Mathematical Geosciences

, 41:105 | Cite as

A Blocking Markov Chain Monte Carlo Method for Inverse Stochastic Hydrogeological Modeling

  • Jianlin FuEmail author
  • J. Jaime Gómez-Hernández


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.


Geostatistics Inverse problem Model calibration History matching Spatial structure MCMC Reservoir modeling Conditional simulation 


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Copyright information

© International Association for Mathematical Geosciences 2008

Authors and Affiliations

  1. 1.Department of Hydraulic and Environmental EngineeringUniversidad Politécnica de ValenciaValenciaSpain

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