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WATER RESOURCES RESEARCH, VOL. 41, W12423, doi:10.1029/2004WR003764, 2005

An efficient two-stage Markov chain Monte Carlo method for dynamic data integration

Y. Efendiev

Department of Mathematics and Institute for Scientific Computation, Texas A&M University, College Station, Texas, USA


A. Datta-Gupta

Department of Petroleum Engineering, Texas A&M University, College Station, Texas, USA


V. Ginting

Department of Mathematics and Institute for Scientific Computation, Texas A&M University, College Station, Texas, USA


X. Ma

Department of Petroleum Engineering, Texas A&M University, College Station, Texas, USA


B. Mallick

Department of Statistics, Texas A&M University, College Station, Texas, USA


Abstract

In this paper, we use a two-stage Markov chain Monte Carlo (MCMC) method for subsurface characterization that employs coarse-scale models. The purpose of the proposed method is to increase the acceptance rate of MCMC by using inexpensive coarse-scale runs based on single-phase upscaling. Numerical results demonstrate that our approach leads to a severalfold increase in the acceptance rate and provides a practical approach to uncertainty quantification during subsurface characterization.

Received 26 October 2004; accepted 7 September 2005; published 20 December 2005.

Keywords: MCMC; upscaling; acceptance rate.

Index Terms: 1873 Hydrology: Uncertainty assessment (3275); 3275 Mathematical Geophysics: Uncertainty quantification (1873); 3260 Mathematical Geophysics: Inverse theory.

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Citation: Efendiev, Y., A. Datta-Gupta, V. Ginting, X. Ma, and B. Mallick (2005), An efficient two-stage Markov chain Monte Carlo method for dynamic data integration, Water Resour. Res., 41, W12423, doi:10.1029/2004WR003764.