Two approaches to direct block-support conditional co-simulation

Change of support is a common issue in the geosciences when the volumetric support of the available data is smaller than that of the blocks on which numerical modeling is required. In this paper, we present two algorithms for the direct block-support simulation of cross-correlated random fields that are monotonic transforms of stationary Gaussian random fields. The first algorithm is a variation of sequential Gaussian co-simulation, in which each block value is simulated in turn, conditionally to the original data and to the previously simulated block values, while the second algorithm is based on spectral co-simulation in the framework of the discrete Gaussian change-of-support model. These two algorithms are implemented in computer programs and applied to a synthetic case study and to a mining case study. Their properties and performances are compared and discussed.