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本文对Kriging插值与序贯高斯条件模拟值的算法联系进行了推导,并将两种计算结果和原始数据的统计参数作了对比。结果表明,Monto-carlo方法求得的序贯高斯条件模拟值经数学变换后等同于已知数据和此前模拟数据共同参与的Kriging插值结果与一个随机偏差的和,该随机偏差的均值为0,方差为Kriging误差方差。最优性条件导致Kriging插值结果的方差较原始数据降低了1个Kriging误差方差,造成Kriging平滑效应,其空间变异函数值降低,但自协方差函数值不变。序贯高斯条件模拟避免了平滑效应,其方差、变异函数和自协方差函数均不变,而其模拟值的误差方差较Kriging误差方差增加了1倍,表明1次随机模拟值的误差比Kriging插值大。然而,多次随机模拟值的平均值与Kriging插值的地理制图效果近似,可以弥补局部估值误差大的不足。因此,在应用中,Kriging插值是提供局部最优估计的方法,但却低估了全局的空间变异。而序贯高斯条件模拟的优点,在于提供若干等可能概率的模拟结果以进行估值的不确定性评价,并再现全局的空间可变性。
In this paper, the algorithm connection between Kriging interpolation and sequential Gaussian condition is deduced, and the comparison between the two calculation results and the statistical data of the original data is made. The results show that the sequential Gaussian condition obtained by Monto-Carlo method is equivalent to the sum of Kriging interpolation of known data and previous simulated data, and the sum of a random deviation, which is 0, The variance is the Kriging error variance. The optimality conditions lead to a Kriging variance variance lower than the original data by one Kriging error variance, resulting in a Kriging smoothing effect with a lower spatial variance function value but a constant autocovariance function value. The sequential Gaussian condition avoids the smoothing effect, and its variance, variogram and autocovariance function are invariant, while the error variance of its simulated value is one time larger than the Kriging error variance, which indicates that the error of the first random simulation is worse than Kriging Large interpolation. However, the average of multiple random simulations is close to the result of Kriging interpolation and can make up for the deficiencies of local estimation errors. Therefore, in applications, Kriging interpolation is a method that provides a local optimal estimation but underestimates the global spatial variation. The advantage of a sequential Gaussian condition simulation is that it provides several possible probabilistic simulations to evaluate the uncertainty of the estimate and reproduce the global spatial variability.