1. New Trends in AVO Brian Russell and Dan Hampson
Hampson-Russell Software
Calgary, Alberta.

2. Outline of Talk
Review of AVO principles
AVO attributes
AVO cross-plotting
3D AVO
AVO and Anisotropy

3. Summary of AVO Methodology
Input Raw Gathers
Optimum Processing
Recon Methods
Modelling
Inversion
Partial
Stacks
Gradient/
Intercept
Wave
Equation
Primaries
only

4. 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.

5. 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

6. The full stack shows a bright spot at 640 ms.
Time
(ms)
600-
700-
The full stack shows a bright spot at 640 ms.

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

8. (a) Near and (b) far trace stacks with color envelope

9. Input gathers showing an amplitude increase with offset.

10. Gathers with color amplitude envelope

11. 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.

12. Picking the common offset stack
(b) Picks from the trough.
(c) Picks
from the
peak.
(a) Common offset stack

13. Mode Conversion of an Incident P-wave
Reflected
S-wave
Reflected
P-wave = R(q) q
VP1 , VS1 , r1
VP2 , VS2 , r2
Transmitted
P-wave
Transmitted
S-wave
If q > 0o, incident P-waves produce P and S reflections
and transmissions.

14. The Aki-Richards Approximation
Using the linearized approximation and keeping only second order terms:
R() = RP + G sin2q
where: RP=1/2(DVP/VP+Dr/r)
= zero-offset P-wave refl.coeff.
and: G = gradient.

15. Common Offset Picks as function of sin2q
+RP +G
sin2q
- G
Time
-RP
(a) Small part of common
offset stack.
(b) Peak/trough picks vs sin2q

16. 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

17. Shuey’s Approximation
Assuming that sav= 1/3, we get the approximation:
G = 9/4Ds - RP
where: Ds= Change in Poisson’s Ratio
This can be rewritten:
Ds = (RP + G)*4/9

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

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

20. 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.

21. Modelling / Inversion Flow
Input Well
Logs
Input CDP
Gathers
Forward
Model
Create
Coffstack
Difference
Update
Model No
Good
Fit?
Yes
Finish

22. Well Logs and Synthetic/Seismic Tie

23. Data Comparison Before Inversion
(a) Synthetic
(b) Real Coffstack

24. Well Logs and Synthetic After Inversion
Black = Before Red = After

25. Data Comparison after Inversion
(a) Synthetic
(b) Real Coffstack

26. 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.

27. The Mudrock Line
The mudrock line is a linear relationship between VP and VS derived by Castagna et al (1985):
VP = 1.16 VS m/sec
Smith and Gidlow (1987) derived the “Fluid Factor” by combining the mudrock line with Aki-Richards:
DF = RP (VP/VS) RS

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

29. 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 contrast
Class 2p: Same as 2, with polarity change
Class 3: Low impedance contrast sands
Class 4: Very low impedance contrast

30. The Rutherford and Williams classification
scheme as modified by Ross and Kinman.

31. Theory of Cross-plotting
Castagna and Swan (1988) start by assuming both the mudrock line and Gardner’s equation:
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]

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

33. Intercept / Gradient Crossplots
(a) Uninterpreted gas zone
(b) Interpreted gas zone

34. Seismic Display from Int/Grad Xplots
(a) Before interpretation
(b) After interpretation

35. 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.

36. 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.

37. Map view of seismic amplitude from 3D channel sand.

38. 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 msec.

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

40. 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.

41. Transverse Isotropy Blangy (Geophysics, 1997) showed that a
transversely 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)

42. Transverse Isotropy - Gas Case
Note that the effect of Dd and De is to increase the
AVO effects. (Blangy, 1997)

43. Transverse Isotropy - Wet Case
Note that the effect of Dd and De is to create
apparent AVO decreases. (Blangy, 1997)

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