Amplitude Variation with
Offset
presented byRoxy Frary
TheoryJust some background
…ok a lot of background
Snell’s Law
Reflection Coefficients
Zoeppritz Equations
(Aki & Richards, 1980)
(Much-needed) Simplifications
Aki & Richards, 1980
attempt to separate the
density dependence, P-
wave, and S-wave
…still complicated…
(Much-needed) Simplifications
Hilterman, 1983
Separates into
“acoustic/fluid” and
“shear” terms – by
assuming constant density
…still complicated…
(Much-needed) Simplifications
Shuey, 1985
Each term describes a
different angular range of
the offset curve
Normal incidence reflection coefficientIntermediate angles
Approaching the critical angle
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
• 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
The “Most Simple”
SimplificationHilterman, 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
Poisson’s RatioKoefoed, 1955
Incidence Angle
Koefoed, 1955
Shuey, 1985
VP Contrast
Koefoed, 1955
Shuey, 1985
Rule #1Theoretical 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
Rule #2Theoretical 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
Rule #3Theoretical 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 GathersOstrander, 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 ExampleOstrander, 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
signaturesRutherford & Williams,
1989
• Class 1: high impedanceo gradient is usually greatest
• Class 2: near-zero impedance contrasto seem to suddenly appear at
larger offsets, when amplitudes rise above noise level
• Class 3: low impedanceo large reflectivities at all offsets
Class 1 Gas Sand Example
Rutherford & Williams,
1989
Arkoma Basin
Pennsylvanian-aged
Hartshorn sand
“dim out”
polarity change at mid-
offset
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 far-
offset 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
Fluid Line
• Substituting and neglecting second-order perturbations yields
Foster & Keys, 1999
plotting in the slope-
intercept domain
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
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
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
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)
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)
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
• Class 3 at the top of the
reservoir section, Class 2
deeper as porosity
decreases
Note change in amplitude convention
Seismic data3D 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 datadark-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 sandsBack 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
More on Poisson’s Ratio
• Fluids cannot support shear, so maximum value of σ is 0.5
• Typical values:o 0.05 for very hard rockso 0.45 for loose,
unconsolidated sedimentso 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 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
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
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
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
Can’t classify sands based on properties of
the sand alone – the advent of
Class 4Castagna, Swan & Foster,
1998
Overlying unit is shale
Class 3
Overlying unit is tight
(calcareous)
Class 4
Key difference: Vs contrast
Case HistoryGulf 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
• Attenuationo Signal/noise decrease with
offset
• NMO errorso Conventional velocity analysis
is not “perfect” enougho Ambiguity between stacking
velocity and reflectivityo Can be corrected with full
waveform inversion
Key Takeaway Conclusions
• Important AVO simplification:
• The Rules:o An increase (decrease) of Poisson’s ratio for the underlying medium produces an
increase (decrease) in the reflection coefficient at larger angles of incidenceo 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 Class 1 – high impedance contrast, high gradient, polarity change, low porosityo Class 2 – near-zero impedance contrast, seem to suddenly appear at larger
offsetso Class 3 – low impedance contrast, high reflectivity at all offsetso 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