Convergence of realization-based statistics to model-based statistics for the LU unconditional simulation algorithm: some numerical tests

In geostatistics, stochastic simulation is often used either as an improved interpolation algorithm or as a measure of the spatial uncertainty. Hence, it is crucial to assess how fast realization-based statistics converge towards model-based statistics (i.e. histogram, variogram) since in theory such a match is guaranteed only on average over a number of realizations. This can be strongly affected by the random number generator being used. Moreover, the usual assumption of independence among simulated realizations of a random process may be affected by the random number generator used. Simulation results, obtained by using three different random number generators implemented in Geostatistical Software Library (GSLib), are compared. Some practical aspects are pointed out and some suggestions are given to users of the unconditional LU simulation method.