Reservoir simulation models are constructed from sparse welldata, dense seismic data, and using geologic concepts to constrainstratigraphy and property variations. Because of thesparseness of well data, stochastically inverted seismic dataoffer important constraints on reservoir geometry and averageproperties. Although seismic data are densely distributed, theyare uninformative about meter-scale features. Conversely, welldata reveal fine-scale features but cannot specify intrawell geometry.To build a consistent model, conceptual stacking andfacies models must be constrained by well and seismic data.Stochastic ensembles of geomodels are used to capture variabilityassociated with seismic downscaling, lateral variability andconceptual models. The resulting geomodels must be griddedfor flow simulation using methods that describe stratal architectureflexibly and efficiently.In this paper, geomodels integrate stochastic seismic inversionresults (for means and variances of “packages” ofmeter-scale beds), geologic modeling (for a framework and priors),rock physics (to relate seismic to flow properties), andgeostatistics (for spatially correlated variability). These elementsare combined in a Bayesian framework. The proposedworkflow produces models with plausible bedding geometries,where each geomodel agrees with seismic data to the level consistentwith the signal-to-noise ratio of the inversion. An ensembleof subseismic models estimates the means and variancesof properties throughout the flow simulation grid.Grid geometries with possible pinchouts can be simulatedusing auxiliary variables in a Markov Chain Monte Carlo(MCMC) method. Efficient implementations of this method requirea posterior covariance matrix for layer thicknesses. Underassumptions that are not too restrictive, the inverse of theposterior covariance matrix can be approximated as a Toeplitzmatrix, which makes the MCMC calculations efficient. Theproposed method is validated and examined using two-layerexamples. Convergence is demonstrated for a synthetic threedimensional,10,000 trace, 10 layer cornerpoint model. Performanceis acceptable (305 s on a 2 GHz Pentium-M processor).The Bayesian framework introduces plausible subseismicfeatures into flow models, whilst avoiding overconstraining toseismic data, well data, or the conceptual geologic model. Themethods outlined in this paper for honoring probabilistic constraintson total thickness are general, and need not be confinedto thickness data obtained from seismic inversion: any spatiallydense estimates of total thickness and its variance can be used,or the truncated geostatistical model could also be used withoutany dense constraints.
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