Thereare no facts,only interpretations.
implies picking and tracking laterally consistent
seismic reflectors for the purpose of mapping geologic structures,stratigraphy and
The ultimategoal is to detecthydrocarbon
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
emphasis put on the physicalunderstanding 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
The most important of thesetechniquesinclude post-stackamplitucle
inversion,and forward seismicmodeling.
These techniques,if used properly, open up new doors for the seismic interpreter.
primarily contrasts elasticproperties
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 cn t e r p r e t a l i o n .
Until a few decades ago, it would be common for seismic interpreters to roll out
l h e i r s e v e r a l - m e t e r s - l op a p e rs e c t i o n s
with seismic data down the hallway, go down
on their knees,and use their colored pencils to interpretthe horizons of interestrn
order to map geologic bodies. Little attention was paid to amplitude variations and
their interpretations. the early 1970sthe so-called"brighrspot" techniqueproved
successful areas the Gulf of Mexico, wherebright amplitudes
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
polarityto lowwould cause
impedance gas sands.Moreover, experienceshowed that gas-filled sands sometimes
could cause"dim spots," not "bright spots," if the sandshad high impedancecompared
With the introductionof 3D seismicdata, the utilization of amplitudesin seismic
interpretation became much more important. Brown (see Brown et ul., l98l) was
one of the pioneersin 3D seismicinterpretation lithofaciesfiom amplitudes.
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
can stepinto a virtual-realityworld of seismic
tools where the interpreter
wiggles and amplitudes, and trace these spatially (3D) and temporally (4D) in a way
that one could only dream of a few decadesago. Certainly, the leap fiom the rolled-out
paper sectionsdown the hallways to the virtual-reality imagesin visualization "caves"
implicationsfor the oil industry.In this sectionwe
is a giant leap with greatbusiness
qualitative aspects seismicamplitude interpretation,before we dig into the
inversion,and seismicmodeling,in fbllowing sections.
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
polarity in our case?Are we dealingwith a zero-phase a minimum-phase
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.
The American standarddefinesa black peak as a "hard" or
There exist two standards.
"positive" event,and a white trough as a "soft" or a "negative"event.On a near-ofl.set
stack section a "hard" event will correspondto an increasein acousticimpedancewith
depth, whereasa "soft" event will correspondto a decrease acousticimpedancewith
depth. According to the European standard,a black peak is a "soft" event, whereas a
white trough is a "hard" event. One way to check the polarity of marine data is to look
at the sea-floorreflector.This reflector should be a strongpositive reflector representing
the boundary between water and sediment.
' American polarity: An increase impedance
displayedas black peak (wiggle r.race) red intensitylcolor displayt.
. European Australian)polarity:An increase impedance
amplitude, normally displayedas white rrough (wiggle trace) or blue intensity(color
(Adaptedfrom Brown. 200la, 2001b)
For optimal quantitative seismic interpretations,we should ensurethat our data are
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.Thesetechniques
voxel tracking, and surfaceslicing (see Dorn (199g) fbr
For extraction of seismic horizon slices, autopicked or voxel-tracked horizons are
very common. The obvious advantageof autotracking is the speed and efficiency.
Furthermore, autopicking ensuresthat the peak amplitude is picked along a horizon.
However,one pitfall is the assumptionthat seismichorizons are locally continuous
and consistent.A lateral change in polarity within an event will not be recognized
during autotracking.Also, in areasof poor signal-to-noise
ratio or where a single event
splits into a doublet, the autopicking may fail to track the corect horizon. Not only
will important reservoirparameters neglected,but the geometriesand volumes may
also be significantly off if we do not regard lateral phaseshifts. It is important that the
realizesthis and reviewsthe seismicpicks for quality control.
Simple rock physicsmodeling can assistthe initial phaseof qualitativeseismicinrerpretation, when we are uncertain about what polarity to expect for diff'erentlithology
boundaries. a siliciclastic
will be associated
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
trends sand shale
basin basin, there be morethanonecross-over.
shalesare mainly affectedby mechanicalcompaction.Hence, cementedsandstones
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
can be relatively soft compared with surounding shales.There
is no rule of thumb fbr what polarity to expect fbr sandsand shales.However, using
rock physics modeling constrainedby local geologic knowledge, one can improve the
understandingof expectedpolarity of seismic reflectors.
During seismicinterpretation a prospect a provenreser"yoir
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 issue
can be solvedby generating
with 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.
. Very shallow sandsat normal pressure
with brine saluration
rocks embedded siliciclastics
' M i x e c ll i t h o l o g i e s h e t e r o l i t h i c s i)k e s h a t ys a n d s m a r l s .v o l c a n i c s h
sands(any pore fluid) embedded normally compacted
accumularions clean.unconsolidated poorly consolidated
' Make sure you know the polarity of the data. Rememberthere are two
standards, US standard
and the European
which are opposire.
' A hard event can changeto a soft laterally (i.e.. lateralphaseshifi;
if there are
will nor derecr
' A d i m s e i s m i cr e f l e c t o r r i n t e r v a lm a y b e s i g n i f i c a n te s p e c i a l l yn
i t h e z o n eo f
AVO analysisshould be underraken reveal
4.2.3 Frequency scaleeffects
Verticalseismicresolution definedas theminimum separation
such that we can identify two interfacesrather than one (SherifTand Geldhart, 199-5).
layer can be resolvedin seismicdataif the layer thickness largerthan
a quarter of a wavelength.The wavelength is given by:
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, can still gain important infbrmation via quanwe
titative analysisof the interference
amplitude.A bed only ),/30 in thicknessmay be
althoughits thicknesscannotbe determinedfiom the wave shape(Sheriff and
thickness a given
amplitude a function layer
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
n - Jgz
where z is the reflector clepth.Roughly, the Fresnel zone is the zone from which all
reflected contributions have a phase difl-erence less than z radians. For a depth of
Fresnelzone radius will be 300-470 m for fiequencies
3 km and velocity of 3 km/s, the
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 increasing lateralseismicresolution(Sheriff and Geldhart,1995).Depending
on the migration aperture, the lateral resolution after migration is of the order of a
the Fresnelzone in the direction
wavelength.However,the migration only collapses
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
seismic wavelengths(-50-100 m), lateral sampling is not the
For typical surf'ace
l i m i t i n gl a c t o r .
Interference and tuning effects
A thin-layered reservoir can cause what is called event tuning, which is interf'erence
betweenthe seismicpulse representing top of the reservoirand the seismicpulse
representingthe baseof the reservoir.This happensif the layer thicknessis less than a
seismicampli(Widess,1973).Figure 4.2 showsthe efTective
quarterof a wavelength
tude as a function of layer thickness for a given wavelength, where a given layer
has higher impedancethan the surrounding sediments.We observethat the amplitude
increasesand becomes larger than the real reflectivity when the layer thickness is
between a half and a quarter of a wavelength. This is when we have constructive
interference between the top and the base of the layer. The rlaximum constructive
interferenceoccurs when the bed thickness is equal to ),14, and this is often referred
to as the tuning thickness.Furthermore, we observethat the amplitucledecreases
approacheszero for layer thicknessesbetween one-quarterof a wavelength and zero
thickness. We refer to this as destructive interferencebetween the top and the base.
give approximatelythe correctgrossthicknesses
larger than a quarterof a wavelength,but no information fbr thicknesses
lessthan a quarterof a wavelength.
The thickness an individualthin-bedunit can be
extractedfrom amplitude measurements the unit is thinner than about ),/4 (Sheriff
and Geldhart,1995).When the layer thicknessequals)./8, Widess(1973) found that
the composite responseapproximatedthe derivative of the original signal. He referred
to this thickness as the theoretical threshold of resolution. The amplitude-thickness
curve is almost linear below ),/8 with decreasing
amplitudeas the layer gets thinner,
but the compositeresponse
4.2.4 Amplitude reflectivity
"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 decrease a negative"bright spot."
However, if the sand is relatively hard (compared with cap-rock), the sand saturated
with brine may induce a "brighlspot" anomaly,while a gas-filledsandmay be 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.
that "the most impnrtant seismic property of a reservoir is whether it is bright spot regime or tlim sltot
One obvious problem in the identification of dim spotsis that they are clim - they are
hard to see.This issuecan be dealt with by investigating
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
analysis the changein near-to far-offsetamplitude,a gradientanalysis,
will be able
to reveal the sand with any considerabledegree of confidence. This is explained in
"brighr spots"are usuallythe first type
During seismicexplorationof hydrocarbons.
of DHI (direct hydrocarbonindicators)one looks for. However.there have been
severalcaseswhere bright-spotanomalieshavebeendrilled. and turned out not lo
Some common "false bright spors"include:
. Volcanicintrusionsand volcanicash layers
. Highly cementedsands.
often calcitecementin thin pinch-outzones
. Coal beds
. Top of salt diapirs
Only the last threeon the list abovewill causethe samepolarity as a gas sand.The
Therefore.if one knows the
first three will causeso-called"hard-kick" amplitudes.
polariryof the dataone shouldbe able lo discriminare
AVO analysisshould permit discrimination
spots from the
from coal, salt or overpressured
A very common seismicamplitude
over a given
rellectionintensity,which is root-mean-square
lime window. This anribute does not distinguish between negativeand positive
thereforegeologic interpretation this attributeshould be made with
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 indiThe
cators. Flat spots can be related to diagenetic events that are depth-dependent.
boundary between opal-A and opal-CT represents impedance increasein the same
way as fbr a fluid contact, and dry wells have been drilled on diagenetic flat spots.
Clinoforms can appear as flat features even if the larger-scalestratigraphy is tilted.
Other "false" flat spotsinclude volcanicsills, paleo-contacts,
flat basesof lobesand channels.
One of f he best DHIs ro look for is a flat spot, the contactbetweengas and water,
gas and oil, or oil and water.However.there are other causes
that can give rise to
. Oceanbottom multiples
. Flat stratigraphy.
The bases sand lobesespecially
tend to be flat.
. Opal-A to opal-CT diagenetic
either relatedto diagenesis residualhydrocarbon
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 delineate
reservoirs. Seismic amplitude maps from 3D seismicdata are often qualitarlvel.finterpreted
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 unsuccessful
effects rather than fluid eff-ects up the bright spot. The consequence the drilling of
holes.In order to reveal"pitfall" amplitude anomaliesit is essential investigatethe
rock physicspropertiesfiom well-log data.However,in new frontier areaswell-1ogdata
are sparse lacking. This requiresrock physicsmodeling constrained reasonable
and/or knowledge about local compactionaland depositional
A common way to extractporosity from seismicdata is to do acousticimpedance
porositycan imply reducedacousticimpedance,
and by extracting empiricalporosity-impedance
trendsfrom well-log data,one can estimate
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-porosity
zone identifiedby this technique
may be shale.
Moreover, the porosity may be constant while fluid saturationvaries, and one sin-rple
model may not be adequate 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,
reflectivity on a near-offset seismic section. This has been reported in several areas
of the world (e.g. Zeng et al., 1996 Avseth et al., 2001b). It is often reported that
fluvial channelsor turbidite channelsare dim on seismic amplitude maps, and the
Plate1,1 SeismicP-P amplitudemap over a submarine
fan. The amplitudes sensitive lithofaciesand
pore fluids, but the relationvariesacrossthe imagebecause
ofthe interplayofsedimentologicand diagenetic
yellow and red high amplitudes.
Blue indicateslow amplitudes,
t) )) D,D ) D,D ) D r,D
D) r )r>),
Plate1,30 Top left, logs penetrating sandyturbidite sequence; right, normal-incidence
50 Hz Ricker wavelet.Bottom: increasing
water saturation from l1a/c 907c(oil API 35, GOR 200)
densityand Vp (left), giving both amplitudeand traveltimechanges
interpretation is usually that the channel is shale-filled. However, a clean sand fillof
ing in the channel can be transparentas well. A geological assessment geometries
indicating differential compaction above the channel may reveal the presenceof sand.
More advancedgeophysical techniquessuch as offset-dependent
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.
Lithology influence on amplitudes can often be recognized by the pattern of amplitudes as observed on horizon slices and by understandinghow different lithologies
system.By relatinglithologiesto depositional
occur within a depositional
The link between amplitude characteristics
often refer to theseas lithofacies or f-acies.
and depositional patternsmakes it easierto distinguish lithofacies variations and fluid
The traditionalmethodologyconsisted purely visual inspection
(e.g.,Mitchum et al., 1977;Weimer and
of geometricpatterns the seismicreflections
Link, l99l ). Brown et al. (1981),by recognizing
information, were amongst the first to interpret depositional facies from 3D seismic
amplitudes.More recent and increasinglyquantitativework includesthat of Ryseth
et al. (.1998)who used acoustic impedance inversions to guide the interpretation of
sand channels, and Zeng et al. (1996) who used forward modeling to improve the
understanding shallow marine facies from seismic amplitudes.Neri (1997) used
neuralnetworksto map faciesfrom seismicpulse shape.
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.
The subsurfaceis by nature a layered medium, where different lithologies or f'acies
have been superimposedduring geologic deposition. Seismic stratigraphicinterpretaof
tion seeksto map geologic stratigraphyfrom geometricexpression seismicreflections
in traveltime and space.Stratigraphic boundariescan be defined by dilferent litholoThese often coincide,but not
gies (taciesboundaries) by time (time boundaries).
always. Examples where facies boundaries and time boundaries do not coincide are
erosional surfacescutting across lithostratigraphy,or the prograding fiont of a delta
within the delta.
almost perpendicularto the lithologic surf'aces
There are severalpittalls when interpretingstratigraphyfiom traveltime infbrmation.
that is, the contrasts
First, the interpretationis basedon layer boundariesor interf'aces,
between diff'erent strata or layers, and not the properties of the layers themselves.
Two layers with different lithology can have the same seismic properties; hence, a
lithostratigraphic boundary may not be observed. Second' a seismic reflection may
occur without a lithology change(e.g.,Hardage,1985).For instance, hiatuswith no
intervalcan give a strongseismicsignature
within a shale
above and below the hiatus have difTerent characteristics.Similarily, amalgamated
sandscan yield internal stratigraphywithin sandy intervals,reflecting different texture
fiom difl-erentdepositionalevents.Third, seismicresolution can be a pitfall in
characteristics seismicinterpretation,asthey can give information
coastal development related to relative sea level changes (e.g., Vail er ai.,
can occur if the thicknessof individual layers reduces
I 977). However, pseudo-onlaps
The layer can still exist,even if the seismicexpression
yields an onlap.
pitfalls in conventional
be avoidedif we usecomplementary
. lmportant lithostratigraphic
betweenlayerswith very weak contrasts
in seismicpropefiiescan easily be missed.However.if different lithologiesare
data.they arenormallyvisiblein pre-stack
dara. AVO analysisis a useful tool to reveal sandswith impedances
c a p p i n gs h a l e s s e eS e c t i o n . 3 1 .
. It is commonlybelieved
events time boundaries. not necessarily
For instance.a hiatus within a shale may causea
strong seismicreflectionif the shaleabovethe hiatus is lesscompactedthan the
onc below.even if the lithology is the same.Rock physicsdiagnostics well-log
data may revealnonlithologicseismicevents
. Because limited seismicresolution,false seismiconlapscan occur.The layer
can improvethe resolution.
may still existbeneath
featuresnot observedin the original seismicdata
and revealsubtle srrailgraphic
( s e eS e c t i o n . 4 ) .
Quantitative interpretation of amplituclescan add information about stratigraphic
patterns,and help us avoid some of the pitfalls mentioned above.First, relating 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
stratigraphicinterpretationof a fluvial systemin Colombia using impedance
inversion of 3D seismicdata. Conducting impedanceinversion of the seismic data will
give us layer propertiesfrom interfhceproperties,and an impedancecross-section
reveal stratigraphicfeaturesnot observedon the original seismic section. Impedance
inversion has the potential to guide the stratigraphicinterpretation,becauseit is less
oscillatorythan the original seismicdata,it is more readily correlated well-log data,
and it tends to averageout random noise, thereby improving the detectability of later(Gluck et a.,1997).Moreover,
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 seismicsignatures
Layer thickness and net-to-gross from seismic amplitude
As mentioned in the previous section, we can extract layer thickness from seismic
amplitudes. depictedin Figure 4.2,the relationship only linear for thin layersin
pinch-out zonesor in sheet-likedeposits,so one shouldavoid correlatinglayer thickness
to seismic amplitudes in areaswhere the top and baseof sandsare resolvedas separate
reflectorsin the seismic data.
Meckel and Nath (.1911)found that, for sands embedded in shale, the amplitude
would depend on the net sand present,given that the thicknessof the entire sequence
is less than ).14. Brown (1996) extended this principle to include beds thicker than
the tuning thickness,assumingthat individual sand layers are below tuning and that
the entire interval of interbeddedsandshas a uniform layering. Brown introduced the
"composite amplitude" defined as the absolute value summation of the top reflection
amplitude and the base reflection amplitude of a reservoir interval. The summation of
the absolute values of the top and the baseemphasizesthe eff'ectof the reservoir and
reducesthe effect of the embedding material.
Zeng et al. (.1996)
studiedthe influenceof reservoir
introduced what they referred to as effective reflection strength, applicable to layers
thinnerthan the tunins thickness:
o'. - 2 " - Z ' n . ,
impedance, is the average
where Z. is the sandstone
and /z is the
layerthickness. more commonway to extractlayerthickness
is by linear regressionof relative amplitude versus net sand thickness as observed at
wells that are available.A recentcasestudy showing the applicationto seismicreservoir
mappingwas providedby Hill and Halvatis(2001).
Vernik et al. (2002) demonstratedhow to estimate net-to-grossfiom P- and 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
where V."n,lis the oil-sand fraction given bv;
where b is the averageslope of the shaleslope(06) and oil-sandslope(b1),whereas
a n d z 7 ti i r e t h e r e s p e c t i v i n t e r c e p t i n t h e A I - S I c r o s s - p l o r .
c a l c u l a t i o no f r e s e r v o i r h i c k n e s s r o m s e i s m i ca m p l i t u d e h o u l db e d o n e o n l y i n
areaswhere sandsare expectedto be thinner than the tuning thickness.that is a
quarterof a wavelength.
and wherewell-log datashow evidence good correlation
belweennet sandlhicknessand relativeamplirude.
It can be difficult to discriminate
from lirhologyand fluid
changes. relativelysoft sands, impactof increasing
tendslo increase seismicamplitude,and thereforeworks in the same
"direction" to Iayerthickness.
However.in relativelyhard sands.
and hydrocarbonsaturationLendto decrease
the relalive amplitude and therefore
work in the opposite"direction" to layer thickness.
In 1984, 12 years afler the bright-spot technology became a commercial tool fbr
hydrocarbon prediction, ostrander published a break-through paper in Geophl-sics
(ostrander, 1984). He showed that the presence gas in a sand cappedby a
would causean amplitude variation with ofTset pre-stackseismicdata.He also found
that this changewasrelatedto the reduced
ratio caused the presence
Then,the yearafter,Shuey(1985)confirmedmathematically approximations the
that 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 seismicamplitudes termsof rock properties.
could be investigated
beforestack,to seeif they also had AVo anomalies
The techniqueproved successfulin certain areasof the world, but in many casesit was
not successful.The technique sufI'eredfrom ambiguities causedby lithology efTects,
Aryle ol inc,d?nca
illustration theprinciples 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 technique
that was incorrect.Lack of shear-wave
informationandthe useof too simplegeologicmodelswerecommonreasons failure.
Processingtechniques that aff'ectednear-ofTset
traces in CDP gathers in a difl-erent
way from far-offset traces could also create talse AVO anomalies. Nevertheless,in
the last decade we have observed a revival of the AVO technique.This is due to the
improvementof 3D seismictechnology,
shear-wavelogging and improved understanding rock physicsproperties,larger data
capacity,more fbcus on cross-disciplinaryaspectsof AVO, and last but not least,mclre
among the usersof the potential pitfalls. The techniqueprovides the seismic
interpreter with more data, but also new physical dimensions that add infbrmation to
the conventional interpretationof seismic facies, stratigraphyand geomorphology.
In this section we describe the practical aspectsof AVO technology, the 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
and interpretation AVO data. For
an excellent overview of the history of AVO and the theory behind this technology,
we refer the reader to Castagna(1993). We expect the luture application of AVO to
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
appliedin casestudiesl, 3 and 4 in
Analysis of AVO, or amplitude variation with ofTset,seeksto extract rock parameters
by analyzing seismic amplitude as a function of offset, or more corectly as a function
of reflection angle. The reflection coefficient for plane elastic waves as a lunction of
reflectionangle at a single interfaceis describedby the complicatedZoeppritz equations
(Zoeppritz,l9l9). For analysisof P-wavereflections, well-known approximationis
given by Aki and Richards( 1980),assumingweak layer contrasts:
, , A
- -1 7 ,-vi )p +
+ p' lt
s i n0 1
I t - -
P : ( . P z I Pr)
Vp : (.Vpz vPt)12
V5 : (V52+ vst)12
and 02 is
In the fbrmulasabove,p is the ray parameter, is the angleof incidence,
the transmissionangle; Vp1and Vp2arethe P-wave velocities above and below a given
Similarly, V51and V5r are the S-wavevelocities,while py and
p2 are densitiesabove and below this interface (Figure 4.4).
The approximation given by Aki and Richards can be further approximated(Shuey,
r9 8 5 ) :
R(01 ;:, R(o) + G sin29+ F(tan2e - sin2o;
and transmissions a singleinterfacebetweentwo elastichalf-space
firr an incidentplaneP-wave.PP(i). There will be both a reflected
p-wave,pp(r). and a transmittecl
P-wave,PP(t).Note that thereare wave mocleconversions the reflectionpoint occurrrng
angles.In additionto the P-waves, reflectedS-wave,pS(r), and a transrnitted
S-wave,PS(t),will be prodr.rced.
This form can be interpreted in terms of difierent angular ranges! where R(0) is
coefficient, describes variationat intermecliate
and is often referred to as the AVO gradient,whereasF dominatesthe far ofTsets.
critical angle. Normally, the range of anglesavailablefor AVO analysisis less
30-40.. Therefbre,we only need to considerthe two first terms,valid fbr ansles less
reflectivity,R(0), is controlled by the contrastin acousticimpedance
acrossan interface.The gradient, G, is more complex in terms of rock properties,
fiom the expressiongiven above we see that not only the contrastsin Vp and density
afrect the gradient, but also vs. The importance of the vplvs ratio (or equivalently
the Poisson'sratio) on the ofTset-dependent
reflectivity was first indicated by Koefoed
(1955). ostrander (1984) showed that a gas-filledfbrmation would
have a very low
ratio comparedwith the Poisson's
ratiosin the surrounding
fbrmations.This would causea significantincreasein positive amplitude versusangle
at the bottom of the gas layer, and a significantincrease negativeamplitudeversus
angle at the top of the gas layer.
4.3.2 Theeffectof anisotropy
Velocity anisotropyought to be taken into accountwhen analyzing the amplitude variation with offset(AVO) response gassands
Although it is generally
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
models(Wright, 1987).In somecases, sign of the AVO slopeor rate of
changeof amplitude with ofliet can be reversedbecauseof anisotropyin the overlying
s h a l e s K i m e t a l . , 1 9 9 3 B l a n g y ,1 9 9 4 ) .
isotropic(TI) media can be expressed
The elasticstiffnesstensorC in transversely
in compactform as fbllows:
(Ctt - 2Coo) C r :
( c 1 1- 2 C 6 6 )
0 C++ 0
and where the 3-axis (z-axis)lies along the axis of symmetry.
components, r, Crr,
The above6 x 6 matrix is symmetric,
Cr, C++,and C66.For weak anisotropy,
parameters, y and 6, as a function of the five elastic components,where
a , - -
The constants can be seento describethe fiactional differenceofthe P-wave velocities
in the vertical and horizontaldirections:
( 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
V s H ( 9 0 1 - V s v ( 9 0 ) 7sH(90") Vss(0')
The physical meaningof 6 is not as clear as s and y, but 6 is the most important
parameterfbr normal moveout velocity and reflection amplitude'
Under the plane wave assumption,Daley and Hron (1911) derived theoretical 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)
Assuming weak anisotropyanclsmall offsets,Banik ( 1987)showedthat the anisotropic
term can be simply expressed fbllows:
R e p p ( d )-
( 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'erence event tuning can occur
as closely spacedreflectorsinterfere with each other.The relative changein traveltime
with increasedtraveltime and off.set.The traveltime
between the reflectors decreases
hyperbolasof the closely spacedreflectorswill thereforebecome even closer at larger
ofTsets.In f-act,the amplitudes may interfere at large ofTsetseven if they do not at
small offsets.The effect of tuning on AVO has been demonstrated Juhlin and Young
( 1993),Bakkeand Ursin ( 1998),andDong ( 1998),amongothers.
( 1993),Lin and Phair
Juhlin and Young (1993) showedthat thin layersembedded a homogeneous
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.
Lin and Phair ( 1993)suggested following expression the amplitudevariation
with angle (AVA) response a thin layer:
R r ( 0 ) : r r . r o A ? ' ( c o sd ' R ( 6 )
where a.re the dominant frequency of the wavelet, Af (0) is the two-way traveltirne
at normal incidencefiom the top to the baseof the thin layer, and R (0) is the reflection
coefficient fiom the top interface.
Bakke and Ursin ( 1998)extended
the work by Lin and Phair by introducingtuning
correctionfactorsfbr a generalseismicwaveletas a function of offset. If the seismic
fiom the top of a thick layer is:
d(t, t') : R(t')p(r)
where R(,1') the primary reflection as a function of ofTset.t', and p(0 is the seismic
pulse as a flnction of time /, then the response
from a thin layer is
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
where 7(0) and Z(-r') are the traveltimes atzero ofliet and at a given nonzero offset,
velocity VBy5, is defined along a ray path:
l' tt)t 'r s,
.l v t t|t
For small velocity contrasts(Vnvs -
y), the last term in equation (4.20) can be
ignored, and the AVO tuning f'actorcan be approximatedas
C(r') :v ----:--
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
S-waves multiples mustbeincluded AVOmodeling
with theprimaries. Primary
wave; (4) primary
converted P-wave, : reflected
baseof the layersbecomesincreasinglyimportantasthe layerthicknesses
often producesa seismogramthat is different fiom one produced under the primariesIn
only Zoeppritzassumption. this case,one shouldusefull elasticmodelingincluding
convertedwave modes and the intrabedmultiples.Martinez (1993) showedthat
multiples and P-to-SV-modeconvertedwavescan interf-ere
Figure 4.5 shows
pre-stackamplitudesand causelargedistortionsin the AVO responses.
the ray images of convertedS-wavesand multiples within a layer.
Structural complexity and heterogeneities the target level as well as in the overburon the wave propagation.These effects include focusing
den can have a great impact
and defbcusing of the wave field, geometric spreading,transmissionlosses,interbed
and surf'acemultiples, P-wave to vertically polarized S-wave mode conversions,and
reflectivity should be corrected for these
anelastic attenuation.The offset-dependent
via robust processingtechniques(see Section 4.3.6). Alterwave propagation effects,
natively, these efTectsshould be included in the AVO modeling (see Sections 4.3.7
and 4.5). Chiburis (1993) provided a simple but robust methodology to correct tor
overburdeneffects as well as certain acquisition effects (seeSection a.3.5) by normalizing a target horizon amplitude to a referencehorizon amplitude. However, in more
recent years there have been severalmore extensivecontributions in the literature on
imaging in complex areasand AVO correctionsdue to overburden
effects, some of which we will summarizebelow.
AVO in structurally
infinite lateralextent.In continuouslysubsidingbasinswith relativelyflat stratigraphy
(suchas Tertiarysediments the North Sea),the useof Zoeppritzequations
valid. However,complex reservoirgeology due to thin beds,vertical heterogeneities,
faultingand tilting will violate theZoeppritzassumptions.
Resnicket at. (1987)discuss
the efl'ectsof geologic dip on AVO signatures,whereasMacleod and Martin (1988)
discussthe eff-ects reflector curvature.Structuralcomplexity can be accountedfor by
depth migration (PSDM). However,one should be awarethat several
PSDM routinesobtain reliable structuralimages without preservingthe amplitudes.
Grubb et ul. (2001) examined the sensitivity both in structure and amplitr-rde
to velocity uncertainties PSDM migrated images.They performed an amplitudein
preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO
both the uncertaintyin AVO cross-plots
AVO attributevaluesalong given structuralhorizons.
AVO effects due to scattering attenuation in heterogeneous overburden
(1996) showedhow to correct a targetAVO response a thinly layered
Widmaier et ztl..
and transmission lossesdue to scatteringattenuation,and theseeflects should be taken into account
when analyzinga targetseismicreflector.
They combinedthe generalized
O'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,
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 heterogeneities
above a target reflector. The generalized O'Doherty-Anstey formr-rlais an approximation of the angle-dependent,
timeharmoniceffectivetransmissivity 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
where.fis the frequency and n and p are the angle- and fiequency-dependent
attenuationand phaseshift coefficients,respectively.The angle g is the initial angle of
an incident plane wave at the top surfaceof a thinly layered composite stack; L is the
thickness the thinly layeredstack;ft denotes transmissivity a homogeneous
medium that causesa phaseshifi. Hence, the equation above representsthe relative amplitude and phasedistortions causedby the thin layers with regard
to the reference
medium. Neglectingthe quantity Zo which describes transmission
responsefor a homogeneousisotropic referencemedium (that is, a pttre phaseshift), a
transmissivity is defined:
f ( f) o
@ t f ' o ) + t P ( l) r
For a P-wave in an acoustic lD medium, the scatteringattenuation,cv,and the phase
B,were derivedfrom Shapiroet al. (1994b)by Widmaier et al. (1996):
cos2o I l6n:a2f2 cos2u
r f'o2 l"
|V r c o s eL
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
seismicamplitude(i.e., the analyticalP-wave particle displaceIf the uncorrected
ment) is defined according to ray theory by:
U ( S ,G , / ) : R c - W ( r - r 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
A reflector beneatha thin-beddedoverburdenwill have the following compensated
u r ( s , G ,t ) :
f r * ( t ) *R . w 1 r- , r ;
4*(r) : irtrc(r)x Zsrvr(r)
The superscriptT of Ur(S, G, r) indicatesthat thin-bed effects have been accounted
fbr. Moreover, equation (4.28) indicatesthat the sourcewavelet,W(0, is convolvedwith
the transient transmissivity both for the downgoing (i5p1 ) and the upgoing raypaths
(f n4c)between source (S), reflection point (M), and receiver (G).
In conclusion, equation (4.28) representsthe angle-dependent
time shift causedby
isotropic velocity behavior of the thinly layeredoverburden.Furthermore,it
describes decrease the AVO response
resultingfrom multiple scatteringadditional
to the amplitude decay related to sphericaldivergence.
Widmaier eI ai. ( I 995) presented
similar lbrmulations for elasticP-waveAVO, where
the elasticcorrection formula dependsnot only on variancesand covariances P-wave
velocity, but also on S-wave velocity and density,and their correlationand 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
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
attenuation be described
in terms of a transt'ertunction Gt.o, t) fbr a plane wave of angular frequency or and
time r (Luh, 1993):
G @ , i : exp(at Qe* i(at lr Q) ln atI tos)
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:
3G ry :-'
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 compensate anisotropiceffects.In most cases,
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
This vector attenuationwill afl'ectAVO responses deeper
to the sea-floorinterf'ace.
include source direcon
The most important acquisition eff-ects AVO measurements
tivity, and source and receivercoupling (Martinez, J993). ln particular,acquisition
footprint is a large problem fbr 3D AVO (Castagna,2001).
Theseeffectscan be corrected
surfacewill causeunevenillumination of the subsurface.
Difl'erent methodsfor this have beenpresentedin the literfor using inverseoperations.
ature(e.g.,Gassaway a.,1986; Krail and Shin, 1990;Cheminguiand Biondi, 2002).
( 1993)method for normalizationof targetamplitudeswith a referenceampliChiburis'
tude provided a fast and simple way of corecting for certain data collection factors
including sourceand receivercharacteristics
of seismic forAVO
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.
Even though the unique goal in AVO processingis to preservethe true relative
sequence. dependson the complexity
amplitudes,there is no unique processing
seismicdata.and whetherthe data will
of the geology.whetherit is land or marine
AVO attributes or more sophisticatedelastic
be used to extract regression-based
Cambois(200 l) definesAVO processing any processing
equation,if that is the model used for the AVO
the data compatiblewith Shuey's
that this can be a very complicated
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 sourcefor
attempts compensate or removethese
but can in the processchange or distort relative trace amplitudes. This is an
important trade-off we need to consider in pre-processing AVO. We thereforeneed
to select basic robust
Common pre-processingstepsbefore AVO analysis
Spiking deconvolution and wavelet processing
In AVO analysis 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
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
variations are often more complicated to correct for, an4 are
attributed to both ofl.set-dependent
absorption (see Section 4.3.4), tuning efl'ects(see
actslike a low-pass,
nonstationaryfilter, and the eff'ects 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
Spherical divergence correction
Spherical divergence, or geometrical spreading, causes the intensity and energy of
spherical waves to decreaseinversely as the square of the distance fiom the source
(Newman, 1973).For a comprehensive
review on ofTset-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
off.setfbllowing Shuey's equation, and then using this behavior as a ret'erence
One of the most deterioratingeff-ects pre-stackamplitudes is the presenceof multion
ples.There are severalmethodsof filtering away multiple energy,but not all of these
adequatefor AVo pre-processing.
The method known asfft multiple filtering, done in
the frequency-wavenumberdomain, is very efficient at removing multiples, but the
in the.l-lr domain is very similar fbr near-offsetprimary energy and near-offsetmultiple
energy.Hence,primary energy can easily be removed from near tracesand not from
traces,resulting in an ar-tificialAVO effect. More robust demultiple techniquesinclude
linear and parabolic Radon transform multiple removal (Hampson, l9g6: Herrmann
NMO (normal moveout) correction
A potential problem during AVO analysis is error in the velocity moveout conection
(Spratt, 1987).When extracting AVO attributes,one assumes
that primaries have been
completely flattenedto a constanttraveltime.This is rarely the case,as there will always
be residual moveout. The reasonfor residualmoveout is almost always associated
erroneousvelocity picking, and greatef'fortsshoukl be put into optimizing the estimated
velocity field (e.g.,Adler, 1999;Le Meur and Magneron,2000).However,anisorropy
and nonhyperbolicmoveoutsdue to complex overburclen
may also causemisalignments
betweennearand far off.sets excellentpracticalexampleon AVO and nonhyperbolic
moveout was publishedby Ross, 1997).Ursin and Ekren (1994) presented method
for analyzing AVO eff-ects the off.setdomain using time windows. This technique
reducesmoveout elrors and createsimproved estimatesof AVO parameters.
be aware of AVO anomalieswith polarity shifts (classIIp, seedefinition below) during
NMO corrections,as thesecan easily be misinterpretedas residualmoveouts(Ratcliffe
and Adler, 2000).
DMO (dip moveout) processinggenerates
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).
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
Pre-stackmigration might be thought to be unnecessary areaswhere the sedimentary
it is an important component of all AVO processing.
section is relatively flat, but
Pre-stackmigration should be used on data for AVO analysis whenever possible,
because will collapsethe diffractions at the targetdepth to be smaller than the Fresnel
the lateral resolution(seeSection4.2.3; Berkhout, 1985;
zone and thereforeincrease
1996).Normally, pre-stacktime migration (PSTM) is preferred to preMosher et at.,
stackdepth migration (PSDM), because former tendsto preserveamplitudesbetter.
with highly structured geology, PSDM will be the most accurate
However, in areas
PSDM routineshouldthen be applied
tool (Cambois,2001).An amplitude-preserving
( B l e i s t e i n , 9 8 7 ;S c h l e i c h ee t c t l . , l 9 9 3 ; H a n i t z s c h 1 9 9 7 ) .
Migration fbr AVO analysis can be implemented in many different ways. Resnick
Kirchet aL. (1987) and Allen and Peddy (1993) among othershave recommended
hoff migration together with AVO analysis.An alternativeapproachis to apply wavederived a wave equation fbr
migration algorithms.Mosher et al. (.1996)
common-angle time migration and used inverse scatteringtheory (see also Weglein,
integration migrationand AVO analysis
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.
Example pre-processing forAVO
( Y i l m a z ,0 0 1 . )
( I ) Pre-stack
(2t Sort to CMP and do sparse
(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.
with the migrateddala'
(8) Detailedvelocity analysisassociated
(9) NMO correclionusing velocity field from step8.
( l0) StackCRP gathers obtainimageof pre-stack
multiplesrevealed lhe stacking.
( l l ) U n m i g r a t e s i n gs a m ev e l o c i t yf i e l d a s i n s t e p6 .
( l2; Post-stack
(13) Remigrateusing migrationvelocity field from step8.
interpretation t0 processing
The phaseof a seismicsectioncan be significantlyalteredduring
processing. rhe phase a sectionis not established the interpreter.
anomaliesthat would be interpretedas indicativeof decreasing
example.can be producedat interfaces
and Peddy. I993).
. Multiple filtering. Not all demultiple techniquesare adequatelor AVO predomain,is very
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
. NMO correction. potentialproblemduring AVO analysis errorsin the velocity
(Spran. 1987).When extractingAVO attributes.
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
reducesmoveoul errorsand creates
windows. This technique
NMO stretch is another problem in AVO analysis. Because
of AVO paramerers.
the amount of normal moveout varies with arrival time. frequenciesare lowered
at large offsets compared with short offsets. Large offsets, where the stretching
effect is significant.should be muted before AVO analysis.Swan (1991), Dong
(1998) and Dong ( 1999)examinethe eft'ectof NMO stretchon offset-dependenl
. AGC amplirude conection. Automatic gain control must be avoided in predata beforedoing AVO analysis.
Pre-processing for elastic impedance inversion
Severalof the pre-processingstepsnecessary AVO analysisare not required when
preparingdatafor elasticimpedanceinversion(seeSection4.4 for detailson the methodology). First of all, the elastic impedanceapproachallows for wavelet variations with
eachlimitedoffset (Cambois,2000). NMO stretchcorrectionscan be skipped,because
to be stationary)is matchedto its
range sub-stack(in which the waveletcan be assumed
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
Figure4,6 AVO curvesfbr differenthalf'-space
models(i.e.,two layers one intertace).
Input rock physics
Finally,residualNMO and multiplesstill must be accounted
(Cambois,2001). Misalignmentsdo not causeinterceptleakageas fbr standard
but near-and far-anglereflections
must still be in phase.
AVO analysisis normally carried out in a deterministicway to predict lithology and
fluids from seismicdata(e.g.,Smith and Gidlow, 1987;RutherfordandWilliams, 1989;
and Smith, 1994;Castagna al., 1998).
Forward modeling of AVO responsesis normally the best way to start an AVO
analysis, as a feasibility study before pre-processing,inversion and interpretation of
real pre-stack data. We show an example in Figure 4.6 where we do AVO modeling
of difTerentlithofacies defined in Section 2.5. The figure shows the AVO curves for
different half-spacemodels, where a silty shale is taken as the cap-rock with difTerent
underlying lithofacies. For each facies, Vp, Vs, and p are extractedfrom well-log data
and used in the modeling. We observea clean sand/pure
and facies V) at near of1iets,whereasclean sandsand shalesare distinguishableat far
offsets.This exampledepictshow AVO is necessary discriminatedifferent lithofacies
in this case.
sandstone unconsolidated capped
shlle.frll brine-saturated oil-saturated
Figure 4.7 shclwsanotherexample,where we considertwo types of clean sands,
cementedand unconsolidated,with brine versushydrocarbonsaturation.We seethat a
with hydrocarbon saturationcan have similar AVO responseto a
The examplesin Figures 4.6 and 4.7 indicate how important it is to understandthe
local geology during AVO analysis.lt is necessary know what type of sandis expected
for a given prospect,and how much one expectsthe sandsto change locally owing to
textural changes,before interpreting fluid content. It is therefore equally important to
coniluct realisticlithology substitutions addition to fluid substitutionduring AVO
the imporrnodelingstudies.The examplesin Figures4.6 and 4.7 also demonstrate
(Chapter 2) during AVO analysis.
tance of the link between rock physics and geology
Whenis AVOanalysisthe appropriate
It is well known that AVO analysisdoes not always work. Owing to the many
caseswhere AVO has been applied withoul success, techniquehas receiveda
bad reputationas an unreliabletool. However.part ol the AVO analysisis to find
out if the techniqueis appropriatein the first place. It will work only if lhe rock
physicsand ffuid characleristics the targetreservoirare expectedto give a good
This must be clarifiedbeforethe AVO analysis real data.Without
a proper feasibility study.one can easily misinterpretAVO signatures the real
data.A good feasibility study could include both simple reflectivitymodeling and
forward seismicmodeling(seeSection4.51.Both thesetechniques
shouldbe foundedon a thoroughunderstanding local geologyand petrophysical
Realisticlithology substitution as importantas fluid substitution
Often, one will find that there is a certain depth interval where AVO will work,
often referred to as the "AVO window." Outside this, AVO will not work well.
That is why analysis of rack physics depth trends should be an integral part of
AVO analysis (see Sections 2.6 and 4.3.16). However. the "AVO window" is also
constrained data quality. With increasingdepth, absorptionof primary energy
ratio. higher frequencies graduallymore attenualed
than lower frequencies. geology usually becomesmore complex causingmore
complexwave propagations, theanglerangereduces a given streamer
All thesefactorsmake AVO lessapplicablewith increasing
4.3.8 Deterministic analysis GDP
AVO modeling, the next step in AVO analysisshould be deterAfter simple half--space
ministic AVO analysis of selectedCDP (common-depth-point)gathers,preferably at
well locations where synthetic gathers can be generatedand compared with the real
CDP gathers. this section,we show an exampleof how the methodcan be appliedto
lithofacies real seismicdata,by analyzingCDP gathers well locations
in a deterministic way. Figure 4.8 shows the real and synthetic CDP gathers at three
well locationsin a North Seafield (the well logs are shownin Figure5.1, case
l). The figure also includesthe picked amplitudesat a top targethorizon superstudy
imposed on exact Zoeppritz calculated reflectivity curves derived fiom the well-log
In Well 2, the reservoir sandsare unconsolidated,
are cappedby silty shales.According to the saturationcurves derived fiom deep resisthe 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
0 323 726 1210 1694 2177
0 1 0 0;
34 (deq) Anqle
29 (deg) Angle
Figure4.8 Real CDP gathers(upper),syntheticCDP gathers(middle),and AVO curvesfor Wells
I 3 (lower).
The correspondingAVO responseshows a negativezero-ofTset
reflectivity and a negative AVO gradient. In Well l, we have a water-saturated
cementedsand below a silty
shale.The correspondingAVO responsein this well showsa strongpositive zero-ofl.set
reflectivity and a relatively strong negative gradient. Finally, in Well 3 we observe a
strongpositive zero-offsetreflectivity and a moderatenegativegradient,corresponding
faciescappedby silty shales.Hence,we observethreedistinct
AVO responsesin the three different wells. The changesare related to both Iithology
and pore-fluid variations within the turbidite system. For more detailed information
about this system,seecase study I in Chapter 5.
Avseth et al. (2000) demonstratedthe etlect of cementationon the AVO responsein
real CDP gathersaround two wells, one where the reservoir sandsare friable, and the
other where the reservoir sands are cemented.They found that if the textural eflects
of the sandswere ignored, the correspondingchangesin AVO responsecould be interjust as depictedin the reflectivitymodeling examplein
lmpodance0f AVOanalysisof individualCDPgathers
Investigations CDP gathersare importanl in order ro confirm AVO anomalies
and gradient,Smith and Gidlow's
fluid factor. etc.). The weighted stackscan contain anomaliesnot related to true
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 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
R(r, : R(/,0) + c(/) sin2g(r,
where 0(r, x) is the incident angle corresponding to the data sample recorded at
( t .r ) .
For a layered Earth, the relationshipbetweenofliet (r) and angle (0) is given approximately by:
s i n0 ( r ,x ) I
where VrNr is the interval velocity and Vnr,,rs the averageroot-mean-square
ity, as calculated from an input velocity profile (fbr example obtained from sonic
For any given value of zero-offsettime, /e, we assumethat R is measuredat N offsets
(xi, i:1, A/).Hence,we can rewrite the defining equationfbr this time as (Hampson
a n d R u s s e l l .1 9 9 5 ) :
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":
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 seisincluding Vp, V5 and density.This is commonly
mic amplitudesfor elasticparameters,
ref'erredto as AVO inversion, and can be performed via nonlinear methods
Buland et al., 1996;Gouveiaand Scales,1998)or linearizedinversion
methods(e.g., Smith and Gidlow, 1987; Loertzer and Berkhout, 1993).Gouveia and
Scales( 1998)clefined Bayesiannonlinearmodel and estimated, a 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 perfbrmedsimultaneously all times in a given time window, which
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.
. A linearapproximation the Zoeppntzequations commonly usedin the calcuof
lation of R(01and G. The two-term Shueyapproximationis known lo be accurate
30'. Make surethat the data inverted
for anglesof incidenceup to approximately
do not exceedthis range,so the approximalionis valid'
. The Zoeppritzequations only valid fbr single interfaces.
will not be valid lor thin-bedded
that are basedon theseequations
. The linear AVO inversionis sensitiveto uncharacteristic
and acquisirioneffects.A few outlying
noise (including multiples.) processing
amplitudes enoughto causeerroneous
valuespresent the pre-stack
packagesfor eslimationof R(0) and
of R(0) and G. Mosr commercial software
C a p p l y r o b u s r s t i m a r i o ne c h n i q u e ( e . g . ,W a l d e n .1 9 9 l ) t o l i m i t t h e d a m a g e l '
AVO inversion is errors
. Another potential problem during sample-by-sample
(Spratt, 1987l. Ursin and Ekren (1994) presented
in the moveout correction
method for analyzing AVO eflects in the offset domain using time windows.
This techniquereducesmoveout errors and createsimproved estimates AVO
A very helpful way to interpret AVO attributesis to make cross-plotsof intercept(R(0))
versusgradient(G). Theseplots are a very helpful and intuitiveway of presenting
of the rock propertiesthan by analyzing the
data, and can give a better understanding
schemeof AVO responses
Rutherfordand Williams ( 1989)suggested classification
(seeFigure 4.9). They defined three AVO classes
fbr 6iflerent types of gas sanils
on where the top of the gas sandswill be locatedin an R(0) versusG cross-plot.
cross-plotis split up into fbur quadrants. a cross-plotwith R(0) along .r-axisand C
along,v-axis, I st quadrantis whereR(0) and G areboth positivevalues(upperright
and G is positive(upperleft quadrant).
The 2nd is whereR(0) is negative
3rd is where borh R(0) and G arenegative(lower left quadrant).Finally, the 4th
is where R(0) is positive and G is negative (lower right quadrant).The AVO classes
after Ruthe(brd and Williams (1989)'
Tabfe AVO classes,
extendecl Castagnaand Smith (1994), and Rossand
K i n m a n( 1 9 9 5 )
No or low contrast
I ctass I cra.i I crass
(classes ll and
Figure Ruthertbrd williamsAVOclasses,
clnsses (Castagna Smith.
Figure aclapted Castagna al. (1998)'
plots in the 4th quadrant
must not be confused with the quadrant numbers. Class I
with positive R(0) and negativegradients.These representhard
class II represents
high impedanceand low vp/vs ratio compared with the cap-rock.
can be hard to see on
sands with weak intercept but strong negatjve gradient. These
sections' Class III
the seismic data, becausethey often yield dim spots on stacked
These plot in the
is the AVO category that is normally associatedwith bright spots'
with soft sandssaturatedwith
3rd quadrant in R(0)-G cross-plots,and are associated
betweena class IIp and class II anomaly'
Ross and Kinman (1995) distinguished
gradient, causing a polarity
Class IIp has a weak but positive intercept and a negative
class II has a weak
changewith oflset. This class will disappearon full stack sections.
polarity change.This class may
but negativeintercept and negativegraclient,henceno
be observedas a negativeamplitude on a full-ofliet stack'
of Rutherford and
Castagnaand Swan (1997) extendeclthe classification scheme
quadrant.These are relatively rare'
Williams to incluclea 4th class,plotting in the 2n<1
stiff shales 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
' AVO classI represents
plot along the background
trend in intercept-gradient
hard sandscan have little sensitivityto fluids. so there may not be an associated
flat spot. Hence.thesesandscan be hard to discoverlrom seismicdata.
. AVo classII. representing
often show up as
they should show up as anomaliesin an Rt0)-c cross-plot.and
plot off the backgroundtrend.
' AVO classIII is the "classical"AVO anomalywith negative
gradient.This class represents
relatively soft sands wirh high fluid sensitivity,
locatedfar away from the background
trend.Hence,they shouldbe easyro derect
on seismic ata.
' AVO classIV aresands
versusoffset.even though Lhese
sandsmay be bright spots(castagnaand Swan.
1997).Class lV anomalies relativelyrare,but occur when soft sandswith gas
characterized vplvs ratiosslightly
( i . e . .v e r y c o m p a c t e d r s i l t y s h a l e s ) .
h i g h e rt h a n i n t h e s a n d s
The AVo classes
were originally defined for gas sands.However.today the AVo
class system is used for descriptiveclassification observedanomaliesthal are
gas sands.An AVO class Il that is drilled can turn out to be brine
sands.It does not mean that the AVo anomaly was not a class ll anomaly.we
therefbresuggestapplying the classification
only as descriptive
terms for observed
A V o a n o m a l i e s , i t h o u t a u l o m a t i c a l l yi n f e r r i n g t h a t w e a r e d e a l i n g w i t h g a s
AVO trends and the effects of porosity, lithology and compaction
When we plot R(0) and G as cross-plots,we can analyzethe trendsthat occur in terms of
changes rock physicsproperties,
trends,as these will have different directionsin the cross-plot(Figure 4. 1l). Using
rock physicsmodels and then calculatingthe corresponding
we can study various "What lf" scenarios,and then compare the modeled trends with
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.
occurring an intercept
Castagnaet at. (1998) presentedan excellent overview and a fiamework for
normally plot in the 4th
gradient and intercept interpretation.The top of the sandswill
quadrant,with positive R(0) and negativeG. The baseof the sandswill normally
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
of the R(O)-G coordinate system. This trend will rotate with contrast in Vp/V5
betweena shaly cap-rockancla sandyreservoir(Castagna al., 1998;Sams'
and the slope of the background
We can extract the relationship between VplVs tatio
trencl(a6) by clividing the gradient, G, by the intercept,R(0):
Assuming the density contrast between shale and wet sand to be zero, we can
how changinE VplVs ratio affects the backgroundtrend. The density contrastbetween
with the velocity
sandand shaleat a given depthis normally relativelysmall compared
(Fosteret a.,1991). Then the backgroundslopeis given by:
^ l - ( V s*r Y s 2 ) A Y s l
" L t Y nt V p : t A V p l
where vp1 and vpz are the P-wave velocities in the cap-rock and in the reservoir,
respectively; Vs1 and V52are the correspondingS-wave velocities, whereas AVp
AV5 are the velocity differencesbetween reservoir anclcap-rock. If the Vp/V5
background trend is - l, that
2 in the cap-rock and 2 in the reservoir,the slope of the
is a 45' slope diagonal to the gradient and intercept axes.Figure 4'12 shows
and the cap-rock.
lines correspondingto varying Vp/V5 ratio in the reservoir
The rotation of the line denoting the background trend will be an implicit function
of rock physics properties such as clay content and porosity. Increasing clay
F i g u r e 4 , 1B a c k g r o u n d t r e n d s i n A V O c r o s s - p l o t s a s a f u n c t i o n o f v a r y i n g V p l V < r a l i o i n c a p - r o c k
andreservoir. assume density
thataVplVsratioof 1.5in thereservoir
ratioof thecap-rock 2.5,thesand
AVOclass to III behavior
ratiois 2.0, sand exhibit
class to IIp behavior
at a reservoirlevel will causea counter-clockwise
rotation, as the Vp/V5 ratio will
increase. Increasing porosity related to less compaction will also cause a 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.
with depth,but the way it changes be complex.
(Luh, 1993),will afI-ect background
trend as a function of depth, but correction should be made fbr this before rock physics
analysisof the AVO cross-plot(see Section4.3.6). Nevertheless, rotation due to
depth trends in the elastic contrastsbetween sandsand shalesis not straightforward,
theVplVs in the cap-rock as well as the reservoirwill decrease
These two efTects
will counteracteach other in terms of rotational direction. as seenin
Figure4. 12.Thus, the rotationwith depthmust be analyzed
locally.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
and Swan, 1997).That would causeseveralslopesto be superimposed
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.
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)
case.However, Castagnaet al. (1998)
and G valuescomparedwith the brine-saturated
sandscould exhibit a variety of AVO behaviors.
fbund that, in particular, gas-saturated
As lisred in Table 4.1. AVO classIII anomalies(Rutherfordand Williams, 1989),
representingsoft sandswith gas, will fall in the 3rd quadrant(the lower left quadrant)
and have negativeR(0) and G. These anomaliesare the easiestto detect fiom seismic
d a t a( s e eS e c t i o n . 3 . 1l ) .
AVO classI anomalies,will plot in the 4th quadrant
(lower right) and have positive R(0) and negative G. Consequently,these sandstend
to show polarity reversalsat some offset. If the sandsare very stiff (i.e., cemented),
they will not show a large change in seismic responsewhen we go from brine to gas
(cf. Chapter l). This type of AVO anomaly will not show up as an anomaly in a product
stack. In fact, they can plot on top of the background trend of some softer, 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
trend,especially the sandsarerelativelydeep.However,classII
with the background
type oil sandscan occur very shallow,causingdim spotsthat stick out comparedwith
(i.e., when heterolithicsand brine-saturated
a bright backgroundresponse
they are dim they
relatively stifT compared with overlying shales).However, because
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
velocity is lower than that of the
showedthat this may occur if the gas-sandshear-wave
overlyingformation.The most likely geologicscenario suchan AVO anomalyis in
unconsolidatedsandswith relatively large VplVs ratio (Fosteret crl., 1997).That means
that if the cap-rockis a shale,it must be a relativelystiff and rigid shale,normally a
very silt-rich shale.This AVO responsecan confusethe interpreter.First, the gradients
of sandsplotting in the 2nd quadranttend to be relatively small, and less sensitiveto
fluid type than the gradientsfor sandsplotting in the 3rd quadrant.Second,theseAVO
anomalieswill actually show up as dim spots in a gradient stack.However, they should
stand out in an R(0)-G cross-plot,with lower R(0) values than the background trend.
they shouldstandout as negative
. Differentrock physicstrencls AVO cross-plots be ambiguous.
The interpretation of AVO trendsshouldbe basedon locally constrained
n o t o n n a i v er u l e so f t h u m b .
. Trendswithin individualclustersthat do not projectthroughthe origin on an AVO
cannot always be interpretedas a hydrocarbonindicator or unusual
lithology.Sams (1998) showedthat it is possiblefortrends to have large offsets
from the origin even when no hydrocarbons presentand the lithology is not
unusual.Only where the rocks on either side of the reflectingsurfacehave the
same Vp/V5 ratio will the lrends (not to be confusedwith backgroundlrends as
shown in Figure 4. l2.l project through the origin. Sams showedan exampleof a
brine sandthat appeared
than a Iessporoushydrocarbon-bearing
. Residualgas saturation
can causesimilar AVO effectsro high saturations gas
or light oil. Three-termAVO where reliableestimates density are oblained.or
can potentiallydiscriminateresidualgas saturations
commercialamountsof hydrocarbons seeSections
4.3.12 and4.3. | 5 for further
betweenR(0) and G will also includea noisetrend,because the correof
lation betweenR(0) and G. BecauseR(0) and G are obtained from least-square
there is a negative correlation between R(0) and G. Larger intercepts are correlated
with smallerslopesfbr a given data set. Hence,uncorrelated
random noise will show
an oval, correlateddistribution in the cross-plotas seen in Figure 4.13 (Cambois,
Furthermore,Cambois (2001) formulated the influenceof noise on R(0), G and
a range-limitedstack (i.e., sub-stack)in terms of approximateequationsof standard
f t - - "ti
o C : V f
Figure4,13 Randomnoisehas a ttend in rR(0)
o,,- Ji .o,
deviation of the full-stack response, is the standard
where d " is the standard
of the sub-stack.and n is the number of sub-stacks the full fold data. As we see,the
stack reducesthe noise in proportion to the squareroot of the fold. These equations
indicate that the intercept is less robust than a half-fold sub-stack,but more robust
than a third-fold sub-stack.The gradient is much more unreliable, since the standard
deviation of the gradient is inversely proportional to the sine squaredof the maximum
angle of incidence. Eventually, the intercept uncertainty related to noise is more or
lessinsensitiveto the maximum incidenceangle, whereasthe gradient uncertainty will
decreasewith increasingaperture(Cambois, 2001).
Simm er a/. (2000) claimed that while rock property infbrmation is containedin AVO
cross-plots,it is not usually detectablein terms of distinct trends, owing to the effect
of noise. The fact that the slope estimationis more uncertainthan the intercept during
a least-squareinversion makes the AVO gradient more uncertain than the zero-offset
reflectivity (e.g., Houck, 2002). Hence,the extensionof a trend parallel to the gradient
axis is an indicationof the amountof noise in the data.