  In this work we are interested in the (ill-posed) inverse problem for
absolute permeability characterization that arises in predictive modeling of
porous media flows. We consider a Bayesian statistical framework with a
preconditioned Markov Chain Monte Carlo (MCMC) algorithm for the solution of
the inverse problem. Reduction of uncertainty can be accomplished by
incorporating measurements at sparse locations (static data) in the prior
distribution. We present a new method to condition Gaussian fields (the log of
permeability fields) to available sparse measurements. A truncated
Karhunen-Lo\`eve expansion (KLE) is used for dimension reduction. In the
proposed method the imposition of static data is made through the projection of
a sample (expressed as a vector of independent, identically distributed normal
random variables) onto the nullspace of a data matrix, that is defined in terms
of the KLE. The numerical implementation of the proposed method is
straightforward. Through numerical experiments for a model of second-order
elliptic equation, we show that the proposed method in multi-chain studies
converges much faster than the MCMC method without conditioning. These studies
indicate the importance of conditioning in accelerating the MCMC convergence.
