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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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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

slide2

Objective

  • determine seismic material properties
  • based on
  • - prestack seismic data
  • - well observations

Characteristics

Multivariate, spatial ill-posed inverse problem

Approach

Bayesian inversion

slide3

Reservoir specific observations

Bayesian graph

Seismic data

Well observation

S,Ss

ds

dw

a

c

r

b

Reservoir variables

slide4

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

slide5

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

slide6

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:

slide7

Seismic data

Well observation

S,Ss

ds

dw

a

c

r

b

Reservoir variables

Prior model

Seismic material properties

multivariate, spatial model:

Note:

slide8

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:

slide9

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:

slide10

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.

slide11

Results

Posterior seismic wavelet:

Prior:

Posterior:

slide12

Results

Posterior seismic observation variance:

slide13

Results

Posterior realization of seismic material properties:

slide14

Results

Prediction of seismic material properties:

slide15

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