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Bayesian Seismic Inversion and Estimation in a Spatial Setting

Bayesian Seismic Inversion and Estimation in a Spatial Setting. Henning Omre Norwegian University of Science & Technology Trondheim Norway Arild Buland Statoil FoU Trondheim Norway. Objective determine seismic material properties based on - prestack seismic data

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Bayesian Seismic Inversion and Estimation in a Spatial Setting

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  1. Bayesian Seismic Inversion and Estimation in a Spatial Setting Henning Omre Norwegian University of Science & Technology Trondheim Norway Arild Buland Statoil FoU Trondheim Norway

  2. Objective • determine seismic material properties • based on • - prestack seismic data • - well observations Characteristics Multivariate, spatial ill-posed inverse problem Approach Bayesian inversion

  3. Reservoir specific observations Bayesian graph Seismic data Well observation S,Ss ds dw a c r b Reservoir variables

  4. Seismic data Well observation S,Ss ds dw a c r b Reservoir variables Likelihood model Prestack seismic data: Observation error Gauss(0,Ss) Wavelet Reflection coefficients

  5. Seismic data Well observation S,Ss ds dw a c r b Reservoir variables Likelihood model Well observations: Observation error Gauss(0,Sw) Well location indicator

  6. Seismic data Well observation S,Ss ds dw a c r b Reservoir variables Prior model Seismic reflection coefficients Aki-Richards three-term-relation: Note:

  7. Seismic data Well observation S,Ss ds dw a c r b Reservoir variables Prior model Seismic material properties multivariate, spatial model: Note:

  8. Seismic data Seiemic data Well observation Well observation S,Ss S,Ss ds ds dw dw a a c c r r b b Reservoir variables Reservoir variables Prior model Seismic wavelet: Seismic observation variance:

  9. Seismic data Seiemic data Well observation Well observation S,Ss S,Ss ds ds dw dw a a c c r r b b Reservoir variables Reservoir variables Posterior model Recall Bayes rule:

  10. Seismic data Seiemic data Well observation Well observation S,Ss S,Ss ds ds dw dw a a c c r r b b Reservoir variables Reservoir variables Solution Explore posterior model: by MCMC simulation. Note: - analytically tractable.

  11. Results Posterior seismic wavelet: Prior: Posterior:

  12. Results Posterior seismic observation variance:

  13. Results Posterior realization of seismic material properties:

  14. Results Prediction of seismic material properties:

  15. Closing remarks • Consistent model • physical relations • spatial coupling • uncertainty • Graphical model • Fast evaluation • realizations • predictions • precision • Extensions • 3D models • Superfast simulation • LFP inversion • Timelaps seismic inversion

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