Population MCMC methods for history matching and uncertainty quantification |
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| Authors: | Linah Mohamed Ben Calderhead Maurizio Filippone Mike Christie Mark Girolami |
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| Institution: | (1) Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK;(2) Institute of Geomatics and Analysis of Risk, University of Lausanne, Lausanne, Switzerland |
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| Abstract: | This paper presents the application of a population Markov Chain Monte Carlo (MCMC) technique to generate history-matched
models. The technique has been developed and successfully adopted in challenging domains such as computational biology but
has not yet seen application in reservoir modelling. In population MCMC, multiple Markov chains are run on a set of response
surfaces that form a bridge from the prior to posterior. These response surfaces are formed from the product of the prior
with the likelihood raised to a varying power less than one. The chains exchange positions, with the probability of a swap
being governed by a standard Metropolis accept/reject step, which allows for large steps to be taken with high probability.
We show results of Population MCMC on the IC Fault Model—a simple three-parameter model that is known to have a highly irregular
misfit surface and hence be difficult to match. Our results show that population MCMC is able to generate samples from the
complex, multi-modal posterior probability distribution of the IC Fault model very effectively. By comparison, previous results
from stochastic sampling algorithms often focus on only part of the region of high posterior probability depending on algorithm
settings and starting points. |
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