COMPUTATIONALLY EFFICIENT GENERATION OF GAUSSIAN CONDITIONAL SIMULATIONS OVER REGULAR SAMPLE GRIDS

The generation over two-dimensional grids of normally distributed rand om 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 t he ensemble of realizations has the correlation structure required onl y if enough harmonics are used in the spectral method, or enough lines are generated in the turning bands approach. Moreover, the spectral m ethod requires fine tuning of process parameters. As for the turning b ands 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 fa ctorization of the covariance matrix representing grid points correlat ion. For fields of large size, however, the Cholesky factorization can be computationally prohibitive. In this paper, we show that if the da ta are stationary and generated over a grid with regular mesh, the str ucture of the data covariance matrix can be exploited to significantly reduce the overall computational burden of conditional simulations ba sed on matrix factorization techniques. A feature of this approach is its computational simplicity and suitability to parallel implementatio n.