bayesian avo inversion and application to a case study
DESCRIPTION
Bayesian AVO Inversion and Application to a Case Study. P ål Dahle * , Ragnar Hauge, and Od d Kolbjørnsen Norwegian Computing Center Nam H. Pham Statoil. Contents. Objective Constrain high resolution 3D reservoirs by seismic AVO data Method - PowerPoint PPT PresentationTRANSCRIPT
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Bayesian AVO Inversion and Application to a Case Study
Pål Dahle*, Ragnar Hauge, and Odd KolbjørnsenNorwegian Computing Center
Nam H. PhamStatoil
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Contents
Objective– Constrain high resolution
3D reservoirs by seismic AVO data
Method– Bayesian inversion,
merging of geophysical and geological models
Contribution– Fast algorithm– Spatial coupling– Uncertainty assessment
Vp
Vs
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Outline
Reservoir
Pro
bab
ilit
y
Geology Seismic
Combined
Combining models3)
Summary4)
Earth model2)
Geophysical model1) Bayesian inversion
Rapid spatially coupled AVO inversion
Case study5)
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d(x,t,) AVO-trace, surface point x, “offset” w (t) Seismic wavelet, angle dependentcpp(x,t,) Seismic reflectivity(x,t,) Error term
w (t) cpp(x,t,)d(x,t,)
Geophysical Model
d(x,t,) = w t cpp(x,t,) + (x,t,)*
Convolutional model:
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Reflectivity
cpp(x,t,) = aVp() lnVp(x,t) + aVs
() lnVs(x,t) + a() ln(x,t)
Weak contrast approximation (continuous version):
t
t
t
d(x,t,) = w t cpp(x,t,) + (x,t,)*
Convolutional model:
Matrix formulation: d = Gm +
m(x,t) = [ lnVp(x,t), lnVs(x,t) , ln(x,t) ]
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Assuming Normal Distributions
m(x,t) = [ lnVp(x,t), lnVs(x,t) , ln(x,t) ]
d~ N( md, d)
m ~ N( m, m) ~ N(0, e)
Matrix formulation: d = Gm +
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Earth Model
m(x,t) = mBG(x,t) +mH(x,t)
Isotropic, inhomogeneous earth:
Vp
m = Cov mH (x1,t1), mH (x2,t2)
Vs
m ~ N(mBG, m)
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lnVs
ln
7.70
7.80
7.75
7.0 7.2 7.4
m : Inter-parameter Dependence
Cov mH (x1,t1), mH (x2,t2) = 0( t1 - t2 ) ( x1 - x2 )
lnVp
7.70
7.80
7.75
ln
7.8 7.9 8.0
lnVs
lnVp
7.8 7.9 8.0
7.0
7.2
7.4
7.6
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m : Vertical Dependence
2100
2200
2300-20 0 20
0
1
Vp
2000 2500 3000
Cov mH (x1,t1), mH (x2,t2) = 0( t1 - t2 ) ( x1 - x2 )
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m: Lateral Dependence
1250
1350
1500 1600 1700
1300
1250
1350
Vp
-400
40 -400
40
1
0
Cov mH (x1,t1), mH (x2,t2) = 0( t1 - t2 ) ( x1 - x2 )
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Combining the Models
d~ N( md, d)
m ~ N( m, m) ~ N(0, e)
m d ~ N( mm|d , m|d)
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The Posterior Distribution
mm|d = mBG+mG*(GmG* + e )-1(d - GmBG)
m|d = m - mG*(GmG* + e )-1G m
m,d m dtoo much time ....
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Solving in Frequency Space
m,d m d
m,d
m d
3D FFT 3D inverse FFT
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Summary
• Bayesian inversion• Convolutional model, weak contrast
• Spatial dependencies of earth parameters
• Fast inversion
• 100 million grid cells ~ 1 hour
• More than inversion• Consistent merging of well logs
• High resolution reservoirs
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Smørbukk Case Study
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The Smørbukk Case
• 32 mill grid cells• 3 angles• 2.5 h
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Frequency Split
• Background freq < 6Hz
• Inversion 6Hz ≤ freq ≤ 40Hz
• Simulation freq > 40Hz
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Background Modelling
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Background Model
Vp6 Vs6 RHOB6
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Inversion Input Data
• Background model: Vp, Vs, and Rho
• Well data: TWT, DT, DTS, and Rho
• Seismic Data • Wavelets
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Predicted AI From Inversion
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AI Prediction in Wells
Well 1 Well 2 Well 3
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SI Prediction in Wells
Well 1 Well 2 Well 3
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Density Prediction in Wells
Well 1 Well 2 Well 3
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AI Cross Sections: Horisontal
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AI Background
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AI Prediction
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AI Prediction Kriged to Wells
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AI Conditional Simulation 1
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AI Conditional Simulation 2
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AI Cross Sections: Vertical
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AI Background
Well
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AI Prediction
Well
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well
AI Prediction Conditioned to Wells
Well
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AI Conditional Simulation 1
Well
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AI Conditional Simulation 2
Well
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Case Study Conclusions
• Good match for AI used for modelling of– Facies– Porosity