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Amplitude Variation with Offset

Amplitude Variation with Offset. p resented by Roxy Frary. Theory. Just some background …ok a lot of background. Snell’s Law. Reflection Coefficients. Zoeppritz Equations. (Aki & Richards, 1980). (Much-needed) Simplifications. Aki & Richards, 1980

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Amplitude Variation with Offset

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  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 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 • near-offset stack images the P-wave impedance contrasts • far-offset stack images Poisson’s ratio contrasts Hilterman, 1989 At small angles, R0 dominates Δσ dominates at larger angles

  11. Poisson’s Ratio Koefoed, 1955

  12. Incidence Angle Koefoed, 1955 Shuey, 1985

  13. VP Contrast Koefoed, 1955 Shuey, 1985

  14. 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. 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. Rule #3 Theoretical Conclusions from Koefoed, 1955 modified by Shuey, 1985 Interchange of the media affects the shape of the curves only slightly – RPPsimply 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 75-135

  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. Class 2 Gas SandExample 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. Class 3 Gas Sand Example Rutherford & Williams, 1989 Gulf of Mexico High Island area Pliocene most typical – large reflectivity at all offsets

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

  28. Industry Use:Fluid Identification Since 1997

  29. Fluid Line • Substituting and neglecting second-order perturbations yields 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

  45. More on A & B: plotting in the slope-intercept domain • The slope of the “background trend” depends only on the background γ 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 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 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) 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 NsogaMahob, Castagna& Young, 1999

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