Applications of Geophysical Inversion and Imaging Part 3 – Shear Wave Analysis

1. Applications ofGeophysical Inversion and ImagingPart 3 – Shear Wave Analysis

2. Introduction • In the section on rock physics we discussed fluid effects on P-wave velocity, S-wave velocity and density. • We then looked at post-stack inversion applied to P-wave data. • In this section, we will look at various options for acquiring, analyzing, and inverting S-wave data. • We will start by analyzing the models that were created in the first section. • We will then look at the analysis of full S-wave data. • Finally, we will discuss converted wave, or PS, data.

3. P- and S-waves (a) P-wave motion (b) S-wave motion Here is a two-dimensional cross-section of P and S-wave motion. The direction of particle motion for a P-wave is in the same direction as its wave movement. The direction of particle motion for the S-wave is at right angles to the direction of its wave movement.

4. P- and S-wave recording (a) (b) (c) The above diagram shows a 3D schematic diagram of (a) P-waves, (b) SH, or horizontal shear-waves, and (c) SV, or vertical shear-waves. Note that the SV wave direction is in the plane of the motion, whereas the SH is out of the plane of motion. (Ensley, 1984)

5. P and S-wave modeling (b) Gas model (a) Wet model Let us return to the two models considered in the rock physics section and look at the P and S-wave synthetic responses. Model A consists of a wet sand, and Model B consists of a gas-saturated sand. Let us next look at the formulae for computing P and S reflection coefficients.

6. P and S reflection coefficients The formula for P-wave reflectivity can be written: This formula can also be applied to the shear wave reflectivity: These equations can also be expanded to give:

7. Model Values To compute the P and S responses from Models A and B, we will use the following values, where the wet and gas cases were computed using the Biot-Gassmann equations: Wet: VPwet= 2500 m/s, VSwet= 1250 m/s,wet = 2.11 g/cc, swet = 0.33,VPwet/VSwet = 2.0 Gas: VP_gas= 2000 m/s, VS_gas= 1305 m/s,gas = 1.95 g/cc,sgas = 0.13, VPgas/VSgas = 1.53 Shale: VPshale= 2250 m/s, VSshale= 1125 m/s,shale = 2.0 g/cc,sshale = 0.33, VPshale/VSshale = 2.0

8. P-wave wet calculations Notice that the P-wave wet calculations show a positive reflector at the top of the sand and, by symmetry, a negative reflector at the base.

9. S-wave wet calculations The S-wave wet calculations also show a positive reflector at the top of the sand and a negative reflector at the base. The values are the same as for the P-wave case since Vp/Vs = 2 in both layers.

10. P-wave gas calculations Notice that the P-wave gas calculations show a negative reflector at the top of the sand and, by symmetry, a positive reflector at the base. This is due to the effect of gas on P-wave velocity.

11. S-wave gas calculations However, the S-wave wet calculations still show a positive reflector at the top of the sand and a negative reflector at the base. The values are different that the P-wave case since Vp/Vs ≠ 2 in both layers.

12. Wet sand synthetics 50 ms (a) P-wave log, density and synthetic from model A 100 ms (b) S-wave log, density and synthetic from model A. Here are the wet sand synthetics, using a 25 Hz Ricker wavelet. Note that the polarity is the same but that the time scales are different.

13. Gas sand synthetics 50 ms (a) P-wave log, density and synthetic from model B 100 ms (b) S-wave log, density and synthetic from model B Here are the gas sand synthetics, using a 25 Hz Ricker wavelet. Note the polarity change and the different time scales.

14. P and SH-waves – Gas Sand (a) (b) The above diagram shows recorded and processed seismic sections of (a) P, or compressional, waves, and (b) SH, or horizontal shear-waves, over the Myrnham gas field in Alberta. The P-waves respond to the gas sand whereas the S-waves do not, allowing us to predict the presence of the gas. The arrows indicate the same events and the ellipses outline the anomaly. (Ensley, 1984)

15. P and SH-waves – Coal (a) (b) The above diagram shows recorded and processed seismic sections of (a) P, or compressional, waves, and (b) SH, or horizontal shear-waves, over a false ”bright spot” due to a coal near the gas field in the previous slide. Note that the P-waves and the S-waves both respond to the coal, allowing us to predict that the “bright-spot” is not due to the presence of gas. (Ensley, 1984)

16. Converted S-waves • The previous example used full S-wave recording, in which S-waves were generated at the surface of the earth using an S-wave vibrator, and the reflections were recorded using multi-component geophones. • However, there is a simpler, and cheaper, way to record S-wave information, as shown in the next slide. • If we use a P-wave source, and record the data at different offsets using multi-component geophones, we can record converted S-waves, and reflected P-waves which contain some influence from the S-waves.

17. Mode Conversion 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 Consider the interface between two geologic horizons of differing P and S-wave velocity and density and an incident P-wave at angle qi. This will produce both P and S reflected and transmitted waves, as shown above. These are SV waves in the in-line direction.

18. Utilizing mode conversion • But how do we utilize mode conversion? • There are actually two ways: • Record the converted S-waves using multi-component receivers (in the X and Z direction). • Interpret the amplitudes of the P-waves as a function of offset, or angle, which contain implied information about the S-waves. This is called the AVO (Amplitude versus Offset) method, and will be discussed in subsequent parts of this course. • When we record the converted waves, we need to be very careful in their processing and interpretation, as will be shown next. • In the AVO method, we can make use of the Zoeppritz equations, to extract pseudo S-wave information from P-wave reflections at different offsets.

19. Amplitudes versus traveltimes • We have just seen how the amplitudes of S-waves versus P-waves can be used to identity gas sands. • We can also use recorded traveltimes of PP and PS waves to interpret gas sands. • The traveltime equations are as follows:

20. Sand Isochrons Assuming a gas sand with a thickness of 20 m, and using the velocities given for the sand, the isochrons are as follows: DtPPgas= 0.020 s = 20 ms DtSSgas= 0.031 s = 31 ms DtPSgas= 0.025 s = 25 ms DtPPwet= 0.016 = 16 ms DtSSwet= 0.032 = 32 ms DtPSwet= 0.024 s = 24 ms

21. Finding the VP/VS ratio • From our earlier discussion of P and S-waves, we know to expect that the VP/VS ratio should go down when we encounter a gas sand, since VPgoes down but VS goes up slightly. • To extract information about the VP/VS ratio using the seismic time picks, we can use the isochron values computed on the previous table and the formula: VP/VS = 2(DtPS/DtPP) – 1, where DtPSis the PS isochron and DtPP is the PP isochron.

22. Exercise 3-1 - VP/VS ratio Using the isochron values given, and the formula on the previous slide, compute the VP/VS ratio for the gas and wet sand example.

23. Converted wave analysis • Before looking at a converted wave interpretation, we will discuss the steps involved in converted wave analysis, using a dataset from Alberta. • The most difficult part of converted wave interpretation is in interpreting events on the PP and PS sections that come from the same geological horizon but have different arrival times and amplitudes. • As we will see, there are two ways to correct for these problems: • (1) Use the well log velocities and perform modeling at the wells. • (2) Use seismic pick analysis.

24. Initial multi-component display (a) (b) Let us consider the data shown above, where (a) shows PP data and (b) shows PS data. Although this data is over the same part of the subsurface, it is hard to correlate between the two sections due to time and amplitude differences.

25. Vp/Vs =2 (a) (b) This slide again shows (a) PP data and (b) PS data. However, now the PS data has been converted to PP time assuming that the Vp/Vs ratio is equal to two. The fit is better, but still not very good.

26. P wave log correlation We have now correlated the P-wave log at the log intersection on the PP data. Notice the good tie on the right, where the blue trace is the synthetic, and the red trace is the seismic trace.

27. PS log correlation We have now correlated the P and S-wave logs at the log intersection on the PS data. Again, notice the good tie on the right, where the blue trace is the synthetic, and the red trace is the seismic trace.

28. PP and PS extracted wavelets The wavelets on the previous synthetics were extracted from the seismic data and are shown on the left, where (a) shows the wavelet extracted from the PP section, (b) shows the amplitude spectrum of the PP wavelet, (c) shows the wavelet extracted from the PS section, and (d) shows the amplitude spectrum of the PS wavelet. Notice the difference in frequency content. (a) (b) (c) (d)

29. Synthetic to seismic correlation PS-wave offset synthetic PP-wave offset synthetic The display above shows the offset synthetics computed from the well logs and using the wavelets shown in the previous slide. We will be discussing offset synthetics in the next section, but for now simply notice that the PS-wave synthetic has zero amplitude at zero offset.

30. Seismic tie using Vp/Vs = 2.0 (a) (b) This slide again shows (a) PP data and (b) PS data, converted to PP time assuming that the Vp/Vs ratio is equal to 2. We have spliced in the synthetics using the correct velocities. Notice the misfit.

31. P - PS seismic and synthetic ties (a) (b) This slide again shows (a) PP data and (b) PS data. However, now the PS data has been converted to PP time using the Vp/Vs ratio from the logs. The fit is very good at the wells but the sections don’t match laterally.

32. PP and PS horizon picks (a) (b) This slide shows a more extensive section of the (a) PP data and (b) PS data. To correct for laterally varying velocities, we have picked the major events on both sections, using the picks from the logs.

33. Horizon matching (a) (b) This slide again shows the (a) PP data and (b) PS data. Now, the horizons have been matched by computing a laterally varying Vp/Vs ratio.

34. Vp/Vs ratio from horizon match This slide shows the laterally varying Vp/Vs ratio that was computed using the horizon picks in the previous slide.

35. VP/VS Ratio maps By applying this technique to all of the lines in the 3D volume, a map of VP/VS ratios can be computed. The maps above show the change in VP/VS ratio between different pairs of events shown in the previous slides.

36. Blackfoot case study • Let us now see how the previous analysis can be applied in a field example. • For our case study, we will go back to the Blackfoot example considered in the last part of the course. • Recall that this case study involved the delineation of a Lower Cretaceous channel sand system. • We will start by re-displaying several of the slides from the previous section, including the PP section. • We will then look at the PS converted wave data to see what can be added to the interpretation.

37. Blackfoot case study The schematic stratigraphy of the Blackfoot area, showing three different incised valleys. The relative age is also indicated, where 30 is oldest and 40 is youngest. (Dufour et al.)

38. Blackfoot case study A map showing seismic cross-line 95, and two east-west cross-sections. The wells are also indicated.

39. Blackfoot case study Seismic cross-line 95 from the PP data, showing a clear indication of the three valleys. (Dufour et al.)

40. Blackfoot case study Seismic cross-line 95 from the PS data. Note that resolution is not as good as the PP data and shows only a single valley. (Dufour et al.)

41. Blackfoot case study A comparison of the (a) PP data, and (b) PS data from line 95. The lack of resolution in the PS data is now clear. (Dufour et al.) (a) (b)

42. Blackfoot case study Extracted amplitude slices from the (a) PP data, extracted from the upper valley (40), and (b) PS data, extracted from the Glauconitic channel. The white outlines shown the outline of the valley and the anomalous amplitudes are defined by the red outlines. (Dufour et al.) (a) (b)

43. Blackfoot case study • In this case study, seismic amplitude inversion was not performed on the PS data. • Instead, the authors extracted information about the VP/VS ratio using the seismic time picks, which can be thought of as a type of inversion. The formula used was (see exercise 3-2): VP/VS = 2(DtPS/DtPP) – 1, where DtPSis the PS isochron and DtPP is the PP isochron. • From our earlier discussion of P and S-waves, we know to expect that the VP/VS ratio should go down when we encounter a gas sand, since VP goes down but VS goes up slightly.

44. Blackfoot case study Computed VP/VS ratio slices the (a) Mannville-Wabamun interval, and (b) top of Glauconitic-incised valley-Wabamun interval. The white outlines shown the outline of the valley. Notice the good match of the anomalously low VP/VS ratios to the productive wells. (Dufour et al.) (a) (b)

45. Conclusions • In this section, we have discussed the use of recorded shear wave sections for the computation of reservoir parameter change. • Our first example showed how we could differentiate a gas sand “bright-spot” from a coal “bright-spot” using SH wave generation and multi-component recording. • We then discussed the use of converted wave data, where the PS conversion (which is an SV wave) is recorded using multi-component geophones. • We showed how to integrate the PP and PS recorded section to produce a Vp/Vs estimate and then showed a case study in which this technique was used to explore for channel sands.

46. Exercise 3-1 - Answers Using the isochron values and formula given earlier, we get: (VP/VS)gas = 2(DtPSgas/DtPPgas) – 1 = 1.53 (VP/VS)wet = 2(DtPSwet/DtPPwet) – 1 = 2.0