Bayesian AVO Inversion and Application to a Case Study

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Bayesian AVO Inversion and Application to a Case
Study
Pål Dahle, Ragnar Hauge, and Odd
Kolbjørnsen Norwegian Computing Center Nam H.
Pham Statoil
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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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Rapid spatially coupled AVO inversion
Probability
Seismic
Reservoir
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Geophysical Model
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Reflectivity
Matrix formulation d Gm ?
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Assuming Normal Distributions
Matrix formulation d Gm ?
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Earth Model
Vp
Isotropic, inhomogeneous earth
m(x,t) mBG(x,t) mH(x,t)
Vs
m N(mBG, ?m)
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?m Inter-parameter Dependence
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?m Vertical Dependence
Vp
2100
1
2200
0
-20
0
20
2300
2000
2500
3000
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?m Lateral Dependence
Vp
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Combining the Models
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The Posterior Distribution
too much time ....
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Solving in Frequency Space
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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 lt 6Hz
• Inversion
• 6Hz freq 40Hz
• Simulation
• freq gt 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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AI Prediction Conditioned to Wells
Well
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