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  • 1. I techniques quantitative for 4 Common seismic interpretation - Thereare no facts,only interpretations. lriedrith Niet:sche - 4.1 Introduction Conventionalseismicinterpretation implies picking and tracking laterally consistent seismic reflectors for the purpose of mapping geologic structures,stratigraphy and reservoir architecture. The ultimategoal is to detecthydrocarbon accumulations, delineatetheir 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 characterization. The most important of thesetechniquesinclude post-stackamplitucle (bright-spot analysis anddim-spotanalysis), (AVO offset-dependent amplitudeanalysis analysis), acousticand elasticimpedance inversion,and forward seismicmodeling. These techniques,if used properly, open up new doors for the seismic interpreter. The seismicamplitudes, representing primarily contrasts elasticproperties in between individual layers,contain information about lithology, porosity,pore-fluid type and saturation, as well as pore pressure- information that cannot be gained fiom conventional s e i s m i cn t e r p r e t a l i o n . i - 4.2 Qualitativeseismicamplitude interpretation Until a few decades ago, it would be common for seismic interpreters to roll out 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 ng with seismic data down the hallway, go down 168
  • 2. 169 - amplitude interpretation 4,2 Qualitative 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 In their interpretations. the early 1970sthe so-called"brighrspot" techniqueproved would coincidewith in of successful areas the Gulf of Mexico, wherebright amplitudes 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 polarityto lowwould cause opposite analysis, hardvolcanicintrusions as waveletphase impedance gas sands.Moreover, experienceshowed that gas-filled sands sometimes could cause"dim spots," not "bright spots," if the sandshad high impedancecompared shales. with surrounding With the introductionof 3D seismicdata, the utilization of amplitudesin seismic interpretation became much more important. Brown (see Brown et ul., l98l) was The of one of the pioneersin 3D seismicinterpretation lithofaciesfiom amplitudes. 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 can stepinto a virtual-realityworld of seismic visualization 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" implicationsfor the oil industry.In this sectionwe is a giant leap with greatbusiness qualitative aspects seismicamplitude interpretation,before we dig into the of review the impedance suchasAVO analysis, techniques more quantitative and rock-physics-based 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 wavelet? or polarity in our case?Are we dealingwith a zero-phase a minimum-phase 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. The American standarddefinesa black peak as a "hard" or There exist two standards. "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 in depth, whereasa "soft" event will correspondto a decrease acousticimpedancewith depth. According to the European standard,a black peak is a "soft" event, whereas a
  • 3. 170 T Gommon techniques quantitative for seismic interpretation 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 amplitude, 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 conesponding with the peak amplitudes that we desire for quanrirativeuse (Brown, l99g). with today's advanced seismic interpretation tools involving the use of interactive workstations,there exist various techniquesfbr horizon picking that allow efficient interpretationof 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 interpreter realizesthis and reviewsthe seismicpicks for quality control. 4.2.2 Sand/shale cross-overs depth with Simple rock physicsmodeling can assistthe initial phaseof qualitativeseismicinrerpretation, when we are uncertain about what polarity to expect for diff'erentlithology boundaries. a siliciclastic In environment, most seismic reflectors will 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, relatively sott sandsare fbund at relatively shallow depths where the sandsare unconsolidated. At greater depths, the sandsbecome consolidatedand cemented.whereas the
  • 4. 171 - 4.2 Qualitative seismic amplitude interpretati0n Sand versus shale impedance trends depth polarity (schematic) andseismic rmpe0ance 1 t Sand-shale cross-over DeDth Figure Schematic 4'1 depth trends sand shale of and impeclances. depth The trends varyfiom can basin basin, there be morethanonecross-over. to and can Localdepth trends should 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 corresponding 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 issue can be solvedby generating synthetic seismograms correlating and these with 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.
  • 5. 172 Common techniques quantitative for seismic interpretation T Typical "hard"events . Very shallow sandsat normal pressure embedded 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, unconsolidated sands(any pore fluid) embedded normally compacted in shales ' Hydrocarbon accumularions 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; if there are 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 sand/shale impedancecross-over. AVO analysisshould be underraken reveal to potentialhydrocarbon accumulations. I ii ji 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 stratigraphic layer 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 seismic 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 quanwe titative analysisof the interference amplitude.A bed only ),/30 in thicknessmay be detectable, althoughits thicknesscannotbe determinedfiom the wave shape(Sheriff and Geldhart.199-5).
  • 6. 173 E interpretation amplitude seismic 4.2 Qualitative tiickness Layer wavelength. fbr thickness a given of as amplitude a function layer 4,2 Figure Seismic 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 of reflected contributions have a phase difl-erence less than z radians. For a depth of Fresnelzone radius will be 300-470 m for fiequencies 3 km and velocity of 3 km/s, the 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 prestack migration we can collapse the difliactions to be smaller than the Fresnel zone, the thus increasing lateralseismicresolution(Sheriff and Geldhart,1995).Depending on the migration aperture, the lateral resolution after migration is of the order of a the Fresnelzone in the direction wavelength.However,the migration only collapses 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 seismic wavelengths(-50-100 m), lateral sampling is not the For typical surf'ace clata. 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 the betweenthe seismicpulse representing top of the reservoirand the seismicpulse representingthe baseof the reservoir.This happensif the layer thicknessis less than a seismicampli(Widess,1973).Figure 4.2 showsthe efTective quarterof a wavelength 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
  • 7. 174 - Gommon techniques quantitative 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 velocity 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 transparent, 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 impnrtant 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 nearoffset 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
  • 8. 175 T interpretation amplitude seismic 4.2 Qualitative 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 . Overpressured sandsor shales . Coal beds . Top of salt diapirs Only the last threeon the list abovewill causethe samepolarity as a gas sand.The Therefore.if one knows the first three will causeso-called"hard-kick" amplitudes. bright hydrocarbon-associated polariryof the dataone shouldbe able lo discriminare "hard-kick" anomalies. AVO analysisshould permit discrimination spots from the sands/shales. from coal, salt or overpressured of hydrocarbons is attributeusedamong seismicinterpreters A very common seismicamplitude over a given amplitudescalculated rellectionintensity,which is root-mean-square lime window. This anribute does not distinguish between negativeand positive ol thereforegeologic interpretation this attributeshould be made with amplitudes; greatcaution. "Flat spots" Flat spotsoccur at the reflectiveboundary betweendifferent fluids, either gas-oil, gaswarer,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 indiThe cators. Flat spots can be related to diagenetic events that are depth-dependent. an boundary between opal-A and opal-CT represents impedance increasein the same 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. and deposits sheet-flood Other "false" flat spotsinclude volcanicsills, paleo-contacts, flat basesof lobesand channels. tl
  • 9. 176 - for Common techniques quantitative seismic interpretation Pitfalls: "flatspots" False 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. The bases sand lobesespecially of tend 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 forward seismicmodeling,as well as AVO analysisof real data(seeSection4.3.8). Lithology, porosity and fluid ambiguities The ultimategoal in seismicexplorationis to discoverand delineate hydrocarbon reservoirs. Seismic amplitude maps from 3D seismicdata are often qualitarlvel.finterpreted t I lt il i, in termsof lithology and fluids.However,rigorousrock physicsmodelingand analysis of available well-log data is required to discriminate fluid effects quantitatively trom lithology effects (Chapters I and 2). The "bright-spot" analysismethod has ofien been unsuccessful becauselithology effects rather than fluid eff-ects up the bright spot. The consequence the drilling of set is holes.In order to reveal"pitfall" amplitude anomaliesit is essential investigatethe dry 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.Increasing porositycan imply reducedacousticimpedance, and by extracting empiricalporosity-impedance trendsfrom well-log data,one can estimate porosity from the inverted impedance.However, this methodology suffers from several ambiguities. Firstly, a clay-rich shalecan have very high porosities,even if the permeability is closeto zero.Hence,a high-porosity zone identifiedby this technique may be shale. Moreover, the porosity may be constant while fluid saturationvaries, and one sin-rple impedance-porosity model may not be adequate seismicporositymapping. fbr In addition to lithology-fluid ambiguities, lithology-porosity ambiguities, and porosity-fluid ambiguities,we may have lithology-lithology ambiguitiesand fluidfluid 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
  • 10. 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. yellow and red high amplitudes. Blue indicateslow amplitudes, 4120 4140 2.92 41 60 2.94 41 B0 5 o 4200 E o o 2.96 F 4220 2.98 4240 3 4260 4280 3.02 4300 rn0 VP rho*l/p lilllWi7", :fff!;"{riii;iiiffr 2.9 ,)) )))t)))l)))))))))f )) )) t) )) D,D ) D,D ) D r,D ) )), D) r )r>), p ), i)P,?),,?l? )?i)i) l?? iriiiiiiii r)ii)i) iiiii ii lrlllliilrlllllil, 10 15 Distance 20 25 Plate1,30 Top left, logs penetrating sandyturbidite sequence; right, normal-incidence a top synthetics with a 50 Hz Ricker wavelet.Bottom: increasing water saturation from l1a/c 907c(oil API 35, GOR 200) S* Lo increases densityand Vp (left), giving both amplitudeand traveltimechanges (right).
  • 11. 177 r interpretation 4.2 Qualitative seismic amplitude interpretation is usually that the channel is shale-filled. However, a clean sand fillof ing in the channel can be transparentas well. A geological assessment geometries indicating differential compaction above the channel may reveal the presenceof sand. reflectivity analysis More advancedgeophysical techniquessuch as offset-dependent 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 amplitudes as observed on horizon slices and by understandinghow different lithologies we systems system.By relatinglithologiesto depositional occur within a depositional The link between amplitude characteristics often refer to theseas lithofacies or f-acies. and depositional patternsmakes it easierto distinguish lithofacies variations and fluid in changes amplitudemaps. Traditional seismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon of The traditionalmethodologyconsisted purely visual inspection seismictraveltimes. (e.g.,Mitchum et al., 1977;Weimer and in of geometricpatterns the seismicreflections from amplitude buriedriver channels Link, l99l ). Brown et al. (1981),by recognizing 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 of understanding shallow marine facies from seismic amplitudes.Neri (1997) used Reliablequantitativelithofacies neuralnetworksto map faciesfrom seismicpulse shape. 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 stratigraphicinterpretaof tion seeksto map geologic stratigraphyfrom geometricexpression seismicreflections in traveltime and space.Stratigraphic boundariescan be defined by dilferent litholoThese often coincide,but not gies (taciesboundaries) by time (time boundaries). or always. Examples where facies boundaries and time boundaries do not coincide are erosional surfacescutting across lithostratigraphy,or the prograding fiont of a delta within the delta. almost perpendicularto the lithologic surf'aces There are severalpittalls when interpretingstratigraphyfiom traveltime infbrmation. that is, the contrasts First, the interpretationis basedon layer boundariesor interf'aces, a
  • 12. 178 interpretation seismic for techniques quantitative Gommon 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 a occur without a lithology change(e.g.,Hardage,1985).For instance, hiatuswith no the because shales intervalcan give a strongseismicsignature within a shale deposition 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 onlapsor downlaps. especiallywhen interpretingstratigraphic seismicinterpretation, in characteristics seismicinterpretation,asthey can give information Theseareessential coastal development related to relative sea level changes (e.g., Vail er ai., about the can occur if the thicknessof individual layers reduces I 977). However, pseudo-onlaps The layer can still exist,even if the seismicexpression the seismicresolution. beneath yields an onlap. Pittalls that interpretation can seismicstratigraphic pitfalls in conventional Thereareseveral quantitative techniques: be avoidedif we usecomplementary . lmportant lithostratigraphic betweenlayerswith very weak contrasts boundaries in seismicpropefiiescan easily be missed.However.if different lithologiesare seismic seismic data.they arenormallyvisiblein pre-stack in transparent post-stack similar to dara. AVO analysisis a useful tool to reveal sandswith impedances 4 { c a p p i n gs h a l e s s e eS e c t i o n . 3 1 . and . It is commonlybelieved are events time boundaries. not necessarily thatseismic For instance.a hiatus within a shale may causea boundaries. lithostratigraphic strong seismicreflectionif the shaleabovethe hiatus is lesscompactedthan the of onc below.even if the lithology is the same.Rock physicsdiagnostics well-log (seeChapter2 ). data may revealnonlithologicseismicevents . Because limited seismicresolution,false seismiconlapscan occur.The layer of can improvethe resolution. inversion Impedance resolution. may still existbeneath 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 lithology 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 stratigraphicinterpretationof a fluvial systemin Colombia using impedance sequence inversion of 3D seismicdata. Conducting impedanceinversion of the seismic data will
  • 13. 179 - 4,2 Qualitative seismic amplitude interpretation give us layer propertiesfrom interfhceproperties,and an impedancecross-section can reveal stratigraphicfeaturesnot observedon the original seismic section. Impedance inversion has the potential to guide the stratigraphicinterpretation,becauseit is less 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(Gluck et a.,1997).Moreover, frequency-band-limited impedance ally weakreflections inversioncan improve on the stratigraphicresolution,and the seismicinterpretationcan be signilicantly modified if the inversionresultsare included in the interpretationprocedure. 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 thickness seismicsignaland on introduced what they referred to as effective reflection strength, applicable to layers thinnerthan the tunins thickness: o'. - 2 " - Z ' n . , Zrr (4.3) impedance, is the average 216 where Z. is the sandstone shaleimpedance and /z is the layerthickness. more commonway to extractlayerthickness A from seismicamplitudes 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 Simpedances 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:
  • 14. r 180 Common techniques quantitative for seismic interpretation E I NIG: Vrung dZ Zrr. AZ (4 4) where V."n,lis the oil-sand fraction given bv; SI-bAI-ce Kano at-ao (4.-5) 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 discriminate layer rhickness changes from lirhologyand fluid changes. relativelysoft sands, impactof increasing In the porosityand hydrocarbon saturation tendslo 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's ratio 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-dependent reflectivity 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-spot anomalies could be investigated beforestack,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,
  • 15. 181 4.3 AVO analysis I CDPgather af interest Stacksection CDPgather CDP locqtion Target harizon . *{bu Time Geolog interpretation ic AVO responseat target horizon Shale 0,1 -0 Sondstone with gos -0, -0 Aryle ol inc,d?nca Figure Schematic 4.3 illustration theprinciples AVOanalysis. 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 technique that 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 improvementof 3D seismictechnology, betterpre-processing routines, rnorefrequent 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 potential 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
  • 16. 182 - for seismic interpretation Common techniques quantitative 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,) I , , A - -1 7 ,-vi )p + ;(r 2 *r4 T AYp W ,AVs + p' lt K (4.6) where: s i n0 1 I t - - e:(0rlu)12=et YPI Lp:pz-pr LVp:Vpz-Vpt AVs-Vs:-Vsr P : ( . P z I Pr) l2 Vp : (.Vpz vPt)12 + V5 : (V52+ vst)12 01 and 02 is In the fbrmulasabove,p is the ray parameter, is the angleof incidence, the transmissionangle; Vp1and Vp2arethe P-wave velocities above and below a given interface,respectively. Similarly, V51and V5r are the S-wavevelocities,while py and 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; where R(o):;(T.T) G::^+-'#(+.'+) -+(:.'#) :R(o) #+ (4.1)
  • 17. 183 n 4.3 AVO analvsis Medium 1 (Vp1, p1) V51, Medium 2 (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 reflected p-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-incidence reflection coefficient, 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 fbrmations.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 variation with offset(AVO) response gassands of encased shales. in Although it is generally * d
  • 18. 184 - interpretation seismic techniques quantitative for Common 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 the models(Wright, 1987).In somecases, sign of the AVO slopeor rate of shale/sand 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 ) . isotropic(TI) media can be expressed The elasticstiffnesstensorC in transversely in compactform as fbllows: (Ctt - 2Coo) C r : Cl ( c 1 1- 2 C 6 6 ) Ctr Cn C - Cr: Cr: 0 0 0 0 0 0 : where C6,6, I t(Crt C:: 0 0 0 0 0 0 0 0 0 0 0 0 C++ 0 0 0 C++ 0 0 Cr,o 0 - Cn) (4e) and where the 3-axis (z-axis)lies along the axis of symmetry. components, r, Crr, Cr andhasfive independent The above6 x 6 matrix is symmetric, three anisotropic Thomsen(1986) expressed Cr, C++,and C66.For weak anisotropy, parameters, y and 6, as a function of the five elastic components,where t, Cl-Cr a , - - (4.10) 2Cr Cor, C++ 2C++ (4. r) r (Cr:*C++)2-(.Cy-Calz 2C.3(Cy (4.12) C++) The constants can be seento describethe fiactional differenceofthe P-wave velocities in the vertical and horizontaldirections: yP(90')- vp(0') Vp(o') ( 4 .l 3 ) 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 propagating S-waves:
  • 19. 185 r analysis 4.3 AVO T - V s H ( 9 0 1 - V s v ( 9 0 ) 7sH(90") Vss(0') Vsn(0') Vsv(90') (4.14) 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 fbrmulas 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 as term can be simply expressed fbllows: R e p p ( d )- sin2e -Ad ( 4 .I 6 ) 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 or As mentioned in the previous section, seismic interf'erence event tuning can occur as closely spacedreflectorsinterfere with each other.The relative changein traveltime with increasedtraveltime and off.set.The traveltime between the reflectors decreases 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 by small offsets.The effect of tuning on AVO has been demonstrated Juhlin and Young ( 1993),Bakkeand Ursin ( 1998),andDong ( 1998),amongothers. ( 1993),Lin and Phair rock in Juhlin and Young (1993) showedthat thin layersembedded a homogeneous 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
  • 20. 186 Common techniques quantitative for seismic interpretation Lin and Phair ( 1993)suggested following expression the amplitudevariation the for with angle (AVA) response a thin layer: of (4.11) R r ( 0 ) : r r . r o A ? ' ( c o sd ' R ( 6 ) 0) 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 response fiom the top of a thick layer is: 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) (4.19) f(.y)AI(0)C(t")p'(t) wherep'(r) is the time derivativeof the pulse,A7"(0)is the traveltimethicknessof the thin layer at zero offset, and C (-v)is the offiet-dependentAVO tuning factor given by c(.v):ffi[' .##"] (4.20) where 7(0) and Z(-r') are the traveltimes atzero ofliet and at a given nonzero offset, respectively. The root-mean-square velocity VBy5, is defined along a ray path: t l' tt)t 'r s, .l v t t|t (4)t VRMS - 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) r(,r') C(r') :v ----:-- (4.22 For large contrast in elastic properties,one ought to include contributions fiom Pwave 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 primariesonly 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
  • 21. 187 4,3 AVO analysis I (2) Single-leg (1) Primaries R$ (3)Double-leg a (4)Reverberations whenwe have in that and S-waves multiples mustbeincluded AVOmodeling 4.5 Figure Converted (l) reflections; interfere with theprimaries. Primary to nrodes causing these thin layers. (After reverberations. (3) and wave; (4) primary shear (2) single-leg waves; double-leg shear Rsp : transmitted fiom converted P-wave, : reflected S-wave 1994.) 7ps and Simmons Backus, etc. fiom S-wave. converted P-wave This decrease. baseof the layersbecomesincreasinglyimportantasthe layerthicknesses often producesa seismogramthat is different fiom one produced under the primariesIn only Zoeppritzassumption. this case,one shouldusefull elasticmodelingincluding convertedwave modes and the intrabedmultiples.Martinez (1993) showedthat the with primary multiples and P-to-SV-modeconvertedwavescan interf-ere surface-related Figure 4.5 shows pre-stackamplitudesand causelargedistortionsin the AVO responses. the ray images of convertedS-wavesand multiples within a layer. propagation effects AVO on and overburden wave 4.3.4 Structuralcomplexity, at Structural complexity and heterogeneities the target level as well as in the overburon the wave propagation.These effects include focusing den can have a great impact and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed and surf'acemultiples, P-wave to vertically polarized S-wave mode conversions,and reflectivity should be corrected for these anelastic attenuation.The offset-dependent via robust processingtechniques(see Section 4.3.6). Alterwave propagation effects, 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 normalizing a target horizon amplitude to a referencehorizon amplitude. However, in more recent years there have been severalmore extensivecontributions in the literature on imaging in complex areasand AVO correctionsdue to overburden amplitude-preserved effects, some of which we will summarizebelow.
  • 22. 188 - Common techniques quantitative for seismic interpretation AVO in structurally complex areas The Zoeppritzequations assume singleinterf-ace a between two 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 pre-stack doing 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 amplitudein preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO signatures they evaluated both the uncertaintyin AVO cross-plots and 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 overburden. thin-bedded A overburden will generate velocity anisotropy and transmission lossesdue to scatteringattenuation,and theseeflects should be taken into account when analyzinga targetseismicreflector. They combinedthe generalized O'DohertyAnstey 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 correcting 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 heterogeneities above a target reflector. The generalized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent, timeharmoniceffectivetransmissivity for scalarwaves(P-wavesin acousticI D medium T or SH-wavesin elastic lD medium) and is given by Tt II u Tue ( ' ' l t ) |i f t l A L (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 representsthe relative amplitude and phasedistortions causedby the thin layers with regard to the reference medium. Neglectingthe quantity Zo which describes transmission the
  • 23. 189 - 4.3 AVoanalysis responsefor a homogeneousisotropic referencemedium (that is, a pttre phaseshift), a phase-reduced transmissivity is defined: 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 coefficient, B,were derivedfrom Shapiroet al. (1994b)by Widmaier et al. (1996): a(.f0) : , | tr'oot.f' cos2o I l6n:a2f2 cos2u V,f (4.25) and B(f.())- r f'o2 l" |V r c o s eL gnz 7'z n: V;+ r4)6r 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 with increasing angleof incidence. decreases seismicamplitude(i.e., the analyticalP-wave particle displaceIf the uncorrected 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: u r ( s , G ,t ) : I f r * ( t ) *R . w 1 r- , r ; (4 )R v is time-reduced transmissivity givenby; where two-way, the 4*(r) : irtrc(r)x Zsrvr(r) (4 )q 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).
  • 24. 190 - Common techniques quantitative for seismic interpretation In conclusion, equation (4.28) representsthe angle-dependent time shift causedby transverse isotropic 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) presented similar 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 crosscorrelationfunctions. Ursin and Stovas(2002) further extendedon the O'Doherty-Anstey fbrmula and calculated 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 complicatethe 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 calculate the relative changein AVo gradient, 6G, due to absorptionin the overburden: ftt 3G ry :-' Q" (4.31) 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 compensate 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
  • 25. 191 r 4,3 AVO analysis of This vector attenuationwill afl'ectAVO responses deeper to the sea-floorinterf'ace. reflectors. on etfects AVO 4.3.5 Acquisition include source direcon The most important acquisition eff-ects AVO measurements tivity, and source and receivercoupling (Martinez, J993). ln particular,acquisition at Inegular'Eoverage the footprint is a large problem fbr 3D AVO (Castagna,2001). Theseeffectscan be corrected surfacewill causeunevenillumination of the subsurface. Difl'erent methodsfor this have beenpresentedin the literfor using inverseoperations. et ature(e.g.,Gassaway a.,1986; Krail and Shin, 1990;Cheminguiand Biondi, 2002). ( 1993)method for normalizationof targetamplitudeswith a referenceampliChiburis' tude provided a fast and simple way of corecting for certain data collection factors and instrumentation. including sourceand receivercharacteristics analysis data of seismic forAVO 4.3.6 Pre-processing AVO processingshould preserveor restorerelative trace amplitudeswithin CMP gathers. This implies two goals: (1) reflectionsmust be correctly positionedin the subsurface; 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 lt sequence. dependson the complexity amplitudes,there is no unique processing seismicdata.and whetherthe data will of the geology.whetherit is land or marine AVO attributes or more sophisticatedelastic be used to extract regression-based inversionattributes. that makes sequence as Cambois(200 l) definesAVO processing any processing equation,if that is the model used for the AVO the data compatiblewith Shuey's task' that this can be a very complicated inversion.Camboisemphasizes 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, converted phases,tuning, anisotropy, and structure. Acquisition-related eft-ectsinclude source and receiver arrays and receiver sensitivity. Noise can be ambient or sourcefor to attempts compensate or removethese or generated. coherent random.Processing but can in the processchange or distort relative trace amplitudes. This is an effects, for important trade-off we need to consider in pre-processing AVO. We thereforeneed
  • 26. 192 r Common techniques quantitative for seismic interpretation to select basic robust a but processing (e.g., scheme ostrander, 1984; chiburis,l9g4; Fouquet,990;Castagna Backus, f and 1993; Yilma4 2001). 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 frequencies 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 Section 4.3.3),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-dependent geometricalspreading, seethe study by Ursin ( 1990). Surface-consistent amplitude balancing Source and receiver eff'ectsas well as water depth variation can produce large deviations 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
  • 27. 't 193 n 4.3 AVO analvsis off.setfbllowing Shuey's equation, and then using this behavior as a ret'erence for the statistical amplitudebalancing. Multiple removal One of the most deterioratingeff-ects pre-stackamplitudes is the presenceof multion 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 sourcereceiver trace that would have the same reflecting point. Therefore, it involves shifting 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 (amplitude variation with angle) gathers in the presence of dip, using partial pre-stack misration.
  • 28. 194 - interpretation seismic for techniques quantitative Common Pre-stack migration in Pre-stackmigration might be thought to be unnecessary areaswhere the sedimentary it is an important component of all AVO processing. section is relatively flat, but Pre-stackmigration should be used on data for AVO analysis whenever possible, it because will collapsethe diffractions at the targetdepth to be smaller than the Fresnel the lateral resolution(seeSection4.2.3; Berkhout, 1985; zone and thereforeincrease 1996).Normally, pre-stacktime migration (PSTM) is preferred to preMosher et at., the stackdepth migration (PSDM), because former tendsto preserveamplitudesbetter. with highly structured geology, PSDM will be the most accurate However, in areas PSDM routineshouldthen be applied tool (Cambois,2001).An amplitude-preserving , ( 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 Kirchet aL. (1987) and Allen and Peddy (1993) among othershave recommended hoff migration together with AVO analysis.An alternativeapproachis to apply wavederived a wave equation fbr migration algorithms.Mosher et al. (.1996) equation-based common-angle time migration and used inverse scatteringtheory (see also Weglein, (i.e.,migration-inversion). Mosher of integration migrationand AVO analysis 1992'7for et at. (1996) usecla finite-difference approachfbr the pre-stack migrations and illustrated the value of pre-stackmigration fbr improving the stratigraphicresolution, data quality, and location accuracyof AVO targets. line of anatysis a2lseismic scheme of Example pre-processing forAVO ( Y i l m a z ,0 0 1 . ) 2 geometric scaling, (source processing. ( I ) Pre-stack signature processing signal and specffalwhitening). spiking deconvolution (2t Sort to CMP and do sparse intervalvelocity 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. with the migrateddala' (8) Detailedvelocity analysisassociated (9) NMO correclionusing velocity field from step8. migrated data.Removeresidual to ( l0) StackCRP gathers obtainimageof pre-stack 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.
  • 29. 195 analysis 4.3 AVO E pitfalls AVO etfects interpretation t0 processing due in Some . Waveletphase. The phaseof a seismicsectioncan be significantlyalteredduring then AVO by processing. rhe phase a sectionis not established the interpreter. of lf impedance,for anomaliesthat would be interpretedas indicativeof decreasing (e.g.,Allen increases wherethe impedance example.can be producedat interfaces and Peddy. I993). . Multiple filtering. Not all demultiple techniquesare adequatelor AVO predomain,is very processing. Multiple filtering,done in the frequency-wavenumber 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 is A (Spran. 1987).When extractingAVO attributes. one assumes moveoutcorrection 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 improvedestimates reducesmoveoul errorsand creates windows. This technique NMO stretch is another problem in AVO analysis. Because of AVO paramerers. 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 predata beforedoing AVO analysis. processing pre-stack of Pre-processing for elastic impedance inversion for Severalof the pre-processingstepsnecessary AVO analysisare not required when preparingdatafor elasticimpedanceinversion(seeSection4.4 for detailson the methodology). First of all, the elastic impedanceapproachallows for wavelet variations with eachlimitedoffset (Cambois,2000). NMO stretchcorrectionscan be skipped,because to be stationary)is matchedto its range sub-stack(in which the waveletcan be assumed and this will removethe waveletvariationswith angle. syntheticseismogram, associated 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 procedure of reliable amplitude corrections becomes much less labor-intensivethan for
  • 30. 196 - Common techniques quantitative for seismic interpretation 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 physics propertie represent meanvalues eachfacies. for standard AVO analysis. Finally,residualNMO and multiplesstill must be accounted fbr (Cambois,2001). Misalignmentsdo not causeinterceptleakageas fbr standard AVO analysis, but near-and far-anglereflections must still be in phase. 4.3.7 AVO modeling 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
  • 31. -T I 197 - analysis 4.3 AVO trend CemellHion I Cemenled {el brino I 0 Ceme|rbd w/ hydruca]ton V tr€ild Hydrocarlon Unconsolidaled w/ brine Unconsolidtlsd w/ hydrocarbon by sands and sandstone unconsolidated capped firr AVOcurves cemented 4.7 Figure Schcgatic cases. and 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 with hydrocarbon saturationcan have similar AVO responseto a cemented sanclstone unconsolidatedsand. brine-saturated. The examplesin Figures 4.6 and 4.7 indicate how important it is to understandthe to local geology during AVO analysis.lt is necessary know what type of sandis expected 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 in coniluct realisticlithology substitutions addition to fluid substitutionduring AVO the imporrnodelingstudies.The examplesin Figures4.6 and 4.7 also demonstrate (Chapter 2) during AVO analysis. tance of the link between rock physics and geology technique? Whenis AVOanalysisthe appropriate It is well known that AVO analysisdoes not always work. Owing to the many the caseswhere AVO has been applied withoul success, techniquehas receiveda 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 of physicsand ffuid characleristics the targetreservoirare expectedto give a good of This must be clarifiedbeforethe AVO analysis real data.Without AVO response. in a proper feasibility study.one can easily misinterpretAVO signatures the real data.A good feasibility study could include both simple reflectivitymodeling and forward seismicmodeling(seeSection4.51.Both thesetechniques more advanced of shouldbe foundedon a thoroughunderstanding local geologyand petrophysical during is Realisticlithology substitution as importantas fluid substitution properties. this exercise.
  • 32. 198 interpretation for seismic Gommon techniques quantitative 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 by constrained data quality. With increasingdepth, absorptionof primary energy are ratio. higher frequencies graduallymore attenualed reduces the signal-to-noise the than lower frequencies. geology usually becomesmore complex causingmore length. for and complexwave propagations, theanglerangereduces a given streamer depth. All thesefactorsmake AVO lessapplicablewith increasing gathers AVO of 4.3.8 Deterministic analysis GDP AVO modeling, the next step in AVO analysisshould be deterAfter 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 In CDP gathers. this section,we show an exampleof how the methodcan be appliedto at in lithofacies real seismicdata,by analyzingCDP gathers well locations discriminate in a deterministic way. Figure 4.8 shows the real and synthetic CDP gathers at three well locationsin a North Seafield (the well logs are shownin Figure5.1, case adjacent l). The figure also includesthe picked amplitudesat a top targethorizon superstudy imposed on exact Zoeppritz calculated reflectivity curves derived fiom the well-log data. representoil-saturatedsands,and In Well 2, the reservoir sandsare unconsolidated, are cappedby silty shales.According to the saturationcurves derived fiom deep resisthe oil saturation in the reservoir varies from 20-807o, with an tivity measurements, 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 uniform 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 density Oil relative density Mud-filtrate pressure reservoir level Pore at level at Temperature reservoir 64 UI 32APT 1.09 g/cm3 20 MPa 77.2',C
  • 33. -v i 199 - 4.3 AVO analysis Well 3 CDP OFF ] t 0 323 726 1210 1694 2177 Rel ectivity Relleclvity - : : 0.r00 weill r 0 050 0.050 i'. -r;r! . 1 I I 0.050 ! ' ' nnqn 0 050 0 r00 I Well 3 0 1 0 0; 0 100 '- l'o" I l .. , .PB : '. 0 i : : 0050 i 0 0 150 Angle 0 1 14 21 28 34 (deq) Anqle 0 8 l5 22 29 (deg) Angle 0 1 14 20 26 32 (deg) Figure4.8 Real CDP gathers(upper),syntheticCDP gathers(middle),and AVO curvesfor Wells I 3 (lower).
  • 34. 200 Common techniques quantitative lor seismic interpretation I The correspondingAVO responseshows a negativezero-ofTset reflectivity and a negative 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 interjust as depictedin the reflectivitymodeling examplein pretedas pore-fluidchanges, Figure 4.7. lmpodance0f AVOanalysisof individualCDPgathers Investigations CDP gathersare importanl in order ro confirm AVO anomalies of (Shuey:s seenin weightedstacksect.ions intercepr and gradient,Smith and Gidlow's 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 multivariate analysis of these. Several different AVO attributescan be extracted,mapped and analyzed.The two most important ones are zero-offsetreflectivity (R(0)) and AVO gradient (G) basedon Shuey'sapproximation. Theseseismicpararneters be extracted, can via a least-squares seismicinversion,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 ) .
  • 35. 201 - analysis 4.3 AVO For a layered Earth, the relationshipbetweenofliet (r) and angle (0) is given approximately by: r s i n0 ( r ,x ) I VrNr (4.33) tt2 YRMS k3+x2fvi^)tt2 velocis where VrNr is the interval velocity and Vnr,,rs the averageroot-mean-square 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 ) : xr sin2o(4 ) sin2g(r,,rz) R(.rr) R(xz) R(r,r,) Inmor-l IcurI I (4.34) ,rr,') sin2g(r, This matrix equation is in the form of b: Ac and representsN equations in the two solutionto this equation is obtained bY unknowns,R(/, 0) and G(r). The least-squares 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 seisincluding Vp, V5 and density.This is commonly mic amplitudesfor elasticparameters, (e'g., Dahl ref'erredto as AVO inversion, and can be performed via nonlinear methods Buland et al., 1996;Gouveiaand Scales,1998)or linearizedinversion Ursin. 19921 ancl methods(e.g., Smith and Gidlow, 1987; Loertzer and Berkhout, 1993).Gouveia and via a Scales( 1998)clefined Bayesiannonlinearmodel and estimated, a nonlinearconjugate 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. fbr The inversionis perfbrmedsimultaneously all times in a given time window, which ^
  • 36. 202 r interpretation seismic for techniques quantitative Common 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 computationally fast estimationof the elasticparameters. inversion of Pittalls AVO is . A linearapproximation the Zoeppntzequations commonly usedin the calcuof lation of R(01and G. The two-term Shueyapproximationis known lo be accurate 30'. Make surethat the data inverted for anglesof incidenceup to approximately do not exceedthis range,so the approximalionis valid' lnversionalgorithms . The Zoeppritzequations only valid fbr single interfaces. are geology. will not be valid lor thin-bedded that are basedon theseequations amplitudescausedby . The linear AVO inversionis sensitiveto uncharacteristic and acquisirioneffects.A few outlying or noise (including multiples.) processing estimates are amplitudes enoughto causeerroneous in valuespresent the pre-stack packagesfor eslimationof R(0) and of R(0) and G. Mosr commercial software o t s e 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 ' outlying amPlitudes. AVO inversion is errors . Another potential problem during sample-by-sample a (Spratt, 1987l. Ursin and Ekren (1994) presented in the moveout correction method for analyzing AVO eflects in the offset domain using time windows. oi This techniquereducesmoveout errors and createsimproved estimates AVO parameters. analysis cross-Plot 4,3.10AVO A very helpful way to interpret AVO attributesis to make cross-plotsof intercept(R(0)) AVO versusgradient(G). Theseplots are a very helpful and intuitiveway of presenting of the rock propertiesthan by analyzing the data, and can give a better understanding standardAVO curves. AVO classes schemeof AVO responses a Rutherfordand Williams ( 1989)suggested classification based (seeFigure 4.9). They defined three AVO classes fbr 6iflerent types of gas sanils The on where the top of the gas sandswill be locatedin an R(0) versusG cross-plot. In cross-plotis split up into fbur quadrants. a cross-plotwith R(0) along .r-axisand C the along,v-axis, I st quadrantis whereR(0) and G areboth positivevalues(upperright The and G is positive(upperleft quadrant). The 2nd is whereR(0) is negative quadrant). quadrant 3rd is where borh R(0) and G arenegative(lower left quadrant).Finally, the 4th is where R(0) is positive and G is negative (lower right quadrant).The AVO classes
  • 37. 203 4.3 AVoanalysis I- after Ruthe(brd and Williams (1989)' 4.1 Tabfe AVO classes, b1' extendecl Castagnaand Smith (1994), and Rossand K i n m a n( 1 9 9 5 ) RelativeimPedance Quadrant sand High-impedance No or low contrast 4th ,lth Low impedance Low impedance Class 3rd 3rd 2nd lll class t -- t a 'r O D R(0) G AVO product Negative Negative Positive Positive Negative 1 r rrp tt I ctass I cra.i I crass t.. [- (classes ll and I, for defined gassands originally and 4,9 Figure Ruthertbrd williamsAVOclasses, 1995)' (Ross Kinman' and and 1994) IIp and IV clnsses (Castagna Smith. withtheadded III),along et fiom is Figure aclapted Castagna al. (1998)' 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' with soft sandssaturatedwith 3rd quadrant in R(0)-G cross-plots,and are associated (seePlate4. l0). hydrocarbons betweena class IIp and class II anomaly' Ross and Kinman (1995) distinguished 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. polarity change.This class may but negativeintercept and negativegraclient,henceno 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 characterbut 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).
  • 38. 204 : Gommon techniques quantitative for seismic interpretation SummaryAVO of classes ' AVO classI represents relativelyhardsands with 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 intercept and negative gradient.This class represents relatively soft sands wirh high fluid sensitivity, locatedfar away from the background trend.Hence,they shouldbe easyro derect on seismic ata. d ' AVO classIV aresands with 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 ( 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 ) . h i g h e rt h a n i n t h e s a n d s o The AVo classes were originally defined for gas sands.However.today the AVo class system is used for descriptiveclassification observedanomaliesthal are of not necessarily gas 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 changes rock physicsproperties, in 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.
  • 39. 205 r analysis 4,3 AVO (Adapted fiom Simm cross-plot' gradient in occurring an intercept trends 4.11 Difl'erent FigUre et al.,2O0O.) AVO Castagnaet at. (1998) presentedan excellent overview and a fiamework for normally plot in the 4th gradient and intercept interpretation.The top of the sandswill plot in quadrant,with positive R(0) and negativeG. The baseof the sandswill normally baseof sands,together the 2nd quadrant,with negativeR(0) and positive G. The top and 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)' et betweena shaly cap-rockancla sandyreservoir(Castagna al., 1998;Sams' and the slope of the background We can extract the relationship between VplVs tatio trencl(a6) by clividing the gradient, G, by the intercept,R(0): G R(0) (4.36) 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 with the velocity sandand shaleat a given depthis normally relativelysmall compared (Fosteret a.,1991). Then the backgroundslopeis given by: contrasts uh-I . ^ l - ( V s*r Y s 2 ) A Y s l " L t Y nt V p : t A V p l (4..r7) where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir, 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 background trend is - l, that 2 in the cap-rock and 2 in the reservoir,the slope of the different is a 45' slope diagonal to the gradient and intercept axes.Figure 4'12 shows and the cap-rock. lines correspondingto varying Vp/V5 ratio in the reservoir 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
  • 40. 206 - Common techniques quantitative for seismic interpretation VplVs=2.5 caP-rock in VplVs=2.QcaP-rock in -0.5 L -0.5 0 B(0) 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 2 (We andreservoir. assume density no contrast.) Notice thataVplVsratioof 1.5in thereservoir can have locations theAVOcross-plot diff'erent in depending thecap-rock on VplV5ratio. Ifthe Vp/V5 (lefi),whereas the ratioof thecap-rock 2.5,thesand is will exhibit AVOclass to III behavior ll if (right). cap-rock Vp/V5 ratiois 2.0, sand exhibit the will class to IIp behavior I 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 counterclockwise 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 (Luh, 1993),will afI-ect background Intrinsicattenuation, discussed Section4.3.4 in 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 analyzed locally.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.
  • 41. T 207 r analysis 4.3 AVO Fluid effects and AVO anomalies As mentionedabove,deviationsfiom the backgroundtrend may be indicative of hydrocarbons,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) case.However, Castagnaet al. (1998) and G valuescomparedwith the brine-saturated 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 4 d a t a( s e eS e c t i o n . 3 . 1l ) . AVO classI anomalies,will plot in the 4th quadrant Harclsandswith gas,representing (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, brinesaturatedsands.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 if trend,especially the sandsarerelativelydeep.However,classII with the background type oil sandscan occur very shallow,causingdim spotsthat stick out comparedwith sandsare (i.e., when heterolithicsand brine-saturated a bright backgroundresponse they are dim they relatively stifT compared with overlying shales).However, because 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 velocity is lower than that of the showedthat this may occur if the gas-sandshear-wave for overlyingformation.The most likely geologicscenario suchan AVO anomalyis in 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
  • 42. 208 - Common techniques quantitative 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 interpretation 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 attributes. can potentiallydiscriminateresidualgas saturations from ( commercialamountsof hydrocarbons seeSections 4.3.12 and4.3. | 5 for further discussions). Noise trends A cross-plot betweenR(0) and G will also includea noisetrend,because the correof lation betweenR(0) and G. BecauseR(0) and G are obtained from least-square fitting, 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: dR(o) : 3 /, ^/; (4.38) ;o, o 'JV-) f t - - "ti o C : V f ^ ) z stn-0n," (4.3e) (I/t(l)) t; . r ^ sln-umrx (4.40)
  • 43. 209 - 4.3 AVO analysis -,:'i.;.d-f,*t 'i;l? ir.} * 4,, r rl , -0.1 "t; -0.15 -0"1 -0.05 0 I (0) 0.05 0.1 0.15 versusG (afterCambois,2000) Figure4,13 Randomnoisehas a ttend in rR(0) and o,,- Ji .o, (4.41) deviation o, deviation of the full-stack response, is the standard where d " is the standard of of the sub-stack.and n is the number of sub-stacks the full fold data. As we see,the stack reducesthe noise in proportion to the squareroot of the fold. These equations indicate that the intercept is less robust than a half-fold sub-stack,but more robust than a third-fold sub-stack.The 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
  • 44. 210 techniques quantitative for seismic interpretation Common I Fluid versus noise trends In areas where fluid changesin sandscause large impedancechanges,we tend to see a right-to-left lateral shift along the interceptdirection. This direction is in almostopposite the noisedirection.which is predominantJy the vertical/gradient to direction. In these casesthere should be a fair chanceof discriminating hydrocarbonsandsfrom brine-saturated sands, even in relativelynoisy data. saturated 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 responses. Moreover,only samplesof the maximum amplitudesshould be included. Sampling parts of the wavefbrmsother than the maxima will infill the area between separate clusters,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 transparent sandswith low or no impedance Theseare significantreflections with very small R(0) contrastwith overlying shales'l valuesthat could be missed if we invert the waveform only at absolutemaxima (in tbr maxima are commonly commercialsoftwarepackages AVO inversion, absolute the Another issueis shale shaleinterfaces. Theseare usually definedfiom R(0) sections). 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 scheme essential is 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 investigate noise versusrock physics trends is to plot the anomaly cluster seen in the AVO cross-plot as colorcodedsamples onto the seismicsection. the clusteris mainly due to random noise,it If randomly around in a seismicsection.However,if the anomaly should be scattered conesponds with a geologic structure and closure, it may represent hydrocarbons ( s e eP l a t e4 . 1 0 ) . Finally, we claim that via statistical rock physics we can estimatethe most likely 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)
  • 45. 211 - 4.3 AVO analysis and G that include the variability and background trends. Houck (2002) presenteda methodology quantifyingand cornbiningthe geologicor rock physicsuncertainties for with uncertainties relatedto noiseand measurement, obtaina full characterization to of lithologic interpretation. Thesemethodthe uncertainty associated with an AVO-based ologiesfbr quantification AVO uncertainties explainedin Section4.3.12. of are How assess noise the in to content AVO 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 sections. 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). for 4.3.11AVO attributes hydrocarbon detection The information in the AVO cross-plotscan be reducedto one-dimensionalparameters This will make the AVO infbrmation basedon linear combinationsof AVO parameters. easier to interpret. Various attributes have been suggestedin the literature, and we attributesare discussedin summarize the most common below (AVO inversion-based 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 difTerence between 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