Post on 03-Jun-2018
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10-4
Seismic Lithology Estimation
Gathers Stack
InversionAVO Analysis
Attribute 1 Attribute 2
Estimate VP, VS, and
Estimate
Z= VP
The AVO method allows us to simultaneously estimate
VP, VS, and , thus inferring fluid and/or lithology.
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Possible Attributes
But which two attributes will give us the best estimate of
these parameters? Various authors have proposed a number of options:
Range-limited stacking
Elastic Impedance
Intercept/Gradient analysis RP/RSextraction followed by inversion.
/analysis.
Lets look at the theory of these methods, and then at
some examples. As we will see, these methods combine all of the ideas
that we have considered in the course so far, starting withrock physics and progressing through AVO and post-stack inversion.
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(a)
(b)
Here are the (a) near
angle (0o-15o) and (b)far angle (15o-30o)
stacks from the Colony
seismic dataset.
Notice that the
amplitude of thebright-spot event at
about 630 ms is
stronger on the far-
angle stack than it is
on the near-anglestack. As we saw
earlier, this is a gas-
sand induced bright-
spot.
Range limited stacking over gas sand
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The zones are mapped back to the seismic. A pitfall in this method relates to
amplitude changes unassociated with fluid change.
Top Gas
Base GAS
Coal
Cross-plotting angle range stacks
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Cross-plotting angle range stacks.
A solution
would be todefine more
detailedzones.
Cross-plotting angle range stacks
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Cross-plotting angle range stacks.
Top GASBase GAS
Coal
Cross-plotting angle range stacks
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The above plot shows the (a) near-angle stack (0-15o), and (b) far-
angle stack (15-30o) over a 3D channel sand. To enhance the
amplitude display, the amplitude envelope has been averaged over a
10 ms window and the Z-score transform has been applied.
Cross-plotting angle range stacks
(a) (b)
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Range Limited Stacking
Gathers
AVO Analysis
Near Stack Far Stack
Fluid/Lithology Interpretation
Range-limited stacking, using constant offsets or
constant angles, is very robust, and avoids misaligned
event problems. But what does it mean?
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Elastic Impedancenear-offset form
Using the Aki-Richards eq., Connolly(1998) proposed
the Elastic Impedance (EI) concept to physically explainrange-limited stacks, where:
)sinK41()sinK8(
S
)tan1(
P
222
VV)(EI
2
P
2
S
V
VKwhere
Note that if =0
o
, EI reduces to Acoustic Impedance(AI), where:
PVAI
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Elastic Impedancefar-offset form
Connolly(1998) proposed proposed a second form of the
Elastic Impedance (EI) concept for far offsets, wheresinreplaces tanin the first equation:
)sinK41()sinK8(
S
)sin1(
P
222
VV)(EI
2
P
2
S
V
VKwhere
Note that if =0o
, far offset EI also reduces to AcousticImpedance (AI):
PVAI
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Exercise 5-1
Let us use a simple example where VP
= 1000 m/s,
VS_wet= 500 m/s, VS_gas= 667 m/s, and = 2.0 g/cc.
Work out the values for elastic impedance at = 0o and
=30ofor the wet and gas cases:
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Exercise 5-1 Answers
For the wet case:
423VV)30(EI 75.05.0S25.1
P
o
20001000*2AI)0(EI o
For the gas case:
53.25VV)30(EI 56.089.0S25.1
P
o
20001000*2AI)0(EI o
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The transformation of an AI log from 0 to 30 results in a generally
similar log but with lower absolute values.
The apparent acoustic impedance decreases with an increase in
angle.
The percentage decrease is greater for an oil sand than for shale.
Connolly 1999
Elastic Impedanceeffect of oil saturation
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Elastic Impedancedata example
The following figure, from Connolly (1999) shows the
computed curves for AI and EI at 30 degrees:
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We will now illustrate the procedure with the shallow gas sand case
study considered in the AVO section. The well logs are shown
above.
Gas sand case study
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The figure above shows the previous logs after fluid substitution in the gas zone. The
EI_Nearlog on in blue was created at 7.5oand the EI_Farlog in red was created at
22.5o. Note that the NearNearinside the sand.
Gas sand case study
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The figure above shows the (a) crossplot between the near and far EI logs, and
(b) the logs themselves.
Gas sand case study
(a) (b)
EI_Near EI_Far
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The figure above now shows the (a) interpreted crossplot between the near and
far EI logs, and (b) the zones marked on the logs themselves. Notice the clear
indication of the gas sand zone.
Gas sand case study
(a) (b)
EI_Near EI_Far
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Gas sand case study
(a)
(b)
Here are the (a) near
and (b) far anglestacks from the
seismic dataset.
Notice that the
amplitude of the
bright-spot event atabout 630 ms is
stronger on the far-
angle stack than it is
on the near-angle
stack. As we saw
earlier, this is a gas-
sand induced bright-
spot.
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Gas sand case study
Above is shown the inversion of the near-angle stack using an
elastic impedance model. The angle range in the stack is from 0oto
15o, so an average value of 7.5
owas used for the model.
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Gas sand case study
Above is shown the inversion of the far-angle stack using an elastic
impedance model. The angle range in the stack is from 15oto 30
o,
so an average value of 22.5owas used for the model.
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Gas sand case study
(a)
(b)
Here is the
comparison between
the inversions of the
(a) near-angle stack
and (b) far-angle
stack, using the
elastic impedance
concept. Notice the
decrease in the
elastic impedance
value on the far-angle stack.
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Gulf coast case study
In the following set of slides, we will consider
a Gulf coast case study (we do not have
permission to tell you where, however).
This is a 3D example which presents adifferent set of problems than the 2D case
study considered last.
Note that we will be able to find the
anomalous zone using crossplot analysis, and
look for similar anomalies throughout the 3D
volume.
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Gulf coast case study
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Near angle
stack (5- 35)
Far angle stack
(35- 65)
Gulf coast case study
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Initial guess acoustic impedance model
Gulf coast case study
Gulf coast case study
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Comparing the Acoustic impedance and the Elastic impedance
logs clearly highlights the hydrocarbon zone.
Gulf coast case study
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Gulf coast case study
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Near (left) and far (right) wavelets used in inversions. Note
the decrease in frequency content with offset.
Gulf coast case study
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Elastic impedance inversion result.
Gulf coast case study
Gulf coast case study
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The cross plot
shows the near
inversion on thex-axis and the far
inversion on the
y-axis.
Using the cross
plot technique
overcomes the
normalisation
issue.
Gulf coast case study
Gulf coast case study
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The cross plot
zones are
plotted in map
view.This is a time
slice at 1200ms
and shows the
track of the
anomalous zone
Gulf coast case study
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RP/RSInversion
Gathers
AVO Analysis
RP Estimate RSEstimate
RP/RSinversion is a powerful method, but is dependent
on the quality of the data and the approximations used.
Invert to ZP Invert to ZS
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Applying P and S inversion to seismic data
We will now look at an application of thepreceding inversion method using the Colony
sand example that we have considered in many
of our examples.
The first slide will show the full stack and the
extracted RPand RSstacks.
The second slide will show the inversions of all
three stacks.
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Colony Sand Example - Gathers
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Colony Sand Example - Gathers
Here are the gathers, with the correlated sonic log displayed at its
proper location.
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Inversion Procedure
The inversion procedure used here involves thefollowing steps:
Insert the appropriate logs at the correct locations,
which has already been done.
Correlate the logs, which has also been done.
Pick the major seismic horizons.
Find an optimum wavelet.
Build the starting model for inversion.
Invert the data.
We will now apply this procedure to the RPandRSsections.
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C l S d E l P M d l
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Colony Sand Example - P-wave Model
Here is the model result, using a single well and the picked
horizons. The model is scaled to P-Impedance.
C l S d E l P I i
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Colony Sand Example - P-wave Inversion
Here is the final P-wave inversion result. The low impedance just below
Horizon 2 represents the gas sand.
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Colony Sand Example -S-Impedance Model
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Colony Sand Example S Impedance Model
We now have the created S-Impedance model, as shown above.
Note that the new colour key represents S-wave impedance
values.
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Colony Sand Example - S-wave Inversion
The result of the S-wave inversion is shown above. Notice that thegas sand below Horizon 2 is now associated with an increase inimpedance.
Th LMR A h
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The LMRApproach
Goodway et al (1998) proposed a new approach to AVO
inversion based on the ,,parameters, called LMR
. Thetheory is shown below:
2
S
2
P
2
P
2
P
2
S
2
S
SP
Z2Zso
)2()V(Zand
)V(Zthen
Vand
2
VSince
PanCanadian Petroleum
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From Goodway et al 1999
Original Zp vs Zs Observations
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Interpreting Lambda-Rho and Mu-Rho
The original paper by Goodway et al, gives the
following physical interpretation of the lambda()
and mu()attributes: The term, or
incompressibility, is sensitive to pore fluid,
whereas the term, or rigidity, is sensitive to therock matrix.
As we saw in the theory, it is impossible to de-
couple the effects of density from and when
extracting this information from seismic data. It is therefore most beneficial to cross-plot vs
to minimize the effects of density.
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Biot theory for porous rocks
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Biot theory for porous rocks
Biot (1941) linked the saturated and dry frame to
the Lame coefficients in the following way:
M2drysat
sat= the Lame coefficient for the saturated rock,
dry= the Lame coefficient for the dry frame,
= the Biot coefficient, or the ratio of the volume
change in the fluid to the volume change in the
formation when hydraulic pressure is constant,
M= the modulus, or the pressure needed to force
water into the formation without changing the
volume.
G f
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Gassmann theory for porous rocks
Gassmann (1951) linked the saturated and dry
frame to the Bulk modulus in the following way:
MKK 2drysat
modulus.theMt,coefficienBiotthe
,framedrytheofmodulusbulktheK
,rocksaturatedtheofmodulusbulktheK
dry
sat
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Biot-Gassmann summary
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Biot Gassmann summary
In summary, we can rewrite the velocity equations inthe following way using the Biot-Gassmann equations:
sat
satP
2V
sat
satP
34KV
.M
,MKK,:where
2
drysat
2
drysat
satdry
sat
SV
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The constant term c and s
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The constant term c and s
Note that the constant term cis simply the square of
the ratio between the dry rock P-wave velocity andthe dry rock S-wave velocity:
3
4K
2V
V
c
drydry
2
dryS
P
The key question is: how do we find the value of c?
Note that the term sis simply given by c(VS)2.
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Extended LMR Analysis
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Gathers
AVO Analysis
RP Estimate RSEstimate
Crossplot
Invert to ZP Invert to ZS
Transform to fand s
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Whiterose example
The next five slides show and example from a well
log in the Whiterose field from offshore eastern
Canada, courtesy of Ken Hedlin and Husky Oil.
As will be seen, we will experiment with fourvalues of c: 1.333, 2, 2.333, and 2.5.
We are expecting a vertical separation between
gas and non-gas sections of the reservoir. There
is no perfect result, but a c value of 2.333 appears
to give the best separation.
S wave, P wave, Density and Porosity for
Whiterose L 08 Cretaceous Shale and Sands
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Whiterose L-08 Cretaceous Shale and Sands
Cretaceous
Shale
Gas sand
Oil sand
Wet sand
Limestone
Vs Vp Den Porosity
85m
97m
95m
Courtesy, Ken Hedlin and Husky Oil
f vs s with c = 1.33 for Whiterose L-08
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rho*f vs rho*s for c = 1.333
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
0.00 2.00 4.00 6.00 8.00
rho*f
rho*s
Shale Gas Oil Wet
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f vs s with c = 2.333 for Whiterose L-08
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rho*f vs rho*s for c = 2.333
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0.00 1.00 2.00 3.00 4.00
rho*f
rho
*s
Shale Gas Oil Wet
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Colony example
Next, we will apply the generalized LMR method tothe Colony seismic example that we were evaluatingearlier.
We will use c values of 2 (which corresponds to
LMR) and 2.333, which corresponds to a dry rockPoissons ratio of 0.125.
For the Kporevs mu result, a value of c = 2.233 wasused.
Colony Sand f with c = 2.0
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Colony Sand f with c 2.0
The extraction of the
f section using a cvalue of 2.0 and the ZPand ZSinverted sections shown earlier.
Colony Sands with c = 2.0
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y
The extraction of the
s section using a cvalue of 2.0 and the ZSinverted section shown earlier.
Colony Sands vs f with c = 2.0
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A cross plot of the the extractedf ands sections using a cvalue of
2.0. Two zones are shown, where red=gas and blue=non-gas.
C = 2.0Gas Zone in Red
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The interpreted zones from the previous cross-plot, shown now onthe seismic section. Note the continuity of the gas sand in red.
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c = 2.0
c = 2.333
Colony Sands with c = 2.333
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y
The extraction of the
s section using a cvalue of 2.333 and theZSinverted section shown earlier.
Colony Sands vs f with c = 2.333
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A cross plot of the the extracted
f and
s sections using a cvalue of2.333. Two zones are shown, where red=gas and blue=non-gas.
C = 2.333Gas Zone in Red
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The interpreted zones from the previous cross-plot, shown now onthe seismic section. Note the slightly improved continuity of thegas sand in red.
Blackfoot Case Study
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Now, let us return to the Blackfoot case study considered earlier in thecourse. The figure above shows the AVO responses of the various events.Note that the Upper Valley porous sandstone shows a class 2 response.
(Dufour et al.)
Blackfoot Case Study
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y
The figure above shows the zero offset P-wave reflectivity, Rp, on line 95.Notice the troughs at the upper and lower valleys. (Dufour et al.)
Blackfoot Case Study
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The figure above shows the zero offset S-wave reflectivity, Rs, on line 95.Notice the different response at the upper and lower valleys than that ofthe Rp section. (Dufour et al.)
Blackfoot Case Study
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The figure above shows the fluid factor (F) on line 95. This wascomputed using the formula F = Rp g (t)Rs. Note the anomalousresponse at the Upper Valley. (Dufour et al.)
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Blackfoot Case Study
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The figure above shows (b) the annotation of the potential hydrocarbon zone
on the
extracted amplitude map, and (b) the annotation of the potential
hydrocarbon zone on the
extracted amplitude map. (Dufour et al.)
(a) (b)
Conclusions
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This has been a brief overview of the ElasticImpedance, R
P
/RS
inversion and LMR approaches, aswell as the general theory behind LMR from a Biot-Gassmann perspective.
The AVO method allows us to estimate two (or more)independent parameters from our prestack data.
Poststack inversion techniques can then be applied tothese extracted attributes.
The crossplot of the inverted attributes allows us toseparate the fluid and matrix effects of the reservoirrock.
In each area, the pair of attributes best suited for theparticular play needs to be evaluated using both welllog and seismic data.
Exercise 5-1 Answers
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Recall that VP= 1000 m/sand VS= 500 m/s(therefore K
= 0.25), and = 2.0 g/cc. At =0o
, we have:
480VV)30(EI94.05.0
S
25.1
P
o
At = 30owe have sin= 0.5, and we get:
20001000*2AI)0(EI o