commotenc hniqufeosr q uantitative
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Commonechniquesorquantitativeseismicnterpretation
Until a few decadesago, it would be
lhei rseveral -meters- longaper ect ions
I
4-
Thereareno facts,only interpretations. lriedrith Niet:sche
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4.1 Introduction
Conventional eismic nterpretationmplies picking and tracking aterallyconsistent
seismic reflectors or the purpose of mapping geologic structures,stratigraphy andreservoir rchitecture. he ultimategoal s to detect ydrocarbon ccumulations,elin-
eate heir extent,and calculate heir volumes.Conventionalseismic nterpretation s an
art that requiresskill and thorough experience n geology and geophysics.
Traditionally, seismic nterpretationhasbeenessentiallyqualitative.The geometrical
expression f seismic eflectors s thoroughly mapped n spaceand raveltime,but litfle
emphasiss pu t on the physicalunderstanding f seismicamplitudevariations. n the
last few decades, owever,seismic nterpretershave put increasingemphasison more
quantitative echniques br seismic interpretation,as thesecan validate hydrocarbon
anomaliesand give additional information during prospectevaluation and reservoir
characterization. he most mportant of these echniques nclude post-stackamplitucle
analysis bright-spot nddim-spotanalysis), ffset-dependentmplitude nalysis AVOanalysis), coustic nd elastic mpedancenversion, nd orwardseismicmodeling.
These echniques, f usedproperly, open up new doors for the seismic interpreter.
Th e seismicamplitudes, epresenting rimarily contrastsn elasticproperties etween
individual ayers,contain nformation about ithol ogy, porosity,pore-fluid ype andsat-
uration,as well aspore pressure information that cannotbe gained iom conventional
seismicnterpreta l ion.
.2 Qualitativeseismicamplitudenterpretation
common for seismic interpreterso roll out
with seismic datadown the hallway, go down
6 8
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4,2 Qualitativeeismic mplitudenterpretation
on their knees,and use their coloredpencils o interpret he horizonsof interest n
order to map geologic bodies. Little attention was paid to amplitude variations and
their interpretations.n th e early 1970s he so-called brighrspot" technique roved
successfuln areas f theGulf of Mexico, wherebrightamplitudes ould coincidewith
gas-filled sands.However, experiencewould show that this technique did not always
work. Some of the bright spots hat were interpretedas gas sands,and subsequently
drilled, werefbund
tobe volcanic intrusionsor other ithologies with high impedance
contrastcomparedwith embeddingshales.These ailures were also related o lack of
wavelet hase nalysis, shardvolcanic ntrusionswouldcause pposite olarity o ow-
impedancegas sands.Moreover, experienceshowed hat gas-filled sands sometimes
could cause dim spots,"not "bright spots," f the sandshad high impedancecompared
with surrounding hales.
With the introductionof 3D seismicdata, he uti l izationof amplitudes n seismic
interpretation became much more important. Brown (see Brown et ul., l98l) was
one of the pioneers n 3D seismic nterpretation f l ithofacies iom amplitudes. he
generationoftime slicesand horizon slices evealed3D geologic patterns hat had been
impossible o discover rom geometric nterpretationof the wiggle traces n 2D stack
sections.Today, the further advance n seismic technology hasprovided
us with 3Dvisualization oolswhere he nterpr eter anstep nto a virtual-realityworld of seismic
wiggles and amplitudes,and trace hesespatially (3D) and temporally (4D) in a way
that one could only dreamof a few decades go.Certainly, he eap iom the rolled-out
papersectionsdown the hallways to the virtual-reality images n visualization"caves"
is a giant eap with greatbusinessmplications or the oil industry . n this sectionwe
review hequalitativeaspects f seismicamplitude nterpretation, eforewe dig into the
morequantitative nd ock-physics-basedechniques uc hasAVO analysis,mpedance
inversion, nd seismicmodeling, n fbllowing sections.
4.2.1 Wavelethase ndpolarity
The very first issue to resolve when interpreting seismic amplitudes s what kind of
wavelct we have.Essentialquestions o ask are the fbllowing. What is the defined
polarity n our case?Are we dealingwith a zero-phase r a minimum-phasewavelet?
Is there a phaseshift in the data?These are not straightfbrward questions o answet,
because he phaseof the wavelet can change both laterally and vertically. However,
there are a f'ewpitfalls to be avoided.
First, we want to make surewhat the defined standard s when processing he data.
There exist two standards. he American standarddefinesa black peak as a "hard" or
"posit ive"event,and a white troughas a "soft" or a "negative"event.On a near-ofl.set
stack sectiona "hard" event will correspond o an increase n acoustic mpedancewith
depth, whereasa "soft" event will correspond o a decreasen acoustic mpedancewithdepth. According to the European standard,a black peak is a "soft" event, whereasa
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170 GommonechniquesorquantitativeeismicnterpretationT
white trough s a "hard" event.One way to checkthe polarity of marine data s to lookat the sea-floor eflector.This reflectorshouldbe a strongpositivereflector epresentingthe boundarybetweenwater and sediment.
Data olarity
' Americanpolarity:An increasen impedance ivespositiveamplitude.normally
displayed s blackpeak wiggle r.race) r red ntensity color displayt.. European or Australian) olarity:An increasen impedance ivesnegal.ivempli-
tude, normally displayedas white rrough (wiggle trace)or blue intensity color
display .
(Adapted ro m Brown. 200la, 2001 )
For optimal quantitativeseismic nterpretations,we should ensure hat our data arezero-phase. hen, the seismicpick shouldbe on the crestof the waveform conespond-ing with the peak amplitudes hat we desire or quanrirativeuse (Brown, l99g). withtoday's advancedseismic interpretation ools involving the use of interactivework-stations, here exist various techniques br horizon picking that allow efficient inter-pretationof largeamountsof seismicdata.These echniquesncludemanualpicking,interpolation, utotracking, oxel tracking,and surfaceslicing (seeDorn (199g) fb rdetaileddescriptions).
For extraction of seismic horizon slices,autopicked or voxel-trackedhorizons arevery common. The obvious advantageof autotracking is the speedand efficiency.Furthermore, autopicking ensures hat the peak amplitude is picked along a horizon.However,one pitfall is th e assumption ha t seismichorizonsare ocally continuousand consistent.A lateral change n polarity within an event will not be recognizedduring autotracking.Also, in areasof poor signal-to-noise atio or wherea singleeventsplits into a doublet, the autopicking may fail to track the corect horizon. Not onlywill important reservoirparameters e neglected, ut the geometriesand volumesmayalso be significantly off if we do not regard ateral phaseshifts. It is important that theinterpreter ealizes hi s and eviews he seismic icks or qualitycontrol.
Sand/shaleross-oversithdepth
Simplerock physicsmodelingca n assist he nit ial phaseof qualitative eismic nrer-pretation, when we are uncertainaboutwhat polarity to expect or diff'erent ithologyboundaries.n a sil iciclastic nvironment, os tseismic eflectors il l beassociated it hsand-shaleboundaries.Hence, he polarity will be related o the contrast n impedancebetweensandand shale.This contrastwill vary with depth (Chapter2). Usually, rela-tively sott sandsare fbund at relatively
shallow depthswhere the sandsare unconsol-idated.At greaterdepths, he sandsbecome consolidatedand cemented.whereas he
4.2.2
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rmpe0ance
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t
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4.2 Qualitativeeismic mplitudenterpretati0n
Sand ersushalempedanceepthrendsand eismicolarityschematic)
Sand-shaleross-over
DeDth
Figure '1 Schematicepthrends f sand ndshalempeclances.hedepthrends anvary iombasino basin, nd here anbemore han ne ross-over.ocaldepthrends hould eestablished
fordifferent asins.
shalesare mainly affectedby mechanicalcompaction.Hence,cemented andstones renormally found to be relatively hard eventson the seismic.Therewill be a correspond-ing cross-overn acoustic mpedanceof sandsandshalesaswe go fiom shallowand softsands o the deepand hard sandstonesseeFigure 4.1). However, he depth trendscanbe much more complex hanshown n Figure 4.1 (Chapter2, seeFigures 2.34 and,2.35').
Shallow sandscan be relatively hardcomparedwith surroundingshales,whereasdeepcementedsandstones an be relatively soft comparedwith surounding shales.Thereis no rule of thumb fbr what polarity to expect br sandsand shales.However,usingrock physicsmodeling constrainedby local geologicknowledge,one can improve
theunderstanding f expectedpolarity of seismic eflectors.
"Hard" eniussoft"events
During seismic nterpretation f a prospect r aproven eser"yoirand. he followingquestionshould be one of the first to be asked:what type of eventdo we expect,
a "hard" or a "soft"? [n otherwords.shouldwe pick a positivepeak,or a negative
trough? fw e havegoodwell control, his ssue anbe solvedby generating ynthetic
seismogramsndcorrelating hesewith realseismic ata. f we haveno well control,we may have to guess.However. a reasonableguesscan be made basedon rockphysicsmodeling.Below we have isted some "rules of thumb" on what type of
reflector we expect -ordifferent geologic scenarios.
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172 CommonechniquesorquantitativeeismicnterpretationT
Typicalhard" vents
. Very shallowsands t normal pressure mbeddedn pelagicshales
. Cemented andstone it h brinesaluration
. Carbonate ocksembeddedn sil iciclastics' Mixecl i thologiesheterol i th ics)ike shaty ands,mar ls. o lcanic shdeposi ts
Typicalsoft"events
. Pelagichale' S.hallow, nconsolidatedands an ypore luid) embeddedn normallycompacted
shales
' Hydrocarbon ccumularionsn clean.unconsolidatedr poorlyconsolidated ancls. Overpressuredones
Some itfallsnconventionalnterpretation
' Make sureyo u know th e polarityof the data.Remember hereare wo different
standards,he US standard nd he European tandard. hich ar eopposire.' A hard eventcan change o a soft laterally i.e.. ateralphaseshifi; if therear e
l: j loloCic.petrographic r pore-fluid hanges. eismicaurotracking il l no rderecrthese.
' A d im seismic ef lector r in tervalmay be signi f icant . specia l lyn the zoneofsand/shalempedance ross-over. VO analysisshouldbe underrakeno revealpotentialhydrocarbon ccumulations.
4.2.3 Frequencyndscale ffects
Seismic resolution
Vertical eismic esolutionsdefined s heminimum separation etweenwo nterfacessuch that we can identify two interfaces ather han one (SherifT
and Geldhart, 199-5).A stratigraphicayercan be resolved n seismic ata f the ayer hicknesss arger hana quarterof a wavelength.The wavelength s given by:
\ - t / / f ( 4 . 1 )
where v is the interval velocity of the layer, and.l is the frequency of the seis-mic wave. lf the wavelet has a peak frequency of 30 Hz, and the layer velocity is3000 m/s, then the dominantwavelength s 100m. In this case,a layer of 25 m canbe resolved.Below this thickness,we ca n stil l gain important nfbrmationvia quan-titativeanalysisof the interference mplitude.A be d only ),/30 in thicknessma y bedetectable, lthough ts thickness annotbedetermined iom thewaveshape Sheriff and
Geldhart.199-5).
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173 4.2 Qualitativeeismic mplitudenterpretationE
Layeriickness
Figure,2 Seismicmplitudesa unction f ayerhicknessbragiven avelength.
The horizontal resolution of unmigratedseismicdatacan be definedby the Fresnel
zone. Approximately, the Fresnelzone is defined by a circle of radius, R, around a
rel lect ion oint :
n - Jgz G.2)
where z is the reflector clepth.Roughly, the Fresnel zone is the zone from which al lreflectedcontributions have a phasedifl-erence f less than z radians.For a depth of
3 km and velocity of 3 km/s, the Fresnelzone adiuswill be 300-470 m for fiequencies
ranging fiom 50 to 20 Hz. When the size of the reflector is somewhat smaller than
th e Fresnelzone, he response s essentially hat of a diffraction point. Using pre-
stackmigration we can collapse he difliactions to be smaller than the Fresnel zone,
thus ncreasinghe ateralseismic esolution Sheriffan dGeldhart,1995).Depending
on the migration aperture, he lateral resolution after migration is of the order of a
wavelength.However, he migrationonly collapses he Fresnelzone n the direction
of the migration, so if it is only performed along inlines of a 3D survey, he lateral
resolutionwill sti l l be limiteclby the Fresnelzone in the cross-linedirection.Th e
lateral resolution is also restrictedby the lateral sampling which is governed by thespacingbetween ndividual CD P gathers,usually 12.5or 18 meters n 3D seismic
clata.For typical surf'ace eismicwavelengths -50-100 m), lateralsampling s not the
l im i t i ng ac t o r .
Interference and tuning effects
A thin-layered reservoircan causewhat is called event tuning, which is interf'erence
between he seismicpulse epresentinghe top of the reservoirand he seismicpulse
representing he baseof the reservoir.This happens f the ayer thickness s less han a
quarterof a wavelength Widess,1973).Figure4.2 shows he efTective eismicampli-
tude as a function of layer thickness for a given wavelength, where a given layer
has higher impedance han the surroundingsediments.We observe hat the amplitude
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174 Gommonechniquesorquantitativeeismicnterpretation-
increasesand becomes arger than the real reflectivity when the layer thickness sbetween a half and a quarter of a wavelength. This is when we have constructive
interferencebetween the top and the baseof the layer. The rlaximum constructiveinterferenceoccurswhen the bed thickness s equal to ),14, and this is often referredto as the tuning thickness.Furthermore,we observe hat the amplitucledecreases ndapproaches ero for layer thicknessesbetweenone-quarterof a wavelengthand zerothickness.We refer to this as destructive nterferencebetween the top and the base.
Trough-to-peakim e measurementsiv e approximately he correctgross hicknessesfor thicknessesarger hana quarterof a wavelength,but no information fbr thicknessesless ha na quarterof a wavelength. he thickness f an ndiv idual hin-bedunit can beextracted rom amplitude measurementsf the unit is thinner than about ),/4 (Sheriff
an d Geldhart,1995).When the ayer hickness quals ./8, Widess 1973) ound thatthe composite esponseapproximated he derivativeof the original signal.He referredto this thicknessas the theoretical threshold of resolution. The amplitude-thickness
curve s almost inearbelow ),/8 with decreasing mplitudeas he ayergets hinner,bu t the composite esponse tays he same.
4.2.4 Amplitudend eflectivitytrength
"Bright spots" and "dim spots"
The first use of amplitude information as hydrocarbon indicators was in the early1970swhen it wa s fbund that bright-spotamplitudeanomalies ould be associatedwith hydrocarbon traps (Hammond, 1974). This discovery increased nterest in thephysical propertiesof rocks and how amplitudeschangedwith difTerent ypesof rocksand pore fluids (Gardner et al., 1914'). n a relatively soft sand, he presenceof gasand/or ight oil wil l increase he compressibil ity f the rock dramatically, he veloc-it y will drop accordingly, nd he amplitudewill decreaseo a negative bright spot."However, f the sand s relatively hard (comparedwith cap-rock),the sand saturatedwith brine may inducea "brighlspot" anomaly,while a gas-fi l led an dmay be trans-
parent,causinga so-calleddim spot, hat is, a very weak reflector. t is very importantbeforestarting o interpretseismicdata o find out what change n amplitude we expectfor different pore fluids, and whether hydrocarbonswill causea relative dimrning orbrightening omparedwith brinesaturation. rown (1999)statesha t"themost mpnr-tant seismic property of a reservoir is whether it is bright spot regime or tlim sltotregime."
One obvious problem in the dentificationof dim spots s that they areclim- they arehard o see.This issue an be dealtwith by investigatingimited-range tacksections.A very weak near-offset eflectormay havea corresponding trong 'ar-oflset eflector.However,some sands,although he y are signif icant,producea weak posit ivenear-offset reflection as well as a weak negative ar-offset reflection. Only a quantitative
analysis f thechange n near- o far-offset mplitude, gradientanalysis,wil l be able
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4.2 Qualitativeeismic mplitudenterpretation
to reveal the sand with any considerabledegree of confidence.This is explained n
Section4.3.
Pitfalls:False bright spots"
During seismic xploration f hydrocarbons.brighrspots"ar eusually he irst ype
of DHI (direct hydrocarbon ndicators)one looks for. However. herehave been
several aseswherebright-spotanomalies av ebeendril led. and turnedou t not lobe hydrocarbons.
Somecommon"falsebright spors" nclude:
. Volcanic ntrusions nd volcanicas h ayers
. Highly cemented ands. ften calcitecement n thin pinch-outzones
. Low-porosityheterolithic ands
. Overpressuredands r shales
. Coal beds
. Top of saltdiapirs
Only th e ast hreeon th e ist abovewill cause he samepolarityas a ga ssand.Th e
first hreewill cause o-called hard-kick" amplitudes. herefore. f oneknows he
polariryof thedataoneshouldbe able o discriminare ydrocarbon-associatedrightspots rom the "hard-kick" anomalies. VO analysis houldpermit discrimination
of hydrocarbonsrom coal,saltor overpressuredands/shales.
A very common seismicamplitudeattributeusedamongseismic nterpreterss
rellection ntensity,which is root-mean-squaremplitudes alculated ver a given
lime window. This anributedoes not distinguishbetweennegativean d positive
amplitudes; hereforegeologic nterpretation l this attribute houldbe madewith
greatcaution.
"Flat spots"
Flat spotsoccur at the reflectiveboundarybetweendifferent fluids, eithergas-oil, gas-
warer,or warer-oil contacts.Thesecanbe easy o detect n areaswhere the background
stratigraphy s tilted, so the flat spotwill stick out. However, f the stratigraphy s more
or less flat, the fluid-related flat spot can be difficult to discover.Then, quantitative
methods ike AVO analysiscanhelp to discriminate he fluid-related lat spot from the
flarlying lithostratigraphy.
One should be awareof severalpitfalls when using flat spots as hydrocarbon ndi-
cators.Flat spots can be related to diageneticevents hat are depth-dependent. he
boundary betweenopal-A and opal-CT represents n impedance ncrease n 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 s tilted.
Other"false" flat spots ncludevolcanicsil ls,paleo-contacts,heet-flood epositsnd
flat bases f lobesan dchannels.
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176 Commonechniquesorquantitativeeismicnterpretation-
Pitfalls:alseflatspots"
One of fhe bestDHIs ro look for is a f lat spot, he contactbetweenga sand water,
ga san d oil, or oil an d water.However. hereare other causes hat can give rise o
flat spots:
. Oceanbottom multiples
. Flat stratigraphy. he bases f sand obesespecially end o be flat.
. Opal-A to opal-CT diagenetic oundary
. Paleo-contacts,ither elated o diagenesis r residualhydrocarbon aturation
. Volcanicsil ls
Rigorous lat-spotanalysis hould ncludedetailed ock physicsanalysis. nd for-
ward seismicmodeling,as well as AVO analysis f realdata se eSection4.3.8).
Lithology, porosity and fluid ambiguities
The ult imategoal n seismic xploration s to discover nddelineate ydrocarboneser-
voirs.Seismic amplitude maps rom 3D seismicdata are oftenqualitarlvel.f nterpreted
in termsof lithologyand luids.However, igorous ockphysicsmodelingand analysis
of available well-log data is required to discriminate fluid effects quantitatively trom
lithology effects(Chapters and 2).
Th e "bright-spot"analysismethod has ofien been unsuccessful ecause ithology
effects ather han fluid eff-ects etup the bright spot.The consequences the drilling of
dry holes. n order o reveal pitfall" amplitudeanomalies t is essential o investigatehe
rock physicsproperties iom well-l og data.However, n new frontier areaswell-1ogdata
are sparse r lacking.This requires ock physicsmodelingconstrained y reasonable
geologic assumptions nd/or knowledgeabout local compactionalan d depositional
trends.
A common wa y to extractporosity rom seismicdata s to do acoustic mpedance
inversion. ncreasing orositycan mply reducedacoustic mpedance, nd by extract-
in g empiricalporosity-impedancerends rom well-logdata,on ecanestimate orosity
from the inverted mpedance.However, his methodology suffers rom severalambi-
guities.Firstly, a clay-rich shalecan havevery high porosities,even f the permeability
is close o zero.Hence,a high-porosity one dentif iedby this echniquemay be shale.
Moreover, the porosity may be constant while fluid saturationvaries,and one sin-rple
impedance-porosity odel may not be adequatebr seismicporositymapping.
In addition to lithology-fluid ambiguities, ithology-porosity ambiguities,an d
porosity-fluid ambiguities,we may have ithology-lithology ambiguitiesand fluid-
fluid ambiguities.Sandand shalecan have he sameacoustic mpedance, ausingno
reflectivity on a near -offset seismic section. This has been reported n severalareas
of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that
fluvial channelsor turbidite channelsare dim on seismic amplitude maps,and the
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:fff!;"{riii;iiiffr,))) ) t )l)))))))))ft) )) D,D)), ) D,D) D r,Dr>),
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iriiiiiiiiiii)ii)i)l r l l l l i i l r l l l l l i
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pore luids,but the relationvariesacross he magebecause fthe interplayofsedimentologicanddiagenetic
influences. lue indi cates ow amplitudes, ellow and ed high amplitudes.
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177r
4.2 Qualitativeeismic mplitudenterpretation
interpretation s usually that the channel is shale-filled. However, a clean sand fill-
ing in the channel can be transparentas well. A geological assessment f geometries
indicating differential compaction above he channelmay reveal he presence f sand.
More advancedgeophysical echniquessuch as offset-dependenteflectivity analysis
may alsoreveal he sands.During conventional nterpretation,one should nterpret op
reservoirhorizons from limited-rangestack sections,avoiding the pitfall of missing a
dim sandon a near-or full-stackseismic ection.
Facies interpretation
Lithology influence on amplitudes can often be recognized by the pattern of ampli-
tudes as observedon horizon slices and by understandinghow different lithologies
occurwithin a depositional ystem.By relating ithologies o depositional ystemswe
often refer to theseas ithofaciesor f-acies. he link betweenamplitude characteristics
and depositionalpatternsmakes t easier o distinguish ithofacies variationsand fluid
changesn amplitudemaps.
Traditional seismic acies nterpretationhasbeenpredominantlyqualitative,basedon
seismic raveltimes. he tradit ionalmethodology onsisted f purely visual nspection
of geometric atternsn the seismic eflectionse.g.,Mitchum et al., 1977;Weimeran d
Link, l99l ). Brown et al. (1981),by recognizing uried iver channelsrom amplitudeinformation, were amongst the first to interpret depositional acies from 3D seismic
amplitudes.More recentan d increasingly uantitativework includes h at of Ryseth
et al. (.1998)who used acoustic mpedance nversions o guide the interpretation of
sand channels, and Zeng et al. (1996) who used forward modeling to improve the
understanding f shallow marine facies rom seismicamplitudes.Neri (1997) used
neuralnetworks o map acies rom seismicpulseshape.Reliablequantitative ithofacies
prediction iom seismicamplitudesdepends n establishing ink between ock physics
propertiesand sedimentary acies. Sections2.4 and2.5 demonstrated ow such inks
might be established.The casestudies n Chapter 5 show how these inks allow us to
predict litholacies from seismic amplitudes.
Stratigraphic interpretation
The subsurface s by nature a layered medium, where different lithologies or f'acies
have been superimposedduring geologic deposition.Seismic stratigraphic nterpreta-
tion seeks o mapgeologicstratigraphy rom geometricexpression f seismic eflections
in traveltime and space.Stratigraphicboundariescan be defined by dilferent litholo-
gies (taciesboundaries) r b y time (time boundaries). heseoften coincide,but not
always. Examples where facies boundariesand time boundariesdo not coincide are
erosionalsurfacescutting across ithostratigraphy,or the prograding fiont of a delta
almost perpendicular o the lithologic surf'aces ithin the delta.
There are several ittalls when nterpretingstratigraphy iom traveltime nfbrmation.
First, the interpretation s basedon layer boundariesor interf'aces,hat is, the contrasts
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Gommonechniquesor quantitativeeismicnterpretation
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
occurwithout a lithology change e.g.,Hardage,1985).Fo r instance, hiatuswith no
depositionwithin a shale ntervalcangivea strongseismic ignature ecausehe shales
above and below the hiatus have difTerentcharacteristics.Similarily, amalgamated
sandscan yield internal stratigraphywithinsandy ntervals, eflectingdifferent texture
of sanclsiom difl-erent epositionalevents.Third, seismic esolutioncan be a pitfall in
seismic nterpretation, speciallywhen interpreting tratigraphic nlapsor downlaps.
Theseareessential haracteristicsn seismic nterpretation, s heycangive nformation
about the coastaldevelopment elated to relative sea evel changes e.g., Vail er ai.,
I 977). However,pseudo-onlaps an occur if the thicknessof individual layersreduces
beneath he seismic esolution. he layer can stil l exist,even f th e seismicexpression
yields an onlap.
Pittalls
Therear eseveral itfalls n conventional eismic tratigraphicnterpretationha tcanbe avoided f we usecomplementary uantitative echniques:
. lmportant ithostratigraphic oundaries etween ayerswith very weak contrasts
in seismicpropefiies an easily be missed.However. f different ithologiesar e
transparentn post-stack eismic ata. heyar enormallyvisible n pre-stack eismic
dara.AVO analysis s a useful tool to revealsandswith impedances imilar to
capping hales seeSect ion .31.
. It is commonlybelievedhatseismic vents re imeboundaries. ndnot necessarily
lithostratigraphic oundaries. or instance. hiatuswithin a shalemay causea
strongseismic eflection f the shaleabove he hiatus s lesscompacted ha n th e
onc below.even f the ithology s the same.Rock physicsdiagnostics f well-log
datamay revealnonlithologic eismicevents se eChapter2).. Because f limited seismic esolution, alseseismiconlapsca n occur.The layer
may sti l l existbeneathesolution. mpedancenversion an mprove he resolution.
an d revealsubtlesrrailgraphiceatures ot observed n the original seismicdata
(seeSect ion .4) .
Quantitative interpretation of amplituclescan add information about stratigraphic
patterns,and help us avoid someof the pitfalls mentionedabove.First, relating ithol-
ogy to seismicproperties Chapter2) can help us understand he nature of reflections,
and improve the geologic understanding f the seismicstratigraphy.Gutierrez (2001)
showedhow stratigraphy-guided ock physics analysisof well-log dataimproved the
sequence tratigraphic nterpretationof a fluvial system n Colombia using mpedance
inversionof 3D seismicdata.Conducting mpedance nversionof the seismicdatawill
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179-
4,2 Qualitativeeismic mplitudenterpretation
give us layer properties rom interfhceproperties,and an impedancecross-section an
reveal stratigraphic eaturesnot observedon the original seismic section. mpedance
inversion has the potential to guide the stratigraphic nterpretation,because t is less
oscil latory han he original seismicdata, t is more readilycorrelatedo well-log data,
and it tends o averageout random noise, hereby mproving the detectability of later-
ally weak eflectionsGlucket a\.,1997).Moreover, requency-band-limitedmpedance
inversioncan mprove on the stratigraphic esolution,and he seismic nterpretation an
be signilicantly modified f the nversion esultsare ncluded n the nterpretationproce-
dure.For brief explanationsof different ypesof impedance nversions, eeSection4.4.
Forwardseismicmodeling s also an excellent ool to study he seismicsignatures f
geologicstratigraphyseeSection4.5).
Layer thickness and net-to-gross from seismic amplitude
As mentioned in the previous section, we can extract layer thickness rom seismic
amplitudes.As depicted n Figure4.2,the relationships only linear or thin layers n
pinch-outzonesor in sheet-likedeposits, o one shouldavoid correlating ayer hickness
to se ismic amplitudes n areaswherethe top and baseof sandsareresolvedas separate
reflectors n the seismic data.Meckel and Nath (.1911) ound that, for sandsembedded n shale, he amplitude
would dependon the net sandpresent,given that the thicknessof the entire sequence
is less than ).14. Brown (1996) extended his principle to include beds thicker than
the tuning thickness, ssuming hat individual sand ayersare below tuning and that
the entire interval of interbeddedsandshas a uniform layering.Brown introduced he
"composite amplitude" defi ned as the absolutevalue summation of the top reflection
amplitude and the base eflection amplitude of a reservoir nterval. The summation of
the absolutevalues of the top and the baseemphasizes he eff'ectof the reservoir and
reduces he effect of the embeddingmaterial.
Zeng et al. (.1996) tudied he nfluence f reservoir hickness n seismic ignalan d
introduced what they referred to as effective eflection strength, applicable to layersthinner han he tunins thickness:
o . - 2 " - Z ' n . , Zrr
(4.3)
whereZ. is the sandstonempedance, 16 s the average hale mpedance nd z s the
layer hickness. morecommonway o extract ayer hicknessrom seismic mplitudes
is by linear regressionof relative amplitude versus net sand hicknessas observedat
wells that are available.A recentcasestudy showing he application o seismic eservoir
mappingwas providedby Hill and Halvatis 2001).
Vernik et al. (2002) demonstratedhow to estimate net-to-gross iom P- and S-
impedances fbr a turb idite system. From acoustic impedance(AI)
versus shearimpedance (SI) cross-plots, he net-to-gross can be calculated with the fbllowing
fbrmulas:
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180 CommonechniquesorquantitativeeismicnterpretationE
Vrung Z
N I G :A Z
where V."n,l s the oil-sand fraction given bv;
KanoS I - b A I - c e
a t - a o
where b is the average lopeof the
andz7t i re he espect iventercepts
(4.-5)
shale lope 06 )an doil-sandslope b1),whereas e
in theAI-SI cross-plor .
IZrr.
(44)
calculat ionof reservoi rh icknessrom seismic mpl i tude houldbe doneonly inareaswhere sandsar e expected o be thinner ha n the tuning thickness. hat is aquarter f a wavelength. ndwherewell-logdatashowevidence f goodcorrelationbelweenne t sand hickness nd relativeamplirude.
It can be diff icult o discriminateayer hickness hanges rom lirhologyand luidchanges.n relatively of t sands, he mpactof increasing orosityand hydrocarbonsaturationends o increasehe seismicamplitude, nd hereforeworks in the same"direction" o Iayer hickness.However. n relatively ar dsands.ncreasing orosityand hydrocarbon aturation en d o decreasehe relaliveamplitudeand thereforework in th e opposite direction" o layer hickness.
ilouo anatysis
In 1984, 12 years afler the bright-spot technology became a commercial tool fbrhydrocarbon prediction, ostrander published a break-through paper in Geophl-sics
(ostrander,1984).He showed ha t the presence f ga s n a sandcappedby a shalewould causean amplitudevariation with ofTsetn pre-stackseismicdata.He also oundthat hischangewas elated o the educed oisson'satiocaused y thepresence fgas.Then, he yearafter,Shuey 1985)confirmedmathematically ia approximations f th eZoeppritzequations ha tPoisson's atio wa s he elasticconstantmost directly relatedto the off.set-dependenteflectivity fbr incident anglesup to 30". AVo technology, acommercial tool for the oil industry,was born.
The AVO techniquebecamevery popular n the oil industry,as onecould physicalyexplain he seismicamplitudesn termsof rock properties. ow , bright-spot nomaliescould be nvestigated eforestack, o see f theyalsoha dAVo anomalies Figure4.3).The techniqueprovedsuccessful n certainareasof the world, but in many cases t was
not successful.The technique sufI'ered rom ambiguities causedby lithology efTects,
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181 4.3 AVO nalysisI
StacksectionCDP
locqtion
. *{buTarget harizon
Geologc interpretation
Shale
Sondstone
with gosAryle ol inc,d?nca
Figure .3 Schematicllustrationf heprinciplesn AVOanalysis.
tuning effects, and overburdeneft'ects.Even processingand acquis ition effects could
cause alseAVO anomalies. ut in many o1'the ailures, t wa sno t the technique tself
that ailed,but the useof the echnique hat was ncorrect. ack of shear-wave elocity
information nd heuseof too simplegeologicmodelswerecommon easonsbr failure.
Processing echniques hat aff'ectednear-ofTset races n CDP gathers n a difl-erent
way from far-offset traces could also create alse AVO anomalies.Nevertheless, n
thelast
decadewe have observeda revival of the AVO technique.This is due to theimprovement f 3D seismic echnology, etterpre-processingoutines, nore requent
shear-wave ogging and mproved understanding f rock physicsproperties, argerdata
capacity,more fbcus on cross-discip linaryaspects f AVO, and ast but not least,mclre
awareness mong he usersof the potential pitfalls. The techniqueprovides he seismic
interpreter with more data, but a lso new physical dimensions hat add infbrmation to
the conventional nte rpretationof seismic acies,stratigraphyand geomorphology.
In this sec tion 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 theoretica l details of wave theory, we
addressssues elated o acquisit ion. rocessing nd nterpretation f AV O data.Fo r
an excellent overview of the history of AVO and the theory behind this technology,we refer the reader o Castagna 1993). We expect the luture application of AVO to
CDPgatheraf interest CDPgather
Time
AVOresponseattargethorizon
0,1
-0
-0 ,
-0
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182 Commonechniquesorquantitativeeismicnterpretation-
expandon today'scommon AVO cross -plotanalysisandhencewe includeoverviewsof
important contributions rom the literature, nclude tuning, attenuationand anisotropy
effectson AVO. Finally, we elaborate n probabilisticAVO analysisconstrained y rock
physicsmodels.These omprise he methodologies pplied n case tudies , 3 an d4 in
Chapter5.
4.3.1 The eflectionoefficient
Analysis of AVO, or amplitude variation with ofTset, eeks o extrac t 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
reflectionangleat a single nterface sdescribedby the complicatedZoeppritz equations
(Zoeppritz, 9l9). For analysisof P-wave eflections, well-known approximation s
givenby Aki and Richards 1980), ssumingweak ayer contrasts:
R ( 0 , ); ( r
, , A p I A Y p , A V s- -17,-vi )T
+2*r4 W
+p' l tK
(4.6)
(4.1)
where:
sin01I t - -
Y P I
L p : p z - p r
L V p : V p z - V p t
A V s - V s : - V s r
e ( 0 r u ) 1 2 = e t
Pr)2+ vPt)12
+ vst)12
P : ( . P z I
Vp : (.Vpz
V5 (V52
In the fbrmulasabove, is th e ray parameter, 1 s the angleof incidence, nd 02 is
the transmissionangle; Vp1and Vp2are he P-wave velocities aboveand below a given
interface, espectively. imilarly, V51and V5r are he S-wavevelocit ies,while py an d
p2 aredensitiesabove and below this interface Figure 4.4).
The approximationgiven by Aki and Richardscan be further approximated Shuey,
r985) :
R(01 :, R(o) + G sin29+ F(tan2e sin2o;
where
R(o) : ; (T .T)
G::^+-'#(+.'+):R(o)+(:.'#)#+
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183 4.3 AVO nalvsisn
Medium(Vp1, 51 , 1)
Medium(Vn, Vsz, i
PS{t)
Figure4'4 Reflections nd ransmissions t a single nterface etween wo elastichalf-spacer-rediafirr an ncidentplaneP-wave.PP(i).Therewill be botha reflected -wave,pp(r). anda transmitteclP-wave,PP(t).Note hat herearewavemocle onversions t thereflectionpointoccurrrng rnonzero ncidence ngles. n addition o the P-waves, reflectedS-wave, S(r),and a transrnittedS-wave,PS(t),will be prodr.rced.
and
_ t a y P
1 r // v D
This form can be interpreted n terms of difierent angular ranges!where R(0) is thenormal-incidenceeflection oefficient,G describeshe variation t ntermecliateffsetsand is often referred o as the AVO gradient,whereasF dominates he far ofTsets. earcrit ical angle.Normally, the rangeof anglesavailable or AVO analysis s less ha n30-40.. Therefbre,we only need o consider he two first terms,valid fb r ansles es st han . l 0 t Shuey .985 , 1 :
R ( P ) = R ( 0 ) + G s i n 2 d (4.8)
The zero-oft'set eflectivity,R(0), is controlledby the contrast n acoustic mpedanceacrossan interface.The gradient,
G, is more complex in terms of rock properties,butfiom the expressiongiven abovewe see hat not only the contrasts n Vp and densityafrect the gradient, but also vs. The importance of the vplvs ratio (or equivalentlythe Poisson's atio) on the ofTset-dependenteflectivity was first indicatedby Koefoed(1955).ostrander (1984) showed ha t a gas-fi l led brmation would havea very lo wPoisson's atio comparedwith the Poisson's atios n th e surrounding ongaseousbr -mations.This would causea signif icant ncrease n posit iveamplitudeversusangleat th e bottomof th e ga s ayer,and a signif icant ncreasen negative mplitudeversusangle at the top of the gas ayer.
Theeffect f anisotropy
Velocity anisotropyoughtto be taken nto accountwhen analyzing he amplitudevaria-tionwith offset AVO) response f ga ssands ncasedn shales. lthough t is generally
PP(r)
4.3.2
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18 4-
Commonechniquesor quantitativeeismicnterpretation
thought that the anisotropy s weak (10-20%) in most geological settings Thomsen,
1986), some eff'ectsof anisotropy on AVO have been shown to be dramatic using
shale/sand odels Wright, 1987). n somecases,he sign of the AVO slopeor rateof
changeof amplitudewith ofliet canbe reversed ecause f anisotropy n the overlying
shalesKim et a l . ,1993 Blangy,1994).
The elasticstiffness ensorC in transverselysotropic TI ) media can be expressed
in compact orm as bllows:
C -
C l
(c11 2C66)
C r :
0
0
0
I
(C t - 2Coo)
C t r
C r :
0
0
0
- Cn)
Cr : 0
C n 0
C:: 0
0 C++
0 0
0 0
0 0
0 0
0 0
0 0
C++ 0
0 Cr,o
whereC6,6,t(Crt
(4e)
and where he 3-axis z-axis) ies along he axisof symmetry.The above x 6 matrix s symmetric, ndhas ive ndependentomponents, r r, Crr,
Cr, C++, nd C66.For weak anisotropy, homsen 1986)expressedhreeanisotropic
parameters, , y and6, as a function of the five el astic components,where
C l - C ra , - -
2Cr
Cor, C++
2C++
( C r : * C + + ) 2 - ( . C y - C a l z
2C.3(Cy C++)
The constants can be seen o describe he fiactional differenceofthe P-wavevelocities
in the verticaland horizontaldirections:
yP(90') vp(0')(4 . 3 )
Vp(o')
and thereforebest describeswhat is usually referred o as "P-wave anisotropy."
In the samemanner, he constanty can be seen o describe he fiactional difference
of SH-wavevelocit iesbetween erticalan d horizontaldirections,which is equivalent
to the differencebetween he vertical and horizontal polarizationsof the horizontallypropagating -waves:
(4 .10)
(4. )
(4.12)
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18 5r
4.3 AVO nalysis
V s H ( 9 0 1 - V s v ( 9 0 )7sH(90") Vss(0') (4 .14)T -
Vsv(90') Vsn(0')
Th e physicalmeaningof 6 is not as clearas s and y, but 6 is the most important
parameter br normal moveout velocity and reflection amplitude'
Under the plane wave assumption,Daley and Hron (1911) derivedtheoretical br-
mulas for reflection and transmissioncoefficients n Tl media.The P-P reflectivity in
the equationcan be decomposed nto isotropic and anisotropic erms as ollows:
Rpp(0) Rrpp(O) R'rpp(0) (4 .1s )
Assuming weak anisotropyanclsmalloffsets,Banik ( 1987)showed hat the anisotropic
term ca n be simply expressed s bllows:
s in2eR e p p ( d ) - Ad
Blangy (lgg4) showed he effect of a transverselysotropic shaleoverlyingan sotropic
gas sand on offset-dependent eflectivity, for the three different types of gas sands.
He found that hard gas sandsoverlain by a soft TI shaleexhibited a larger decrease
in positive amplitude with offset than if the shalehad been sotropic. Similarly, soft
gas san4soverlain by a relatively hard TI shaleexhibited a larger ncrease n negative
amplitude with offset than if the shalehad been sotropic. Furthermore, t is possible
fbr a soft isotropic water sand to exhibit an "unexpectedly" Iarge AVO eff'ect f the
overlyingshale s sufficientlyanisotropic'
Theeffectof uningonAVO
As mentioned n the previous section,seismic nterf'erence r event uning can occur
as closely spaced eflectors nterferewith eachother.The relativechange n traveltime
between the reflectorsdecreaseswith increased raveltime and off.set.The traveltime
hyperbolasof the closely spaced eflectorswill thereforebecomeevencloser at larger
ofTsets. n f-act, he amplitudes may interfere at large ofTsetseven if they do not at
small offsets.The effectof tuning on AVO hasbeendemonstrated y Juhlin andYoung
( 1993), in an dPhair 1993),Bakkean dUrsin (1998), ndDong ( 1998), mongothers.
Juhlin an d Young 1993)showed ha t hi n layersembeddedn a homogeneousoc k
can producea significantly different AVO response iom that of a simple interfaceof
the same ithology. They showed hat, or weak contrasts n elasticpropertiesacross he
layer boundaries, he AVO responseof a thin bed may be approximatedby modeling
it as an interferencephenomenonbetween plane P-waves iom a thin layer' ln this
case hin-bedtuning affects he AVO responseof a high-velocity layer embedded n a
homogeneous ock more than it affects he response f a low-velocity layer.
(4 . 6 )
4.3.3
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186 Commonechniquesor quantitativeeismicnterpretation
Lin andPhair 1993)suggestedhe ollowing expressionor the amplitude ariation
with angle AVA) response f a thin layer:
Rr(0) rr . roA?' (0)osd' R(6)
where a.res the dominant frequencyof the wavelet, Af (0) is the two-way traveltirne
at normal incidence iom the top to the baseof the thin layer, and R (0) is the reflection
coefficient iom the top interface.Bakkeand Ursin ( 1998)extended he work by Li n and Phair by introducing u ning
correction actors br a generalseismicwaveletas a function of offset. f the seismic
responseiom the top of a thick layer s:
(4 .11)
( 4 . l 8 )
theseismic
(4.19)
( 4 ) t \
d( t , t ' ) : R(t ' )p(r)
where R(,1')s the primary reflection as a function of ofTset t' ,andp(0 is
pulseas a flnction of t ime /, then he responserom a thin layer s
t l ( r , y) f ( .y)AI (0)C(t " )p ' ( t )
wherep'(r) is the time derivative f the pulse,A7"(0) s the traveltime hickness f the
thin layer at zero offset, and C (-v) s the offiet-dependentAVO tun ing factor given by
(4.20)
where 7(0) and Z(-r')are the traveltimes atzero ofliet and at a given nonzerooffset,
respectively. he root-mean-square elocity VBy5, s defined along a ray path:
c(.v):ffi['##"]
t
l ' t t ) t ' r s ,. l v \ t t \ | t
V R M S -
J d t0
Fo r small velocity contrasts Vnvs - y) , the last term in equation 4.20) ca n beignored, and the AVO tuning f'actorcan be approximatedas
r(0)C(r') :v ----:-- (4.22\
r(,r')
For large contrast n elastic properties,one ought to inc lude contributions iom P-
wave multiples and convertedshearwaves.The locally convertedshearwave is ofien
neglected n ray-tracing modeling when reproductionof the AVO response f potential
hydrocarbon reservoirs s attempted.Primaries-only ray-trace modeling in which the
Zoeppritz equationsdescribe he reflectionamplitudes s most common. But primaries-
only Zoeppritz modeling can be very misleading,because he locally conve rtedshear
wavesoften have a first-order eff-ecton the seismic response Simmons and Backus,1994). nterferencebetween he convertedwaves and the primary reflections iom the
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(1 )Primaries
187I
4,3 AVO nalysis
(2 )Single-leg
a
(3 )Double-leg (4)Reverberations
Figure .5 Converted-wavesndmultipleshatmust e ncludedn AVOmodeling henwehave
thin ayers.ausinghese rodeso nterfere ith heprimaries.l) Primaryeflections;
(2)single-leghear aves;3)double-leghear ave; nd 4)primaryeverberations.After
SimmonsndBackus, 994.) ps transmitted-waveonvertediomP-wave, sp reflected
P-waveonvertediom S-wave.tc.
baseof the ayersbecomesncreasingly mportantas he ayerthicknesses ecrease. his
often producesa seismogram hat is different fiom one produced under he primaries-
only Zoeppritzassumption.n thiscase, ne shouldus e ull elasticmodeling ncluding
th e convertedwave modesan d th e intrabedmultiples.Martinez (1993) showed ha t
surface-relatedmultiples andP-to-SV-modeconvertedwavescan nterf-ere ith primary
pre-stackamplitudesand cause argedistortions n theAVO responses. igure4.5 shows
the ray imagesof convertedS-wavesand multiples within a layer.
Structuralcomplexity,verburdenndwave ropagationffects nAVO
Structural complexity and heterogeneities t the target evel as well as n theoverbur-
den can havea great mpact on the wave propagation.Theseeffects nclude focusing
and defbcusingof the wave field, geometric spreading, ransmission osses, nterbed
and surf'acemultiples, P-wave to vertically polarized S-wavemode conversions,and
anelasticattenuation.The offset-dependent eflectivity should be corrected or these
wave propagationeffects,via robustprocessing echniques seeSection4.3.6). Alter-
natively, these efTectsshould be included in the AVO modeling (see Sections4.3.7
and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor
overburdeneffectsas well as certainacquisitioneffects seeSectiona.3.5) by normal-
izing a target horizon amplitude to a referencehorizon amplitude. However, n more
recentyears here have been severalmore extensivecontributions n the literatureon
amplitude-preservedmaging in complexareasandAVO correctionsdue o overburdeneffects,someof which we will summarizebelow.
R$
4.3.4
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188 Commonechniquesorquantitativeeismicnterpretation-
AVO in structurally complex areas
The Zoeppritzequations ssume single nterf-aceetweenwo semi-infiniteayerswith
infinite ateralextent. n continuously ubsiding asinswith relatively la t stratigraphy
(suchasTertiarysedimentsn the North Sea), he useof Zoeppritzequations houldbe
valid. However,complex eservoirgeologydue to thin beds,verticalheterogeneities,
fault ingand ilt ing will violate heZoeppritz ssumptions. esnicket at . (1987)discuss
the efl'ectsof geologic dip on AVO signatures,whereasMacleod and Martin (1988)
discuss he eff-ects f reflectorcurvature.Structuralcomplexity can be accounted or by
doing pre-stack epthmigration PSDM). However,one shouldbe aware hat several
PSDM routinesobtain reliablestructural mageswithout preserving he amplitudes.
Grubb et ul . (2001) examined the sensitivity both in structureand amplitr-rde elated
to velocity uncertaintiesn PSDM migrated mages.They performedan amplitude-
preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO
signatureshey evaluated oth th e uncertainty n AV O cross-plots nd uncertainty f
AV O attribute aluesalonggivenstructural orizons.
AVO effects due to scattering attenuation in heterogeneous overburden
Widmaier et ztl..1996)showedhow to correcta targetAVO responsebr a thinly layered
overburden. thin-bedded verburdenwill generate elocityanisotropy nd ransmis-
sion ossesdue to scatteringattenuation,and theseeflects shouldbe taken nto account
when analyzinga targetseismic eflector. he y combined he generalized 'Doherty-
Anstey formula (Shapiroet ul., 1994a)with amplitude-preservingmigration/inversion
algorithms and AVO analysis o compensate or the influence of thin-bedded ayers
on traveltimesand amplitudesof seismic data. In particr-rlar,hey demonstratedhow
the estimation of zero-offsetamplitude and AVO gradient can be improved by cor-
recting fbr scatteringattenuationdue to thin-bed efl'ects.Sick er at. (2003) extendecl
Widmaier's work andprovided a methodof compensating or the scatteringattenuation
eflects of randomly distributed heterogeneities bove a target reflector.The general-
ized O'Doherty-Anstey formr-rla s an approximation of the angle-dependent, ime-
harmoniceffective ransmissivity fo r scalarwaves P-wavesn acoustic D medium
or SH-waves n elastic D medium)and s givenby
Tt I I u Tue( ' ' l t ) \ | f t l A\ \L
(4.23)
where.f s the frequencyandn andp are he angle- and iequency-dependent cattering
attenuationandphaseshift coefficients, espectively.The angleg is the initial angle of
an incident plane wave at the top surfaceof a thinly layeredcomposite stack; L is the
thickness f the thinly layered tack; t denoteshe transmissivitybr a homogeneous
isotropic ref-erence edium that causes phaseshifi. Hence, he equationaboverepre-
sents he relativeamplitudeandphasedistortionscausedby the thin layerswith regard
to the referencemedium.Neglecting he quantityZo which describeshe transmission
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190 Commonechniquesorquantitativeeismicnterpretation-
In conclusion,equation (4.28) represents he angle-dependen time shift causedby
transversesotropic velocity behaviorof the thinly layeredoverburden.Furthermore, t
describeshe decrease f the AVO response esulting rom multiple scatteringadditional
to the amplitude decay related o sphericaldivergence.
Widmaier e ai. ( I 995) presented imilar brmulations or elasticP-waveAVO, where
the elasticcorrection ormula dependsnot only on variancesandcovariances f P-wave
velocity, but also on S-wave velocity and density,and their correlationan d cross-
correlation unctions.
Ursin and Stovas 2002) urther extendedon the O'Doherty-Anstey fbrmula and cal-
culated scatteringattenuation br a thin-bedded,viscoelasticmedium. They found that
in the seismic requencyrange, he intrinsic attenuationdominatesover the scattering
attenuation.
AVO and intrinsic attenuation (absorption)
Intrinsic attenuation,also referred o as anelasticabsorption, s causedby the fact that
even homogeneoussedimentary ocks are not perf'ectlyelastic. This effect can com-
plicate he AVO re sponsee.g.,Martinez, 1993).Intrinsic ttenuation an be described
in terms of a transt'er unction Gt.o, t) fbr a plane wave of angular frequency or andpropagationim e r (Luh, 1993):
G@ i : exp(at 2Qe* i(at lr Q) ln at tos) (4.30)
where Q" is the effective quality f'actorof the overburdenalong the wave propagation
path and are s an angular reference requency.
Luh demonstratedhow to correct for horizontal, vertical and ofTset-dependent
wavelet attenuation.He suggestedan approximate, "rule of thumb" equation to cal-
culate the relativechange n AVo gradient,6G, due to absorption n the overburden:
f t t3G ry :- 'Q"
( 4 . 31 )
wherei is the peak frequencyof the wavelet, and z is the zero-offset wo-way travel
time at the studied eflector.
Carcioneet al. (1998) showed hat the presenceof intrinsic attenuationaffects he
P-wave eflectioncoefficientnear he critical angleand beyond t. They also ound that
the combined effect of attenuationand anisotropyaff'ects he reflection coefficientsat
non-normal ncidence,but that he ntrinsic attenuation n somecases anactually com-
pensatehe anisotropiceffects. n mostcases, owever,anisotropiceffectsaredominant
over attenuationeffects.Carcione (1999) furthermore showed hat the unconsolidated
sedimentsnear he seabottom in offshore environments an be highly attenuating,andthat these waves will for any incidenceangle have a vector attenuationperpendicular
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191 4,3 AVO nalysisr
4.3.5
to the sea-floor nterf'ace. his vec tor attenuationwill afl'ectAVO responses f deeper
reflectors.
AcquisitiontfectsnAVO
The most important acquisition eff-ects n AVO measurementsnclude sourcedirec-
tivity, and sourcean d receivercoupling (Martinez,J993). ln particular,acquisit ionfootprint s a largeproblem br 3D AVO (Castagna,2001).negular'Eoverage t the
surfacewill causeuneven llumination of the subsurface. heseeffectscan be corrected
for using nverseoperations.Difl'erentmethods or this havebeenpresented n the iter-
ature e.g.,Gassaway t a\.,1986;Krail andShin,1990;Cheminguian dBiondi, 2002).
Chiburis' ( 1993)method or normalizationof targetamplitudeswith a referenceampli-
tude provided a fast and simple way of corecting for certain data collection factors
including sourceand receivercharacteristics nd nstrumentation.
Pre-processingfseismicataorAVO nalysis
AVO processingshouldpreserveor restore elative raceamplitudeswithin CMP gath-
ers. This implies two goals: (1 ) reflectionsmust be correctlyposit ioned n the sub-
surface;and (2) data quality should be sufficient to ensure hat reflection amplitudes
contain nfbrmation aboutreflection coefficients.
AVO rocessing
Even though the unique goal in AV O processings to preserve he true relative
amplitudes, here s no uniqueprocessing equence.t depends n the complexity
of the geology.whether t is land or marineseismicdata.an dwhether he datawill
be used to extract regression-based VO attributesor more sophisticatedelastic
inversionattributes.
Cambois 20 0 ) definesAV O processing s any processing equenceha t makes
th e data compatiblewith Shuey'sequation, f that s th e model used or the AVO
inversion.Camboisemphasizesha t his can be a very complicated ask'
Factors hatchange heamplitudesof seismic races anbe grouped nto Earth effects,
acquisition-relatedeffects, and noise (Dey-Sarkar and Suatek, 1993). Earth effects
include sphericaldivergence,absorption, ransmission osses, nterbedmultiples, con-
verted phases, uning, anisotropy, and structure.Acquisition-related eft-ects nclude
sourceand receiver arrays and receiver sensitivity.Noise can be ambient or source-
generated. oherent r random.Processing ttemptso compensateor or remove hese
effects, but can in the processchangeor distort relative trace amplitudes.This is animportant trade-offwe need o consider n pre-process ing or AVO. We thereforeneed
4.3.6
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192r
Commonechniquesorquantitativeeismicnterpretation
to select basic ut obust rocessingchemee.g., strander, 984; hiburis, 9g4;Fouquet,990;CastagnandBackus, 993; ilma42001).
Common pre-processing tepsbefore AVO analysis
Spiking deconvolution and wavelet processing
In AVO analysiswe normallywant zero-phaseata.However, heoriginalseismic ulse
is causal, suallysomesort of minimum phasewaveletwith noise.Deconvolution sdefined as convolving the seismic trace with an inverse ilter in order to extract the
impulse response rom the seismic trace. This procedure will restorehigh frequen-
cies and therefore mprove the vertical resolution and recognition of events.One canmake two-sided, non-causal ilters,or shaping ilters, to producea zero-phasewavelet(e.g. , e inbach, 995;Berkhout , 977).
Th e wavelet shapeca n vary vertically (with rime), larerally spatially),and with
offset. The vertical variationscan be handledwith deterministic Q-cornpensation see
Section4.3.4).However,AVO analysis s normally carriedou t within a limited time
window where one can assumestationarity.Lateral changes n the wavelet shapecan
be handledwith surface-consistentmplitudebalancing e.g.,Camboisan d Magesan,
1997).Offset-dependent ariationsare often more complicated o correct for, an4 areattributed o both ofl.set-dependent bsorption(seeSection 4.3.4), tuning efl'ects see
Section .3.3),an dNM o stretching. Mo stretching cts ikea ow-pass,mixed-phase,
nonstationary ilter, and heeff'ects re very difficult to eliminate ully (Cambois,2001 .Dong (1999) examined how AVO detectability of lithology and fluids was afl'ected
by tuning and NMo stretching,and suggesteda procedure or removing the tuning
and stretchingeffects n order to improve AVO detectability.Cambois recommendecl
picking the reflections of interest prior to NMo corrections,and flattening them forAVO analysis.
Spherical divergence correction
Spherical divergence,or geometrical spreading,causes he intensity and energy ofsphericalwaves to decrease nversely as the squareof the distance iom the source(Newman, 1973).For a comprehensive eviewon ofTset-dependenteometricalspread-
ing, se e he studyby Ursin ( 1990).
Surface-consistent amplitude balancing
Sourceand receivereff'ectsas well as water depth variation can produce large devi-ations in amplitude that do not coffespond to ta rget reflector properties.Commonly,
statistical amplitude balancing s carried out both fbr time and offset. However. thisprocedurecan have a dramatic efl'ect on the AVO parameters. t easily contributes
to intercept eakageand consequentlyerroneousgradient estimates Cambois, 2000).
Cambois (2001) suggestedmodeling the expectedaverageamplituclevariation with
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19 3 4.3 AVO nalvsisn
off.set bllowing Shuey'sequation,and then using this behavior as a ret'erenceor thestatistical mplitudebalancing.
Multiple removal
One of the most deterioratingeff-ects n pre-stackamplitudes s the presence f multi-ples.Thereareseveralmethodsof filtering awaymultiple energy,but not al l of theseareadequate or AVo pre-processing. he methodknown asfft multiple filtering, done nthe frequency-wavenumberdomain, s very efficient at removing multiples, but the dipin the.l-lr domain is very similar fbr near-offset rimary energyandnear-offsetmultipleenergy.Hence,primary energycaneasilybe removed rom near racesandnot from fartraces, esulting n an ar-tificialAVO effect.More robustdemultiple techniques ncludelinear and parabolic Radon transform multiple removal (Hampson, l9g6: Herrmannet a1.,2000).
NMO (normal moveout) correction
A potential problem during AVO analysis s error in the velocity moveout conection(Spratt, 1987).When
extractingAVO attributes,one assumes hat primaries havebeencompletely lattened o a constant raveltime.This is rarely thecase,as herewill alwaysbe residualmoveout.The reason or residualmoveout s almostalways associatedwitherroneous elocity picking, andgreatef'forts houklbe put into optimizing theestimatedvelocity ield (e.g.,Adler, 1999;Le Meur and Magneron,2000).However,anisorropyandnonhyperbolicmoveoutsdue o complex overburclenmay alsocausemisalignmentsbetweennearand ar off.setsan excellentpracticalexampleon AVO andnonhyperbolicmoveoutwas publishedby Ross,1997).Ursin an d Ekren (1994)presented methodfor analyzingAVO eff-ectsn the off.setdomain using time windows. This techniquereducesmoveoutelrors andcreatesmprovedestimates f AVO parameters.Oneshoulclbe awareof AVO anomalieswith polarity shifts (class Ip, seedefinition below) duringNMO corrections,
as hesecaneasilybe misinterpretedas residualmoveouts Ratcliffeand Adler, 2000).
DMO correction
DMO (dip moveout) processinggenerates ommon-reflection-pointgathers. t movesthe reflection observed on an off'set race to the location of the coincident source-receiver race that would have the samereflecting point. Therefore, t involves shift-ing both time and location. As a result, the reflection moveout no longer dependson dip, reflection-point smear of dipping reflections is eliminated, and events withvarious dips have the same sracking velocity (Sheriff and Geldhart, 1995). Shanget al . (1993) published a rechnique on how to extract reliable AVA (ampli-
tude variation with angle) gathers in the presenceof dip, using partial pre-stackmisration.
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194 Commonechniquesorquantitativeeismicnterpretation-
Pre-stack migration
Pre-stackmigration might be thought o be unnecessaryn areaswhere he sedimentary
section s relatively flat, but it is an importantcomponentof all AVO processing.
Pre-stackmigration should be used on data for AVO analysiswheneverpossible,
becauset will collapse he diffractions at the targetdepth o be smaller han he Fresnel
zonean d herefore ncrease he ateral esolution seeSection4.2.3;Berkhout, 1985;
Mosher et at., 1996).Normally, pre-stack imemigration (PSTM) is preferred o pre-
stackdepthmigration (PSDM), becausehe former tends o preserveamplitudesbetter.
However, n areaswith highly structuredgeology, PSDM will be the most accurate
tool (Cambois,2001).An amplitude-preservingSDM routineshould he nbe applied
(Ble iste in, 987;Schle icher t ct l . , l993;Hani tzsch, 997).
Migration fbr AVO analysiscan be implemented n many different ways. Resnick
et aL. 1987) an d Allen and Peddy (1993) among othershave recommendedKirch-
hoff migration togetherwith AVO analysis.An alternativeapproach s to apply wave-
equation-basedmigration algorithms.Mosher et al. (.1996) eriveda waveequation br
common-angle time migration and used nverse scattering heory (seealso Weglein,
1992'7forntegration f migrationan dAVO analysis i.e.,migration-inversion). osher
et at. (1996) usecla finite-difference approach br the pre-stackmigrations and illus-
trated he value of pre-stackmigration fbr improving the stratigraphic esolution,data
quality, and ocation accuracyof AVO targets.
Examplefpre-processingchemeorAVO natysisf a2lseismicine
(Y i lmaz,001. )( ) Pre-stackignal rocessingsourceignaturerocessing.eometriccaling,
spikingdeconvolution ndspecffalwhitening).
(2 t Sort o CMP and do sparsentervalvelocityanalysis.
(3 ) NM O usingvelocity ield rom step2.
(4 ) DemultipleusingdiscreteRadon ransform.
(5) Sort to common-offsetand do DMO correction.
(6 ) Zero-offsetFK time migration.
(7) Sort data o common-reflection-pointCRP) an d do inverseNM O using th e
velocity ield from step2.
(8 ) Detailedvelocityanalysis ssociated ith the migrated ala'
(9 ) NM O correclionusingvelocity ield from step8.
( l0) StackCR Pgatherso obtain mageof pre-stackmigrated ata.Remove esidual
multiples evealed y lhe stacking.
( l l ) Unmigrate singsame eloci ty ie ldas n step6.
( 2; Post-stack pikingdeconvolution.
(13) Remigrate singmigrationvelocity ield from step8.
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195 4.3 AVO nalysisE
Someitfallsn AVOnterpretationue0processingtfects
. Waveletphase. he phase f a seismicsection an be signif icantly ltered uring
processing.f rhephase f a section s not established y the nterpre ter.he nAV O
anomalies ha t would be interpreted s indicativeof decreasingmpedance, or
example. an beproduced t nterfaces here he mpedancencreasese.g.,Allen
and Peddy. 993).
. Multiple fi ltering. No t all demultiple techniquesare adequate or AVO pre-
processing. ult iple fi ltering,done n the requency-wavenumberomain, s very
efficientar removing multiples.bu t the dip in the/-k domain is very similar or
near-offsetprimary energyand near-offsetmultiple energy.Hence,primary energy
can easlly be removed from the near-offset races. esulting n an artificial AVO
effect.
. NMO correction. potential roblemduringAVO analysiss errors n thevelocity
moveoutcorrection Spran. 1987).When extractingAVO attributes. ne assumes
that primarieshave been completely lattened o a constant raveltime.This is
rarely he case. s herewill alwaysbe residualmoveout.Ursin an d Ekren 1994)
presenteda method for analyzing AVO effects in rhe offset domain using time
windows.This technique educesmoveoulerrorsand createsmprovedestimates
of AVO paramerers.NMO stretch s 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 s signif icant. hould be muted beforeAVO analysis.Swan (1991),Dong
(1998)an d Dong ( 1999)examine he eft 'ect f NMO stretchon offset-dependenl
reflectivity.
. AG C amplirude conection. Automatic gain control must be avoided n pre-
processing f pre-stack at abeforedoing AVO analysis.
Pre-processing for elastic impedance inversion
Severalof the pre-processing tepsnecessaryor AVO analysisare not requiredwhen
preparingdata or elastic mpedance nversion seeSection4.4 for detailson themethod-
ology). First of all, the elastic mpedanceapproachallows for wavelet variationswith
offset (Cambois,2000).NMO stretchcorrectionscan be skipped,because ach imited-
rangesub-stack in which the waveletcanbe assumedo be stationary) s matched o its
associated yntheticseismogram, nd his will remove he waveletvariationswith angle.
It is, however,desirable o obtain similar bandwidth fbr each nvertedsub-stackcube,
since theseshould be comparable.Furthermore, he data used for elastic mpedance
inversionare calibrated o well logs before stack,which means hat averageamplitude
variations with offset are automatically accountedor. Hence, the complicated pro-
cedureof reliable amplitude correctionsbecomesmuch less abor-intensive han for
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196 Commonechniquesorquantitativeeismicnterpretation-
4.3.7
u 1 0 2 0 3 0 4 0 5 0 6 0Anglef ncidencedegree)
Figure ,6 AVO curves br differenthalf'-space odels i.e., wo layers one ntertace). acies V
is cap-rock.nput ockphysics ropert ie\epresent ean alues or each acies.
standard VO analysis. inally, esidualNMO andmultiplessti l l mustbe accountedbr
(Cambois,2001).Misalignments o no t cause ntercept eakageas br standardAVO
analysis, ut near-and ar-angle eflectionsmuststi l l be n phase.
AVOmodelingnd eismic etectability
AV O analysis s normally carriedout in a deterministicwa y to predict ithology an d
fluids rom seismic at a e.g.,Smithan dGidlow, 1987;Rutherford ndWill iams, 1989;
Hilterman, 1990;Castagna nd Smith, 1994;Castagna t al., 1998).
Forward modeling of AVO responses s normally the best way to start an AVO
analysis,as a feasibility study before pre-processing,nversionand interpretationof
real pre-stackdata. We show an example in Figure 4.6 where we do AVO modeling
of difTerent ithofacies defined in Section 2.5. The figure shows the AVO curves for
different half-spacemodels, where a silty shale s taken as he cap-rock with difTerent
underlying lithofacies.For each acies , Vp, Vs, and p are extracted rom well-log data
and used n the modeling.We observea clean sand/pure haleambiguity (facies Ib
and faciesV) at near of1iets,whereascleansandsand shalesare distinguishableat far
offsets.This exampledepictshow AVO is necessaryo discriminatedifferent ithofacies
in this case.
I
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197-
4.3 AVO nalysis
V
Hydrocarlonr€ild
Cemenled{el brino
0
Ceme|rbdw/ hydruca]ton
Unconsolidaledw/ brine
Unconsolidtlsdw/ hydrocarbon
Figure .7 Schcgatic VOcurvesirr cementedandstonendunconsolidatedands appedy
shlle. rll brine-saturatedndoil-saturatedases.
Figure 4.7 shclwsanotherexample,where we consider wo types of clean sands,
cementedandunconsolidated,with brine versushydrocarbonsaturation.We see hat a
cementedsanclstone ith hydrocarbonsaturationcan have similar AVO response o a
brine-saturated. nconsolidatedsand.
The examples n Figures4.6 and 4.7 indicate how important t is to understand he
localgeology during AVO analysis. t is necessaryo know what ypeof sand s expected
for a given prospect,and how much one expects he sands o change ocally owing to
textural changes,before interpreting luid content. t is thereforeequally important to
coniluct realistic ithology substitutionsn addition o fluid substitution uring AVO
rnodelingstudies.The examples n Figures4.6 and 4.7 alsodemonstratehe impor-
tance of the link between ock physicsand geology (Chapter2) during AVO analysis.
When s AVO nalysishe appropriateechnique?
It is well known that AV O analysisdoes no t always work. Owing to the many
caseswhere AV O has beenappliedwithoul success,he technique as receiveda
bad reputationas an unreliable ool. However.part ol th e AVO analysis s to find
out if the technique s appropriate n the first place. t wil l work only if lhe rock
physicsan d ffuid characleristics f the target eservoir reexpected o give a good
AV O response. hi s must be clarif iedbefore he AVO analysis f realdata.Without
a proper easibil ity study.on e can easily misinterpretAVO signaturesn th e real
data.A good feasibil itystudycould ncludeboth simple reflectivitymodelingan d
more advancedorward seismicmodeling seeSection4.51.Both these echniques
shouldbe foundedon a thoroughunderstanding f local geologyan d petrophysical
properties. ealistic ithologysubstitutions as mportant s luid substitution uring
thisexercise.
CemellHionrend
I
I
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198 GommonechniquesorquantitativeeismicnterpretationI
4.3.8
Often, one will find that there is a certain depth interval where AVO will work,
often referred o as th e "AVO window." Outside his, AVO will not work well.
That is why analysis of rack physics depth trends should be an integral part of
AVO analysis (see Sections2.6 and 4.3.16). However. the "AVO window" is also
constrained y dataquality. With increasing epth,absorptionof primary energy
reduces he signal-to-noiseatio. higher requencies regraduallymore attenualed
than ower frequencies.he geology usuallybecomesmore complex causingmore
complexwavepropagations,nd heangle ange educes or agivenstreamerength.
All these actorsmakeAVO lessapplicablewith increasing epth.
DeterministicVO nalysisf GDP athers
After simple half--space VO modeling, the next step n AVO analysisshouldbe deter-
ministic AVO analysisof selectedCDP (common-depth-point)gathers,preferably at
well locations where synthetic gatherscan be generatedand compared with the real
CD P gathers.n this section,we showan example f how the methodcan be applied o
discriminateithofaciesn real seismic ata, y analyzingCD P gathers t well locationsin a deterministic way. Figure 4.8 shows he real and synthetic CDP gathersat three
adjacentwell locations n a North Sea ield (thewell logsar eshown n Figure5.1,case
study ). The figure also ncludes he pickedamplitudes t a top targethorizon super-
imposed on exact Zoeppritz calculatedreflectivity curves derived fiom the well-log
data.
In Well 2, the reservoirsandsare unconsolidated, epresentoil-saturatedsands,and
are cappedby silty shales.According to the saturationcurves derived iom deep esis-
tivity measurements, he oil saturation n the reservoirvaries from 20-807o, with an
averageof about 60Va.The sonic and density logs are found to measure he 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 saturationmodel (the processof fluid substitution s described n 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 rom Batzle and Wang's relations
(see Chapter l). For this case, he input parameters or the fluid substitution are as
fbllows.
o i lGoR
Oil relative ensity
Mud-filtrate ensity
Pore ressure t reservoirevel
Temperaturet reservoirevel
64 UI
32APT
1.09g/cm3
20 MPa
77.2 ' ,C
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199 4.3 AVO nalysis-
Well
0 323 726 1210 1694 2177CD P ]
OF F t
Relleclvity Rel ctivity
0 100
0 050
0 050
0
- weill
i'. -r -r;r!
. 1 ' '
, . P B
0.r00
0.050
Well 3:0 1 0 0
:II
0.050 !
:.0 i::
0 0 5 0
n n q n I'-
I l ' o " . .0 r0 0
l
0 150
Angle 1 14 21 28 34 (deq) Anqle 8 l5 22 29 (deg) Angle 1 14 20 26 32 (deg)
Figure .8 RealCDP gathers upper), yntheticCDP gathers middle),andAVO curves or Wells
I 3 (lower).
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200 Commonechniquesor quantitativeeismicnterpretationI
The correspondingAVO responseshows a negativezero-ofTseteflectivity and a neg-
ative AVO gradient. n Well l, we have a water-saturated ementedsandbelow a silty
shale.The correspondingAVO response n this well showsa strongpositive zero-ofl.set
reflectivity and a relatively strong negative gradient. Finally, in Well 3 we observea
strongpositive zero-offset eflectivity and a moderatenegativegradient,corresponding
to interbedded and/shaleaciescappedby silty shales.Hence,we observe hreedistinct
AVO responses n the three different wells. Thechangesare related o both Iithology
and pore-fluid variations within the turbidite system. For more detailed information
about his system,seecasestudy I in Chapter 5.
Avseth et al. (2000) demonstrated he etlect of cementationon the AVO response n
real CDP gathersaround wo wells, one where the reservoirsandsare friable, and the
other where the reservoir sandsare cemented.They found that if the textural eflects
of the sandswere ignored, he corresponding hanges n AVO response ould be inter-
pretedas pore-fluidchanges,ust as depicted n the reflectivitymodelingexample n
Figure4.7.
lmpodance0f AVOanalysisof individualCDP athers
Investigations f CDP gathersare importanl n order ro confirm AVO anomalies
seen n weightedstack ect.ionsShuey:sntercepr ndgradient,Smithan dGidlow's
fluid factor.etc.). The weightedstackscan contain anomaliesnot related o true
offset-dependentmplitudevariations.
4.3.9 EstimationfAVO arameters
Estimating intercept and gradient
The next step n an AVO analysisshouldbe to extract AVO attributesand do multivari-
ate analysis of these.Severaldifferent AVO attributescan be extracted,mapped andanalyzed.The two most mportantonesare zero-offset eflectivity (R(0))and AVO gra-
dient G) based n Shuey's pproximation. heseseismic ararnetersanbe extracted,
via a least-squareseismic nversion, or eachsample n a CDP gatherovera selected
portionof a 3D seismicvolume.
For a given NMO-conected CDP gather, R(/,,r), it is assumed that for each
time sample, /, the reflectivity data can be expressedas Shuey's formula (equation
(4.8)) :
R(r, ) : R(/,0) + c(/) sin2g(r,r) ( 4 7 ) \
where 0(r, x) is the incident angle correspondingto the data sample recorded at( t . ) .
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201-
4.3 AVO nalysis
For a ayeredEarth, he relationshipbetweenofliet (r ) andangle(0) is given approx-
imatelyby :
r VrNr (4.33)sin0(r ,x) I
k3+x2fv i^ ) t t2
where VrNr is the interval velocity and Vnr,,rss the average oot-mean-square eloc-
ity, as calculated from an input velocity profile (fbr example obtained from sonic
log).
For any given valueof zero-offset ime, /e,we assume hatR is measured t N offsets
(xi, i:1, A/).Hence,we can rewrite he definingequation br this time as (Hampson
andRussel l . 995):
t t 2YRMS
R( . r r )
R(xz)
s in2o(4r )
sin2g(r , , rz)
Inmor-lI c u r I
(4.34)
N equations n the two
equation s obtainedbY
R(r,r,) I sin2g(r,rr,')
This matrix equation s in the form of b: Ac and represents
unknowns,R(/, 0) and G(r).Th e least-squaresolution o this
solving he so-called normal equation":
c : (A rA) -1 (ATb) (4.3s)
us he east-squaresolution br R(0) an d G at time t.
Inversion for elastic Parameters
Going beyond the estimation of interceptand gradient,one can invert pre-stackseis-
mic amplitudes or elasticparameters,ncluding Vp, V5 and density.This is commonly
ref'erred o as AVO inversion,and can be performed via nonlinearmethods(e'g., Dahl
anclUrsin. 19921 ulandet al., 1996;Gouveiaan dScales, 998)or inearizednversion
methods e.g.,Smith an d Gidlow, 1987;Loertzeran d Berkhout, 1993).Gouveiaan d
Scales 1998)clefined Bayesian onlinearmodelan destimated, ia a nonlinear on -
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 ntensive.Loertzer andBerkhout ( 1993)performed inearizedBayesian
inversionbasedon single interface heory on a sample-by-sample asis.Buland and
Omre (2003) extended he work of Loertzer and Berkhout and developeda linearized
Bayesian AVO inversion method where the wavelet s accounted or by convolution.Th e nversion s perfbrmed imultaneouslybr all t imes n a given ime window,which
^
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202r
Commonechniquesor quantitativeeismicnterpretation
makes it possible to obtain temporal correlation between model parameters lose n
time. Furthermore, hey solved the AVO inversion problem via Gaussianpriors and
obtainedan explicit analytical orm for the posteriordensity,providing a computation-
ally fastestimation f the elasticparameters.
PittallsfAVOnversion
. A l inearapproximation f th eZoeppntzequationss commonlyused n thecalcu-lation of R(01an dG. The two-termShueyapproximations known o be accurate
for anglesof incidence p to approximately 0'. Make sure hat he data nverted
do not exceed hi s range, o the approximalion s valid'
. Th e Zoeppritzequations reonly valid fbr single nterfaces.nversionalgorithms
thatare based n these quationswill not be valid or thin-bedded eology.
. Th e linear AV O inversion s sensitive o uncharacteristic mplitudes ausedby
noise includingmultiples.) r processing nd acquisirion ffects.A few outlying
values resent n thepre-stack mplitudes reenough o cause rroneous stimates
of R(0) an d G. Mosr commercialsoftwarepackages or eslimationof R(0) an d
C apply obusr st imar ionechniquese.g. ,Walden.199l ) o l imi t thedamage l '
outlying amPlitudes.. Another potential problem during sample-by-sample VO inversion s errors
in th e moveoutcorrection Spratt, 1987. Ursin an d Ekren (1994) presented
method for analyzingAVO eflects n the offset domain using time windows.
This technique educesmoveouterrorsand creates mprovedestimates i AVO
parameters.
4,3.10AVOross-Plotnalysis
A very helpful way to interpretAVO attributes s to makecross-plotsof intercept R(0))
versus radient G) .Theseplotsar ea veryhelpfulan d ntuit iveway ofpresenting VO
data,and can give a better understanding f the rock properties han by analyzing he
standardAVO curves.
AVO classes
Rutherfordan dWill iams ( 1989)suggested classif ication cheme f AV O responses
fbr 6iflerent typesof gas sanils seeFigure 4.9). They defined hreeAVO classes ased
on where he top of th e ga ssandswill be located n a n R(0) versusG cross-plot. he
cross-plot s split up into fbur quadrants.n a cross-plotwith R(0) along r-axisand C
along v-axis,he I stquadrant s whereR(0) and G ar ebothpositive alues upper ight
quadrant). he 2nd s whereR(0) s negative ndG is positive upper eft quadrant). he
3rd is whereborhR(0) and G arenegative lower ef t quadrant).Finally, the4th quadrant
is where R(0) is positive and G is negative(lower right quadrant).The AVO classes
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203I-
4.3 AVoanalysis
Tabfe .1AVO classes, fter Ruthe(brd and Williams (1989)'
extendecl 1'Castagnaand Smith (1994),and Rossand
Kinman 1995)
Class Relative mPedance Quadrant R(0) G AVO product
High-impedancean d
No or low contrast
Low impedance
Low impedance
4th
,lth
3rd
3rd
2nd
Negative
Negative
Positive
Positive
Negative
classl lt
a
t -- Ictasstt..
' rO
D \ 1
I cra.irp I crass[ -
Figure ,9 RuthertbrdndwilliamsAVOclasses,riginally efinedor gas andsclasses, ll and
III),along it h headdedlnssesV (CastagnandSmith. 994) nd Ip (Ross ndKinman' 995)'
Figures aclaptediomCastagnatal . (1998)'
must not be confused with the quadrant numbers. Class I plots in the 4th quadrant
with positive R(0) and negativegradients.Theserepresenthard eventswith relatively
high impedanceand low vp/vs ratio comparedwith the cap-rock.class II represents
sandswith weak intercept but strong negatjvegradient.These can be hard to seeon
the seismic data, because hey often yield dim spots on stackedsections' Class II I
is the AVO category that is normally associatedwithbright spots' These plot in the
3rd quadrant n R(0)-G cross-plots,and are associatedwith soft sandssaturatedwith
hydrocarbons se ePlate4. 0).
Ross and Kinman (1995) distinguished etweena class Ip an d class I anomaly'
ClassIIp has a weak but positive nterceptand a negativegradient,causinga polarity
changewith oflset. This classwill disappear n full stacksections. lass II hasa weak
but negative nterceptand negativegraclient, enceno polarity change.This classmay
be observedas a negativeamplitude on a full-ofliet stack'
Castagnaand Swan (1997) extendecl he classification schemeof Rutherford and
Williams to incluclea 4th class,plotting in the 2n<1 uadrant.Theseare relatively rare'
but occur when soft sandswith gas are capped by relatively stiff shalescharacter-
ized by Vp/Vs ratios slightly higher than in the sandsi'e" very compactedor silty
shales).
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204 Gommonechniquesor quantitativeeismicnterpretation:
SummaryfAVOlasses
' AV Oclass representselatively ar dsandswith hydrocarbons. hese ands end "o
plot along he background rend n intercept-gradientross-plots.Moreover, er y
hardsands an have itt le sensitivity o fluids.so theremay no t be an associated
flat spot.Hence. hese ands an be hard o discover rom seismicdata.. AV o class I. representingransparent andswith hydrocarbons, ftenshowup as
di m spotsorweaknegativereflectorsonheseismic.However. ecauseof elatively
largegradients. he y should show up as anomalies n an Rt0)-c cross-plot. nd
plot off the background rend.
' AVO class II is th e"classical"AV O anomalywith negativentercept ndnegative
gradient.This class representselativelysoft sandswirh high fluid sensitivity,
located ar away rom th e background rend.Hence, he yshouldbe easy o derect
on seismic ata.
' AVO class V ar esandswith negativentercept ut posit ive radient. he reflection
coefficient ecomeses snegaLive ith increasing ffset,and amplitudedecreases
versusoffset.even houghLhese andsmay be bright spots castagnaan d Swan.
1997).Class V anomalies re relatively are,but occur when soft sandswith gas
ar ecapped y relatively tiffcap-rockshales haracterizedy vplvs ratios lightly
higher han n thesands i .e. . erycompacted r s i l ty shales).
Th e AVo classeswere originally defined or ga s sands.However. oday he AVo
classsystem s used or descriptive lassif ication f observedanomalies hal are
not necessarily as sands.An AVO class l that s dril led can turn out to be brine
sands. t does not mean that the AVo anomaly was not a class l anomaly.we
therefbre uggest pplying he classif ication nly asdescriptive erms or observed
AVo anomal ies,wi thout aulomat ical lynferr ing hat we are deal ingwi th gas
sands.
AVO trends and the effects of porosity, lithology and compaction
When we plot R(0) andG ascross-plots,we can analyze he rends hatoccur n termsof
changesn rock physics roperties,ncluding luid trends, orosity rendsand ithology
trends,as thesewill have differentdirections n the cross-plot Figure 4. 1l). Using
rock physicsmodelsand then calculating he correspondingnterceptand gradients,
we can study various "What lf" scenarios, nd then compare he modeled rends with
the inverteddata.
Brine-saturated ands nterbeddedwith shales, ituatedwithin a limited depth range
and at a particular ocality, normally follow a well-defined"background rend" in AVO
cross-plot (Castagnaand Swan, 1991). A common and recommendedapproach n
qualitativeAVO cross-plotanalysis s to recognize he "background"trend and thenlook fbr datapoints that deviate rom this trend.
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205r
4,3 AVO nalysis
FigUre.11Difl'erentrends ccurringn an ntercept radientross-plot'AdaptediomSimm
etal.,2O0O.)
Castagnaet at . (1998) presentedan excellentoverview and a fiamework for AVO
gradientand ntercept nterpretation.The top of the sandswill normally plot in the 4th
quadrant,with positiveR(0) andnegativeG. The baseof the sandswill normally plot in
the 2ndquadrant,with negativeR(0) andpositive G. The top andbaseof sands,ogether
with shale-shale ntertaces,will createa nice trend or ellipse with center n the origin
of the R(O)-G coordinate system.This trend will rotate with contrast n Vp/V5 ratio
betweena shalycap-rockancla sandy eservoir Castagna t al., 1998;Sams' 1998)'
We can extract he relationship between VplVs tatio and the slope of the background
trencl a6)by clividing he gradient,G, by the intercept,R(0):
G
R(0)
Assuming the density contrastbetween shaleand wet sand o be zero, we can study
how changinE Vp Vs ratio affects he background rend.The density contrastbetween
sandan dshaleat a givendepth s normally elatively mallcomparedwith th e velocity
contrasts Foster t a\.,1991).Then he background lope s givenby :
. ^ l - ( V s r Y s 2 ) A Y s lu h - I " L t Y nt V p : t A V p l
(4..r7)
where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir,
respectively;Vs1and V52are the correspondingS-wavevelocities, whereasAVp and
AV5 are he velocity differencesbetween eservoiranclcap-rock. f the Vp/V5 ratio is
2 in the cap-rockand 2 in the reservoir, he slopeof the background rend is - l, that
is a 45' slopediagonal to the gradient and interceptaxes.Figure 4'12 showsdifferent
lines corresponding o varying Vp/V5 ratio in the reservoirand the cap-rock.
The rotation of the line denoting the background rend willbe an implicit function
of rock physicspropertiessuch as clay contentand porosity.Increasingclay content
(4.36)
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VplVs=2.5ncaP-rock
206 Commonechniquesorquantitativeeismicnterpretation-
0B(0)
-0.5L-0.5
Figure4,12ackgroundtrendsinAVOcross-plotsasafunct ionofvaryingVplV<ral io incap-rock
and eservoir.Weassumeo density ontrast.) oticehataVplVs atioof 1.5 n the eservoiran
have iff'erentocationsn theAVOcross-plotependingn hecap-rock plV5ratio.fthe Vp/V5
ratioof thecap-rocks 2.5, hesandwill exhibitAVOclassl to III behaviorlefi),whereasf the
cap-rock p/V5atio s2.0, hesand il l exhibit lass to Ipbehaviorright).
at a reservoir evel wil l causea counter-clockwiseotation,as the Vp/V5 ratio wil l
increase. ncreasing porosity related to less compaction will also cause a counter-
clockwise rotation, as less-compacted ediments end to have relatively high VplVg
ratio. However, ncreasingporosity related o lessclay contentor improved sortingwill
normally cause a clockwise rotation, as clean sands end to have lower Vp/V5 ratio
than shaly sands.Hence, t can be a pitfall to relateporosity to AVO responsewithout
identifying the causeof the porosity change.
Th ebackgroundrendwill changewith depth, ut heway it changes anbe complex.
Intrinsicattenuation, iscussedn Section .3.4 Luh, 1993),wil l afI-ecthebackground
trend as a function of depth, but correction shouldbe made br this before rock physics
analysisof the AV O cross-plot se eSection4.3.6).Nevertheless,he rotationdue to
depth trends n the elastic contrastsbetween sandsand shales s not straightforward,
because heVplVs in the cap-rockas well as the reservoirwil l decrease ith depth.
These wo efTectswill counteracteachother n terms of rotationaldirection. as seen n
Figure4. 12.Thus, he rotationwith depthmustbe analyzed ocally.Also, the contrasts
between cap-rock and reservoir will change as a function of lithology, clay content,
sorting, and diagenesis, ll geologic factors hat can be unrelated o dep th. That being
said,we shouldnot nclude oo argea depth ntervalwhen we extractbackground rends
(Castagna nd Swan, 1997).That would cause everal lopes o be superimposed nd
result n a less defined background rend. For instance,note that the top of a soft sand
will plot in the 3r d quadrant,while the baseof a soft sandwill plot in the I st quadrant,
giving a background rendrotated n the oppositedirection to the trend or hard sands.
VplVs=2.QncaP-rock
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207r
4.3 AVO nalysis
Fluid effects and AVO anomalies
As mentionedabove,deviations iom the background rendmay be ndicativeof hydro-
carbons,or some ocal lithology or diagenesis ffect with anomalouselasticproperties
(Castagna t at., 1998).Fosteret al . (1991)mathematicallyderivedhydrocarbon rends
that would be nearly parallel to the background rend,but would not pass hrough the
origin in R(0) versusG cross-plots.For both hard and soft sandswe expect he top of
hydrocarbon-fillecl ocksto plot to the left of the background trend, with lower R(0)
and G valuescomparedwith the brine-saturated ase.However,Castagnaet al . (1998)
fbund that, n particular,gas-saturated andscould exhibit a variety of AVO behaviors.
As lisred n Table4.1. AVO class II anomalies Rutherfordan d Will iams, 1989),
representingsoft sandswith gas, will fall in the 3rd quadrant the lower left quadrant)
and havenegativeR(0) and G. Theseanomaliesare he easiest o detect iom seismic
data seeSect ion .3.1 ) .
Harclsandswith gas, epresentingAVO class anomalies,will plot in the4th quadrant
(lower right) and have positive R(0) and negative G. Consequently, hese sands end
to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented),
they will not show a large change n seismicresponsewhen we go from brine to gas
(cf. Chapter ). This type of AVO anomalywill not showup as ananomaly n a product
stack. In fact, they can plot on top of the background trend of some softer, brine-
saturated ands.Hence,very stifTsandswith hydrocarbons an be hardto discriminate
with AVO analysis.
AVO class II anomalies, epresentingsandssaturatedwith hydrocarbons hat have
very weak zero-offset contrast compared with the cap-rock,can show great overlap
with the backgroundrend,especiallyf the sands re elativelydeep.However, lass I
type oil sands an occurvery shallow, ausingdim spots ha t stickout comparedwith
a bright background esponse i.e.,when heterolithics nd brine-saturatedandsar e
relatively stifTcomparedwith overlying shales).However, because hey are dim they
are easy o miss n near-or full-stack seismicsections,andAVO analysiscan therefore
be a very helpful tool in areaswith class I anomalies.Castagnaand Swan (199'l) discovereda diff'erent ype of AVO response or some
gas sands,which they ref-erredo as class IV AVO anomalies (see Table 4. ), or a
"false negative." They found that in some rare cases,gas sandscould have negative
R(0) and positive G, henceplotting in the 2nd quadrant (upper left quadrant).They
showed hat this may occur if the gas-sand hear-wave elocity is lower than hat of the
overlying ormation.The most ikely geologicscenarioor suchan AV O anomaly s n
unconsolidated andswith relatively arge Vp Vs ratio(Fosteret crl.,1997).That means
that f the cap-rock s a shale, t must be a relativelystiff and rigid shale,normally a
very silt-rich shale.This AVO response an confuse he nterpreter.First, the gradients
of sandsplotting in the 2nd quadrant end to be relatively small, and less sensitive o
fluid type than the gradients or sandsplotting in the 3rdquadrant.Second, heseAVO
anomalieswill actually showup as dim spots n a gradientstack.However, hey should
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208 Commonechniquesor quantitativeeismicnterpretation-
standout in an R(0)-G cross-plot,with lower R(0) values han the background rend.
Seismically,hey shouldstandout as negative right spots.
Pitfalls
. Different ockphysics renclsn AVO cross-plots anbe ambiguous. he nterpreta-
tion of AVO trends houldbe basedn
locallyconstrainedock physicsmodeling.
not on naive u lesof thumb.
. Trendswithin individualclusters ha tdo not project hrough heorigin on an AVO
cross-plol. annot always be interpreted s a hydroc arbon ndicatoror unusual
l ithology.Sams 1998) showed hat t is possible ortrends to have ar geoffsets
from the origin even when no hydrocarbons re present nd the lithology is not
unusual.Only where the rocks on eitherside of th e reflectingsurfacehave the
same Vp/V5 ratio will the lrends not to be confusedwith background rendsas
shown n Figure4. 2.l project hrough he origin. Samsshowedan exampleof a
brine sand hat appearedmoreanomalousha na Iessporoushydrocarbon-bearing
sand.
. Residualga ssaturation an causesimilar AV O effects o high saturations f ga s
or l ight oil. Three-termAVO where reliableestimates f densityar eoblained.or
attenuation ttributes. an potentiallydiscriminate esidualga s saturationsrom
commercialamountsof hydrocarbons se eSections .3.12 an d4.3. 5 for further
discussions).
Noise trends
A cross-plot etweenR(0) and G will also ncludea noise rend,because f the corre-
lation betweenR(0) and G. BecauseR(0) and G are obtained rom least-square itting,
there is a negativecorrelation between R(0) and G. Larger interceptsare correlated
with smallerslopes br a given dataset.Hence,uncorrelatedandomnoisewill showan oval, correlateddistribution n the cross-plotas seen n Figure 4.13 (Cambois,
2000).
Furthermore,Cambois (2001) formulated he influenceof noise on R(0), G and
a range-limited tack i.e.,sub-stack) n termsof approximate quations f standard
deviations:
3dR(o) :
;o,/,^ / ;' J V - ) o \
f t - - -" t i
-^ )
z s tn-0n, "
t;
( I/t( l ) )
o C : V f . r ^sln-umrx
(4.38)
(4.3e)
(4.40)
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209-
4.3 AVO nalysis
-0.1
ir .}
*
,l
"t;
-0.15 -0"1 -0.05 0
I (0)
0.05 0. 1 0.15
Figure ,13 Randomnoisehasa ttend n rR(0) ersusG (afterCambois,2000)
and
o,, Ji .o, (4.41)
whered"
s the standard eviationof the ull-stackresponse, , is the standard eviation
of the sub-stack.and n is the number of sub-stacks f the full fold data.As we see, he
stack reduces he noise in proportion to the square oot of the fold. These equationsindicate that the intercept is less robust than a half-fold sub-stack,but more robust
than a third-fold sub-stack.The gradient s much more unreliable,since he standard
deviation of the gradient s inverselyproportional o the sinesquaredof the maximum
angle of incidence. Eventually, the intercept uncertainty related to noise is more or
less nsensitive o the maximum incidenceangle,whereas he gradientuncertaintywill
decreasewith increasingaperture Cambois,2001 .
Simm er a/. (2000)claimed hatwhile rock property nfbrmation is contained n AVO
cross-plots, t is not usually detectable n terms of distinct trends,owing to the effect
of noise.The fact that the slopeestimation s more uncertain han the interceptduring
a least-squarenversion makes he AVO gradient more uncertain han the zero-offset
reflectivity (e.g.,Houck, 2002).Hence, he extensionof a trendparallel o the gradientaxis s an indicationof the amountof noise n the data.
-,:'i.;.d-f,*t'i;l?4 , , r
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211 4.3 AVO nalysis-
and G that include the variability and background rends. Houck (2002) presenteda
methodology or quantifyingan dcornbining hegeologicor rockphysicsuncertainties
with uncertaintieselated o noiseand measurement,o obtaina full characterizationf
the uncertainty ssociated ith an AVO-basedithologic nterpretation. hesemethod-
ologies br quantif ication f AVO uncertainties reexplained n Section4.3.12.
Howo assesshenoiseontentnAVOross-plots
. Make cross-plots f full stackversusgradient. n addition o R(01versusC. Th e
stackshould have no comelationwith th e gradient.so if trends n R(0t-C plots
are sti l l observed n stackvs. G, these rends houldbe real and nol randomnoise
(Cambois.2000).
. ldentify the location of AVO anomalies n seismic sections.Color-code AVO
anomalies n R (0)-6 plots and then superimpose hemonto your seismicsec-
tions.Do the anomaliesmakegeologicsenseshape. ocation), r do they spread
out randomly?
. Plot he regression oefficient f RlO)and C inversion nto the seismic o identify
the areaswhereR(0) and
G areess eliable.
. Cross-plota limiteclnumber of samples rom the samehorizon from a seismic
section. he extension f the rendalong hegradient xis ndicates he amountof
noise n the data Simm et a\..2000).
4.3.11AVOttributesorhydrocarbonetection
The information in the AVO cross-plots an be reduced o one-dimensional arameters
basedon linear combinationsof AVO parameters. his will make he AVO infbrmation
easier to interpret. Various attributes have been suggested n the literature , and we
summarize he most common below (AVO inversion-based ttributesare discussed n
Section4.4).
Far- versus near-stack attributes
One can createseveralAVO attributes rom limited-rangestack sections.The far stack
minus the near stack FN) is a "rough" estimateof an AVO gradient,and n particular t
is fbund to be a good attribute rom which to detectclass I AVO anomalies Rossand
Kinman, 1995).For class I type prospects, he f-arstack alone can be a good attribute
for improved delineation.However, br class Ip anomalies,both the near and the thr
stackcan be relatively dim, but with oppositepolarities. Then the difTerence e tween
far andnear will manifest he significantnegativegradient hat s present. n contrast,a
conventional ull stack will completely zero-out a class Ip anomaly.Rossand Kinman(1995) suggestedhe fbllowing equation for the FN attribute depending on whethe r