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: κ t ∈ { sand-gas, sand-brine, shale } , t = 1 , . . . , n Posterior density of interest: p ( κ | d ) = const × p ( d | κ ) p ( κ )

Visualization of model in 1D Inverse problem: Convolved model: d 1 κ 1 d 1 κ 1 d 2 κ 2 d 2 κ 2 . . . . . . . . . . . . d n − 1 κ n − 1 κ n − 1 d n − 1 κ n d n κ n d n

Markov random field prior model in 2D Current trace Left neighbours Right neighbours ? ? ? ? ? ? ? ?

... 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.

Conditional realizations lithology/fluids lf lf lf lf lf

Extends to rock properties and elastic attributes por por por por por ip ip ip ip ip