基于指示和普通克里金的不连续地层厚度估计方法

A combined indicator-ordinary Kriging method for estimating thicknesses of discontinuous geological strata

因为克里金插值方法考虑了样本的空间统计特征而被广泛应用于地层建模。但对于地层尖灭、缺失等不连续地层情况，常用的克里金方法（如普通克里金方法）通常给出较为平滑的地层厚度估计结果，在地层分布边缘的局部范围内与实际情况相差较大。针对不连续地层，提出一种采用指示克里金和普通克里金相结合的地层厚度估计方法。该方法首先采用指示克里金方法估计地层分布范围，然后采用普通克里金方法估计分布范围内的地层厚度，并根据估计标准差来评价地层厚度的不确定性。将提出的方法应用于上海长江隧道的地层建模，通过交叉验证，证明了该方法在地层分布边缘的局部范围内能明显改善地厚度估计结果，标准差降低了15%～18%，得到了比普通克里金和线性插值方法更接近真实情况的地层厚度估计值。

Kriging interpolation methods are widely applied to geological modeling because spatial characteristics of borehole samples are considered by using geostatistics. However, most commonly used Kriging techniques （e.g. the ordinary Kriging method） produce smoothed estimation results, those will lead to an inaccurate regionalization of discontinuous geological stratum around zero value zones, such as pinch-out stratum or stratum with missing segments in some areas. In this paper, a combined indicator-ordinary Kriging method is presented to estimate thicknesses of discontinuous geological stratum. In this method, the estimation of stratum thickness is divided into two steps. Firstly, the indicator Kriging method is used to estimate the distributed area of a geological stratum. Secondly, the ordinary Kriging method is employed to estimate the thicknesses of the geological layer in the distributed area. In addition, a standard error is obtained to evaluate the estimation uncertainty of stratum thickness. The proposed method is applied to estimate the thickness of geological stratum in the Shanghai Yangtze River tunnel project. Through cross validations, the case study shows that the proposed method improves the estimation results by reducing the standard deviation by 15%to 18%, and produces more accurate estimates of thickness of discontinuous geological stratum around zero value zones than that given by the ordinary Kriging method and conventional linear interpolation method.