An effective method for simulating conditional Gaussian processes in the problems of geological modeling

In problems of geological modeling, methods are often employed for generating the implementations of stationary Gaussian fields under preset values in the wells. Basic simulation algorithms for Gaussian processes are the correction of unconditional Gaussian fields by taking into account the residuals in the wells, sequential Gaussian simulation, and the Cholesky decomposition of the covariance matrix. Neither of these methods, however, is free from drawbacks. Implementations by the first two techniques have an incorrect correlation function, which can lead eventually to incorrect values of hydrocarbon flow rates. The Cholesky decomposition, despite its high accuracy, is not applicable to geological modeling problems due to the high computational complexity of the algorithm. In this paper, we have developed a method based on the generation of the Fourier transform of Gaussian random process implementations. It is shown in this work that in Fourier space the covariance of two harmonics of a random process can be represented as a product of functions of these harmonics. In this case, the Cholesky decomposition algorithm can be significantly simplified. A distinctive feature of the algorithm is its accuracy and relatively low computational complexity.