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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

-

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



16 9-

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



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



rmpe0ance

1

t

171-

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.



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).



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



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



175T

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.



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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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



178T

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



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:



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,



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




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)+(:.'#)#+



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



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)



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



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



(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




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




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



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



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



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.




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.



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




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



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



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



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).



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 . ) .



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

^



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



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).



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.



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)



VplVs=2.5ncaP-rock


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



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



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)



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



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

commotenc hniqufeosr q uantitative

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