1. Amplitude Variation with Offset
presented by
Roxy Frary

2. Theory
Just some background
…ok a lot of background

3. Snell’s Law

4. Reflection Coefficients

5. Zoeppritz Equations
(Aki & Richards, 1980)

6. (Much-needed) Simplifications
Aki & Richards, 1980
attempt to separate the density dependence, P-wave, and S-wave
…still complicated…

7. (Much-needed) Simplifications
Hilterman, 1983
Separates into “acoustic/fluid” and “shear” terms – by assuming constant density
…still complicated…

8. (Much-needed) Simplifications
Shuey, 1985
Each term describes a different angular range of the offset curve
Normal incidence reflection coefficient
Intermediate angles
Approaching the critical angle

9. Weighted Stacking (Geostack)
A (or R0) is the normal incidence, or “zero-offset” stack
B is the AVO “slope” or “gradient”
3rd term is the “far-offset” stack
Weighted Stacking (Geostack)
Smith and Gidlow, 1987
reducing the prestack information to AVO attribute traces
compute local incident angle at each time, then do a regression analysis

10. The “Most Simple” Simplification
Hilterman, 1989
At small angles, R0 dominates
Δσ dominates at larger angles
near-offset stack images the P-wave impedance contrasts
far-offset stack images Poisson’s ratio contrasts

11. Poisson’s Ratio
Koefoed, 1955

12. Incidence Angle
Koefoed, 1955
Shuey, 1985

13. VP Contrast
Koefoed, 1955
Shuey, 1985

14. Theoretical Conclusions from
Rule #1
Theoretical Conclusions from
Koefoed, 1955
modified by
Shuey, 1985
An increase (decrease) of Poisson’s ratio for the underlying medium produces an increase (decrease) in the reflection coefficient at larger angles of incidence

15. Theoretical Conclusions from
Rule #2
Theoretical Conclusions from
Koefoed, 1955
modified by
Shuey, 1985
When Poisson’s ratio of the media are equal, an increase (decrease) of Poisson’s ratio causes an increase (decrease) in reflection coefficient at larger angles of incidence

16. Theoretical Conclusions from
Rule #3
Theoretical Conclusions from
Koefoed, 1955
modified by
Shuey, 1985
Interchange of the media affects the shape of the curves only slightly – RPP simply changes sign when the elastic properties are interchanged – except at large angles

17. Industry Use: Gas Sands
Since 1982

18. Gas Sands
Ostrander, 1984
Hypothetical gas model

19. But how do we see this in seismic data?
Ostrander, 1984
Sacramento Valley
Sand reservoir at 1.75 s
Fault at SP 95
Reservoir limits SP

20. CDP Gathers Ostrander, 1984 offset increases to the left
A & B show an increase in amplitude with offset –
change in Poisson’s ratio –
gas-saturated sand
C shows a decrease in amplitude with offset –
uniform Poisson’s ratio –
no gas sand

21. Another Example Ostrander, 1984 Nevada Amplitude anomaly at 1.6 s
Decrease in amplitude with offset on gathers –
uniform Poisson’s ratio –
BASALT

22. But different Gas Sands have different signatures
Rutherford & Williams, 1989
Class 1: high impedance
gradient is usually greatest
Class 2: near-zero impedance contrast
seem to suddenly appear at larger offsets, when amplitudes rise above noise level
Class 3: low impedance
large reflectivities at all offsets

23. Class 1 Gas Sand Example Rutherford & Williams, 1989 Arkoma Basin
Pennsylvanian-aged Hartshorn sand
“dim out”
polarity change at mid-offset

24. not a classic “gas sand” anomaly – 2.1 s
Class 2 Gas Sand Example
Rutherford & Williams, 1989
Gulf of Mexico
Brazos area
mid-Miocene
not a classic “gas sand” anomaly – 2.1 s

25. Class 2 Gas Sand Example (Cont’d)
Rutherford & Williams, 1989
AVO effects are pronounced in mid- and far-offset synthetics
constant reflection angle display confirms synthetic data

26. most typical – large reflectivity at all offsets
Class 3 Gas Sand Example
Rutherford & Williams, 1989
Gulf of Mexico
High Island area
Pliocene
most typical – large reflectivity at all offsets

27. Low impedance as well, but reflectivity decreases with offset
Class 4 Gas Sand
Castagna & Swan, 1997
Low impedance as well, but reflectivity decreases with offset

28. Industry Use: Fluid Identification
Since 1997

29. plotting in the slope-intercept domain
Substituting and neglecting second-order perturbations yields
Fluid Line
Foster & Keys, 1999
plotting in the slope-intercept domain

30. Fluid Line (Cont’d) Foster & Keys, 1999
Reflections from wet sands/shales fall on the Fluid Line (little contrast in γ) – hydrocarbon-bearing sands do not
Abrupt decrease (increase) in γ causes the reflection to fall above (below) the Fluid Line – like the tops and bases of sands

31. Fluid Line and Gas Sands
Foster & Keys, 1999
Class 1: high-impedance – below Fluid Line, to the right of the slope axis
Class 2: negligible impedance contrast – intersection with slope axis
Class 3: low-impedance – negative intercept and slope
Class 4: even lower impedance – negative intercept, slope is zero or positive

32. Fluid Line, Gas Sands, and Rock Properties
Foster & Keys, 1999
Start with top of Class 3 gas sand at point 1
To get to point 2:
increase porosity
Alternatively, to get to point 3:
reduce porosity
Point 4:
replace gas with brine
To get to point 5:
reduce porosity of brine

33. Fluid Line, Gas Sands, and Rock Properties (Cont’d)
Foster, Keys & Lane, 1999
Point 1: at normal incidence, the reflection is negative, and becomes more negative with increasing offset
Point 2: reflection is more negative, but less variation with offset than Point 1
Point 3: small amplitude at normal incidence, but will be more negative with increasing offset (more than 1 or 2)
Point 4: small positive amplitude at normal incidence, and decreases with offset
Point 5: large positive amplitude, decreases with offset (more than 4)

34. Fluid Line, Gas Sands, and Rock Properties (Cont’d)
Foster, Keys & Lane, 2010
Increasing the shale content increases acoustic impedance by reducing porosity (solid brown line) – must also decrease γ because pure shale lies on the Fluid Line
Adding clay past the critical concentration reduces acoustic impedance (dashed brown line)

35. AVO for hydrocarbon detection
Foster, Keys & Lane, 2010

36. Evaluation of potential to differentiate hydrocarbons from water
Well 1: central structure
Well 2: west structure
Step 1 – forward model the expected AVO response for brine- and hydrocarbon-filled sands from well log information

37. Well information Well 1: a & b Well 2: c & d
a & c indicate the expected AVO for individual sand units
b & d are derived from synthetic gathers modeled from the well logs
We should expect a reflection from the top of a gas sand to peak at zero offset and become larger with increasing angle
Amplitudes should decrease downdip from a gas/water contact
Class 3 at the top of the reservoir section, Class 2 deeper as porosity decreases
Note change in amplitude convention

38. Seismic data 3D prestack time-migrated gathers
Blue points are background data, containing wet sands and shales – used to define the Fluid Line
Red points are the reservoir – predominantly Class 3 sand

39. Applying AVO scheme to stacked seismic data
dark-green over light-green: top and bottom of Class 3 sand
purple (Class 2) sands seen at depth
gas/water contact (AVO anomaly) terminates downdip

40. Check with structure in map view
anomaly extends to the eastern structure as well

41. AVO for lithology discrimination
Foster, Keys & Lane, 2010

42. Evaluation of potential to differentiate reservoir sands
Back to basics: thicker sands in a main channel feeding a turbidite fan, porosity decreases further from the sediment source
Class 2 sands (b) have lower porosity than Class 3 sands (a)

43. AVO extraction to map view
Well A found a commercial reservoir
Well B found poor porosity

44. More on Poisson’s Ratio
Fluids cannot support shear, so maximum value of σ is 0.5
Typical values:
0.05 for very hard rocks
0.45 for loose, unconsolidated sediments
Close to 0.0 for gas sands
At 0.33, S-wave velocity is half P-wave velocity
As gas saturation increases, Poisson’s ratio decreases
More on Poisson’s Ratio

45. More on A & B: plotting in the slope-intercept domain
The slope of the “background trend” depends only on the background γ
More on A & B: plotting in the slope-intercept domain
Castagna, Swan & Foster, 1998
A – normal incidence
B – AVO gradient/slope

46. More on A & B: plotting in the slope-intercept domain (Cont’d)
Shale/brine sand and shale/gas sand reflections
More on A & B: plotting in the slope-intercept domain (Cont’d)
Castagna, Swan & Foster, 1998
A – normal incidence
B – AVO gradient/slope

47. More on A & B: plotting in the slope-intercept domain (Cont’d)
Shale/brine sand and shale/gas sand reflections – laboratory measurements
More on A & B: plotting in the slope-intercept domain (Cont’d)
Castagna, Swan & Foster, 1998
A – normal incidence
B – AVO gradient/slope
Porosity differences account for variation
Background velocity is different for each sand, so they don’t all plot on same trend

48. More on A & B: plotting in the slope-intercept domain (Cont’d)
A & B become more negative by adding hydrocarbons (decreasing Poisson’s ratio)
More on A & B: plotting in the slope-intercept domain (Cont’d)
Castagna, Swan & Foster, 1998
A – normal incidence
B – AVO gradient/slope
Top of said layer plots below background trend
Bottom of said layer plots above the background trend

49. Can’t classify sands based on properties of the sand alone – the advent of Class 4
Castagna, Swan & Foster, 1998
Overlying unit is shale
Class 3
Overlying unit is tight (calcareous)
Class 4
Key difference: Vs contrast

50. Case History Gulf of Mexico Bright Spot
Nsoga Mahob, Castagna & Young, 1999

51. Amplitude Anomaly

52. AVO Inversion – Brine Model
max changes:
used near-offset inverted P-wave velocity curve
VP – 1000 ft/s
VS – 3000 ft/s
S-wave and Poisson’s ratio curves related
layer thickness – 100 ft
density – 1.0 g/cm3

53. AVO Inversion – Brine Model
not really all that close…

54. AVO Inversion – Gas Model
max changes:
used near-offset inverted P-wave velocity curve
VP – 1000 ft/s
VS – 3000 ft/s
constant Poisson’s ratio of 0.1 in pay zone
layer thickness – 100 ft
density – 1.0 g/cm3

55. AVO Inversion – Gas Model
decently close!
gas model, with appropriate mechanical properties, converges to the real seismic data

56. Some Issues Thin-bed tuning Attenuation NMO errors
Can cause amplitude to increase/decrease with offset depending on time-thickness and frequency
Attenuation
Signal/noise decrease with offset
NMO errors
Conventional velocity analysis is not “perfect” enough
Ambiguity between stacking velocity and reflectivity
Can be corrected with full waveform inversion

57. Key Takeaway Conclusions
Important AVO simplification:
The Rules:
An increase (decrease) of Poisson’s ratio for the underlying medium produces an increase (decrease) in the reflection coefficient at larger angles of incidence
When Poisson’s ratio of the media are equal, an increase (decrease) of Poisson’s ratio causes an increase (decrease) in reflection coefficient at larger angles of incidence
Interchange of the media affects the shape of the curves only slightly – RPP simply changes sign when the elastic properties are interchanged – except at large angles
Gas Sand Classification:
Class 1 – high impedance contrast, high gradient, polarity change, low porosity
Class 2 – near-zero impedance contrast, seem to suddenly appear at larger offsets
Class 3 – low impedance contrast, high reflectivity at all offsets
Class 4 – low impedance contrast, reflectivity decreases with offset, high porosity
Lithology and fluid identification

58. Key Takeaway Conclusions

59. References Aki & Richards, 1980 Hilterman, 1983 Shuey, 1985
Smith and Gidlow, 1987
Hilterman, 1989
Koefoed, 1955
Ostrander, 1984
Rutherford & Williams, 1989
Castagna & Swan, 1997
Foster & Keys, 1999
Foster, Keys & Lane, 2010
Castagna, Swan & Foster, 1998
Nsoga Mahob, Castagna & Young, 1999
Fatti, Smith, Vail, Strauss & Levitt, 1994