Direct sequential simulation and cosimulation

Sequential simulation of a continuous variable usually requires its transfo rmation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simula tion. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the co variance model, provided that the simulated values are drawn from local dis tributions centered at the simple kriging estimates with a variance corresp onding to the simple kriging estimation variance. Unfortunately. it does no t reproduce the histogram of the original variable, which is one of the bas ic requirements of any simulation method. This has been the most serious li mitation to the practical application of the direct simulation approach. In this paper. a new approach for the direct sequential simulation is propose d. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf which are calculated with the local estimates of the mean and variance. One of the ma in advantages of the direct sequential simulation method is that it allows joint simulation of N-nu variables without any transformation. A set of exa mples of direct simulation and cosimulation are presented.