A Gauss Markov approach to conditioning to block data

Integration of data defined at different scales is a recurring problem in Earth Science applications. Integrating seismic data with well data defined on a much smaller scale is one such application. Currently sequential and iterative simulation algorithms are not equipped to combine data which are non-linearly related with each other over different scales. This paper proposes a novel technique based on the theory of Gauss-Markov random functions (GMrf). The conditioning of point simulations to point data and nonlinear block data is performed by using a Metropolis-Hastings sampler on a Markovtype random field. The efficiency of the algorithm is demonstrated with an example based on an exhaustive synthetic data set. Simulations honor a strongly anisotropic covariance, a bimodal histogram and are conditioned to point data and imprecise block data. A second example of conditioning to weighted harmonic averages along irregularly shaped blocks is discussed. The general applicability of the algorithm to problems of greater complexity is discussed.