Computationally efficient generation of Gaussian conditional simulations in geological modeling problems

The generation 2D and 3D normally distributed random fields conditioned on well data are often required in reservoir modeling. Such fields can be obtained by using: unconditional simulation with kriging interpolation, sequential Gaussian simulation, Cholesky factorization of the covariance matrix. However, all methods have disadvantages. First and second one have a fallible correlation function of realizations. This disadvantage could cause incorrect values of oil flow rates. Cholesky factorization, which has the advantage of being general and exact, has high computational costs for geological modeling problems. In this work we use spectral representation of conditional process. It is shown that covariance of two arbitrary spectral components could be factorized into functions of corresponding harmonics. In this case the Cholesky decomposition could be considerably simplified. A feature of this approach is its accuracy and computational simplicity.