Journal
MATHEMATICAL GEOSCIENCES
Volume 41, Issue 2, Pages 105-128Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s11004-008-9206-0
Keywords
Geostatistics; Inverse problem; Model calibration; History matching; Spatial structure; MCMC; Reservoir modeling; Conditional simulation
Funding
- Spanish Ministry of Education [2004-02008]
- Technical University of Valencia, Spain
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An adequate representation of the detailed spatial variation of subsurface parameters for underground flow and mass transport simulation entails heterogeneous models. Uncertainty characterization generally calls for a Monte Carlo analysis of many equally likely realizations that honor both direct information (e.g., conductivity data) and information about the state of the system (e.g., piezometric head or concentration data). Thus, the problems faced is how to generate multiple realizations conditioned to parameter data, and inverse-conditioned to dependent state data. We propose using Markov chain Monte Carlo approach (MCMC) with block updating and combined with upscaling to achieve this purpose. Our proposal presents an alternative block updating scheme that permits the application of MCMC to inverse stochastic simulation of heterogeneous fields and incorporates upscaling in a multi-grid approach to speed up the generation of the realizations. The main advantage of MCMC, compared to other methods capable of generating inverse-conditioned realizations (such as the self-calibrating or the pilot point methods), is that it does not require the solution of a complex optimization inverse problem, although it requires the solution of the direct problem many times.
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