Avo_talk

8/10/2019 Avo_talk

http://slidepdf.com/reader/full/avotalk 1/44

New Trends in AVO

Brian Russell and Dan Hampson

Hampson-Russell Software

Calgary, Alberta.

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Outline of Talk

Review of AVO principles

AVO attributes

AVO cross-plotting

3D AVO

AVO and Anisotropy

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Summary of AVO Methodology

Input Raw Gathers

Optimum Processing

Recon Methods InversionModelling

Gradient/

Intercept

Partial

StacksPrimaries

only

Wave

Equation

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AVO Example

• We will illustrate AVO with a Cretaceous

gas sand example from Alberta.

• Traditionally, wells were drilled in this

area based on “bright-spot” anomalies.

• Many dry holes were encountered due to

false “bright-spots” caused by coals.

• Drilling success was been enhanced

through the use of AVO.

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Basic AVO Analysis

• We will start our AVO analysis by looking

at some simple displays of the gas sand

example:

• The CMP stack

• Near and far trace stacks

• The common offset stack

• Amplitude envelope displays

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The full stack shows a bright spot at 640 ms.

600-

700-

Time

(ms)

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Note increase in amplitude from (a) Near to (b) Far trace

stack.

(b)

(a)

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(a) Near and (b) far trace stacks with color

envelope

(a)

(b)

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Input gathers showing an amplitude increase

with offset.

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http://slidepdf.com/reader/full/avotalk 10/44Gathers with color amplitude envelope

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More Advanced AVO Analysis

• We will continue our AVO analysis by

looking at the picked top and base of the

common offset stack of the gas sand

example. This will lead to severalconclusions:

• The amplitudes change as a function of

offset or angle.

• These changes can be quantified using

the Zoeppritz or Aki-Richards equations.

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Picking the common offset stack

(a) Common offset stack

(b) Picks

from the

trough.

(c) Picks

from the

peak.

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Reflected

P-wave = R(q

Reflected

S-wave

Transmitted

P-wave

Incident

P-wave

Transmitted

S-wave

Mode Conversion of an Incident P-wave

VP1 , VS1 ,r

1

VP2 , VS2 , r2

If q > 0o, incident P-waves produce P and S reflections

and transmissions.

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The Aki-Richards Approximation

• Using the linearized approximationand keeping only second order terms:

R(q) = RP + G sin2q

where: RP=1/2(DVP/VP+Dr/r)

= zero-offset P-wave refl.coeff.

and: G = gradient.

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Common Offset Picks as function of sin2q

+RP

-RP

+G

- G

Offset

sin2q

Time

(a) Small part of commonoffset stack.

(b) Peak/trough picks vs

sin2q

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Wiggens’ Approximation

• Assuming that VP/VS = 2, in Aki-Richards eq:

G = RP - 2*RS

where: RS = 1/2(DVS/VS+Dr/r)

= zero-offset S-wave refl. coeff.

• This can be rewritten:

RS = (RP - G) / 2

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Shuey’s Approximation

• Assuming thats

av= 1/3, we get theapproximation:

G = 9/4Ds

- RP

where: Ds= Change in Poisson’s Ratio

• This can be rewritten:

Ds

= (RP + G)*4/9

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http://slidepdf.com/reader/full/avotalk 18/44(a) Intercept (P-wave) and (b) Gradient Stacks

(a)

(b)

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http://slidepdf.com/reader/full/avotalk 19/44(a) (P + G) and (b) Rs (P - G) StacksDs

(a)

(b)

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AVO Modeling and Inversion

•Finally, AVO effects can be quantified using

modeling and inversion:

• Modeling involves building a blocked log

model and then creating a synthetic byray-tracing and Zoeppritz amplitude

calculation.

• Inversion involves updating the model to

create a better fit between synthetic and

observed common offset stack.

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Modelling / Inversion Flow

Input Well

Logs

Input CDP

Gathers

Forward

Model

Create

Coffstack

Difference

Update

Model

Finish

Good

Fit?

No

Yes

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Well Logs and Synthetic/Seismic Tie

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Well Logs and Synthetic After Inversion

Black = Before Red = After

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Data Comparison after Inversion

(a) Synthetic (b) Real Coffstack

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AVO Cross-plotting

AVO cross-plotting involves plotting theintercept against the gradient and identifying

anomalies. The theory of cross-plotting was

developed by Castagna el al (TLE, 1997,Geophysics, 1998) and Verm and Hilterman

(TLE, 1995) and is based on two ideas:

(1) The Mudrock line

(2) The Rutherford/Williams

classification scheme.

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The Mudrock Line

The mudrock line is a linear relationshipbetween VP and VS derived by Castagna et al

(1985):

VP

= 1.16 VS

+ 1360 m/sec

Smith and Gidlow (1987) derived the “Fluid

Factor” by combining the mudrock line with

Aki-Richards:DF = RP - 1.16 (VP/VS) RS

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ARCO’s original mudrock derivation

(Castagna et al, Geophysics, 1985.)

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Rutherford/Williams Classification

Rutherford and Williams (1989) derived the

following classification scheme for AVOanomalies, with further modifications by Ross

and Kinman (1995) and Castagna (1997):

Class 1: High acoustic impedance contrast

Class 2: Near-zero impedance contrast

Class 2p: Same as 2, with polarity change

Class 3: Low impedance contrast sands

Class 4: Very low impedance contrast

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The Rutherford and Williams classification

scheme as modified by Ross and Kinman.

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Theory of Cross-plotting

Castagna and Swan (1988) start by assuming

both the mudrock line and Gardner’sequation:

r = a VP1/4

They then show that the linear relationship

can be written:

G = RP [4/5 -32/5c(VS/VP)-1/2(VS/VP)2]

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Mudrock lines on a crossplot for various

Vp/Vs ratios (Castagna and Swan, 1998)

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Intercept / Gradient Crossplots

(b) Interpreted gas

zone

(a) Uninterpreted gas

zone

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Seismic Display from Int/Grad Xplots

(a) Before interpretation

(b) After interpretation

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3D AVO

3D AVO is an simply an extension of 2D

AVO using gradient/intercept analysis.

Using 3D allows us to map spatial

variations in AVO effects. We must be careful to get good offset

coverage in the 3D design stage.

It may be possible to detect azimuthal

anisotropy by restricting azimuths in the

attribute calculation.

Lines from a 3D Channel Sand

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Lines from a 3D Channel Sand

Example

(a) Inline 10, channel

at Xline 9, 650 msec.

(b) Inline 20, channel

at Xline 24, 650 msec.

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Map view of seismic amplitude

from 3D channel sand.

Pseudo Poisson’s ratio over 3D channel

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Pseudo-Poisson’s ratio over 3D channel

sand

(a) Inline 10, channel

at xline 9, 650 msec.

(b) Inline 20,

channel

at xline 24, 650

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Map view of pseudo-Poisson’s

Ratio over channel sand.

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AVO and Anisotropy

Two types of anisotropy most common:

Transverse isotropy - caused by horizontal

layering

Azimuthal anisotropy - caused by fractures

Transverse isotropy can be modelled using

Thomsen parameters.

Azimuthal anisotropy may be observed by

restricting azimuths when performing

intercept/gradient analysis.

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Transverse Isotropy

Blangy (Geophysics, 1997) showed that atransversely isotropic term could be added

to the Aki-Richards’ equation using the

Thomsen weak anisotropic parameters d and e :

Ran(q) = Ris(q) + Dd/2 sin2

(q)- 1/2(Dd - De) sin2(q)tan2(q)

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Transverse Isotropy - Gas Case

Note that the effect of Dd and De is to increase the

AVO effects. (Blangy, 1997)

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Transverse Isotropy - Wet Case

Note that the effect of Dd and De is to create

apparent AVO decreases. (Blangy, 1997)

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CONCLUSIONS

This talk was intended to give an

overview of the AVO method. The various techniques used in AVO

were illustrated using a gas sand.

Traditional AVO methods consist ofcomputing intercept/gradient attributes.

Newer techniques include:

- cross-plotting of attributes

- extension to 3D

- analysis of anisotropic effects.

Avo_talk

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