Estimation of a Stochastic Discontinuous Permeability Using a Multidimensional Markov Chain
S. Zein, V. Rath and C. Clauser
January 19, 2009
Abstract
In this paper, we are interested in estimating a stochastic permeability distribution
by considering the steady flow inverse problem (Poisson problem) over
a two-dimensional domain. The permeability is discretised over a regular rectangular
gird and considered to be constant by cell but it can take randomly a
finite number of values. Such permeability is modeled using a multidimensional
Markov chain and it is constrained by some permeability measures and some
pressure measures at some points of the domain.
The difficulty of this inverse problem is the non-uniqueness of the solution, in the
classical least-squares sens. To overcome this difficulty we propose a solution for
this inverse problem, in a probabilistic sens, by coupling the MCMC sampling
technique with the multidimensional Markov chain model.
Keywords: Discontinuous Parameter Estimation, Poisson Problem, Multidimensional
Markov Chain, MCMC.
http://www.geophysik.rwth-aachen.de/Downloads/pdf/ZeinRathClauser_InverseProblemsInScienceAndEngineering_2009.pdf