1. Some current research in P-S AVO and multicomponent OBS
Jim Brown
, Yan Yan
, Alex Vant
and Hongbo Zhang

2. Suppression of water-column multiples by wavefield separation and cross-correlation
(with Yan Yan)
Reverberations
Air
Water
Seafloor sediment
Downgoing waves

3. Receiver-side multiples
Air
Water
Seafloor sediment
Downgoing waves

4. Source-side multiples
Air
Water
Seafloor sediment
Upgoing waves

5. Dual-sensor method Upgoing Downgoing Hydrophone (W)
Vertical geophone (Z)
Upgoing
Downgoing

6. In the dual-sensor method:
Upgoing P waves register with same polarity on W and Z.
Downgoing P waves register with opposite polarity on W and Z.
We can extract the upgoing wavefield by summation.
This can be considered as a kind of wavefield-separation technique.
In fact, the wavefield-separation technique can be derived directly from the wave equation.

7. The wave equation as a 1st-order ordinary differential equation in stress and particle velocity (Aki and Richards, 1980):
[p1 and p2 are horizontal slowness components.]

8. Inline Horizontal geophone
Considering boundary conditions, the upgoing wavefield for every component can finally be expressed (after Amundsen and Reitan, 1995; Osen et al., 1999) as:
Upgoing wavefield
Hydrophone
Vertical geophone
Upgoing wavefield
Inline Horizontal geophone
Upgoing wavefield

9. After applying the wavefield-separation technique, the downgoing multiples in OBS data can be suppressed.
However, source-side and peg-leg multiple energy remains as part of the upgoing wavefield.
We have devised a method based on cross-correlation to further attenuate the source-side upgoing multiple energy.

10. Cross-correlation method
In laterally homogeneous cases (uniform water depth), source-side multiples will have raypaths that are equivalent in length to those of corresponding receiver-side multiples on the vertical geophone records.
Air
Water
Seafloor sediment
Consolidated sediment
The two types of multiples are of comparable energy but have opposite polarities on the vertical-component geophone records.

11. Model: Air Water Vp = 1500 m/s D = 500 m Hydrophone Geophones
Seafloor sediment
Consolidated sediment

12. Hydrophone component Modelled total wavefield
Decomposed upgoing wavefield
Upgoing wavefield after eliminating source-side multiple
Direct Arrival
1st Reverberation
2nd Primary
1st Primary
Source- and receiver-side multiple
2nd Reverberation
1st Primary
2nd Primary
Source- and receiver-side multiple
2nd Primary
1st Primary

13. Vertical geophone component
Modelled total wavefield
Decomposed upgoing wavefield
Upgoing wavefield after eliminating source-side multiple
Direct Arrival
1st Reverberation
2nd Primary
1st Primary
2nd Reverberation
Source- & receiver-side multiples
1st Primary
2nd Primary
Source- & receiver-side multiple
2nd Primary
1st Primary

14. Horizontal geophone component
Modelled total wavefield
Decomposed upgoing wavefield
Upgoing wavefield after eliminating source-side multiple
Direct Arrival
1st Reverberation
2nd Primary
1st Primary
2nd Reverberation
Source- & receiver-side multiples
1st Primary
2nd Primary
Source- & receiver-side multiple
2nd Primary
1st Primary

15. Still ahead…
Improving the cross-correlation technique for using the downgoing field to locate multiples in the upgoing field and to suppress them.
Applying the entire multiple-suppression method to real OBS data, probably Mahogany.
Future: Improving the robustness of the cross-correlation technique so that it applies also in the presence of dip.

16. A new approximation to the P-S reflection coefficient for small incidence angles
(with Alexandru Vant)
An approximation to the Zoeppritz equations for the converted-wave reflection coefficient, RPS
Assumption: near-vertical incidence, i.e., small angles.
No assumption of small changes in rock properties.

17. Zoeppritz expression for RPS:
(Aki & Richards, 1980)

20. Model 1: The ‘normal’ situation, i1 = 5
1 = 2000
2 = 3500
(m/s)
1 = 800
2 = 1800
1 = 1900
2 = 2400
(kg/m3)
Variation of RPS with 1
Variation of RPS with 2

21. Model 1: The ‘normal’ situation, i1 = 5
1 = 2000
2 = 3500
(m/s)
1 = 800
2 = 1800
1 = 1900
2 = 2400
(kg/m3)
Variation of RPS with b1
Variation of RPS with r1

22. Model 2: Clastic over salt, i1 = 5
1 = 3600
2 = 4500
(m/s)
1 = 2400
2 = 2500
1 = 2600
2 = 2100
(kg/m3)
Variation of RPS with 1
Variation of RPS with r1

23. Model 3: Shale over gas sand, i1 = 5
1 = 2150
2 = 1750
(m/s)
1 = 860
2 = 1500
1 = 2200
2 = 1950
(kg/m3)
Variation of RPS with 1
Variation of RPS with b1

24. Model 3: Shale over gas sand, i1 = 10, 30
1 = 2150
2 = 1750
(m/s)
1 = 860
2 = 1500
1 = 2200
2 = 1950
(kg/m3)
i1=10, variation of RPS with 1
i1=30, variation of RPS with 1

25. Model 3: Shale over gas sand, i1 = 10, 30
1 = 2150
2 = 1750
(m/s)
1 = 860
2 = 1500
1 = 2200
2 = 1950
(kg/m3)
i1=10, variation of RPS with r1
i1=30, variation of RPS with r1

26. Model 1: The ‘normal’ situation, i1 = 0-90
1 = 2000
2 = 3500
(m/s)
1 = 800
2 = 1800
1 = 1900
2 = 2400
(kg/m3)

27. Model 2: Clastic over salt, i1 = 0-90
1 = 3600
2 = 4500
(m/s)
1 = 2400
2 = 2500
1 = 2600
2 = 2100
(kg/m3)

28. Model 3: Shale over gas sand, i1 = 0-90
1 = 2150
2 = 1750
(m/s)
1 = 860
2 = 1500
1 = 2200
2 = 1950
(kg/m3)

29. Model 1: Variation of the approximation error with i1

30. Model 2: Variation of the approximation error with i1

31. Model 3: Variation of the approximation error with i1

32. A review of AVO analysis (with Hongbo Zhang)
Review of AVO from its early beginnings to P-S AVO
A foundation for further research in P-S AVO and inversion
About 55 papers referenced

33. Milestones in P-wave AVO
Koefoed (1955)
Bortfeld (1961)
Aki and Richards (1980)
Shuey (1985)
Smith and Gidlow (1987)
Hilterman (1989)
Rutherford and Williams (1989)
Fatti et al. (1994)
Castagna and Swan (1997)

34. AVO classification Rutherford and Williams (1989)
Castagna and Swan (1997)

35. More recent P & P-S AVO, anisotropy
Goodway et al. (1997)
Gray et al. (1999)
Garotta and Granger (1987)
Carcione and Tinivella, 2000)
Rüger (1997, 1998)
Kelly and Ford (2000a, b)
Kelly et al. (2000)
Larsen et al. (1999)
Jin (1999)
Jin and Michelena (2000)
Ronen (2000)

36. P-S AVO
Ronen et al. (2000)
Jin and Michelena (2000)

37. Thanks to the sponsors of CREWES!
At the Burgess shale