advertisement

Amplitude Variation with Offset presented by Roxy Frary Theory Just some background …ok a lot of background Snell’s Law sin(Q1 ) sin(Q2 ) sin(F1 ) sin(F 2 ) = = = VP1 VP 2 VS1 VS 2 Reflection Coefficients r2VP 2 - r1VP1 RC = r2VP 2 + r1VP1 I P 2 - I P1 = I P 2 + I P1 DI P = 2I PA Zoeppritz Equations (Aki & Richards, 1980) R(q ) = f (r1, r2,VP1,VP2,VS1,VS2,q ) (Much-needed) Simplifications Aki & Richards, 1980 1 1 DVP 2 2 æ Dr ö 2 2 DVS RPP (Qa ) » (1- 4 p VSa ) ç ÷ + - 4 p VSa 2 2 VSa è ra ø 2 cos (Q a ) VPa attempt to separate the density dependence, Pwave, and S-wave …still complicated… 2 æ sinQ1 ö VP 2 cosQ1 - VP1 cosQ2 2 2 RPP (Q1 ) » + 2ç (V V S1 S2 ) ÷ VP2 cosQ1 + VP1 cosQ2 è VP1 ø (Much-needed) Simplifications Hilterman, 1983 Separates into “acoustic/fluid” and “shear” terms – by assuming constant density …still complicated… é Ds ù 2 1 DVP 2 2 RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan q sin q1 ) 1 1 2ú (1- s a ) û 2 VP ë (Much-needed) 1- 2s Simplifications A0 = B0 - 2(1+ B0 ) DVP B0 = DVP VPa 1- s VPa + Dr Shuey, 1985 ra Normal incidence reflection coefficient Intermediate angles Approaching the critical angle Each term describes a different angular range of the offset curve RPP (q1 ) » A + Bsin2 q1 + Csin 2 q1 tan2 q1 • A (or R0) is the normal incidence, or “zerooffset” stack Weighted Stacking (Geostack) Smith and Gidlow, 1987 reducing the prestack • B is the AVO “slope” or “gradient” information to AVO attribute traces compute local incident angle at each time, then do • 3rd term is the “faroffset” stack a regression analysis RPP (q1 ) » A + Bsin2 q1 + Csin 2 q1 tan2 q1 é Ds ù 2 1 DVP RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan 2 q1 - sin 2 q1 ) 1 2ú (1- s a ) û 2 VP ë RPP (q1 ) » R0 cos q1 + 2.25Ds sin q1 2 2 • near-offset stack images the P-wave impedance contrasts • far-offset stack images Poisson’s ratio contrasts The “Most Simple” Simplification Hilterman, 1989 At small angles, R0 dominates Δσ dominates at larger angles Poisson’s Ratio Koefoed, 1955 ( ) ( ) VP s= 2 VS é VP 2ê V S ë -2 2 ù -1ú û Incidence Angle Koefoed, 1955 Shuey, 1985 é Ds ù 2 1 DVP RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan 2 q1 - sin 2 q1 ) 1 2ú (1- s a ) û 2 VP ë VP Contrast Koefoed, 1955 Shuey, 1985 é Ds ù 2 1 DVP RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan 2 q1 - sin 2 q1 ) 1 2ú (1- s a ) û 2 VP ë é Ds ù 2 1 DVP RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan 2 q1 - sin 2 q1 ) 1 2ú (1- s a ) û 2 VP ë 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 é Ds ù 2 1 DVP RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan 2 q1 - sin 2 q1 ) 1 2ú (1- s a ) û 2 VP ë Rule #2 Theoretical Conclusions from 1- 2s A0 = B0 - 2(1+ B0 ) 1- s 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 é Ds ù 2 1 DVP RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan 2 q1 - sin 2 q1 ) 1 2ú (1- s a ) û 2 VP ë 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 Industry Use: Gas Sands Since 1982 Gas Sands • Ostrander, 1984 • Hypothetical gas model 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 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 Another Example Ostrander, 1984 Nevada Amplitude anomaly at 1.6 s Decrease in amplitude with offset on gathers – uniform Poisson’s ratio – BASALT But different Gas Sands have different signatures Rutherford & Williams, 1989 • Class 1: high impedance o gradient is usually greatest • Class 2: near-zero impedance contrast o seem to suddenly appear at larger offsets, when amplitudes rise above noise level • Class 3: low impedance o large reflectivities at all offsets Class 1 Gas Sand Example Rutherford & Williams, 1989 Arkoma Basin Pennsylvanian-aged Hartshorn sand “dim out” polarity change at midoffset Class 2 Gas Sand Example Rutherford & Williams, 1989 Gulf of Mexico Brazos area mid-Miocene not a classic “gas sand” anomaly – 2.1 s Class 2 Gas Sand Example (Cont’d) Rutherford & Williams, 1989 AVO effects are pronounced in mid- and faroffset synthetics constant reflection angle display confirms synthetic data Class 3 Gas Sand Example Rutherford & Williams, 1989 Gulf of Mexico High Island area Pliocene most typical – large reflectivity at all offsets Class 4 Gas Sand Castagna & Swan, 1997 Low impedance as well, but reflectivity decreases with offset Industry Use: Fluid Identification Since 1997 • Substituting and neglecting secondorder perturbations yields B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A VS g = V P Fluid Line Foster & Keys, 1999 plotting in the slopeintercept domain R(q ) » A + Bsin2 q +... DVPa Dra A= + 2VPa 2 ra DVPa VSa2 é Dra DVSa ù B= -4 2 ê + ú 2VPa VPa ë 2 ra VSa û Fluid Line (Cont’d) Foster & Keys, 1999 R(q ) » A + Bsin2 q +... B = (1- 8g 2 )A - 4gDg • 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 B = (1- 8g 2 )A g = VS V P B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P 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 Fluid Line, Gas Sands, and Rock Properties B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P • Foster & Keys, 1999 Start with top of Class 3 gas sand at point 1 • To get to point 2: • • Alternatively, to get to point 3: • • reduce porosity Point 4: • • increase porosity replace gas with brine To get to point 5: • reduce porosity of brine 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) B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P 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) B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P AVO for hydrocarbon detection Foster, Keys & Lane, 2010 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 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 Note change in amplitude convention • Class 3 at the top of the reservoir section, Class 2 deeper as porosity decreases 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 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 Check with structure in map view anomaly extends to the eastern structure as well AVO for lithology discrimination Foster, Keys & Lane, 2010 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) AVO extraction to map view Well A found a commercial reservoir Well B found poor porosity • Fluids cannot support shear, so maximum value of σ is 0.5 • Typical values: o 0.05 for very hard rocks o 0.45 for loose, unconsolidated sediments o 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 ( ) ( ) VP s= 2 VS é VP 2ê V S ë -2 2 ù -1ú û • The slope of the “background trend” depends only on the background γ B = (1- 8g 2 )A More on A & B: plotting in the slope-intercept domain Castagna, Swan & Foster, 1998 R(q ) » A + Bsin2 q +... DVPa Dra A= + 2VPa 2 ra DVPa VSa2 é Dra DVSa ù B= -4 2 ê + ú 2VPa VPa ë 2 ra VSa û A – normal incidence B – AVO gradient/slope B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P • Shale/brine sand and shale/gas sand reflections More on A & B: plotting in the slope-intercept domain (Cont’d) Castagna, Swan & Foster, 1998 R(q ) » A + Bsin2 q +... DVPa Dra A= + 2VPa 2 ra DVPa VSa2 é Dra DVSa ù B= -4 2 ê + ú 2VPa VPa ë 2 ra VSa û A – normal incidence B – AVO gradient/slope B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P • 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 R(q ) » A + Bsin2 q +... A – normal incidence B – AVO gradient/slope B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P Porosity differences account for variation Background velocity is different for each sand, so they don’t all plot on same trend • 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 B = (1- 8g 2 )A - 4gDg B = (1- 8g 2 )A g = VS V P Top of said layer plots below background trend Bottom of said layer plots above the background trend 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 Case History Gulf of Mexico Bright Spot Nsoga Mahob, Castagna & Young, 1999 Amplitude Anomaly AVO Inversion – Brine Model max changes: VP – 1000 ft/s VS – 3000 ft/s layer thickness – 100 ft density – 1.0 g/cm3 used near-offset inverted P-wave velocity curve S-wave and Poisson’s ratio curves related AVO Inversion – Brine Model not really all that close… AVO Inversion – Gas Model max changes: VP – 1000 ft/s VS – 3000 ft/s layer thickness – 100 ft density – 1.0 g/cm3 used near-offset inverted P-wave velocity curve constant Poisson’s ratio of 0.1 in pay zone AVO Inversion – Gas Model decently close! gas model, with appropriate mechanical properties, converges to the real seismic data Some Issues • Thin-bed tuning o Can cause amplitude to increase/decrease with offset depending on time-thickness and frequency • Attenuation o Signal/noise decrease with offset • NMO errors o Conventional velocity analysis is not “perfect” enough o Ambiguity between stacking velocity and reflectivity o Can be corrected with full waveform inversion Key Takeaway Conclusions • Important AVO simplification: • The Rules: é Ds ù 2 1 DVP 2 2 RPP (q1 ) » R0 + ê A0 R0 + sin q + (tan q sin q1 ) 1 1 2ú (1- s a ) û 2 VP ë o An increase (decrease) of Poisson’s ratio for the underlying medium produces an increase (decrease) in the reflection coefficient at larger angles of incidence o 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 o 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: o o o o 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 Key Takeaway Conclusions 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