Common echniques or quantitative seismic nterpretation Until a few decades ago, it would be lheir several-meters-long aper ections I 4 - There ar e no facts, only interpretations. lriedrith Niet:sche - 4.1 Introduction Conventional eismic nterpretation mplies picking and tracking aterally consistent seismic reflectors or th e purpose of mapping geologic structures, stratigraphy an d reservoir rchitecture. he ultimate goal s to detect ydrocarbon ccumulations, elin- eate heir extent, and calculate heir volumes. Conventional seismic nterpretation s an art that requires skill and thorough experience n geology an d geophysics. Traditionally, seismic nterpretation ha s been essentially qualitative. Th e geometrical expression f seismic eflectors s thoroughly mapped n space and raveltime, bu t litfle emphasis s pu t on th e physical understanding f seismic amplitude variations. n the last few decades, owever, seismic nterpreters have put increasing emphasis on more quantitative echniques br seismic interpretation, as these can validate hydrocarbon anomalies an d give additional information during prospect evaluation and reservoir characterization. he most mportant of these echniques nclude post-stack amplitucle analysis bright-spot nd dim-spot analysis), ffset-dependent mplitude nalysis A VO analysis), coustic nd elastic mpedance nversion, nd orward seismic modeling. These echniques, f used properly, open up ne w doors for the seismic interpreter. Th e seismic amplitudes, epresenting rimarily contrasts n elastic properties etween individual ayers, contain nformation about ithology, porosity, pore-fluid ype and sat- uration, as well as pore pressure information that cannot be gained io m conventional seismic nterpretalion. - 4 . 2 Qualitativeseismicamplitude nterpretation common for seismic interpreters o roll ou t with seismic data down the hallway, go down 16 8
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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.
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
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.
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
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.
' 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
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,
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
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
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.
:fff!;"{riii;iiiffr,))) ) t )l)))))))))ft) )) D,D)), ) D,D) D r,Dr>),
i)P,?),,?l?,l?? )?i)i)
iriiiiiiiiiii)ii)i)l r l l l l i i l r l l l l l i
Plate1,1 SeismicP-P amplitudemap overa sub marine an. Theamplitudes re sensitiveo lithofacies nd
pore luids,but the relationvariesacross he magebecause fthe interplayofsedimentologicanddiagenetic
influences. lue indi cates ow amplitudes, ellow and ed high amplitudes.
2.9 lilllWi7",4120
4140
41 0
41B0
5 4200oo
4220
4240
4260
4280
4300
VP rho* /p
Distance
Plate1,30 Top eft, ogs penetrating sandy urbiditesequence;op right, normal-incidenceyntheticswith a
50 Hz Rickerwavelet.Bottom: ncreasingwatersaturation * from l1a/c o907c oi l API 35, GOR 200)increases ensityand Vp left), giving both amplitudeand raveltime hangesright).
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
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,
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
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
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
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
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.
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
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
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.
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
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 . ) .
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
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
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.
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