COMPUTATIONALLY EFFICIENT GENERATION OF GAUSSIAN CONDITIONAL SIMULATIONS OVER REGULAR SAMPLE GRIDS

The generation over two-dimensional grids of normally distributed random fields conditioned on available data is often required in reservoir modeling and mining investigations. Such fields can be obtained from application of turning band or spectral methods. However, both methods have limitations. First, they are only asymptotically exact in that the ensemble of realizations has the correlation structure required only if enough harmonics are used in the spectral method, or enough lines are generated in the turning bands approach. Moreover, the spectral method requires fine tuning of process parameters. As for the turning bands method, it is essentially restricted to processes with stationary and radially symmetric correlation functions. Another approach, which has the advantage of being general and exact, is to use a Cholesky factorization of the covariance matrix representing grid points correlation. For fields of large size, however, the Cholesky factorization can be computationally prohibitive. In this paper, we show that if the data are stationary and generated over a grid with regular mesh, the structure of the data covariance matrix can be exploited to significantly reduce the overall computational burden of conditional simulations based on matrix factorization techniques. A feature of this approach is its computational simplicity and suitability to parallel implementation.