Quantitative seismic interpretation by southraze

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4 Common
      techniques quantitative

      Thereare no facts,only interpretations.                                                   lriedrith   Niet:sche

4.1 Introduction

      Conventionalseismicinterpretationimplies picking and tracking laterally consistent
      seismic reflectors for the purpose of mapping geologic structures,stratigraphy and
      reservoirarchitecture. The ultimategoal is to detecthydrocarbonaccumulations,
      eatetheir extent, and calculatetheir volumes.Conventionalseismic interpretationis an
      art that requires skill and thorough experiencein geology and geophysics.
        Traditionally, seismicinterpretationhasbeenessentiallyqualitative.The geometrical
      expressionof seismic reflectorsis thoroughly mapped in spaceand traveltime,but litfle
      emphasis put on the physicalunderstanding seismicamplitudevariations.In the
                is                                  of
      last few decades,however, seismic interpretershave put increasingemphasison more
      quantitative techniques fbr seismic interpretation,as these can validate hydrocarbon
      anomalies and give additional information during prospect evaluation and reservoir
                      The most important of thesetechniquesinclude post-stackamplitucle
      analysis           anddim-spotanalysis), offset-dependentamplitudeanalysis(AVO
               acousticand elasticimpedance
      analysis),                           inversion,and forward seismicmodeling.
        These techniques,if used properly, open up new doors for the seismic interpreter.
      The seismicamplitudes, representingprimarily contrasts elasticproperties
                                                           in                   between
      individual layers,contain information about lithology, porosity,pore-fluid type and sat-
      uration, as well as pore pressure- information that cannot be gained fiom conventional
      s e i s m i cn t e r p r e t a l i o n .


4.2 Qualitativeseismicamplitude
      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
                                                                        with seismic data down the hallway, go down
    169   4,2 Qualitative             interpretation

          on their knees,and use their colored pencils to interpretthe horizons of interestrn
          order to map geologic bodies. Little attention was paid to amplitude variations and
          their interpretations. the early 1970sthe so-called"brighrspot" techniqueproved
          successful areas the Gulf of Mexico, wherebright amplitudes
                      in    of                                           would coincidewith
          gas-filled sands.However, experiencewould show that this technique did not always
          work. Some of the bright spots that were interpreted as gas sands,and subsequently
          drilled, were fbund to be volcanic intrusions or other lithologies with high impedance
          contrast compared with embedding shales.These tailures were also related to lack of
          waveletphase   analysis, hardvolcanicintrusions
                                  as                         would cause  opposite polarityto low-
          impedance gas sands.Moreover, experienceshowed that gas-filled sands sometimes
          could cause"dim spots," not "bright spots," if the sandshad high impedancecompared
          with surroundingshales.
             With the introductionof 3D seismicdata, the utilization of amplitudesin seismic
          interpretation became much more important. Brown (see Brown et ul., l98l) was
          one of the pioneersin 3D seismicinterpretation lithofaciesfiom amplitudes.
                                                         of                             The
          generationoftime slicesand horizon slicesrevealed3D geologic patternsthat had been
          impossible to discover from geometric interpretationof the wiggle tracesin 2D stack
          sections.Today, the further advance in seismic technology has provided us with 3D
          visualization                          can stepinto a virtual-realityworld of seismic
                       tools where the interpreter
          wiggles and amplitudes, and trace these spatially (3D) and temporally (4D) in a way
          that one could only dream of a few decadesago. Certainly, the leap fiom the rolled-out
          paper sectionsdown the hallways to the virtual-reality imagesin visualization "caves"
          is a giant leap with greatbusiness implicationsfor the oil industry.In this sectionwe
          review the  qualitative aspects seismicamplitude interpretation,before we dig into the
                          and rock-physics-based
          more quantitative                                               impedance
                                                        suchasAVO analysis,
          inversion,and seismicmodeling,in fbllowing sections.

               phase polarity
    4.2.1 Wavelet  and
          The very first issue to resolve when interpreting seismic amplitudes is what kind of
          wavelct we have. Essentialquestionsto ask are the fbllowing. What is the defined

I         polarity in our case?Are we dealingwith a zero-phase a minimum-phase
                                                                  or                    wavelet?
          Is there a phase shift in the data? These are not straightfbrward questions to answet,
          becausethe phase of the wavelet can change both laterally and vertically. However,
          there are a f'ew pitfalls to be avoided.
            First, we want to make sure what the defined standardis when processingthe data.
          There exist two standards.    The American standarddefinesa black peak as a "hard" or
          "positive" event,and a white trough as a "soft" or a "negative"event.On a near-ofl.set
          stack section a "hard" event will correspondto an increasein acousticimpedancewith
          depth, whereasa "soft" event will correspondto a decrease acousticimpedancewith
          depth. According to the European standard,a black peak is a "soft" event, whereas a
170         techniques quantitative
       Gommon        for                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.

        ' American polarity: An increase impedance
                                         in           gives positiveamplitude.normally
          displayedas black peak (wiggle r.race) red intensitylcolor displayt.
        . European Australian)polarity:An increase impedance
                   (or                                in           givesnegal.ive
          tude, normally displayedas white rrough (wiggle trace) or blue intensity(color
        (Adaptedfrom Brown. 200la, 2001b)

         For optimal quantitative seismic interpretations,we should ensurethat our data are
      zero-phase. Then, the seismicpick should be on the crest of the waveform conespond-
      ing with the peak amplitudes that we desire for quanrirativeuse (Brown, l99g). with
      today's advanced seismic interpretation tools involving the use of interactive work-
      stations,there exist various techniquesfbr horizon picking that allow efficient inter-
      pretationof large amountsof seismicdata.Thesetechniques       include manualpicking,
      interpolation,autotracking,voxel tracking, and surfaceslicing (see Dorn (199g) fbr
        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
      also be significantly off if we do not regard lateral phaseshifts. It is important that the
      interpreterrealizesthis and reviewsthe seismicpicks for quality control.

4.2.2 Sand/shale
              cross-overs depth
      Simple rock physicsmodeling can assistthe initial phaseof qualitativeseismicinrer-
      pretation, when we are uncertain about what polarity to expect for diff'erentlithology
      boundaries. a siliciclastic
                  In            environment,  most seismic reflectorswill be associated with
      sand-shaleboundaries.Hence, the polarity will be related to the contrastin impedance
      between sand and shale.This contrastwill vary with depth (Chapter 2). Usually, rela-
      tively sott sandsare fbund at relatively shallow depths where the sandsare unconsol-
      idated. At greater depths, the sandsbecome consolidatedand cemented.whereas the
171   4.2 Qualitative

                 Sand         impedance trends
                          shale         depth
                      andseismic     (schematic)






      Figure Schematic
             4'1          depthtrends sand shale
                                    of   and   impeclances. depth
                                                         The      trends varyfiom
      basin basin, there be morethanonecross-over.
            to      and     can                    Localdepthtrendsshould established
      for different

      shalesare mainly affectedby mechanicalcompaction.Hence, cementedsandstones
      normally found to be relatively hard eventson the seismic.There will be a correspond-
      ing cross-overin acousticimpedanceof sandsand shalesas we go fiom shallow and soft
      sandsto the deep and hard sandstones   (seeFigure 4.1). However, the depth trends can
      be much more complex than shown in Figure 4.1 (Chapter2, seeFigures 2.34 and,2.35').
      Shallow sandscan be relatively hard comparedwith surroundingshales,whereasdeep
      cementedsandstones    can be relatively soft compared with surounding shales.There
      is no rule of thumb fbr what polarity to expect fbr sandsand shales.However, using
      rock physics modeling constrainedby local geologic knowledge, one can improve the
      understandingof expectedpolarity of seismic reflectors.

       "Hard"    "soft"events
       During seismicinterpretation a prospect a provenreser"yoir
                                  of         or                sand.the following
       questionshould be one of the first to be asked:what type of event do we expect,
       a "hard" or a "soft"? [n other words. should we pick a positivepeak, or a negative
       trough?lfwe havegood well control,this issuecan be solvedby generating
       seismograms correlating
                   and           thesewith realseismicdata.If we haveno well control,
       we may have to guess. However. a reasonableguess can be made based on rock
       physics modeling. Below we have listed some "rules of thumb" on what type of
       reflector we expect l-ordifferent geologic scenarios.
       172            techniques quantitative
                 Common        for          seismic

                 . Very shallow sandsat normal pressureembedded pelagicshales
                 . Cementedsandstone  with brine saluration
                 . Carbonate rocks embedded siliciclastics
                 ' 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

                       "soft" events
                 . Pelagic
                 ' S.hallow,            sands(any pore fluid) embedded normally compacted
                           unconsolidated                             in
                 ' Hydrocarbonaccumularions clean.unconsolidated poorly consolidated
                                           in                     or               sancls
                 . Overpressured

                    pitfalls conventional
                 Some      in          interpretation
                 ' Make sure you know the polarity of the data. Rememberthere are two
                   standards, US standard
                                 the                        and the European           standard.        which are opposire.
                 ' A hard event can changeto a soft laterally (i.e.. lateralphaseshifi;
 I                                                                                                                              if there are
 ii                              petrographic pore-fluidchanges.
                                                       or                               Seismicaurotracking                  will nor derecr
                 ' 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.

      4.2.3 Frequency scaleeffects
      Seismic resolution
             Verticalseismicresolution definedas theminimum separation
                                        is                                  between two interfaces
             such that we can identify two interfacesrather than one (SherifTand Geldhart, 199-5).
             A stratigraphiclayer can be resolvedin seismicdataif the layer thickness largerthan
             a quarter of a wavelength.The wavelength is given by:

             \   -   t/ /f

             where v is the interval velocity of the layer, and.l is the frequency of the seis-
             mic wave. lf the wavelet has a peak frequency of 30 Hz, and the layer velocity is
             3000 m/s, then the dominant wavelengthis 100 m. In this case,a layer of 25 m can
             be resolved.Below this thickness, can still gain important infbrmation via quan-
             titative analysisof the interference
                                                amplitude.A bed only ),/30 in thicknessmay be
             detectable,althoughits thicknesscannotbe determinedfiom the wave shape(Sheriff and
173                                interpretation
        4.2 Qualitative


        Figure Seismic                        thickness a given
                     amplitude a function layer
                             as         of           fbr      wavelength.

          The horizontal resolution of unmigrated seismic data can be defined by the Fresnel
        zone. Approximately, the Fresnel zone is defined by a circle of radius, R, around a
        rellection oint:

        n - Jgz                                                                         G.2)
        where z is the reflector clepth.Roughly, the Fresnel zone is the zone from which all
        reflected contributions have a phase difl-erence less than z radians. For a depth of
        3 km and velocity of 3 km/s, the Fresnelzone radius will be 300-470 m for fiequencies
        ranging fiom 50 to 20 Hz. When the size of the reflector is somewhat smaller than
        the Fresnel zone, the responseis essentiallythat of a diffraction point. Using pre-
        stack migration we can collapse the difliactions to be smaller than the Fresnel zone,
        thus increasing lateralseismicresolution(Sheriff and Geldhart,1995).Depending
        on the migration aperture, the lateral resolution after migration is of the order of a
        wavelength.However,the migration only collapses      the Fresnelzone in the direction
        of the migration, so if it is only performed along inlines of a 3D survey, the lateral
        resolution will still be limitecl by the Fresnelzone in the cross-linedirection. The
        lateral resolution is also restricted by the lateral sampling which is governed by the
        spacing between individual CDP gathers,usually 12.5 or 18 meters in 3D seismic
             For typical surf'ace
        clata.                    seismic wavelengths(-50-100 m), lateral sampling is not the
        l i m i t i n gl a c t o r .

Interference and tuning effects
         A thin-layered reservoir can cause what is called event tuning, which is interf'erence
         betweenthe seismicpulse representing top of the reservoirand the seismicpulse
         representingthe baseof the reservoir.This happensif the layer thicknessis less than a
        quarterof a wavelength (Widess,1973).Figure 4.2 showsthe efTective seismicampli-
        tude as a function of layer thickness for a given wavelength, where a given layer
        has higher impedancethan the surrounding sediments.We observethat the amplitude
174          techniques quantitative
        Gommon        for          seismic

        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
        extractedfrom amplitude measurements the unit is thinner than about ),/4 (Sheriff
        and Geldhart,1995).When the layer thicknessequals)./8, Widess(1973) found that
        the composite responseapproximatedthe derivative of the original signal. He referred
        to this thickness as the theoretical threshold of resolution. The amplitude-thickness
        curve is almost linear below ),/8 with decreasing  amplitudeas the layer gets thinner,
        but the compositeresponse   staysthe same.

4.2.4 Amplitude reflectivity
              and          strength
"Bright spots" and "dim spots"
        The first use of amplitude information as hydrocarbon indicators was in the early
        1970swhen it was fbund that bright-spotamplitude anomaliescould be associated
        with hydrocarbon traps (Hammond, 1974). This discovery increased interest in the
       physical propertiesof rocks and how amplitudeschangedwith difTerenttypes of rocks
       and pore fluids (Gardner et al., 1914').In a relatively soft sand, the presenceof gas
       and/or light oil will increasethe compressibilityof the rock dramatically,the veloc-
       ity will drop accordingly, and the amplitudewill decrease a negative"bright spot."
       However, if the sand is relatively hard (compared with cap-rock), the sand saturated
       with brine may induce a "brighlspot" anomaly,while a gas-filledsandmay be trans-
       parent, causing a so-calleddim spot, that is, a very weak reflector.It is very important
       before startingto interpret seismicdata to find out what changein amplitude we expect
       for different pore fluids, and whether hydrocarbonswill cause a relative dimrning or
       brighteningcomparedwith brine saturation.  Brown (1999)states   that "the most impnr-
       tant seismic property of a reservoir is whether it is bright spot regime or tlim sltot
          One obvious problem in the identification of dim spotsis that they are clim - they are
       hard to see.This issuecan be dealt with by investigating  limited-range  stack sections.
       A very weak near-offsetreflector may have a correspondingstrong f'ar-oflsetreflector.
       However,some sands,although they are significant,produce a weak positive near-
       offset reflection as well as a weak negative far-offset reflection. Only a quantitative
       analysis the changein near-to far-offsetamplitude,a gradientanalysis,
                of                                                                  will be able
     175                                interpretation
            4.2 Qualitative

             to reveal the sand with any considerabledegree of confidence. This is explained in

              Pitfalls:False"bright spots"

                                                      "brighr spots"are usuallythe first type
              During seismicexplorationof hydrocarbons.
              of DHI (direct hydrocarbonindicators)one looks for. However.there have been
              severalcaseswhere bright-spotanomalieshavebeendrilled. and turned out not lo
              be hydrocarbons.
                Some common "false bright spors"include:
              . Volcanicintrusionsand volcanicash layers
              . Highly cementedsands. often calcitecementin thin pinch-outzones
              . Low-porosityheterolithicsands
              . Overpressuredsandsor shales
              . Coal beds
              . Top of salt diapirs
              Only the last threeon the list abovewill causethe samepolarity as a gas sand.The
              first three will causeso-called"hard-kick" amplitudes.Therefore.if one knows the
              polariryof the dataone shouldbe able lo discriminarehydrocarbon-associated bright
              spots from the    "hard-kick" anomalies.
                                                     AVO analysisshould permit discrimination
              of hydrocarbons from coal, salt or overpressuredsands/shales.
                 A very common seismicamplitude     attributeusedamong seismicinterpreters is
              rellectionintensity,which is root-mean-square  amplitudescalculatedover a given
              lime window. This anribute does not distinguish between negativeand positive
                        thereforegeologic interpretation this attributeshould be made with
              amplitudes;                               ol

     "Flat spots"
             Flat spotsoccur at the reflectiveboundary betweendifferent fluids, either gas-oil, gas-
             warer,or warer-oil contacts.Thesecan be easyto detectin areaswhere the background
             stratigraphyis tilted, so the flat spot will stick out. However, if the stratigraphyis more
             or less flat, the fluid-related flat spot can be difficult to discover. Then, quantitative
             methods like AVO analysiscan help to discriminate the fluid-related flat spot from the
             fl arlying lithostratigraphy.
                 One should be aware of severalpitfalls when using flat spots as hydrocarbon indi-
             cators. Flat spots can be related to diagenetic events that are depth-dependent. The
             boundary between opal-A and opal-CT represents impedance increasein the same
             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.
             Other "false" flat spotsinclude volcanicsills, paleo-contacts,          deposits  and
             flat basesof lobesand channels.

         176         techniques quantitative
                Common        for                interpretation

                  Pitfalls: "flatspots"
                  One of f he best DHIs ro look for is a flat spot, the contactbetweengas and water,
                  gas and oil, or oil and water.However.there are other causes    that can give rise to
                  flat spots:
                  . Oceanbottom multiples
                  . Flat stratigraphy.        of
                                     The bases sand lobesespeciallytend to be flat.
                  . Opal-A to opal-CT diagenetic boundary
                  . Paleo-contacts,
                                  either relatedto diagenesis residualhydrocarbon
                                                            or                   saturation
                  . Volcanicsills
                  Rigorousflat-spotanalysisshould include detailedrock physicsanalysis.and for-
                  ward seismicmodeling,as well as AVO analysisof real data(seeSection4.3.8).

         Lithology, porosity and fluid ambiguities
                 The ultimategoal in seismicexplorationis to discoverand delineate
                voirs. Seismic amplitude maps from 3D seismicdata are often qualitarlvel.finterpreted
     t          in termsof lithology and fluids.However,rigorousrock physicsmodelingand analysis
                of available well-log data is required to discriminate fluid effects quantitatively trom
                lithology effects (Chapters I and 2).
lt                 The "bright-spot" analysismethod has ofien been unsuccessful
i,              effects rather than fluid eff-ects up the bright spot. The consequence the drilling of
                                                 set                                    is
                dry holes.In order to reveal"pitfall" amplitude anomaliesit is essential investigatethe
                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
                  A common way to extractporosity from seismicdata is to do acousticimpedance
                inversion.Increasingporositycan imply reducedacousticimpedance,   and by extract-
                ing empiricalporosity-impedancetrendsfrom well-log data,one can estimateporosity
                from the inverted impedance.However, this methodology suffers from several ambi-
                guities. Firstly, a clay-rich shalecan have very high porosities,even if the permeability
                is closeto zero.Hence,a high-porosityzone identifiedby this techniquemay be shale.
                Moreover, the porosity may be constant while fluid saturationvaries, and one sin-rple
                                 model may not be adequate seismicporositymapping.
                impedance-porosity                       fbr
                  In addition to lithology-fluid ambiguities, lithology-porosity ambiguities, and
                porosity-fluid ambiguities,we may have lithology-lithology ambiguitiesand fluid-
                fluid ambiguities.Sand and shalecan have the sameacousticimpedance,
                reflectivity on a near-offset seismic section. This has been reported in several areas
                of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that
                fluvial channelsor turbidite channelsare dim on seismic amplitude maps, and the
Plate1,1 SeismicP-P amplitudemap over a submarine       fan. The amplitudes sensitive lithofaciesand
                                                                            are       to
pore fluids, but the relationvariesacrossthe imagebecause   ofthe interplayofsedimentologicand diagenetic
influences.Blue indicateslow amplitudes,   yellow and red high amplitudes.



     4140                                2.92



                                                ,)) )))t)))l)))))))))f
                                                     ))                 ))
     4200                            E
                                         2.96   t) )) D,D ) D,D ) D r,D
                                                        ) )), D) r )r>),
                                                i)P,?),,?l? )?i)i)

     4260                                   3
                                                iriiiiiiii r)ii)i)
                                                        iiiii ii
            rn0      VP    rho*l/p                                 10          15         20          25

Plate1,30 Top left, logs penetrating sandyturbidite sequence; right, normal-incidence
                                    a                         top                             with a
50 Hz Ricker wavelet.Bottom: increasing   water saturation from l1a/c 907c(oil API 35, GOR 200)
                                                         S*          Lo
increasesdensityand Vp (left), giving both amplitudeand traveltimechanges
    177     4.2 Qualitative
                         seismic       interpretation

            interpretation is usually that the channel is shale-filled. However, a clean sand fill-
            ing in the channel can be transparentas well. A geological assessment geometries
            indicating differential compaction above the channel may reveal the presenceof sand.
            More advancedgeophysical techniquessuch as offset-dependent    reflectivity analysis
            may also reveal the sands.During conventionalinterpretation,one should interpret top
            reservoir horizons from limited-range stack sections,avoiding the pitfall of missing a
            dim sandon a near-or full-stackseismicsection.

    Facies interpretation
            Lithology influence on amplitudes can often be recognized by the pattern of ampli-
            tudes as observed on horizon slices and by understandinghow different lithologies
                                      system.By relatinglithologiesto depositional
            occur within a depositional                                            systemswe
                                                         The link between amplitude characteristics
            often refer to theseas lithofacies or f-acies.
            and depositional patternsmakes it easierto distinguish lithofacies variations and fluid
            changes amplitudemaps.
              Traditional seismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon
            seismictraveltimes.The traditionalmethodologyconsisted purely visual inspection
                                                      (e.g.,Mitchum et al., 1977;Weimer and
            of geometricpatterns the seismicreflections
            Link, l99l ). Brown et al. (1981),by recognizing buriedriver channels  from amplitude
            information, were amongst the first to interpret depositional facies from 3D seismic
            amplitudes.More recent and increasinglyquantitativework includesthat of Ryseth
            et al. (.1998)who used acoustic impedance inversions to guide the interpretation of
            sand channels, and Zeng et al. (1996) who used forward modeling to improve the
            understanding shallow marine facies from seismic amplitudes.Neri (1997) used
            neuralnetworksto map faciesfrom seismicpulse shape.Reliablequantitativelithofacies
            prediction fiom seismicamplitudesdependson establishinga link betweenrock physics
            properties and sedimentaryfacies. Sections2.4 and 2.5 demonstratedhow such links
            might be established.The case studies in Chapter 5 show how these links allow us to
            predict litholacies from seismic amplitudes.

    Stratigraphic interpretation
            The subsurfaceis by nature a layered medium, where different lithologies or f'acies
             have been superimposedduring geologic deposition. Seismic stratigraphicinterpreta-
            tion seeksto map geologic stratigraphyfrom geometricexpression seismicreflections
            in traveltime and space.Stratigraphic boundariescan be defined by dilferent litholo-
            gies (taciesboundaries) by time (time boundaries).
                                  or                           These often coincide,but not
            always. Examples where facies boundaries and time boundaries do not coincide are
            erosional surfacescutting across lithostratigraphy,or the prograding fiont of a delta
            almost perpendicularto the lithologic surf'aceswithin the delta.
              There are severalpittalls when interpretingstratigraphyfiom traveltime infbrmation.
                                                                              that is, the contrasts
            First, the interpretationis basedon layer boundariesor interf'aces,

178        techniques quantitative
      Gommon        for                interpretation

      between diff'erent strata or layers, and not the properties of the layers themselves.
      Two layers with different lithology can have the same seismic properties; hence, a
      lithostratigraphic boundary may not be observed. Second' a seismic reflection may
      occur without a lithology change(e.g.,Hardage,1985).For instance, hiatuswith no
      deposition  within a shaleintervalcan give a strongseismicsignature because shales
      above and below the hiatus have difTerent characteristics.Similarily, amalgamated
      sandscan yield internal stratigraphywithin sandy intervals,reflecting different texture
              fiom difl-erentdepositionalevents.Third, seismicresolution can be a pitfall in
      of sancls
      seismicinterpretation,especiallywhen interpretingstratigraphic   onlapsor downlaps.
      Theseareessential  characteristics seismicinterpretation,asthey can give information
      about the coastal development related to relative sea level changes (e.g., Vail er ai.,
      I 977). However, pseudo-onlaps  can occur if the thicknessof individual layers reduces
      beneath                      The layer can still exist,even if the seismicexpression
              the seismicresolution.
      yields an onlap.

       Thereareseveral                         seismicstratigraphic
                        pitfalls in conventional                                that
                                                                   interpretation can
       be avoidedif we usecomplementary      quantitativetechniques:
       . lmportant lithostratigraphic boundaries betweenlayerswith very weak contrasts
         in seismicpropefiiescan easily be missed.However.if different lithologiesare
         transparent post-stack
                   in          seismic                                        seismic
                                       data.they arenormallyvisiblein pre-stack
         dara. AVO analysisis a useful tool to reveal sandswith impedances  similar to
          c a p p i n gs h a l e s s e eS e c t i o n . 3 1 .
        . It is commonlybelieved             thatseismic      events time boundaries. not necessarily
                                                                   are                 and
          lithostratigraphic         boundaries.        For instance.a hiatus within a shale may causea
          strong seismicreflectionif the shaleabovethe hiatus is lesscompactedthan the
          onc below.even if the lithology is the same.Rock physicsdiagnostics well-log
          data may revealnonlithologicseismicevents    (seeChapter2 ).
        . Because limited seismicresolution,false seismiconlapscan occur.The layer
          may still existbeneathresolution. Impedance inversioncan improvethe resolution.
                                       featuresnot observedin the original seismicdata
          and revealsubtle srrailgraphic
          ( s e eS e c t i o n . 4 ) .

         Quantitative interpretation of amplituclescan add information about stratigraphic
       patterns,and help us avoid some of the pitfalls mentioned above.First, relating lithol-
       ogy to seismic properties(Chapter 2) can help us understandthe nature of reflections,
       and improve the geologic understandingof the seismic stratigraphy.Gutierrez (2001)
       showed how stratigraphy-guidedrock physics analysis of well-log data improved the
       sequence  stratigraphicinterpretationof a fluvial systemin Colombia using impedance
       inversion of 3D seismicdata. Conducting impedanceinversion of the seismic data will
179                  seismic
       4,2 Qualitative             interpretation

        give us layer propertiesfrom interfhceproperties,and an impedancecross-sectioncan
       reveal stratigraphicfeaturesnot observedon the original seismic section. Impedance
       inversion has the potential to guide the stratigraphicinterpretation,becauseit is less
       oscillatorythan the original seismicdata,it is more readily correlated well-log data,
        and it tends to averageout random noise, thereby improving the detectability of later-
        ally weakreflections (Gluck et a\.,1997).Moreover,frequency-band-limited impedance
       inversioncan improve on the stratigraphicresolution,and the seismicinterpretationcan
       be signilicantly modified if the inversionresultsare included in the interpretationproce-
       dure. For brief explanationsof different types of impedanceinversions,seeSection4.4.
       Forward seismicmodeling is also an excellenttool to study the seismicsignatures

Layer thickness and net-to-gross from seismic amplitude
       As mentioned in the previous section, we can extract layer thickness from seismic
                   As                                        is
       amplitudes. depictedin Figure 4.2,the relationship only linear for thin layersin
       pinch-out zonesor in sheet-likedeposits,so one shouldavoid correlatinglayer thickness
       to seismic amplitudes in areaswhere the top and baseof sandsare resolvedas separate
       reflectorsin the seismic data.
          Meckel and Nath (.1911)found that, for sands embedded in shale, the amplitude
       would depend on the net sand present,given that the thicknessof the entire sequence
       is less than ).14. Brown (1996) extended this principle to include beds thicker than
       the tuning thickness,assumingthat individual sand layers are below tuning and that
       the entire interval of interbeddedsandshas a uniform layering. Brown introduced the
       "composite amplitude" defined as the absolute value summation of the top reflection
       amplitude and the base reflection amplitude of a reservoir interval. The summation of
       the absolute values of the top and the baseemphasizesthe eff'ectof the reservoir and
       reducesthe effect of the embedding material.
         Zeng et al. (.1996)studiedthe influenceof reservoir        on
                                                           thickness seismicsignaland
        introduced what they referred to as effective reflection strength, applicable to layers
       thinnerthan the tunins thickness:

        o'. - 2 " - Z ' n . ,                                                             (4.3)

                               impedance, is the average
       where Z. is the sandstone        216             shaleimpedanceand /z is the
                      A                                       from seismicamplitudes
        layerthickness. more commonway to extractlayerthickness
       is by linear regressionof relative amplitude versus net sand thickness as observed at
       wells that are available.A recentcasestudy showing the applicationto seismicreservoir
       mappingwas providedby Hill and Halvatis(2001).
         Vernik et al. (2002) demonstratedhow to estimate net-to-grossfiom P- and S-
       impedances fbr a turbidite system. From acoustic impedance (AI) versus shear
       impedance (SI) cross-plots, the net-to-gross can be calculated with the fbllowing
    180          techniques quantitative
            Common        for          seismic

                          I    Vrung
           NIG:                                                                                                                       (4 4)
           where V."n,lis the oil-sand fraction given bv;

           Kano                                                                                                                      (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 discriminatelayer rhickness
                                                                changesfrom lirhologyand fluid
            changes. relativelysoft sands, impactof increasing
                     In                    the                     porosityand hydrocarbon
            saturationtendslo increase seismicamplitude,and thereforeworks in the same
            "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
          that this changewasrelatedto the reduced   Poisson'sratio caused the presence
                                                                            by          ofgas.
          Then,the yearafter,Shuey(1985)confirmedmathematically approximations the
                                                                        via              of
          Zoeppritz equations that Poisson'sratio was the elasticconstantmost directly related
          to the off.set-dependentreflectivity fbr incident angles up to 30". AVo technology, a
          commercial tool for the oil industry, was born.
             The AVO techniquebecamevery popular in the oil industry,as one could physicaly
          explainthe seismicamplitudes termsof rock properties.
                                       in                          Now, bright-spotanomalies
          could be investigatedbeforestack,to seeif they also had AVo anomalies  (Figure4.3).
          The techniqueproved successfulin certain areasof the world, but in many casesit was
          not successful.The technique sufI'eredfrom ambiguities causedby lithology efTects,
181     4.3 AVOanalysis

    Stacksection               af interest                    CDPgather

                                                                                      Target harizon
             . *{bu


                                                   AVO responseat
    Geolog interpretation
         ic                                        target horizon



                      Sondstone                     -0,

                       with gos                         -0

                                                                 Aryle ol inc,d?nca

             4.3      illustration theprinciples AVOanalysis.
        Figure Schematic         of            in

        tuning effects, and overburdeneft'ects.Even processingand acquisition effects could
        causefalse AVO anomalies.    But in many o1'thefailures,it was not the techniqueitself
        that failed,but the useof the techniquethat was incorrect.Lack of shear-wave velocity
        informationandthe useof too simplegeologicmodelswerecommonreasons failure.
        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,                          rnorefrequent
        shear-wavelogging and improved understanding rock physicsproperties,larger data
        capacity,more fbcus on cross-disciplinaryaspectsof AVO, and last but not least,mclre
        awareness among the usersof the potential pitfalls. The techniqueprovides the seismic
        interpreter with more data, but also new physical dimensions that add infbrmation to
        the conventional interpretationof seismic facies, stratigraphyand geomorphology.
            In this section we describe the practical aspectsof AVO technology, the poten-
        tial of this technique as a direct hydrocarbon indicator, and the pitfalls associated
        with this technique. Without going into the theoretical details of wave theory, we
        addressissuesrelatedto acquisition.processing and interpretation AVO data. For
        an excellent overview of the history of AVO and the theory behind this technology,
        we refer the reader to Castagna(1993). We expect the luture application of AVO to
182        techniques quantitative
      Common        for                interpretation

      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

4.3.1 Thereflection
      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
      given by Aki and Richards( 1980),assumingweak layer contrasts:

                              , , A
                         - -1 7 ,-vi )p +    I    AYp         ,AVs
                                                        + p' lt                          (4.6)
                     ;(r           T      2 *r4   W               K

                s i n0 1
      I t - -                    e:(0rlu)12=et
      Lp:pz-pr                                   l2
                                 P : ( . P z I Pr)
      LVp:Vpz-Vpt                Vp : (.Vpz vPt)12
      AVs-Vs:-Vsr                V5 : (V52+ vst)12

                                                                               and 02 is
          In the fbrmulasabove,p is the ray parameter, is the angleof incidence,
      the transmissionangle; Vp1and Vp2arethe P-wave velocities above and below a given
                            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;                                          (4.1)


          :R(o)    #+
       183    4.3 AVOanalvsis

              (Vp1, p1)

              (Vn, Vsz,


              Figure4'4 Reflections and transmissions a singleinterfacebetweentwo elastichalf-space
                                                       at                                               rr-redia
              firr an incidentplaneP-wave.PP(i). There will be both a reflectedp-wave,pp(r). and a transmittecl
              P-wave,PP(t).Note that thereare wave mocleconversions the reflectionpoint occurrrng
                                                                       at                             ar
              nonzeroincidence   angles.In additionto the P-waves, reflectedS-wave,pS(r), and a transrnitted
              S-wave,PS(t),will be prodr.rced.


              _     tayP
                    1   r/
                    /   vD

             This form can be interpreted in terms of difierent angular ranges! where R(0) is
             normal-incidencereflectioncoefficient, describes variationat intermecliate
                                                   G           the                        offsets
             and is often referred to as the AVO gradient,whereasF dominatesthe far ofTsets.
             critical angle. Normally, the range of anglesavailablefor AVO analysisis less
             30-40.. Therefbre,we only need to considerthe two first terms,valid fbr ansles less
             than.l0 tShuey.985,1:

             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,
             fiom the expressiongiven above we see that not only the contrastsin Vp and density
             afrect the gradient, but also vs. The importance of the vplvs ratio (or equivalently
             the Poisson'sratio) on the ofTset-dependent  reflectivity was first indicated by Koefoed
             (1955). ostrander (1984) showed that a gas-filledfbrmation would
                                                                                      have a very low
             Poisson's  ratio comparedwith the Poisson's   ratiosin the surrounding   nongaseous  fbr-
             mations.This would causea significantincreasein positive amplitude versusangle
             at the bottom of the gas layer, and a significantincrease negativeamplitudeversus
             angle at the top of the gas layer.

      4.3.2 Theeffectof anisotropy
             Velocity anisotropyought to be taken into accountwhen analyzing the amplitude varia-
             tion with offset(AVO) response gassands
                                          of        encased shales.
                                                          in      Although it is generally

* d
184        techniques quantitative
      Common        for                interpretation

      thought that the anisotropy is weak (10-20%) in most geological settings (Thomsen,
      1986), some eff'ectsof anisotropy on AVO have been shown to be dramatic using
      shale/sand models(Wright, 1987).In somecases, sign of the AVO slopeor rate of
      changeof amplitude with ofliet can be reversedbecauseof anisotropyin the overlying
      s h a l e s K i m e t a l . , 1 9 9 3 B l a n g y ,1 9 9 4 ) .
         The elasticstiffnesstensorC in transversely                 isotropic(TI) media can be expressed
      in compactform as fbllows:

                        Cl          (Ctt - 2Coo) C r :    0  0  0
                 ( c 1 1- 2 C 6 6 )      Ctr     Cn       0  0  0
                      Cr:             Cr:        C::      0  0  0
      C -
                        0               0         0      C++ 0  0
                        0               0         0       0 C++ 0
                        0               0         0       0  0 Cr,o
                            I   - Cn)
      where C6,6,                                                                                (4e)

      and where the 3-axis (z-axis)lies along the axis of symmetry.
        The above6 x 6 matrix is symmetric,  andhasfive independent            Cr
                                                                    components, r, Crr,
      Cr, C++,and C66.For weak anisotropy,     Thomsen(1986) expressed three anisotropic
      parameters, y and 6, as a function of the five elastic components,where

      a , - -                                                                                   (4.10)
                Cor, C++
                                                                                                (4. r)
                     2C.3(Cy      C++)

      The constants can be seento describethe fiactional differenceofthe P-wave velocities
      in the vertical and horizontaldirections:

                yP(90')- vp(0')
                                                                                                ( 4 .l 3 )

      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
185   4.3 AVOanalysis

               V s H ( 9 0 1 - V s v ( 9 0 ) 7sH(90") Vss(0')                          (4.14)
      T    -
                     Vsv(90')                    Vsn(0')

        The physical meaningof 6 is not as clear as s and y, but 6 is the most important
      parameterfbr normal moveout velocity and reflection amplitude'
        Under the plane wave assumption,Daley and Hron (1911) derived theoretical fbr-
      mulas for reflection and transmissioncoefficientsin Tl media. The P-P reflectivity in
      the equation can be decomposedinto isotropic and anisotropicterms as follows:

      Rpp(0): Rrpp(O) R'rpp(0)

      Assuming weak anisotropyanclsmall offsets,Banik ( 1987)showedthat the anisotropic
      term can be simply expressed fbllows:

                       -Ad                                                              ( 4 .I 6 )
      R e p p ( d )-

      Blangy (lgg4) showedthe effect of a transverselyisotropic shaleoverlying an isotropic
      gas sand on offset-dependentreflectivity, for the three different types of gas sands.
      He found that hard gas sandsoverlain by a soft TI shale exhibited a larger decrease
      in positive amplitude with offset than if the shale had been isotropic. Similarly, soft
      gas san4soverlain by a relatively hard TI shale exhibited a larger increasein negative
      amplitude with offset than if the shale had been isotropic. Furthermore, it is possible
      fbr a soft isotropic water sand to exhibit an "unexpectedly" Iarge AVO eff'ect if the
      overlying shaleis sufficientlyanisotropic'

4.3.3 Theeffectof tuningon AVO
          As mentioned in the previous section, seismic interf'erence event tuning can occur
          as closely spacedreflectorsinterfere with each other.The relative changein traveltime
          between the reflectors decreases with increasedtraveltime and off.set.The traveltime
          hyperbolasof the closely spacedreflectorswill thereforebecome even closer at larger
          ofTsets.In f-act,the amplitudes may interfere at large ofTsetseven if they do not at
          small offsets.The effect of tuning on AVO has been demonstrated Juhlin and Young
          ( 1993),Lin and Phair ( 1993),Bakkeand Ursin ( 1998),andDong ( 1998),amongothers.
            Juhlin and Young (1993) showedthat thin layersembedded a homogeneous
                                                                      in                 rock

          can produce a significantly different AVO responsefiom that of a simple interface of
          the samelithology. They showedthat, for weak contrastsin elasticpropertiesacrossthe
          layer boundaries,the AVO responseof a thin bed may be approximatedby modeling
          it as an interference phenomenon between plane P-waves fiom a thin layer' ln this
          casethin-bed tuning affects the AVO responseof a high-velocity layer embeddedin a
          homogeneousrock more than it affects the responseof a low-velocity layer.

186        techniques quantitative
      Common        for                interpretation

        Lin and Phair ( 1993)suggested following expression the amplitudevariation
                                     the                  for
      with angle (AVA) response a thin layer:

      R r ( 0 ) : r r . r o A ? ' ( c o sd ' R ( 6 )
                                    0)                                                      (4.11)

      where a.re the dominant frequency of the wavelet, Af (0) is the two-way traveltirne
      at normal incidencefiom the top to the baseof the thin layer, and R (0) is the reflection
      coefficient fiom the top interface.
        Bakke and Ursin ( 1998)extended   the work by Lin and Phair by introducingtuning
      correctionfactorsfbr a generalseismicwaveletas a function of offset. If the seismic
             fiom the top of a thick layer is:

      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
      pulse as a flnction of time /, then the response
                                                     from a thin layer is

      tl(r, y)      f(.y)AI(0)C(t")p'(t)                                                    (4.19)

      wherep'(r) is the time derivativeof the pulse,A7"(0)is the traveltimethicknessof the
      thin layer at zero offset, and C (-v)is the offiet-dependentAVO tuning factor given by

            .##"]                                                                           (4.20)

      where 7(0) and Z(-r') are the traveltimes atzero ofliet and at a given nonzero offset,
                  The root-mean-square
      respectively.                  velocity VBy5, is defined along a ray path:
                   l' tt)t 'r s,
                  .l v \t t\|t

      VRMS -                                                                               (4)t\


         For small velocity contrasts(Vnvs -           y), the last term in equation (4.20) can be
      ignored, and the AVO tuning f'actorcan be approximatedas

      C(r') :v ----:--                                                                     (4.22\
        For large contrast in elastic properties,one ought to include contributions fiom P-
      wave multiples and convertedshearwaves. The locally convertedshear wave is ofien
      neglectedin ray-tracing modeling when reproductionof the AVO responseof potential
      hydrocarbon reservoirs is attempted.Primaries-only ray-trace modeling in which the
      Zoeppritz equationsdescribethe reflectionamplitudesis most common. But primaries-
      only Zoeppritz modeling can be very misleading, becausethe locally converted shear
      waves often have a first-order eff-ecton the seismic response(Simmons and Backus,
      1994).lnterferencebetween the convertedwaves and the primary reflectionsfiom the
187      4,3 AVOanalysis

                Primaries               (2)

                                   R$            a

            (3)Double-leg          (4)Reverberations

         Figure Converted
                4.5          S-waves multiples mustbeincluded AVOmodeling
                                     and         that                in             whenwe have
         thin layers.      thesenrodesto         with theprimaries. Primary
                                         interfere               (l)        reflections;
         (2) single-leg
                      shear      (3)
                           waves; double-leg   shearwave; (4) primary
                                                          and                        (After
         Simmons Backus,
                   and             7ps
                              1994.)   : transmittedS-wave  converted P-wave, : reflected
                                                                     fiom        Rsp
         P-wave          fiom S-wave.
                 converted            etc.

         baseof the layersbecomesincreasinglyimportantasthe layerthicknesses decrease.This
         often producesa seismogramthat is different fiom one produced under the primaries-
         only Zoeppritzassumption. this case,one shouldusefull elasticmodelingincluding
         the convertedwave modes and the intrabedmultiples.Martinez (1993) showedthat
         surface-related                                                     with primary
                        multiples and P-to-SV-modeconvertedwavescan interf-ere
                                                                         Figure 4.5 shows
         pre-stackamplitudesand causelargedistortionsin the AVO responses.
         the ray images of convertedS-wavesand multiples within a layer.

    4.3.4 Structuralcomplexity,                  effects AVO
                          overburden wave
                                  and                  on
         Structural complexity and heterogeneities the target level as well as in the overbur-
         den can have a great impact on the wave propagation.These effects include focusing
         and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed
         and surf'acemultiples, P-wave to vertically polarized S-wave mode conversions,and
         anelastic attenuation.The offset-dependent  reflectivity should be corrected for these
         wave propagation effects, via robust processingtechniques(see Section 4.3.6). Alter-
         natively, these efTectsshould be included in the AVO modeling (see Sections 4.3.7
         and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor
         overburdeneffects as well as certain acquisition effects (seeSection a.3.5) by normal-
         izing a target horizon amplitude to a referencehorizon amplitude. However, in more
         recent years there have been severalmore extensivecontributions in the literature on
         amplitude-preserved  imaging in complex areasand AVO correctionsdue to overburden
         effects, some of which we will summarizebelow.
188          techniques quantitative
        Common        for                interpretation

AVO in structurally  complex areas
        The Zoeppritzequations
                             assume singleinterf-ace
                                   a               betweentwo semi-infinite
        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
        doing pre-stack depth migration (PSDM). However,one should be awarethat several
        PSDM routinesobtain reliable structuralimages without preservingthe amplitudes.
        Grubb et ul. (2001) examined the sensitivity both in structure and amplitr-rde
        to velocity uncertainties PSDM migrated images.They performed an amplitude-
        preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO
       signaturesthey evaluatedboth the uncertaintyin AVO cross-plotsand uncertaintyof
       AVO attributevaluesalong given structuralhorizons.

AVO effects due to scattering attenuation in heterogeneous overburden
                       (1996) showedhow to correct a targetAVO response a thinly layered
       Widmaier et ztl..                                               fbr
       overburden. thin-bedded    overburden will generate velocity anisotropyand transmis-
       sion lossesdue to scatteringattenuation,and theseeflects should be taken into account
       when analyzinga targetseismicreflector. They combinedthe generalized  O'Doherty-
       Anstey formula (Shapiro et ul., 1994a)with amplitude-preservingmigration/inversion
       algorithms and AVO analysis to compensatefor the influence of thin-bedded layers
       on traveltimes and amplitudes of seismic data. In particr-rlar,
                                                                     they demonstratedhow
       the estimation of zero-offset amplitude and AVO gradient can be improved by cor-
       recting fbr scattering attenuationdue to thin-bed efl'ects.Sick er at. (2003) extendecl
       Widmaier's work and provided a method of compensatingfor the scatteringattenuation
       eflects of randomly distributed heterogeneitiesabove a target reflector. The general-
       ized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent,
       harmoniceffectivetransmissivity for scalarwaves(P-wavesin acousticI D medium
       or SH-wavesin elastic lD medium) and is given by
                      ( ' ' l t ) \ |i f t l A \ \ L
       Tt II u Tue                                                                     (4.23)
       where.fis the frequency and n and p are the angle- and fiequency-dependent   scattering
       attenuationand phaseshift coefficients,respectively.The angle g is the initial angle of
       an incident plane wave at the top surfaceof a thinly layered composite stack; L is the
       thickness the thinly layeredstack;ft denotes transmissivity a homogeneous
                  of                                the                fbr
       isotropic ref-erence
                          medium that causesa phaseshifi. Hence, the equation above repre-
       sentsthe relative amplitude and phasedistortions causedby the thin layers with regard
       to the referencemedium. Neglectingthe quantity Zo which describes transmission
189   4.3 AVoanalysis

      responsefor a homogeneousisotropic referencemedium (that is, a pttre phaseshift), a
                  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
                 B,were derivedfrom Shapiroet al. (1994b)by Widmaier et al. (1996):

                           |              tr'oot.f'
      a(.f0) :
         ,                                                                              (4.25)
                     cos2o I l6n:a2f2 cos2u


                      r f'o2 l-                       gnz 7'z
      B(f.())-          "       |-                                                      r4)6r
                     V r c o s eL               V;+   t6n)02.t2cor2e

      where the statistical parametersof the referencemedium include spatial correlation
      length a, standarddeviationo, and mean velocity Vs. The medium is modeled as a
      1D random medium with fluctuating P-wave velocities that are characterizedby an
      exponential correlation function. The transmissivity (absolute value) of the P-wave
      decreases with increasing angleof incidence.
        If the uncorrected seismicamplitude(i.e., the analyticalP-wave particle displace-
      ment) is defined according to ray theory by:

      U ( S ,G , / ) : R c - W ( r - r v )                                              (4 )1\
      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
         A reflector beneatha thin-beddedoverburdenwill have the following compensated

      u r ( s , G ,t ) :       f r * ( t ) *R . w 1 r- , r ;                            (4 )R\
           the                           is
                             transmissivity givenby;
      where two-way,
                                                                                        (4 )q\
      4*(r) : irtrc(r)x Zsrvr(r)

        The superscriptT of Ur(S, G, r) indicatesthat thin-bed effects have been accounted
      fbr. Moreover, equation (4.28) indicatesthat the sourcewavelet,W(0, is convolvedwith
      the transient transmissivity both for the downgoing (i5p1 ) and the upgoing raypaths
      (f n4c)between source (S), reflection point (M), and receiver (G).
190         techniques quantitative
       Common        for          seismic

          In conclusion, equation (4.28) representsthe angle-dependent  time shift causedby
       transverseisotropic velocity behavior of the thinly layeredoverburden.Furthermore,it
       describes decrease the AVO response
                the          of                   resultingfrom multiple scatteringadditional
       to the amplitude decay related to sphericaldivergence.
         Widmaier eI ai. ( I 995) presentedsimilar lbrmulations for elasticP-waveAVO, where
       the elasticcorrection formula dependsnot only on variancesand covariances P-wave
       velocity, but also on S-wave velocity and density,and their correlationand cross-
         Ursin and Stovas(2002) further extendedon the O'Doherty-Anstey fbrmula and cal-
       culated scatteringattenuationfbr a thin-bedded,viscoelasticmedium. They found that
       in the seismic frequency range, the intrinsic attenuationdominatesover the scattering

AVO and intrinsic attenuation (absorption)
       Intrinsic attenuation,also referred to as anelasticabsorption,is causedby the fact that
       even homogeneoussedimentaryrocks are not perf'ectlyelastic. This effect can com-
       plicatethe AVO response   (e.g.,Martinez, 1993).Intrinsic attenuation be described
       in terms of a transt'ertunction Gt.o, t) fbr a plane wave of angular frequency or and
       propagation time r (Luh, 1993):

       G @ , i : exp(at Qe* i(at lr Q) ln atI tos)
                      12                                                                 (4.30)

       where Q" is the effective quality f'actorof the overburdenalong the wave propagation
       path and areis an angular referencefrequency.
         Luh demonstrated how to correct for horizontal, vertical and ofTset-dependent
       wavelet attenuation.He suggestedan approximate, "rule of thumb" equation to cal-
       culate the relative changein AVo gradient, 6G, due to absorptionin the overburden:

       3G ry :-'                                                                         (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 com-
       pensate anisotropiceffects.In most cases,
               the                                   however,anisotropiceffectsare dominant
       over attenuationeffects.Carcione (1999) furthermore showed that the unconsolidated
       sedimentsnear the seabottom in offshore environmentscan be highly attenuating,and
       that these waves will for any incidence angle have a vector attenuationperpendicular
191   4,3 AVOanalysis

                                This vector attenuationwill afl'ectAVO responses deeper
      to the sea-floorinterf'ace.

               etfects AVO
4.3.5 Acquisition    on
      The most important acquisition eff-ects AVO measurements
                                             on                     include source direc-
      tivity, and source and receivercoupling (Martinez, J993). ln particular,acquisition
      footprint is a large problem fbr 3D AVO (Castagna,2001).                       at
                                                                   Inegular'Eoverage the
      surfacewill causeunevenillumination of the subsurface.  Theseeffectscan be corrected
      for using inverseoperations.Difl'erent methodsfor this have beenpresentedin the liter-
      ature(e.g.,Gassaway a\.,1986; Krail and Shin, 1990;Cheminguiand Biondi, 2002).
      Chiburis' ( 1993)method for normalizationof targetamplitudeswith a referenceampli-
      tude provided a fast and simple way of corecting for certain data collection factors
      including sourceand receivercharacteristicsand instrumentation.

                 of seismic forAVO
4.3.6 Pre-processing      data
      AVO processingshould preserveor restorerelative trace amplitudeswithin CMP gath-
      ers. This implies two goals: (1) reflectionsmust be correctly positionedin the sub-
      surface; and (2) data quality should be sufficient to ensure that reflection amplitudes
      contain infbrmation about reflection coefficients.

       Even though the unique goal in AVO processingis to preservethe true relative
       amplitudes,there is no unique processing sequence. dependson the complexity
       of the geology.whetherit is land or marine seismicdata.and whetherthe data will
                                         AVO attributes or more sophisticatedelastic
       be used to extract regression-based
         Cambois(200 l) definesAVO processing any processing
                                              as                 sequence  that makes
       the data compatiblewith Shuey'sequation,if that is the model used for the AVO
                                 that this can be a very complicated
       inversion.Camboisemphasizes                                  task'

        Factorsthat changethe amplitudesof seismictracescan be groupedinto Earth effects,
      acquisition-relatedeffects, and noise (Dey-Sarkar and Suatek, 1993). Earth effects
      include sphericaldivergence,absorption,transmissionlosses,interbed multiples, con-
      verted phases,tuning, anisotropy, and structure. Acquisition-related eft-ectsinclude
      source and receiver arrays and receiver sensitivity. Noise can be ambient or source-
      generated. coherent random.Processing
                           or                   attempts compensate or removethese
                                                          to            for
      effects, but can in the processchange or distort relative trace amplitudes. This is an
      important trade-off we need to consider in pre-processing AVO. We thereforeneed
192         techniques quantitative
       Common        for          seismic

       to select basic robust
               a      but   processing
       Fouquet,990;Castagna Backus,
                f          and           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 frequen-
      cies and therefore improve the vertical resolution and recognition of events.One can
      make two-sided, non-causalfilters, or shaping filters, to produce a zero-phasewavelet
      ( e . g . ,L e i n b a c h ,1 9 9 5 ;B e r k h o u t ,1 9 7 7 ) .
          The wavelet shapecan vary vertically (with rime), larerally (spatially),and with
      offset. The vertical variations can be handled with deterministic Q-cornpensation(see
      Section4.3.4). However,AVO analysisis normally carriedout within a limited time
      window where one can assumestationarity.Lateral changesin the wavelet shapecan
      be handledwith surface-consistent   amplitudebalancing(e.g.,Camboisand Magesan,
      1997). Offset-dependent   variations are often more complicated to correct for, an4 are
      attributed to both ofl.set-dependent absorption (see Section 4.3.4), tuning efl'ects(see
      Section4.3.3),andNMo stretching.      NMo stretching   actslike a low-pass,mixed-phase,
      nonstationaryfilter, and the eff'ects very difficult to eliminate fully (Cambois,2001
                                           are                                             ).
      Dong (1999) examined how AVO detectability of lithology and fluids was afl'ected
      by tuning and NMo stretching, and suggesteda procedure for removing the tuning
      and stretching effects in order to improve AVO detectability.Cambois recommendecl
      picking the reflections of interest prior to NMo corrections, and flattening them for
      AVO analysis.

      Spherical divergence correction
      Spherical divergence, or geometrical spreading, causes the intensity and energy of
      spherical waves to decreaseinversely as the square of the distance fiom the source
      (Newman, 1973).For a comprehensive   review on ofTset-dependentgeometricalspread-
      ing, seethe study by Ursin ( 1990).

      Surface-consistent amplitude balancing
      Source and receiver eff'ectsas well as water depth variation can produce large devi-
      ations in amplitude that do not coffespond to target reflector properties.Commonly,
      statistical amplitude balancing is carried out both fbr time and offset. However. this
      procedure can have a dramatic efl'ect on the AVO parameters.It easily contributes
      to intercept leakage and consequentlyerroneousgradient estimates(Cambois, 2000).
      Cambois (2001) suggestedmodeling the expected averageamplitucle variation with
     193    4.3 AVO

            off.setfbllowing Shuey's equation, and then using this behavior as a ret'erence
                                                                                          for the

            Multiple removal
            One of the most deterioratingeff-ects pre-stackamplitudes is the presenceof multi-
            ples.There are severalmethodsof filtering away multiple energy,but not all of these
            adequatefor AVo pre-processing.       The method known asfft multiple filtering, done in
            the frequency-wavenumberdomain, is very efficient at removing multiples, but the
            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
            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
           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
           reducesmoveout elrors and createsimproved estimatesof AVO parameters.    One shoulcl
           be aware of AVO anomalieswith polarity shifts (classIIp, seedefinition below) during
           NMO corrections,as thesecan easily be misinterpretedas residualmoveouts(Ratcliffe
           and Adler, 2000).

           DMO correction
           DMO (dip moveout) processinggenerates      common-reflection-pointgathers.It moves
           the reflection observed on an off'set trace to the location of the coincident source-
           receiver trace that would have the same reflecting point. Therefore, it involves
           ing both time and location. As a result, the reflection moveout no longer depends
           on dip, reflection-point smear of dipping reflections is eliminated, and events with
           various dips have the same sracking velocity (Sheriff and Geldhart, 1995).
           et al. (1993) published a rechnique on how to extract reliable AVA (ampli-
           tude variation with angle) gathers in the presence of dip, using partial pre-stack
194        techniques quantitative
      Common        for                interpretation

      Pre-stack migration
      Pre-stackmigration might be thought to be unnecessary areaswhere the sedimentary
      section is relatively flat, but it is an important component of all AVO processing.
      Pre-stackmigration should be used on data for AVO analysis whenever possible,
      because will collapsethe diffractions at the targetdepth to be smaller than the Fresnel
      zone and thereforeincreasethe lateral resolution(seeSection4.2.3; Berkhout, 1985;
      Mosher et at., 1996).Normally, pre-stacktime migration (PSTM) is preferred to pre-
      stackdepth migration (PSDM), because former tendsto preserveamplitudesbetter.
      However, in areas with highly structured geology, PSDM will be the most accurate
      tool (Cambois,2001).An amplitude-preserving   PSDM routineshouldthen be applied
      ( B l e i s t e i n , 9 8 7 ;S c h l e i c h ee t c t l . , l 9 9 3 ; H a n i t z s c h 1 9 9 7 ) .
                          1                         r                                         ,
         Migration fbr AVO analysis can be implemented in many different ways. Resnick
      et aL. (1987) and Allen and Peddy (1993) among othershave recommended                               Kirch-
      hoff migration together with AVO analysis.An alternativeapproachis to apply wave-
      equation-based  migration algorithms.Mosher et al. (.1996)derived a wave equation fbr
      common-angle time migration and used inverse scatteringtheory (see also Weglein,
      1992'7forintegration migrationand AVO analysis
                          of                                                      Mosher
      et at. (1996) usecla finite-difference approachfbr the pre-stack migrations and illus-
      trated the value of pre-stackmigration fbr improving the stratigraphicresolution, data
      quality, and location accuracyof AVO targets.

                                          of          line
                                    anatysis a2lseismic
        Example pre-processing forAVO
             of            scheme
        ( Y i l m a z ,0 0 1 . )
          ( I ) Pre-stack   signal       (source
                                 processing                    geometric
                                               signature              scaling,
             spiking deconvolutionand specffalwhitening).
         (2t Sort to CMP and do sparseintervalvelocity analysis.
         (3) NMO using velocity field from step2.
         (4) Demultipleusing discreteRadontransform.
         (5) Sort to common-offset and do DMO correction.
         (6) Zero-offsetFK time migration.
                                                (CRP) and do inverseNMO using the
         (7) Sort data to common-reflection-point
             velocity field from step2.
         (8) Detailedvelocity analysisassociatedwith the migrateddala'
         (9) NMO correclionusing velocity field from step8.
        ( l0) StackCRP gathers obtainimageof pre-stack
                                           to                                           migrateddata.Removeresidual
                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 .
        ( l2; Post-stack
                       spiking deconvolution.
        (13) Remigrateusing migrationvelocity field from step8.
195    4.3 AVOanalysis

                       interpretation t0 processing
            pitfalls AVO
         Some      in              due           etfects
         . Waveletphase. The phaseof a seismicsectioncan be significantlyalteredduring
           processing. rhe phase a sectionis not established the interpreter.
                     lf         of                          by               then AVO
           anomaliesthat would be interpretedas indicativeof decreasingimpedance,for
                                              wherethe impedance
           example.can be producedat interfaces                   increases (e.g.,Allen
           and Peddy. I993).
         . Multiple filtering. Not all demultiple techniquesare adequatelor AVO pre-
           processing. Multiple filtering,done in the frequency-wavenumberdomain,is very
           efficientar removing multiples.but the dip in the/-k domain is very similar for
          near-offsetprimary energy and near-offsetmultiple energy.Hence,primary energy
          can easlly be removed from the near-offsettraces. resulting in an artificial AVO
         . NMO correction. potentialproblemduring AVO analysis errorsin the velocity
                            A                                     is
           moveoutcorrection  (Spran. 1987).When extractingAVO attributes. one assumes
           that primaries have been completely flattenedto a constanttraveltime.This is
          rarely the case.as therewill alwaysbe residualmoveout.Ursin and Ekren (1994)
          presenteda method for analyzing AVO effects in rhe offset domain using time
          windows. This technique  reducesmoveoul errorsand creates improvedestimates
          of AVO paramerers.    NMO stretch is another problem in AVO analysis. Because
          the amount of normal moveout varies with arrival time. frequenciesare lowered
          at large offsets compared with short offsets. Large offsets, where the stretching
          effect is significant.should be muted before AVO analysis.Swan (1991), Dong
           (1998) and Dong ( 1999)examinethe eft'ectof NMO stretchon offset-dependenl
         . AGC amplirude conection. Automatic gain control must be avoided in pre-
           processing pre-stack
                       of      data beforedoing AVO analysis.

Pre-processing for elastic impedance inversion
        Severalof the pre-processingstepsnecessary AVO analysisare not required when
        preparingdatafor elasticimpedanceinversion(seeSection4.4 for detailson the method-
        ology). First of all, the elastic impedanceapproachallows for wavelet variations with
        offset (Cambois,2000). NMO stretchcorrectionscan be skipped,because      eachlimited-
        range sub-stack(in which the waveletcan be assumed   to be stationary)is matchedto its
        associated syntheticseismogram,   and this will removethe waveletvariationswith angle.
        It is, however,desirableto obtain similar bandwidth fbr each inverted sub-stackcube,
        since these should be comparable.Furthermore, the data used for elastic impedance
        inversion are calibratedto well logs before stack,which meansthat averageamplitude
        variations with offset are automatically accountedfor. Hence, the complicated pro-
        cedure of reliable amplitude corrections becomes much less labor-intensivethan for
196        techniques quantitative
      Common        for                interpretation

            u         1   0     2     0      3     0      4     0      5     0      6      0
                                          Angle incidence

      Figure4,6 AVO curvesfbr differenthalf'-space
                                                 models(i.e.,two layers one intertace).
      is cap-rock.
                 Input rock physicspropertie\        meanvalues eachfacies.
                                             represent           for

             AVO analysis.
      standard            Finally,residualNMO and multiplesstill must be accounted
      (Cambois,2001). Misalignmentsdo not causeinterceptleakageas fbr standard  AVO
              but near-and far-anglereflectionsmust still be in phase.

4.3.7 AVOmodeling seismic
                and     detectability
      AVO analysisis normally carried out in a deterministicway to predict lithology and
      fluids from seismicdata(e.g.,Smith and Gidlow, 1987;RutherfordandWilliams, 1989;
      Hilterman, 1990;Castagna     and Smith, 1994;Castagna al., 1998).
        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
      in this case.


     197   4.3 AVOanalysis


                  I                                                    Cemenled

                                                                       {el brino

                                                                          w/ hydruca]ton
                         V                                             w/ brine

                                                                       w/ hydrocarbon

           Figure Schcgatic
                  4.7           AVOcurves cemented
                                           firr                            sands   by
                                                     sandstone unconsolidated capped
                                   and           cases.
           shlle.frll brine-saturated oil-saturated

             Figure 4.7 shclwsanotherexample,where we considertwo types of clean sands,
           cementedand unconsolidated,with brine versushydrocarbonsaturation.We seethat a
           cemented sanclstonewith hydrocarbon saturationcan have similar AVO responseto a
              The examplesin Figures 4.6 and 4.7 indicate how important it is to understandthe
           local geology during AVO analysis.lt is necessary know what type of sandis expected
           for a given prospect,and how much one expectsthe sandsto change locally owing to
           textural changes,before interpreting fluid content. It is therefore equally important to
           coniluct realisticlithology substitutions addition to fluid substitutionduring AVO
           rnodelingstudies.The examplesin Figures4.6 and 4.7 also demonstrate           the impor-
           tance of the link between rock physics and geology    (Chapter 2) during AVO analysis.

             Whenis AVOanalysisthe appropriate

             It is well known that AVO analysisdoes not always work. Owing to the many
             caseswhere AVO has been applied withoul success, techniquehas receiveda
             bad reputationas an unreliabletool. However.part ol the AVO analysisis to find
             out if the techniqueis appropriatein the first place. It will work only if lhe rock
             physicsand ffuid characleristics the targetreservoirare expectedto give a good
             AVO response. This must be clarifiedbeforethe AVO analysis real data.Without
             a proper feasibility study.one can easily misinterpretAVO signatures the real
             data.A good feasibility study could include both simple reflectivitymodeling and
             more advanced forward seismicmodeling(seeSection4.51.Both thesetechniques
             shouldbe foundedon a thoroughunderstanding local geologyand petrophysical
                       Realisticlithology substitution as importantas fluid substitution
             properties.                             is
             this exercise.
198        techniques quantitative
      Gommon        for                interpretation

         Often, one will find that there is a certain depth interval where AVO will work,
       often referred to as the "AVO window." Outside this, AVO will not work well.
       That is why analysis of rack physics depth trends should be an integral part of
       AVO analysis (see Sections 2.6 and 4.3.16). However. the "AVO window" is also
       constrained data quality. With increasingdepth, absorptionof primary energy
       reduces the signal-to-noiseratio. higher frequencies graduallymore attenualed
       than lower frequencies. geology usually becomesmore complex causingmore
       complexwave propagations, theanglerangereduces a given streamer
                                and                      for
       All thesefactorsmake AVO lessapplicablewith increasingdepth.

                AVO        of  gathers
4.3.8 Deterministic analysis GDP
                             AVO modeling, the next step in AVO analysisshould be deter-
      After simple half--space
      ministic AVO analysis of selectedCDP (common-depth-point)gathers,preferably at
      well locations where synthetic gathers can be generatedand compared with the real
      CDP gathers. this section,we show an exampleof how the methodcan be appliedto
      discriminate lithofacies real seismicdata,by analyzingCDP gathers well locations
                             in                                        at
      in a deterministic way. Figure 4.8 shows the real and synthetic CDP gathers at three
      adjacent well locationsin a North Seafield (the well logs are shownin Figure5.1, case
      study l). The figure also includesthe picked amplitudesat a top targethorizon super-
      imposed on exact Zoeppritz calculated reflectivity curves derived fiom the well-log
         In Well 2, the reservoir sandsare unconsolidated, representoil-saturatedsands,and
      are cappedby silty shales.According to the saturationcurves derived fiom deep resis-
      tivity measurements,  the oil saturation in the reservoir varies from 20-807o, with an
      average of about 60Va. The sonic and density logs are found to measure the mud
      filtrate invaded zone (0-l0o/o oil). Hence, we do fluid substitution to calculate the
      seismic properties of the reservoir from the Biot-Gassmann theory assuming a uni-
      form saturation model (the process of fluid substitution is described in Chapter l).
      Before we do the fluid substitution, we need to know the acoustic properties of
      the oil and the mud filtrate. These are calculated from Batzle and Wang's relations
      (see Chapter l). For this case, the input parametersfor the fluid substitution are as

       oilGoR                             64 UI
       Oil relative                       32APT
       Mud-filtratedensity                1.09 g/cm3
       Pore                  level
            pressure reservoir
                     at                   20 MPa
       Temperature reservoirlevel         77.2',C

 i   199
           4.3 AVOanalysis


            CDP    ]
            OFF    0 323 726 1210 1694 2177

                                                            Relleclvity                                 ectivity

                      -             weill                  0.r00                                            :
                                                                                                     0 1 0 0;
                                                                                                                                 Well 3
           0 100
                               i'. -                                                                       I
                           r       -r;r!                                                                   I
                                                                                                     0.050 !                       ,      .PB
           0 050
                                            . 1   ' '
           0 050                                           nnqn    I
                                                                                                         0 i
                                                                   I                 l'o"    ..            :
                                                           0 r00
              0                                                                                      0050i
                                                           0 150

           Angle     1    14       21       28    34 (deq) Anqle
                                                               0            8   l5   22     29 (deg) Angle
                                                                                                         0         1   14   20   26       32 (deg)

           Figure4.8 Real CDP gathers(upper),syntheticCDP gathers(middle),and AVO curvesfor Wells
           I 3 (lower).
200         techniques quantitative
       Common        lor                interpretation

       The correspondingAVO responseshows a negativezero-ofTset   reflectivity and a neg-
       ative AVO gradient. In Well l, we have a water-saturated
                                                              cementedsand below a silty
       shale.The correspondingAVO responsein this well showsa strongpositive zero-ofl.set
       reflectivity and a relatively strong negative gradient. Finally, in Well 3 we observe a
       strongpositive zero-offsetreflectivity and a moderatenegativegradient,corresponding
       to interbeddedsand/shale
                              faciescappedby silty shales.Hence,we observethreedistinct
       AVO responsesin the three different wells. The changesare related to both Iithology
       and pore-fluid variations within the turbidite system. For more detailed information
       about this system,seecase study I in Chapter 5.
         Avseth et al. (2000) demonstratedthe etlect of cementationon the AVO responsein
       real CDP gathersaround two wells, one where the reservoir sandsare friable, and the
       other where the reservoir sands are cemented.They found that if the textural eflects
       of the sandswere ignored, the correspondingchangesin AVO responsecould be inter-
       pretedas pore-fluidchanges,  just as depictedin the reflectivitymodeling examplein
       Figure 4.7.

        lmpodance0f AVOanalysisof individualCDPgathers

        Investigations CDP gathersare importanl in order ro confirm AVO anomalies
        seenin weightedstacksect.ions               and gradient,Smith and Gidlow's
        fluid factor. etc.). The weighted stackscan contain anomaliesnot related to true
        offset-dependent   amplitudevariations.

4.3.9 EstimationAVO
Estimating intercept and gradient
       The next stepin an AVO analysisshould be to extract AVO attributesand do multivari-
       ate analysis of these. Several different AVO attributescan be extracted,mapped and
       analyzed.The two most important ones are zero-offsetreflectivity (R(0)) and AVO gra-
       dient (G) basedon Shuey'sapproximation.  Theseseismicpararneters be extracted,
       via a least-squaresseismicinversion,for each samplein a CDP gatherover a selected
       portion of a 3D seismicvolume.
         For a given NMO-conected CDP gather, R(/,,r), it is assumed that for each
       time sample, /, the reflectivity data can be expressedas Shuey's formula (equation

       R(r, : R(/,0) + c(/) sin2g(r,
          r)                      -r)                                                 (4 7)\

       where 0(r, x) is the incident angle corresponding to the data sample recorded at
       ( t .r ) .
    201     4.3 AVOanalysis

               For a layered Earth, the relationshipbetweenofliet (r) and angle (0) is given approx-
            imately by:

                                               r           VrNr                              (4.33)
            s i n0 ( r ,x ) I                              tt2
            where VrNr is the interval velocity and Vnr,,rs the averageroot-mean-square
                                                          is                            veloc-
            ity, as calculated from an input velocity profile (fbr example obtained from sonic
              For any given value of zero-offsettime, /e, we assumethat R is measuredat N offsets
            (xi, i:1, A/).Hence,we can rewrite the defining equationfbr this time as (Hampson
            a n d R u s s e l l .1 9 9 5 ) :

                  R(.rr)                         xr
                                           sin2o(4 )
                  R(xz)                    sin2g(r,,rz)
                                                            Inmor-l                           (4.34)
                  R(r,r,)            I            ,rr,')

             This matrix equation is in the form of b: Ac and representsN equations in the two
             unknowns,R(/, 0) and G(r). The least-squaressolutionto this equation is obtained bY
             solving the so-called"normal equation":

             c:     (ArA)-1(ATb)                                                              (4.3s)

                                                   solutionfbr R(0) and G at time t.
                                us the least-squares

     Inversion for elastic Parameters
             Going beyond the estimation of intercept and gradient, one can invert pre-stack seis-
             mic amplitudesfor elasticparameters,  including Vp, V5 and density.This is commonly
                                                                                        (e'g., Dahl
             ref'erredto as AVO inversion, and can be performed via nonlinear methods
             anclUrsin. 19921 Buland et al., 1996;Gouveiaand Scales,1998)or linearizedinversion
             methods(e.g., Smith and Gidlow, 1987; Loertzer and Berkhout, 1993).Gouveia and
             Scales( 1998)clefined Bayesiannonlinearmodel and estimated, a nonlinearcon-
                                  a                                        via
             jugate gradient method, the maximum a-posteriori (MAP) distributions of the elastic
             parameters.However, the nonlinearity of the inversion problem makes their method
             very compurer intensive.Loertzer and Berkhout ( 1993)performed linearized Bayesian
             inversion based on single interface theory on a sample-by-samplebasis. Buland and
             Omre (2003) extendedthe work of Loertzer and Berkhout and developeda linearized
              Bayesian AVO inversion method where the wavelet is accountedfor by convolution.
              The inversionis perfbrmedsimultaneously all times in a given time window, which

202        techniques quantitative
      Common        for                interpretation

      makes it possible to obtain temporal correlation between model parametersclose in
      time. Furthermore, they solved the AVO inversion problem via Gaussianpriors and
      obtained an explicit analytical form for the posterior density,providing a computation-
      ally fast estimationof the elasticparameters.

       Pittalls AVO
       . A linearapproximation the Zoeppntzequations commonly usedin the calcu-
                                of                      is
         lation of R(01and G. The two-term Shueyapproximationis known lo be accurate
         for anglesof incidenceup to approximately30'. Make surethat the data inverted
         do not exceedthis range,so the approximalionis valid'
       . The Zoeppritzequations only valid fbr single interfaces.
                                are                                  lnversionalgorithms
         that are basedon theseequations will not be valid lor thin-beddedgeology.
       . The linear AVO inversionis sensitiveto uncharacteristic    amplitudescausedby
         noise (including multiples.) processing
                                    or           and acquisirioneffects.A few outlying
         valuespresent the pre-stack
                       in              amplitudes enoughto causeerroneous
                                                 are                         estimates
         of R(0) and G. Mosr commercial software   packagesfor eslimationof R(0) and
         C a p p l y r o b u s r s t i m a r i o ne c h n i q u e ( e . g . ,W a l d e n .1 9 9 l ) t o l i m i t t h e d a m a g e l '
                               e                 t                s
         outlying amPlitudes.
       . Another potential problem during sample-by-sample                                    AVO inversion is errors
         in the moveout correction                 (Spratt, 1987l. Ursin and Ekren (1994) presented                                 a
         method for analyzing AVO eflects in the offset domain using time windows.
         This techniquereducesmoveout errors and createsimproved estimates AVO

4,3.10AVO      analysis
      A very helpful way to interpret AVO attributesis to make cross-plotsof intercept(R(0))
      versusgradient(G). Theseplots are a very helpful and intuitiveway of presenting  AVO
      data, and can give a better understanding of the rock propertiesthan by analyzing the
       standardAVO curves.

AVO classes
       Rutherfordand Williams ( 1989)suggested classification
                                                    a              schemeof AVO responses
       fbr 6iflerent types of gas sanils(seeFigure 4.9). They defined three AVO classesbased
       on where the top of the gas sandswill be locatedin an R(0) versusG cross-plot.   The

       cross-plotis split up into fbur quadrants. a cross-plotwith R(0) along .r-axisand C
       along,v-axis, I st quadrantis whereR(0) and G areboth positivevalues(upperright
       quadrant).The 2nd is whereR(0) is negative and G is positive(upperleft quadrant).  The
       3rd is where borh R(0) and G arenegative(lower left quadrant).Finally, the 4th quadrant
       is where R(0) is positive and G is negative (lower right quadrant).The AVO classes
203   4.3 AVoanalysis

      Tabfe AVO classes,
             4.1             after Ruthe(brd and Williams (1989)'
      extendecl Castagnaand Smith (1994), and Rossand
      K i n m a n( 1 9 9 5 )

      Class      RelativeimPedance      Quadrant   R(0)   G   AVO product

                 High-impedance  sand   4th                   Negative
                 No or low contrast     ,lth                  Negative
                                        3rd                   Positive
                 Low impedance          3rd                   Positive
                 Low impedance          2nd                   Negative

                      t           O
          class           a   D    \    1
          t --
                    I ctass I cra.i I crass
                          tt     rrp
                    t..       [-
                                                        defined gassands
                                               originally     for       (classes ll and
       Figure Ruthertbrd williamsAVOclasses,
              4,9           and
                              clnsses (Castagna Smith.
                                   IV        and      1994) IIp
                                                            and   (Ross Kinman'
                                                                      and         1995)'
       III),along withtheadded
       Figure aclapted Castagna al. (1998)'
              is        fiom       et

                                                                   plots in the 4th quadrant
       must not be confused with the quadrant numbers. Class I
                                                                       eventswith relatively
       with positive R(0) and negativegradients.These representhard
                                                                          class II represents
       high impedanceand low vp/vs ratio compared with the cap-rock.
                                                                       can be hard to see on
       sands with weak intercept but strong negatjve gradient. These
                                                                           sections' Class III
       the seismic data, becausethey often yield dim spots on stacked
                                                                            These plot in the
       is the AVO category that is normally associatedwith bright spots'
       3rd quadrant in R(0)-G cross-plots,and are associated  with soft sandssaturatedwith

       hydrocarbons   (seePlate4. l0).
          Ross and Kinman (1995) distinguished     betweena class IIp and class II anomaly'
                                                                  gradient, causing a polarity
       Class IIp has a weak but positive intercept and a negative
                                                                          class II has a weak
       changewith oflset. This class will disappearon full stack sections.
       but negativeintercept and negativegraclient,henceno   polarity change.This class may

       be observedas a negativeamplitude on a full-ofliet stack'
                                                                          of Rutherford and
         Castagnaand Swan (1997) extendeclthe classification scheme
                                                          quadrant.These are relatively rare'
       Williams to incluclea 4th class,plotting in the 2n<1
                                                                      stiff shales character-
       but occur when soft sands with gas are capped by relatively
                                                              (i'e" very compacted or silty
       ized by Vp/Vs ratios slightly higher than in the sands
204          techniques quantitative
        Gommon       for                 interpretation

               of  classes
          ' AVO classI represents
                                relativelyhardsandswith hydrocarbons.
            plot along the background trend in intercept-gradient cross-plots.Moreover,very
            hard sandscan have little sensitivityto fluids. so there may not be an associated
            flat spot. Hence.thesesandscan be hard to discoverlrom seismicdata.
          . AVo classII. representing transparent sandswith hydrocarbons,   often show up as
            dim spotsorweaknegativereflectorson    theseismic.  However. becauseof  relatively
            large gradients.they should show up as anomaliesin an Rt0)-c cross-plot.and
           plot off the backgroundtrend.
         ' AVO classIII is the "classical"AVO anomalywith negative    interceptand negative
           gradient.This class represents  relatively soft sands wirh high fluid sensitivity,
           locatedfar away from the backgroundtrend.Hence,they shouldbe easyro derect
           on seismic ata.
         ' AVO classIV aresandswith negative
                                           intercept positivegradient.
                                                   but               The reflection
           coefficientbecomeslessnegaLive with increasing
                                                        offset,and amplitudedecreases
           versusoffset.even though Lhese
                                        sandsmay be bright spots(castagnaand Swan.
           1997).Class lV anomalies relativelyrare,but occur when soft sandswith gas
           arecappedby relativelystiffcap-rockshales                             characterized vplvs ratiosslightly
           h i g h e rt h a n i n t h e s a n d s( i . e . .v e r y c o m p a c t e d r s i l t y s h a l e s ) .
         The AVo classeswere originally defined for gas sands.However.today the AVo
         class system is used for descriptiveclassification observedanomaliesthal are
         not necessarilygas sands.An AVO class Il that is drilled can turn out to be brine
         sands.It does not mean that the AVo anomaly was not a class ll anomaly.we
         therefbresuggestapplying the classification                         only as descriptive           terms for observed
         A V o a n o m a l i e s , i t h o u t a u l o m a t i c a l l yi n f e r r i n g t h a t w e a r e d e a l i n g w i t h g a s

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,
                                      includingfluid trends,
                                                           porositytrendsand lithology
        trends,as these will have different directionsin the cross-plot(Figure 4. 1l). Using
        rock physicsmodels and then calculatingthe corresponding    interceptand gradients,
        we can study various "What lf" scenarios,and then compare the modeled trends with
        the inverteddata.
          Brine-saturatedsandsinterbeddedwith shales,situatedwithin a limited depth range
        and at a particular locality, normally follow a well-defined "background trend" in AVO
        cross-plot (Castagnaand Swan, 1991). A common and recommended approach in
        qualitative AVO cross-plot analysis is to recognize the "background" trend and then
        look fbr data points that deviatefrom this trend.
205   4,3 AVOanalysis

      FigUre 4.11 Difl'erent                         gradient
                                occurring an intercept
                           trends       in                           (Adapted
                                                            cross-plot'     fiom Simm
      et al.,2O0O.)

        Castagnaet at. (1998) presentedan excellent overview and a fiamework for
      gradient and intercept interpretation.The top of the sandswill normally plot in the 4th
                                                                                       plot in
      quadrant,with positive R(0) and negativeG. The baseof the sandswill normally
      the 2nd quadrant,with negativeR(0) and positive G. The top and  baseof sands,together
      with shale-shaleintertaces,will createa nice trend or ellipse with center in the origin
       of the R(O)-G coordinate system. This trend will rotate with contrast in Vp/V5
       betweena shaly cap-rockancla sandyreservoir(Castagna al., 1998;Sams'
       We can extract the relationship between VplVs tatio     and the slope of the background
       trencl(a6) by clividing the gradient, G, by the intercept,R(0):
              G                                                                         (4.36)
       Assuming the density contrast between shale and wet sand to be zero, we can
       how changinE VplVs ratio affects the backgroundtrend. The density contrastbetween
       sandand shaleat a given depthis normally relativelysmall compared with the velocity

       contrasts(Fosteret a\.,1991). Then the backgroundslopeis given by:

              .   ^ l - ( V s*r Y s 2 ) A Y s l                                         (4..r7)
       uh-I       " L t Y nt V p : t A V p l

       where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir,
       respectively; Vs1 and V52are the correspondingS-wave velocities, whereas AVp
                                                                                      ratio is
       AV5 are the velocity differencesbetween reservoir anclcap-rock. If the Vp/V5
       2 in the cap-rock and 2 in the reservoir,the slope of the background trend is - l, that
       is a 45' slope diagonal to the gradient and intercept axes.Figure 4'12 shows
       lines correspondingto varying Vp/V5 ratio in the reservoir  and the cap-rock.
          The rotation of the line denoting the background trend will be an implicit function
       of rock physics properties such as clay content and porosity. Increasing clay
206        techniques quantitative
      Common        for                interpretation

                  VplVs=2.5 caP-rock

                                                                        -0.5 L
                                                                           -0.5                            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
      andreservoir. assume density       no              contrast.) Notice    thataVplVsratioof 1.5in thereservoir                    can
      have   diff'erent  locations theAVOcross-plot
                                     in                          depending thecap-rock
                                                                                 on                      VplV5ratio.       Ifthe Vp/V5
      ratioof thecap-rock 2.5,thesand
                                 is                   will exhibit   AVOclass to III behavior
                                                                                     ll                      (lefi),whereas the  if
      cap-rock     Vp/V5   ratiois 2.0, sand exhibit
                                          the          will          class to IIp behavior
                                                                             I                      (right).

      at a reservoirlevel will causea counter-clockwise  rotation, as the Vp/V5 ratio will
      increase. Increasing porosity related to less compaction will also cause a counter-
      clockwise rotation, as less-compactedsedimentstend to have relatively high VplVg
      ratio. However, increasingporosity relatedto less clay contentor improved sorting will
      normally cause a clockwise rotation, as clean sands tend to have lower Vp/V5 ratio
      than shaly sands.Hence, it can be a pitfall to relate porosity to AVO responsewithout
      identifying the causeof the porosity change.
         The background   trendwill change  with depth,but the way it changes be complex.
      Intrinsicattenuation, discussed Section4.3.4
                                       in             (Luh, 1993),will afI-ect background
      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
      depth trends in the elastic contrastsbetween sandsand shalesis not straightforward,
      because  theVplVs in the cap-rock as well as the reservoirwill decrease    with depth.
      These two efTects will counteracteach other in terms of rotational direction. as seenin
      Figure4. 12.Thus, the rotationwith depthmust be analyzedlocally.Also, the contrasts
      between cap-rock and reservoir will change as a function of lithology, clay content,
      sorting, and diagenesis,all geologic factors that can be unrelatedto depth. That being
      said,we shouldnot include too large a depth interval when we extractbackgroundtrends
      (Castagna and Swan, 1997).That would causeseveralslopesto be superimposed        and
      result in a less defined background trend. For instance,note that the top of a soft sand
      will plot in the 3rd quadrant,while the baseof a soft sandwill plot in the I st quadrant,
      giving a backgroundtrend rotated in the oppositedirection to the trend for hard sands.

        207     4.3 AVOanalysis

        Fluid effects and AVO anomalies
                As mentionedabove,deviationsfiom the backgroundtrend may be indicative of hydro-
                carbons,or some local lithology or diagenesiseffect with anomalouselastic properties
                (Castagnaet at., 1998).Fosteret al. (1991) mathematicallyderivedhydrocarbontrends
                that would be nearly parallel to the background trend, but would not pass through the
                origin in R(0) versus G cross-plots.For both hard and soft sandswe expect the top of
                hydrocarbon-filleclrocks to plot to the left of the background trend, with lower R(0)
                and G valuescomparedwith the brine-saturated      case.However, Castagnaet al. (1998)
                                                       sandscould exhibit a variety of AVO behaviors.
                fbund that, in particular, gas-saturated
                  As lisred in Table 4.1. AVO classIII anomalies(Rutherfordand Williams, 1989),
                representingsoft sandswith gas, will fall in the 3rd quadrant(the lower left quadrant)
                and have negativeR(0) and G. These anomaliesare the easiestto detect fiom seismic
                d a t a( s e eS e c t i o n . 3 . 1l ) .
                   Harclsandswith gas,representing       AVO classI anomalies,will plot in the 4th quadrant
                (lower right) and have positive R(0) and negative G. Consequently,these sandstend
                to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented),
                they will not show a large change in seismic responsewhen we go from brine to gas
                (cf. Chapter l). This type of AVO anomaly will not show up as an anomaly in a product
                stack. In fact, they can plot on top of the background trend of some softer, brine-
                saturatedsands.Hence, very stifTsandswith hydrocarbonscan be hard to discriminate
                with AVO analysis.
                  AVO class II anomalies,representingsandssaturatedwith hydrocarbonsthat have
                very weak zero-offset contrast compared with the cap-rock, can show great overlap
                with the backgroundtrend,especially the sandsarerelativelydeep.However,classII
                type oil sandscan occur very shallow,causingdim spotsthat stick out comparedwith
                a bright backgroundresponse    (i.e., when heterolithicsand brine-saturatedsandsare
                relatively stifT compared with overlying shales).However, because  they are dim they
                are easy to miss in near- or full-stack seismic sections,and AVO analysiscan therefore
                be a very helpful tool in areaswith classII anomalies.
                   Castagnaand Swan (199'l) discovereda diff'erenttype of AVO responsefor some
                gas sands, which they ref-erredto as class IV AVO anomalies (see Table 4. l), or a
                "false negative." They found that in some rare cases,gas sandscould have negative
                 R(0) and positive G, hence plotting in the 2nd quadrant (upper left quadrant). They
                 showedthat this may occur if the gas-sandshear-wave  velocity is lower than that of the
                 overlyingformation.The most likely geologicscenario suchan AVO anomalyis in
                 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

208          techniques quantitative
        Common        for                interpretation

        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.

           . Differentrock physicstrencls AVO cross-plots be ambiguous.
                                        in              can           The interpreta-
               tion of AVO trendsshouldbe basedon locally constrained
                                                                    rock physicsmodeling.
             n o t o n n a i v er u l e so f t h u m b .
           . Trendswithin individualclustersthat do not projectthroughthe origin on an AVO
                         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
              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
          . Residualgas saturation    can causesimilar AVO effectsro high saturations gas
            or light oil. Three-termAVO where reliableestimates density are oblained.or
            attenuation             can potentiallydiscriminateresidualgas saturations
                          attributes.                                                    from
            commercialamountsof hydrocarbons seeSections        4.3.12 and4.3. | 5 for further

Noise trends
       A cross-plotbetweenR(0) and G will also includea noisetrend,because the corre-
       lation betweenR(0) and G. BecauseR(0) and G are obtained from least-squarefitting,
       there is a negative correlation between R(0) and G. Larger intercepts are correlated
       with smallerslopesfbr a given data set. Hence,uncorrelated  random noise will show
       an oval, correlateddistribution in the cross-plotas seen in Figure 4.13 (Cambois,
          Furthermore,Cambois (2001) formulated the influenceof noise on R(0), G and
       a range-limitedstack (i.e., sub-stack)in terms of approximateequationsof standard

       dR(o) :       ;o,                                                                (4.38)
                   'JV-)            o\
       f t - - -
       "ti           ^                 )                                                (4.3e)
                     z         stn-0n,"
       o C : V f           .     r ^                                                    (4.40)
    209   4.3 AVOanalysis

                              'i;l?               ir.}
                                                         4,, r

                                                rl ,

                      -0.15    -0"1    -0.05      0           0.05   0.1   0.15
                                                I (0)
                                                   versusG (afterCambois,2000)
          Figure4,13 Randomnoisehas a ttend in rR(0)


          o,,- Ji .o,                                                                     (4.41)

          where d " is the standarddeviation of the full-stack response, is the standard
                                                                       o,               deviation
          of the sub-stack.and n is the number of sub-stacks the full fold data. As we see,the
          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.

210        techniques quantitative
      Common        for                interpretation

       Fluid        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
       almostopposite the noisedirection.which is predominantJy the vertical/gradient
                       to                                           in
       direction. In these casesthere should be a fair chanceof discriminating hydrocarbon-
       saturated  sandsfrom brine-saturated   sands,  even in relativelynoisy data.

        Simm er al. (2000) furthermore stressedthat one should create AVO cross-plots
      aroundhorizons,not from time windows. Horizon cross-plotclearly targetsthe reservoir
      of interest and helps determine the noise trend while revealing the more subtle AVO
               Moreover,only samplesof the maximum amplitudesshould be included.
      Sampling parts of the wavefbrmsother than the maxima will infill the area between
      separateclusters,and a lot of sampleswith no physical significancewould scatter
                                               However,picking only peaksand troughs
      around the origin in an R(0) G cross-plot.
      raisesa delicatequestion:what about transparentsandswith low or no impedance
                                    Theseare significantreflections
      contrastwith overlying shales'l                              with very small R(0)
      valuesthat could be missed if we invert the waveform only at absolutemaxima (in
      commercialsoftwarepackages AVO inversion, absolute
                                              the       maxima are commonly
                                Another issueis shale shaleinterfaces.
      definedfiom R(0) sections).                                    Theseare usually
      very weak reflectionsthat would be located close to the origin in an AVO cross-plot,
      but they are still important for assessment a local backgroundtrend.
        There are also other types of noise aff-ecting AVO cross-plotdata,such as residual
      moveout.It is essential try to reducethe noisetrend in the databeforeanalyzingthe
      cross-plot termsof rock physicsproperties. goodpre-processing
                 in                              A                      is
                                                                  scheme essential
      in order to achievethis (seeSection4.3.6).
        Cambois (2000) is doubtful that AVO cross-plotscan be usedquantitatively,because
      of the noise effect. With that in mind, it should still be possibleto separate
                                                                                   the real
      rock physics trends fiom the noise trends. One way to distinguishthe noise trend
      is to cross-plota limited number of samplesfrom the same horizon from a seismic
      section.The extensionof the trend along the gradient axis indicatesthe amount of
      noise in the data (Simm et al., 2000). Another way to investigatenoise versusrock
      physics trends is to plot the anomaly cluster seen in the AVO cross-plot as color-
      codedsamples                       If
                  onto the seismicsection. the clusteris mainly due to random noise,it
      should be scatteredrandomly around in a seismicsection.However,if the anomaly
      conesponds with a geologic structure and closure, it may represent hydrocarbons
      ( s e eP l a t e4 . 1 0 ) .
                                             rock physics we can estimatethe most likely
        Finally, we claim that via statistical
      fluid and lithology fiom AVO cross-plots   even in the presence some noise. This
      is ref'erredto as probabilistic AVO analysis,and was first introduced by Avseth er a/.
      (1998b).This method works by estimatingprobability distributionfunctionsof R(0)

    211    4.3 AVOanalysis

           and G that include the variability and background trends. Houck (2002) presenteda
           methodology quantifyingand cornbiningthe geologicor rock physicsuncertainties
                            relatedto noiseand measurement, obtaina full characterization
           with uncertainties                            to                             of
           the uncertainty        with an AVO-based                         Thesemethod-
                                                   lithologic interpretation.
           ologiesfbr quantification AVO uncertainties explainedin Section4.3.12.
                                   of                are

                      the   content AVO
             How assess noise
                to               in   cross-plots
             . Make cross-plots full stack versusgradient.in addition lo R(01versusC. The
               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
             . ldentify the location of AVO anomaliesin seismic sections.Color-code AVO
               anomaliesin R(0)-6 plots and then superimpose Lhemonto your seismic sec-
              tions. Do the anomaliesmake geologic senselshape.location),or do they spread
              out randomly?
             . Plot the regression
                                 coefficientof RlO)and C inversiononto the seismicto identify
               the areaswhere R(0) and G are lessreliable.
             . Cross-plota limitecl number of samplesfrom the same horizon from a seismic
               section. The extension the trend along the gradientaxis indicates amountof
                                     of                                         the
               noise in the data (Simm et a\..2000).

            attributes hydrocarbon
    4.3.11AVO        for        detection
           The information in the AVO cross-plotscan be reducedto one-dimensionalparameters
           basedon linear combinationsof AVO parameters.   This will make the AVO infbrmation
           easier to interpret. Various attributes have been suggestedin the literature, and we
           summarize the most common below (AVO inversion-based      attributesare discussedin

    Far- versus near-stack attributes
           One can createseveralAVO attributesfrom limited-range stack sections.The far stack
           minus the near stack (FN) is a "rough" estimateof an AVO gradient,and in particular it
           is fbund to be a good attribute from which to detect class II AVO anomalies(Ross and
           Kinman, 1995). For class II type prospects,the f-arstack alone can be a good attribute
           for improved delineation. However, fbr class IIp anomalies,both the near and the thr
           stack can be relatively dim, but with opposite polarities. Then the difTerencebetween
           far and near will manifest the significant negativegradient that is present.In contrast,a
           conventionalfull stack will completely zero-out a classIIp anomaly.Ross and Kinman
           (1995) suggestedthe fbllowing equation for the FN attribute depending on whether

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