1.
I
techniques quantitative
for
4 Common
seismic
interpretation

Thereare no facts,only interpretations.
lriedrith
Niet:sche

4.1 Introduction
Conventionalseismicinterpretation
implies picking and tracking laterally consistent
seismic reflectors for the purpose of mapping geologic structures,stratigraphy and
reservoir
architecture.
The ultimategoal is to detecthydrocarbon
accumulations,
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
is
of
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 poststackamplitucle
(brightspot
analysis
anddimspotanalysis),
(AVO
offsetdependent
amplitudeanalysis
analysis),
acousticand elasticimpedance
inversion,and forward seismicmodeling.
These techniques,if used properly, open up new doors for the seismic interpreter.
The seismicamplitudes,
representing
primarily contrasts elasticproperties
in
between
individual layers,contain information about lithology, porosity,porefluid 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 .
i

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 op a p e rs e c t i o n s
ng
with seismic data down the hallway, go down
168
2.
169

amplitude
interpretation
4,2 Qualitative
seismic
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
In
their interpretations. the early 1970sthe socalled"brighrspot" techniqueproved
would coincidewith
in
of
successful areas the Gulf of Mexico, wherebright amplitudes
gasfilled 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
opposite
analysis, hardvolcanicintrusions
as
waveletphase
impedance gas sands.Moreover, experienceshowed that gasfilled sands sometimes
could cause"dim spots," not "bright spots," if the sandshad high impedancecompared
shales.
with surrounding
With the introductionof 3D seismicdata, the utilization of amplitudesin seismic
interpretation became much more important. Brown (see Brown et ul., l98l) was
The
of
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 virtualrealityworld of seismic
visualization
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 rolledout
paper sectionsdown the hallways to the virtualreality 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
of
review the
impedance
suchasAVO analysis,
techniques
more quantitative
and rockphysicsbased
inversion,and seismicmodeling,in fbllowing sections.
phase polarity
4.2.1 Wavelet
and
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
wavelet?
or
polarity in our case?Are we dealingwith a zerophase a minimumphase
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 nearofl.set
stack section a "hard" event will correspondto an increasein acousticimpedancewith
in
depth, whereasa "soft" event will correspondto a decrease acousticimpedancewith
depth. According to the European standard,a black peak is a "soft" event, whereas a
3.
170
T
Gommon
techniques quantitative
for
seismic
interpretation
white trough is a "hard" event. One way to check the polarity of marine data is to look
at the seafloorreflector.This reflector should be a strongpositive reflector representing
the boundary between water and sediment.
polarity
Data
' American polarity: An increase impedance
in
gives positiveamplitude.normally
displayedas black peak (wiggle r.race) red intensitylcolor displayt.
or
. European Australian)polarity:An increase impedance
(or
in
givesnegal.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
zerophase.
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
include manualpicking,
interpolation,autotracking,
voxel tracking, and surfaceslicing (see Dorn (199g) fbr
detaileddescriptions).
For extraction of seismic horizon slices, autopicked or voxeltracked 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 signaltonoise
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
be
also be significantly off if we do not regard lateral phaseshifts. It is important that the
interpreter
realizesthis and reviewsthe seismicpicks for quality control.
4.2.2 Sand/shale
crossovers depth
with
Simple rock physicsmodeling can assistthe initial phaseof qualitativeseismicinrerpretation, when we are uncertain about what polarity to expect for diff'erentlithology
boundaries. a siliciclastic
In
environment,
most seismic
reflectors
will be associated
with
sandshaleboundaries.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
4.
171

4.2 Qualitative
seismic
amplitude
interpretati0n
Sand
versus
shale
impedance trends
depth
polarity
(schematic)
andseismic
rmpe0ance
1
t
Sandshale
crossover
DeDth
Figure Schematic
4'1
depth
trends sand shale
of
and
impeclances. depth
The
trends varyfiom
can
basin basin, there be morethanonecrossover.
to
and
can
Localdepth
trends
should established
be
for different
basins.
shalesare mainly affectedby mechanicalcompaction.Hence, cementedsandstones
are
normally found to be relatively hard eventson the seismic.There will be a corresponding crossoverin 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
cementedsandstones
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.
venius
"Hard"
"soft"events
During seismicinterpretation a prospect a provenreser"yoir
of
or
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 issue
can be solvedby generating
synthetic
seismograms correlating
and
these
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 lordifferent geologic scenarios.
5.
172
Common
techniques quantitative
for
seismic
interpretation
T
Typical
"hard"events
. Very shallow sandsat normal pressure
embedded pelagicshales
in
. Cementedsandstone
with brine saluration
. Carbonate
rocks embedded siliciclastics
in
' 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
(
l
,
a deposits
Typical
"soft" events
. Pelagic
shale
' S.hallow,
unconsolidated
sands(any pore fluid) embedded normally compacted
in
shales
' Hydrocarbon
accumularions clean.unconsolidated poorly consolidated
in
or
sancls
. Overpressured
zones
pitfalls conventional
Some
in
interpretation
' Make sure you know the polarity of the data. Rememberthere are two
different
standards, US standard
the
and the European
standard.
which are opposire.
' A hard event can changeto a soft laterally (i.e.. lateralphaseshifi;
if there are
petrographic porefluidchanges.
or
Seismicaurotracking
will nor derecr
l:jloloCic.
these.
' 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
o
.
i t h e z o n eo f
sand/shale
impedancecrossover.
AVO analysisshould be underraken reveal
to
potentialhydrocarbon
accumulations.
I
ii
ji
4.2.3 Frequency scaleeffects
and
Seismic resolution
Verticalseismicresolution definedas theminimum separation
is
between
two interfaces
such that we can identify two interfacesrather than one (SherifTand Geldhart, 1995).
A stratigraphic
layer can be resolvedin seismicdataif the layer thickness largerthan
is
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, can still gain important infbrmation via quanwe
titative analysisof the interference
amplitude.A bed only ),/30 in thicknessmay be
detectable,
althoughits thicknesscannotbe determinedfiom the wave shape(Sheriff and
Geldhart.1995).
6.
173
E
interpretation
amplitude
seismic
4.2 Qualitative
tiickness
Layer
wavelength.
fbr
thickness a given
of
as
amplitude a function layer
4,2
Figure Seismic
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
p
rellection oint:
n  Jgz
G.2)
where z is the reflector clepth.Roughly, the Fresnel zone is the zone from which all
of
reflected contributions have a phase diflerence less than z radians. For a depth of
Fresnelzone radius will be 300470 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,
the
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 crosslinedirection. 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(50100 m), lateral sampling is not the
For typical surf'ace
clata.
l i m i t i n gl a c t o r .
Interference and tuning effects
A thinlayered reservoir can cause what is called event tuning, which is interf'erence
the
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
7.
174

Gommon
techniques quantitative
for
seismic
interpretation
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
and
approacheszero for layer thicknessesbetween onequarterof a wavelength and zero
thickness. We refer to this as destructive interferencebetween the top and the base.
Troughtopeak
time measurements
give approximatelythe correctgrossthicknesses
for thicknesses
larger than a quarterof a wavelength,but no information fbr thicknesses
lessthan a quarterof a wavelength.
The thickness an individualthinbedunit can be
of
extractedfrom amplitude measurements the unit is thinner than about ),/4 (Sheriff
if
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 amplitudethickness
curve is almost linear below ),/8 with decreasing
amplitudeas the layer gets thinner,
but the compositeresponse
staysthe same.
4.2.4 Amplitude reflectivity
and
strength
"Bright spots" and "dim spots"
The first use of amplitude information as hydrocarbon indicators was in the early
1970swhen it was fbund that brightspotamplitude 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."
to
However, if the sand is relatively hard (compared with caprock), the sand saturated
with brine may induce a "brighlspot" anomaly,while a gasfilledsandmay be transparent, causing a socalleddim 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)states
that "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 investigating
limitedrange
stack sections.
A very weak nearoffsetreflector may have a correspondingstrong f'aroflsetreflector.
However,some sands,although they are significant,produce a weak positive nearoffset reflection as well as a weak negative faroffset reflection. Only a quantitative
analysis the changein nearto faroffsetamplitude,a gradientanalysis,
of
will be able
8.
175
T
interpretation
amplitude
seismic
4.2 Qualitative
to reveal the sand with any considerabledegree of confidence. This is explained in
Section4.3.
Pitfalls:False"bright spots"
"brighr spots"are usuallythe first type
During seismicexplorationof hydrocarbons.
of DHI (direct hydrocarbonindicators)one looks for. However.there have been
severalcaseswhere brightspotanomalieshavebeendrilled. and turned out not lo
be hydrocarbons.
Some common "false bright spors"include:
. Volcanicintrusionsand volcanicash layers
. Highly cementedsands.
often calcitecementin thin pinchoutzones
. Lowporosityheterolithicsands
. Overpressured
sandsor shales
. 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 causesocalled"hardkick" amplitudes.
bright
hydrocarbonassociated
polariryof the dataone shouldbe able lo discriminare
"hardkick" anomalies.
AVO analysisshould permit discrimination
spots from the
sands/shales.
from coal, salt or overpressured
of hydrocarbons
is
attributeusedamong seismicinterpreters
A very common seismicamplitude
over a given
amplitudescalculated
rellectionintensity,which is rootmeansquare
lime window. This anribute does not distinguish between negativeand positive
ol
thereforegeologic interpretation this attributeshould be made with
amplitudes;
greatcaution.
"Flat spots"
Flat spotsoccur at the reflectiveboundary betweendifferent fluids, either gasoil, gaswarer,or wareroil 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 fluidrelated flat spot can be difficult to discover. Then, quantitative
methods like AVO analysiscan help to discriminate the fluidrelated 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 depthdependent.
an
boundary between opalA and opalCT 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 largerscalestratigraphy is tilted.
and
deposits
sheetflood
Other "false" flat spotsinclude volcanicsills, paleocontacts,
flat basesof lobesand channels.
tl
9.
176

for
Common
techniques quantitative
seismic
interpretation
Pitfalls: "flatspots"
False
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
flat spots:
. Oceanbottom multiples
. Flat stratigraphy.
The bases sand lobesespecially
of
tend to be flat.
. OpalA to opalCT diagenetic
boundary
. Paleocontacts,
either relatedto diagenesis residualhydrocarbon
or
saturation
. Volcanicsills
Rigorousflatspotanalysisshould 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
hydrocarbon
reservoirs. 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 welllog data is required to discriminate fluid effects quantitatively trom
lithology effects (Chapters I and 2).
The "brightspot" analysismethod has ofien been unsuccessful
becauselithology
effects rather than fluid effects up the bright spot. The consequence the drilling of
set
is
holes.In order to reveal"pitfall" amplitude anomaliesit is essential investigatethe
dry
to
rock physicspropertiesfiom welllog data.However,in new frontier areaswell1ogdata
are sparse lacking. This requiresrock physicsmodeling constrained reasonable
or
by
geologic assumptions
and/or knowledge about local compactionaland depositional
trends.
A common way to extractporosity from seismicdata is to do acousticimpedance
inversion.Increasing
porositycan imply reducedacousticimpedance,
and by extracting empiricalporosityimpedance
trendsfrom welllog data,one can estimate
porosity
from the inverted impedance.However, this methodology suffers from several ambiguities. Firstly, a clayrich shalecan have very high porosities,even if the permeability
is closeto zero.Hence,a highporosity
zone identifiedby this technique
may be shale.
Moreover, the porosity may be constant while fluid saturationvaries, and one sinrple
impedanceporosity
model may not be adequate seismicporositymapping.
fbr
In addition to lithologyfluid ambiguities, lithologyporosity ambiguities, and
porosityfluid ambiguities,we may have lithologylithology ambiguitiesand fluidfluid ambiguities.Sand and shalecan have the sameacousticimpedance,
causingno
reflectivity on a nearoffset 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
10.
Plate1,1 SeismicPP amplitudemap over a submarine
fan. The amplitudes sensitive lithofaciesand
are
to
pore fluids, but the relationvariesacrossthe imagebecause
ofthe interplayofsedimentologicand diagenetic
influences.
yellow and red high amplitudes.
Blue indicateslow amplitudes,
4120
4140
2.92
41
60
2.94
41
B0
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 r,D
) )),
D) r )r>),
p
),
i)P,?),,?l? )?i)i)
l??
iriiiiiiii r)ii)i)
iiiii ii
lrlllliilrlllllil,
10
15
Distance
20
25
Plate1,30 Top left, logs penetrating sandyturbidite sequence; right, normalincidence
a
top
synthetics
with a
50 Hz Ricker wavelet.Bottom: increasing
water saturation from l1a/c 907c(oil API 35, GOR 200)
S*
Lo
increases
densityand Vp (left), giving both amplitudeand traveltimechanges
(right).
11.
177
r
interpretation
4.2 Qualitative
seismic
amplitude
interpretation is usually that the channel is shalefilled. 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.
reflectivity analysis
More advancedgeophysical techniquessuch as offsetdependent
may also reveal the sands.During conventionalinterpretation,one should interpret top
reservoir horizons from limitedrange stack sections,avoiding the pitfall of missing a
dim sandon a nearor fullstackseismicsection.
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
we
systems
system.By relatinglithologiesto depositional
occur within a depositional
The link between amplitude characteristics
often refer to theseas lithofacies or facies.
and depositional patternsmakes it easierto distinguish lithofacies variations and fluid
in
changes amplitudemaps.
Traditional seismicfaciesinterpretationhasbeenpredominantlyqualitative,basedon
of
The traditionalmethodologyconsisted purely visual inspection
seismictraveltimes.
(e.g.,Mitchum et al., 1977;Weimer and
in
of geometricpatterns the seismicreflections
from amplitude
buriedriver channels
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
of
understanding shallow marine facies from seismic amplitudes.Neri (1997) used
Reliablequantitativelithofacies
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.
Stratigraphic interpretation
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).
or
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,
a
12.
178
interpretation
seismic
for
techniques quantitative
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
a
occur without a lithology change(e.g.,Hardage,1985).For instance, hiatuswith no
the
because shales
intervalcan give a strongseismicsignature
within a shale
deposition
above and below the hiatus have difTerent characteristics.Similarily, amalgamated
sandscan yield internal stratigraphywithin sandy intervals,reflecting different texture
fiom diflerentdepositionalevents.Third, seismicresolution can be a pitfall in
of sancls
onlapsor downlaps.
especiallywhen interpretingstratigraphic
seismicinterpretation,
in
characteristics seismicinterpretation,asthey can give information
Theseareessential
coastal development related to relative sea level changes (e.g., Vail er ai.,
about the
can occur if the thicknessof individual layers reduces
I 977). However, pseudoonlaps
The layer can still exist,even if the seismicexpression
the seismicresolution.
beneath
yields an onlap.
Pittalls
that
interpretation can
seismicstratigraphic
pitfalls in conventional
Thereareseveral
quantitative
techniques:
be avoidedif we usecomplementary
. lmportant lithostratigraphic
betweenlayerswith very weak contrasts
boundaries
in seismicpropefiiescan easily be missed.However.if different lithologiesare
seismic
seismic
data.they arenormallyvisiblein prestack
in
transparent poststack
similar to
dara. AVO analysisis a useful tool to reveal sandswith impedances
4
{
c a p p i n gs h a l e s s e eS e c t i o n . 3 1 .
and
. It is commonlybelieved
are
events time boundaries. not necessarily
thatseismic
For instance.a hiatus within a shale may causea
boundaries.
lithostratigraphic
strong seismicreflectionif the shaleabovethe hiatus is lesscompactedthan the
of
onc below.even if the lithology is the same.Rock physicsdiagnostics welllog
(seeChapter2 ).
data may revealnonlithologicseismicevents
. Because limited seismicresolution,false seismiconlapscan occur.The layer
of
can improvethe resolution.
inversion
Impedance
resolution.
may still existbeneath
featuresnot observedin the original seismicdata
and revealsubtle srrailgraphic
( s e eS e c t i o n . 4 ) .
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 stratigraphyguidedrock physics analysis of welllog data improved the
stratigraphicinterpretationof a fluvial systemin Colombia using impedance
sequence
inversion of 3D seismicdata. Conducting impedanceinversion of the seismic data will
13.
179

4,2 Qualitative
seismic
amplitude
interpretation
give us layer propertiesfrom interfhceproperties,and an impedancecrosssection
can
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 welllog data,
to
and it tends to averageout random noise, thereby improving the detectability of later(Gluck et a.,1997).Moreover,
frequencybandlimited
impedance
ally weakreflections
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
of
(seeSection4.5).
geologicstratigraphy
Layer thickness and nettogross from seismic amplitude
As mentioned in the previous section, we can extract layer thickness from seismic
As
is
amplitudes. depictedin Figure 4.2,the relationship only linear for thin layersin
pinchout zonesor in sheetlikedeposits,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
thickness seismicsignaland
on
introduced what they referred to as effective reflection strength, applicable to layers
thinnerthan the tunins thickness:
o'.  2 "  Z ' n . ,
Zrr
(4.3)
impedance, is the average
216
where Z. is the sandstone
shaleimpedance
and /z is the
layerthickness. more commonway to extractlayerthickness
A
from 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 nettogrossfiom P and Simpedances fbr a turbidite system. From acoustic impedance (AI) versus shear
impedance (SI) crossplots, the nettogross can be calculated with the fbllowing
fbrmulas:
14.
r
180
Common
techniques quantitative
for
seismic
interpretation
E
I
NIG:
Vrung
dZ
Zrr.
AZ
(4 4)
where V."n,lis the oilsand fraction given bv;
SIbAIce
Kano
atao
(4.5)
where b is the averageslope of the shaleslope(06) and oilsandslope(b1),whereas
ae
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 .
e
s
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
t
f
s
areaswhere sandsare expectedto be thinner than the tuning thickness.that is a
quarterof a wavelength.
and wherewelllog datashow evidence good correlation
of
belweennet sandlhicknessand relativeamplirude.
It can be difficult to discriminate
layer rhickness
changes
from lirhologyand fluid
changes. relativelysoft sands, impactof increasing
In
the
porosityand hydrocarbon
saturation
tendslo increase seismicamplitude,and thereforeworks in the same
the
"direction" to Iayerthickness.
However.in relativelyhard sands.
increasing
porosity
and hydrocarbonsaturationLendto decrease
the relalive amplitude and therefore
work in the opposite"direction" to layer thickness.
ilouo
anatysis
In 1984, 12 years afler the brightspot technology became a commercial tool fbr
hydrocarbon prediction, ostrander published a breakthrough paper in Geophlsics
(ostrander, 1984). He showed that the presence gas in a sand cappedby a
of
shale
would causean amplitude variation with ofTset prestackseismicdata.He also found
in
that this changewasrelatedto the reduced
Poisson's
ratio caused the presence
by
ofgas.
Then,the yearafter,Shuey(1985)confirmedmathematically approximations the
via
of
Zoeppritz equations
that Poisson'sratio was the elasticconstantmost directly related
to the off.setdependent
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.
in
Now, brightspot
anomalies
could be investigated
beforestack,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,
15.
181
4.3 AVO
analysis
I
CDPgather
af interest
Stacksection
CDPgather
CDP
locqtion
Target harizon
. *{bu
Time
Geolog interpretation
ic
AVO responseat
target horizon
Shale
0,1
0
Sondstone
with gos
0,
0
Aryle ol inc,d?nca
Figure Schematic
4.3
illustration theprinciples AVOanalysis.
of
in
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 shearwave
velocity
informationandthe useof too simplegeologicmodelswerecommonreasons failure.
fbr
Processingtechniques that aff'ectednearofTset
traces in CDP gathers in a diflerent
way from faroffset 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,
betterpreprocessing
routines,
rnorefrequent
shearwavelogging and improved understanding rock physicsproperties,larger data
of
capacity,more fbcus on crossdisciplinaryaspectsof AVO, and last but not least,mclre
awareness
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
addressissuesrelatedto acquisition.processing
and interpretation AVO data. For
of
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
16.
182

for
seismic
interpretation
Common
techniques quantitative
expandon today's common AVO crossplotanalysisand hencewe include overviewsof
important contributions from the literature,include tuning, attenuationand anisotropy
effectson AVO. Finally, we elaborateon probabilistic AVO analysisconstrainedby rock
physicsmodels.Thesecomprisethe methodologies
appliedin casestudiesl, 3 and 4 in
Chapter5.
4.3.1 Thereflection
coefficient
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 Pwavereflections, wellknown approximationis
a
given by Aki and Richards( 1980),assumingweak layer contrasts:
R(0,)
I
, , A
 1 7 ,vi )p +
;(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:pzpr
LVp:VpzVpt
AVsVs:Vsr
P : ( . P z I Pr)
l2
Vp : (.Vpz vPt)12
+
V5 : (V52+ vst)12
01
and 02 is
In the fbrmulasabove,p is the ray parameter, is the angleof incidence,
the transmissionangle; Vp1and Vp2arethe Pwave velocities above and below a given
interface,respectively.
Similarly, V51and V5r are the Swavevelocities,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)
17.
183
n
4.3 AVO
analvsis
Medium
1
(Vp1, p1)
V51,
Medium
2
(Vn, Vsz,
Pi
PP(r)
PS{t)
Figure4'4 Reflections
and transmissions a singleinterfacebetweentwo elastichalfspace
at
rrredia
firr an incidentplanePwave.PP(i). There will be both a reflected
pwave,pp(r). and a transmittecl
Pwave,PP(t).Note that thereare wave mocleconversions the reflectionpoint occurrrng
at
ar
nonzeroincidence
angles.In additionto the Pwaves, reflectedSwave,pS(r), and a transrnitted
a
Swave,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
normalincidence
reflection
coefficient, describes variationat intermecliate
G
the
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
3040.. Therefbre,we only need to considerthe two first terms,valid fbr ansles less
than.l0 tShuey.985,1:
I
R(P)=R(0)+Gsin2d
(4.8)
The zerooft'set
reflectivity,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 ofTsetdependent
reflectivity was first indicated by Koefoed
(1955). ostrander (1984) showed that a gasfilledfbrmation would
have a very low
Poisson's
ratio comparedwith the Poisson's
ratiosin the surrounding
nongaseous
fbrmations.This would causea significantincreasein positive amplitude versusangle
at the bottom of the gas layer, and a significantincrease negativeamplitudeversus
in
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
of
encased shales.
in
Although it is generally
* d
18.
184

interpretation
seismic
techniques quantitative
for
Common
thought that the anisotropy is weak (1020%) in most geological settings (Thomsen,
1986), some eff'ectsof anisotropy on AVO have been shown to be dramatic using
the
models(Wright, 1987).In somecases, sign of the AVO slopeor rate of
shale/sand
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 :
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 3axis (zaxis)lies along the axis of symmetry.
components, r, Crr,
Cr
andhasfive independent
The above6 x 6 matrix is symmetric,
three anisotropic
Thomsen(1986) expressed
Cr, C++,and C66.For weak anisotropy,
parameters, y and 6, as a function of the five elastic components,where
t,
ClCr
a ,  
(4.10)
2Cr
Cor, C++
2C++
(4. r)
r
(Cr:*C++)2(.CyCalz
2C.3(Cy
(4.12)
C++)
The constants can be seento describethe fiactional differenceofthe Pwave velocities
in the vertical and horizontaldirections:
yP(90') vp(0')
Vp(o')
( 4 .l 3 )
and thereforebest describeswhat is usually referred to as "Pwave anisotropy."
In the same manner,the constant y can be seento describethe fiactional difference
of SHwavevelocitiesbetweenverticaland horizontaldirections,which is equivalent
to the difference between the vertical and horizontal polarizationsof the horizontally
propagating
Swaves:
19.
185
r
analysis
4.3 AVO
T

V s H ( 9 0 1  V s v ( 9 0 ) 7sH(90") Vss(0')
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 PP 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
as
term can be simply expressed fbllows:
R e p p ( d )
sin2e
Ad
( 4 .I 6 )
Blangy (lgg4) showedthe effect of a transverselyisotropic shaleoverlying an isotropic
gas sand on offsetdependentreflectivity, 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
or
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 fact,the amplitudes may interfere at large ofTsetseven if they do not at
by
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
rock
in
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 Pwaves fiom a thin layer' ln this
casethinbed tuning affects the AVO responseof a highvelocity layer embeddedin a
homogeneousrock more than it affects the responseof a lowvelocity layer.
l
20.
186
Common
techniques quantitative
for
seismic
interpretation
Lin and Phair ( 1993)suggested following expression the amplitudevariation
the
for
with angle (AVA) response a thin layer:
of
(4.11)
R r ( 0 ) : r r . r o A ? ' ( c o sd ' R ( 6 )
0)
where a.re the dominant frequency of the wavelet, Af (0) is the twoway traveltirne
is
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
response
fiom the top of a thick layer is:
d(t, t') : R(t')p(r)
(4.l8)
where R(,1') the primary reflection as a function of ofTset.t', and p(0 is the seismic
is
pulse as a flnction of time /, then the response
from 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 offietdependentAVO 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 rootmeansquare
velocity VBy5, is defined along a ray path:
t
l' tt)t 'r s,
.l v t tt
(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 raytracing modeling when reproductionof the AVO responseof potential
hydrocarbon reservoirs is attempted.Primariesonly raytrace 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 firstorder effecton the seismic response(Simmons and Backus,
1994).lnterferencebetween the convertedwaves and the primary reflectionsfiom the
21.
187
4,3 AVO
analysis
I
(2)
Singleleg
(1)
Primaries
R$
(3)Doubleleg
a
(4)Reverberations
whenwe have
in
that
and
Swaves multiples mustbeincluded AVOmodeling
4.5
Figure Converted
(l)
reflections;
interfere
with theprimaries. Primary
to
nrodes
causing
these
thin layers.
(After
reverberations.
(3)
and
wave; (4) primary
shear
(2) singleleg
waves; doubleleg
shear
Rsp
: transmitted
fiom
converted Pwave, : reflected
Swave
1994.)
7ps
and
Simmons Backus,
etc.
fiom Swave.
converted
Pwave
This
decrease.
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
the
with primary
multiples and PtoSVmodeconvertedwavescan interfere
surfacerelated
Figure 4.5 shows
prestackamplitudesand causelargedistortionsin the AVO responses.
the ray images of convertedSwavesand multiples within a layer.
propagation
effects AVO
on
and
overburden wave
4.3.4 Structuralcomplexity,
at
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, Pwave to vertically polarized Swave mode conversions,and
reflectivity should be corrected for these
anelastic attenuation.The offsetdependent
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
amplitudepreserved
effects, some of which we will summarizebelow.
22.
188

Common
techniques quantitative
for
seismic
interpretation
AVO in structurally
complex areas
The Zoeppritzequations
assume singleinterface
a
between
two semiinfinite
layerswith
infinite lateralextent.In continuouslysubsidingbasinswith relativelyflat stratigraphy
(suchas Tertiarysediments the North Sea),the useof Zoeppritzequations
in
shouldbe
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 effects reflector curvature.Structuralcomplexity can be accountedfor by
of
prestack
doing
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 amplitrrde
related
to velocity uncertainties PSDM migrated images.They performed an amplitudein
preserving (weighted Kirchhof1) PSDM followed by AVO inversion. For the AVO
signatures
they evaluated
both the uncertaintyin AVO crossplots
and uncertaintyof
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..
fbr
overburden. thinbedded
A
overburden
will generate
velocity anisotropy
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 amplitudepreservingmigration/inversion
algorithms and AVO analysis to compensatefor the influence of thinbedded layers
on traveltimes and amplitudes of seismic data. In particrrlar,
they demonstratedhow
the estimation of zerooffset amplitude and AVO gradient can be improved by correcting fbr scattering attenuationdue to thinbed 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'DohertyAnstey formrrlais an approximation of the angledependent,
timeharmoniceffectivetransmissivity for scalarwaves(Pwavesin acousticI D medium
T
or SHwavesin 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 fiequencydependent
scattering
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
of
the
fbr
isotropic reference
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
the
23.
189

4.3 AVoanalysis
responsefor a homogeneousisotropic referencemedium (that is, a pttre phaseshift), a
phasereduced
transmissivity is defined:
f ( f) o
a)
@ t f ' o ) + t P ( l) r
(4.24)
"
For a Pwave in an acoustic lD medium, the scatteringattenuation,cv,and the phase
coefficient,
B,were derivedfrom Shapiroet al. (1994b)by Widmaier et al. (1996):
a(.f0) :
,

tr'oot.f'
cos2o I l6n:a2f2 cos2u
V,f
(4.25)
and
B(f.())
r f'o2 l"
V r c o s eL
gnz 7'z
n:
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 Pwave velocities that are characterizedby an
exponential correlation function. The transmissivity (absolute value) of the Pwave
with increasing
angleof incidence.
decreases
seismicamplitude(i.e., the analyticalPwave particle displaceIf the uncorrected
ment) 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 thinbeddedoverburdenwill have the following compensated
seismicamplitude:
u r ( s , G ,t ) :
I
f r * ( t ) *R . w 1 r , r ;
(4 )R
v
is
timereduced
transmissivity givenby;
where twoway,
the
4*(r) : irtrc(r)x Zsrvr(r)
(4 )q
The superscriptT of Ur(S, G, r) indicatesthat thinbed 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).
24.
190

Common
techniques quantitative
for
seismic
interpretation
In conclusion, equation (4.28) representsthe angledependent
time shift causedby
transverse
isotropic velocity behavior of the thinly layeredoverburden.Furthermore,it
describes decrease the AVO response
the
of
resultingfrom multiple scatteringadditional
to the amplitude decay related to sphericaldivergence.
Widmaier eI ai. ( I 995) presented
similar lbrmulations for elasticPwaveAVO, where
the elasticcorrection formula dependsnot only on variancesand covariances Pwave
of
velocity, but also on Swave velocity and density,and their correlationand crosscorrelationfunctions.
Ursin and Stovas(2002) further extendedon the O'DohertyAnstey fbrmula and calculated scatteringattenuationfbr a thinbedded,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).Intrinsic
attenuation be described
can
in terms of a transt'ertunction Gt.o, t) fbr a plane wave of angular frequency or and
propagation
time r (Luh, 1993):
G @ , i : exp(at Qe* i(at lr Q) ln atI tos)
12
(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 ofTsetdependent
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 zerooffsettwoway travel
time at the studied reflector.
Carcione et al. (1998) showed that the presenceof intrinsic attenuationaffects the
Pwave reflection coefficient near the critical angle and beyond it. They also found that
the combined effect of attenuationand anisotropy aff'ectsthe reflection coefficientsat
nonnormal incidence,but that the intrinsic attenuationin somecasescan actually compensate anisotropiceffects.In most cases,
the
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
25.
191
r
4,3 AVO
analysis
of
This vector attenuationwill afl'ectAVO responses deeper
to the seafloorinterf'ace.
reflectors.
on
etfects AVO
4.3.5 Acquisition
include source direcon
The most important acquisition effects AVO measurements
tivity, and source and receivercoupling (Martinez, J993). ln particular,acquisition
at
Inegular'Eoverage the
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.
et
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
and instrumentation.
including sourceand receivercharacteristics
analysis
data
of seismic forAVO
4.3.6 Preprocessing
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.
processing
AVO
Even though the unique goal in AVO processingis to preservethe true relative
lt
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 regressionbased
inversionattributes.
that makes
sequence
as
Cambois(200 l) definesAVO processing any processing
equation,if that is the model used for the AVO
the data compatiblewith Shuey's
task'
that this can be a very complicated
inversion.Camboisemphasizes
Factorsthat changethe amplitudesof seismictracescan be groupedinto Earth effects,
acquisitionrelatedeffects, and noise (DeySarkar and Suatek, 1993). Earth effects
include sphericaldivergence,absorption,transmissionlosses,interbed multiples, converted phases,tuning, anisotropy, and structure. Acquisitionrelated eftectsinclude
source and receiver arrays and receiver sensitivity. Noise can be ambient or sourcefor
to
attempts compensate or removethese
or
generated.
coherent random.Processing
but can in the processchange or distort relative trace amplitudes. This is an
effects,
for
important tradeoff we need to consider in preprocessing AVO. We thereforeneed
26.
192
r
Common
techniques quantitative
for
seismic
interpretation
to select basic robust
a
but
processing
(e.g.,
scheme
ostrander,
1984;
chiburis,l9g4;
Fouquet,990;Castagna Backus,
f
and
1993;
Yilma4 2001).
Common preprocessingstepsbefore AVO analysis
Spiking deconvolution and wavelet processing
In AVO analysis normally want zerophase
we
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 twosided, noncausalfilters, or shaping filters, to produce a zerophasewavelet
( 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 Qcornpensation
(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 surfaceconsistent
amplitudebalancing(e.g.,Camboisand Magesan,
1997). Offsetdependent
variations are often more complicated to correct for, an4 are
attributed to both ofl.setdependent
absorption (see Section 4.3.4), tuning efl'ects(see
Section
4.3.3),andNMo stretching.
NMo stretching
actslike a lowpass,
mixedphase,
nonstationaryfilter, and the eff'ects very difficult to eliminate fully (Cambois,2001
are
).
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 comprehensive
review on ofTsetdependent
geometricalspreading, seethe study by Ursin ( 1990).
Surfaceconsistent 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
27.
't
193
n
4.3 AVO
analvsis
off.setfbllowing Shuey's equation, and then using this behavior as a ret'erence
for the
statistical
amplitudebalancing.
Multiple removal
One of the most deterioratingeffects prestackamplitudes is the presenceof multion
ples.There are severalmethodsof filtering away multiple energy,but not all of these
are
adequatefor AVo preprocessing.
The method known asfft multiple filtering, done in
the frequencywavenumberdomain, is very efficient at removing multiples, but the
dip
in the.llr domain is very similar fbr nearoffsetprimary energy and nearoffsetmultiple
energy.Hence,primary energy can easily be removed from near tracesand not from
far
traces,resulting in an artificialAVO 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 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
with
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
(an
moveout was publishedby Ross, 1997).Ursin and Ekren (1994) presented method
a
for analyzing AVO effects the off.setdomain using time windows. This technique
in
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) processinggenerates
commonreflectionpointgathers.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, reflectionpoint 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 prestack
misration.
28.
194

interpretation
seismic
for
techniques quantitative
Common
Prestack migration
in
Prestackmigration might be thought to be unnecessary areaswhere the sedimentary
it is an important component of all AVO processing.
section is relatively flat, but
Prestackmigration should be used on data for AVO analysis whenever possible,
it
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, prestacktime migration (PSTM) is preferred to preMosher et at.,
the
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 amplitudepreserving
,
( 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 ) .
1
r
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)
equationbased
commonangle time migration and used inverse scatteringtheory (see also Weglein,
(i.e.,migrationinversion).
Mosher
of
integration migrationand AVO analysis
1992'7for
et at. (1996) usecla finitedifference approachfbr the prestack migrations and illustrated the value of prestackmigration fbr improving the stratigraphicresolution, data
quality, and location accuracyof AVO targets.
line
of
anatysis a2lseismic
scheme
of
Example preprocessing forAVO
( Y i l m a z ,0 0 1 . )
2
geometric
scaling,
(source
processing.
( I ) Prestack
signature
processing
signal
and specffalwhitening).
spiking deconvolution
(2t Sort to CMP and do sparse
intervalvelocity analysis.
(3) NMO using velocity field from step2.
(4) Demultipleusing discreteRadontransform.
(5) Sort to commonoffset and do DMO correction.
(6) ZerooffsetFK time migration.
(CRP) and do inverseNMO using the
(7) Sort data to commonreflectionpoint
velocity field from step2.
with the migrateddala'
(8) Detailedvelocity analysisassociated
(9) NMO correclionusing velocity field from step8.
migrated
data.Removeresidual
to
( l0) StackCRP gathers obtainimageof prestack
by
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 .
u
( l2; Poststack
spiking deconvolution.
(13) Remigrateusing migrationvelocity field from step8.
29.
195
analysis
4.3 AVO
E
pitfalls AVO
etfects
interpretation t0 processing
due
in
Some
. Waveletphase.
The phaseof a seismicsectioncan be significantlyalteredduring
then AVO
by
processing. rhe phase a sectionis not established the interpreter.
of
lf
impedance,for
anomaliesthat would be interpretedas indicativeof decreasing
(e.g.,Allen
increases
wherethe impedance
example.can be producedat interfaces
and Peddy. I993).
. Multiple filtering. Not all demultiple techniquesare adequatelor AVO predomain,is very
processing.
Multiple filtering,done in the frequencywavenumber
efficientar removing multiples.but the dip in the/k domain is very similar for
nearoffsetprimary energy and nearoffsetmultiple energy.Hence,primary energy
can easlly be removed from the nearoffsettraces. resulting in an artificial AVO
effect.
. NMO correction. potentialproblemduring AVO analysis errorsin the velocity
is
A
(Spran. 1987).When extractingAVO attributes.
one assumes
moveoutcorrection
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
improvedestimates
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 offsetdependenl
reflectivity.
. AGC amplirude conection. Automatic gain control must be avoided in predata beforedoing AVO analysis.
processing prestack
of
Preprocessing for elastic impedance inversion
for
Severalof the preprocessingstepsnecessary 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 substack(in which the waveletcan be assumed
and this will removethe waveletvariationswith angle.
syntheticseismogram,
associated
It is, however,desirableto obtain similar bandwidth fbr each inverted substackcube,
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 laborintensivethan for
30.
196

Common
techniques quantitative
for
seismic
interpretation
u
1
0
2
0
3
0
4
0
5
0
6
0
(degree)
Angle incidence
of
Figure4,6 AVO curvesfbr differenthalf'space
models(i.e.,two layers one intertace).
FaciesIV
is caprock.
Input rock physics
propertie
represent
meanvalues eachfacies.
for
standard
AVO analysis.
Finally,residualNMO and multiplesstill must be accounted
fbr
(Cambois,2001). Misalignmentsdo not causeinterceptleakageas fbr standard
AVO
analysis,
but nearand faranglereflections
must still be in phase.
4.3.7 AVO
modeling seismic
and
detectability
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;Castagna
and Smith, 1994;Castagna al., 1998).
et
Forward modeling of AVO responsesis normally the best way to start an AVO
analysis, as a feasibility study before preprocessing,inversion and interpretation of
real prestack 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 halfspacemodels, where a silty shale is taken as the caprock with difTerent
underlying lithofacies. For each facies, Vp, Vs, and p are extractedfrom welllog data
and used in the modeling. We observea clean sand/pure
shaleambiguity (faciesIIb
and facies V) at near of1iets,whereasclean sandsand shalesare distinguishableat far
offsets.This exampledepictshow AVO is necessary discriminatedifferent lithofacies
to
in this case.
I
31.
T
I
197

analysis
4.3 AVO
trend
CemellHion
I
Cemenled
{el brino
I
0
Cemerbd
w/ hydruca]ton
V
trâ‚¬ild
Hydrocarlon
Unconsolidaled
w/ brine
Unconsolidtlsd
w/ hydrocarbon
by
sands
and
sandstone unconsolidated capped
firr
AVOcurves cemented
4.7
Figure Schcgatic
cases.
and
shlle.frll brinesaturated oilsaturated
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
cemented sanclstone
unconsolidatedsand.
brinesaturated.
The examplesin Figures 4.6 and 4.7 indicate how important it is to understandthe
to
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
in
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
technique?
Whenis AVOanalysisthe appropriate
It is well known that AVO analysisdoes not always work. Owing to the many
the
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
of
physicsand ffuid characleristics the targetreservoirare expectedto give a good
of
This must be clarifiedbeforethe AVO analysis real data.Without
AVO response.
in
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
more advanced
of
shouldbe foundedon a thoroughunderstanding local geologyand petrophysical
during
is
Realisticlithology substitution as importantas fluid substitution
properties.
this exercise.
32.
198
interpretation
for
seismic
Gommon
techniques quantitative
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
by
constrained data quality. With increasingdepth, absorptionof primary energy
are
ratio. higher frequencies graduallymore attenualed
reduces
the signaltonoise
the
than lower frequencies. geology usually becomesmore complex causingmore
length.
for
and
complexwave propagations, theanglerangereduces a given streamer
depth.
All thesefactorsmake AVO lessapplicablewith increasing
gathers
AVO
of
4.3.8 Deterministic analysis GDP
AVO modeling, the next step in AVO analysisshould be deterAfter simple halfspace
ministic AVO analysis of selectedCDP (commondepthpoint)gathers,preferably at
well locations where synthetic gathers can be generatedand compared with the real
In
CDP gathers. this section,we show an exampleof how the methodcan be appliedto
at
in
lithofacies real seismicdata,by analyzingCDP gathers well locations
discriminate
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
adjacent
l). The figure also includesthe picked amplitudesat a top targethorizon superstudy
imposed on exact Zoeppritz calculated reflectivity curves derived fiom the welllog
data.
representoilsaturatedsands,and
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 20807o, with an
tivity measurements,
average of about 60Va. The sonic and density logs are found to measure the mud
filtrate invaded zone (0l0o/o oil). Hence, we do fluid substitution to calculate the
seismic properties of the reservoir from the BiotGassmann 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
density
Oil relative
density
Mudfiltrate
pressure reservoir
level
Pore
at
level
at
Temperature reservoir
64 UI
32APT
1.09 g/cm3
20 MPa
77.2',C
33.
v
i
199

4.3 AVO
analysis
Well
3
CDP
OFF
]
t
0 323 726 1210 1694 2177
Rel
ectivity
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
:
:
0050
i
0
0 150
Angle
0
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).
34.
200
Common
techniques quantitative
lor
seismic
interpretation
I
The correspondingAVO responseshows a negativezeroofTset
reflectivity and a negative AVO gradient. In Well l, we have a watersaturated
cementedsand below a silty
shale.The correspondingAVO responsein this well showsa strongpositive zeroofl.set
reflectivity and a relatively strong negative gradient. Finally, in Well 3 we observe a
strongpositive zerooffsetreflectivity and a moderatenegativegradient,corresponding
to interbeddedsand/shale
faciescappedby silty shales.Hence,we observethreedistinct
AVO responsesin the three different wells. The changesare related to both Iithology
and porefluid 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
pretedas porefluidchanges,
Figure 4.7.
lmpodance0f AVOanalysisof individualCDPgathers
Investigations CDP gathersare importanl in order ro confirm AVO anomalies
of
(Shuey:s
seenin weightedstacksect.ions
intercepr
and gradient,Smith and Gidlow's
fluid factor. etc.). The weighted stackscan contain anomaliesnot related to true
offsetdependent
amplitudevariations.
parameters
4.3.9 EstimationAVO
of
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 zerooffsetreflectivity (R(0)) and AVO gradient (G) basedon Shuey'sapproximation.
Theseseismicpararneters be extracted,
can
via a leastsquares
seismicinversion,for each samplein a CDP gatherover a selected
portion of a 3D seismicvolume.
For a given NMOconected CDP gather, R(/,,r), it is assumed that for each
time sample, /, the reflectivity data can be expressedas Shuey's formula (equation
(4.8)):
R(r, : R(/,0) + c(/) sin2g(r,
r)
r)
(4 7)
where 0(r, x) is the incident angle corresponding to the data sample recorded at
( t .r ) .
35.
201

analysis
4.3 AVO
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
velocis
where VrNr is the interval velocity and Vnr,,rs the averagerootmeansquare
ity, as calculated from an input velocity profile (fbr example obtained from sonic
log).
For any given value of zerooffsettime, /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 ) :
xr
sin2o(4 )
sin2g(r,,rz)
R(.rr)
R(xz)
R(r,r,)
Inmorl
IcurI
I
(4.34)
,rr,')
sin2g(r,
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 leastsquares
solving the socalled"normal equation":
c:
(ArA)1(ATb)
(4.3s)
solutionfbr R(0) and G at time t.
us the leastsquares
Inversion for elastic Parameters
Going beyond the estimation of intercept and gradient, one can invert prestack seisincluding Vp, V5 and density.This is commonly
mic amplitudesfor elasticparameters,
(e'g., Dahl
ref'erredto as AVO inversion, and can be performed via nonlinear methods
Buland et al., 1996;Gouveiaand Scales,1998)or linearizedinversion
Ursin. 19921
ancl
methods(e.g., Smith and Gidlow, 1987; Loertzer and Berkhout, 1993).Gouveia and
via
a
Scales( 1998)clefined Bayesiannonlinearmodel and estimated, a nonlinearconjugate gradient method, the maximum aposteriori (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 samplebysamplebasis. Buland and
Omre (2003) extendedthe work of Loertzer and Berkhout and developeda linearized
Bayesian AVO inversion method where the wavelet is accountedfor by convolution.
fbr
The inversionis perfbrmedsimultaneously all times in a given time window, which
^
36.
202
r
interpretation
seismic
for
techniques quantitative
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.
inversion
of
Pittalls AVO
is
. A linearapproximation the Zoeppntzequations commonly usedin the calcuof
lation of R(01and G. The twoterm Shueyapproximationis known lo be accurate
30'. Make surethat the data inverted
for anglesof incidenceup to approximately
do not exceedthis range,so the approximalionis valid'
lnversionalgorithms
. The Zoeppritzequations only valid fbr single interfaces.
are
geology.
will not be valid lor thinbedded
that are basedon theseequations
amplitudescausedby
. The linear AVO inversionis sensitiveto uncharacteristic
and acquisirioneffects.A few outlying
or
noise (including multiples.) processing
estimates
are
amplitudes enoughto causeerroneous
in
valuespresent the prestack
packagesfor eslimationof R(0) and
of R(0) and G. Mosr commercial software
o
t
s
e
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 '
outlying amPlitudes.
AVO inversion is errors
. Another potential problem during samplebysample
a
(Spratt, 1987l. Ursin and Ekren (1994) presented
in the moveout correction
method for analyzing AVO eflects in the offset domain using time windows.
oi
This techniquereducesmoveout errors and createsimproved estimates AVO
parameters.
analysis
crossPlot
4,3.10AVO
A very helpful way to interpret AVO attributesis to make crossplotsof intercept(R(0))
AVO
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
standardAVO curves.
AVO classes
schemeof AVO responses
a
Rutherfordand Williams ( 1989)suggested classification
based
(seeFigure 4.9). They defined three AVO classes
fbr 6iflerent types of gas sanils
The
on where the top of the gas sandswill be locatedin an R(0) versusG crossplot.
In
crossplotis split up into fbur quadrants. a crossplotwith R(0) along .raxisand C
the
along,vaxis, I st quadrantis whereR(0) and G areboth positivevalues(upperright
The
and G is positive(upperleft quadrant).
The 2nd is whereR(0) is negative
quadrant).
quadrant
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
37.
203
4.3 AVoanalysis
I
after Ruthe(brd and Williams (1989)'
4.1
Tabfe AVO classes,
b1'
extendecl Castagnaand Smith (1994), and Rossand
K i n m a n( 1 9 9 5 )
RelativeimPedance
Quadrant
sand
Highimpedance
No or low contrast
4th
,lth
Low impedance
Low impedance
Class
3rd
3rd
2nd
lll
class
t 
t
a
'r
O
D
R(0)
G
AVO product
Negative
Negative
Positive
Positive
Negative
1
r
rrp
tt
I ctass I cra.i I crass
t..
[
(classes ll and
I,
for
defined gassands
originally
and
4,9
Figure Ruthertbrd williamsAVOclasses,
1995)'
(Ross Kinman'
and
and
1994) IIp
and
IV
clnsses (Castagna Smith.
withtheadded
III),along
et
fiom
is
Figure aclapted Castagna al. (1998)'
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 caprock.
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 crossplots,and are associated
(seePlate4. l0).
hydrocarbons
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 fullofliet 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
shales).
38.
204
:
Gommon
techniques quantitative
for
seismic
interpretation
SummaryAVO
of
classes
' AVO classI represents
relativelyhardsands
with hydrocarbons.
Thesesands
tendl"o
plot along the background
trend in interceptgradient
crossplots.
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. representing
transparent
sandswith hydrocarbons,
often show up as
dim spotsorweaknegativereflectorson
theseismic.
However.
becauseof
relatively
large gradients.
they should show up as anomaliesin an Rt0)c crossplot.and
plot off the backgroundtrend.
' AVO classIII is the "classical"AVO anomalywith negative
intercept
and 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.
d
' AVO classIV aresands
with negative
intercept positivegradient.
but
The reflection
coefficientbecomeslessnegaLive
with increasing
offset,and amplitudedecreases
versusoffset.even though Lhese
sandsmay be bright spots(castagnaand Swan.
1997).Class lV anomalies relativelyrare,but occur when soft sandswith gas
are
arecappedby relativelystiffcaprockshales
characterized vplvs ratiosslightly
by
( 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
o
The AVo classes
were originally defined for gas sands.However.today the AVo
class system is used for descriptiveclassification observedanomaliesthal are
of
not necessarily
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
w
sands.
AVO trends and the effects of porosity, lithology and compaction
When we plot R(0) and G as crossplots,we can analyzethe trendsthat occur in terms of
changes rock physicsproperties,
in
includingfluid trends,
porositytrendsand lithology
trends,as these will have different directionsin the crossplot(Figure 4. 1l). Using
rock physicsmodels and then calculatingthe corresponding
interceptand gradients,
we can study various "What lf" scenarios,and then compare the modeled trends with
the inverteddata.
Brinesaturatedsandsinterbeddedwith shales,situatedwithin a limited depth range
and at a particular locality, normally follow a welldefined "background trend" in AVO
crossplot (Castagnaand Swan, 1991). A common and recommended approach in
qualitative AVO crossplot analysis is to recognize the "background" trend and then
look fbr data points that deviatefrom this trend.
39.
205
r
analysis
4,3 AVO
(Adapted
fiom Simm
crossplot'
gradient
in
occurring an intercept
trends
4.11 Difl'erent
FigUre
et al.,2O0O.)
AVO
Castagnaet at. (1998) presentedan excellent overview and a fiamework for
normally plot in the 4th
gradient and intercept interpretation.The top of the sandswill
plot in
quadrant,with positive R(0) and negativeG. The baseof the sandswill normally
baseof sands,together
the 2nd quadrant,with negativeR(0) and positive G. The top and
with shaleshaleintertaces,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)'
et
betweena shaly caprockancla 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):
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
with the velocity
sandand shaleat a given depthis normally relativelysmall compared
(Fosteret a.,1991). Then the backgroundslopeis given by:
contrasts
uhI
.
^ 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 Pwave velocities in the caprock and in the reservoir,
and
respectively; Vs1 and V52are the correspondingSwave velocities, whereas AVp
ratio is
AV5 are the velocity differencesbetween reservoir anclcaprock. If the Vp/V5
background trend is  l, that
2 in the caprock 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
and the caprock.
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
40.
206

Common
techniques quantitative
for
seismic
interpretation
VplVs=2.5 caProck
in
VplVs=2.QcaProck
in
0.5 L
0.5
0
B(0)
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
2
(We
andreservoir. assume density
no
contrast.)
Notice
thataVplVsratioof 1.5in thereservoir
can
have
locations theAVOcrossplot
diff'erent
in
depending thecaprock
on
VplV5ratio.
Ifthe Vp/V5
(lefi),whereas the
ratioof thecaprock 2.5,thesand
is
will exhibit
AVOclass to III behavior
ll
if
(right).
caprock
Vp/V5
ratiois 2.0, sand exhibit
the
will
class to IIp behavior
I
at a reservoirlevel will causea counterclockwise
rotation, as the Vp/V5 ratio will
increase. Increasing porosity related to less compaction will also cause a counterclockwise rotation, as lesscompactedsedimentstend 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 background
trendwill change
with depth,but the way it changes be complex.
can
(Luh, 1993),will afIect background
Intrinsicattenuation,
discussed Section4.3.4
in
the
trend as a function of depth, but correction should be made fbr this before rock physics
analysisof the AVO crossplot(see Section4.3.6). Nevertheless, rotation due to
the
depth trends in the elastic contrastsbetween sandsand shalesis not straightforward,
because
theVplVs in the caprock as well as the reservoirwill decrease
with depth.
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 caprock 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
(Castagna
and Swan, 1997).That would causeseveralslopesto be superimposed
and
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.
41.
T
207
r
analysis
4.3 AVO
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 crossplots.For both hard and soft sandswe expect the top of
hydrocarbonfilleclrocks to plot to the left of the background trend, with lower R(0)
case.However, Castagnaet al. (1998)
and G valuescomparedwith the brinesaturated
sandscould exhibit a variety of AVO behaviors.
fbund that, in particular, gassaturated
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
4
d a t a( s e eS e c t i o n . 3 . 1l ) .
AVO classI anomalies,will plot in the 4th quadrant
Harclsandswith gas,representing
(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 zerooffset contrast compared with the caprock, can show great overlap
if
trend,especially the sandsarerelativelydeep.However,classII
with the background
type oil sandscan occur very shallow,causingdim spotsthat stick out comparedwith
sandsare
(i.e., when heterolithicsand brinesaturated
a bright backgroundresponse
they are dim they
relatively stifT compared with overlying shales).However, because
are easy to miss in near or fullstack 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 referredto 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 gassandshearwave
for
overlyingformation.The most likely geologicscenario suchan AVO anomalyis in
unconsolidatedsandswith relatively large VplVs ratio (Fosteret crl., 1997).That means
that if the caprockis a shale,it must be a relativelystiff and rigid shale,normally a
very siltrich 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
42.
208

Common
techniques quantitative
for
interpretation
seismic
stand out in an R(0)G crossplot,with lower R(0) values than the background trend.
Seismically,
they shouldstandout as negative
bright spots.
Pitfalls
. Differentrock physicstrencls AVO crossplots be ambiguous.
in
can
The interpretation of AVO trendsshouldbe basedon locally constrained
rock 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
crossplol.
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
are
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
more anomalous
than a Iessporoushydrocarbonbearing
sand.
. Residualgas saturation
can causesimilar AVO effectsro high saturations gas
of
or light oil. ThreetermAVO where reliableestimates density are oblained.or
of
attenuation
attributes.
can potentiallydiscriminateresidualgas saturations
from
(
commercialamountsof hydrocarbons seeSections
4.3.12 and4.3.  5 for further
discussions).
Noise trends
A crossplot
betweenR(0) and G will also includea noisetrend,because the correof
lation betweenR(0) and G. BecauseR(0) and G are obtained from leastsquare
fitting,
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 crossplotas seen in Figure 4.13 (Cambois,
2000).
Furthermore,Cambois (2001) formulated the influenceof noise on R(0), G and
a rangelimitedstack (i.e., substack)in terms of approximateequationsof standard
deviations:
dR(o) :
3
/,
^/;
(4.38)
;o,
o
'JV)
f t   "ti
o C : V f
^
)
z
stn0n,"
(4.3e)
(I/t(l))
t;
.
r ^
slnumrx
(4.40)
43.
209

4.3 AVO
analysis
,:'i.;.df,*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
versusG (afterCambois,2000)
Figure4,13 Randomnoisehas a ttend in rR(0)
and
o,, Ji .o,
(4.41)
deviation
o,
deviation of the fullstack response, is the standard
where d " is the standard
of
of the substack.and n is the number of substacks 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 halffold substack,but more robust
than a thirdfold substack.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
crossplots,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 leastsquareinversion makes the AVO gradient more uncertain than the zerooffset
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
44.
210
techniques quantitative
for
seismic
interpretation
Common
I
Fluid
versus
noise
trends
In areas where fluid changesin sandscause large impedancechanges,we tend
to see a righttoleft lateral shift along the interceptdirection. This direction is
in
almostopposite the noisedirection.which is predominantJy the vertical/gradient
to
direction. In these casesthere should be a fair chanceof discriminating hydrocarbonsandsfrom brinesaturated
sands,
even in relativelynoisy data.
saturated
Simm er al. (2000) furthermore stressedthat one should create AVO crossplots
aroundhorizons,not from time windows. Horizon crossplotclearly 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
separate
clusters,and a lot of sampleswith no physical significancewould scatter
However,picking only peaksand troughs
around the origin in an R(0) G crossplot.
raisesa delicatequestion:what about transparent
sandswith low or no impedance
Theseare significantreflections
with very small R(0)
contrastwith overlying shales'l
valuesthat could be missed if we invert the waveform only at absolutemaxima (in
tbr
maxima are commonly
commercialsoftwarepackages AVO inversion, absolute
the
Another issueis shale shaleinterfaces.
Theseare usually
definedfiom R(0) sections).
very weak reflectionsthat would be located close to the origin in an AVO crossplot,
but they are still important for assessment a local backgroundtrend.
of
There are also other types of noise affecting AVO crossplotdata,such as residual
the
moveout.It is essential try to reducethe noisetrend in the databeforeanalyzingthe
to
crossplot termsof rock physicsproperties. goodpreprocessing
in
A
scheme essential
is
in order to achievethis (seeSection4.3.6).
Cambois (2000) is doubtful that AVO crossplotscan be usedquantitatively,because
of the noise effect. With that in mind, it should still be possibleto separate
the real
rock physics trends fiom the noise trends. One way to distinguishthe noise trend
is to crossplota 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 investigate
noise versusrock
physics trends is to plot the anomaly cluster seen in the AVO crossplot as colorcodedsamples
onto the seismicsection. the clusteris mainly due to random noise,it
If
randomly around in a seismicsection.However,if the anomaly
should be scattered
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 statistical
rock physics we can estimatethe most likely
fluid and lithology fiom AVO crossplots
even in the presence some noise. This
of
is ref'erredto as probabilistic AVO analysis,and was first introduced by Avseth er a/.
(1998b).This method works by estimatingprobability distributionfunctionsof R(0)
45.
211

4.3 AVO
analysis
and G that include the variability and background trends. Houck (2002) presenteda
methodology quantifyingand cornbiningthe geologicor rock physicsuncertainties
for
with uncertainties
relatedto noiseand measurement, obtaina full characterization
to
of
lithologic interpretation.
Thesemethodthe uncertainty
associated
with an AVObased
ologiesfbr quantification AVO uncertainties explainedin Section4.3.12.
of
are
How assess noise
the
in
to
content AVO
crossplots
. Make crossplots full stack versusgradient.in addition lo R(01versusC. The
of
stack should have no comelationwith the gradient.so if trends in R(0tC plots
are still observedin stack vs. G, thesetrendsshouldbe real and nol randomnoise
(Cambois.2000).
. ldentify the location of AVO anomaliesin seismic sections.Colorcode AVO
anomaliesin R(0)6 plots and then superimpose
Lhemonto your seismic sections. Do the anomaliesmake geologic senselshape.location),or do they spread
out randomly?
. Plot the regression
coefficientof RlO)and C inversiononto the seismicto identify
the areaswhere R(0) and G are lessreliable.
. Crossplota limitecl number of samplesfrom the same horizon from a seismic
section.
The extension the trend along the gradientaxis indicates amountof
of
the
noise in the data (Simm et a..2000).
for
4.3.11AVO
attributes hydrocarbon
detection
The information in the AVO crossplotscan be reducedto onedimensionalparameters
This will make the AVO infbrmation
basedon linear combinationsof AVO parameters.
easier to interpret. Various attributes have been suggestedin the literature, and we
attributesare discussedin
summarize the most common below (AVO inversionbased
Section4.4).
Far versus nearstack attributes
One can createseveralAVO attributesfrom limitedrange 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 farstack 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 difTerence
between
far and near will manifest the significant negativegradient that is present.In contrast,a
conventionalfull stack will completely zeroout a classIIp anomaly.Ross and Kinman
(1995) suggestedthe fbllowing equation for the FN attribute depending on whether
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