The sequential spectral turning band simulator as an alternative to Gibbs sampler in large truncated- or pluri- Gaussian simulations

The Sequential Spectral Turning Bands Method (S-STBM) builds Gaussian random fields (GRF) calibrated to desired response functions. An interesting application of S-STBM concerns the simulation of GRF subject to inequality constraints. S-STBM works by choosing the phase of each cosine function of the STBM algorithm instead of perturbating nodes of the GRF many thousand times using conditional distributions as in Gibbs sampler. Each chosen phase increasingly constrains the nodes to the desired inequalities. A method based on the sequential Gaussian simulation is introduced to accelerate convergence at the end of the process. Examples shown compare S-STBM approach to Gibbs sampler. Orders of magnitude reduction in computation time is achieved with our spectral method. Furthermore, examples show that the phase selection has no significant influence on the spatial correlation. Our approach is easily generalized to pluriGaussian simulations. Compared to Gibbs sampler, S-STBM is not limited to small systems (no memory limitation) and its complexity ofO(n) makes it an efficient tool to simulate large GRF subject to inequality constraints.