New Trends in AVO

Brian Russell and Dan Hampson

Hampson-Russell Software

Calgary, Alberta.

Outline of Talk

Review of AVO principles

AVO attributes

AVO cross-plotting

3D AVO

AVO and Anisotropy

Summary of AVO Methodology

Input Raw Gathers

Optimum Processing

Recon Methods InversionModelling

Gradient/Intercept

PartialStacks

Primaries only

WaveEquation

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.

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

The full stack shows a bright spot at 640 ms.

600-

700-

Time(ms)

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

stack.

(b)

(a)

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

envelope

(a)

(b)

Input gathers showing an amplitude increase with offset.

Gathers with color amplitude envelope

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 several

conclusions:

• The amplitudes change as a function of

offset or angle.

• These changes can be quantified using

the Zoeppritz or Aki-Richards equations.

Picking the common offset stack

(a) Common offset stack

(b) Picks from the trough.

(c) Picks from the peak.

Reflected P-wave = R(

Reflected S-wave

Transmitted P-wave

Incident P-wave

Transmitted S-wave

Mode Conversion of an Incident P-wave

VP1 , VS1 , 1

VP2 , VS2 , 2

If > 0o, incident P-waves produce P and S reflectionsand transmissions.

The Aki-Richards Approximation

• Using the linearized approximation

and keeping only second order terms:

R() = RP + G sin2

where: RP=1/2(VPVP+)

= zero-offset P-wave refl.coeff.

and: G = gradient.

Common Offset Picks as function of sin2

+RP

-RP

+G

- G

Offset

sin2

Time

(a) Small part of commonoffset stack.

(b) Peak/trough picks vs sin2

Wiggens’ Approximation

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

G = RP - 2*RS

where: RS = 1/2(VSVS+)

= zero-offset S-wave refl. coeff.

• This can be rewritten:

RS = (RP - G) / 2

Shuey’s Approximation

• Assuming that av= 1/3, we get the

approximation:

G = 9/4 - RP

where: = Change in Poisson’s Ratio

• This can be rewritten:

= (RP + G)*4/9

(a) Intercept (P-wave) and (b) Gradient Stacks

(a)

(b)

(a) (P + G) and (b) Rs (P - G) Stacks

(a)

(b)

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 by

ray-tracing and Zoeppritz amplitude

calculation.

• Inversion involves updating the model to

create a better fit between synthetic and

observed common offset stack.

Modelling / Inversion Flow

Input Well Logs

Input CDP Gathers

Forward Model

CreateCoffstack

Difference

Update Model

Finish

Good Fit?

No

Yes

Well Logs and Synthetic/Seismic Tie

(a) Synthetic(b) Real

Coffstack

Data Comparison Before Inversion

Well Logs and Synthetic After Inversion

Black = Before Red = After

Data Comparison after Inversion

(a) Synthetic (b) Real Coffstack

AVO Cross-plotting

AVO cross-plotting involves plotting the intercept 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.

The Mudrock Line

The mudrock line is a linear relationship between 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:

F = RP - 1.16 (VP/VS) RS

ARCO’s original mudrock derivation (Castagna et al, Geophysics, 1985.)

Rutherford/Williams Classification

Rutherford and Williams (1989) derived the following classification scheme for AVO anomalies, with further modifications by Ross and Kinman (1995) and Castagna (1997):

Class 1: High acoustic impedance contrast Class 2: Near-zero impedance contrastClass 2p: Same as 2, with polarity changeClass 3: Low impedance contrast sandsClass 4: Very low impedance contrast

The Rutherford and Williams classificationscheme as modified by Ross and Kinman.

Theory of Cross-plotting

Castagna and Swan (1988) start by assuming both the mudrock line and Gardner’s equation: = a VP

1/4

They then show that the linear relationship can be written:

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

Mudrock lines on a crossplot for various Vp/Vs ratios (Castagna and Swan, 1998)

Intercept / Gradient Crossplots

(b) Interpreted gas zone

(a) Uninterpreted gas zone

Seismic Display from Int/Grad Xplots

(a) Before interpretation

(b) After interpretation

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 Example

(a) Inline 10, channelat Xline 9, 650 msec.

(b) Inline 20, channelat Xline 24, 650 msec.

Map view of seismic amplitude from 3D channel sand.

Pseudo-Poisson’s ratio over 3D channel sand

(a) Inline 10, channelat xline 9, 650 msec.

(b) Inline 20, channelat xline 24, 650 msec.

Map view of pseudo-Poisson’s Ratio over channel sand.

AVO and AnisotropyTwo 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.

Transverse Isotropy

Blangy (Geophysics, 1997) showed that atransversely isotropic term could be added to the Aki-Richards’ equation using the Thomsen weak anisotropic parameters and :

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

- 1/2() sin2()tan2()

Transverse Isotropy - Gas Case

Note that the effect of and is to increase theAVO effects. (Blangy, 1997)

Transverse Isotropy - Wet Case

Note that the effect of and is to create apparent AVO decreases. (Blangy, 1997)

CONCLUSIONSThis 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 of

computing intercept/gradient attributes.Newer techniques include: - cross-plotting of attributes - extension to 3D - analysis of anisotropic effects.