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Lithology/fluid prediction subsurface Torstein Fjeldstad Department - - PowerPoint PPT Presentation
Lithology/fluid prediction subsurface Torstein Fjeldstad Department - - PowerPoint PPT Presentation
Lithology/fluid prediction subsurface Torstein Fjeldstad Department of Mathematical sciences NTNU, Trondheim January 10, 2017 Observe (continuous-valued) convolved seismic reflections ( d 1 , . . . , d n ) . Variable of interest: t {
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Observe (continuous-valued) convolved seismic reflections (d1, . . . , dn). Variable of interest: κt ∈ {sand-gas, sand-brine, shale}, t = 1, . . . , n Posterior density of interest: p (κ| d) = const × p (d| κ) p (κ)
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Visualization of model in 1D
Convolved model:
κ1 κ2
. . .
κn−1 κn d1 d2
. . .
dn−1 dn
Inverse problem:
κ1 κ2
. . .
κn−1 κn d1 d2
. . .
dn−1 dn
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Markov random field prior model in 2D
?
Current trace
Left neighbours Right neighbours
? ? ? ? ? ? ?
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... the problem
We can not compute the normalizing constant in p (κ| d) = const × p (d| κ) p (κ) . Assess by Markov chain Monte Carlo sampling.
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Conditional realizations lithology/fluids
lf lf lf lf lf
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Extends to rock properties and elastic attributes
por por por por por ip ip ip ip ip