EQUIVALENCE BETWEEN KRIGING AND CPDF METHODS FOR CONDITIONAL SIMULATION

Currently the kriging and conditional probability density function (CP DF) methods are widely used in solving the conditional simulation prob lems involving stochastic processes and fields. For the fundamental un derstanding of these two methods, this paper considers their applicati ons to the conditional simulation of a one-dimensional, univariate and stationary stochastic process or field, The major findings of this st udy are as follows. First, the two methods are completely equivalent i f the stochastic process is Gaussian with a zero mean. Specifically th e best linear unbiased estimate (BLUE) and the kriging variance ate id entical to the corresponding conditional mean and variance, respective ly. Second, when the kriging method is used, the conditional simulatio n of a nonzero mean stochastic process (with a known value of the mean ) is not equivalent to the (nonzero) mean plus the conditional simulat ion of the zero mean stochastic process obtained by subtracting the no nzero mean from the original process. Third, it can be shown that the second moment of the process conditionally simulated with the help of the kriging method are not identical to the target second moment (a pr iori known statistics). Finally, the kriging method is not suitable fo r the conditional simulation of non-Gaussian stochastic processes if n o other assumptions or conditions are made for the reasons indicated i n the paper, although the estimation (BLUE) may still be performed, as claimed by its proponents.