by Brian Russell Hampson-Russell Software Calgary, Alberta.

1. by Brian RussellHampson-Russell SoftwareCalgary, Alberta. New Trends in AVO

2. Introduction • In this presentation, I will review the principles of the AVO (Amplitude Variations with Offset) method and then look at some of the new trends that are emerging. • These new trends involve alternate ways of extracting information about the fluid content and lithology of the reservoir. • I will illustrate these ideas with examples taken from Canada, the Gulf Coast and the West of Shetlands, UK.

3. Seismic Lithology Estimation Gathers Stack Inversion Estimate ZP= VP Traditional methods of seismic lithology estimation involve stack followed by inversion. This allows only for the estimation of acoustic impedance, which is not sufficient for inferring fluid content.

4. Seismic Lithology Estimation Gathers Stack AVO Analysis Inversion Attribute 1 Estimate ZP= VP Attribute 2 Estimate VP, VS, and  The AVO method allows us to use multiple attributes to simultaneously estimate VP, VS, and , thus inferring fluid and/or lithology.

5. Possible Attributes • But which two attributes will give us the best estimate of these reservoir parameters? • A number of different possibilities have been proposed, which can be grouped into three main categories: • Offset or angle-limited stacks • Difference (pseudo-gradient). • Relative acoustic impedance (RAI) inversion. • Elastic Impedance inversion. • Extraction of Intercept and Gradient • Sum (Ds) and difference (RS). • Cross-plot analysis. • Extraction of RP and RS reflectivity • Inversion of RP and RS to give ZP and ZS. • Lambda-Mu-Rho analysis of ZP and ZS. • Extraction of Kpore

6. Basic Theory Incident P-wave Reflected S-wave Reflected P-wave = RP r i r VP1 , VS1 , r1 VP2 , VS2 , r2 t t Transmitted P-wave Transmitted S-wave If q > 0o, an incident P-wave will produce both P and S reflected and transmitted waves. This is called mode conversion. The amplitudes can be modelled by the Zoeppritz equations.

7. AVO Modeling • Before performing an AVO analysis on seismic data, it is important to model the expected AVO response. • The modeling can be done using the Zoeppritz equations for primaries only, or using the full elastic wave equation to include converted waves and multiples. • The Aki-Richards linearized approximation can be used to both understand the modeled results and to interpret the AVO response. The next slide shows this equation.

8. The Aki-Richards equation • The Aki-Richards linearized approximation to the Zoeppritz equation can be written as the sum of 3 terms: where: or (using Shuey’s approximation):

9. A real data example (b) Picks Zoeppritz Amplitudes (a) Gas Sand (c) (a) Common offset stack over a gas sand, where (b) represents model and picks over trough, and (c) represents model and picks over peak.

10. Estimating A and B from Seismic Data Offset +A +B sin2q -B Time -A (a) Small part of common offset stack. (b) Peak/trough picks vs sin2q,where A=intercept, and B=gradient.

11. 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 Class 4: Very low impedance contrast

12. Rutherford/Williams Classification Class 4 The Rutherford and Williams classification scheme as modified by Ross and Kinman (1995) and Castagna (1997).

13. Range-limited Stacking Gathers AVO Processing Near Stack Far Stack Invert (Optional) Invert (Optional) The near and far stacks can be created either from angle or offset gathers, and can be optionally inverted.

14. 3D Channel Sand Example (a) Time slice showing amplitudes of near-trace stack for Alberta channel sand with known gas. (b) Time slice showing amplitudes of far-trace stack for Alberta channel sand.

15. Faroe Shetlands Basin Line 99/116 Below: 10–20 degree stack. Above: 0–10 degree stack.

16. Inversion and Elastic Impedance • Inversion can be done using a standard inversion algorithm, or using an elastic impedance model. • Using the Aki-Richards equation, Connolly(1998) proposed the Elastic Impedance (EI) concept to physically explain range-limited stacks, where: • Note that if =0o, EI reduces to Acoustic Impedance (AI), where:

17. Faroe Shetlands Basin Line 99/116 Below: 10–20 degree inversion to relative acoustic impedance (RAI). Above: 0–10 degree inversion to relative acoustic impedance (RAI).

18. Faroe Shetlands Basin Line 99/116 Below: Impedance vs Offset (IVO) amplitude stack, or difference between RAI stacks. Above: pseudo-gradient stack, or difference between near and far stacks.

19. Faroe Shetlands Basin Line 99/116 AVOC (AVO Classification) = IVO x Pseudo-gradient

20. Intercept/Gradient Analysis Gathers AVO Processing Intercept Gradient Crossplot The Intercept (A) and Gradient (B)approach is the most common AVO method. A and B can be combined in variousways and displayed, or cross-plotted and interpreted.

21. Approximate Aki-Richards • Assuming that VP/VS = 2 in the full Aki-Richards equation, it can be shown that: • Assuming that s= 1/3 in Shuey’s equation (which is identical to VP/VS = 2), it can be shown that:

22. 3D Channel Sand Example (b) Pseudo-Poisson’s Ratio over channel sand. (a) Time slice of amplitudes from stack of 3D channel sand.

23. Colony Sand Example - Gathers Here are the gathers around the zone of interest, with the correlated sonic log inserted.

24. Picked Events Here are thepicked horizons on the stack. Note that Horizon 2 is picked on the trough at the top of the gas sand.

25. Intercept and Gradient (a) (b) (a) Intercept (A) and (b) gradient(B) stacks

26. Pseudo-poisson and Rs stacks (a) (b) (a) Ds = (A + B)* 9/4 and (b) RS = 1/2 (A - B)

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

28. Seismic Display from Cross-plots (a) Before interpretation (b) After interpretation

29. Gulf of Mexico Example (a) Figure (a) shows a relative amplitude seismic line over a Gulf of Mexico gas sand bright spot, (b) shows a crossplot of the A and B attributes, and(c) shows the position on the line of the ellipses from(b), where gray=wet trend,yellow and blue=gas sand. (Chris Ross, Geophysics May/June 2000) (b) (c)

30. Model Cross-plotExample (b) Trace display of the models, with crossplot colors superimposed. In-situ case on left and gas case on right. (Chris Ross, Geophysics May/June 2000) (a) Simultaneous crossplot of two models, wet=green points, and gas= purple points. The gray ellipse is the wet trend and the yellow/blue the gas.

31. RP/RSExtraction and Inversion Gathers AVO Processing RP Estimate RS Estimate Invert to ZP Invert to ZS The Rp/Rsapproach is similar to A/B extraction. However, Rp and Rs have more a physical interpretation and can be inverted to P and S-impedance.

32. Extracting RP and RS • As we have seen, the intercept (A) gives us a good estimate of zero offset P-wave reflectivity, RP. • We also saw that, if VP/VS = 2, we could extract an estimate of zero offset S-wave reflectivity, RS, by subtracting B from A. • A more rigorous approach, utilizing the ARCO mudrock line, was given by Fatti et al (Geophysics, Sept. 1994), and is used here.

33. Rp Section Here is the extracted P-wave intercept section (A) from the Colony sand example.

34. RS Section Here is a display of the RS section. Notice that the picked horizons from the RP section are still present.

35. Inverting RP and RS • Once we have estimated both Rp and Rs, we can then proceed to invert both attributes. • Inverting Rp will give acoustic impedance ZP=rVP, and Inverting Rs will give S-wave impedance ZS = rVS. • The inverted sections can then be further combined or cross-plotted. • The next two slides show the inversion of the extracted Rp and Rs sections from the Colony sand.

36. P-wave Inversion Here is the final P-wave inversion result. The low impedance just below Horizon 2 represents the gas sand.

37. S-wave Inversion The S-wave inversion result is shown above. Notice that the gas sand below Horizon 2 is now associated with an increase in impedance.

38. LMR or KpMRAnalysis Gathers AVO Analysis RP Estimate RS Estimate Invert to ZP Invert to ZS Transform to ,,kP Cross-plot

39. Lambda-Mu-Rho and Kp-Mu-Rho • Goodway et al (SEG Expanded Abstracts, 1997) proposed extracting the Lamé parameters  and , and density , or Lambda-Mu-Rho. Recently, Hedlin (SEG expanded abstracts, 2000) and Hilterman (personal communication), have suggested extracting pore bulk modulus:

40. Lambda-Rho, Mu-Rho, and Kp-Rho • Goodway et al give the following physical interpretation of the lambda (l) and mu(m) attributes: The lterm, or incompressibility, is sensitive to pore fluid, whereas the m term, or rigidity, is sensitive to the rock matrix.KPis the Biot-Gassmann fluid term. • As we saw in the theory, it is impossible to de-couple the effects of density from Kp, l and m when extracting this information from seismic data. • It is therefore most beneficial to cross-plot lr vs mror Kp vs mrto minimize the effects of density. • The next three slides show a well log example from offshore eastern Canada.

41. S wave, P wave, Density and Porosity for Whiterose L-08 Cretaceous Shale and Sands Vp Den Vs Porosity Cretaceous Shale Gas sand 85m Oil sand 97m Wet sand 95m Limestone

42. Kp vs Mu Whiterose L-08 Cretaceous Courtesy, Ken Hedlin and Husky Oil

43. Lambda vs Mu - Whiterose L-08 Courtesy, Ken Hedlin and Husky Oil

44. Mu-Rho Result – Colony Sand Here is the Mu-Rho result for the Colony sand. Notice that the increase in the Mu-Rho value below Horizon 2 indicates that, as expected, Mu-Rho is responding to the matrix.

45. Lambda-Rho Result Here is the Lambda-Rho result. The drop in the value of Lambda-Rho below Horizon 2 is indicating that, as expected, Lambda-Rho is responding to the gas.

46. Cross-plotting mu-rho vs lambda-rho Here is the initial uninterpreted result of the cross-plot.

47. Colony Sand Example - Cross-plotting The interpreted cross-plot is on the left. Note that the two zones have been chosen to give separation along a vertical line, and that the low values of Lambda-rho represent the known gas sand. Choosing the position of the line could be facilitated by modeling with the well values. The position of the gas sand on the line is shown below:

48. Conclusions • This has been a overview of both basic AVO concepts and new trends in AVO analysis. • The advantage of AVO over post-stack methods is that two independent parameters can be estimated from the seismic data, although there is no consensus as to what these two parameters should be. • The most robust approach is to extract and interpret near and far trace stacks. • The most popular current approach is to extract and interpret the intercept and gradient. • More recent approaches involve Rp/Rs inversion and the LMR and KpMR approaches. • A future paper by my colleague Chris Ross will explore each method using a single model example.

49. Acknowledgements • I wish to thank Ken Hedlin and Husky Oil for permission to use the Whiterose well log example. • I also want to thank Chris Ross in our Houston office for permission to use his Gulf Coast and model examples. • Finally, I want to thank Anthony Fogg from our London office and TGS-Nopec for permission to use the West of Shetlands example.