1. Upscaling Petrophysical Properties to the Seismic Scale
Greg A. Partyka, Jack B. Thomas, and Kevin P. Turco, bp
Dan J. Hartmann, DJH Energy Consulting

2. Seismic Reservoir Imaging
8hz Spectral Amplitude Map
WELL #1
Zone 1
1 mile

3. Seismic Reservoir Imaging
Stratigraphy ?
SEISMIC
Petrophysics
Structure
Sensitivity Issues:
Do acoustic properties respond to variability in petrophysical properties?
Scale Issues:
How much seismic resolution is required?

4. Uncertainty and Errors
are embedded at all measurement scales.
Measurement Scale
Uncertainty/Error Examples
microns-to-centimetres
sampling bias; damaged plugs
CORE SCALE
centimetres-to-metres
washouts; tool problems
WELL-LOG SCALE
SEISMIC SCALE
metres-to-decimetres
acquisition & processing artifacts

5. Upscaling
Three Steps:
Scoping at the well-log scale.
Determining upscaling sensitivity.
Predicting petrophysical properties from seismic impedance.

6. Scoping at the Well-Log Scale
Cross-plot well-log-scale acoustic properties versus petrophysical properties.
Are acoustic measurements sensitive
to petrophysical properties
at the well-log scale?
Hope for seismic detection/resolution
Game Continues to Next Step
Game Over
Seismic will provide little value NO
YES

7. Seismic Reservoir Imaging
8hz Spectral Amplitude Map
WELL #1
Zone 1
1 mile

8. Scoping at the Well-Log Scale
Vp=7445 ft/s
Vs=3115 ft/s
Den=2.23 gm/cc
Vp=6755 ft/s
Vs=3485 ft/s
Den=2.17 gm/cc
Vp=7945 ft/s
Vs=3260 ft/s
Den=2.26 gm/cc
overlying shale
underlying shale
reservoir
Zone 1
Backus Averaged
Acoustic Properties

9. Scoping at the Well-Log Scale
Zone 1 Thickness = 57 feet
Backus Filter = None
Effective Porosity
Acoustic Impedance
Water Saturation

10. Upscaling
Three Steps:
Scoping at the well-log scale.
Determining upscaling sensitivity.
Predicting petrophysical properties from seismic impedance.

11. Upscaling Sensitivity
THICKNESS
FLOW-UNIT
STACKING
RESOLUTION
VELOCITY
BANDWIDTH

12. Upscaling Sensitivity Analysis
As we scale-up the acoustic data (e.g. bandlimit or decrease thickness):
acoustic resolution of petrophysical properties degrades.

13. Zone 1 Thickness = 057 ft Backus Filter = None Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
Here, we have the same well-log scale, reservoir zone, cross-plot you saw previously, with acoustic impedance increasing along the vertical, and porosity increasing along the horizontal.
If you had an acoustic impedance map for this reservoir interval, and wanted to create a porosity map. It would be tempting to use this well-log-scale cross-plot to do the job. Doing that however, would ignore the upscaling/tuning issues that must be addressed.
Let’s see what happens as we progressively hi-cut filter the acoustic properties from 100hz down to 10hz (keeping thickness constant at 50ft).

14. Zone 1 Thickness = 050 ft Backus Filter = 100 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
100hz

15. Zone 1 Thickness = 050 ft Backus Filter = 090 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
90hz

16. Zone 1 Thickness = 050 ft Backus Filter = 080 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
80hz

17. Zone 1 Thickness = 050 ft Backus Filter = 070 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
70hz

18. Zone 1 Thickness = 050 ft Backus Filter = 060 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
60hz

19. Zone 1 Thickness = 050 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
50hz

20. Zone 1 Thickness = 050 ft Backus Filter = 040 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
40hz

21. Zone 1 Thickness = 050 ft Backus Filter = 030 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
30hz

22. Zone 1 Thickness = 050 ft Backus Filter = 020 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
20hz

23. Zone 1 Thickness = 050 ft Backus Filter = 010 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
10hz
The the resolving ability of Acoustic Impedance with respect to porosity, progressively decreases.
We can create similar behaviour by keeping the hi-cut filter constant at 50hz, and progressively change the thickness from 10 to 100ft.

24. Zone 1 Thickness = 010 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
10 ft

25. Zone 1 Thickness = 020 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
20 ft

26. Zone 1 Thickness = 030 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
30 ft

27. Zone 1 Thickness = 040 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
40 ft

28. Zone 1 Thickness = 050 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
50 ft

29. Zone 1 Thickness = 060 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
60 ft

30. Zone 1 Thickness = 070 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
70 ft

31. Zone 1 Thickness = 080 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
80 ft

32. Zone 1 Thickness = 090 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
90 ft

33. Zone 1 Thickness = 100 ft Backus Filter = 050 Hz Acoustic Impedance
Effective Porosity
Acoustic Impedance
Water Saturation
0.0
0.1
0.2
0.3
0.4
24,000
23,000
22,000
21,000
20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
1.00
0.83
0.67
0.50
0.33
0.17
0.00 20 40 60 80
100
Gross Reservoir Thickness (ft)
Backus Filter (Hz)
100 ft
In effect this is the seismic-petrophysics equivalent of a seismic upsum filter analysis....except for one big difference:
The conventional upsum filter analysis indicates resolution with respect to wavelength.
This analysis on the other hand indicates resolution with respect to petrophysical properties.

34. Scoping at the well-log scale. Determining upscaling sensitivity.
Three Steps:
Scoping at the well-log scale.
Determining upscaling sensitivity.
Predicting petrophysical properties from seismic impedance. x y
depth
SEISMIC
IMPEDANCE
PETROPHYSICAL
PROPERTY
RESERVOIR
ASSESSMENT

35. To Predict Petrophysical Properties from Seismic
Requires:
seismic wavelet,
seismic-derived impedance,
upscaling sensitivity relationships, and
gross thickness.

36. Thickness Estimation
Spectral Decomposition
to compute a Tuning Cube for the zone-of-interest.
Thickness Modeling
to derive amplitude vs thickness vs frequency relationships.
Thickness Calibration
to determine gross reservoir thickness.

37. Spectral Decompositionx y z
freq
Interpret
3-D Seismic Volume
Subset
Compute
Animate
Interpreted
Zone-of-Interest
Subvolume
Tuning Cube
(cross-section view)
Frequency Slices
through Tuning Cube
(plan view)

38. Zone 1 08hz spectral amplitude
Well # 1
1 mile
Here is the result of that approach for our reservoir...going from 8 to 20 hz.

39. Zone 1 10hz spectral amplitude
Well # 1
1 mile
10 hz

40. Zone 1 12hz spectral amplitude
Well # 1
1 mile
12 hz

41. Zone 1 14hz spectral amplitude
Well # 1
1 mile
14 hz

42. Zone 1 16hz spectral amplitude
Well # 1
1 mile
16 hz

43. Zone 1 18hz spectral amplitude
Well # 1
1 mile
18 hz

44. Zone 1 20hz spectral amplitude
Well # 1
1 mile
20 hz

45. Thickness Estimation
Spectral Decomposition
to compute a Tuning Cube for the zone-of-interest.
Thickness Modeling
to derive amplitude vs thickness vs frequency relationships.
Thickness Calibration
to determine gross reservoir thickness.

46. Well-Log Interpretation
Thickness Modeling
Gross Pay Thickness (ft) 40 20 80 60
100
Frequency (hz) 10 30 50 70
amplitude 1
Spectral Signatures
Well-Log Interpretation
(Zone 1)
shale
Seismic Modeling
Two-Way Traveltime (ms)
200
150 -1
depth (feet)
sand
oil
Temporal Wedge Model
6hz
8hz

47. Thickness Estimation
Spectral Decomposition
to compute a Tuning Cube for the zone-of-interest.
Thickness Modeling
to derive amplitude vs thickness vs frequency relationships.
Thickness Calibration
to determine gross reservoir thickness.

48. Thickness Calibration
6hz amplitude
8hz amplitude
Amplitude
08hz Spectral Amplitude
Zone 1
Gross Reservoir Thickness from 6hz and 8hz energy
WELL #1
06hz Spectral Amplitude
Modeled Spectral Signatures vs Thickness
Frequency (hz)
0.008
0.007
0.006
0.005
0.004
0.003
100 50 1
1 mile 40 20 10 30 60 70 80 90
Gross Reservoir Thickness (ft)
6hz
8hz

49. To Predict Petrophysical Properties from Seismic
Requires:
seismic wavelet,
seismic-derived impedance,
upscaling sensitivity relationships, and
gross thickness.

50. Upscaling Cross-Plots
Gross Thickness
Well #1
100 50
Thickness (ft)
Zone 1
Petrophysical
Property at
the Seismic Scale
For Example:
If: frequencyupper = 50 hz Then: effective porosity = 0.2
thickness = 80 ft
impedance = 15,000
Impedance
1 mile
Note: Scale-induced uncertainty manifests itself along the axis that represents the smallest scale of measurement.
Upscaling Cross-Plots
Zone 1 Thickness = 40 ft;
Backus Filter = 50 Hz
Effective Porosity
Acoustic Impedance
Zone 1 Thickness = 80 ft;
If you know the hi-cut frequency, you can look up the impedance and gross thickness for any x,y location on the reservoir map, then use that information to look up the petrophysical property value from the appropriate-scale cross-plot.
For example, if the hi-cut is 50hz, the combination of an 80ft thickness and AI=15,000, and the appropriate scale crossplot gives a porosity estimate of .2

51. Summary
By example we have shown that with proper upscaling, it is possible to merge:
seismic data,
well-log data,
petrophysical data, and
geologic data,
into a better calibrated model.

52. Summary
This interdisciplinary approach can be adjusted for specific fields by calibrating the flow-units.
Uncertainty and errors are embedded at all measurement scales.
Quality of upscaling is dependent on the degree to which petrophysical cross-plots are representative of reservoir flow-units.