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Abstract

Mesoscale (~10 m) models using rock-physics concepts and effective-media ideas are a manageable basis for Bayesian seismic integration because seismic is usefully informative at this scale. An attractive route to geocellular scale (~1 m) models is downscaling mesoscale models using categorical (facies) simulations that honor effective media laws, and using well data and geologic concepts to formulate priors. <br><br>In this nonlinear downscaling, it is unclear whether the overall posterior distributions for fine-scale models can be approximated as the product of conditional distributions using local neighborhoods, which is necessary for accurate sequential simulation. The factorization requires computing analytical marginal distributions (integrating over “unvisited” sites) and conditional distributions dependent only on “visited” sites. Analytical techniques fail for nonlinearly constrained problems; the only alternatives are expensive MCMC or analytical approximations within a sequential method. An approximation based on an expansion assuming weak correlation between visited and unvisited sites is developed in this paper.<br><br>We test and illustrate by comparing global methods (with rigorous marginals) to local approximations. Local method errors increase as correlation length increases, especially if seismic data are highly informative or the marginals are poorly approximated. Using the proposed marginal approximation improves sequential simulation accuracy for these cases.

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/content/papers/10.3997/2214-4609.201403065
2007-09-10
2020-06-05
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201403065
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