AVO Preserntation CGG

DPST07 - overview slide 1 June 02 Geoscience Training Centre

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Course DPST07 Course DPST07 -- AVOAVO


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Course ContentsCourse Contents

1 - Introduction

2 - Basic Rock Physics

3 - Basic AVO theory

4 - GeoCluster AVO modules

5 - Preparing data for AVO– Overview

– 2D Land example

– 3D Land example

– 3D Marine example


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Course AimsCourse Aims

• Understand ….

– the basics of AVO theory

– parameters of GeoCluster batch modules• DINAT• MUTAN• ANGLE• AMPVO

– AVO attributes / products


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AVO AVO -- IntroductionIntroduction

•• What is the meaning of AVO ?What is the meaning of AVO ?

–– AMPLITUDE VERSUS OFFSETAMPLITUDE VERSUS OFFSET

OROR

–– AMPLITUDE VARIATION with OFFSETAMPLITUDE VARIATION with OFFSET


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• Reflected Amplitudes

– are determined by the Reflection Coefficients

– being depend upon the rock’s Physical Properties• velocity• density

– which will differ according to • reflection angle - AVA (amplitude variation with angle)• trace offset - AVO (amplitude variation with offset)


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• The presence of hydrocarbons may dramatically alter

– the rock properties

– thus the reflected amplitude

• AVO analysis - provides circumstantial evidence for the

possible presence of hydrocarbons

X X X

gas


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Basic AVO AssumptionsBasic AVO Assumptions

• Basic Assumptions ….

the Earth acts as a discretely layered medium

hydrocarbons change the rock properties

amplitude changes across a CMP gather represent true variations of the reflection coefficient with incidence angle


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Introduction Introduction -- AVO Origins AVO Origins

•• Historically a very basic AVO analysis called Historically a very basic AVO analysis called Bright Spot Bright Spot

AnalysisAnalysis was used in the 1960’s and 1970’swas used in the 1960’s and 1970’s

–– this analysis was mainly this analysis was mainly postpost--stackstack and often ‘by chance’and often ‘by chance’

–– but very worthwhile: located many gas rich HC accumulationsbut very worthwhile: located many gas rich HC accumulations

•• Since the mid 1980’s several additional types of AVO Since the mid 1980’s several additional types of AVO

analysis have been developedanalysis have been developed

–– this analysis is mainly this analysis is mainly prepre--stackstack


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Introduction Introduction -- AVO Summary AVO Summary

• AVO – Amplitude Versus Offset– An attempt to extract information from seismic traces as to how

reflection amplitude varies with incidence angle.– As reflection amplitude also changes with the rocks physical

properties this allows conclusions to be made about the rocks, including the possibility that some amplitude changes may indicate the presence of hydrocarbons.

• AVO theory is complex ….– giving the impression that the method doesn’t or can’t work

• HOWEVER ….– can be an extremely valuable method– has been used to reduce the number of dry wells being drilled

Geoscience Training Centre

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DPST07 - Part 2 Page 1 January 2002



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Basic Rock PropertiesBasic Rock Properties

• Review of…

– Basic Rock Properties• Isotropy and Homogeneity• Porosity and Permiability• Density

– Elastic moduli

– Velocity• Body waves Vp and Vs • Hydrocarbon saturation effects • Wyllie’s formula• Biot-Gassmann model

– Poisson’s ratio in terms of Vp and Vs


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AnisotropyAnisotropy

• Anisotropic media – the physical property of the rock changes according to the direction in which it is measured…

Isotropic rock e.g. crystalline basement

Anisotropic rock e.g. shales


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HomogeneityHomogeneity

• Homogeneous media has physical properties which are the same everywhere within the material….

Examples of homogeneous media:Examples of homogeneous media:•• EvaporitesEvaporites

•• Halite, AnhydriteHalite, Anhydrite•• Crystalline basementCrystalline basement•• WaterWater


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Homogeneity and IsotropyHomogeneity and Isotropy

• Homogeneity does not mean the same thing as Isotropy:– a material may be both homogeneous and anisotropic

• There is also effect of scale to consider

• Each individual layer may be considered homogeneous and isotropic

• If considered as a whole however, the cliff section is neither!


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Sedimentary Rock ConstructionSedimentary Rock Construction

• At small scales sedimentary rocks can be considered to consist of several components….

10 mm

clasts, grains

Cement

matrixmatrix

Grain sizes….Sandstone:0.0625mm - 2mm

diameterShale:<0.07mm diameter

Pores (fluid filled)

Note : this is non-homogeneous at microscopic scale


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Porosity and PermeabilityPorosity and Permeability

• Porosity– pore volume per unit material

– high porosity = 35%, low = 10 %

• Permeability– the ease with which a fluid can

travel through the pore spaces


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Density Density -- homogeneous mediumhomogeneous medium

• Density of a homogeneous medium is simply = massunit volume

XY

ZVolume V = X x Y x Z

mass = m

Vm

=ρRho, ρ = density


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Density of a NonDensity of a Non--homogeneous Medium homogeneous Medium -- One FluidOne Fluid• For a medium consisting of both solid and fluid components

we can define a ‘bulk density’….

clasts, grains

Cement

MatrixMatrixPores(fluid filled)

( ) φρφρρ fm +−= 1Wyllie’s Equation….Wyllie’s Equation….

porosity = density fluid =

densitymatrix = rock ofdensity bulk

φρρρ

f

m

=


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Density of a NonDensity of a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids

• The interstitial fluid is most commonly water.

• However in areas in which we are most likely to be interested the fluid will consist of water and hydrocarbons...

water

gasoil

• In reality the fluids will be mixed into an emulsion containing different percentages of the different phases


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Density of a NonDensity of a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids

• If the fluid is a combination of a fluid and a gas..– The fluid density term can be replaced by a term weighting the

fluid and gas densities according to their relative degree of saturation….

fρ

clasts, grains

Cement

MatrixMatrixPores (fluid and gas filled)

density gas = density liquid =

saturation gas =

fluid ofdensity

g

l

ρρ

ρ

Sf =

( ) glf SS ρρρ +−= 1Therefore:


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Elastic Elastic ModuliModuli

• Elastic Moduli are physical properties of material which relate....

Stress = Modulus x Strain

• Stress - the Force per unit area

• Strain - the degree of deformation

AND

• There are various forces (tensional, compressional, pressure, shear) leading to different types of deformation related via a series of different elastic moduli....

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Bulk ModulusBulk Modulus

• Bulk Modulus is the modulus of incompressibility….

F VVKPH

∆=

K = Bulk ModulusPH = Hydrostatic Stress (acts equally in all directions)

∆V/V = Volumetric Strain

V = original volume

V2 = new volume

∆V = (V - V2)F

F

Examples….Limestone 3.7 – 5.7Granite 2.7 – 3.3Sandstone ~1.25

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Shear ModulusShear Modulus

• Shear Modulus - also known as Rigidity…...

F ∆Y

θ XYPs ∆

= µX

PS = Shear Stress

Mu, µ = Shear modulusFExamples…Limestone 2.1 – 3.0Granite 1.5 – 2.4Sandstone ~0.6

Note: The Shear Modulus is zero for a fluid!µ gives information about the rock matrix.


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POISSON’S RATIOPOISSON’S RATIO

F

F

R δR

δ l

L

Ll

RR

δ

δ

σ−

−

=

σ = Poisson’s Ratio

• Poisson’s Ratio, Sigma (σ) is another elastic modulus….

• In physical terms it relates the degree of lateral extension to vertical compression…..

Original volume

Final volume

• Later, we see σ can also be expressed in terms of the velocities of body waves (Vp and Vs)

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Dilation

P WAVE WavelengthDirection ofpropagation

Compression

Double amplitude

SV WAVEWavelength

VERTICALMOVEMENT

Direction ofpropagation

Double amplitude

SH WAVEWavelength

HORIZONTALMOVEMENT

Direction ofpropagation

Types of Body WavesTypes of Body Waves

P (compressional) waves….

• Body waves can be either….

….or S (shear) waves

Velocity = VP

Velocity = VS


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Seismic Velocity Seismic Velocity -- DefinitionsDefinitions

• Instantaneous Velocity is the rate at which a seismic pulse or energy moves through rock.

• In reality most rocks are anisotropic. In practice we traditionally assume isotropy:

VVertical

VHorizontalX

VHorizontalY

VVertical

VHorizontalX

VHorizontalY

IsotropicVVertical = VHorizontalY = VHorizontalX

AnisotropicVVertical = VHorizontalY = VHorizontalX


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Velocity in a Homogeneous MediumVelocity in a Homogeneous Medium

• For a isotropic, homogeneous medium the body wave velocities can be shown (see Sheriff & Geldart 1994) to be dependent upon both the elastic moduli and density...

1/2

34

⎥⎦

⎤⎢⎣

⎡ +=

ρµK

Vpwhere

density=rigidityor modulusshear =

ibilityincompressor modulusbulk =K

ρµ

2/1

⎥⎦

⎤⎢⎣

⎡ρµ

=Vs • As liquids can not be sheared µ = 0and therefore Vs = 0

• Shear waves can not travel through liquids.

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BehaviourBehaviour of a Nonof a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids

• Consider a rock model consisting of a matrix and pores where the interstitial fluid is partially replaced by gas.

• What effects would we expect on the factors K, µ and ρ which control velocity?

• The introduction of gas will reduce the effective bulk density ρ of the rock.• In this case there is a linear relationship between the %gas and ρ.

• Effect on bulk density ρ

ρ

Water saturation 100% Water100% Gas


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BehaviourBehaviour of a Nonof a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids

• Effect on bulk modulus Κ• Gas is very compressible compared to water - by a factor of about 100 times. • A small percentage of gas replacing water in the pore space will lower the effective

bulk modulus K of a rock by a large amount. – Increasing the percentage of gas further then has only a small effect on the

bulk modulus.

Κ



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Bulk Modulus of a NonBulk Modulus of a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids• To explain the behaviour in the change of effective bulk modulus

K….• Consider a sponge in a sealed plastic bag which we want to

squeeze to 90% of its original volume….

• 1) If the sponge is saturated i.e. the pore space is 100% water saturated, the compression is extremely hard to achieve - water is basically incompressible, i.e. it has a high K.

• 2) If some water is squeezed out so the pore spaces contain 90% water and 10% air - the 90% compression is easily achieved. It is the air filled pores which compress.

• 3) If more water is allowed to escape so only 80% of the pore spaces are water filled - compressing the sponge to 90% of its original volume is very little different to the effort required in case 2.


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P wave velocity in a NonP wave velocity in a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids

1/2

34

⎥⎦

⎤⎢⎣

⎡ +=

ρµKVp

• Considering the P wave velocity VP....

• A reduction in density ρ which results in an increase in VP.

….we expect that the introduction of gas will create….

• A reduction in bulk modulus K which results in a reduction in VP.

• The net result is that the progressive introduction of gas theoretically causes an initial sharp reduction in VPafter which there is a small increase.

VP



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S wave velocity in a NonS wave velocity in a Non--homogeneous Medium homogeneous Medium -- Two FluidsTwo Fluids

1/2

⎥⎦

⎤⎢⎣

⎡=

ρµ

SV

• Considering the S wave velocity VS....

• A reduction in density ρ which results in an increase in VS.

….we expect that the introduction of gas will create...

• No change in overall shear modulus µ as fluids can not be sheared.

• The net result is that theoretically the progressive introduction of gas causes a small increase in VS.

VS



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Velocities in Real RocksVelocities in Real Rocks

• In reality rocks have complex structure and there are many parameters which affect the velocity…..

The nature of the mineral phasesCrystallography and mineralogyTexture of the rock

PorosityGeometry of porous network

Nature of saturating fluid (gas, liquid) Saturation (oil, water…)Water contentDensity

Pressure regimeDepth of burialCompactionTemperature

AnisotropyDegree of ‘shaliness’

• Do we see such relationships in actual rocks?

• Unfortunately, until holes are drilled we usually do not know the values of these parameters.

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How physical properties influence V, How physical properties influence V, ρ, Κρ, Κ and and µµ

Increases in…

VVPP

VVSS

ρρ

ΚΚ

µµ

Temperature Pressure Pore Pressure

Porosity Clay content

Gas Saturation

+

-

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Velocities in Real RocksVelocities in Real Rocks• Controls on Shear wave velocity…..

Major Controls

Modest Controls• Rock Type• Clay content

Minor Controls• Saturant

• Cementation• If no cementation

– Grain shape– Degree of grain

sorting (by size)– Overburden

pressure

• Conclusion: The effects on Shear wave velocity caused by hydrocarbons being present in the saturant are relatively minor ones!

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Depth Of Burial Effects on VelocityDepth Of Burial Effects on Velocity

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5.0

20001000Velocity

3000

0.0

1.0

2.0

3.0

4.0

Oil SandGas

Sand

BrineSand

Below about 2.5 kms depth the curves tend to converge- the implication is that velocity

effects due to the presence of hydrocarbons will be difficult to see in the deeper parts of a section.

Why should the curves converge Why should the curves converge ––i.e. why does the influence of i.e. why does the influence of hydrocarbons become diminished?hydrocarbons become diminished?

Depth(kms)

4000


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Control of Velocity by PorosityControl of Velocity by Porosity

•• Porosity Porosity decreases ‘rapidly’ with decreases ‘rapidly’ with burial depth. burial depth.

•• Leads to an increase in density Leads to an increase in density and (a more rapid) increase in bulk and (a more rapid) increase in bulk modulus. modulus.

•• Leads to an increase in velocityLeads to an increase in velocity

•• Beyond a certain depth the Beyond a certain depth the porosity is so low that the fluid porosity is so low that the fluid composition has little influence on composition has little influence on the average velocity.the average velocity.

•• Small separation between gas and Small separation between gas and water sands water sands -- DHI/AVO anomaly DHI/AVO anomaly less likelyless likely

2.0 2.5 3.0 2.0 2.5 3.0 VpVp (km/s)(km/s)

Gas SandGas Sand Water SandWater Sand

Probability

How does this effect correlate with How does this effect correlate with the depth of real oil fields?the depth of real oil fields?

DEPTH

OF B

UR

IAL

DEPTH

OF B

UR

IAL

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Depth Of Known Oil FieldsDepth Of Known Oil Fields0.0

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5.0

200 30

Oil SandGas

Sand

Percentage of fields

Depth(kms)

50

BrineSand

Based on 200 fields distributed around the world

4010

PotentiallyPotentiallysignificant AVOsignificant AVOeffectseffects

Small AVOSmall AVOeffectseffects

76% of fields

24% of fields

1.0

2.0

3.0

4.0


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Predicting Velocity: Wyllie’s Time AveragePredicting Velocity: Wyllie’s Time Average• “Wyllie’s time - average” equation applies to the calculation of

average velocity through a layered earth….

V1 V2

VPr

opor

tion

r 1

Prop

ortio

n r 2

Z

V2

V2

V2

V1

V1

V1

V1

1

2

2

1

1

Vr

Vr

VA

+=

It is a method of computing average velocity based on

the velocities of the different layers and their relative

preponderance.

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Predicting Velocity in a NonPredicting Velocity in a Non--homogeneous Mediumhomogeneous Medium• “Wyllie’s time - average” equation can be modified to compute

velocity in a medium containing both solid and liquid parts…..

1 11

1V Vm Vf

= − +( )φ φ

VVmVf

is bulk velocity is m atrix velocity

is fluid velocity is porosityφ

It is often stated that porosity is the most important factor determining the velocity of sedimentary rocks

clasts, grains

Pores (fluid filled)

Cement

MatrixMatrix

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Predicting Velocity in a NonPredicting Velocity in a Non--homogeneous Mediumhomogeneous Medium• Consider a ‘typical’ rock where…..

Porosity = 25%

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.2501480

175.05700

11+=

V

What predictions does Wyllies equation give for V when hydrocarbons are introduced?

Matrix Vel = 5700m/s

Fluid Vel (Water) = 1480m/s

• “Wyllie’s time - average” equation gives…..

3328m/s=V


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Predicting Velocity: Wyllie’s FormulaPredicting Velocity: Wyllie’s Formula

• Applying Wyllie’s time average Equation to Water saturation vs. P-wave velocity….

10.20

Water saturation WaterOil or Gas

P wave Velocity(kms/s)

Porosity = 25%Matrix Vel = 5700m/s

0.4 0.6 0.8 1.0

3.5

3.0

2.5

2.0

1.5

Oil Sand(V = 1300m/s)

Gas Sand(V = 300m/s)

• This equation gives a Vp curve for gas sands with a continuing reduction in velocity!

3.328

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Efficacy of Wyllie’s Time AverageEfficacy of Wyllie’s Time Average• The Wyllie time average works well in predicting velocity when applied to fluid saturated sediments at depth.• It does not correctly predict the effects seen in shallow, gas-saturated sands…..

P wave Velocity

Shallow Gas Sand

Wyllie prediction Measured• For shallow sands, experiments show a more dramatic dip in velocity as soon as gas is introduced than predicted by Wyllie time averaging.

Deep Gas Sand

0 0.8 1.0

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0.2Water saturation0.4 0.6

Oil or Gas Water


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Predicting velocity: Predicting velocity: BiotBiot -- Gassmann modelGassmann model• The Biot-Gassmann model (Gassman 1951, Biot 1956) gives an

expression for velocity involving the bulk moduli of both the solid and the liquid components…..

2/13/4

⎟⎟⎠

⎞⎜⎜⎝

⎛ ++=

ρµ FKV bb

p

1/2

⎥⎦

⎤⎢⎣

⎡=

ρµ b

SV

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This is an extended form of the equation forhomogeneous material....

1/234

⎥⎦

⎤⎢⎣

⎡ +=

ρµK

Vp with the added ‘fluid term’ F

densitybulk = modulusshear =

(average) modulusbulk =K velocitywave-S = V velocitywave-P = V

b

S

P

ρµb


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Biot Biot -- Gassmann model Fluid FactorGassmann model Fluid Factor

The added ‘fluid term’ or ‘Fluid Factor’ F is given by….

1

1 = 2

fssb

sb

/K+)/K/K-K-()/K-K(F

φφ

Note:porosity = φ

Where...

(average) modulusbulk =Kb

(solid) modulusbulk KS =

(fluid) modulusbulk Kf =

• This becomes zero if Kb/Ks = 1 i.e. the medium is solid with no fluids.

• This fluid factor is NOT the same as that we will see later in GeoCluster module AMPVO.

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BIOT BIOT -- GASSMANN MODEL GASSMANN MODEL -- FLUID SUBSTITUITIONFLUID SUBSTITUITIONStudy of the Biot-Gassman expression shows that the body wave

velocities are a function of K, K, µµ, , ρρ andand φφ......2/1

3/4⎟⎟⎠

⎞⎜⎜⎝

⎛ ++=

ρµ FKV bb

p VVpp = f( K, = f( K, µµ, , ρρ, , φ φ ))

1/2

⎥⎦

⎤⎢⎣

⎡=

ρµ

SV VVss = f( = f( µµ, , ρρ ))

Therefore given ….Therefore given ….VpVp, density , density ρ ρ , porosity , porosity φφ , fluid fill, fluid fill

..it is possible to generate models using new porosities or flui..it is possible to generate models using new porosities or fluid fills.d fills.

e.g. What happens if interstitial water is replaced by gas or oie.g. What happens if interstitial water is replaced by gas or oil?l?

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BIOT BIOT -- GASSMANN MODEL GASSMANN MODEL -- ApplicabilityApplicability

• No fluid enters or leaves any volume of the system and no cavitation occurs.

• Biot-Gassman also has limitations in its applicability. It works well when the following assumptions are met….

• The porous rock framework (skeleton) is macroscopically isotropic and homogeneous

• The skeleton, grains, fluids and saturated rock obey Hooke’s law.

• The pore space is interconnected

• The fluid pressure is uniform.

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BIOT BIOT -- GASSMANN MODEL GASSMANN MODEL -- LimitationsLimitations

• The higher the shale content of the rock, the more likely these assumptions are violated.

• The pore space likely to be disconnected

• Rock becomes increasingly aisotropic

• Biot Gassman is mathematically complex and also falls down

when applied to small grained clastic rocks (e.g. mudstones)

• Low permiability

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BiotBiot--Gassman Plot (1)Gassman Plot (1)• Water saturation versus P-wave and S-wave velocities based on

the Biot-Gassmann expression...

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Domenico Effect

P wave Velocity(kms/s)

Gas sandPorosity = 33%

1.20.20

100% Gas Water saturation0.4 0.6 0.8 1.0

2.7

2.4

2.1

1.8

1.5

VP

100% Water

VS

• The Vp curve models the sharp change at small %gas better than the Wyllie Formula.

The sharp change in Vp is known as the

• This porosity chosen as it represents a potentially good, economic reservoir


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VVPP/ V/ VSS ratio in a Homogeneous Mediumratio in a Homogeneous Medium• For a homogeneous medium a relationship between P-wave and S-wave

velocities can be derived by using the earlier given expressions…

34

+=µK

VV

S

P

•• The The VpVp/Vs/Vs ratio is ratio is potentially an important potentially an important diagnostic tool in seismicdiagnostic tool in seismiclithologicallithological determination.determination.

•• The initial drop in the The initial drop in the VVPP/V/VSSratio is an HCI indicator. ratio is an HCI indicator.

VsVsVVPP

VP

VS

Where..Κ = bulk modulus or incompressibilityµ = shear modulus or rigidity


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VVPP/ V/ VSS ratio in typical rocksratio in typical rocks

• Typical VpVp/Vs /Vs ratios ratios are…

VpVp/Vs/Vs1.5

Sandstone

2.0 2.5 3.0 3.5

Unconsolidated Sandstone

Gas Sands

Shale

Limestone

CoalSalt

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CASTAGNA’S EMPRICAL VCASTAGNA’S EMPRICAL VPP/V/VSS RELATIONSHIPRELATIONSHIP

• Castagna (1985) derived a simple empirical relationship between Vp and Vs by using measurements made on real rocks.

• This turns out to be the equation for a straight line – the so called Mud-rock line….

10

.. ...... ..

..

. ......

..

......... .

.... ..........

.... .

. ...

2

4

6

2 3

Vp (km/sec)

Vs (km/sec)

Vp = 1.16Vs + 1.36 (km/sec)Shale (or mud-rock) line

......... .

.... ..........

.... ....

. .......

.. ... . .

.

.. ..

... . ..

.

..

.. .

. .Can be used to predict S wave

velocities where no such data has been recorded.

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CASTAGNA’S EMPRICAL VCASTAGNA’S EMPRICAL VPP/V/VSS RELATIONSHIPRELATIONSHIP

10

2

4

6

2 3

Vp(km/sec)

Vs (km/sec)

Shale (or mud-rock) linefor the basin under study

Any rocks showing a variation from this line may be an indication of the presence of hydrocarbons.. . ... .. .. .... .

• The mud-rock line is therefore an expected ‘normal’ velocity relationship between Vp and Vs. This has been found to hold quite well for most shales.

• Note however that the mudrock line does vary between sedimentary basins. There is not a single global value for the mudrock line that can be used for every survey used for AVO studies.

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POISSON’S RATIOPOISSON’S RATIO• We saw earlier that Poisson’s Ratio can be defined in terms of

its change in lateral dimension relative to its change in vertical dimension

• In fact Poisson’s Ratio can also be expressed purely in terms of Vp and Vs….

1

121

2

2

−⎟⎠⎞

⎜⎝⎛

−⎟⎠⎞

⎜⎝⎛

=

s

p

s

p

VV

VV

σσ

σ

−

−=

121

P

S

VV

OR

• If a rock has a Vp of 3600m/s and a Vs of 2000m/s what is it’s Poisson’s Ratio?

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POISSON’S RATIOPOISSON’S RATIO

• Plotting Poisson’s Ratio for various ratios of Vp and Vs….

Vp / VsVp / Vs11 33 55 77

0.10.1

0.50.5

00

--0.10.1

--0.20.2

0.20.2

0.30.3

0.40.4

σσ

Poisson’s Ratio is a key Poisson’s Ratio is a key factor controlling AVOfactor controlling AVO

For most rocks For most rocks σσ is of the is of the order of 0.2 order of 0.2 -- 0.450.45

σσ is is abnormally lowabnormally low for gas for gas filled reservoir (~0.1)filled reservoir (~0.1)

A small change in the A small change in the VpVp/Vs ratio /Vs ratio in the range of 1.5 to 2 generates in the range of 1.5 to 2 generates a large change in a large change in σσ

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POISSON’S RATIOPOISSON’S RATIO• Effect of water saturation on Poisson’s Ratio vs. P-wave

velocity….

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00

P wave Velocity (kms/s)2.0 4.0

0.5

0.4

0.2

0.1

100% Water saturation

Poisson’s Ratio σ

0.399%

96%

90%75%

50% 0%

Introducing a small %gas causes a large drop in σ.


= 100% Gas saturation

Beyond about 10% gas changes in σ become small


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BiotBiot--Gassman Plot (2)Gassman Plot (2)

• Poisson’s Ratio v Water Saturation…...Poisson’s Ratio σ

00.20

100% Gas


Water saturation0.4 0.6 0.8 1.0

0.5

0.4

0.3

0.2

0.1

100% Water

• With the introduction of a little gas…

Vp drops rapidly but Vsdoesn’t

Therefore VP/VS also drops rapidly.

As σ is closely related to VP/VS then σ shows a similar drop.

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Summary of effects of GAS SaturationSummary of effects of GAS Saturation

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•• Low Low σσ observed for gas filled observed for gas filled reservoir…reservoir…•• Forms basis of the AVO Forms basis of the AVO method for direct hydrocarbon method for direct hydrocarbon detection (DCI). detection (DCI).

•• Domenico effectDomenico effect for for lowlow gas gas saturationsaturation

Potential AVO pitfallPotential AVO pitfall

VelocityVelocity

Water saturationWater saturation

VVpp

VVss

0.50.500 11

Poisson’s ratio Poisson’s ratio σσ


0.000.00

0.250.25

0.500.50

0.50.500 11WaterWaterGasGas WaterWaterGasGas


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Summary of effects of Light Oil SaturationSummary of effects of Light Oil Saturation

0.50.500 11

VelocityVelocity


VVpp

VVss

Sandstone reservoir (Sandstone reservoir (φφ = 0.33)= 0.33)Light oil (API = 40°)Light oil (API = 40°)Poisson’s ratio Poisson’s ratio σσ


0.000.00

0.250.25

0.500.50

0.50.500 11WaterWaterOilOilWaterWaterOilOil

• Oil has less effect on rock properties than gas• Nevertheless AVO method useful for certain oil cases

– Useful in cases of ‘live’ oil (oil containing dissolved gas), but not so useful in cases of ‘dead’ oil (oil without gas)

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PP--wave Velocity and wave Velocity and LithologyLithology

• Can P-wave velocity be used as a diagnostic tool for indicating lithology?

• A plot of P-wave Velocity against occurrence for commonly found rocks…..

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Occurrence(normalised)

0 2.0 P-wave Velocity (kms/s)

SandstoneGraniteClay

• Conclusion is that this diagnostic may be of some limited use.

• There is a large degree of overlap between the different types of rock.

LimestoneSalt

4.0 6.0 7.0


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Poisson’s Ratio vs. PPoisson’s Ratio vs. P--wave Velocitywave Velocity

• A plot of Poisson’s Ratio against P-wave Velocity for commonly found sedimentary rocks…..

• Can Poisson’s Ratio be used as a diagnostic tool for indicating lithology?

Poisson’sRatio

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P-wave Velocity (kms/s)0 2.0 7.04.0 6.00

0.5

0.4

0.3

0.2

0.1

Water Sand

Gas Sand

ShaleLimestone/Dolomite

Gas/OilCarbonates

Salt

• Conclusion is that, again the diagnostic may be of some limited use.

• There is still a large degree of overlap between the different types and classes of rock.

0


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Rock Properties Rock Properties -- SummarySummary

• Key rock properties:– Density

– P-wave velocity

– S-wave velocity

– Elastic Constants• Incompressibility (Bulk Modulus)

• Rigidity (Shear modulus)

• Poisson’s ratio

• If well data available can perform Vp/Vs, ρ and Poisson’s ratio studies.

• Poisson’s ratio is the key factor controlling AVO


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`̀


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ContentsContents

• Reflections at normal and non-normal incidence

• Zoeppritz equations and their approximations

• AVO classes - Rutherford and Williams


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Factors controlling Reflection AmplitudesFactors controlling Reflection Amplitudes

P & S transmissionP & S transmission/reflection coefficients/reflection coefficients

Porosity, fluid contentPorosity, fluid content

Rock propertiesRock properties

P & S velocitiesP & S velocities

DeterminesDetermines



• Rock properties depend on porosity and fluid content

• P & S wave velocities depend on rock properties

• Transmission and Reflection coefficients for P & S waves depend on wave velocities and density.

AVOAVO


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Reflection Amplitudes at Normal IncidenceReflection Amplitudes at Normal Incidence

V1 . ρ1 = Z1

V2 . ρ2 = Z2

Normal incidence Normal incidence = 90= 9000 to interface to interface = zero offset

Incident P Reflected P

Transmitted P

= zero offset

12

12

1122

11220

ZZZZ

VVVVR

+−

=+−

=ρρρρ

ZZ = acoustic impedance = acoustic impedance (velocity x density)(velocity x density)

RR0 0 = zero offset reflection coefficient= zero offset reflection coefficient

ρρ = density= densityVV = velocity= velocity


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Typical Reflection CoefficientsTypical Reflection Coefficients

• Typical (RR00) reflection coefficients between two media….

Interface 1st medium 2nd medium

Sandstone on Limestone 2.0 2.4 3.0 2.4 0.67 0.2Limestone on sandstone 3.0 2.4 2.0 2.4 1.5 - 0.2Soft ocean bottom 1.5 1.0 1.5 2.0 0.5 0.33Hard ocean bottom 1.5 1.0 3.0 2.5 0.2 0.67Base of weathering 0.5 1.5 2.0 2.0 0.19 0.68Shale over water sand 2.4 2.3 2.5 2.3 0.96 0.02Shale over gas sand 2.4 2.3 2.2 1.8 1.39 - 0.16Gas sand over water sand 2.2 1.8 2.5 2.3 0.69 0.18

V ρ V ρ Z1/Z2 R0

Minus sign indicates a reversal of polarityValues extracted from Sherrif and Geldart


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Reflection at NonReflection at Non--normal Incidencenormal Incidence

V1p V1s V1p V1s ρρ1 1

V2p V2s V2p V2s ρρ2 2

Incident PIncident PReflected PReflected P

Reflected SReflected S

Transmitted PTransmitted P

Transmitted STransmitted S

• Mode conversion occurs at non-normal incidence.

• Conversion of P-wave energy to S-wave energy….


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Reflection at NonReflection at Non--normal Incidencenormal Incidence• In fact there are 16 possible reflection coefficients which exist at a

boundary ….


Incident PIncident PReflected PReflected P




Incident SIncident SReflected PReflected P




Incident PIncident P Reflected PReflected P




Incident SIncident S Reflected PReflected P




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Reflection Coefficients: Fully described by theReflection Coefficients: Fully described by the ZoeppritzZoeppritz equationsequations

Sin Sin θθ11 CosCos λλ1 1 --Sin Sin θθ22 CosCos θθ22

CosCos θθ1 1 Sin Sin λλ1 1 --CosCos θθ2 2 Sin Sin θθ22

Sin2Sin2θθ1 1 CosCos22λλ1 1 Sin Sin θθ2 2 CosCos22α2α2

Cos2Cos2λλ1 1 SinSinλλ1 1 Cos2Cos2λλ2 2 Sin2 Sin2 λλ2 2

dd22ββ22 λλ11

dd22ββ11 λλ2222β1β1α1α1 22 --dd22ββ22αα11

dd11ββ11

α1α1--β1β1 --dd22αα22

dd11αα11

--dd22ββ22

dd11αα11

AA

BB

CC

DD

==

--Sin Sin θθ11

--CosCos θθ11

Sin2Sin2θθ11

--CosCos λλ11

BB AA

CCDD

θθ11λλ11

SS

PP

PP

SS

θθ22

λλ22

θθ11αα11ββ11dd11

αα22ββ22dd22

R (A)R (A)

• Complex - yield little physical insight into what is happening to amplitudes• Even more powerful digital computers needed before using routinely in exploration applications

• Equations developed by Zoeppritz (1919) after earlier work by Knott (1899).


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Modelling Modelling ZoeppritzZoeppritz -- Richards 1961Richards 1961

• Classic diagram in Geophysical textbooks BUT Richards used...– Vp /Vs = 2 for all layers in the model– Poisson’s ratio is the same in all layers

σ = 0.33 in all casesModel A Model B Model C

Vp Vp = 4877 m/s Vs= 2438 m/s= 4877 m/s Vs= 2438 m/sρ ρ = 2.40 g/cc= 2.40 g/cc

RR00=0.16=0.16

Vp Vp = 3048 m/s Vs =1524m/s= 3048 m/s Vs =1524m/sρ ρ = 2.20 g/cc= 2.20 g/cc

RR00=0.41=0.41

Vp Vp = 1829 m/s Vs = 914 m/s= 1829 m/s Vs = 914 m/sρ ρ = 2.02g/cc= 2.02g/cc

R0=0.63Vp Vp = 6096 m/s Vs = 3048 m/s= 6096 m/s Vs = 3048 m/s

ρ ρ = 2.65 g/cc= 2.65 g/cc

Zoeppritz equations show how the reflection coefficient changes with incidence angle..


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Modelling the Zoeppritz EquationsModelling the Zoeppritz Equations

P-wave reflection coefficient versus incidence angle for 3 different interface models

Model AModel A Model BModel B

Model CModel C

• Local maxima may occur at several angles

• At low angles….– change in reflection

coefficient is small – between normal

incidence and small angles there is initially a small decrease in R.


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Allow Poisson’s Ratio to Vary across the InterfaceAllow Poisson’s Ratio to Vary across the Interface

• Koefoed (1955) made models by varying Poisson’s Ratio (σ)….

σσ = 0.25= 0.25

σσ = 0.40= 0.40

σσ = 0.25= 0.25

σσ = 0.15= 0.15

Reflection coefficientReflection coefficient

Incident angleIncident angle

Indicated Indicated AVO effects!AVO effects!

Change in Change in σσof lower rockof lower rock


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Approximations of the Zoeppritz equationsApproximations of the Zoeppritz equations

• Various approximations to the Zoeppritz equations have been made….

18991899 19191919

KnottKnott

ZoepritzZoepritz

19611961

BortfieldBortfield

19801980 19851985 19861986 19871987

Aki / RichardsAki / Richards

ShueyShuey

GelfandGelfand

Smith / Smith / GidlowGidlowApproximation adopted by CGGApproximation adopted by CGG


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Shuey’sShuey’s Original ApproximationOriginal Approximation

• Shuey’s original 3 term approximation….

( )θθθρρ

ρρ

θ222

2

2

2

2

)( sintan21sin24

21

21

−∆

+⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−

∆−

∆+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ∆+

∆=

p

p

p

s

sp

ss

p

p

p

p

VV

VV

VVVV

VV

VV

R

Where…R(θ) = P wave reflection coefficient

∆VP = Change in P wave velocity (VP2 – VP1)

VP = Average P wave velocity (VP2 + VP1)/2

∆VS = Change in S wave velocity (VS2 – VS1)

VS = Average S wave velocity (VS2 + VS1)/2∆ρ = Change in density (ρ2 – ρ1)

ρ = Average density (ρ2 + ρ1)/2

αα

ββ

VP1 VS1ρ1

VP2 VS2ρ2

( )2

βαθ +=

αα

In practice In practice θθ is approximated by is approximated by αα. .


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Shuey’sShuey’s Original ApproximationOriginal Approximation

( )θθθρρ

ρρθ 222

2

2

2

2

sintan21sin24

21

21)( −

∆+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ∆−

∆−

∆+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ∆+

∆=

p

p

p

s

sp

ss

p

p

p

p

VV

VV

VVVV

VV

VV

R

• Meaning of Shuey’s 3 term approximation….

Normal incidence Normal incidence reflection reflection coefficient, Rcoefficient, R00

Dominates at larger Dominates at larger Angles. Angles.

Dominates at angles Dominates at angles up to 30 deg.up to 30 deg.Involves change in Involves change in Poisson’s ratio (Poisson’s ratio (∆σ∆σ))

αα

ββ

αα

ββ


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Shuey’sShuey’s Original ApproximationOriginal Approximation• Reviewing Shuey’s 3 term approximation….

( )θθθρρ

ρρθ 222

2

2

2

2

sintan21sin24

21

21)( −

∆+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ∆−

∆−

∆+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ∆+

∆=

p

p

p

s

sp

ss

p

p

p

p

VV

VV

VVVV

VV

VV

R

Dominates a ‘near trace’ stack which Dominates a ‘near trace’ stack which can be considered to image P can be considered to image P wave impedance contrasts.

Dominates a ‘far trace’ stack which Dominates a ‘far trace’ stack which can be considered to image can be considered to image Poisson’s ratio contrasts. wave impedance contrasts. Poisson’s ratio contrasts.

Typically, as seismic surveys only used to involve incidence angles to about 300, this term may be dropped.

Although offset is limited by acquisition, mute and NMO stretch effects the third term will be required in future!


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Important Approximations to ZoeppritzImportant Approximations to Zoeppritz• Comparison of Zoeppritz with approximations for a simple

gas sand model….

0.0100

Angle of Incidence (degrees)20 30 40 50

0.5

0.4

Approximations give…Shuey = 2% error at 300

Aki & Richards = 5% error at 400

ZoeppritzAki & RichardsZoeppritzShuey

Amplitude

0.3

0.2

0.1


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Shuey’sShuey’s TwoTwo-- term Approximationterm Approximation

• Assumes maximum angles between about 30 to 40 degrees• Drops the third term

– makes it easier for fitting algorithms but may be required in future with increasingly longer offset acquisition.

• Allows the approximation to be written as….

• Shuey’s 2 term approximation….

Where….

θσθ2

00)( sin49

⎥⎦⎤

⎢⎣⎡ −∆+= RRR

R(θ) = reflection coefficient at any incidence angleR0 = zero offset reflection coefficient

∆σ = Change in Poisson’s Ratio (σ1 – σ2)θ = angle of incidence


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Intercept and GradientIntercept and Gradient

• Shuey’s 2 term approximation can be rewritten…

R (R (θθ))

RR00

Sin Sin θθ22

Where, Gradient…Where, Gradient…

Intercept =Intercept =

• Note that the horizontal axis is in terms of incidence angle θ - not offset x !

θθ2

0)( sinGRR +=θσθ2

00)( sin49

⎥⎦⎤

⎢⎣⎡ −∆+= RRR

⎥⎦⎤

⎢⎣⎡ −∆= 049 RG σ


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Offset to Angle TransformationsOffset to Angle Transformations

• Need to transform common offset data to common incidence angle.• Can then use measured amplitudes from the seismic data• Derive attributes R0 and G….

• Therefore to make use of Shuey’s approximation….

Reflectionamplitude R(θ)

sin2 θ

0R

θ2sin∆∆

=RG

+ = Observed picksTheoretical curve

∆sin2 θ∆R • R0 and G are

major AVO attributes


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e.g. Gas / water contact

Simplified AVO Responses to changes in Simplified AVO Responses to changes in σσ and V and V -- 11

AI = acoustic impedanceσ = Poisson’s ratio

Increasing Increasing positivepositive

Increasing Increasing negativenegative

AIAI σσ

++veve --veve

TimeTime

Offset

R0

PolarityPolarityreversalreversal

+

-

AIAI σσ

++veve ++veve

TimeTime

OffsetR0

+

-

offsetoffsetoffsetoffset

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AI = acoustic impedanceσ = Poisson’s ratio

Simplified AVO Responses to changes in Simplified AVO Responses to changes in σσ and V and V -- 22

Increasing Increasing positivepositive

Increasing Increasing negativenegative

AIAI σσ

--veve --veve

TimeTime

OffsetR0

+

-

AIAI σσ

--veve++veve

TimeTime

OffsetR0

+

-

offsetoffset offsetoffset

e.g. Top low impedance gas sand

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RUTHERFORD & WILLIAMS Classification scheme RUTHERFORD & WILLIAMS Classification scheme -- CLASS 1CLASS 1

• Rutherford and Williams (1989) introduced the concept of classification of AVO anomalies.

In this paper a simple earth model was proposed to represent a ‘In this paper a simple earth model was proposed to represent a ‘typical’ typical’ potential hydrocarbon trap potential hydrocarbon trap –– a gas filled sandstone layer sandwiched a gas filled sandstone layer sandwiched between two impervious between two impervious shalesshales….….

ShaleShale

ShaleShale

Gas sandGas sandThe consequences of changing The consequences of changing

the Acoustic Impedance of the Acoustic Impedance of the gas sand relative to that the gas sand relative to that of the encasingof the encasing shalesshales is is considered…considered…

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RR((θθ))

θ (degrees)

low impedance shalelow impedance shale


Significantly higher impedance gas sand encased within lower impedance shales…

Reflection from upper interface...Reflection from upper interface...Peak decreasing with offset, possible Peak decreasing with offset, possible polarity reversal at far offsetspolarity reversal at far offsets

Class 1Class 1

+

-

RR00

high impedancehigh impedancegas sandgas sand

Characterised by, and defined as…Characterised by, and defined as…A positive RA positive R00A negative gradientA negative gradient


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Class 2Class 2Gas sand impedance very similar to surrounding shale, either slightly above or below..

Reflection from upper interface...Reflection from upper interface...Peak decreasing or trough Peak decreasing or trough

increasing with offsetincreasing with offset

θ (degrees)

RR((θθ)) +

-

shaleshale

shaleshale

RR00

RR00

Gas sand with slightly higher impedanceGas sand with slightly higher impedance

Gas sand with slightly lower impedanceGas sand with slightly lower impedance small impedancesmall impedancecontrast gas sandcontrast gas sand

Characterised by, and defined as…Characterised by, and defined as…RR0 0 close to zeroclose to zeroA negative gradientA negative gradient


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Class 3Class 3• Significantly lower impedance gas sand encased within higher impedance

shales…

Reflection from upper interface...Reflection from upper interface...Trough increasing with offsetTrough increasing with offset

RR((θθ))

θ (degrees)

+

-

high impedance shalehigh impedance shale


RR0 low impedancelow impedancegas sandgas sand

0

Characterised by, and defined as…Characterised by, and defined as…Negative RNegative R0 0

A negative gradientA negative gradient


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RUTHERFORD & WILLIAMS Classification schemeRUTHERFORD & WILLIAMS Classification scheme• In all three classes the reflection from the bottom interface is close to a mirror

image of of the upper interface about the incidence angle axis….



high impedance high impedance gas sandgas sand

shaleshale

shaleshale

small impedance small impedance contrast gas sandcontrast gas sand

low impedance low impedance gas sandgas sand



θ (degrees)

Upper interface...Upper interface...+

-RR00

θ (degrees)

Lower interface...Lower interface...+

-RR00

θ (degrees)


-RR00

θ (degrees)


-RR00

θ (degrees)


-RR00

θ (degrees)


-RR00

Class 1Class 1

Class 2Class 2

Class 3Class 3

• In fact the Zoeppritz equations show that the exact solution is not a true mirror image.

• The Shuey approximation does not however recognise this.

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AVO Class CharacteristicsAVO Class Characteristics

• The effects of the 3 classes can be seen on seismic data to have the following characteristics…

• Often produces a ‘DIM OUT’ on the seismic section– Stack will always underestimate the R0 section amplitude.– May even produce stack amplitudes of almost zero.

Class 1Class 1

Class 2Class 2 • Can appear as a ‘POLARITY REVERSAL’ on the seismic section– Where S/N ratio is poor, signal can appear on long offset traces.– Class 2 anomalies are usually not seen on seismic data.

Class 3Class 3 • Often produces a ‘BRIGHT SPOT’ on the seismic section– This is the classic use of AVO anomalies.

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RUTHERFORD & WILLIAMS AVO Classes plus Class 4 (RUTHERFORD & WILLIAMS AVO Classes plus Class 4 (CastagnaCastagna))

• Overlying all 3 R&W classes, plus an additional class defined byCastagna et al....

• R&W classes are ‘arbitrary’ and in future other, or more specific classes may be recognised and used….

55 1010 1515 2525 3030 35°35°2020

--11

--22

11

22

Angle of incidenceAngle of incidence

class 1class 1

class 2class 2

class 3class 3

Note : 4th. class added by Castagna et alclass 1class 1

class 2class 2

class 3class 3


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AVO effects in Carbonate sequencesAVO effects in Carbonate sequences

0% 20%

Near Far

Porosity Porosity

Peak, fairly constant w.r.t offset

Near Far

Trough, reducing w.r.t offset

Tight Limestone

PorousLimestone

0% 20%

Near Far

Porosity Porosity

Peak, reducing w.r.t offset

Near Far

Trough, slightly reducing w.r.t offset

Tight Limestone

Gas in PorousDolomite


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AVO effects in Carbonate sequencesAVO effects in Carbonate sequences

0% 20%

Near Far

Porosity Porosity

Peak, fairly constant w.r.t offset

Near Far

Trough, reducing w.r.t offset

Anhydrite

PorousDolomite

0% 20%

Near Far

Porosity Porosity

Peak, reducing w.r.t offset

Near Far

Trough, increasing w.r.t offset

High velocityshale

PorousLimestone


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AVO PitfallsAVO Pitfalls

• AVO anomaly may not necessarily involve fluid hydrocarbons

– e.g. coal seams

• Hydrocarbons may not necessarily cause AVO anomalies

– e.g. oil-filled reservoirs, low impedance contrast, small effects at

larger depth

• The AVO effect may not show true variation of reflection

coefficient with incidence angle

– e.g. processing artefacts, noise interference, tuning effects (lower

frequency on far traces)


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AVO Pitfalls: Amplitudes and AVO Pitfalls: Amplitudes and AzimuthalAzimuthal AnisotropyAnisotropy•• The The azimuthal azimuthal variation of AVO turns out to be elliptical.variation of AVO turns out to be elliptical.

YAmindirection Amax

direction

ϕ0

Amplitude measured for a 2D survey: A(x,0)

Amplitude measured for a 3D survey: A(x,y)

X

•• This implies that wide azimuthally acquired data should be analyThis implies that wide azimuthally acquired data should be analysed in terms sed in terms of elliptical variation of amplitude!of elliptical variation of amplitude!

•• For details see the CEFOGA course DPST22 AnisotropyFor details see the CEFOGA course DPST22 Anisotropy


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SummarySummary

• Reflection amplitudes at non-normal incidence

governed by Zoeppritz equations

• These require approximations to be useful

• Shuey approximation (as used in Geocluster)

• AVO response falls into four classes

• There are several AVO pitfalls waiting to trap the

unwary!

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AVO ProductsAVO Products

• It follows from the previous section that all reflecting interfaces have an AVO response.

X X X

gas

• Therefore it is the changes, the anomalies, in this response which we are seeking..

• The basic AVO attributes extracted from the data are R0 and G.• It is possible to combine theses attributes in various ways in

order to enhance the anomalous areas

Rθ

sin2θ

Rθ

sin2θ

Rθ

sin2θ


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Geocluster AVO ProductsGeocluster AVO Products

The range of AVO products which can be generated include….

• Intercept (R0) • Gradient (G)

– Amplitude– Envelope

• ‘Angle’ stacks• Hydrocarbon Indicators (HCI)….

– Intercept (R0) vs. Sign of Gradient (G)– Intercept (R0) * Gradient (G)

– Fluid Factor: Intercept (R0) plus Gradient (G)

– a * Intercept (R0) plus b * Gradient (G)


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Shuey’sShuey’s Approximation to the Approximation to the Zoeppritz Zoeppritz EquationsEquations• Recall that the Zoeppritz Equations fully describe the changes in

Reflection Coefficients for different incidence angles.

• It is timely to recall the ShueyApproximation that can be written in the form….

Where….

R0 = zero offset reflection coefficient

θθ2

0)( sinGRR +≈

θ = angle of incidence

R(θ) = reflection coefficient at any incidence angle

RR((θθ))

RR00

Sin Sin θθ22

Gradient…Gradient…

Intercept Intercept ⎥⎦⎤

⎢⎣⎡ −∆= 049 RG σ

G = gradient = a complicated combination of density contrast and reflection coefficients and is related to the change in Poisson’s ratio, ∆σ = (σ1 – σ2)


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AVO In PracticeAVO In Practice

• For a given sample time on a CMP gather….

sample time

offset

11 Measure amplitudes for each offset trace…

22 Convert offsets into incidence angles (θθ)

Fit a linear regression line to create a single R0 and G….

RR((θθ))

RR00

Sin Sin θθ22

GG

**** ****

** **** **

**

33


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RR00 PlotPlot

R0 - Intercept computed from the regression analysis….

Stack Amplitudes R0


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G plotG plot

G – The Gradient is computed from the regression analysis

Recall that the gradient is given by…

Gradient is directly related to the elastic parameters.

⎥⎦⎤

⎢⎣⎡ −∆= 049 RG σ

Where ∆σ = change in Poisson’s Ratio (σ1 – σ2)

1

121

2

2

−⎟⎠⎞

⎜⎝⎛

−⎟⎠⎞

⎜⎝⎛

=

s

p

s

p

VV

VV

σAnd Poisson’s ratio…

• Changes in Vp/VS produce changes in the Gradient.• The presence of gas in porous rocks affects the Vp/VS.• It follows that Gradient could be a good indicator of gas reservoirs.


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G plotG plot

G - values can be based on absolute amplitudes…

Stack Amplitudes G

• However Gradient based on amplitude may be somewhat unstable andsusceptible to small variations in phase and residual velocity errors!


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G (envelope) computationG (envelope) computation

• In order to resolve the potential problems with Gradient based on amplitude it can be based on trace envelope.

Differences between Gradient based on Amplitude and Gradient based on Envelope….

Envelope Gradient notEnvelope Gradient noteffected by alternating signeffected by alternating signof the seismic waveletof the seismic waveletBUT: Can result in loss of BUT: Can result in loss of

resolution.resolution.


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Comparison of G (amplitude) and G (envelope)Comparison of G (amplitude) and G (envelope)

G (amplitude) G (envelope)

• Comparison of example of Gradient based on Amplitude and Gradient based on Envelope….

The anomaly in the G (envelope) stands out better from the background but the display is lower frequency.


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ANGLE StacksANGLE StacksCMP gatherCMP gather

time

offsetoffset

Angle rangesAngle rangesto be stackedto be stacked

Angle rangesAngle ranges

Angle stacks are computed for defined ‘angle ranges’….

• Angle stacks….

STACKSSTACKS


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Hydrocarbon Indicators Hydrocarbon Indicators -- DefinitionDefinition

• As the name Hydrocarbon Indicators (HCI) implies these are any seismic attributes in which high values indicate the possible presence of hydrocarbons.

• A HCI is usually generated by combining (or projecting) more than one AVO attribute.– Therefore a number of AVO attributes is reduced to produce a single HCI

value.– This leads to a certain loss of information. – However they can be useful in highlighting areas worthy of further

investigation.

• The concept is to produce a plot of the value of the HCI at its correct position in t.w.t. time and space.


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Hydrocarbon Indicator Hydrocarbon Indicator -- LimitationsLimitations

• If Hydrocarbon Indicators were certain and unambiguous we could, in theory, dispense with normal seismic amplitude plots and with the simple AVO attribute plots.

• However it must understood that….

– Some HCI’s only respond to specific types of AVO anomalies.

– There are problems with the estimation of the HCI’s and their information content.

• They are based on statistical information extracted from the seismic amplitudes. These are dependant, to some extent, on S/N ratio and processing artefacts.

– Noise and sensitivity can cloud the interpretation of HCI’s.


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Hydrocarbon Indicator Hydrocarbon Indicator -- TypesTypes

•There are several HCIs in common use today, including…

• ‘Unbiased’ version of productG (amplitude) x STACK(amplitude)

• ‘AVO Response Indicator’G (amplitude) x sign(R0)

• ‘AVO Product Indicator’G (amplitude) x R0(amplitude)

All are used for identifying CLASS IIItype anomalies.

• Fluid Factor Indicator


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HCI target: Class 3 AVO AnomalyHCI target: Class 3 AVO Anomaly

The CLASS III type anomaly is the classic Bright Spot…

low impedancelow impedancegas sandgas sand

high impedance high impedance shaleshale

high impedance high impedance shaleshale

RR00 < 0 G < 0< 0 G < 0

RR00 > 0 G > 0> 0 G > 0Increasing positive

Increasing negative

A.I.A.I.

Both top and bottom reflections Both top and bottom reflections produce an produce an increaseincrease in amplitude in amplitude with offsetwith offset

θ (degrees)

+

-

Upper interface...Upper interface...

RR00

Class 3Class 3

θ (degrees)

Lower interface...Lower interface...

+

-

RR00


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‘AVO Response Indicator’‘AVO Response Indicator’

• This is the product of G (amplitude) and the Sign of R0…

• R0 denotes the starting point for variation in the reflection coefficient.• G contains information about how R(θ) changes with offset.

Product = G (amplitude) x sign(R0) The result is a HCI that shows any interface where the absolute value of the

reflection coefficient increases (as a + value) or decreases (as a - value) with offset.

Increasing negativeamplitude

θ (degrees)

+

---RR00

Increasing positiveamplitude

+R+R00

+ G

- G

++++ Decreasing negative

amplitude

θ (degrees)

+

-

Decreasing positiveamplitude

- G

+ G

----

+R+R00

--RR00


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‘AVO Response Indicator’ example‘AVO Response Indicator’ example

• The AVO Response Indicator on a Class 3 anomaly is characterised by a ‘red doublet’ when displayed with a ‘standard’ colour palette…

Colour palette….

ZeroPositive

Negative

The red doublet shows a layer where both the top and bottom reflections have an overall increase in amplitude magnitude with increasing offset.


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‘AVO Product Indicator’‘AVO Product Indicator’

• This is the product of G (amplitude) and R0…

The result is a HCI that shows any Class 3 anomaly as a strong red doublet.

Other Class anomalies and non-hydrocarbon related interfaces should not show this response.

• Similar to the AVO Response Indicator..

Increasing negativeamplitude

θ (degrees)

+

---RR00

Increasing positiveamplitude

+R+R00

+ G

- G

Product = G (amplitude) x R0

++++ Decreasing negative

amplitude

θ (degrees)

+

-

Decreasing positiveamplitude

+R+R00

--RR00

- G

+ G

----

Now the larger the initial values of R0 and/or G the higher the product.


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‘AVO Product Indicator’ Pitfall‘AVO Product Indicator’ Pitfall

• If we consider a distribution of amplitude with offset which is random then we could draw many regression curves through the scatter with equal validity…

• Statistically this is a negative relationship – an increase in Gresults in a decrease in R0

.. ..

.... .

.

..

. ...

... ..

.

.

...

.

..

....

..

.

.......

....

.

.

..

.

..

...

.

.

.

.

.

.. .

.

. .

..

..

..

..

.

.

.

..

....

.

..

.

....

.

.

.

.

. .

. ..

.

.. .

.

.

..

.

. .

...

... θ (degrees)

R(R(θθ))

+G1

-G2

+R02

-R01 -G3

+R03

• The values created for R0 and G are strongly related

– i.e. a change in G produces a change in R0

• This is likely to be the situation where there is no signal present, only noise. In this case, the product of R0 and G produces a negative value.

• In summary, the presence of noise will bias the product towards negative values.


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‘Unbiased AVO Product Indicator’‘Unbiased AVO Product Indicator’

• This is the product of G (amplitude) and Stack.

• The product is unbiased and is therefore an alternative and better HCIthen the AVO Product Indicator...

Product = G (amplitude) * Stack

• The amplitude used for the ‘stack’ is calculated from….

– Predicted amplitudes are summed (stacked)

– Stack amplitude normalised by the stack fold.

.... . ......

.. .. . .. ... ..

.

. ........

. .... .

θ (degrees)

R(R(θθ)) - Amplitudes projected to best fit line

i.e. Method uses the amplitudes from the best fit line - not the raw data amplitudes themselves.


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Using G (envelope)Using G (envelope)

• Any of the foregoing HCI can be computed using, instead of the Gradient based on Amplitude the Gradient based on the Envelope.

Product = G (envelope) x Stack

Product = G (envelope) x Sign R0

Product = G (envelope) x R0

• These products are likely to be less sensitive to mild phase and residual velocity (NMO correction) errors than the G (amplitude) HCI’s.


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Fluid FactorFluid Factor• The Fluid Factor HCI is used to highlight the presence of gas, regardless of the class of AVO anomaly.

• The exact meaning of the Fluid Factor is still being debated. This is because there are several ways in which it can be derived e.g. either theoretically or empirically.• This should not be confused with the fluid factor in the Bio-Gassmann equations.

• The underlying rational is to find a ‘regional’ trend which, when subtracted from the input data zeroes all values except potential Hydrocarbon zones…

Subtract‘Background’ from input

Output = Difference = Fluid Factor Section

Determine‘Background’ trend

Input data‘Background’ Trend

Anomaly – hard to see!


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Fluid FactorFluid Factor

• Expanding the graph to include different rocks and fluid fills….

10

.. .

..... ..

..

...

....

..

......... .

.... ..........

...

. .. ...

2

4

6

2 3

Vp (km/sec)

Vs (km/sec)

Vp = 1.16Vs + 1.36 (km/sec)

Shale (or mud-rock) line- Water Filled

..........

.... ..........

...

. ..... ...

....

.. ..

. . .

.

...

.

... . ..

.

..

...

. .

• Recalling Castagna’s Mud rock line …

1 2 3Vs (km/sec)

0

2

4

6Vp (km/sec)

Mud-rock line

Dry SandsHigh porosity rocks

Low porosityrocks

Gas Sands

Water Sands

Carbonates

Thus if the background trend is assumed to be the mud rock line, when it is subtracted..

• Water filled sands should ‘disappear’ • Gas filled sands will remain as an

anomaly.

The Fluid Factor can be considered to be the difference between the background trend and the residual values.

However there are other rocks (e.g. Carbonates) that will not lie along the mud rock line!


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Calculating the Fluid FactorCalculating the Fluid Factor

• The concepts of the Fluid Factor was first conceived by Smith and Gidlow (1987).– For a detailed discussion on this topic see the CGG Advanced Technical

Description linked to the AMPVO module in XDOC

• Smith and Gidlow did some hard sums and came up with a theoretical Fluid Factor given by…

S

S

P

S

P

P

VV

VV

VVFF ∆

−∆

= 16.1

• The presence of a coefficient of 1.16 is a clue to the involvement of Castagna’smud rock line for the Vp/Vs relationship during the derivation of this equation.

• In fact this Fluid Factor turns out to not very useful when applied to real rocks.

• It is for this reason that various empirical estimated methods have been developed.


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• Smith and Gidlow’s work involved using Shuey’s original 3 term equation, however CGG uses a simplified approach using the 2 term approximation.– The theory shows the CGG fluid factor should, in certain circumstances

be a better estimate. Practice indicates the differences to be negligible.

•• Consider Consider Shuey’sShuey’s 2 term equation where it is assumed that 2 term equation where it is assumed that VpVp = 2Vs= 2Vs

• This coincides with Castagna’s Mudrock line where Vp = 3238m/sand Vs = 1619m/s.

• This corresponds to the zone of high porosity sandstones

1 2 3Vs (km/sec)

0

2

4

6Vp (km/sec)

Mud-rock line

High porosity rocks

Water Sands


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• When VP = 2VS Shuey’s 2 term equation becomes….

( ) θρρ

ρρ

θ2sin

21

21

21

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆−

∆−

∆+⎟⎟

⎠

⎞⎜⎜⎝

⎛ ∆+

∆≈

S

S

P

P

P

P

VV

VV

VVR

• The normal incidence reflection coefficient is given by…

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆+

∆=

S

SS V

VRρρ

21

0 for S waves⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆+

∆=

ρρ

P

P

VVR

21

0 Also…for P waves

• Substituting into Shuey’s equation produces….

( ) ( ) θθ2

000 sin2 SRRRR −+≈

• Therefore the Gradient G = (R0 – 2R0S)


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• Using these relationships for R0, the assumption that Vp = 2VS and assuming Garner’s Law which states that for water bearing strata …

4σ∝PV

• Smith and Gidlow’s theoretical value of the Fluid Factor can be modified to become…

GRFF 58.0252.1 0 +≈

• Therefore a Fluid Factor can be obtained by summing the scaled AVO attributes R0 and G.

• The result of summing normalised values of R0 and G produces what is called the ‘fluid factor’ section.


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Theoretical R0 and G CrossTheoretical R0 and G Cross--plotplot

• Generating a cross-plot of Normalised Intercept (R0) against Normalised Gradient G can produce a well defined relationship…..

NormalisedIntercept R0

The sum R0 + G = 0 for any point along this line.

Nor

mal

ised

Gra

dien

t G

0.0

-2.0

-1.0

1.0

2.0

0.0-0.1-0.2 0.20.1

Rocks which have Vp = 2Vswill plot along this fluid line which represents the background trend.

Any points not lying on the trend are indicative of a HCI anomaly.

• Performing the sum therefore causes samples lying on the ‘fluid line’ to ‘disappear’

• This is not true of anomalous points.

• Performing the summation therefore causes anomalous samples to be relatively emphasised.


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AVO Anomaly Classes on the CrossAVO Anomaly Classes on the Cross--plotplot

• The recognised Rutherford & Williams Anomalies fall into distinct areas of the cross-plot…..

0.0-0.5-1.0 1.00.5

0.0

-1.0

-0.5

0.5

1.0N

orm

alis

edN

orm

alis

edgr

adie

ntgr

adie

nt

NormalisedNormalised interceptintercept

backgroundbackgroundtrendtrend

(fluid line)(fluid line)

Class IIIClass III Class IIClass II

Class IVClass IV

Class IClass I


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AVO Anomaly Classes on the CrossAVO Anomaly Classes on the Cross--plotplot• Summarising the anomaly classes….


Class IClass I

0.0-0.5-1.0 1.00.5

0.0

-1.0

-0.5

0.5

1.0

GG

RR00

AIAI Amplitude Amplitude decreases decreases with offset =with offset =‘Dim Spot’‘Dim Spot’

AIAI Amplitude Amplitude small small increase or increase or decreases decreases with offset. with offset. Possible Possible sign changesign change

AIAIAmplitude Amplitude increases increases with with offset = offset = ‘Bright ‘Bright Spot’Spot’

Class IVClass IVAIAI

Amplitude Amplitude decreases decreases with offsetwith offset

R0, G Cross-plot

ZZ

ZZZZ

ZZ


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‘Raw’ R0 and G Cross‘Raw’ R0 and G Cross--plotplot

• In a raw cross-plot of R0 and G…

0.0-0.1-0.2 0.20.1

0.0

-2.0

-1.0

1.0

2.0

grad

ient

Intercept

Anomalous points which do not have plot along the background trend.

Background trend, related to the mud rock line

The gradient amplitudes are approx 10 times intercept in this case.


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Fluid Factor (2)Fluid Factor (2)

R0 G

• Usually R0 and G are different orders of magnitude.Gradients are always much higher then intercepts….

•• Therefore, before generating the crossTherefore, before generating the cross--plot it is necessary to find plot it is necessary to find scaling factors…scaling factors…


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Ro and G NormalisationRo and G Normalisation

• To find the scaling factors for R0 and G there are three possible options:– Theoretical

• As noted, not really applicable to real data.

– Empirical• Choose scaling visually• Apply to the anomaly

– ‘Far Offset stack’• Data derived scalars


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Empirical Normalisation methodEmpirical Normalisation method

• The Fluid Factor (FF) is given in terms of….

0 bGaRFF +=

sincos0 φφ GRFF +=

• It is possible to combine the scaling coefficients a and b into one

coefficient φ as….

φ is determined empirically by scanning with several values


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Empirical Normalisation MethodEmpirical Normalisation Method• Choose location away from anomaly and run a scan….

φ

• Select the value of φ where the energy in the panel is the weakest • Apply that value to the region of the anomaly.


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Far Offset Stack MethodFar Offset Stack Method

• The second method that can be used finds time and space-variant scalars and produces the fluid factor section automatically.

• Essentially the method calculates a series of scalars for R0 from analysis of time and space windows, then multiplies R0 by the scalar before adding to the G value…

FF= C(x,t)R0 + GWhere …C is the variable, in time and space, scaling factor.

• In practice the result is a stack, with amplitudes weighted by offset - hence far-offset stack method.


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Far Offset Stack Method ExampleFar Offset Stack Method Example

This method simply finds the time and space-variant scalars and produces the fluid factor section automatically….


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Wide Angle DataWide Angle Data

The use of long offsets (in range of 3kms to 10kms) implies that the ‘near trace’ assumptions made to justify the use of the 2 term Shuey approximation become inappropriate.

3kms10kms

The 3 term Shuey approximation now becomes preferable. It can be expressed in the form…

00 5535 −≈θ 035<θ

( ) ρθ ∆+∆+∆≈ cZbZaR SP

Where, across the boundary…

impedance Pin change=∆ PZimpedance Sin change=∆ SZ

densityin change=∆ρ


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ConclusionsConclusions

• The main AVO attribute are…– The Normal Incidence angle

• Intercept (R0) – The rate of change in Amplitude with incidence angle

• Gradient (G)– The gradient can be measured using actual amplitudes or an

envelope

• Combinations of AVO attributes can be used to create Hydrocarbon Indicators (HCI)…– Intercept (R0) vs. Sign of Gradient (G)– Intercept (R0) * Gradient (G)– Fluid Factor: Normalised Intercept (R0) plus Gradient (G)


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• DINAT - incidence angle computation

• ANGLE - computation of angle stacks and gathers

• MUTAN - muting according to angle value (level 8100)

• AMPVO

– Intercept (R0) and Gradient (G) outputs

– QC of R0 and G computation

– HCI indicators

• TAVOF - time averaged AVO (level 8100)


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DINATDINAT

• Computation of angles of incidence

– Uses the input velocities

– Computation based on:• straight line approximation• ray bending (parameter ALPHA)

– direct smoothing of angles (SMTHANG)– indirect smoothing (SMTHVEL)


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DINAT DINAT -- Straight RayStraight Ray

• Compute angle from average velocity

Offset , X

S R


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DINAT DINAT -- Ray Bending (1)Ray Bending (1)

Offset , XOffset , X

SS RR

θ

Vint(1)

Vint(2)

Vint(3)


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• Compute angle from interval velocities

Blocky interval velocities can causecorresponding blockiness in the angle computation


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DINAT DINAT -- Direct Smoothing , SMTHANGDirect Smoothing , SMTHANG

Parameter SMTHANGsmoothing function

- recommended value is 64 samples (i.e.256 ms @4 ms)

no SMTHANG SMTHANG


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DINAT DINAT -- Indirect Smoothing, SMTHVELIndirect Smoothing, SMTHVEL

Parameter SMTHVELsmooths velocities prior to interval velocity and angle computation


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MUTAN MUTAN -- Muting Based on AnglesMuting Based on Angles

DINAT display

MUTAN result


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ANGLE (1)ANGLE (1)

• Computation of angle stacks and /or gathers

• Angle computation method same as DINAT

– straight ray

– ray bending (SMTHANG , SMTHVEL)

SS RRSS RR


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ANGLE (2)ANGLE (2)

• Angle stacksSTACKSTACK

5 degrees5 degrees

15 degrees15 degrees


timetime

offsetoffset

angle stacksangle stacks

angle ranges angle ranges -- parameter RANGEparameter RANGE

CMPCMP


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ANGLE (3)ANGLE (3)

• Angle stacks on real data

5 deg 10 deg 15 deg 20 deg


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AMPVOAMPVO

• Regression analysis based on Shuey’s approximation

– output of (R0), (G) and variants

• Wide ranging QC tools

• HCI indicators

– AVO Response

– AVO product

– Fluid factor


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AMPVO AMPVO -- Regression CurvesRegression Curves

• Based on Shueys’ (2 term approximation)

can be written as

R Rp G( ) sinθ θ= + 2

WhereRRp G

...( ) ( )θ θ= change of reflection coeff with at angle

= zero (normal) incidence P wave reflection coeff= gradient term depending upon change in Poisson' s ratio

R (R (θθ))

RRoo

Sin Sin θθ22

gradient G= 9/4 gradient G= 9/4 ∆ ∆ σσ -- RRoo


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AMPVO AMPVO -- In PracticeIn Practice

• For a given sample time

– measure amplitudes for each offset

– convert offsets to angles

– linear regression to create a single R0 and G for each sample

time

sample time

offset

How to compute the linear regression ??


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AMPVO AMPVO -- Fitting Strategies for the RegressionFitting Strategies for the Regression

• Least Squares (sensitive to outliers)– minimise square of difference between model and observed

With ELIM, remove outliers

Second fit

θ

Initial fit to all points

**

**** **

**

****

** **

**

A

sin2 θ


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**** **

**

****

** **

**

**

A

sin2 θ

• L1 norms - less sensitive to outliers

– minimise difference between model and observed


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θ

LORENTZ

ANDREWS

weight the residuals

**** **

**

****

** **

**

**

A

sin2 θ

• Robust statistics - weighting of points


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divide into 3 groupsdivide into 3 groups

find median of each groupfind median of each group

fit using least squares regressionfit using least squares regression**

**** **

****

** ****

**

A

sin2 θ

• Tri-median fitting


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AMPVO AMPVO -- Time Windowed Method (1)Time Windowed Method (1)

• Assumes events originate from single reflectors• Assumes seismic data are convolution of zero offset

data with AVO response

R (R (θθ))

RRoo

Sin Sin θθ22

gradient G= 9/4 gradient G= 9/4 ∆ ∆ σσ -- RRoo*


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• Perform AVO analysis in rolling time window (WLEN) centred on current sample time

• Estimate wavelet from near mid or full stacks• Use samples of estimated wavelet and actual wavelet to

extract the AVO response along the offsets

WLEN

0 deg 10 deg 20 deg 30 degnear far

full


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WLENWLEN

• WLEN – too large, then possibly more than one event - small gradient

values– too small, full benefits in improvement of S/N not achieved


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AMPVO AMPVO -- R0R0

• Main output

– R0 computed from regression analysis

stack R0


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AMPVO AMPVO -- GaGa

• Gradient based on trace amplitudes

– May be weighted by correlation coefficient (see later)

stack Gradient (Ga)


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AMPVO AMPVO -- GeGe ComputationComputation

• Gradient based on trace envelope

– May be weighted by correlation coefficient (see later)

Difference between Ga and Ge

Gradient not effected by Gradient not effected by alternating sign of the alternating sign of the

seismic waveletseismic waveletBUT: Can cause loss of resolution.BUT: Can cause loss of resolution.


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AMPVO AMPVO -- Ge Ge and and GaGa

• Example of Ga and Ge

Ga Ge


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AMPVO QC Tools (1)AMPVO QC Tools (1)

• A so called ‘best-fit’ line is always returned

– even if data contains only noise!

• Can we believe our estimated AVO attributes?

• Do we believe our AVO model’s assumptions?


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• Confidence in:

– estimated AVO attributes • attribute error estimate• correlation coefficient

– AVO model’s assumptions answered by• runs statistic• residual CMP gathers


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AMPVO QC Tools AMPVO QC Tools -- Correlation Coefficient (1)Correlation Coefficient (1)• Correlation Coefficient (‘goodness’ of regression fit)

– In Geocluster varies between +10000 and -10000– ENV parameter allows calculation on the envelopes

Coefficient = 0.94Coefficient = 0.94 Coefficient = 0.32Coefficient = 0.32


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AMPVO QC Tools AMPVO QC Tools -- Correlation Coefficient (2)Correlation Coefficient (2)

• Comparison with Ga

gradient

Correlation coefficient Correlation coefficient

Gradient Gradient


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AMPVO QC Tools AMPVO QC Tools -- Runs StatisticRuns Statistic

• Shows if straight line fit represents a realistic model– A run is a group of consecutive residuals having the same

sign– A residual is the difference between measured and modelled

amplitudes– compute a relationship between number of observed and

expected runs

xx

xx x

x

xx x x x x x x

x x x

x

xx x

xx

Which models are believable ?

Z=+veZ=-ve Z=+/-0

xx

xx

x x

residual

run


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AMPVO QC Tools AMPVO QC Tools -- Residual Gathers (1)Residual Gathers (1)

• difference between observed and predicted

– residual samples create residual traces and gathers

θ

**** **

**

****

** **

**

**

A

observedobserved

predictedpredicted


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AMPVO QC Tools AMPVO QC Tools -- Residual Gathers (2) Residual Gathers (2)

• Stack of residual gathers should be white noise!• Data which stacks up may be due to Residual NMO,

Statics, Multiples etc.

Residual stack Residual gathers


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AMPVO AMPVO -- HCI’sHCI’s

• HYDROCARBON INDICATORS (HCI’s)

– A seismic attribute in which large amplitudes indicate the

presence of hydrocarbons

• Three HCI’s are in common use today - all may be output

from AMPVO

– 1) AVO Response Indicator

– 2) AVO Product Indicator

– 3) Fluid Factor Indicator


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AMPVO AMPVO -- Reminder of AVO ClassesReminder of AVO Classes

class 1

class 2

class 3

shale

shale

shale

shale

shale

shale

sand

sand

sand

• Stack response - “dimming”• Decrease in amp with offset polarity reversal

• Near zero impedance contrast between sand and shale• Zero synthetic gives very poor tie to stack

• Classic “bright spot” DHI• Easiest to detect using AVO attributes (e.g. Ro * G)

5 10 15 25 30 35°20

-1

-2

1

2

Angle of incidence

class 1

class 2

class 3

class 1

class 2

class 3AI

Note : 4th. class added Castagna et al


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AMPVO AMPVO -- Product and Response (1)Product and Response (1)• (Ga)* sign(R0 ) - ‘AVO Response Indicator’• (Ga)* (R0 ) - product• (Ga* STACK) - ‘unbiased’ version of product

– All used for identifying CLASS III anomalies:

RR

RR

--R0R0

+R0+R0

R0 < 0, G < 0R0 < 0, G < 0

R0 > 0, G > 0R0 > 0, G > 0

Both top and bottom Both top and bottom reflections produce reflections produce increase in amplitudeincrease in amplitudewith offsetwith offset

GAS SANDGAS SAND

sinsin22θθ

sinsin22θθ

SHALESHALE

SHALESHALE


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AMPVO AMPVO -- Product and Response (2)Product and Response (2)

• Ga* sign(R0 ) - ‘AVO Response Indicator’ - CLASS III anomaly– Characteristic ‘red doublet’ with standard colour palette


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AMPVO AMPVO -- Vs/Vs/Vp Vp RelationshipRelationship

• Recall Castagna’s empirical relationship

1100

.. ...... ..

..

. ......

..

......... .

.... ..........

.... .

. ...

22

44

66

22 33

VVpp (km/sec)(km/sec)

Vs (km/sec)Vs (km/sec)

Shale (or mudShale (or mud--rock) linerock) line

......... .

.... ..........

.... ....

. .......

.. ... . .

.

.. ..

... . ..

.

..

.. .

. .

For fluid factor, assume For fluid factor, assume VpVp approx 2Vsapprox 2Vs


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R0 and G R0 and G CrossplotCrossplot• Background trend related to mudrock line

0.0-0.1-0.2 0.20.1

0.0

-2.0

-1.0

1.0

2.0

interceptanomalies

Background trend

grad

ient


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AMPVO AMPVO -- Fluid Factor (1)Fluid Factor (1)• ‘Normalise’ Intercept and Gradient to same amplitude range• Summation of Intercept and Gradient causes background to

‘disappear’

0.0-0.5-1.0 1.00.5

0.0

-1.0

-0.5

0.5

1.0

interceptintercept

backgroundbackgroundtrendtrend

(fluid line)(fluid line)


Class IVClass IV

grad

ient

grad

ient


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AMPVO AMPVO -- Fluid Factor (2)Fluid Factor (2)

• Usually R0 and G are different orders of magnitude•• Need to find scaling factorsNeed to find scaling factors

R0 Ga


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AMPVO AMPVO -- Fluid Factor (3)Fluid Factor (3)

• Three options:

– Theoretical (not applicable to real data)

– Empirical• choose scaling visually• apply to the anomaly

– ‘Far Offset stack’• data derived scalars


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AMPVO AMPVO -- Empirical Fluid Factor (1)Empirical Fluid Factor (1)

• Appropriately scaled addition of R0 and Ga causes the

‘background’ to be extinguished

FFEMPparameter by triggered...

yempiricall determined is

sincos... as in contained are and AMPVOIn

0

0

φ

φφ

φ

GaRFFba

bGaaRFF

+=

+=


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AMPVO AMPVO -- Empirical Fluid Factor (2)Empirical Fluid Factor (2)

• Choose location away from anomaly and run a scan

φ

Pick a value and apply to the anomalous areaPick a value and apply to the anomalous area


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AMPVO AMPVO -- Far Offset Stack Fluid FactorFar Offset Stack Fluid Factor

• Also scaled estimate of R0 + Ga• Scalars are data-derived• Triggered by parameter FFSTACK

– In practice it is a stack, with amplitudes weighted by offset

(hence far offset stack)


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TAVOF (Time windowed AVO) TAVOF (Time windowed AVO) -- 11

• Computation of amplification factor

**

**** **

**

****

** **

**

stack

gradientAmplification Factor =

A

θsin2 θ


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• Relationship between R0, G, Stack and A

**

**** **

**

****

** **

**

A

ts

( )sxtttpredxt

xttpredxt

sAsx

GRx

θθ

θ

22,

2,0,

sinsin... shown that becan it

sin,Shuey From

−+=

+=predx xt ,

)(sin2 xθ )(sin2 sθ sin2 θ


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• In practice amplification factor is derived from measured

amplitudes within a time window

Sample time to output

Analysis window


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• Ro and G are then derived from the amplification factor

and stack amplitudes

Amplification factor gradient intercept


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• AMPVO



– HCI indicators

• TAVOF - time averaged AVO (level 8100)


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• MUTAN - muting according to angle (level 8100)

• AMPVO

– Main and auxiliary (HCI) outputs


• TAVOF - time averaged AVO (level 8100 onwards)


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DINATDINATX

• DINAT computations based on either:• straight line approximation• ray bending (parameter ALPHA)

– direct smoothing of angles (SMTHANG)– indirect smoothing (SMTHVEL)

• Optimum mapping from offset to angle requires full ray tracing.– This however is time consuming and expensive. DINAT allows

simple approximations to be made.

• DINAT computes angles of incidence, θ– Uses the input velocities and trace

offsets.– Does not use the seismic traces

V


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DINAT DINAT -- Straight RayStraight Ray

• DINAT straight line approximation

– Computes angle from average velocity...Offset , X

S R The approximation is made that Vrms equals Vstacking in the input velocity library.

Vavg

t0/2

tX/2tX/2 θ

Angle computed from...

XavgXavg

tVX

tV

X

==

2

2sin θ

(one way)

Where….

2

220

avgX V

Xtt +=Method assumes that the event of interest is a flat interface with only one layer above it.


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DINAT DINAT -- Straight Ray ConsiderationsStraight Ray Considerations

• DINAT straight line approximation

The simplicity of this method makes it quite appealing but, unfortunately, also makes it (in some places) a poor approximation.

This method is, in general, not self-consistent for varying travel times - it assigns a different constant velocity to the region above each reflector.


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Offset , Offset , XX

SS RR

θ

Vint(1)

Vint(2)

Vint(3)

Assumes that the input velocity picks are on geological interfaces.

It builds up a flat-layered horizon model from the picks.

The ray paths are allowed to bend across these interfaces but are otherwise straight.

• DINAT ray bending method…•This method is chosen by coding the ALPHA option...

A schematic diagram of the ray geometry in the ray-bending approximation.

H1H1

H2H2

t0/2

Vrms


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DINAT DINAT -- Ray Bending (2)Ray Bending (2)The estimate of the incidence angle, θ , uses the (Dix) interval velocity, Vint, and the Vrms, where….

1,,

1,2

1,,2

,2int,

−

−−

−−

=nono

nonrmsnonrmsn tt

tVtVV

∑

∑

=

=

∆

∆= n

jj

n

jjj

nrms

t

tVV

1

1

2int,

2,

Assuming that Vrms can be approximated by the stacking velocity, the hyperbolic NMO equation is t2(x) = t0

2 + x2/V2rms.

By differentiating this with respect to offset, x, we get…

and

)()(

2 xtVx

dxxdt

rms

=

dt(x)/dx is also the slope of the time-distance curve.It can be shown (!) that for every layer n (for example, see Yilmaz 1987, pages 429-431), dt(x)/dx is given by…

nVdxxdt

int,

)sin()( θ=


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We can equate these two expressions for dt(x)/dx…

)()sin(

2int, xtV

xV rmsn

=θ

Substituting for t(x) and rearranging gives an equation for sin(θ) …

2

220

2

int)sin(

rmsrms V

xtV

xV

+

=θ

Note that as the interval velocity function is not smooth it will cause discontinuities in the computed angles across the layer interfaces (when Vint ‘jumps’).


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DINAT DINAT -- Ray Bending (4)Ray Bending (4)• The discrete picking of the input velocity library defines the layer - this implies that the interval velocity will be a "blocky" function.

As the Incidence angles are computed from the Interval velocities - blocky interval velocities can cause corresponding ‘blockiness’ in the angle computation

A typical interval velocity function.Based on picks made on average at 500msec apart!

To correct this problem the incidence angles can be smoothed in DINAT in either of two ways - Directly or Indirectly.

Sometimes the ‘blocky’ effect is large enough to produce unwanted artefacts in the AVO attribute sections.


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DINAT DINAT -- Direct Smoothing , SMTHANGDirect Smoothing , SMTHANG

Direct Smoothing chosen with the SMTHANG parameter….

First calculates the angles, then smooths the sin(θ)'s over time (at constant offset) with a simple sinc function.

The length of the sinc filter can be changed using the SMTHANGparameter…

• recommended value is 64 samples (i.e.256 ms @4 ms)

SMTHANGno SMTHANG


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DINAT DINAT -- Indirect Smoothing, SMTHVELIndirect Smoothing, SMTHVELIndirect Smoothing invoked by parameter SMTHVEL…

The initial Vrms function (from the velocity library) is smoothed over time by fitting a polynomial function to the picks. This essentially produces a velocity pick at every time sample – it becomes a continuous, smooth function.

The method then follows the ray-bending approximation and calculates the interval velocity and sin(θ).

As the input Vrms are smoothed so are the computed interval velocities and consequently so are the calculated angles i.e. the smoothing of input velocity has indirectly smoothed the incidence angles.


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DINAT DINAT –– Considerations for SmoothingConsiderations for Smoothing

V Direct smoothing, SMTHANG, is likely to produce better results if the velocity picks are on real, geological horizons.

Indirect smoothing, SMTHVEL, allows the degree of polynomial fit to be changed (namely linear, quadratic or cubic).

Because it applies a sinc function it cannot work on the very ends of the trace

Note that the indirect smoothing will not, in general, preserve the details of the velocity function.


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MUTAN MUTAN -- Muting Based on AnglesMuting Based on Angles

DINAT display

MUTAN result

MUTAN allows mutes to computed in terms of angle instead of offset distance.

MUTAN basically computes angles using the identical methods as described for module DINAT.

Key parameters defining mute limits


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ANGLE (1)ANGLE (1)

• ANGLE computes angle stacks and /or gathers– Angle computation method same as DINAT and MUTAN

• Computation by…

Straight ray Ray bending SMTHANG , SMTHVEL

SS RR SS RR


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ANGLE (2)ANGLE (2)• Angle stacks….

To compute angle stacks the user supplies a set of angles, plus a parameter RANGE…

STACKSSTACKSCMP gatherCMP gather

5 degrees5 degrees



time

offsetoffset

Angle rangesAngle rangesto be stackedto be stacked

Angle ranges Angle ranges -- parameter RANGEparameter RANGE

For an angle of 5 deg and a value of RANGE = 1 the program creates a corridor stack 4-6 degrees.

The angle is written in WORD 7, allowing sorting into angle ’gathers’


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ANGLE (3) ExampleANGLE (3) Example

• Angle stacks on real data…

5 deg 10 deg 15 deg 20 deg

Note the variation in amplitude with respect to angle.


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AMPVOAMPVO

• AMPVO module carries out a general amplitude with Offset (AVO) analysis.

• It performs regression analysis based on

Shuey’s 2 term approximation and outputs…

– Intercept (R0), Gradient (G) and variants

– Produces a wide range of QC tools

– Produces HCI indicators• AVO Response• AVO product• Fluid factor


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AMPVO AMPVO –– Basic ConceptsBasic Concepts• For a given sample time….

sample time

offset

• Measure amplitudes for each offset

But, how best to compute thelinear regression ??

R (R (θθ))

Intercept Intercept RRoo

Sin Sin θθ22

Gradient Gradient GG = (9/4 = (9/4 ∆∆σσ –– Ro)Ro)

• Convert offsets to angles

• Plot amplitudes against sin2θ**

** **

**

**

**

** **

**

• Compute linear regression to create a single R0 and G for each sample time


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With parameter ELIM, remove outliers

Beyond defined number of Standard Deviations from first fit

Second fit

Initial fit to all points

****

**** **

** ****

**

**

A

sin2 θ

• Least Squares method – Default Blank Option– Minimises the square of differences between model and observed

values..

• AMPVO offers several methods for fitting of the regression curve…

• Advantage: Fast• Disadvantage: sensitive to outliers

Solution!


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• L1 norms – L1 first option• - Minimises the absolute value difference between model and

observed values….

**** **

**

****

**

**

**

A

sin2 θ

• Advantage: less sensitive to outliers - Will provide a better result than least squares if anomalous values in the data.• Disadvantage: Is applied iteratively. Process may become divergent.


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LORENTZ

ANDREWS

**** **

**

****

** **

**

**

A


• Robust statistics – RB first optionSimilar to least squares but a weighting after initial fit to the residuals, followed by a second fit….

2 types of weighting curve available…

Second fit

Initial fit

sin2 θ


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• Tri-median fitting – MD first option

1) divide into 3 groups1) divide into 3 groups

2) find median 2) find median of each groupof each group

3) fit using least squares regression3) fit using least squares regression

**** **

**** **

** ****

**sin2 θ

**

**

A


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• Working on individual time samples is susceptible to small errors in NMO correction or residual static ‘jitter’….

Near FarNear Far

AA

** ** ****** ** ** ** ****

sin2 θsin2 θ

• To minimise this effect instead of using single samples measurements using a wavelet of defined length can be used.


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• Method makes use of the redundancy inherent in the seismic data – namely, because a single reflector is represented by many samples i.e. the seismic wavelet.

• In other words, the convolution of the seismic wavelet with the underlying reflectivity function

• Method assumes therefore…– An event originates from a single, isolated reflector.– Seismic data are the result of a convolution of zero offset wavelet with

the AVO response…

-50

-25

0

25

50R (R (θθ))

RRooSin Sin θθ22

gradient G= 9/4 gradient G= 9/4 ∆ ∆ σσ -- RRoo*


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– No interference between events– No phase changes with offset

• Ratcliffe and Adler (CGG 2000) developed a method to improve results where there is….

• Time Windowed Method – TW first option.

– Critical parameter is WLEN the length of the rolling time window• Default = 50ms.• The window is centred on the current sample time.• Should be about the same length as the dominant wavelength

WLEN WLEN

If WLEN too large, then

possibly more than one event

- small gradient values

If WLEN too small, full benefits in

improvement of S/N not achieved


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AMPVO AMPVO -- Time Windowed Method (4)Time Windowed Method (4)• Method uses samples of an estimated wavelet and the actual wavelets to extract the AVO response along the offsets.

• To establish the best estimated wavelet amplitudes in the window are stacked into near (0o-10o), far (20o-30o) and full (0o-30o) bins.

WLEN

0 deg 10 deg 20 deg 30 degnear far

full0 deg 30 deg

• The stack with maximum energy is used as the characteristic wavelet shape.

• Advantages: The inclusion of more data and hence noise influence in the analysis results.• Disadvantages: A poor gradient result if the actual wavelet is inconsistent


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AMPVO AMPVO –– Main outputs R0 and GMain outputs R0 and GMain AMPVO outputs computed from the regression analysis …

Gradient (Ga)R0

TraditionalAmplitudeStack


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AMPVO AMPVO -- Ge Ge and and GaGa

• Comparison of examples of Gradients based on Amplitude (Ga) and Envelope (Ge)….

Ga Ge

Notice how the Ge stands out much better from the background

May be weighted by a correlation coefficient (see later)


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A so called ‘best-fit’ line is always returned - even if data contains only random noise!…..

• AVO analysis pitfall…

• Can we believe our estimated AVO attributes?

• Do we believe our AVO model’s assumptions?

**

****

**

****

** **

**

**

A

Sin 2 θ

** **

**

** **

**

**

**

G?G?

G?G?G?G?

R0?R0?

R0?R0?

R0?R0?


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We can envisage therefore producing an AVO analysis with a largeanomaly – but how meaningful is it?

• We seek to quantify the confidence level in results byusing statistical measures:

• For good QC analysis we require to know…

– An estimation of the believability of the AVO attributes… • Make an attribute error estimate• Measure the correlation coefficient

– How believably does the model represent the actual data…• Runs statistic• Residual CMP gathers


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AMPVO QC Tools AMPVO QC Tools -- Attribute Error EstimateAttribute Error Estimate• Various error estimates may be output as follows…

• R0 Intercept error: Output in auxiliary buffer OS8• Ga Gradient error: Output in auxiliary buffer OS9• Ge Gradient error: Output in auxiliary buffer OS10

• The error is given in term of standard deviations...

**

** ****

****

** **

**

** ****

**

**

**

**

****

GG

G + 1G + 1

A

Relatively small error estimate= High confidence level

**

** ****

****

**

**

**

**

** **

**

**

**

**

**

**

GG

G + 10G + 10

A

Relatively high error estimate= Low confidence level

Sin 2 θSin 2 θ

• Suggested in XDOC that error estimates are plotted as a grey scale section. For derivation of the error see Advanced Technical Description or Draper & Smith 1981


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AMPVO QC Tools AMPVO QC Tools -- Correlation Coefficient (1)Correlation Coefficient (1)• Correlation Coefficient (‘goodness’ of regression fit)

– Is a measure of how well the data points line up in a straight line...

Coefficient = 0.94Coefficient = 0.94 Coefficient = 0.32Coefficient = 0.32

(A coefficient of 1 or -1 is a perfect fit)

(A coefficient of 0 represents random distribution of points)

• Parameter ENV allows calculation on the envelopes

For derivation of the coefficient see Advanced Technical Description or Press et al 1992


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AMPVO QC Tools AMPVO QC Tools -- Correlation Coefficient (2)Correlation Coefficient (2)

• Comparison of Correlation Coefficient CC with Ga….

Gradient Gradient Ga Ga Correlation coefficient CC Correlation coefficient CC

Red and Blue represent high coefficients

Green represents low coefficient

– In Geocluster CC varies between +10000 and -10000


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AMPVO QC Tools AMPVO QC Tools -- Runs Statistic (1)Runs Statistic (1)

• Runs statistics - Output in auxiliary buffer 7– AMPVO attempts to fit a straight line to the data, however there may be

other curves which much better fit the data, e.g...

**** **

** ** **** **

**

****

**** **

****

****

Here a straight line is a reasonable fit….

**

**

** **

**

**

**

****

**

**

**

** **

**

**

**

**

But is a straight linea reasonable fit here….

??

The runs statistic therefore gives a measure of how well a straight line fit represents a realistic model.


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AMPVO QC Tools AMPVO QC Tools -- Runs Statistic (2)Runs Statistic (2)• Runs statistics are computed by counting the number of runs• A run is a group of consecutive residuals (differences between the line and the

observed value) having the same sign)….

• In some cases comparing the number of runs to the total number of points is regarded as the statistic – the smaller the ratio the better!

**** **

** ** **** **

**

****

**** **

****

****

11

22

33

44

55

66

77

88

99

1010

1111

1212

1313

• However, in this example that particular statistic would give the same result…

• Number of runs =13• Number of points = 18

• Number of runs =13• Number of points = 18

****

**

**

**

**

**

**

11

22

33

44

****

**

**

**

**

**

**

55

66

77

88

****

**

**

**

**

**

**

99

1010

1111

1212

**

**1313


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AMPVO QC Tools AMPVO QC Tools -- Runs Statistic (3)Runs Statistic (3)• A better runs statistic, and that used in AMPVO, is...

– Compute ‘Z’ which is the difference between the number of observed and expected runs….

σµ 5.0±−

=uZ

where…. 12

21

21 ++

=nnnnµ

and….( ) ( )

11

)2(2

212

21

212122

2 1 +−++

−−=

nnnnnnnnnn

σ

Where..u is the number of observed runsµ is the number of expected runsn1 is the number of positive residual pointsn2 is the number of negative residual points

If result is….

Large -ve Zmeans too few runs.

Near zero Z: means a near correct

number of runs - the model line is appropriate for the line.

Large +ve Zmeans too many runs.

Run statistic value of Z is multiplied by 10000 in Geocluster.


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AMPVO QC Tools AMPVO QC Tools -- Residual Gathers (1)Residual Gathers (1)• Residual Gathers Output in auxiliary buffer 14

– Involves computing the difference between observed and predicted amplitude values for each incidence angle.

– Result is effectively ‘residual amplitude’ traces after the AVO effects have been removed.

Convert back to offset to generate offset gathers.

At each sample time the resulting values for the offset range should, on average, be random…

sin2θ

**** **

**

****

****

**

**

A

observedobserved

predictedpredicted ResiduResidualal

** ** **** ** **

****

**…so a stack of these gathers should produce white noise!

Consistent values on the stack may indication processing errors.

Residual A


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AMPVO QC Tools AMPVO QC Tools -- Residual Gathers (2) Residual Gathers (2) • Stack of residual gathers

should be white noise!

Residual stackResidual gathers

Data which stacks up may be due to Residual NMO,Statics, Multiples etc….


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AMPVO AMPVO -- HCI’sHCI’s

• HYDROCARBON INDICATORS (HCI’s)– Are seismic attributes in which large amplitudes indicate the

presence of hydrocarbons.

• Several of the HCI’s in common use today may be output from AMPVO…

• ‘AVO Response Indicator’ - (Ga) x sign(R0 )• ‘AVO Product Indicator’ - (Ga) x (R0 )• ‘Unbiased’ version of product - (Ga x STACK)

– All used for identifying CLASS III anomalies:

• Fluid Factor Indicator


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AMPVO AMPVO –– HCI examplesHCI examples

• Far Offset Stack Fluid Factor– Triggered by parameter

FFSTACK– In practice this is a stack, with

amplitudes weighted by offset (hence far-offset stack)

• Ga x sign(R0) - ‘AVO Response Indicator’ - CLASS III anomaly– Characteristic ‘red doublet’ with

standard colour palette…..


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AMPVO AMPVO –– Recommended Processing StrategyRecommended Processing Strategy

• Suggested in XDOC to use a 3 pass approach…

Pass 1• Output R0 and G plus a few QC options

– E.g. Regression plots, residual CDP gathers• Test the regression fitting

Pass 1• Output R0 and G plus a few QC options

– E.g. Regression plots, residual CDP gathers• Test the regression fitting

Pass 2• Output all AVO displays• Perform an in-depth QC analysis

Pass 2• Output all AVO displays• Perform an in-depth QC analysis

Pass 3• Final pass to tweak input parameters

Pass 3• Final pass to tweak input parameters


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Stack amplitudegradient

Amplification Factor is theratio of gradient to stackamplitude =

• TAVOF module carries out time averaged Amplitude Versus Offset (AVO) analysis.– Requires input velocity field to be regularly sampled at 100ms.– Outputs similar to those produced by AMPVO (R0 and G) plus an

Amplification factor section.

**

** ** ****

** **** **

A

sin2 θR0

G

S


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• In practice the Amplification factor is derived from measured amplitudes within a sliding time window…..

Sample timeto output

Analysis Window = parameter TWIN

Recommended that TWIN be made about 50ms as a starting point for testing

A triangular scaling function is applied to the amplitudes within the window

0 1


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TAVOF (Time windowed AVO) TAVOF (Time windowed AVO) -- 44• Test for parameter TWIN …

TWIN = 10ms TWIN = 30ms TWIN = 50ms TWIN = 70ms

General increase in temporal smoothness(Default)


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• Relationship between R0, G, Stack and A…

**

**** **

**

****

**

A

**

**

sin2 θ

ts

)(sin2 xθ )(sin2 sθ

( )sxtttpredxt

xttpredxt

sAsx

GRx

θθ

θ

22,

2,0,

sinsin...shown thatbecan it

sin,ShueyFrom

−+=

+=predxt ,x


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• R0 and G are then derived from the Amplification factor and stack amplitudes….

Amplification factor gradient intercept


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TAVOF (Time windowed AVO) TAVOF (Time windowed AVO) -- 44• Test for parameter THOLD …

THOLD= 0.01 THOLD= 0.05 THOLD = 0.1 THOLD= 0.2

General increase in stability (especially at greater times)(Default)


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• The approach for TAVOF analysis involves the creation of 3 data sets….

– Zero offset projection section• Derived from the amplification factor.

– Angle stack for 00 to 300

– Angle stack from 300 to 500

(if long offset data exists)

– Generated by module ANGLE

• The production of these robust sections reduces the need for in house storage of large data sets.


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• AMPVO



– HCI indicators

• TAVOF - time averaged AVO (level 8100 onwards)

Documents

AVO Preserntation CGG