I
techniques
forquantitative
4 Common
seismic
interpretation
-
Thereare no facts,only interpretations.
lriedrith
Niet:sche
-
4.1 Introduction
Conventionalseismicinterpretationimplies picking and tracking laterally consistent
seismic reflectors for the purpose of mapping geologic structures,stratigraphy and
reservoirarchitecture.
The ultimategoal is to detecthydrocarbonaccumulations,
delineatetheir extent, and calculatetheir volumes.Conventionalseismic interpretationis an
art that requires skill and thorough experiencein geology and geophysics.
Traditionally, seismicinterpretationhasbeenessentiallyqualitative.The geometrical
expressionof seismic reflectorsis thoroughly mapped in spaceand traveltime,but litfle
emphasisis put on the physicalunderstandingof seismicamplitudevariations.In the
last few decades,however, seismic interpretershave put increasingemphasison more
quantitative techniques fbr seismic interpretation,as these can validate hydrocarbon
anomalies and give additional information during prospect evaluation and reservoir
characterization.The most important of thesetechniquesinclude post-stackamplitucle
analysis(bright-spotanddim-spotanalysis),offset-dependent
amplitudeanalysis(AVO
analysis),acousticand elasticimpedanceinversion,and forward seismicmodeling.
These techniques,if used properly, open up new doors for the seismic interpreter.
The seismicamplitudes,representingprimarily contrastsin elasticpropertiesbetween
individual layers,contain information about lithology, porosity,pore-fluid type and saturation, as well as pore pressure- information that cannot be gained fiom conventional
s e i s m i ci n t e r p r e t a l i o n .
-
4.2 Qualitativeseismicamplitude
interpretation
Until a few decades ago, it would be common for seismic interpreters to roll out
l h e i r s e v e r a l - m e t e r s - l opnagp e rs e c t i o n swith seismic data down the hallway, go down
168
169
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interpretation
4,2 Qualitative
seismicamplitude
on their knees,and use their colored pencils to interpretthe horizons of interestrn
order to map geologic bodies. Little attention was paid to amplitude variations and
their interpretations.In the early 1970sthe so-called"brighrspot" techniqueproved
successfulin areasof the Gulf of Mexico, wherebright amplitudeswould coincidewith
gas-filled sands.However, experiencewould show that this technique did not always
work. Some of the bright spots that were interpreted as gas sands,and subsequently
drilled, were fbund to be volcanic intrusions or other lithologies with high impedance
contrast compared with embedding shales.These tailures were also related to lack of
waveletphaseanalysis,ashardvolcanicintrusionswould causeoppositepolarityto lowimpedance gas sands.Moreover, experienceshowed that gas-filled sands sometimes
could cause"dim spots," not "bright spots," if the sandshad high impedancecompared
with surroundingshales.
With the introductionof 3D seismicdata, the utilization of amplitudesin seismic
interpretation became much more important. Brown (see Brown et ul., l98l) was
one of the pioneersin 3D seismicinterpretationof lithofaciesfiom amplitudes.The
generationoftime slicesand horizon slicesrevealed3D geologic patternsthat had been
impossible to discover from geometric interpretationof the wiggle tracesin 2D stack
sections.Today, the further advance in seismic technology has provided us with 3D
visualizationtools where the interpretercan stepinto a virtual-realityworld of seismic
wiggles and amplitudes, and trace these spatially (3D) and temporally (4D) in a way
that one could only dream of a few decadesago. Certainly, the leap fiom the rolled-out
paper sectionsdown the hallways to the virtual-reality imagesin visualization "caves"
is a giant leap with greatbusinessimplicationsfor the oil industry.In this sectionwe
review the qualitative aspectsof seismicamplitude interpretation,before we dig into the
techniquessuchasAVO analysis,impedance
more quantitativeand rock-physics-based
inversion,and seismicmodeling,in fbllowing sections.
phaseandpolarity
4.2.1 Wavelet
The very first issue to resolve when interpreting seismic amplitudes is what kind of
wavelct we have. Essentialquestionsto ask are the fbllowing. What is the defined
I
polarity in our case?Are we dealingwith a zero-phaseor a minimum-phasewavelet?
Is there a phase shift in the data? These are not straightfbrward questions to answet,
becausethe phase of the wavelet can change both laterally and vertically. However,
there are a f'ew pitfalls to be avoided.
First, we want to make sure what the defined standardis when processingthe data.
There exist two standards.The American standarddefinesa black peak as a "hard" or
"positive" event,and a white trough as a "soft" or a "negative"event.On a near-ofl.set
stack section a "hard" event will correspondto an increasein acousticimpedancewith
depth, whereasa "soft" event will correspondto a decreasein acousticimpedancewith
depth. According to the European standard,a black peak is a "soft" event, whereas a
170
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techniques
for quantitative
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white trough is a "hard" event. One way to check the polarity of marine data is to look
at the sea-floorreflector.This reflector should be a strongpositive reflector representing
the boundary between water and sediment.
Datapolarity
' American polarity: An increasein impedancegives positiveamplitude.
normally
displayedas black peak (wiggle r.race)or red intensitylcolor displayt.
. European(or Australian)polarity:An increasein impedancegives
negal.ive
amplitude, normally displayedas white rrough (wiggle trace) or blue intensity(color
display).
(Adaptedfrom Brown. 200la, 2001b)
For optimal quantitative seismic interpretations,we should ensurethat our data are
zero-phase.Then, the seismicpick should be on the crest of the waveform conesponding with the peak amplitudes that we desire for quanrirativeuse (Brown, l99g). with
today's advanced seismic interpretation tools involving the use of interactive workstations,there exist various techniquesfbr horizon picking that allow efficient interpretationof large amountsof seismicdata.Thesetechniquesinclude manualpicking,
interpolation,autotracking,voxel tracking, and surfaceslicing (see Dorn (199g) fbr
detaileddescriptions).
For extraction of seismic horizon slices, autopicked or voxel-tracked horizons are
very common. The obvious advantageof autotracking is the speed and efficiency.
Furthermore, autopicking ensuresthat the peak amplitude is picked along a horizon.
However,one pitfall is the assumptionthat seismichorizons are locally continuous
and consistent.A lateral change in polarity within an event will not be recognized
during autotracking.Also, in areasof poor signal-to-noiseratio or where a single event
splits into a doublet, the autopicking may fail to track the corect horizon. Not only
will important reservoirparametersbe neglected,but the geometriesand volumes may
also be significantly off if we do not regard lateral phaseshifts. It is important that the
interpreterrealizesthis and reviewsthe seismicpicks for quality control.
4.2.2 Sand/shale
cross-overs
with depth
Simple rock physicsmodeling can assistthe initial phaseof qualitativeseismicinrerpretation, when we are uncertain about what polarity to expect for diff'erentlithology
boundaries.
In a siliciclasticenvironment,most seismicreflectorswill be associated
with
sand-shaleboundaries.Hence, the polarity will be related to the contrastin impedance
between sand and shale.This contrastwill vary with depth (Chapter 2). Usually, relatively sott sandsare fbund at relatively shallow depths where the sandsare unconsolidated. At greater depths, the sandsbecome consolidatedand cemented.whereas the
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4.2 Qualitative
seismicamplitude
interpretati0n
Sandversus
shaleimpedance
depthtrends
polarity
(schematic)
andseismic
rmpe0ance
1
t
Sand-shale
cross-over
DeDth
Figure4'1 Schematic
depthtrendsof sandandshaleimpeclances.
Thedepthtrendscanvaryfiom
basinto basin,andtherecanbe morethanonecross-over.
Localdepthtrendsshouldbeestablished
for differentbasins.
shalesare mainly affectedby mechanicalcompaction.Hence, cementedsandstonesare
normally found to be relatively hard eventson the seismic.There will be a corresponding cross-overin acousticimpedanceof sandsand shalesas we go fiom shallow and soft
sandsto the deep and hard sandstones(seeFigure 4.1). However, the depth trends can
be much more complex than shown in Figure 4.1 (Chapter2, seeFigures 2.34 and,2.35').
Shallow sandscan be relatively hard comparedwith surroundingshales,whereasdeep
cementedsandstonescan be relatively soft compared with surounding shales.There
is no rule of thumb fbr what polarity to expect fbr sandsand shales.However, using
rock physics modeling constrainedby local geologic knowledge, one can improve the
understandingof expectedpolarity of seismic reflectors.
"Hard"venius"soft"events
During seismicinterpretationof a prospector a provenreser"yoir
sand.the following
questionshould be one of the first to be asked:what type of event do we expect,
a "hard" or a "soft"? [n other words. should we pick a positivepeak, or a negative
trough?lfwe havegood well control,this issuecan be solvedby generatingsynthetic
seismograms
and correlatingthesewith realseismicdata.If we haveno well control,
we may have to guess. However. a reasonableguess can be made based on rock
physics modeling. Below we have listed some "rules of thumb" on what type of
reflector we expect l-ordifferent geologic scenarios.
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Common
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T
Typical
"hard"events
. Very shallow sandsat normal pressureembeddedin pelagicshales
. Cementedsandstonewith brine saluration
. Carbonaterocks embeddedin siliciclastics
' M i x e c ll i t h o l o g i e s( h e t e r o l i t h i c sl i)k e s h a t ys a n d s m
, a r l s .v o l c a n i ca s hd e p o s i t s
Typical"soft" events
. Pelagic
shale
' S.hallow,unconsolidated
sands(any pore fluid) embeddedin normally compacted
shales
' Hydrocarbonaccumularionsin clean.unconsolidated
or poorly consolidatedsancls
. Overpressured
zones
Somepitfallsin conventional
interpretation
' Make sure you know the polarity of the data. Rememberthere are two
different
standards,the US standardand the Europeanstandard.which are opposire.
' A hard event can changeto a soft laterally (i.e.. lateralphaseshifi;
if there are
petrographicor pore-fluidchanges.Seismicaurotrackingwill nor derecr
l:jloloCic.
these.
' A d i m s e i s m i cr e f l e c t o ro r i n t e r v a lm a y b e s i g n i f i c a n te. s p e c i a l l yi n
t h e z o n eo f
sand/shaleimpedancecross-over.AVO analysisshould be underrakento reveal
potentialhydrocarbonaccumulations.
I
ii
ji
4.2.3 Frequency
andscaleeffects
Seismic resolution
Verticalseismicresolutionis definedas theminimum separationbetweentwo interfaces
such that we can identify two interfacesrather than one (SherifTand Geldhart, 199-5).
A stratigraphiclayer can be resolvedin seismicdataif the layer thicknessis largerthan
a quarter of a wavelength.The wavelength is given by:
\
-
t/ /f
(4.1)
where v is the interval velocity of the layer, and.l is the frequency of the seismic wave. lf the wavelet has a peak frequency of 30 Hz, and the layer velocity is
3000 m/s, then the dominant wavelengthis 100 m. In this case,a layer of 25 m can
be resolved.Below this thickness,we can still gain important infbrmation via quantitative analysisof the interferenceamplitude.A bed only ),/30 in thicknessmay be
detectable,althoughits thicknesscannotbe determinedfiom the wave shape(Sheriff and
Geldhart.199-5).
173
E
interpretation
seismicamplitude
4.2 Qualitative
tiickness
Layer
fbr a givenwavelength.
of layerthickness
asa function
amplitude
4,2 Seismic
Figure
The horizontal resolution of unmigrated seismic data can be defined by the Fresnel
zone. Approximately, the Fresnel zone is defined by a circle of radius, R, around a
r e l l e c t i o np o i n t :
n - Jgz
G.2)
where z is the reflector clepth.Roughly, the Fresnel zone is the zone from which all
reflected contributions have a phase difl-erenceof less than z radians. For a depth of
3 km and velocity of 3 km/s, the Fresnelzone radius will be 300-470 m for fiequencies
ranging fiom 50 to 20 Hz. When the size of the reflector is somewhat smaller than
the Fresnel zone, the responseis essentiallythat of a diffraction point. Using prestack migration we can collapse the difliactions to be smaller than the Fresnel zone,
thus increasingthe lateralseismicresolution(Sheriff and Geldhart,1995).Depending
on the migration aperture, the lateral resolution after migration is of the order of a
wavelength.However,the migration only collapsesthe Fresnelzone in the direction
of the migration, so if it is only performed along inlines of a 3D survey, the lateral
resolution will still be limitecl by the Fresnelzone in the cross-linedirection. The
lateral resolution is also restricted by the lateral sampling which is governed by the
spacing between individual CDP gathers,usually 12.5 or 18 meters in 3D seismic
clata.For typical surf'aceseismic wavelengths(-50-100 m), lateral sampling is not the
l i m i t i n gl a c t o r .
Interference and tuning effects
A thin-layered reservoir can cause what is called event tuning, which is interf'erence
betweenthe seismicpulse representingthe top of the reservoirand the seismicpulse
representingthe baseof the reservoir.This happensif the layer thicknessis less than a
quarterof a wavelength(Widess,1973).Figure 4.2 showsthe efTectiveseismicamplitude as a function of layer thickness for a given wavelength, where a given layer
has higher impedancethan the surrounding sediments.We observethat the amplitude
174
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techniques
for quantitative
seismicinterpretation
increasesand becomes larger than the real reflectivity when the layer thickness is
between a half and a quarter of a wavelength. This is when we have constructive
interference between the top and the base of the layer. The rlaximum constructive
interferenceoccurs when the bed thickness is equal to ),14, and this is often referred
to as the tuning thickness.Furthermore, we observethat the amplitucledecreasesand
approacheszero for layer thicknessesbetween one-quarterof a wavelength and zero
thickness. We refer to this as destructive interferencebetween the top and the base.
Trough-to-peaktime measurements
give approximatelythe correctgrossthicknesses
for thicknesseslarger than a quarterof a wavelength,but no information fbr thicknesses
lessthan a quarterof a wavelength.The thicknessof an individualthin-bedunit can be
extractedfrom amplitude measurementsif the unit is thinner than about ),/4 (Sheriff
and Geldhart,1995).When the layer thicknessequals)./8, Widess(1973) found that
the composite responseapproximatedthe derivative of the original signal. He referred
to this thickness as the theoretical threshold of resolution. The amplitude-thickness
curve is almost linear below ),/8 with decreasingamplitudeas the layer gets thinner,
but the compositeresponsestaysthe same.
4.2.4 Amplitude
andreflectivity
strength
"Bright spots" and "dim spots"
The first use of amplitude information as hydrocarbon indicators was in the early
1970swhen it was fbund that bright-spotamplitude anomaliescould be associated
with hydrocarbon traps (Hammond, 1974). This discovery increased interest in the
physical propertiesof rocks and how amplitudeschangedwith difTerenttypes of rocks
and pore fluids (Gardner et al., 1914').In a relatively soft sand, the presenceof gas
and/or light oil will increasethe compressibilityof the rock dramatically,the velocity will drop accordingly,and the amplitudewill decreaseto a negative"bright spot."
However, if the sand is relatively hard (compared with cap-rock), the sand saturated
with brine may induce a "brighlspot" anomaly,while a gas-filledsandmay be transparent, causing a so-calleddim spot, that is, a very weak reflector.It is very important
before startingto interpret seismicdata to find out what changein amplitude we expect
for different pore fluids, and whether hydrocarbonswill cause a relative dimrning or
brighteningcomparedwith brine saturation.Brown (1999)statesthat "the most impnrtant seismic property of a reservoir is whether it is bright spot regime or tlim sltot
regime."
One obvious problem in the identification of dim spotsis that they are clim - they are
hard to see.This issuecan be dealt with by investigatinglimited-rangestack sections.
A very weak near-offsetreflector may have a correspondingstrong f'ar-oflsetreflector.
However,some sands,although they are significant,produce a weak positive nearoffset reflection as well as a weak negative far-offset reflection. Only a quantitative
analysisof the changein near-to far-offsetamplitude,a gradientanalysis,will be able
175
T
interpretation
seismicamplitude
4.2 Qualitative
to reveal the sand with any considerabledegree of confidence. This is explained in
Section4.3.
Pitfalls:False"bright spots"
During seismicexplorationof hydrocarbons."brighr spots"are usuallythe first type
of DHI (direct hydrocarbonindicators)one looks for. However.there have been
severalcaseswhere bright-spotanomalieshavebeendrilled. and turned out not lo
be hydrocarbons.
Some common "false bright spors"include:
. Volcanicintrusionsand volcanicash layers
. Highly cementedsands.often calcitecementin thin pinch-outzones
. Low-porosityheterolithicsands
. Overpressured
sandsor shales
. Coal beds
. Top of salt diapirs
Only the last threeon the list abovewill causethe samepolarity as a gas sand.The
first three will causeso-called"hard-kick" amplitudes.Therefore.if one knows the
bright
polariryof the dataone shouldbe able lo discriminarehydrocarbon-associated
"hard-kick"
permit
discrimination
should
AVO
analysis
anomalies.
spots from the
sands/shales.
of hydrocarbonsfrom coal, salt or overpressured
among seismicinterpretersis
used
attribute
A very common seismicamplitude
amplitudescalculatedover a given
rellectionintensity,which is root-mean-square
lime window. This anribute does not distinguish between negativeand positive
amplitudes;thereforegeologic interpretationol this attributeshould be made with
greatcaution.
"Flat spots"
Flat spotsoccur at the reflectiveboundary betweendifferent fluids, either gas-oil, gaswarer,or warer-oil contacts.Thesecan be easyto detectin areaswhere the background
stratigraphyis tilted, so the flat spot will stick out. However, if the stratigraphyis more
or less flat, the fluid-related flat spot can be difficult to discover. Then, quantitative
methods like AVO analysiscan help to discriminate the fluid-related flat spot from the
fl arlying lithostratigraphy.
One should be aware of severalpitfalls when using flat spots as hydrocarbon indicators. Flat spots can be related to diagenetic events that are depth-dependent.The
boundary between opal-A and opal-CT representsan impedance increasein the same
way as fbr a fluid contact, and dry wells have been drilled on diagenetic flat spots.
Clinoforms can appear as flat features even if the larger-scalestratigraphy is tilted.
sheet-flooddepositsand
Other "false" flat spotsinclude volcanicsills, paleo-contacts,
flat basesof lobesand channels.
tl
176
-
for quantitative
Common
techniques
seismicinterpretation
Pitfalls:
False
"flatspots"
One of f he best DHIs ro look for is a flat spot, the contactbetweengas and water,
gas and oil, or oil and water.However.there are other causesthat can give rise to
flat spots:
. Oceanbottom multiples
. Flat stratigraphy.The basesof sand lobesespeciallytend to be flat.
. Opal-A to opal-CT diageneticboundary
. Paleo-contacts,
either relatedto diagenesisor residualhydrocarbonsaturation
. Volcanicsills
Rigorousflat-spotanalysisshould include detailedrock physicsanalysis.and forward seismicmodeling,as well as AVO analysisof real data(seeSection4.3.8).
Lithology, porosity and fluid ambiguities
The ultimategoal in seismicexplorationis to discoverand delineatehydrocarbonreservoirs. Seismic amplitude maps from 3D seismicdata are often qualitarlvel.finterpreted
t
I
lt
il
i,
in termsof lithology and fluids.However,rigorousrock physicsmodelingand analysis
of available well-log data is required to discriminate fluid effects quantitatively trom
lithology effects (Chapters I and 2).
The "bright-spot" analysismethod has ofien been unsuccessfulbecauselithology
effects rather than fluid eff-ectsset up the bright spot. The consequenceis the drilling of
dry holes.In order to reveal"pitfall" amplitude anomaliesit is essentialto investigatethe
rock physicspropertiesfiom well-log data.However,in new frontier areaswell-1ogdata
are sparseor lacking. This requiresrock physicsmodeling constrainedby reasonable
geologic assumptionsand/or knowledge about local compactionaland depositional
trends.
A common way to extractporosity from seismicdata is to do acousticimpedance
inversion.Increasingporositycan imply reducedacousticimpedance,and by extracting empiricalporosity-impedance
trendsfrom well-log data,one can estimateporosity
from the inverted impedance.However, this methodology suffers from several ambiguities. Firstly, a clay-rich shalecan have very high porosities,even if the permeability
is closeto zero.Hence,a high-porosityzone identifiedby this techniquemay be shale.
Moreover, the porosity may be constant while fluid saturationvaries, and one sin-rple
impedance-porositymodel may not be adequatefbr seismicporositymapping.
In addition to lithology-fluid ambiguities, lithology-porosity ambiguities, and
porosity-fluid ambiguities,we may have lithology-lithology ambiguitiesand fluidfluid ambiguities.Sand and shalecan have the sameacousticimpedance,causingno
reflectivity on a near-offset seismic section. This has been reported in several areas
of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that
fluvial channelsor turbidite channelsare dim on seismic amplitude maps, and the
Plate1,1 SeismicP-P amplitudemap over a submarinefan. The amplitudesare sensitiveto lithofaciesand
pore fluids, but the relationvariesacrossthe imagebecauseofthe interplayofsedimentologicand diagenetic
influences.Blue indicateslow amplitudes,yellow and red high amplitudes.
4120
4140
2.92
4160
2.94
41B0
5
o
4200
E
o
o
2.96
F
4220
2.98
4240
3
4260
4280
3.02
4300
rn0
VP
rho*l/p
lilllWi7",
:fff!;"{riii;iiiffr
2.9
,)))))))t)))l)))))))))f
))
t) )) D,D
) )), ) D,D
D)) Dr r,D)r>),
),l?? )?i)i)p
i)P,?),,?l?
iriiiiiiii
iiiiir)ii)i)
ii
lrlllliilrlllllil,
10
15
Distance
20
25
Plate1,30 Top left, logs penetratinga sandyturbidite sequence;top right, normal-incidencesyntheticswith a
50 Hz Ricker wavelet.Bottom: increasingwater saturationS* from l1a/cLo907c(oil API 35, GOR 200)
increasesdensityand Vp (left), giving both amplitudeand traveltimechanges(right).
177
r
interpretation
4.2 Qualitative
seismicamplitude
interpretation is usually that the channel is shale-filled. However, a clean sand filling in the channel can be transparentas well. A geological assessmentof geometries
indicating differential compaction above the channel may reveal the presenceof sand.
More advancedgeophysical techniquessuch as offset-dependentreflectivity analysis
may also reveal the sands.During conventionalinterpretation,one should interpret top
reservoir horizons from limited-range stack sections,avoiding the pitfall of missing a
dim sandon a near-or full-stackseismicsection.
Facies interpretation
Lithology influence on amplitudes can often be recognized by the pattern of amplitudes as observed on horizon slices and by understandinghow different lithologies
occur within a depositionalsystem.By relatinglithologiesto depositionalsystemswe
often refer to theseas lithofacies or f-acies.The link between amplitude characteristics
and depositional patternsmakes it easierto distinguish lithofacies variations and fluid
changesin amplitudemaps.
Traditional seismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon
seismictraveltimes.The traditionalmethodologyconsistedof purely visual inspection
of geometricpatternsin the seismicreflections(e.g.,Mitchum et al., 1977;Weimer and
Link, l99l ). Brown et al. (1981),by recognizingburiedriver channelsfrom amplitude
information, were amongst the first to interpret depositional facies from 3D seismic
amplitudes.More recent and increasinglyquantitativework includesthat of Ryseth
et al. (.1998)who used acoustic impedance inversions to guide the interpretation of
sand channels, and Zeng et al. (1996) who used forward modeling to improve the
understandingof shallow marine facies from seismic amplitudes.Neri (1997) used
neuralnetworksto map faciesfrom seismicpulse shape.Reliablequantitativelithofacies
prediction fiom seismicamplitudesdependson establishinga link betweenrock physics
properties and sedimentaryfacies. Sections2.4 and 2.5 demonstratedhow such links
might be established.The case studies in Chapter 5 show how these links allow us to
predict litholacies from seismic amplitudes.
Stratigraphic interpretation
The subsurfaceis by nature a layered medium, where different lithologies or f'acies
have been superimposedduring geologic deposition. Seismic stratigraphicinterpretation seeksto map geologic stratigraphyfrom geometricexpressionof seismicreflections
in traveltime and space.Stratigraphic boundariescan be defined by dilferent lithologies (taciesboundaries)or by time (time boundaries).These often coincide,but not
always. Examples where facies boundaries and time boundaries do not coincide are
erosional surfacescutting across lithostratigraphy,or the prograding fiont of a delta
almost perpendicularto the lithologic surf'aceswithin the delta.
There are severalpittalls when interpretingstratigraphyfiom traveltime infbrmation.
First, the interpretationis basedon layer boundariesor interf'aces,that is, the contrasts
a
178
seismicinterpretation
for quantitative
techniques
Gommon
T
between diff'erent strata or layers, and not the properties of the layers themselves.
Two layers with different lithology can have the same seismic properties; hence, a
lithostratigraphic boundary may not be observed. Second' a seismic reflection may
occur without a lithology change(e.g.,Hardage,1985).For instance,a hiatuswith no
depositionwithin a shaleintervalcan give a strongseismicsignaturebecausethe shales
above and below the hiatus have difTerent characteristics.Similarily, amalgamated
sandscan yield internal stratigraphywithin sandy intervals,reflecting different texture
of sanclsfiom difl-erentdepositionalevents.Third, seismicresolution can be a pitfall in
seismicinterpretation,especiallywhen interpretingstratigraphiconlapsor downlaps.
Theseareessentialcharacteristicsin seismicinterpretation,asthey can give information
about the coastal development related to relative sea level changes (e.g., Vail er ai.,
I 977). However, pseudo-onlapscan occur if the thicknessof individual layers reduces
beneaththe seismicresolution.The layer can still exist,even if the seismicexpression
yields an onlap.
Pittalls
that can
Thereareseveralpitfalls in conventionalseismicstratigraphicinterpretation
be avoidedif we usecomplementaryquantitativetechniques:
. lmportant lithostratigraphicboundariesbetweenlayerswith very weak contrasts
in seismicpropefiiescan easily be missed.However.if different lithologiesare
transparentin post-stackseismicdata.they arenormallyvisiblein pre-stackseismic
dara. AVO analysisis a useful tool to reveal sandswith impedancessimilar to
c a p p i n gs h a l e s{ s e eS e c t i o n4 . 3 1 .
. It is commonlybelievedthatseismiceventsaretime boundaries.andnot necessarily
lithostratigraphicboundaries.For instance.a hiatus within a shale may causea
strong seismicreflectionif the shaleabovethe hiatus is lesscompactedthan the
onc below.even if the lithology is the same.Rock physicsdiagnosticsof well-log
data may revealnonlithologicseismicevents(seeChapter2 ).
. Becauseof limited seismicresolution,false seismiconlapscan occur.The layer
may still existbeneathresolution.Impedanceinversioncan improvethe resolution.
and revealsubtle srrailgraphicfeaturesnot observedin the original seismicdata
( s e eS e c t i o n4 . 4 ) .
Quantitative interpretation of amplituclescan add information about stratigraphic
patterns,and help us avoid some of the pitfalls mentioned above.First, relating lithology to seismic properties(Chapter 2) can help us understandthe nature of reflections,
and improve the geologic understandingof the seismic stratigraphy.Gutierrez (2001)
showed how stratigraphy-guidedrock physics analysis of well-log data improved the
sequencestratigraphicinterpretationof a fluvial systemin Colombia using impedance
inversion of 3D seismicdata. Conducting impedanceinversion of the seismic data will
179
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4,2 Qualitative
seismicamplitude
interpretation
give us layer propertiesfrom interfhceproperties,and an impedancecross-sectioncan
reveal stratigraphicfeaturesnot observedon the original seismic section. Impedance
inversion has the potential to guide the stratigraphicinterpretation,becauseit is less
oscillatorythan the original seismicdata,it is more readily correlatedto well-log data,
and it tends to averageout random noise, thereby improving the detectability of laterimpedance
ally weakreflections(Gluck et a\.,1997).Moreover,frequency-band-limited
inversioncan improve on the stratigraphicresolution,and the seismicinterpretationcan
be signilicantly modified if the inversionresultsare included in the interpretationprocedure. For brief explanationsof different types of impedanceinversions,seeSection4.4.
Forward seismicmodeling is also an excellenttool to study the seismicsignaturesof
geologicstratigraphy(seeSection4.5).
Layer thickness and net-to-gross from seismic amplitude
As mentioned in the previous section, we can extract layer thickness from seismic
amplitudes.As depictedin Figure 4.2,the relationshipis only linear for thin layersin
pinch-out zonesor in sheet-likedeposits,so one shouldavoid correlatinglayer thickness
to seismic amplitudes in areaswhere the top and baseof sandsare resolvedas separate
reflectorsin the seismic data.
Meckel and Nath (.1911)found that, for sands embedded in shale, the amplitude
would depend on the net sand present,given that the thicknessof the entire sequence
is less than ).14. Brown (1996) extended this principle to include beds thicker than
the tuning thickness,assumingthat individual sand layers are below tuning and that
the entire interval of interbeddedsandshas a uniform layering. Brown introduced the
"composite amplitude" defined as the absolute value summation of the top reflection
amplitude and the base reflection amplitude of a reservoir interval. The summation of
the absolute values of the top and the baseemphasizesthe eff'ectof the reservoir and
reducesthe effect of the embedding material.
Zeng et al. (.1996)studiedthe influenceof reservoirthicknesson seismicsignaland
introduced what they referred to as effective reflection strength, applicable to layers
thinnerthan the tunins thickness:
o'. - 2 " - Z ' n . ,
Zrr
(4.3)
where Z. is the sandstoneimpedance,216is the averageshaleimpedanceand /z is the
layerthickness.A more commonway to extractlayerthicknessfrom seismicamplitudes
is by linear regressionof relative amplitude versus net sand thickness as observed at
wells that are available.A recentcasestudy showing the applicationto seismicreservoir
mappingwas providedby Hill and Halvatis(2001).
Vernik et al. (2002) demonstratedhow to estimate net-to-grossfiom P- and Simpedances fbr a turbidite system. From acoustic impedance (AI) versus shear
impedance (SI) cross-plots, the net-to-gross can be calculated with the fbllowing
fbrmulas:
r
180
Common
techniques
for quantitative
seismicinterpretation
E
I
NIG:
VrungdZ
Zrr.
AZ
(4 4)
where V."n,lis the oil-sand fraction given bv;
SI-bAI-ce
Kano
at-ao
(4.-5)
where b is the averageslope of the shaleslope(06) and oil-sandslope(b1),whereasae
a n d z 7 ti i r e t h e r e s p e c t i v ien t e r c e p t isn t h e A I - S I c r o s s - p l o r .
c a l c u l a t i o no f r e s e r v o i rt h i c k n e s sf r o m s e i s m i ca m p l i t u d es h o u l db e d o n e o n l y i n
areaswhere sandsare expectedto be thinner than the tuning thickness.that is a
quarterof a wavelength.and wherewell-log datashow evidenceof good correlation
belweennet sandlhicknessand relativeamplirude.
It can be difficult to discriminatelayer rhicknesschangesfrom lirhologyand fluid
changes.In relativelysoft sands,the impactof increasingporosityand hydrocarbon
saturationtendslo increasethe seismicamplitude,and thereforeworks in the same
"direction" to Iayerthickness.However.in relativelyhard sands.increasingporosity
and hydrocarbonsaturationLendto decreasethe relalive amplitude and therefore
work in the opposite"direction" to layer thickness.
ilouo
anatysis
In 1984, 12 years afler the bright-spot technology became a commercial tool fbr
hydrocarbon prediction, ostrander published a break-through paper in Geophl-sics
(ostrander, 1984). He showed that the presenceof gas in a sand cappedby a
shale
would causean amplitude variation with ofTsetin pre-stackseismicdata.He also found
that this changewasrelatedto the reducedPoisson'sratio causedby the presenceofgas.
Then,the yearafter,Shuey(1985)confirmedmathematicallyvia approximationsof the
Zoeppritz equationsthat Poisson'sratio was the elasticconstantmost directly related
to the off.set-dependent
reflectivity fbr incident angles up to 30". AVo technology, a
commercial tool for the oil industry, was born.
The AVO techniquebecamevery popular in the oil industry,as one could physicaly
explainthe seismicamplitudesin termsof rock properties.Now, bright-spotanomalies
could be investigatedbeforestack,to seeif they also had AVo anomalies(Figure4.3).
The techniqueproved successfulin certain areasof the world, but in many casesit was
not successful.The technique sufI'eredfrom ambiguities causedby lithology efTects,
181
4.3 AVOanalysis
I
CDPgather
af interest
Stacksection
CDPgather
CDP
locqtion
Target harizon
. *{bu
Time
Geologic interpretation
AVO responseat
target horizon
Shale
0,1
-0
Sondstone
with gos
-0,
-0
Aryle ol inc,d?nca
Figure
4.3 Schematic
illustration
of theprinciples
in AVOanalysis.
tuning effects, and overburdeneft'ects.Even processingand acquisition effects could
causefalse AVO anomalies.But in many o1'thefailures,it was not the techniqueitself
that failed,but the useof the techniquethat was incorrect.Lack of shear-wavevelocity
informationandthe useof too simplegeologicmodelswerecommonreasonsfbr failure.
Processingtechniques that aff'ectednear-ofTsettraces in CDP gathers in a difl-erent
way from far-offset traces could also create talse AVO anomalies. Nevertheless,in
the last decade we have observed a revival of the AVO technique.This is due to the
improvementof 3D seismictechnology,betterpre-processing
routines,rnorefrequent
shear-wavelogging and improved understandingof rock physicsproperties,larger data
capacity,more fbcus on cross-disciplinaryaspectsof AVO, and last but not least,mclre
awarenessamong the usersof the potential pitfalls. The techniqueprovides the seismic
interpreter with more data, but also new physical dimensions that add infbrmation to
the conventional interpretationof seismic facies, stratigraphyand geomorphology.
In this section we describe the practical aspectsof AVO technology, the potential of this technique as a direct hydrocarbon indicator, and the pitfalls associated
with this technique. Without going into the theoretical details of wave theory, we
addressissuesrelatedto acquisition.processingand interpretationof AVO data. For
an excellent overview of the history of AVO and the theory behind this technology,
we refer the reader to Castagna(1993). We expect the luture application of AVO to
182
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Common
techniques
expandon today's common AVO cross-plotanalysisand hencewe include overviewsof
important contributions from the literature,include tuning, attenuationand anisotropy
effectson AVO. Finally, we elaborateon probabilistic AVO analysisconstrainedby rock
physicsmodels.Thesecomprisethe methodologiesappliedin casestudiesl, 3 and 4 in
Chapter5.
4.3.1 Thereflectioncoefficient
Analysis of AVO, or amplitude variation with ofTset,seeksto extract rock parameters
by analyzing seismic amplitude as a function of offset, or more corectly as a function
of reflection angle. The reflection coefficient for plane elastic waves as a lunction of
reflectionangle at a single interfaceis describedby the complicatedZoeppritz equations
(Zoeppritz,l9l9). For analysisof P-wavereflections,a well-known approximationis
given by Aki and Richards( 1980),assumingweak layer contrasts:
R ( 0 ,- )
I
, , Ap
- -1 7
,-vi ) +
;(r
2 *r4
T
AYp
W
,AVs
+ p' lt
K
(4.6)
where:
s i n0 1
I t - -
e:(0rlu)12=et
YPI
Lp:pz-pr
LVp:Vpz-Vpt
AVs-Vs:-Vsr
P : ( . P z I Pr)
l2
Vp : (.Vpz+ vPt)12
V5 : (V52+ vst)12
In the fbrmulasabove,p is the ray parameter,01 is the angleof incidence,and 02 is
the transmissionangle; Vp1and Vp2arethe P-wave velocities above and below a given
interface,respectively.Similarly, V51and V5r are the S-wavevelocities,while py and
p2 are densitiesabove and below this interface (Figure 4.4).
The approximation given by Aki and Richards can be further approximated(Shuey,
r9 8 5 ) :
R(01 ;:, R(o) + G sin29+ F(tan2e - sin2o;
where
R(o):;(T.T)
G::^+-'#(+.'+)
-+(:.'#)#+
:R(o)
(4.1)
183
n
4.3 AVOanalvsis
Medium1
(Vp1,V51,p1)
Medium
2
(Vn, Vsz,
Pi
PP(r)
PS{t)
Figure4'4 Reflectionsand transmissionsat a singleinterfacebetweentwo elastichalf-space
rr-redia
firr an incidentplaneP-wave.PP(i). There will be both a reflectedp-wave,pp(r). and
a transmittecl
P-wave,PP(t).Note that thereare wave mocleconversionsat the reflectionpoint occurrrng
ar
nonzeroincidenceangles.In additionto the P-waves,a reflectedS-wave,pS(r), and a
transrnitted
S-wave,PS(t),will be prodr.rced.
and
_
tayP
1
/
r/
vD
This form can be interpreted in terms of difierent angular ranges! where R(0) is
the
normal-incidence
reflectioncoefficient,G describesthe variationat intermecliate
offsets
and is often referred to as the AVO gradient,whereasF dominatesthe far ofTsets.near
critical angle. Normally, the range of anglesavailablefor AVO analysisis less
than
30-40.. Therefbre,we only need to considerthe two first terms,valid fbr ansles less
t h a n . l 0 t S h u e y .I 9 8 5 , 1 :
R(P)=R(0)+Gsin2d
(4.8)
The zero-oft'setreflectivity,R(0), is controlled by the contrastin acousticimpedance
acrossan interface.The gradient, G, is more complex in terms of rock properties,
but
fiom the expressiongiven above we see that not only the contrastsin Vp and density
afrect the gradient, but also vs. The importance of the vplvs ratio (or equivalently
the Poisson'sratio) on the ofTset-dependent
reflectivity was first indicated by Koefoed
(1955). ostrander (1984) showed that a gas-filledfbrmation would
have a very low
Poisson'sratio comparedwith the Poisson'sratiosin the surroundingnongaseous
fbrmations.This would causea significantincreasein positive amplitude versusangle
at the bottom of the gas layer, and a significantincreasein negativeamplitudeversus
angle at the top of the gas layer.
4.3.2 Theeffectof anisotropy
Velocity anisotropyought to be taken into accountwhen analyzing the amplitude variation with offset(AVO) responseof gassandsencasedin shales.Although it is generally
* d
184
-
seismicinterpretation
techniques
for quantitative
Common
thought that the anisotropy is weak (10-20%) in most geological settings (Thomsen,
1986), some eff'ectsof anisotropy on AVO have been shown to be dramatic using
shale/sandmodels(Wright, 1987).In somecases,the sign of the AVO slopeor rate of
changeof amplitude with ofliet can be reversedbecauseof anisotropyin the overlying
s h a l e s( K i m e t a l . , 1 9 9 3 B l a n g y ,1 9 9 4 ) .
The elasticstiffnesstensorC in transverselyisotropic(TI) media can be expressed
in compactform as fbllows:
(Ctt - 2Coo) C r :
Cl
( c 1 1- 2 C 6 6 )
Ctr
Cn
C -
Cr:
Cr:
0
0
0
0
0
0
:
where C6,6,
I
t(Crt
C::
0
0
0
0
0
0
0
0
0
0
0
0
C++ 0
0
0 C++ 0
0 Cr,o
0
- Cn)
(4e)
and where the 3-axis (z-axis)lies along the axis of symmetry.
The above6 x 6 matrix is symmetric,andhasfive independentcomponents,Cr r, Crr,
Cr, C++,and C66.For weak anisotropy,Thomsen(1986) expressedthree anisotropic
parameters,t, y and 6, as a function of the five elastic components,where
Cl-Cr
a , - -
(4.10)
2Cr
Cor, C++
2C++
(4.r r)
(Cr:*C++)2-(.Cy-Calz
2C.3(Cy
(4.12)
C++)
The constants can be seento describethe fiactional differenceofthe P-wave velocities
in the vertical and horizontaldirections:
yP(90')- vp(0')
Vp(o')
( 4 .l 3 )
and thereforebest describeswhat is usually referred to as "P-wave anisotropy."
In the same manner,the constant y can be seento describethe fiactional difference
of SH-wavevelocitiesbetweenverticaland horizontaldirections,which is equivalent
to the difference between the vertical and horizontal polarizationsof the horizontally
propagatingS-waves:
185
r
4.3 AVOanalysis
T
-
- Vss(0')
V s H ( 9 0 1 - V s v ( 9 0 ) 7sH(90")
Vsn(0')
Vsv(90')
(4.14)
The physical meaningof 6 is not as clear as s and y, but 6 is the most important
parameterfbr normal moveout velocity and reflection amplitude'
Under the plane wave assumption,Daley and Hron (1911) derived theoretical fbrmulas for reflection and transmissioncoefficientsin Tl media. The P-P reflectivity in
the equation can be decomposedinto isotropic and anisotropicterms as follows:
Rpp(0): Rrpp(O)* R'rpp(0)
(4.1s)
Assuming weak anisotropyanclsmall offsets,Banik ( 1987)showedthat the anisotropic
term can be simply expressedas fbllows:
R e p p ( d )-
sin2e
-Ad
( 4 .I 6 )
Blangy (lgg4) showedthe effect of a transverselyisotropic shaleoverlying an isotropic
gas sand on offset-dependentreflectivity, for the three different types of gas sands.
He found that hard gas sandsoverlain by a soft TI shale exhibited a larger decrease
in positive amplitude with offset than if the shale had been isotropic. Similarly, soft
gas san4soverlain by a relatively hard TI shale exhibited a larger increasein negative
amplitude with offset than if the shale had been isotropic. Furthermore, it is possible
fbr a soft isotropic water sand to exhibit an "unexpectedly" Iarge AVO eff'ect if the
overlying shaleis sufficientlyanisotropic'
4.3.3 Theeffectof tuningon AVO
As mentioned in the previous section, seismic interf'erenceor event tuning can occur
as closely spacedreflectorsinterfere with each other.The relative changein traveltime
between the reflectors decreaseswith increasedtraveltime and off.set.The traveltime
hyperbolasof the closely spacedreflectorswill thereforebecome even closer at larger
ofTsets.In f-act,the amplitudes may interfere at large ofTsetseven if they do not at
small offsets.The effect of tuning on AVO has been demonstratedby Juhlin and Young
( 1993),Lin and Phair ( 1993),Bakkeand Ursin ( 1998),andDong ( 1998),amongothers.
Juhlin and Young (1993) showedthat thin layersembeddedin a homogeneousrock
can produce a significantly different AVO responsefiom that of a simple interface of
the samelithology. They showedthat, for weak contrastsin elasticpropertiesacrossthe
layer boundaries,the AVO responseof a thin bed may be approximatedby modeling
it as an interference phenomenon between plane P-waves fiom a thin layer' ln this
casethin-bed tuning affects the AVO responseof a high-velocity layer embeddedin a
homogeneousrock more than it affects the responseof a low-velocity layer.
l
186
Common
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Lin and Phair ( 1993)suggestedthe following expressionfor the amplitudevariation
with angle (AVA) responseof a thin layer:
(4.11)
R r ( 0 ) : r r . r o A ? ' ( c0o) sd ' R ( 6 )
where a.reis the dominant frequency of the wavelet, Af (0) is the two-way traveltirne
at normal incidencefiom the top to the baseof the thin layer, and R (0) is the reflection
coefficient fiom the top interface.
Bakke and Ursin ( 1998)extendedthe work by Lin and Phair by introducingtuning
correctionfactorsfbr a generalseismicwaveletas a function of offset. If the seismic
responsefiom the top of a thick layer is:
d(t, t') : R(t')p(r)
(4.l8)
where R(,1')is the primary reflection as a function of ofTset.t', and p(0 is the seismic
pulse as a flnction of time /, then the responsefrom a thin layer is
tl(r, y)
(4.19)
f(.y)AI(0)C(t")p'(t)
wherep'(r) is the time derivativeof the pulse,A7"(0)is the traveltimethicknessof the
thin layer at zero offset, and C (-v)is the offiet-dependentAVO tuning factor given by
c(.v):ffi['
.##"]
(4.20)
where 7(0) and Z(-r') are the traveltimes atzero ofliet and at a given nonzero offset,
respectively.The root-mean-squarevelocity VBy5, is defined along a ray path:
t
l' tt)t 'r s,
.l v \t t\|t
(4)t\
VRMS -
Jdt
0
For small velocity contrasts(Vnvs -
y), the last term in equation (4.20) can be
ignored, and the AVO tuning f'actorcan be approximatedas
r(0)
r(,r')
C(r') :v ----:--
(4.22\
For large contrast in elastic properties,one ought to include contributions fiom Pwave multiples and convertedshearwaves. The locally convertedshear wave is ofien
neglectedin ray-tracing modeling when reproductionof the AVO responseof potential
hydrocarbon reservoirs is attempted.Primaries-only ray-trace modeling in which the
Zoeppritz equationsdescribethe reflectionamplitudesis most common. But primariesonly Zoeppritz modeling can be very misleading, becausethe locally converted shear
waves often have a first-order eff-ecton the seismic response(Simmons and Backus,
1994).lnterferencebetween the convertedwaves and the primary reflectionsfiom the
187
4,3 AVOanalysis
I
(2)Single-leg
(1)Primaries
R$
(3)Double-leg
a
(4)Reverberations
andmultiplesthatmustbeincludedin AVOmodelingwhenwe have
S-waves
Figure4.5 Converted
(l) Primaryreflections;
thesenrodesto interferewith theprimaries.
thin layers.causing
(After
(4)
reverberations.
primary
(3)
and
wave;
shear
(2) single-leg
shearwaves; double-leg
:
reflected
Rsp
:
P-wave,
fiom
converted
S-wave
transmitted
andBackus,1994.)7ps
Simmons
etc.
fiom S-wave.
P-waveconverted
baseof the layersbecomesincreasinglyimportantasthe layerthicknessesdecrease.This
often producesa seismogramthat is different fiom one produced under the primariesonly Zoeppritzassumption.In this case,one shouldusefull elasticmodelingincluding
the convertedwave modes and the intrabedmultiples.Martinez (1993) showedthat
surface-relatedmultiples and P-to-SV-modeconvertedwavescan interf-erewith primary
pre-stackamplitudesand causelargedistortionsin the AVO responses.Figure 4.5 shows
the ray images of convertedS-wavesand multiples within a layer.
effects
onAVO
andwavepropagation
overburden
4.3.4 Structuralcomplexity,
Structural complexity and heterogeneitiesat the target level as well as in the overburden can have a great impact on the wave propagation.These effects include focusing
and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed
and surf'acemultiples, P-wave to vertically polarized S-wave mode conversions,and
anelastic attenuation.The offset-dependentreflectivity should be corrected for these
wave propagation effects, via robust processingtechniques(see Section 4.3.6). Alternatively, these efTectsshould be included in the AVO modeling (see Sections 4.3.7
and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor
overburdeneffects as well as certain acquisition effects (seeSection a.3.5) by normalizing a target horizon amplitude to a referencehorizon amplitude. However, in more
recent years there have been severalmore extensivecontributions in the literature on
amplitude-preservedimaging in complex areasand AVO correctionsdue to overburden
effects, some of which we will summarizebelow.
188
-
Common
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for quantitative
seismicinterpretation
AVO in structurally
complex areas
The Zoeppritzequationsassumea singleinterf-ace
betweentwo semi-infinitelayerswith
infinite lateralextent.In continuouslysubsidingbasinswith relativelyflat stratigraphy
(suchas Tertiarysedimentsin the North Sea),the useof Zoeppritzequationsshouldbe
valid. However,complex reservoirgeology due to thin beds,vertical heterogeneities,
faultingand tilting will violate theZoeppritzassumptions.
Resnicket at. (1987)discuss
the efl'ectsof geologic dip on AVO signatures,whereasMacleod and Martin (1988)
discussthe eff-ectsof reflector curvature.Structuralcomplexity can be accountedfor by
doing pre-stackdepth migration (PSDM). However,one should be awarethat several
PSDM routinesobtain reliable structuralimages without preservingthe amplitudes.
Grubb et ul. (2001) examined the sensitivity both in structure and amplitr-rderelated
to velocity uncertaintiesin PSDM migrated images.They performed an amplitudepreserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO
signaturesthey evaluatedboth the uncertaintyin AVO cross-plotsand uncertaintyof
AVO attributevaluesalong given structuralhorizons.
AVO effects due to scattering attenuation in heterogeneous overburden
Widmaier et ztl..(1996) showedhow to correct a targetAVO responsefbr a thinly layered
overburden.A thin-beddedoverburdenwill generatevelocity anisotropyand transmission lossesdue to scatteringattenuation,and theseeflects should be taken into account
when analyzinga targetseismicreflector.They combinedthe generalizedO'DohertyAnstey formula (Shapiro et ul., 1994a)with amplitude-preservingmigration/inversion
algorithms and AVO analysis to compensatefor the influence of thin-bedded layers
on traveltimes and amplitudes of seismic data. In particr-rlar,they demonstratedhow
the estimation of zero-offset amplitude and AVO gradient can be improved by correcting fbr scattering attenuationdue to thin-bed efl'ects.Sick er at. (2003) extendecl
Widmaier's work and provided a method of compensatingfor the scatteringattenuation
eflects of randomly distributed heterogeneitiesabove a target reflector. The generalized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent,timeharmoniceffectivetransmissivityT for scalarwaves(P-wavesin acousticI D medium
or SH-wavesin elastic lD medium) and is given by
Tt II u Tue
( ' ' l t ) \ |i f t l A \ \ L
(4.23)
where.fis the frequency and n and p are the angle- and fiequency-dependentscattering
attenuationand phaseshift coefficients,respectively.The angle g is the initial angle of
an incident plane wave at the top surfaceof a thinly layered composite stack; L is the
thicknessof the thinly layeredstack;ft denotesthe transmissivityfbr a homogeneous
isotropic ref-erencemedium that causesa phaseshifi. Hence, the equation above representsthe relative amplitude and phasedistortions causedby the thin layers with regard
to the referencemedium. Neglectingthe quantity Zo which describesthe transmission
189
-
4.3 AVoanalysis
responsefor a homogeneousisotropic referencemedium (that is, a pttre phaseshift), a
phase-reducedtransmissivity is defined:
f ( f) o
@ t f ' o ) + t Pa()l) r
(4.24)
"
For a P-wave in an acoustic lD medium, the scatteringattenuation,cv,and the phase
coefficient,B,were derivedfrom Shapiroet al. (1994b)by Widmaier et al. (1996):
a ( . f, 0 ) :
|
tr'oot.f'
cos2oV,f I l6n:a2f2 cos2u
(4.25)
and
B(f.())-
r f'o2 l"
|V r c o s eL
gnzn: 7'z
V;+
r4)6r
t6n)02.t2cor2e
where the statistical parametersof the referencemedium include spatial correlation
length a, standarddeviationo, and mean velocity Vs. The medium is modeled as a
1D random medium with fluctuating P-wave velocities that are characterizedby an
exponential correlation function. The transmissivity (absolute value) of the P-wave
with increasingangleof incidence.
decreases
If the uncorrectedseismicamplitude(i.e., the analyticalP-wave particle displacement) is defined according to ray theory by:
I
U ( S ,G , / ) : R c - W ( r - r v )
(4 )1\
v
where U is the seismic trace, S denotes the source, G denotes the receiver, t is the
varying traveltime along the ray path, Rs is the reflection coefficient at the reflection
point M, y is the spherical divergence factor, W is the soutce wavelet, and ry is
the traveltime fbr the ray between source S, via reflection point M, and back to the
receiverG.
A reflector beneatha thin-beddedoverburdenwill have the following compensated
seismicamplitude:
u r ( s , G ,t ) :
I
f r * ( t ) *R . w 1 r- , r ;
(4 )R\
v
is givenby;
transmissivity
wherethetwo-way,time-reduced
4*(r) : irtrc(r)x Zsrvr(r)
(4 )q\
The superscriptT of Ur(S, G, r) indicatesthat thin-bed effects have been accounted
fbr. Moreover, equation (4.28) indicatesthat the sourcewavelet,W(0, is convolvedwith
the transient transmissivity both for the downgoing (i5p1 ) and the upgoing raypaths
(f n4c)between source (S), reflection point (M), and receiver (G).
190
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Common
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seismicinterpretation
In conclusion, equation (4.28) representsthe angle-dependenttime shift causedby
transverseisotropic velocity behavior of the thinly layeredoverburden.Furthermore,it
describesthe decreaseof the AVO responseresultingfrom multiple scatteringadditional
to the amplitude decay related to sphericaldivergence.
Widmaier eI ai. ( I 995) presentedsimilar lbrmulations for elasticP-waveAVO, where
the elasticcorrection formula dependsnot only on variancesand covariancesof P-wave
velocity, but also on S-wave velocity and density,and their correlationand crosscorrelationfunctions.
Ursin and Stovas(2002) further extendedon the O'Doherty-Anstey fbrmula and calculated scatteringattenuationfbr a thin-bedded,viscoelasticmedium. They found that
in the seismic frequency range, the intrinsic attenuationdominatesover the scattering
attenuation.
AVO and intrinsic attenuation (absorption)
Intrinsic attenuation,also referred to as anelasticabsorption,is causedby the fact that
even homogeneoussedimentaryrocks are not perf'ectlyelastic. This effect can complicatethe AVO response(e.g.,Martinez, 1993).Intrinsicattenuationcan be described
in terms of a transt'ertunction Gt.o, t) fbr a plane wave of angular frequency or and
propagationtime r (Luh, 1993):
G @ , i : exp(at12Qe* i(at lr Q) ln atI tos)
(4.30)
where Q" is the effective quality f'actorof the overburdenalong the wave propagation
path and areis an angular referencefrequency.
Luh demonstrated how to correct for horizontal, vertical and ofTset-dependent
wavelet attenuation.He suggestedan approximate, "rule of thumb" equation to calculate the relative changein AVo gradient, 6G, due to absorptionin the overburden:
ftt
3G ry :-'
Q"
(4.31)
wherei
is the peak frequency of the wavelet, and z is the zero-offsettwo-way travel
time at the studied reflector.
Carcione et al. (1998) showed that the presenceof intrinsic attenuationaffects the
P-wave reflection coefficient near the critical angle and beyond it. They also found that
the combined effect of attenuationand anisotropy aff'ectsthe reflection coefficientsat
non-normal incidence,but that the intrinsic attenuationin somecasescan actually compensatethe anisotropiceffects.In most cases,however,anisotropiceffectsare dominant
over attenuationeffects.Carcione (1999) furthermore showed that the unconsolidated
sedimentsnear the seabottom in offshore environmentscan be highly attenuating,and
that these waves will for any incidence angle have a vector attenuationperpendicular
191
r
4,3 AVOanalysis
to the sea-floorinterf'ace.This vector attenuationwill afl'ectAVO responsesof deeper
reflectors.
onAVO
etfects
4.3.5 Acquisition
The most important acquisition eff-ectson AVO measurementsinclude source directivity, and source and receivercoupling (Martinez, J993). ln particular,acquisition
footprint is a large problem fbr 3D AVO (Castagna,2001).Inegular'Eoverageat the
surfacewill causeunevenillumination of the subsurface.Theseeffectscan be corrected
for using inverseoperations.Difl'erent methodsfor this have beenpresentedin the literature(e.g.,Gassawayet a\.,1986; Krail and Shin, 1990;Cheminguiand Biondi, 2002).
Chiburis' ( 1993)method for normalizationof targetamplitudeswith a referenceamplitude provided a fast and simple way of corecting for certain data collection factors
including sourceand receivercharacteristicsand instrumentation.
dataforAVOanalysis
of seismic
4.3.6 Pre-processing
AVO processingshould preserveor restorerelative trace amplitudeswithin CMP gathers. This implies two goals: (1) reflectionsmust be correctly positionedin the subsurface; and (2) data quality should be sufficient to ensure that reflection amplitudes
contain infbrmation about reflection coefficients.
AVOprocessing
Even though the unique goal in AVO processingis to preservethe true relative
amplitudes,there is no unique processingsequence.lt dependson the complexity
of the geology.whetherit is land or marineseismicdata.and whetherthe data will
be used to extract regression-basedAVO attributes or more sophisticatedelastic
inversionattributes.
Cambois(200 l) definesAVO processingas any processingsequencethat makes
the data compatiblewith Shuey'sequation,if that is the model used for the AVO
inversion.Camboisemphasizesthat this can be a very complicatedtask'
Factorsthat changethe amplitudesof seismictracescan be groupedinto Earth effects,
acquisition-relatedeffects, and noise (Dey-Sarkar and Suatek, 1993). Earth effects
include sphericaldivergence,absorption,transmissionlosses,interbed multiples, converted phases,tuning, anisotropy, and structure. Acquisition-related eft-ectsinclude
source and receiver arrays and receiver sensitivity. Noise can be ambient or sourcegenerated.coherentor random.Processingattemptsto compensatefor or removethese
effects, but can in the processchange or distort relative trace amplitudes. This is an
important trade-off we need to consider in pre-processingfor AVO. We thereforeneed
192
r
Common
techniques
for quantitative
seismicinterpretation
to selecta basicbutrobustprocessing
scheme(e.g.,ostrander,1984;chiburis,l9g4;
Fouquet,f 990;Castagna
andBackus,1993;Yilma4 2001).
Common pre-processingstepsbefore AVO analysis
Spiking deconvolution and wavelet processing
In AVO analysiswe normally want zero-phase
data.However,the original seismicpulse
is causal,usually some sort of minimum phasewaveletwith noise.Deconvolutionis
defined as convolving the seismic trace with an inverse filter in order to extract the
impulse responsefrom the seismic trace. This procedure will restore high frequencies and therefore improve the vertical resolution and recognition of events.One can
make two-sided, non-causalfilters, or shaping filters, to produce a zero-phasewavelet
( e . g . ,L e i n b a c h ,1 9 9 5 ;B e r k h o u t ,1 9 7 7 ) .
The wavelet shapecan vary vertically (with rime), larerally (spatially),and with
offset. The vertical variations can be handled with deterministic Q-cornpensation(see
Section4.3.4). However,AVO analysisis normally carriedout within a limited time
window where one can assumestationarity.Lateral changesin the wavelet shapecan
be handledwith surface-consistent
amplitudebalancing(e.g.,Camboisand Magesan,
1997). Offset-dependentvariations are often more complicated to correct for, an4 are
attributed to both ofl.set-dependent
absorption (see Section 4.3.4), tuning efl'ects(see
Section4.3.3),andNMo stretching.NMo stretchingactslike a low-pass,mixed-phase,
nonstationaryfilter, and the eff'ectsare very difficult to eliminate fully (Cambois,2001
).
Dong (1999) examined how AVO detectability of lithology and fluids was afl'ected
by tuning and NMo stretching, and suggesteda procedure for removing the tuning
and stretching effects in order to improve AVO detectability.Cambois recommendecl
picking the reflections of interest prior to NMo corrections, and flattening them for
AVO analysis.
Spherical divergence correction
Spherical divergence, or geometrical spreading, causes the intensity and energy of
spherical waves to decreaseinversely as the square of the distance fiom the source
(Newman, 1973).For a comprehensivereview on ofTset-dependent
geometricalspreading, seethe study by Ursin ( 1990).
Surface-consistent amplitude balancing
Source and receiver eff'ectsas well as water depth variation can produce large deviations in amplitude that do not coffespond to target reflector properties.Commonly,
statistical amplitude balancing is carried out both fbr time and offset. However. this
procedure can have a dramatic efl'ect on the AVO parameters.It easily contributes
to intercept leakage and consequentlyerroneousgradient estimates(Cambois, 2000).
Cambois (2001) suggestedmodeling the expected averageamplitucle variation with
't
193
n
4.3 AVOanalvsis
off.setfbllowing Shuey's equation, and then using this behavior as a ret'erencefor
the
statisticalamplitudebalancing.
Multiple removal
One of the most deterioratingeff-ectson pre-stackamplitudes is the presenceof multiples.There are severalmethodsof filtering away multiple energy,but not all of these
are
adequatefor AVo pre-processing.The method known asfft multiple filtering, done in
the frequency-wavenumberdomain, is very efficient at removing multiples, but the
dip
in the.l-lr domain is very similar fbr near-offsetprimary energy and near-offsetmultiple
energy.Hence,primary energy can easily be removed from near tracesand not from
far
traces,resulting in an ar-tificialAVO effect. More robust demultiple techniquesinclude
linear and parabolic Radon transform multiple removal (Hampson, l9g6: Herrmann
et a1.,2000).
NMO (normal moveout) correction
A potential problem during AVO analysis is error in the velocity moveout conection
(Spratt, 1987).When extracting AVO attributes,one assumesthat primaries
have been
completely flattenedto a constanttraveltime.This is rarely the case,as there will always
be residual moveout. The reasonfor residualmoveout is almost always associatedwith
erroneousvelocity picking, and greatef'fortsshoukl be put into optimizing the estimated
velocity field (e.g.,Adler, 1999;Le Meur and Magneron,2000).However,anisorropy
and nonhyperbolicmoveoutsdue to complex overburclenmay also causemisalignments
betweennearand far off.sets(an excellentpracticalexampleon AVO and nonhyperbolic
moveout was publishedby Ross, 1997).Ursin and Ekren (1994) presenteda method
for analyzing AVO eff-ectsin the off.setdomain using time windows. This technique
reducesmoveout elrors and createsimproved estimatesof AVO parameters.One
shoulcl
be aware of AVO anomalieswith polarity shifts (classIIp, seedefinition below) during
NMO corrections,as thesecan easily be misinterpretedas residualmoveouts(Ratcliffe
and Adler, 2000).
DMO correction
DMO (dip moveout) processinggeneratescommon-reflection-pointgathers.It moves
the reflection observed on an off'set trace to the location of the coincident sourcereceiver trace that would have the same reflecting point. Therefore, it involves
shifting both time and location. As a result, the reflection moveout no longer depends
on dip, reflection-point smear of dipping reflections is eliminated, and events with
various dips have the same sracking velocity (Sheriff and Geldhart, 1995).
Shang
et al. (1993) published a rechnique on how to extract reliable AVA (amplitude variation with angle) gathers in the presence of dip, using partial pre-stack
misration.
194
-
seismicinterpretation
for quantitative
techniques
Common
Pre-stack migration
Pre-stackmigration might be thought to be unnecessaryin areaswhere the sedimentary
section is relatively flat, but it is an important component of all AVO processing.
Pre-stackmigration should be used on data for AVO analysis whenever possible,
becauseit will collapsethe diffractions at the targetdepth to be smaller than the Fresnel
zone and thereforeincreasethe lateral resolution(seeSection4.2.3; Berkhout, 1985;
Mosher et at., 1996).Normally, pre-stacktime migration (PSTM) is preferred to prestackdepth migration (PSDM), becausethe former tendsto preserveamplitudesbetter.
However, in areas with highly structured geology, PSDM will be the most accurate
PSDM routineshouldthen be applied
tool (Cambois,2001).An amplitude-preserving
, 997).
( B l e i s t e i n ,1 9 8 7 ;S c h l e i c h eer t c t l . , l 9 9 3 ; H a n i t z s c h 1
Migration fbr AVO analysis can be implemented in many different ways. Resnick
et aL. (1987) and Allen and Peddy (1993) among othershave recommendedKirchhoff migration together with AVO analysis.An alternativeapproachis to apply waveequation-basedmigration algorithms.Mosher et al. (.1996)derived a wave equation fbr
common-angle time migration and used inverse scatteringtheory (see also Weglein,
Mosher
integrationof migrationand AVO analysis(i.e.,migration-inversion).
1992'7for
et at. (1996) usecla finite-difference approachfbr the pre-stack migrations and illustrated the value of pre-stackmigration fbr improving the stratigraphicresolution, data
quality, and location accuracyof AVO targets.
of a2lseismicline
forAVO
anatysis
scheme
of pre-processing
Example
( Y i l m a z2,0 0 1 . )
geometric
scaling,
(source
processing.
( I ) Pre-stack
signature
signalprocessing
spiking deconvolutionand specffalwhitening).
(2t Sort to CMP and do sparseintervalvelocity analysis.
(3) NMO using velocity field from step2.
(4) Demultipleusing discreteRadontransform.
(5) Sort to common-offset and do DMO correction.
(6) Zero-offsetFK time migration.
(CRP) and do inverseNMO using the
(7) Sort data to common-reflection-point
velocity field from step2.
(8) Detailedvelocity analysisassociatedwith the migrateddala'
(9) NMO correclionusing velocity field from step8.
( l0) StackCRP gathersto obtainimageof pre-stackmigrateddata.Removeresidual
multiplesrevealedby lhe stacking.
( l l ) U n m i g r a t eu s i n gs a m ev e l o c i t yf i e l d a s i n s t e p6 .
( l2; Post-stackspiking deconvolution.
(13) Remigrateusing migrationvelocity field from step8.
195
4.3 AVOanalysis
E
etfects
duet0 processing
Somepitfallsin AVOinterpretation
. Waveletphase.The phaseof a seismicsectioncan be significantlyalteredduring
processing.lf rhe phaseof a sectionis not establishedby the interpreter.then AVO
anomaliesthat would be interpretedas indicativeof decreasingimpedance,for
example.can be producedat interfaceswherethe impedanceincreases(e.g.,Allen
and Peddy. I993).
. Multiple filtering. Not all demultiple techniquesare adequatelor AVO predomain,is very
processing.Multiple filtering,done in the frequency-wavenumber
efficientar removing multiples.but the dip in the/-k domain is very similar for
near-offsetprimary energy and near-offsetmultiple energy.Hence,primary energy
can easlly be removed from the near-offsettraces. resulting in an artificial AVO
effect.
. NMO correction.A potentialproblemduring AVO analysisis errorsin the velocity
moveoutcorrection(Spran. 1987).When extractingAVO attributes.one assumes
that primaries have been completely flattenedto a constanttraveltime.This is
rarely the case.as therewill alwaysbe residualmoveout.Ursin and Ekren (1994)
presenteda method for analyzing AVO effects in rhe offset domain using time
windows. This techniquereducesmoveoul errorsand createsimprovedestimates
of AVO paramerers.NMO stretch is another problem in AVO analysis. Because
the amount of normal moveout varies with arrival time. frequenciesare lowered
at large offsets compared with short offsets. Large offsets, where the stretching
effect is significant.should be muted before AVO analysis.Swan (1991), Dong
(1998) and Dong ( 1999)examinethe eft'ectof NMO stretchon offset-dependenl
reflectivity.
. AGC amplirude conection. Automatic gain control must be avoided in preprocessingof pre-stackdata beforedoing AVO analysis.
Pre-processing for elastic impedance inversion
Severalof the pre-processingstepsnecessaryfor AVO analysisare not required when
preparingdatafor elasticimpedanceinversion(seeSection4.4 for detailson the methodology). First of all, the elastic impedanceapproachallows for wavelet variations with
offset (Cambois,2000). NMO stretchcorrectionscan be skipped,becauseeachlimitedrange sub-stack(in which the waveletcan be assumedto be stationary)is matchedto its
associatedsyntheticseismogram,and this will removethe waveletvariationswith angle.
It is, however,desirableto obtain similar bandwidth fbr each inverted sub-stackcube,
since these should be comparable.Furthermore, the data used for elastic impedance
inversion are calibratedto well logs before stack,which meansthat averageamplitude
variations with offset are automatically accountedfor. Hence, the complicated procedure of reliable amplitude corrections becomes much less labor-intensivethan for
196
-
Common
techniques
for quantitative
seismicinterpretation
u
1
0
2
0
3
0
4
0
5
0
6
0
(degree)
Angle
of incidence
Figure4,6 AVO curvesfbr differenthalf'-space
models(i.e.,two layers one intertace).FaciesIV
is cap-rock.Input rock physicspropertie\represent
meanvaluesfor eachfacies.
standardAVO analysis.Finally,residualNMO and multiplesstill must be accountedfbr
(Cambois,2001). Misalignmentsdo not causeinterceptleakageas fbr standardAVO
analysis,but near-and far-anglereflectionsmust still be in phase.
4.3.7 AVOmodeling
andseismicdetectability
AVO analysisis normally carried out in a deterministicway to predict lithology and
fluids from seismicdata(e.g.,Smith and Gidlow, 1987;RutherfordandWilliams, 1989;
Hilterman, 1990;Castagnaand Smith, 1994;Castagnaet al., 1998).
Forward modeling of AVO responsesis normally the best way to start an AVO
analysis, as a feasibility study before pre-processing,inversion and interpretation of
real pre-stack data. We show an example in Figure 4.6 where we do AVO modeling
of difTerentlithofacies defined in Section 2.5. The figure shows the AVO curves for
different half-spacemodels, where a silty shale is taken as the cap-rock with difTerent
underlying lithofacies. For each facies, Vp, Vs, and p are extractedfrom well-log data
and used in the modeling. We observea clean sand/pureshaleambiguity (faciesIIb
and facies V) at near of1iets,whereasclean sandsand shalesare distinguishableat far
offsets.This exampledepictshow AVO is necessaryto discriminatedifferent lithofacies
in this case.
I
-T
I
197
-
4.3 AVOanalysis
CemellHiontrend
I
Cemenled
{el brino
I
0
Ceme|rbd
w/ hydruca]ton
V
Hydrocarlontr€ild
Unconsolidaled
w/ brine
Unconsolidtlsd
w/ hydrocarbon
sandscappedby
andunconsolidated
sandstone
Figure4.7 SchcgaticAVOcurvesfirr cemented
cases.
andoil-saturated
shlle.frll brine-saturated
Figure 4.7 shclwsanotherexample,where we considertwo types of clean sands,
cementedand unconsolidated,with brine versushydrocarbonsaturation.We seethat a
cemented sanclstonewith hydrocarbon saturationcan have similar AVO responseto a
brine-saturated.unconsolidatedsand.
The examplesin Figures 4.6 and 4.7 indicate how important it is to understandthe
local geology during AVO analysis.lt is necessaryto know what type of sandis expected
for a given prospect,and how much one expectsthe sandsto change locally owing to
textural changes,before interpreting fluid content. It is therefore equally important to
coniluct realisticlithology substitutionsin addition to fluid substitutionduring AVO
rnodelingstudies.The examplesin Figures4.6 and 4.7 also demonstratethe importance of the link between rock physics and geology (Chapter 2) during AVO analysis.
Whenis AVOanalysisthe appropriatetechnique?
It is well known that AVO analysisdoes not always work. Owing to the many
caseswhere AVO has been applied withoul success,the techniquehas receiveda
bad reputationas an unreliabletool. However.part ol the AVO analysisis to find
out if the techniqueis appropriatein the first place. It will work only if lhe rock
of the targetreservoirare expectedto give a good
physicsand ffuid characleristics
AVO response.This must be clarifiedbeforethe AVO analysisof real data.Without
a proper feasibility study.one can easily misinterpretAVO signaturesin the real
data.A good feasibility study could include both simple reflectivitymodeling and
more advancedforward seismicmodeling(seeSection4.51.Both thesetechniques
shouldbe foundedon a thoroughunderstandingof local geologyand petrophysical
properties.Realisticlithology substitutionis as importantas fluid substitutionduring
this exercise.
198
for quantitative
seismicinterpretation
Gommon
techniques
I
Often, one will find that there is a certain depth interval where AVO will work,
often referred to as the "AVO window." Outside this, AVO will not work well.
That is why analysis of rack physics depth trends should be an integral part of
AVO analysis (see Sections 2.6 and 4.3.16). However. the "AVO window" is also
constrainedby data quality. With increasingdepth, absorptionof primary energy
reducesthe signal-to-noiseratio. higher frequenciesare graduallymore attenualed
than lower frequencies.the geology usually becomesmore complex causingmore
and theanglerangereducesfor a given streamerlength.
complexwave propagations,
All thesefactorsmake AVO lessapplicablewith increasingdepth.
AVOanalysis
of GDPgathers
4.3.8 Deterministic
After simple half--spaceAVO modeling, the next step in AVO analysisshould be deterministic AVO analysis of selectedCDP (common-depth-point)gathers,preferably at
well locations where synthetic gathers can be generatedand compared with the real
CDP gathers.In this section,we show an exampleof how the methodcan be appliedto
discriminatelithofaciesin real seismicdata,by analyzingCDP gathersat well locations
in a deterministic way. Figure 4.8 shows the real and synthetic CDP gathers at three
adjacentwell locationsin a North Seafield (the well logs are shownin Figure5.1, case
study l). The figure also includesthe picked amplitudesat a top targethorizon superimposed on exact Zoeppritz calculated reflectivity curves derived fiom the well-log
data.
In Well 2, the reservoir sandsare unconsolidated,representoil-saturatedsands,and
are cappedby silty shales.According to the saturationcurves derived fiom deep resistivity measurements,the oil saturation in the reservoir varies from 20-807o, with an
average of about 60Va. The sonic and density logs are found to measure the mud
filtrate invaded zone (0-l0o/o oil). Hence, we do fluid substitution to calculate the
seismic properties of the reservoir from the Biot-Gassmann theory assuming a uniform saturation model (the process of fluid substitution is described in Chapter l).
Before we do the fluid substitution, we need to know the acoustic properties of
the oil and the mud filtrate. These are calculated from Batzle and Wang's relations
(see Chapter l). For this case, the input parametersfor the fluid substitution are as
fbllows.
oilGoR
Oil relativedensity
Mud-filtratedensity
Porepressureat reservoirlevel
at reservoirlevel
Temperature
64 UI
32APT
1.09 g/cm3
20 MPa
77.2',C
-v
i
199
-
4.3 AVOanalysis
Well3
CDP
OFF
]
t0 323 726 1210 1694 2177
Relectivity
Relleclvity
-
:
:
0.r00
weill
r
0 050
0.050
i'. -r;r!
. 1
I
I
0.050 !
' '
nnqn
0 050
0 r00
I
Well 3
0 1 0 0;
0 100
'-
l'o"
I
l
..
,
.PB
:'.
0 i
::
0 0 5 0i
0
0 150
Angle0
1
14
21
28
34 (deq) Anqle
0
8
l5
22
29 (deg) Angle
0
1
14
20
26
32 (deg)
Figure4.8 Real CDP gathers(upper),syntheticCDP gathers(middle),and AVO curvesfor Wells
I 3 (lower).
200
Common
techniques
lor quantitative
seismicinterpretation
I
The correspondingAVO responseshows a negativezero-ofTsetreflectivity and a negative AVO gradient. In Well l, we have a water-saturatedcementedsand below a silty
shale.The correspondingAVO responsein this well showsa strongpositive zero-ofl.set
reflectivity and a relatively strong negative gradient. Finally, in Well 3 we observe a
strongpositive zero-offsetreflectivity and a moderatenegativegradient,corresponding
to interbeddedsand/shalefaciescappedby silty shales.Hence,we observethreedistinct
AVO responsesin the three different wells. The changesare related to both Iithology
and pore-fluid variations within the turbidite system. For more detailed information
about this system,seecase study I in Chapter 5.
Avseth et al. (2000) demonstratedthe etlect of cementationon the AVO responsein
real CDP gathersaround two wells, one where the reservoir sandsare friable, and the
other where the reservoir sands are cemented.They found that if the textural eflects
of the sandswere ignored, the correspondingchangesin AVO responsecould be interpretedas pore-fluidchanges,just as depictedin the reflectivitymodeling examplein
Figure 4.7.
lmpodance0f AVOanalysisof individualCDPgathers
Investigationsof CDP gathersare importanl in order ro confirm AVO anomalies
(Shuey:sinterceprand gradient,Smith and Gidlow's
seenin weightedstacksect.ions
fluid factor. etc.). The weighted stackscan contain anomaliesnot related to true
offset-dependent
amplitudevariations.
4.3.9 Estimation
ofAVOparameters
Estimating intercept and gradient
The next stepin an AVO analysisshould be to extract AVO attributesand do multivariate analysis of these. Several different AVO attributescan be extracted,mapped and
analyzed.The two most important ones are zero-offsetreflectivity (R(0)) and AVO gradient (G) basedon Shuey'sapproximation.Theseseismicpararneters
can be extracted,
via a least-squares
seismicinversion,for each samplein a CDP gatherover a selected
portion of a 3D seismicvolume.
For a given NMO-conected CDP gather, R(/,,r), it is assumed that for each
time sample, /, the reflectivity data can be expressedas Shuey's formula (equation
(4.8)):
R(r,r) : R(/,0) + c(/) sin2g(r,
-r)
(4 7)\
where 0(r, x) is the incident angle corresponding to the data sample recorded at
( t .r ) .
201
-
4.3 AVOanalysis
For a layered Earth, the relationshipbetweenofliet (r) and angle (0) is given approximately by:
r
s i n0 ( r ,x ) I
VrNr
(4.33)
tt2
YRMS
k3+x2fvi^)tt2
where VrNr is the interval velocity and Vnr,,rsis the averageroot-mean-squarevelocity, as calculated from an input velocity profile (fbr example obtained from sonic
log).
For any given value of zero-offsettime, /e, we assumethat R is measuredat N offsets
(xi, i:1, A/).Hence,we can rewrite the defining equationfbr this time as (Hampson
a n d R u s s e l l .1 9 9 5 ) :
s i n 2 o (x4r )
sin2g(r,,rz)
R(.rr)
R(xz)
R(r,r,)
Inmor-l
IcurI
I
(4.34)
sin2g(r,,rr,')
This matrix equation is in the form of b: Ac and representsN equations in the two
solutionto this equation is obtained bY
unknowns,R(/, 0) and G(r). The least-squares
solving the so-called"normal equation":
c:
(ArA)-1(ATb)
(4.3s)
solutionfbr R(0) and G at time t.
us the least-squares
Inversion for elastic Parameters
Going beyond the estimation of intercept and gradient, one can invert pre-stack seismic amplitudesfor elasticparameters,including Vp, V5 and density.This is commonly
(e'g., Dahl
ref'erredto as AVO inversion, and can be performed via nonlinear methods
anclUrsin. 19921Buland et al., 1996;Gouveiaand Scales,1998)or linearizedinversion
methods(e.g., Smith and Gidlow, 1987; Loertzer and Berkhout, 1993).Gouveia and
Scales( 1998)clefineda Bayesiannonlinearmodel and estimated,via a nonlinearconjugate gradient method, the maximum a-posteriori (MAP) distributions of the elastic
parameters.However, the nonlinearity of the inversion problem makes their method
very compurer intensive.Loertzer and Berkhout ( 1993)performed linearized Bayesian
inversion based on single interface theory on a sample-by-samplebasis. Buland and
Omre (2003) extendedthe work of Loertzer and Berkhout and developeda linearized
Bayesian AVO inversion method where the wavelet is accountedfor by convolution.
The inversionis perfbrmedsimultaneouslyfbr all times in a given time window, which
^
202
r
seismicinterpretation
for quantitative
techniques
Common
makes it possible to obtain temporal correlation between model parametersclose in
time. Furthermore, they solved the AVO inversion problem via Gaussianpriors and
obtained an explicit analytical form for the posterior density,providing a computationally fast estimationof the elasticparameters.
ofAVOinversion
Pittalls
. A linearapproximationof the Zoeppntzequationsis commonly usedin the calculation of R(01and G. The two-term Shueyapproximationis known lo be accurate
for anglesof incidenceup to approximately30'. Make surethat the data inverted
do not exceedthis range,so the approximalionis valid'
. The Zoeppritzequationsare only valid fbr single interfaces.lnversionalgorithms
that are basedon theseequationswill not be valid lor thin-beddedgeology.
. The linear AVO inversionis sensitiveto uncharacteristicamplitudescausedby
noise (including multiples.)or processingand acquisirioneffects.A few outlying
valuespresentin the pre-stackamplitudesareenoughto causeerroneousestimates
of R(0) and G. Mosr commercial software packagesfor eslimationof R(0) and
C a p p l y r o b u s re s t i m a r i o nt e c h n i q u e (se . g . ,W a l d e n .1 9 9 l ) t o l i m i t t h e d a m a g eo l '
outlying amPlitudes.
. Another potential problem during sample-by-sampleAVO inversion is errors
in the moveout correction (Spratt, 1987l. Ursin and Ekren (1994) presenteda
method for analyzing AVO eflects in the offset domain using time windows.
This techniquereducesmoveout errors and createsimproved estimatesoi AVO
parameters.
analysis
cross-Plot
4,3.10AVO
A very helpful way to interpret AVO attributesis to make cross-plotsof intercept(R(0))
versusgradient(G). Theseplots are a very helpful and intuitiveway of presentingAVO
data, and can give a better understandingof the rock propertiesthan by analyzing the
standardAVO curves.
AVO classes
Rutherfordand Williams ( 1989)suggesteda classificationschemeof AVO responses
fbr 6iflerent types of gas sanils(seeFigure 4.9). They defined three AVO classesbased
on where the top of the gas sandswill be locatedin an R(0) versusG cross-plot.The
cross-plotis split up into fbur quadrants.In a cross-plotwith R(0) along .r-axisand C
along,v-axis,the I st quadrantis whereR(0) and G areboth positivevalues(upperright
quadrant).The 2nd is whereR(0) is negativeand G is positive(upperleft quadrant).The
3rd is where borh R(0) and G arenegative(lower left quadrant).Finally, the 4th quadrant
is where R(0) is positive and G is negative (lower right quadrant).The AVO classes
203
4.3 AVoanalysis
I-
Tabfe4.1 AVO classes,after Ruthe(brd and Williams (1989)'
extendeclb1'Castagnaand Smith (1994), and Rossand
K i n m a n( 1 9 9 5 )
Class
RelativeimPedance
Quadrant
sand
High-impedance
No or low contrast
4th
,lth
Low impedance
Low impedance
3rd
3rd
2nd
classlll
t --
t
a
'r
O
D
\
R(0)
G
AVO product
Negative
Negative
Positive
Positive
Negative
1
r
tt I cra.irrp I crass
I ctass
t..
[-
I, ll and
originallydefinedfor gassands(classes
andwilliamsAVOclasses,
Figure4,9 Ruthertbrd
1995)'
Kinman'
(Ross
and
andSmith.1994)andIIp
IV (Castagna
clnsses
III),alongwiththeadded
et al. (1998)'
fiom Castagna
Figureis aclapted
plots in the 4th quadrant
must not be confused with the quadrant numbers. Class I
eventswith relatively
with positive R(0) and negativegradients.These representhard
class II represents
high impedanceand low vp/vs ratio compared with the cap-rock.
be hard to see on
can
sands with weak intercept but strong negatjve gradient. These
sections' Class III
the seismic data, becausethey often yield dim spots on stacked
These plot in the
is the AVO category that is normally associatedwith bright spots'
sandssaturatedwith
3rd quadrant in R(0)-G cross-plots,and are associatedwith soft
hydrocarbons(seePlate4. l0).
and class II anomaly'
Ross and Kinman (1995) distinguishedbetweena class IIp
causing a polarity
gradient,
Class IIp has a weak but positive intercept and a negative
class II has a weak
changewith oflset. This class will disappearon full stack sections.
This class may
change.
polarity
but negativeintercept and negativegraclient,henceno
be observedas a negativeamplitude on a full-ofliet stack'
of Rutherford and
Castagnaand Swan (1997) extendeclthe classification scheme
are relatively rare'
Williams to incluclea 4th class,plotting in the 2n<1quadrant.These
stiff shales characterbut occur when soft sands with gas are capped by relatively
(i'e" very compacted or silty
ized by Vp/Vs ratios slightly higher than in the sands
shales).
204
:
Gommon
techniques
for quantitative
seismicinterpretation
Summary
ofAVOclasses
' AVO classI represents
relativelyhardsandswith hydrocarbons.
Thesesandstendl"o
plot along the backgroundtrend in intercept-gradient
cross-plots.Moreover,very
hard sandscan have little sensitivityto fluids. so there may not be an associated
flat spot. Hence.thesesandscan be hard to discoverlrom seismicdata.
. AVo classII. representingtransparentsandswith hydrocarbons,often show up as
dim spotsorweaknegativereflectorson
theseismic.However.becauseofrelatively
large gradients.they should show up as anomaliesin an Rt0)-c cross-plot.and
plot off the backgroundtrend.
' AVO classIII is the "classical"AVO anomalywith negativeinterceptand negative
gradient.This class representsrelatively soft sands wirh high fluid sensitivity,
locatedfar away from the backgroundtrend.Hence,they shouldbe easyro derect
o n s e i s m i cd a t a .
' AVO classIV aresandswith negativeinterceptbut positivegradient.The reflection
coefficientbecomeslessnegaLivewith increasingoffset,and amplitudedecreases
versusoffset.even though Lhesesandsmay be bright spots(castagnaand Swan.
1997).Class lV anomaliesare relativelyrare,but occur when soft sandswith gas
arecappedby relativelystiffcap-rockshalescharacterized
by vplvs ratiosslightly
(
i
.
e
.
.
h i g h e rt h a n i n t h e s a n d s
v e r y c o m p a c t e do r s i l t y s h a l e s ) .
The AVo classeswere originally defined for gas sands.However.today the AVo
class system is used for descriptiveclassificationof observedanomaliesthal are
not necessarilygas sands.An AVO class Il that is drilled can turn out to be brine
sands.It does not mean that the AVo anomaly was not a class ll anomaly.we
therefbresuggestapplying the classificationonly as descriptiveterms for observed
A V o a n o m a l i e s ,w i t h o u t a u l o m a t i c a l l yi n f e r r i n g t h a t w e a r e d e a l i n g w i t h g a s
sands.
AVO trends and the effects of porosity, lithology and compaction
When we plot R(0) and G as cross-plots,we can analyzethe trendsthat occur in terms of
changesin rock physicsproperties,includingfluid trends,porositytrendsand lithology
trends,as these will have different directionsin the cross-plot(Figure 4. 1l). Using
rock physicsmodels and then calculatingthe correspondinginterceptand gradients,
we can study various "What lf" scenarios,and then compare the modeled trends with
the inverteddata.
Brine-saturatedsandsinterbeddedwith shales,situatedwithin a limited depth range
and at a particular locality, normally follow a well-defined "background trend" in AVO
cross-plot (Castagnaand Swan, 1991). A common and recommended approach in
qualitative AVO cross-plot analysis is to recognize the "background" trend and then
look fbr data points that deviatefrom this trend.
205
r
4,3 AVOanalysis
(Adapted
fiom Simm
trendsoccurringin an interceptgradientcross-plot'
4.11 Difl'erent
FigUre
et al.,2O0O.)
AVO
Castagnaet at. (1998) presentedan excellent overview and a fiamework for
4th
in
the
plot
normally
gradient and intercept interpretation.The top of the sandswill
plot in
quadrant,with positive R(0) and negativeG. The baseof the sandswill normally
together
sands,
of
base
the 2nd quadrant,with negativeR(0) and positive G. The top and
with shale-shaleintertaces,will createa nice trend or ellipse with center in the origin
ratio
of the R(O)-G coordinate system. This trend will rotate with contrast in Vp/V5
1998)'
betweena shaly cap-rockancla sandyreservoir(Castagnaet al., 1998;Sams'
background
the
of
slope
the
and
We can extract the relationship between VplVs tatio
trencl(a6) by clividing the gradient, G, by the intercept,R(0):
G
R(0)
(4.36)
study
Assuming the density contrast between shale and wet sand to be zero, we can
how changinE VplVs ratio affects the backgroundtrend. The density contrastbetween
velocity
sandand shaleat a given depthis normally relativelysmall comparedwith the
contrasts(Fosteret a\.,1991). Then the backgroundslopeis given by:
uh-I
.
^ l - ( V s*r Y s 2 ) A Y s l
" L t Y nt V p : t A V p l
(4..r7)
where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir,
and
respectively; Vs1 and V52are the correspondingS-wave velocities, whereas AVp
ratio is
AV5 are the velocity differencesbetween reservoir anclcap-rock. If the Vp/V5
l, that
is
trend
background
2 in the cap-rock and 2 in the reservoir,the slope of the
different
is a 45' slope diagonal to the gradient and intercept axes.Figure 4'12 shows
cap-rock.
the
and
lines correspondingto varying Vp/V5 ratio in the reservoir
The rotation of the line denoting the background trend will be an implicit function
content
of rock physics properties such as clay content and porosity. Increasing clay
206
-
Common
techniques
for quantitative
seismicinterpretation
VplVs=2.5
in caP-rock
VplVs=2.Q
in caP-rock
-0.5 L
-0.5
0
B(0)
F i g u r e 4 , 1B2a c k g r o u n d t r e n d s i n A V O c r o s s - p l o t s a s a f u n c t i o n o f v a r y i n g V p l V < r a l i o i n c a p - r o c k
(Weassume
andreservoir.
no densitycontrast.)
NoticethataVplVsratioof 1.5in thereservoir
can
havediff'erent
locations
in theAVOcross-plot
depending
on thecap-rockVplV5ratio.Ifthe Vp/V5
ratioof thecap-rockis 2.5,thesandwill exhibitAVOclassll to III behavior(lefi),whereas
if the
(right).
cap-rock
Vp/V5ratiois 2.0,thesandwill exhibitclassI to IIp behavior
at a reservoirlevel will causea counter-clockwiserotation, as the Vp/V5 ratio will
increase. Increasing porosity related to less compaction will also cause a counterclockwise rotation, as less-compactedsedimentstend to have relatively high VplVg
ratio. However, increasingporosity relatedto less clay contentor improved sorting will
normally cause a clockwise rotation, as clean sands tend to have lower Vp/V5 ratio
than shaly sands.Hence, it can be a pitfall to relate porosity to AVO responsewithout
identifying the causeof the porosity change.
The backgroundtrendwill changewith depth,but the way it changescanbe complex.
Intrinsicattenuation,discussedin Section4.3.4(Luh, 1993),will afI-ectthe background
trend as a function of depth, but correction should be made fbr this before rock physics
analysisof the AVO cross-plot(see Section4.3.6). Nevertheless,
the rotation due to
depth trends in the elastic contrastsbetween sandsand shalesis not straightforward,
becausetheVplVs in the cap-rock as well as the reservoirwill decreasewith depth.
These two efTectswill counteracteach other in terms of rotational direction. as seenin
Figure4. 12.Thus, the rotationwith depthmust be analyzedlocally.Also, the contrasts
between cap-rock and reservoir will change as a function of lithology, clay content,
sorting, and diagenesis,all geologic factors that can be unrelatedto depth. That being
said,we shouldnot include too large a depth interval when we extractbackgroundtrends
(Castagnaand Swan, 1997).That would causeseveralslopesto be superimposedand
result in a less defined background trend. For instance,note that the top of a soft sand
will plot in the 3rd quadrant,while the baseof a soft sandwill plot in the I st quadrant,
giving a backgroundtrend rotated in the oppositedirection to the trend for hard sands.
T
207
r
4.3 AVOanalysis
Fluid effects and AVO anomalies
As mentionedabove,deviationsfiom the backgroundtrend may be indicative of hydrocarbons,or some local lithology or diagenesiseffect with anomalouselastic properties
(Castagnaet at., 1998).Fosteret al. (1991) mathematicallyderivedhydrocarbontrends
that would be nearly parallel to the background trend, but would not pass through the
origin in R(0) versus G cross-plots.For both hard and soft sandswe expect the top of
hydrocarbon-filleclrocks to plot to the left of the background trend, with lower R(0)
and G valuescomparedwith the brine-saturatedcase.However, Castagnaet al. (1998)
fbund that, in particular, gas-saturatedsandscould exhibit a variety of AVO behaviors.
As lisred in Table 4.1. AVO classIII anomalies(Rutherfordand Williams, 1989),
representingsoft sandswith gas, will fall in the 3rd quadrant(the lower left quadrant)
and have negativeR(0) and G. These anomaliesare the easiestto detect fiom seismic
d a t a( s e eS e c t i o n4 . 3 . 1l ) .
Harclsandswith gas,representingAVO classI anomalies,will plot in the 4th quadrant
(lower right) and have positive R(0) and negative G. Consequently,these sandstend
to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented),
they will not show a large change in seismic responsewhen we go from brine to gas
(cf. Chapter l). This type of AVO anomaly will not show up as an anomaly in a product
stack. In fact, they can plot on top of the background trend of some softer, brinesaturatedsands.Hence, very stifTsandswith hydrocarbonscan be hard to discriminate
with AVO analysis.
AVO class II anomalies,representingsandssaturatedwith hydrocarbonsthat have
very weak zero-offset contrast compared with the cap-rock, can show great overlap
with the backgroundtrend,especiallyif the sandsarerelativelydeep.However,classII
type oil sandscan occur very shallow,causingdim spotsthat stick out comparedwith
a bright backgroundresponse(i.e., when heterolithicsand brine-saturatedsandsare
relatively stifT compared with overlying shales).However, becausethey are dim they
are easy to miss in near- or full-stack seismic sections,and AVO analysiscan therefore
be a very helpful tool in areaswith classII anomalies.
Castagnaand Swan (199'l) discovereda diff'erenttype of AVO responsefor some
gas sands, which they ref-erredto as class IV AVO anomalies (see Table 4. l), or a
"false negative." They found that in some rare cases,gas sandscould have negative
R(0) and positive G, hence plotting in the 2nd quadrant (upper left quadrant). They
showedthat this may occur if the gas-sandshear-wavevelocity is lower than that of the
overlyingformation.The most likely geologicscenariofor suchan AVO anomalyis in
unconsolidatedsandswith relatively large VplVs ratio (Fosteret crl., 1997).That means
that if the cap-rockis a shale,it must be a relativelystiff and rigid shale,normally a
very silt-rich shale.This AVO responsecan confusethe interpreter.First, the gradients
of sandsplotting in the 2nd quadranttend to be relatively small, and less sensitiveto
fluid type than the gradientsfor sandsplotting in the 3rd quadrant.Second,theseAVO
anomalieswill actually show up as dim spots in a gradient stack.However, they should
a
208
-
Common
techniques
for quantitative
seismicinterpretation
stand out in an R(0)-G cross-plot,with lower R(0) values than the background trend.
Seismically,they shouldstandout as negativebright spots.
Pitfalls
. Differentrock physicstrenclsin AVO cross-plotscan be ambiguous.The interpretation of AVO trendsshouldbe basedon locally constrainedrock physicsmodeling.
n o t o n n a i v er u l e so f t h u m b .
. Trendswithin individualclustersthat do not projectthroughthe origin on an AVO
cross-plol.cannot always be interpretedas a hydrocarbonindicator or unusual
lithology.Sams (1998) showedthat it is possiblefortrends to have large offsets
from the origin even when no hydrocarbonsare presentand the lithology is not
unusual.Only where the rocks on either side of the reflectingsurfacehave the
same Vp/V5 ratio will the lrends (not to be confusedwith backgroundlrends as
shown in Figure 4. l2.l project through the origin. Sams showedan exampleof a
brine sandthat appearedmore anomalousthan a Iessporoushydrocarbon-bearing
sand.
. Residualgas saturationcan causesimilar AVO effectsro high saturationsof gas
or light oil. Three-termAVO where reliableestimatesof density are oblained.or
attenuationattributes.can potentiallydiscriminateresidualgas saturationsfrom
commercialamountsof hydrocarbons( seeSections4.3.12 and4.3. | 5 for further
discussions).
Noise trends
A cross-plotbetweenR(0) and G will also includea noisetrend,becauseof the correlation betweenR(0) and G. BecauseR(0) and G are obtained from least-squarefitting,
there is a negative correlation between R(0) and G. Larger intercepts are correlated
with smallerslopesfbr a given data set. Hence,uncorrelatedrandom noise will show
an oval, correlateddistribution in the cross-plotas seen in Figure 4.13 (Cambois,
2000).
Furthermore,Cambois (2001) formulated the influenceof noise on R(0), G and
a range-limitedstack (i.e., sub-stack)in terms of approximateequationsof standard
deviations:
dR(o) :
3
/,
^/;
(4.38)
;o,
o\
'JV-)
f t - - "ti
o C : V f
^
)
z
stn-0n,"
(4.3e)
(I/t(l))
t;
.
r ^
sln-umrx
(4.40)
209
-
4.3 AVOanalysis
-,:'i.;.d-f,*t
'i;l?
ir.}
*
4,, r
rl ,
-0.1
"t;
-0.15
-0"1
-0.05
0
I (0)
0.05
0.1
0.15
Figure4,13 Randomnoisehas a ttend in rR(0)versusG (afterCambois,2000)
and
o,,- Ji .o,
(4.41)
where d " is the standarddeviation of the full-stack response,o, is the standarddeviation
of the sub-stack.and n is the number of sub-stacksof the full fold data. As we see,the
stack reducesthe noise in proportion to the squareroot of the fold. These equations
indicate that the intercept is less robust than a half-fold sub-stack,but more robust
than a third-fold sub-stack.The gradient is much more unreliable, since the standard
deviation of the gradient is inversely proportional to the sine squaredof the maximum
angle of incidence. Eventually, the intercept uncertainty related to noise is more or
lessinsensitiveto the maximum incidenceangle, whereasthe gradient uncertainty will
decreasewith increasingaperture(Cambois, 2001).
Simm er a/. (2000) claimed that while rock property infbrmation is containedin AVO
cross-plots,it is not usually detectablein terms of distinct trends, owing to the effect
of noise. The fact that the slope estimationis more uncertainthan the intercept during
a least-squareinversion makes the AVO gradient more uncertain than the zero-offset
reflectivity (e.g., Houck, 2002). Hence,the extensionof a trend parallel to the gradient
axis is an indicationof the amountof noise in the data.
I
A
210
techniques
for quantitative
seismicinterpretation
Common
I
Fluidversus
noisetrends
In areas where fluid changesin sandscause large impedancechanges,we tend
to see a right-to-left lateral shift along the interceptdirection. This direction is
in the vertical/gradient
almostoppositeto the noisedirection.which is predominantJy
direction. In these casesthere should be a fair chanceof discriminating hydrocarbonsands,even in relativelynoisy data.
saturatedsandsfrom brine-saturated
Simm er al. (2000) furthermore stressedthat one should create AVO cross-plots
aroundhorizons,not from time windows. Horizon cross-plotclearly targetsthe reservoir
of interest and helps determine the noise trend while revealing the more subtle AVO
responses.Moreover,only samplesof the maximum amplitudesshould be included.
Sampling parts of the wavefbrmsother than the maxima will infill the area between
separateclusters,and a lot of sampleswith no physical significancewould scatter
around the origin in an R(0) G cross-plot.However,picking only peaksand troughs
raisesa delicatequestion:what about transparentsandswith low or no impedance
contrastwith overlying shales'lTheseare significantreflectionswith very small R(0)
valuesthat could be missed if we invert the waveform only at absolutemaxima (in
commercialsoftwarepackagestbr AVO inversion,the absolutemaxima are commonly
definedfiom R(0) sections).Another issueis shale shaleinterfaces.Theseare usually
very weak reflectionsthat would be located close to the origin in an AVO cross-plot,
but they are still important for assessmentof a local backgroundtrend.
There are also other types of noise aff-ectingthe AVO cross-plotdata,such as residual
moveout.It is essentialto try to reducethe noisetrend in the databeforeanalyzingthe
cross-plotin termsof rock physicsproperties.A goodpre-processing
schemeis essential
in order to achievethis (seeSection4.3.6).
Cambois (2000) is doubtful that AVO cross-plotscan be usedquantitatively,because
of the noise effect. With that in mind, it should still be possibleto separatethe real
rock physics trends fiom the noise trends. One way to distinguishthe noise trend
is to cross-plota limited number of samplesfrom the same horizon from a seismic
section.The extensionof the trend along the gradient axis indicatesthe amount of
noise in the data (Simm et al., 2000). Another way to investigatenoise versusrock
physics trends is to plot the anomaly cluster seen in the AVO cross-plot as colorcodedsamplesonto the seismicsection.If the clusteris mainly due to random noise,it
should be scatteredrandomly around in a seismicsection.However,if the anomaly
conesponds with a geologic structure and closure, it may represent hydrocarbons
( s e eP l a t e4 . 1 0 ) .
Finally, we claim that via statisticalrock physics we can estimatethe most likely
fluid and lithology fiom AVO cross-plotseven in the presenceof some noise. This
is ref'erredto as probabilistic AVO analysis,and was first introduced by Avseth er a/.
(1998b).This method works by estimatingprobability distributionfunctionsof R(0)
\
211
-
4.3 AVOanalysis
and G that include the variability and background trends. Houck (2002) presenteda
methodologyfor quantifyingand cornbiningthe geologicor rock physicsuncertainties
with uncertaintiesrelatedto noiseand measurement,
to obtaina full characterization
of
Thesemethodthe uncertaintyassociatedwith an AVO-basedlithologic interpretation.
ologiesfbr quantificationof AVO uncertaintiesare explainedin Section4.3.12.
Howto assess
thenoisecontent
inAVO
cross-plots
. Make cross-plotsof full stack versusgradient.in addition lo R(01versusC. The
stack should have no comelationwith the gradient.so if trends in R(0t-C plots
are still observedin stack vs. G, thesetrendsshouldbe real and nol randomnoise
(Cambois.2000).
. ldentify the location of AVO anomaliesin seismic sections.Color-code AVO
anomaliesin R(0)-6 plots and then superimposeLhemonto your seismic sections. Do the anomaliesmake geologic senselshape.location),or do they spread
out randomly?
. Plot the regressioncoefficientof RlO)and C inversiononto the seismicto identify
the areaswhere R(0) and G are lessreliable.
. Cross-plota limitecl number of samplesfrom the same horizon from a seismic
section.The extensionof the trend along the gradientaxis indicatesthe amountof
noise in the data (Simm et a\..2000).
forhydrocarbon
4.3.11AVOattributes
detection
The information in the AVO cross-plotscan be reducedto one-dimensionalparameters
basedon linear combinationsof AVO parameters.This will make the AVO infbrmation
easier to interpret. Various attributes have been suggestedin the literature, and we
summarize the most common below (AVO inversion-basedattributesare discussedin
Section4.4).
Far- versus near-stack attributes
One can createseveralAVO attributesfrom limited-range stack sections.The far stack
minus the near stack (FN) is a "rough" estimateof an AVO gradient,and in particular it
is fbund to be a good attribute from which to detect class II AVO anomalies(Ross and
Kinman, 1995). For class II type prospects,the f-arstack alone can be a good attribute
for improved delineation. However, fbr class IIp anomalies,both the near and the thr
stack can be relatively dim, but with opposite polarities. Then the difTerencebetween
far and near will manifest the significant negativegradient that is present.In contrast,a
conventionalfull stack will completely zero-out a classIIp anomaly.Ross and Kinman
(1995) suggestedthe fbllowing equation for the FN attribute depending on whether