: . Oceanbottom multiples . Flat stratigraphy. of The bases sand lobesespeciallytend to be flat. . Opal-A to opal-CT diagenetic boundary . Paleo-contacts, either relatedto diagenesis residualhydrocarbon or saturation . Volcanicsills Rigorousflat-spotanalysisshould include detailedrock physicsanalysis.and for- ward seismicmodeling,as well as AVO analysisof real data(seeSection4.3.8). Lithology, porosity and fluid ambiguities The ultimategoal in seismicexplorationis to discoverand delineate hydrocarbon reser- voirs. Seismic amplitude maps from 3D seismicdata are often qualitarlvel.finterpreted t in termsof lithology and fluids.However,rigorousrock physicsmodelingand analysis of available well-log data is required to discriminate fluid effects quantitatively trom I lithology effects (Chapters I and 2). lt The "bright-spot" analysismethod has ofien been unsuccessful becauselithology il i, effects rather than fluid eff-ects up the bright spot. The consequence the drilling of set is dry holes.In order to reveal"pitfall" amplitude anomaliesit is essential investigatethe to rock physicspropertiesfiom well-log data.However,in new frontier areaswell-1ogdata are sparse lacking. This requiresrock physicsmodeling constrained reasonable or by geologic assumptions and/or knowledge about local compactionaland depositional trends. A common way to extractporosity from seismicdata is to do acousticimpedance inversion.Increasingporositycan imply reducedacousticimpedance, and by extract- ing empiricalporosity-impedancetrendsfrom well-log data,one can estimateporosity from the inverted impedance.However, this methodology suffers from several ambi- guities. Firstly, a clay-rich shalecan have very high porosities,even if the permeability is closeto zero.Hence,a high-porosityzone identifiedby this techniquemay be shale. Moreover, the porosity may be constant while fluid saturationvaries, and one sin-rple model may not be adequate seismicporositymapping. impedance-porosity fbr In addition to lithology-fluid ambiguities, lithology-porosity ambiguities, and porosity-fluid ambiguities,we may have lithology-lithology ambiguitiesand fluid- fluid ambiguities.Sand and shalecan have the sameacousticimpedance, causingno reflectivity on a near-offset seismic section. This has been reported in several areas of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that fluvial channelsor turbidite channelsare dim on seismic amplitude maps, and the Plate1,1 SeismicP-P amplitudemap over a submarine fan. The amplitudes sensitive lithofaciesand are to pore fluids, but the relationvariesacrossthe imagebecause ofthe interplayofsedimentologicand diagenetic influences.Blue indicateslow amplitudes, yellow and red high amplitudes. lilllWi7", :fff!;"{riii;iiiffr 2.9 4120 4140 2.92 4160 41B0 o 2.94 ,)) )))t)))l)))))))))f )) )) 5 o o 4200 E F 2.96 t) )) D,D ) D,D ) D r,D ) )), D) r )r>), 4220 2.98 p i)P,?),,?l? )?i)i) ), l?? 4240 4260 3 iriiiiiiii r)ii)i) iiiii ii lrlllliilrlllllil, 4280 3.02 4300 rn0 VP rho*l/p 10 15 20 25 Distance Plate1,30 Top left, logs penetrating sandyturbidite sequence; right, normal-incidence a top with a synthetics 50 Hz Ricker wavelet.Bottom: increasing water saturation from l1a/c 907c(oil API 35, GOR 200) S* Lo increasesdensityand Vp (left), giving both amplitudeand traveltimechanges (right). 177 4.2 Qualitative seismic interpretation amplitude r interpretation is usually that the channel is shale-filled. However, a clean sand fill- ing in the channel can be transparentas well. A geological assessment geometries of indicating differential compaction above the channel may reveal the presenceof sand. More advancedgeophysical techniquessuch as offset-dependent reflectivity analysis may also reveal the sands.During conventionalinterpretation,one should interpret top reservoir horizons from limited-range stack sections,avoiding the pitfall of missing a dim sandon a near-or full-stackseismicsection. Facies interpretation Lithology influence on amplitudes can often be recognized by the pattern of ampli- tudes as observed on horizon slices and by understandinghow different lithologies system.By relatinglithologiesto depositional occur within a depositional systemswe The link between amplitude characteristics often refer to theseas lithofacies or f-acies. and depositional patternsmakes it easierto distinguish lithofacies variations and fluid changes amplitudemaps. in Traditional seismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon seismictraveltimes.The traditionalmethodologyconsisted purely visual inspection of (e.g.,Mitchum et al., 1977;Weimer and of geometricpatterns the seismicreflections in Link, l99l ). Brown et al. (1981),by recognizing buriedriver channels from amplitude information, were amongst the first to interpret depositional facies from 3D seismic amplitudes.More recent and increasinglyquantitativework includesthat of Ryseth et al. (.1998)who used acoustic impedance inversions to guide the interpretation of sand channels, and Zeng et al. (1996) who used forward modeling to improve the understanding shallow marine facies from seismic amplitudes.Neri (1997) used of neuralnetworksto map faciesfrom seismicpulse shape.Reliablequantitativelithofacies prediction fiom seismicamplitudesdependson establishinga link betweenrock physics properties and sedimentaryfacies. Sections2.4 and 2.5 demonstratedhow such links might be established.The case studies in Chapter 5 show how these links allow us to predict litholacies from seismic amplitudes. Stratigraphic interpretation The subsurfaceis by nature a layered medium, where different lithologies or f'acies have been superimposedduring geologic deposition. Seismic stratigraphicinterpreta- tion seeksto map geologic stratigraphyfrom geometricexpression seismicreflections of in traveltime and space.Stratigraphic boundariescan be defined by dilferent litholo- gies (taciesboundaries) by time (time boundaries). or These often coincide,but not always. Examples where facies boundaries and time boundaries do not coincide are erosional surfacescutting across lithostratigraphy,or the prograding fiont of a delta almost perpendicularto the lithologic surf'aceswithin the delta. There are severalpittalls when interpretingstratigraphyfiom traveltime infbrmation. that is, the contrasts First, the interpretationis basedon layer boundariesor interf'aces, a 178 techniques quantitative Gommon for interpretation seismic T between diff'erent strata or layers, and not the properties of the layers themselves. Two layers with different lithology can have the same seismic properties; hence, a lithostratigraphic boundary may not be observed. Second' a seismic reflection may occur without a lithology change(e.g.,Hardage,1985).For instance, hiatuswith no a deposition within a shaleintervalcan give a strongseismicsignature because shales the above and below the hiatus have difTerent characteristics.Similarily, amalgamated sandscan yield internal stratigraphywithin sandy intervals,reflecting different texture fiom difl-erentdepositionalevents.Third, seismicresolution can be a pitfall in of sancls seismicinterpretation,especiallywhen interpretingstratigraphic onlapsor downlaps. Theseareessential characteristics seismicinterpretation,asthey can give information in about the coastal development related to relative sea level changes (e.g., Vail er ai., I 977). However, pseudo-onlaps can occur if the thicknessof individual layers reduces beneath The layer can still exist,even if the seismicexpression the seismicresolution. yields an onlap. Pittalls Thereareseveral seismicstratigraphic pitfalls in conventional that interpretation can be avoidedif we usecomplementary quantitativetechniques: . lmportant lithostratigraphic boundaries betweenlayerswith very weak contrasts in seismicpropefiiescan easily be missed.However.if different lithologiesare transparent post-stack in seismic seismic data.they arenormallyvisiblein pre-stack dara. AVO analysisis a useful tool to reveal sandswith impedances similar to 4 c a p p i n gs h a l e s s e eS e c t i o n . 3 1 . { . It is commonlybelieved thatseismic events time boundaries. not necessarily are and lithostratigraphic boundaries. For instance.a hiatus within a shale may causea strong seismicreflectionif the shaleabovethe hiatus is lesscompactedthan the onc below.even if the lithology is the same.Rock physicsdiagnostics well-log of data may revealnonlithologicseismicevents (seeChapter2 ). . Because limited seismicresolution,false seismiconlapscan occur.The layer of may still existbeneathresolution. Impedance inversioncan improvethe resolution. featuresnot observedin the original seismicdata and revealsubtle srrailgraphic ( s e eS e c t i o n . 4 ) . 4 Quantitative interpretation of amplituclescan add information about stratigraphic patterns,and help us avoid some of the pitfalls mentioned above.First, relating lithol- ogy to seismic properties(Chapter 2) can help us understandthe nature of reflections, and improve the geologic understandingof the seismic stratigraphy.Gutierrez (2001) showed how stratigraphy-guidedrock physics analysis of well-log data improved the sequence stratigraphicinterpretationof a fluvial systemin Colombia using impedance inversion of 3D seismicdata. Conducting impedanceinversion of the seismic data will 179 seismic 4,2 Qualitative interpretation amplitude - give us layer propertiesfrom interfhceproperties,and an impedancecross-sectioncan reveal stratigraphicfeaturesnot observedon the original seismic section. Impedance inversion has the potential to guide the stratigraphicinterpretation,becauseit is less oscillatorythan the original seismicdata,it is more readily correlated well-log data, to and it tends to averageout random noise, thereby improving the detectability of later- ally weakreflections (Gluck et a\.,1997).Moreover,frequency-band-limited impedance inversioncan improve on the stratigraphicresolution,and the seismicinterpretationcan be signilicantly modified if the inversionresultsare included in the interpretationproce- dure. For brief explanationsof different types of impedanceinversions,seeSection4.4. Forward seismicmodeling is also an excellenttool to study the seismicsignatures of (seeSection4.5). geologicstratigraphy Layer thickness and net-to-gross from seismic amplitude As mentioned in the previous section, we can extract layer thickness from seismic As is amplitudes. depictedin Figure 4.2,the relationship only linear for thin layersin pinch-out zonesor in sheet-likedeposits,so one shouldavoid correlatinglayer thickness to seismic amplitudes in areaswhere the top and baseof sandsare resolvedas separate reflectorsin the seismic data. Meckel and Nath (.1911)found that, for sands embedded in shale, the amplitude would depend on the net sand present,given that the thicknessof the entire sequence is less than ).14. Brown (1996) extended this principle to include beds thicker than the tuning thickness,assumingthat individual sand layers are below tuning and that the entire interval of interbeddedsandshas a uniform layering. Brown introduced the "composite amplitude" defined as the absolute value summation of the top reflection amplitude and the base reflection amplitude of a reservoir interval. The summation of the absolute values of the top and the baseemphasizesthe eff'ectof the reservoir and reducesthe effect of the embedding material. Zeng et al. (.1996)studiedthe influenceof reservoir on thickness seismicsignaland introduced what they referred to as effective reflection strength, applicable to layers thinnerthan the tunins thickness: o'. - 2 " - Z ' n . , (4.3) Zrr impedance, is the average where Z. is the sandstone 216 shaleimpedanceand /z is the A from seismicamplitudes layerthickness. more commonway to extractlayerthickness is by linear regressionof relative amplitude versus net sand thickness as observed at wells that are available.A recentcasestudy showing the applicationto seismicreservoir mappingwas providedby Hill and Halvatis(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-gross can be calculated with the fbllowing fbrmulas: r 180 techniques quantitative Common for seismic interpretation E I Vrung dZ Zrr. NIG: (4 4) AZ where V."n,lis the oil-sand fraction given bv; SI-bAI-ce Kano (4.-5) at-ao where b is the averageslope of the shaleslope(06) and oil-sandslope(b1),whereas ae a n d z 7 ti i r e t h e r e s p e c t i v i n t e r c e p t i n t h e A I - S I c r o s s - p l o r . e s c a l c u l a t i o no f r e s e r v o i r h i c k n e s s r o m s e i s m i ca m p l i t u d e h o u l db e d o n e o n l y i n t f s areaswhere sandsare expectedto be thinner than the tuning thickness.that is a quarterof a wavelength. and wherewell-log datashow evidence good correlation of belweennet sandlhicknessand relativeamplirude. It can be difficult to discriminatelayer rhickness changesfrom lirhologyand fluid changes. relativelysoft sands, impactof increasing In the porosityand hydrocarbon saturationtendslo increase seismicamplitude,and thereforeworks in the same the "direction" to Iayerthickness. However.in relativelyhard sands.increasing porosity and hydrocarbonsaturationLendto decrease the relalive amplitude and therefore work in the opposite"direction" to layer thickness. 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 showed that the presence gas in a sand cappedby a of shale would causean amplitude variation with ofTset pre-stackseismicdata.He also found in that this changewasrelatedto the reduced Poisson'sratio caused the presence by ofgas. Then,the yearafter,Shuey(1985)confirmedmathematically approximations the via of Zoeppritz equations that Poisson'sratio was the elasticconstantmost directly related to the off.set-dependentreflectivity fbr incident angles up to 30". AVo technology, a commercial tool for the oil industry, was born. The AVO techniquebecamevery popular in the oil industry,as one could physicaly explainthe seismicamplitudes termsof rock properties. in Now, bright-spotanomalies could be investigatedbeforestack,to seeif they also had AVo anomalies (Figure4.3). The techniqueproved successfulin certain areasof the world, but in many casesit was not successful.The technique sufI'eredfrom ambiguities causedby lithology efTects, 181 4.3 AVOanalysis I CDPgather Stacksection af interest CDPgather CDP locqtion Target harizon . *{bu Time AVO responseat Geolog interpretation ic target horizon Shale 0,1 -0 Sondstone -0, with gos -0 Aryle ol inc,d?nca 4.3 illustration theprinciples AVOanalysis. Figure Schematic of in tuning effects, and overburdeneft'ects.Even processingand acquisition effects could causefalse AVO anomalies. But in many o1'thefailures,it was not the techniqueitself that failed,but the useof the techniquethat was incorrect.Lack of shear-wave velocity informationandthe useof too simplegeologicmodelswerecommonreasons failure. fbr Processingtechniques that aff'ectednear-ofTset traces in CDP gathers in a difl-erent way from far-offset traces could also create talse AVO anomalies. Nevertheless,in the last decade we have observed a revival of the AVO technique.This is due to the betterpre-processing improvementof 3D seismictechnology, rnorefrequent routines, shear-wavelogging and improved understanding rock physicsproperties,larger data of capacity,more fbcus on cross-disciplinaryaspectsof AVO, and last but not least,mclre awareness among the usersof the potential pitfalls. The techniqueprovides the seismic interpreter with more data, but also new physical dimensions that add infbrmation to the conventional interpretationof seismic facies, stratigraphyand geomorphology. In this section we describe the 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 AVO data. For of an excellent overview of the history of AVO and the theory behind this technology, we refer the reader to Castagna(1993). We expect the luture application of AVO to 182 techniques quantitative Common for interpretation seismic - expandon today's common AVO cross-plotanalysisand hencewe include overviewsof important contributions from the literature,include tuning, attenuationand anisotropy effectson AVO. Finally, we elaborateon probabilistic AVO analysisconstrainedby rock physicsmodels.Thesecomprisethe methodologies appliedin casestudiesl, 3 and 4 in Chapter5. 4.3.1 Thereflection coefficient Analysis of AVO, or amplitude variation with ofTset,seeksto extract rock parameters by analyzing seismic amplitude as a function of offset, or more corectly as a function of reflection angle. The reflection coefficient for plane elastic waves as a lunction of reflectionangle at a single interfaceis describedby the complicatedZoeppritz equations (Zoeppritz,l9l9). For analysisof P-wavereflections, well-known approximationis a given by Aki and Richards( 1980),assumingweak layer contrasts: - R(0,) , , A - -1 7 ,-vi )p + I AYp ,AVs + p' lt (4.6) ;(r T 2 *r4 W K where: s i n0 1 I t - - e:(0rlu)12=et YPI Lp:pz-pr l2 P : ( . P z I Pr) LVp:Vpz-Vpt Vp : (.Vpz vPt)12 + AVs-Vs:-Vsr V5 : (V52+ vst)12 and 02 is In the fbrmulasabove,p is the ray parameter, is the angleof incidence, 01 the transmissionangle; Vp1and Vp2arethe P-wave velocities above and below a given Similarly, V51and V5r are the S-wavevelocities,while py and interface,respectively. p2 are densitiesabove and below this interface (Figure 4.4). The approximation given by Aki and Richards can be further approximated(Shuey, r9 8 5 ) : R(01 ;:, R(o) + G sin29+ F(tan2e - sin2o; (4.1) where R(o):;(T.T) G::^+-'#(+.'+) -+(:.'#) :R(o) #+ 183 4.3 AVOanalvsis n Medium1 (Vp1, p1) V51, Medium2 (Vn, Vsz, Pi PP(r) PS{t) Figure4'4 Reflections and transmissions a singleinterfacebetweentwo elastichalf-space at rr-redia firr an incidentplaneP-wave.PP(i). There will be both a reflectedp-wave,pp(r). and a transmittecl P-wave,PP(t).Note that thereare wave mocleconversions the reflectionpoint occurrrng at ar nonzeroincidence angles.In additionto the P-waves, reflectedS-wave,pS(r), and a transrnitted a S-wave,PS(t),will be prodr.rced. and _ tayP 1 r/ / vD This form can be interpreted in terms of difierent angular ranges! where R(0) is the normal-incidencereflectioncoefficient, describes variationat intermecliate G the offsets and is often referred to as the AVO gradient,whereasF dominatesthe far ofTsets. near critical angle. Normally, the range of anglesavailablefor AVO analysisis less than 30-40.. Therefbre,we only need to considerthe two first terms,valid fbr ansles less than.l0 tShuey.985,1: I R(P)=R(0)+Gsin2d (4.8) The zero-oft'set reflectivity,R(0), is controlled by the contrastin acousticimpedance acrossan interface.The gradient, G, is more complex in terms of rock properties, but fiom the expressiongiven above we see that not only the contrastsin Vp and density afrect the gradient, but also vs. The importance of the vplvs ratio (or equivalently the Poisson'sratio) on the ofTset-dependent reflectivity was first indicated by Koefoed (1955). ostrander (1984) showed that a gas-filledfbrmation would have a very low Poisson's ratio comparedwith the Poisson's ratiosin the surrounding nongaseous fbr- mations.This would causea significantincreasein positive amplitude versusangle at the bottom of the gas layer, and a significantincrease negativeamplitudeversus in angle at the top of the gas layer. 4.3.2 Theeffectof anisotropy Velocity anisotropyought to be taken into accountwhen analyzing the amplitude varia- tion with offset(AVO) response gassands of encased shales. in Although it is generally * d 184 techniques quantitative Common for interpretation seismic - thought that the anisotropy is 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, sign of the AVO slopeor rate of the changeof amplitude with ofliet can be reversedbecauseof anisotropyin the overlying ( s h a l e s K i m e t a l . , 1 9 9 3 B l a n g y ,1 9 9 4 ) . The elasticstiffnesstensorC in transversely isotropic(TI) media can be expressed in compactform as fbllows: Cl (Ctt - 2Coo) C r : 0 0 0 ( c 1 1- 2 C 6 6 ) Ctr Cn 0 0 0 Cr: Cr: C:: 0 0 0 C - 0 0 0 C++ 0 0 0 0 0 0 C++ 0 0 0 0 0 0 Cr,o I - Cn) : where C6,6, (4e) t(Crt and where the 3-axis (z-axis)lies along the axis of symmetry. The above6 x 6 matrix is symmetric, andhasfive independent Cr components, r, Crr, Cr, C++,and C66.For weak anisotropy, Thomsen(1986) expressed three anisotropic parameters, y and 6, as a function of the five elastic components,where t, Cl-Cr a , - - (4.10) 2Cr Cor, C++ (4. r) r 2C++ (Cr:*C++)2-(.Cy-Calz (4.12) 2C.3(Cy C++) The constants can be seento describethe fiactional differenceofthe P-wave velocities in the vertical and horizontaldirections: yP(90')- vp(0') ( 4 .l 3 ) Vp(o') and thereforebest describeswhat is usually referred to as "P-wave anisotropy." In the same manner,the constant y can be seento describethe fiactional difference of SH-wavevelocitiesbetweenverticaland horizontaldirections,which is equivalent to the difference between the vertical and horizontal polarizationsof the horizontally propagatingS-waves: 185 4.3 AVOanalysis r - V s H ( 9 0 1 - V s v ( 9 0 ) 7sH(90") Vss(0') (4.14) T - Vsv(90') Vsn(0') The physical meaningof 6 is not as clear as s and y, but 6 is the most important parameterfbr normal moveout velocity and reflection amplitude' Under the plane wave assumption,Daley and Hron (1911) derived theoretical fbr- mulas for reflection and transmissioncoefficientsin Tl media. The P-P reflectivity in the equation can be decomposedinto isotropic and anisotropicterms as follows: Rpp(0): Rrpp(O) R'rpp(0) * (4.1s) Assuming weak anisotropyanclsmall offsets,Banik ( 1987)showedthat the anisotropic term can be simply expressed fbllows: as sin2e -Ad ( 4 .I 6 ) R e p p ( d )- Blangy (lgg4) showedthe effect of a transverselyisotropic shaleoverlying an isotropic gas sand on offset-dependentreflectivity, for the three different types of gas sands. He found that hard gas sandsoverlain by a soft TI shale exhibited a larger decrease in positive amplitude with offset than if the shale had been isotropic. Similarly, soft gas san4soverlain by a relatively hard TI shale exhibited a larger increasein negative amplitude with offset than if the shale had been isotropic. Furthermore, it is possible fbr a soft isotropic water sand to exhibit an "unexpectedly" Iarge AVO eff'ect if the overlying shaleis sufficientlyanisotropic' 4.3.3 Theeffectof tuningon AVO As mentioned in the previous section, seismic interf'erence event tuning can occur or as closely spacedreflectorsinterfere with each other.The relative changein traveltime between the reflectors decreases with increasedtraveltime and off.set.The traveltime hyperbolasof the closely spacedreflectorswill thereforebecome even closer at larger ofTsets.In f-act,the amplitudes may interfere at large ofTsetseven if they do not at small offsets.The effect of tuning on AVO has been demonstrated Juhlin and Young by ( 1993),Lin and Phair ( 1993),Bakkeand Ursin ( 1998),andDong ( 1998),amongothers. Juhlin and Young (1993) showedthat thin layersembedded a homogeneous in rock can produce a significantly different AVO responsefiom that of a simple interface of the samelithology. They showedthat, for weak contrastsin elasticpropertiesacrossthe layer boundaries,the AVO responseof a thin bed may be approximatedby modeling it as an interference phenomenon between plane P-waves fiom a thin layer' ln this casethin-bed tuning affects the AVO responseof a high-velocity layer embeddedin a homogeneousrock more than it affects the responseof a low-velocity layer. l 186 techniques quantitative Common for interpretation seismic Lin and Phair ( 1993)suggested following expression the amplitudevariation the for with angle (AVA) response a thin layer: of R r ( 0 ) : r r . r o A ? ' ( c o sd ' R ( 6 ) 0) (4.11) where a.re the dominant frequency of the wavelet, Af (0) is the two-way traveltirne is at normal incidencefiom the top to the baseof the thin layer, and R (0) is the reflection coefficient fiom the top interface. Bakke and Ursin ( 1998)extended the work by Lin and Phair by introducingtuning correctionfactorsfbr a generalseismicwaveletas a function of offset. If the seismic fiom the top of a thick layer is: response d(t, t') : R(t')p(r) (4.l8) where R(,1') the primary reflection as a function of ofTset.t', and p(0 is the seismic is pulse as a flnction of time /, then the response from a thin layer is tl(r, y) f(.y)AI(0)C(t")p'(t) (4.19) 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 c(.v):ffi[' .##"] (4.20) where 7(0) and Z(-r') are the traveltimes atzero ofliet and at a given nonzero offset, The root-mean-square respectively. velocity VBy5, is defined along a ray path: t l' tt)t 'r s, .l v \t t\|t VRMS - (4)t\ Jdt 0 For small velocity contrasts(Vnvs - y), the last term in equation (4.20) can be ignored, and the AVO tuning f'actorcan be approximatedas r(0) C(r') :v ----:-- (4.22\ r(,r') For large contrast in elastic properties,one ought to include contributions fiom P- wave multiples and convertedshearwaves. The locally convertedshear wave is ofien neglectedin ray-tracing modeling when reproductionof the AVO responseof potential hydrocarbon reservoirs is attempted.Primaries-only ray-trace modeling in which the Zoeppritz equationsdescribethe reflectionamplitudesis most common. But primaries- only Zoeppritz modeling can be very misleading, becausethe locally converted shear waves often have a first-order eff-ecton the seismic response(Simmons and Backus, 1994).lnterferencebetween the convertedwaves and the primary reflectionsfiom the 187 4,3 AVOanalysis I (1) Primaries (2) Single-leg R$ a (3)Double-leg (4)Reverberations Figure Converted 4.5 S-waves multiples mustbeincluded AVOmodeling and that in whenwe have causing thin layers. thesenrodesto with theprimaries. Primary interfere (l) reflections; (2) single-leg shear (3) waves; double-leg shearwave; (4) primary and (After reverberations. Simmons Backus, and 7ps 1994.) : transmittedS-wave converted P-wave, : reflected fiom Rsp P-wave fiom S-wave. converted etc. baseof the layersbecomesincreasinglyimportantasthe layerthicknesses decrease.This often producesa seismogramthat is different fiom one produced under the primaries- only Zoeppritzassumption. this case,one shouldusefull elasticmodelingincluding In the convertedwave modes and the intrabedmultiples.Martinez (1993) showedthat surface-related with primary multiples and P-to-SV-modeconvertedwavescan interf-ere Figure 4.5 shows pre-stackamplitudesand causelargedistortionsin the AVO responses. the ray images of convertedS-wavesand multiples within a layer. 4.3.4 Structuralcomplexity, effects AVO propagation overburden wave and on Structural complexity and heterogeneities the target level as well as in the overbur- at den can have a great impact on the wave propagation.These effects include focusing and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed and surf'acemultiples, P-wave to vertically polarized S-wave mode conversions,and anelastic attenuation.The offset-dependent reflectivity should be corrected for these wave propagation effects, via robust processingtechniques(see Section 4.3.6). Alter- natively, these efTectsshould be included in the AVO modeling (see Sections 4.3.7 and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor overburdeneffects as well as certain acquisition effects (seeSection a.3.5) by normal- izing a target horizon amplitude to a referencehorizon amplitude. However, in more recent years there have been severalmore extensivecontributions in the literature on amplitude-preserved imaging in complex areasand AVO correctionsdue to overburden effects, some of which we will summarizebelow. 188 techniques quantitative Common for interpretation seismic - AVO in structurally complex areas The Zoeppritzequations assume singleinterf-ace a betweentwo semi-infinite layerswith infinite lateralextent.In continuouslysubsidingbasinswith relativelyflat stratigraphy (suchas Tertiarysediments the North Sea),the useof Zoeppritzequations in shouldbe valid. However,complex reservoirgeology due to thin beds,vertical heterogeneities, faultingand tilting will violate theZoeppritzassumptions. Resnicket at. (1987)discuss the efl'ectsof geologic dip on AVO signatures,whereasMacleod and Martin (1988) discussthe eff-ects reflector curvature.Structuralcomplexity can be accountedfor by of doing pre-stack depth migration (PSDM). However,one should be awarethat several PSDM routinesobtain reliable structuralimages without preservingthe amplitudes. Grubb et ul. (2001) examined the sensitivity both in structure and amplitr-rde related to velocity uncertainties PSDM migrated images.They performed an amplitude- in preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO signaturesthey evaluatedboth the uncertaintyin AVO cross-plotsand uncertaintyof AVO attributevaluesalong given structuralhorizons. AVO effects due to scattering attenuation in heterogeneous overburden (1996) showedhow to correct a targetAVO response a thinly layered Widmaier et ztl.. fbr A overburden. thin-bedded overburden will generate velocity anisotropyand transmis- sion lossesdue to scatteringattenuation,and theseeflects should be taken into account when analyzinga targetseismicreflector. They combinedthe generalized O'Doherty- Anstey formula (Shapiro et ul., 1994a)with amplitude-preservingmigration/inversion algorithms and AVO analysis to compensatefor the influence of thin-bedded layers on traveltimes and amplitudes of seismic data. In particr-rlar, they demonstratedhow the estimation of zero-offset amplitude and AVO gradient can be improved by cor- recting fbr scattering attenuationdue to thin-bed efl'ects.Sick er at. (2003) extendecl Widmaier's work and provided a method of compensatingfor the scatteringattenuation eflects of randomly distributed heterogeneitiesabove a target reflector. The general- ized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent, time- harmoniceffectivetransmissivity for scalarwaves(P-wavesin acousticI D medium T or SH-wavesin elastic lD medium) and is given by ( ' ' l t ) \ |i f t l A \ \ L Tt II u Tue (4.23) where.fis the frequency and n and p are the angle- and fiequency-dependent scattering attenuationand phaseshift coefficients,respectively.The angle g is the initial angle of an incident plane wave at the top surfaceof a thinly layered composite stack; L is the thickness the thinly layeredstack;ft denotes transmissivity a homogeneous of the fbr isotropic ref-erence medium that causesa phaseshifi. Hence, the equation above repre- sentsthe relative amplitude and phasedistortions causedby the thin layers with regard to the referencemedium. Neglectingthe quantity Zo which describes transmission the 189 4.3 AVoanalysis - responsefor a homogeneousisotropic referencemedium (that is, a pttre phaseshift), a transmissivity is defined: phase-reduced f ( f) o a) @ t f ' o ) + t P ( l) r (4.24) " For a P-wave in an acoustic lD medium, the scatteringattenuation,cv,and the phase B,were derivedfrom Shapiroet al. (1994b)by Widmaier et al. (1996): coefficient, | tr'oot.f' a(.f0) : , (4.25) cos2o I l6n:a2f2 cos2u V,f and r f'o2 l- gnz 7'z n: B(f.())- " |- r4)6r V r c o s eL V;+ t6n)02.t2cor2e where the statistical parametersof the referencemedium include spatial correlation length a, standarddeviationo, and mean velocity Vs. The medium is modeled as a 1D random medium with fluctuating P-wave velocities that are characterizedby an exponential correlation function. The transmissivity (absolute value) of the P-wave decreases with increasing angleof incidence. If the uncorrected seismicamplitude(i.e., the analyticalP-wave particle displace- ment) is defined according to ray theory by: I U ( S ,G , / ) : R c - W ( r - r v ) (4 )1\ v where U is the seismic trace, S denotes the source, G denotes the receiver, t is the varying traveltime along the ray path, Rs is the reflection coefficient at the reflection point M, y is the spherical divergence factor, W is the soutce wavelet, and ry is the traveltime fbr the ray between source S, via reflection point M, and back to the receiverG. A reflector beneatha thin-beddedoverburdenwill have the following compensated seismicamplitude: I u r ( s , G ,t ) : f r * ( t ) *R . w 1 r- , r ; (4 )R\ v the is transmissivity givenby; time-reduced where two-way, (4 )q\ 4*(r) : irtrc(r)x Zsrvr(r) The superscriptT of Ur(S, G, r) indicatesthat thin-bed effects have been accounted fbr. Moreover, equation (4.28) indicatesthat the sourcewavelet,W(0, is convolvedwith the transient transmissivity both for the downgoing (i5p1 ) and the upgoing raypaths (f n4c)between source (S), reflection point (M), and receiver (G). 190 techniques quantitative Common for seismic interpretation - In conclusion, equation (4.28) representsthe angle-dependent time shift causedby transverseisotropic velocity behavior of the thinly layeredoverburden.Furthermore,it describes decrease the AVO response the of resultingfrom multiple scatteringadditional to the amplitude decay related to sphericaldivergence. Widmaier eI ai. ( I 995) presentedsimilar lbrmulations for elasticP-waveAVO, where the elasticcorrection formula dependsnot only on variancesand covariances P-wave of velocity, but also on S-wave velocity and density,and their correlationand cross- correlationfunctions. Ursin and Stovas(2002) further extendedon the O'Doherty-Anstey fbrmula and cal- culated scatteringattenuationfbr a thin-bedded,viscoelasticmedium. They found that in the seismic frequency range, the intrinsic attenuationdominatesover the scattering attenuation. AVO and intrinsic attenuation (absorption) Intrinsic attenuation,also referred to as anelasticabsorption,is causedby the fact that even homogeneoussedimentaryrocks are not perf'ectlyelastic. This effect can com- plicatethe AVO response (e.g.,Martinez, 1993).Intrinsic attenuation be described can 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 Qe* i(at lr Q) ln atI tos) 12 (4.30) where Q" is the effective quality f'actorof the overburdenalong the wave propagation path and areis an angular referencefrequency. Luh demonstrated how to correct for horizontal, vertical and ofTset-dependent wavelet attenuation.He suggestedan approximate, "rule of thumb" equation to cal- culate the relative changein AVo gradient, 6G, due to absorptionin the overburden: ftt 3G ry :-' (4.31) Q" wherei is the peak frequency of the wavelet, and z is the zero-offsettwo-way travel time at the studied reflector. Carcione et al. (1998) showed that the presenceof intrinsic attenuationaffects the P-wave reflection coefficient near the critical angle and beyond it. They also found that the combined effect of attenuationand anisotropy aff'ectsthe reflection coefficientsat non-normal incidence,but that the intrinsic attenuationin somecasescan actually com- pensate anisotropiceffects.In most cases, the however,anisotropiceffectsare dominant over attenuationeffects.Carcione (1999) furthermore showed that the unconsolidated sedimentsnear the seabottom in offshore environmentscan be highly attenuating,and that these waves will for any incidence angle have a vector attenuationperpendicular 191 4,3 AVOanalysis r of This vector attenuationwill afl'ectAVO responses deeper to the sea-floorinterf'ace. reflectors. etfects AVO 4.3.5 Acquisition on The most important acquisition eff-ects AVO measurements on include source direc- tivity, and source and receivercoupling (Martinez, J993). ln particular,acquisition footprint is a large problem fbr 3D AVO (Castagna,2001). at Inegular'Eoverage the surfacewill causeunevenillumination of the subsurface. Theseeffectscan be corrected for using inverseoperations.Difl'erent methodsfor this have beenpresentedin the liter- ature(e.g.,Gassaway a\.,1986; Krail and Shin, 1990;Cheminguiand Biondi, 2002). et Chiburis' ( 1993)method for normalizationof targetamplitudeswith a referenceampli- tude provided a fast and simple way of corecting for certain data collection factors including sourceand receivercharacteristicsand instrumentation. analysis of seismic forAVO 4.3.6 Pre-processing data AVO processingshould preserveor restorerelative trace amplitudeswithin CMP gath- ers. This implies two goals: (1) reflectionsmust be correctly positionedin the sub- surface; and (2) data quality should be sufficient to ensure that reflection amplitudes contain infbrmation about reflection coefficients. processing AVO Even though the unique goal in AVO processingis to preservethe true relative amplitudes,there is no unique processing sequence. dependson the complexity lt of the geology.whetherit is land or marine seismicdata.and whetherthe data will AVO attributes or more sophisticatedelastic be used to extract regression-based inversionattributes. Cambois(200 l) definesAVO processing any processing as sequence that makes the data compatiblewith Shuey'sequation,if that is the model used for the AVO that this can be a very complicated inversion.Camboisemphasizes task' Factorsthat changethe amplitudesof seismictracescan be groupedinto Earth effects, acquisition-relatedeffects, and noise (Dey-Sarkar and Suatek, 1993). Earth effects include sphericaldivergence,absorption,transmissionlosses,interbed multiples, con- verted phases,tuning, anisotropy, and structure. Acquisition-related eft-ectsinclude source and receiver arrays and receiver sensitivity. Noise can be ambient or source- generated. coherent random.Processing or attempts compensate or removethese to for effects, but can in the processchange or distort relative trace amplitudes. This is an important trade-off we need to consider in pre-processing AVO. We thereforeneed for 192 techniques quantitative Common for seismic interpretation r to select basic robust a but processing scheme(e.g., ostrander, 1984; chiburis,l9g4; Fouquet,990;Castagna Backus, f and Yilma4 2001). 1993; Common pre-processingstepsbefore AVO analysis Spiking deconvolution and wavelet processing In AVO analysis normally want zero-phase we data.However,the original seismicpulse is causal,usually some sort of minimum phasewaveletwith noise.Deconvolutionis defined as convolving the seismic trace with an inverse filter in order to extract the impulse responsefrom the seismic trace. This procedure will restore high frequen- cies and therefore improve the vertical resolution and recognition of events.One can make two-sided, non-causalfilters, or shaping filters, to produce a zero-phasewavelet ( e . g . ,L e i n b a c h ,1 9 9 5 ;B e r k h o u t ,1 9 7 7 ) . The wavelet shapecan vary vertically (with rime), larerally (spatially),and with offset. The vertical variations can be handled with deterministic Q-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 variations are often more complicated to correct for, an4 are attributed to both ofl.set-dependent absorption (see Section 4.3.4), tuning efl'ects(see Section4.3.3),andNMo stretching. NMo stretching actslike a low-pass,mixed-phase, nonstationaryfilter, and the eff'ects very difficult to eliminate fully (Cambois,2001 are ). Dong (1999) examined how AVO detectability of lithology and fluids was afl'ected by tuning and NMo stretching, and suggesteda procedure for removing the tuning and stretching effects in order to improve AVO detectability.Cambois recommendecl picking the reflections of interest prior to NMo corrections, and flattening them for AVO analysis. Spherical divergence correction Spherical divergence, or geometrical spreading, causes the intensity and energy of spherical waves to decreaseinversely as the square of the distance fiom the source (Newman, 1973).For a comprehensive review on ofTset-dependentgeometricalspread- ing, seethe study by Ursin ( 1990). Surface-consistent amplitude balancing Source and receiver eff'ectsas well as water depth variation can produce large devi- ations in amplitude that do not coffespond to target reflector properties.Commonly, statistical amplitude balancing is carried out both fbr time and offset. However. this procedure can have a dramatic efl'ect on the AVO parameters.It easily contributes to intercept leakage and consequentlyerroneousgradient estimates(Cambois, 2000). Cambois (2001) suggestedmodeling the expected averageamplitucle variation with 't 193 4.3 AVO analvsis n off.setfbllowing Shuey's equation, and then using this behavior as a ret'erence for the statisticalamplitudebalancing. Multiple removal One of the most deterioratingeff-ects pre-stackamplitudes is the presenceof multi- on ples.There are severalmethodsof filtering away multiple energy,but not all of these are adequatefor AVo pre-processing. The method known asfft multiple filtering, done in the frequency-wavenumberdomain, is very efficient at removing multiples, but the dip in the.l-lr domain is very similar fbr near-offsetprimary energy and near-offsetmultiple energy.Hence,primary energy can easily be removed from near tracesand not from far traces,resulting in an ar-tificialAVO effect. More robust demultiple techniquesinclude linear and parabolic Radon transform multiple removal (Hampson, l9g6: Herrmann et a1.,2000). NMO (normal moveout) correction A potential problem during AVO analysis is error in the velocity moveout conection (Spratt, 1987).When extracting AVO attributes,one assumes that primaries have been completely flattenedto a constanttraveltime.This is rarely the case,as there will always be residual moveout. The reasonfor residualmoveout is almost always associated with erroneousvelocity picking, and greatef'fortsshoukl be put into optimizing the estimated velocity field (e.g.,Adler, 1999;Le Meur and Magneron,2000).However,anisorropy and nonhyperbolicmoveoutsdue to complex overburclen may also causemisalignments betweennearand far off.sets excellentpracticalexampleon AVO and nonhyperbolic (an moveout was publishedby Ross, 1997).Ursin and Ekren (1994) presented method a for analyzing AVO eff-ects the off.setdomain using time windows. This technique in reducesmoveout elrors and createsimproved estimatesof AVO parameters. One shoulcl be aware of AVO anomalieswith polarity shifts (classIIp, seedefinition below) during NMO corrections,as thesecan easily be misinterpretedas residualmoveouts(Ratcliffe and Adler, 2000). DMO correction DMO (dip moveout) processinggenerates common-reflection-pointgathers.It moves the reflection observed on an off'set trace to the location of the coincident source- receiver trace that would have the same reflecting 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 events with 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 presence of dip, using partial pre-stack misration. 194 techniques quantitative Common for interpretation seismic - Pre-stack migration Pre-stackmigration might be thought to be unnecessary areaswhere the sedimentary in section is relatively flat, but it is an important component of all AVO processing. Pre-stackmigration should be used on data for AVO analysis whenever possible, because will collapsethe diffractions at the targetdepth to be smaller than the Fresnel it zone and thereforeincreasethe lateral resolution(seeSection4.2.3; Berkhout, 1985; Mosher et at., 1996).Normally, pre-stacktime migration (PSTM) is preferred to pre- stackdepth migration (PSDM), because former tendsto preserveamplitudesbetter. the However, in areas with highly structured geology, PSDM will be the most accurate tool (Cambois,2001).An amplitude-preserving PSDM routineshouldthen be applied ( B l e i s t e i n , 9 8 7 ;S c h l e i c h ee t c t l . , l 9 9 3 ; H a n i t z s c h 1 9 9 7 ) . 1 r , Migration fbr AVO analysis can be implemented in many different ways. Resnick et aL. (1987) and Allen and Peddy (1993) among othershave recommended Kirch- hoff migration together with AVO analysis.An alternativeapproachis to apply wave- equation-based migration algorithms.Mosher et al. (.1996)derived a wave equation fbr common-angle time migration and used inverse scatteringtheory (see also Weglein, 1992'7forintegration migrationand AVO analysis of Mosher (i.e.,migration-inversion). et at. (1996) usecla finite-difference approachfbr the pre-stack migrations and illus- trated the value of pre-stackmigration fbr improving the stratigraphicresolution, data quality, and location accuracyof AVO targets. of line anatysis a2lseismic Example pre-processing forAVO of scheme ( Y i l m a z ,0 0 1 . ) 2 ( I ) Pre-stack signal (source processing geometric processing. signature scaling, spiking deconvolutionand specffalwhitening). (2t Sort to CMP and do sparseintervalvelocity analysis. (3) NMO using velocity field from step2. (4) Demultipleusing discreteRadontransform. (5) Sort to common-offset and do DMO correction. (6) Zero-offsetFK time migration. (CRP) and do inverseNMO using the (7) Sort data to common-reflection-point velocity field from step2. (8) Detailedvelocity analysisassociatedwith the migrateddala' (9) NMO correclionusing velocity field from step8. ( l0) StackCRP gathers obtainimageof pre-stack to migrateddata.Removeresidual by multiplesrevealed lhe stacking. ( l l ) U n m i g r a t e s i n gs a m ev e l o c i t yf i e l d a s i n s t e p6 . u ( l2; Post-stack spiking deconvolution. (13) Remigrateusing migrationvelocity field from step8. 195 4.3 AVOanalysis E interpretation t0 processing pitfalls AVO Some in due etfects . Waveletphase. The phaseof a seismicsectioncan be significantlyalteredduring processing. rhe phase a sectionis not established the interpreter. lf of by then AVO anomaliesthat would be interpretedas indicativeof decreasingimpedance,for wherethe impedance example.can be producedat interfaces increases (e.g.,Allen and Peddy. I993). . Multiple filtering. Not all demultiple techniquesare adequatelor AVO pre- processing. Multiple filtering,done in the frequency-wavenumberdomain,is very efficientar removing multiples.but the dip in the/-k domain is very similar for near-offsetprimary energy and near-offsetmultiple energy.Hence,primary energy can easlly be removed from the near-offsettraces. resulting in an artificial AVO effect. . NMO correction. potentialproblemduring AVO analysis errorsin the velocity A is moveoutcorrection (Spran. 1987).When extractingAVO attributes. one assumes that primaries have been completely flattenedto a constanttraveltime.This is rarely the case.as therewill alwaysbe residualmoveout.Ursin and Ekren (1994) presenteda method for analyzing AVO effects in rhe offset domain using time windows. This technique reducesmoveoul errorsand creates improvedestimates of AVO paramerers. NMO stretch is another problem in AVO analysis. Because the amount of normal moveout varies with arrival time. frequenciesare lowered at large offsets compared with short offsets. Large offsets, where the stretching effect is significant.should be muted before AVO 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 pre-stack of data beforedoing AVO analysis. Pre-processing for elastic impedance inversion Severalof the pre-processingstepsnecessary AVO analysisare not required when for preparingdatafor elasticimpedanceinversion(seeSection4.4 for detailson the method- ology). First of all, the elastic impedanceapproachallows for wavelet variations with offset (Cambois,2000). NMO stretchcorrectionscan be skipped,because eachlimited- range sub-stack(in which the waveletcan be assumed to be stationary)is matchedto its associated syntheticseismogram, and this will removethe waveletvariationswith angle. It is, however,desirableto obtain similar bandwidth fbr each inverted sub-stackcube, since these should be comparable.Furthermore, the data used for elastic impedance inversion are calibratedto well logs before stack,which meansthat averageamplitude variations with offset are automatically accountedfor. Hence, the complicated pro- cedure of reliable amplitude corrections becomes much less labor-intensivethan for 196 techniques quantitative Common for interpretation seismic - u 1 0 2 0 3 0 4 0 5 0 6 0 (degree) Angle incidence of Figure4,6 AVO curvesfbr differenthalf'-space models(i.e.,two layers one intertace). FaciesIV is cap-rock. Input rock physicspropertie\ meanvalues eachfacies. represent for AVO analysis. standard Finally,residualNMO and multiplesstill must be accounted fbr (Cambois,2001). Misalignmentsdo not causeinterceptleakageas fbr standard AVO analysis, but near-and far-anglereflectionsmust still be in phase. 4.3.7 AVOmodeling seismic and detectability AVO analysisis normally carried out in a deterministicway to predict lithology and fluids from seismicdata(e.g.,Smith and Gidlow, 1987;RutherfordandWilliams, 1989; Hilterman, 1990;Castagna and Smith, 1994;Castagna al., 1998). et Forward modeling of AVO responsesis normally the best way to start an AVO analysis, as a feasibility study before pre-processing,inversion and interpretation of real pre-stack data. 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 shale is taken as the cap-rock with difTerent underlying lithofacies. For each facies, Vp, Vs, and p are extractedfrom well-log data and used in the modeling. We observea clean sand/pure shaleambiguity (faciesIIb and facies V) at near of1iets,whereasclean sandsand shalesare distinguishableat far offsets.This exampledepictshow AVO is necessary discriminatedifferent lithofacies to in this case. I -T I 197 4.3 AVOanalysis - trend CemellHion I Cemenled I {el brino 0 Ceme|rbd w/ hydruca]ton Unconsolidaled V w/ brine tr€ild Hydrocarlon Unconsolidtlsd w/ hydrocarbon Figure Schcgatic 4.7 AVOcurves cemented firr sands by sandstone unconsolidated capped and and cases. shlle.frll brine-saturated oil-saturated Figure 4.7 shclwsanotherexample,where we considertwo types of clean sands, cementedand unconsolidated,with brine versushydrocarbonsaturation.We seethat a cemented sanclstonewith hydrocarbon saturationcan have similar AVO responseto a brine-saturated.unconsolidatedsand. The examplesin Figures 4.6 and 4.7 indicate how important it is to understandthe local geology during AVO analysis.lt is necessary know what type of sandis expected to for a given prospect,and how much one expectsthe sandsto change locally owing to textural changes,before interpreting fluid content. It is therefore equally important to coniluct realisticlithology substitutions addition to fluid substitutionduring AVO in rnodelingstudies.The examplesin Figures4.6 and 4.7 also demonstrate the impor- tance of the link between rock physics and geology (Chapter 2) during AVO analysis. technique? Whenis AVOanalysisthe appropriate It is well known that AVO analysisdoes not always work. Owing to the many caseswhere AVO has been applied withoul success, techniquehas receiveda the 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 the targetreservoirare expectedto give a good of AVO response. This must be clarifiedbeforethe AVO analysis real data.Without of a proper feasibility study.one can easily misinterpretAVO signatures the real in data.A good feasibility study could include both simple reflectivitymodeling and more advanced forward seismicmodeling(seeSection4.51.Both thesetechniques shouldbe foundedon a thoroughunderstanding local geologyand petrophysical of during Realisticlithology substitution as importantas fluid substitution properties. is this exercise. 198 techniques quantitative Gommon for interpretation seismic I Often, one will find that there is a certain depth interval where AVO will work, often referred to 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 (see Sections 2.6 and 4.3.16). However. the "AVO window" is also constrained data quality. With increasingdepth, absorptionof primary energy by reduces the signal-to-noiseratio. higher frequencies graduallymore attenualed are than lower frequencies. geology usually becomesmore complex causingmore the length. complexwave propagations, theanglerangereduces a given streamer and for All thesefactorsmake AVO lessapplicablewith increasingdepth. AVO of gathers 4.3.8 Deterministic analysis GDP AVO modeling, the next step in AVO analysisshould be deter- After simple half--space ministic AVO analysis of selectedCDP (common-depth-point)gathers,preferably at well locations where synthetic gathers can be generatedand compared with the real CDP gathers. this section,we show an exampleof how the methodcan be appliedto In discriminate lithofacies real seismicdata,by analyzingCDP gathers well locations in at in a deterministic way. Figure 4.8 shows the real and synthetic CDP gathers at three adjacent well locationsin a North Seafield (the well logs are shownin Figure5.1, case study l). The figure also includesthe picked amplitudesat a top targethorizon super- imposed on exact Zoeppritz calculated reflectivity curves derived fiom the well-log data. In Well 2, the reservoir sandsare unconsolidated, representoil-saturatedsands,and are cappedby silty shales.According to the saturationcurves derived fiom deep resis- tivity measurements, the oil saturation in the reservoir varies from 20-807o, with an average of about 60Va. The sonic and density logs are found to measure the mud filtrate invaded zone (0-l0o/o oil). Hence, we do fluid substitution to calculate the seismic properties of the reservoir from the Biot-Gassmann theory assuming a uni- form saturation model (the process of fluid substitution is described in Chapter l). Before we do the fluid substitution, we need to know the acoustic properties of the oil and the mud filtrate. These are calculated from Batzle and Wang's relations (see Chapter l). For this case, the input parametersfor the fluid substitution are as fbllows. oilGoR 64 UI density Oil relative 32APT Mud-filtratedensity 1.09 g/cm3 Pore level pressure reservoir at 20 MPa at Temperature reservoirlevel 77.2',C -v i 199 - 4.3 AVOanalysis 3 Well CDP ] OFF 0 323 726 1210 1694 2177 t Relleclvity ectivity Rel - weill 0.r00 : 0 1 0 0; Well 3 0 100 0.050 : i'. - I r -r;r! I 0.050 ! , .PB 0 050 . 1 ' ' : '. '- 0 050 nnqn I 0 i I l'o" .. : : 0 r00 l 0 0050i 0 150 0 Angle 1 14 21 28 34 (deq) Anqle 0 8 l5 22 29 (deg) Angle 0 1 14 20 26 32 (deg) Figure4.8 Real CDP gathers(upper),syntheticCDP gathers(middle),and AVO curvesfor Wells I 3 (lower). 200 techniques quantitative Common lor interpretation seismic I The correspondingAVO responseshows a negativezero-ofTset reflectivity and a neg- ative AVO gradient. In Well l, we have a water-saturated cementedsand below a silty shale.The correspondingAVO responsein this well showsa strongpositive zero-ofl.set reflectivity and a relatively strong negative gradient. Finally, in Well 3 we observe a strongpositive zero-offsetreflectivity and a moderatenegativegradient,corresponding to interbeddedsand/shale faciescappedby silty shales.Hence,we observethreedistinct AVO responsesin the three different wells. The changesare related to both Iithology and pore-fluid variations within the turbidite system. For more detailed information about this system,seecase study I in Chapter 5. Avseth et al. (2000) demonstratedthe etlect of cementationon the AVO responsein real CDP gathersaround two wells, one where the reservoir sandsare friable, and the other where the reservoir sands are 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 reflectivitymodeling examplein Figure 4.7. lmpodance0f AVOanalysisof individualCDPgathers Investigations CDP gathersare importanl in order ro confirm AVO anomalies of (Shuey:s seenin weightedstacksect.ions and gradient,Smith and Gidlow's intercepr fluid factor. etc.). The weighted stackscan contain anomaliesnot related to true offset-dependent amplitudevariations. parameters 4.3.9 EstimationAVO of Estimating intercept and gradient The next stepin an AVO analysisshould be to extract AVO attributesand do multivari- ate analysis of these. Several different AVO attributescan be extracted,mapped and analyzed.The two most important ones are zero-offsetreflectivity (R(0)) and AVO gra- dient (G) basedon Shuey'sapproximation. Theseseismicpararneters be extracted, can via a least-squaresseismicinversion,for each samplein a CDP gatherover a selected portion of 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(/,0) + c(/) sin2g(r, r) -r) (4 7)\ where 0(r, x) is the incident angle corresponding to the data sample recorded at ( t .r ) . 201 4.3 AVOanalysis - For a layered Earth, the relationshipbetweenofliet (r) and angle (0) is given approx- imately by: r VrNr (4.33) s i n0 ( r ,x ) I tt2 YRMS k3+x2fvi^)tt2 where VrNr is the interval velocity and Vnr,,rs the averageroot-mean-square is veloc- ity, as calculated from an input velocity profile (fbr example obtained from sonic log). For any given value of zero-offsettime, /e, we assumethat R is measuredat N offsets (xi, i:1, A/).Hence,we can rewrite the defining equationfbr this time as (Hampson a n d R u s s e l l .1 9 9 5 ) : R(.rr) xr sin2o(4 ) R(xz) sin2g(r,,rz) Inmor-l (4.34) IcurI R(r,r,) I ,rr,') sin2g(r, This matrix equation is in the form of b: Ac and representsN equations in the two unknowns,R(/, 0) and G(r). The least-squaressolutionto this equation is obtained bY solving the so-called"normal equation": c: (ArA)-1(ATb) (4.3s) solutionfbr R(0) and G at time t. us the least-squares Inversion for elastic Parameters Going beyond the estimation of intercept and gradient, one can invert pre-stack seis- mic amplitudesfor elasticparameters, including Vp, V5 and density.This is commonly (e'g., Dahl ref'erredto as AVO inversion, and can be performed via nonlinear methods anclUrsin. 19921 Buland et al., 1996;Gouveiaand Scales,1998)or linearizedinversion methods(e.g., Smith and Gidlow, 1987; Loertzer and Berkhout, 1993).Gouveia and Scales( 1998)clefined Bayesiannonlinearmodel and estimated, a nonlinearcon- a via jugate gradient method, the maximum a-posteriori (MAP) distributions of the elastic parameters.However, the nonlinearity of the inversion problem makes their method very compurer intensive.Loertzer and Berkhout ( 1993)performed linearized Bayesian inversion based on single interface theory on a sample-by-samplebasis. Buland and Omre (2003) extendedthe work of Loertzer and Berkhout and developeda linearized Bayesian AVO inversion method where the wavelet is accountedfor by convolution. The inversionis perfbrmedsimultaneously all times in a given time window, which fbr ^ 202 techniques quantitative Common for interpretation seismic r makes it possible to obtain temporal correlation between model parametersclose in time. Furthermore, they solved the AVO inversion problem via Gaussianpriors and obtained an explicit analytical form for the posterior density,providing a computation- ally fast estimationof the elasticparameters. inversion Pittalls AVO of . A linearapproximation the Zoeppntzequations commonly usedin the calcu- of is lation of R(01and G. The two-term Shueyapproximationis known lo be accurate for anglesof incidenceup to approximately30'. Make surethat the data inverted do not exceedthis range,so the approximalionis valid' . The Zoeppritzequations only valid fbr single interfaces. are lnversionalgorithms that are basedon theseequations will not be valid lor thin-beddedgeology. . The linear AVO inversionis sensitiveto uncharacteristic amplitudescausedby noise (including multiples.) processing or and acquisirioneffects.A few outlying valuespresent the pre-stack in amplitudes enoughto causeerroneous are estimates of R(0) and G. Mosr commercial software packagesfor eslimationof R(0) and o C a p p l y r o b u s r s t i m a r i o ne c h n i q u e ( e . g . ,W a l d e n .1 9 9 l ) t o l i m i t t h e d a m a g e l ' e t s outlying amPlitudes. . Another potential problem during sample-by-sample AVO inversion is errors in the moveout correction (Spratt, 1987l. Ursin and Ekren (1994) presented a method for analyzing AVO eflects in the offset domain using time windows. This techniquereducesmoveout errors and createsimproved estimates AVO oi parameters. 4,3.10AVO analysis cross-Plot A very helpful way to interpret AVO attributesis to make cross-plotsof intercept(R(0)) versusgradient(G). Theseplots are a very helpful and intuitiveway of presenting AVO data, and can give a better understanding of the rock propertiesthan by analyzing the standardAVO curves. AVO classes Rutherfordand Williams ( 1989)suggested classification a schemeof AVO responses fbr 6iflerent types of gas sanils(seeFigure 4.9). They defined three AVO classesbased on where the top of the gas sandswill be locatedin an R(0) versusG cross-plot. The cross-plotis split up into fbur quadrants. a cross-plotwith R(0) along .r-axisand C In along,v-axis, I st quadrantis whereR(0) and G areboth positivevalues(upperright the quadrant).The 2nd is whereR(0) is negative and G is positive(upperleft quadrant). The 3rd is where borh R(0) and G arenegative(lower left quadrant).Finally, the 4th quadrant is where R(0) is positive and G is negative (lower right quadrant).The AVO classes 203 4.3 AVoanalysis I- Tabfe AVO classes, 4.1 after Ruthe(brd and Williams (1989)' extendecl Castagnaand Smith (1994), and Rossand b1' K i n m a n( 1 9 9 5 ) Class RelativeimPedance Quadrant R(0) G AVO product High-impedance sand 4th Negative No or low contrast ,lth Negative 3rd Positive Low impedance 3rd Positive Low impedance 2nd Negative 'r t O lll class a D \ 1 t -- r I ctass I cra.i I crass tt rrp t.. [- defined gassands originally for (classes ll and I, Figure Ruthertbrd williamsAVOclasses, 4,9 and clnsses (Castagna Smith. IV and 1994) IIp and (Ross Kinman' and 1995)' III),along withtheadded Figure aclapted Castagna al. (1998)' is fiom et plots in the 4th quadrant must not be confused with the quadrant numbers. Class I eventswith relatively with positive R(0) and negativegradients.These representhard class II represents high impedanceand low vp/vs ratio compared with the cap-rock. can be hard to see on sands with weak intercept but strong negatjve gradient. These sections' Class III the seismic data, becausethey often yield dim spots on stacked These plot in the is the AVO category that is normally associatedwith bright spots' 3rd quadrant in R(0)-G cross-plots,and are associated with soft sandssaturatedwith hydrocarbons (seePlate4. l0). Ross and Kinman (1995) distinguished betweena class IIp and class II anomaly' gradient, causing a polarity Class IIp has a weak but positive intercept and a negative class II has a weak changewith oflset. This class will disappearon full stack sections. but negativeintercept and negativegraclient,henceno polarity change.This class may be observedas a negativeamplitude on a full-ofliet stack' of Rutherford and Castagnaand Swan (1997) extendeclthe classification scheme quadrant.These are relatively rare' Williams to incluclea 4th class,plotting in the 2n<1 stiff shales character- but occur when soft sands with gas are capped by relatively (i'e" very compacted or silty ized by Vp/Vs ratios slightly higher than in the sands shales). 204 techniques quantitative Gommon for interpretation seismic : SummaryAVO of classes ' AVO classI represents relativelyhardsandswith hydrocarbons. Thesesands tendl"o plot along the background trend in intercept-gradient cross-plots.Moreover,very hard sandscan have little sensitivityto fluids. so there may not be an associated flat spot. Hence.thesesandscan be hard to discoverlrom seismicdata. . AVo classII. representing transparent sandswith hydrocarbons, often show up as dim spotsorweaknegativereflectorson theseismic. However. becauseof relatively large gradients.they should show up as anomaliesin an Rt0)-c cross-plot.and plot off the backgroundtrend. ' AVO classIII is the "classical"AVO anomalywith negative interceptand negative gradient.This class represents relatively soft sands wirh high fluid sensitivity, locatedfar away from the backgroundtrend.Hence,they shouldbe easyro derect on seismic ata. d ' AVO classIV aresandswith negative intercept positivegradient. but The reflection coefficientbecomeslessnegaLive with increasing offset,and amplitudedecreases versusoffset.even though Lhese sandsmay be bright spots(castagnaand Swan. 1997).Class lV anomalies relativelyrare,but occur when soft sandswith gas are arecappedby relativelystiffcap-rockshales characterized vplvs ratiosslightly by h i g h e rt h a n i n t h e s a n d s( i . e . .v e r y c o m p a c t e d r s i l t y s h a l e s ) . o The AVo classeswere originally defined for gas sands.However.today the AVo class system is used for descriptiveclassification observedanomaliesthal are of not necessarilygas sands.An AVO class Il 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 therefbresuggestapplying the classification only as descriptive terms for observed A V o a n o m a l i e s , i t h o u t a u l o m a t i c a l l yi n f e r r i n g t h a t w e a r e d e a l i n g w i t h g a s w sands. AVO trends and the effects of porosity, lithology and compaction When we plot R(0) and G as cross-plots,we can analyzethe trendsthat occur in terms of in changes rock physicsproperties, includingfluid trends, porositytrendsand lithology trends,as these will have different directionsin the cross-plot(Figure 4. 1l). Using rock physicsmodels and then calculatingthe corresponding interceptand gradients, we can study various "What lf" scenarios,and then compare the modeled trends with the inverteddata. Brine-saturatedsandsinterbeddedwith shales,situatedwithin a limited depth range and at a particular locality, normally follow a well-defined "background trend" in AVO cross-plot (Castagnaand Swan, 1991). A common and recommended approach in qualitative AVO cross-plot analysis is to recognize the "background" trend and then look fbr data points that deviatefrom this trend. 205 4,3 AVOanalysis r FigUre 4.11 Difl'erent gradient occurring an intercept trends in (Adapted cross-plot' fiom Simm et al.,2O0O.) AVO Castagnaet at. (1998) presentedan excellent overview and a fiamework for gradient and intercept interpretation.The top of the sandswill normally plot in the 4th plot in quadrant,with positive R(0) and negativeG. The baseof the sandswill normally the 2nd quadrant,with negativeR(0) and positive G. The top and baseof sands,together with shale-shaleintertaces,will createa nice trend or ellipse with center in the origin ratio of the R(O)-G coordinate system. This trend will rotate with contrast in Vp/V5 1998)' betweena shaly cap-rockancla sandyreservoir(Castagna al., 1998;Sams' et We can extract the relationship between VplVs tatio and the slope of the background trencl(a6) by clividing the gradient, G, by the intercept,R(0): G (4.36) R(0) study Assuming the density contrast between shale and wet sand to be zero, we can how changinE VplVs ratio affects the backgroundtrend. The density contrastbetween sandand shaleat a given depthis normally relativelysmall compared with the velocity contrasts(Fosteret a\.,1991). Then the backgroundslopeis given by: . ^ l - ( V s*r Y s 2 ) A Y s l (4..r7) uh-I " L t Y nt V p : t A V p l where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir, and respectively; Vs1 and V52are the correspondingS-wave velocities, whereas AVp ratio is AV5 are the velocity differencesbetween reservoir anclcap-rock. If the Vp/V5 2 in the cap-rock and 2 in the reservoir,the slope of the background trend is - l, that different is a 45' slope diagonal to the gradient and intercept axes.Figure 4'12 shows lines correspondingto varying Vp/V5 ratio in the reservoir and the cap-rock. The rotation of the line denoting the background trend will be an implicit function content of rock physics properties such as clay content and porosity. Increasing clay 206 techniques quantitative Common for interpretation seismic - in VplVs=2.5 caP-rock in VplVs=2.QcaP-rock -0.5 L -0.5 0 B(0) 2 F i g u r e 4 , 1B a c k g r o u n d t r e n d s i n A V O c r o s s - p l o t s a s a f u n c t i o n o f v a r y i n g V p l V < r a l i o i n c a p - r o c k (We andreservoir. assume density no contrast.) Notice thataVplVsratioof 1.5in thereservoir can have diff'erent locations theAVOcross-plot in depending thecap-rock on VplV5ratio. Ifthe Vp/V5 ratioof thecap-rock 2.5,thesand is will exhibit AVOclass to III behavior ll (lefi),whereas the if cap-rock Vp/V5 ratiois 2.0, sand exhibit the will class to IIp behavior I (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, increasingporosity relatedto less clay contentor improved sorting will normally cause a clockwise rotation, as clean sands tend to have lower Vp/V5 ratio than shaly sands.Hence, it can be a pitfall to relate porosity to AVO responsewithout identifying the causeof the porosity change. The background trendwill change with depth,but the way it changes be complex. can Intrinsicattenuation, discussed Section4.3.4 in (Luh, 1993),will afI-ect background the trend as a function of depth, but correction should be made fbr this before rock physics analysisof the AVO cross-plot(see Section4.3.6). Nevertheless, rotation due to the depth trends in the elastic contrastsbetween sandsand shalesis not straightforward, because theVplVs in the cap-rock as well as the reservoirwill decrease with depth. These two efTects will counteracteach other in terms of rotational direction. as seenin Figure4. 12.Thus, the rotationwith depthmust be analyzedlocally.Also, the contrasts between cap-rock and reservoir will change as a function of lithology, clay content, sorting, and diagenesis,all geologic factors that can be unrelatedto depth. That being said,we shouldnot include too large a depth interval when we extractbackgroundtrends (Castagna and Swan, 1997).That would causeseveralslopesto be superimposed and result in a less defined background trend. For instance,note that the top of a soft sand will plot in the 3rd quadrant,while the baseof a soft sandwill plot in the I st quadrant, giving a backgroundtrend rotated in the oppositedirection to the trend for hard sands. T 207 4.3 AVOanalysis r Fluid effects and AVO anomalies As mentionedabove,deviationsfiom the backgroundtrend may be indicative of hydro- carbons,or some local lithology or diagenesiseffect with anomalouselastic properties (Castagnaet at., 1998).Fosteret al. (1991) mathematicallyderivedhydrocarbontrends that would be nearly parallel to the background trend, but would not pass through the origin in R(0) versus G cross-plots.For both hard and soft sandswe expect the top of hydrocarbon-filleclrocks to plot to the left of the background trend, with lower R(0) and G valuescomparedwith the brine-saturated case.However, Castagnaet al. (1998) sandscould exhibit a variety of AVO behaviors. fbund that, in particular, gas-saturated As lisred in Table 4.1. AVO classIII anomalies(Rutherfordand Williams, 1989), representingsoft sandswith gas, will fall in the 3rd quadrant(the lower left quadrant) and have negativeR(0) and G. These anomaliesare the easiestto detect fiom seismic d a t a( s e eS e c t i o n . 3 . 1l ) . 4 Harclsandswith gas,representing AVO classI anomalies,will plot in the 4th quadrant (lower right) and have positive R(0) and negative G. Consequently,these sandstend to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented), they will not show a large change in seismic responsewhen we go from brine to gas (cf. Chapter l). This type of AVO anomaly will not show up as an anomaly in a product stack. In fact, they can plot on top of the background trend of some softer, brine- saturatedsands.Hence, very stifTsandswith hydrocarbonscan be hard to discriminate with AVO analysis. AVO class II anomalies,representingsandssaturatedwith hydrocarbonsthat have very weak zero-offset contrast compared with the cap-rock, can show great overlap with the backgroundtrend,especially the sandsarerelativelydeep.However,classII if type oil sandscan occur very shallow,causingdim spotsthat stick out comparedwith a bright backgroundresponse (i.e., when heterolithicsand brine-saturatedsandsare relatively stifT compared with overlying shales).However, because they are dim they are easy to miss in near- or full-stack seismic sections,and AVO analysiscan therefore 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, hence plotting in the 2nd quadrant (upper left quadrant). They showedthat this may occur if the gas-sandshear-wave velocity is lower than that of the overlyingformation.The most likely geologicscenario suchan AVO anomalyis in for unconsolidatedsandswith relatively large 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 responsecan confusethe interpreter.First, the gradients of sandsplotting in the 2nd quadranttend to be relatively small, and less sensitiveto fluid type than the gradientsfor sandsplotting in the 3rd quadrant.Second,theseAVO anomalieswill actually show up as dim spots in a gradient stack.However, they should a 208 techniques quantitative Common for interpretation seismic - stand out in an R(0)-G cross-plot,with lower R(0) values than the background trend. Seismically, they shouldstandout as negative bright spots. Pitfalls . Differentrock physicstrencls AVO cross-plots be ambiguous. in can The interpreta- tion of AVO trendsshouldbe basedon locally constrained rock physicsmodeling. n o t o n n a i v er u l e so f t h u m b . . Trendswithin individualclustersthat do not projectthroughthe origin on an AVO cross-plol. cannot always be interpretedas a hydrocarbonindicator or unusual lithology.Sams (1998) showedthat it is possiblefortrends to have large offsets from the origin even when no hydrocarbons presentand the lithology is not are unusual.Only where the rocks on either side of the reflectingsurfacehave the same Vp/V5 ratio will the lrends (not to be confusedwith backgroundlrends as shown in Figure 4. l2.l project through the origin. Sams showedan exampleof a brine sandthat appeared more anomalous than a Iessporoushydrocarbon-bearing sand. . Residualgas saturation can causesimilar AVO effectsro high saturations gas of or light oil. Three-termAVO where reliableestimates density are oblained.or of attenuation can potentiallydiscriminateresidualgas saturations attributes. from ( commercialamountsof hydrocarbons seeSections 4.3.12 and4.3. | 5 for further discussions). Noise trends A cross-plotbetweenR(0) and G will also includea noisetrend,because the corre- of lation betweenR(0) and G. BecauseR(0) and G are obtained from least-squarefitting, there is a negative correlation between R(0) and G. Larger intercepts are correlated with smallerslopesfbr a given data set. Hence,uncorrelated random noise will show an oval, correlateddistribution in the cross-plotas seen in Figure 4.13 (Cambois, 2000). Furthermore,Cambois (2001) formulated the influenceof noise on R(0), G and a range-limitedstack (i.e., sub-stack)in terms of approximateequationsof standard deviations: 3 dR(o) : ;o, (4.38) /, ^/; 'JV-) o\ f t - - - "ti ^ ) (4.3e) z stn-0n," (I/t(l)) t; o C : V f . r ^ (4.40) sln-umrx 209 4.3 AVOanalysis - -,:'i.;.d-f,*t 'i;l? ir.} * 4,, r rl , -0.1 "t; -0.15 -0"1 -0.05 0 0.05 0.1 0.15 I (0) versusG (afterCambois,2000) Figure4,13 Randomnoisehas a ttend in rR(0) and o,,- Ji .o, (4.41) where d " is the standarddeviation of the full-stack response, is the standard o, deviation of the sub-stack.and n is the number of sub-stacks the full fold data. As we see,the of 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 gradient is much more unreliable, since the standard deviation of the gradient is inversely proportional to the sine squaredof the maximum angle of incidence. Eventually, the intercept uncertainty related to noise is more or lessinsensitiveto the maximum incidenceangle, whereasthe gradient uncertainty will decreasewith increasingaperture(Cambois, 2001). Simm er a/. (2000) claimed that while rock property infbrmation is containedin AVO cross-plots,it is not usually detectablein terms of distinct trends, owing to the effect of noise. The fact that the slope estimationis more uncertainthan the intercept during a least-squareinversion makes the AVO gradient more uncertain than the zero-offset reflectivity (e.g., Houck, 2002). Hence,the extensionof a trend parallel to the gradient axis is an indicationof the amountof noise in the data. I A 210 techniques quantitative Common for interpretation seismic I versus Fluid trends noise In areas where fluid changesin sandscause large impedancechanges,we tend to see a right-to-left lateral shift along the interceptdirection. This direction is almostopposite the noisedirection.which is predominantJy the vertical/gradient to in direction. In these casesthere should be a fair chanceof discriminating hydrocarbon- saturated sandsfrom brine-saturated sands, even in relativelynoisy data. Simm er al. (2000) furthermore stressedthat one should create AVO cross-plots aroundhorizons,not from time windows. Horizon cross-plotclearly targetsthe reservoir of interest and helps determine the noise trend while revealing the more subtle AVO Moreover,only samplesof the maximum amplitudesshould be included. responses. Sampling parts of the wavefbrmsother than the maxima will infill the area between separateclusters,and a lot of sampleswith no physical significancewould scatter However,picking only peaksand troughs around the origin in an R(0) G cross-plot. raisesa delicatequestion:what about transparentsandswith low or no impedance Theseare significantreflections contrastwith overlying shales'l with very small R(0) valuesthat could be missed if we invert the waveform only at absolutemaxima (in tbr commercialsoftwarepackages AVO inversion, absolute the maxima are commonly Another issueis shale shaleinterfaces. definedfiom R(0) sections). Theseare usually very weak reflectionsthat would be located close to the origin in an AVO cross-plot, but they are still important for assessment a local backgroundtrend. of There are also other types of noise aff-ecting AVO cross-plotdata,such as residual the moveout.It is essential try to reducethe noisetrend in the databeforeanalyzingthe to cross-plot termsof rock physicsproperties. goodpre-processing in A is scheme essential in order to achievethis (seeSection4.3.6). Cambois (2000) is doubtful that AVO cross-plotscan be usedquantitatively,because of the noise effect. With that in mind, it should still be possibleto separate the real rock physics trends fiom the noise trends. One way to distinguishthe noise trend is to cross-plota limited number of samplesfrom the same horizon from a seismic section.The extensionof the trend along the gradient axis indicatesthe amount of noise in the data (Simm et al., 2000). Another way to investigatenoise versusrock physics trends is to plot the anomaly cluster seen in the AVO cross-plot as color- codedsamples If onto the seismicsection. the clusteris mainly due to random noise,it should be scatteredrandomly around in a seismicsection.However,if the anomaly conesponds with a geologic structure and closure, it may represent hydrocarbons ( s e eP l a t e4 . 1 0 ) . rock physics we can estimatethe most likely Finally, we claim that via statistical fluid and lithology fiom AVO cross-plots even in the presence some noise. This of is ref'erredto as probabilistic AVO analysis,and was first introduced by Avseth er a/. (1998b).This method works by estimatingprobability distributionfunctionsof R(0) \ 211 4.3 AVOanalysis - and G that include the variability and background trends. Houck (2002) presenteda methodology quantifyingand cornbiningthe geologicor rock physicsuncertainties for relatedto noiseand measurement, obtaina full characterization with uncertainties to of associated the uncertainty with an AVO-based Thesemethod- lithologic interpretation. ologiesfbr quantification AVO uncertainties explainedin Section4.3.12. of are the content AVO How assess noise to in cross-plots . Make cross-plots full stack versusgradient.in addition lo R(01versusC. The of stack should have no comelationwith the gradient.so if trends in R(0t-C plots are still observedin stack vs. G, thesetrendsshouldbe real and nol randomnoise (Cambois.2000). . ldentify the location of AVO anomaliesin seismic sections.Color-code AVO anomaliesin R(0)-6 plots and then superimpose Lhemonto your seismic sec- tions. Do the anomaliesmake geologic senselshape.location),or do they spread out randomly? . Plot the regression coefficientof RlO)and C inversiononto the seismicto identify the areaswhere R(0) and G are lessreliable. . Cross-plota limitecl number of samplesfrom the same horizon from a seismic section. The extension the trend along the gradientaxis indicates amountof of the noise in the data (Simm et a\..2000). attributes hydrocarbon 4.3.11AVO for detection The information in the AVO cross-plotscan be reducedto one-dimensionalparameters basedon linear combinationsof AVO parameters. This will make the AVO infbrmation easier to interpret. Various attributes have been suggestedin the literature, and we summarize the most common below (AVO inversion-based attributesare discussedin Section4.4). Far- versus near-stack attributes One can createseveralAVO attributesfrom limited-range stack sections.The far stack minus the near stack (FN) is a "rough" estimateof an AVO gradient,and in particular it is fbund to be a good attribute from which to detect class II AVO anomalies(Ross and Kinman, 1995). For class II type prospects,the f-arstack alone can be a good attribute for improved delineation. However, fbr class IIp anomalies,both the near and the thr stack can be relatively dim, but with opposite polarities. Then the difTerencebetween far and near will manifest the significant negativegradient that is present.In contrast,a conventionalfull stack will completely zero-out a classIIp anomaly.Ross and Kinman (1995) suggestedthe fbllowing equation for the FN attribute depending on whether

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