变异函数模型对渗透系数克里格插值的影响研究

A comparative study of the ordinary kriging applied to hydraulic conductivity interpolation based on different variogram models

在克里格计算或其它地质统计学研究中,变异函数模型选取的适当性直接影响渗透系数的结构分析与插值结果的合理性。分别基于高斯模型、球状模型、指数模型对同一沉积相介质的渗透系数进行结构分析,并采用普通克里格法进行插值,结果分析表明:变异函数模型对渗透系数克里格插值的影响主要体现在变程值的不同;变程值过小,搜索邻域内各数据点之间的相关性降低甚至消失,克里格法退化为简单的算术平均;随着变程值增大,参与克里格计算的实测点增多,插值结果趋近于平稳;当变程值与实际值较为吻合时,克里格插值精度达到最大。

A variogram model is directly involved in the Kriging calculation or other geostatistic study,therefore,the choice of variogram models is to affect not only the structure analysis of hydraulic conductivity,but also the Kriging interpolation results. Three variogram models,the Gaussian model,spherical model and exponential model,were used to fit the experimental variogram,and the ordinary Kriging was chosen to yield the estimated hydraulic conductivity. Analysis of the interpolation results shows that the impact of variogram models on the ordinary Kriging interpolation of hydraulic conductivity mainly reflects the difference of range. The smaller the range is,the weaker the correlation between the observation and estimation points is. As a result,the Kriging degenerates into a traditional interpolation method. Contrarily,the larger range means a stronger correlation,therefore,the interpolation result tends to be smoother. Ideally,when the range is close to the reality,the Kriging interpolation may provide a hydraulic conductivity field with low estimation variance.