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**Amplitude Variation with Offset**

presented by Roxy Frary

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Theory Just some background …ok a lot of background

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Snell’s Law

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**Reflection Coefficients**

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Zoeppritz Equations (Aki & Richards, 1980)

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**(Much-needed) Simplifications**

Aki & Richards, 1980 attempt to separate the density dependence, P-wave, and S-wave …still complicated…

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**(Much-needed) Simplifications**

Hilterman, 1983 Separates into “acoustic/fluid” and “shear” terms – by assuming constant density …still complicated…

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**(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

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**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

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**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

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Poisson’s Ratio Koefoed, 1955

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Incidence Angle Koefoed, 1955 Shuey, 1985

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VP Contrast Koefoed, 1955 Shuey, 1985

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**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

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**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

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**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

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**Industry Use: Gas Sands**

Since 1982

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Gas Sands Ostrander, 1984 Hypothetical gas model

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**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

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**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

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**Another Example Ostrander, 1984 Nevada Amplitude anomaly at 1.6 s**

Decrease in amplitude with offset on gathers – uniform Poisson’s ratio – BASALT

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**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

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**Class 1 Gas Sand Example Rutherford & Williams, 1989 Arkoma Basin**

Pennsylvanian-aged Hartshorn sand “dim out” polarity change at mid-offset

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**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

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**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

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**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

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**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

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**Industry Use: Fluid Identification**

Since 1997

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**plotting in the slope-intercept domain**

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

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**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

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**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

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**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

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**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)

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**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)

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**AVO for hydrocarbon detection**

Foster, Keys & Lane, 2010

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**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

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**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

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**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

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**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

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**Check with structure in map view**

anomaly extends to the eastern structure as well

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**AVO for lithology discrimination**

Foster, Keys & Lane, 2010

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**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)

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**AVO extraction to map view**

Well A found a commercial reservoir Well B found poor porosity

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**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

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**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

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**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

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**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

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**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

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**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

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**Case History Gulf of Mexico Bright Spot**

Nsoga Mahob, Castagna & Young, 1999

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Amplitude Anomaly

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**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

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**AVO Inversion – Brine Model**

not really all that close…

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**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

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**AVO Inversion – Gas Model**

decently close! gas model, with appropriate mechanical properties, converges to the real seismic data

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**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

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**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

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**Key Takeaway Conclusions**

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**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

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