基岩露头采样密度对黄土古地形重建的影响

下伏古地形对黄土地貌的形成、演化与发育具有重要的控制作用。基于下伏地层露头的采样数据,通过空间插值方法进行古地形数字模型(DEM)重建是研究黄土地貌的重要方法。其中,采样点密度是下伏地形DEM重建精度的主要影响因子。本文以1:20万绥德幅地质图所涉及区域为实验样区,研究采样点密度及样条函数方法对下伏古地形重建精度的影响。实验结果表明,在高密度样本条件下,采用规则样条插值方法进行古地形重建时,插值结果呈现显著的“龙格现象”,即多项式插值结果出现剧烈波动现象,且随着样本密度增加,样条插值结果的误差呈逐步趋缓的降低趋势,并逐步趋于稳定。同时,基于古地形DEM提取的特征点,其局部最高点和局部最低点的数目呈直线上升趋势,说明在一定程度上基于有限数据采用样条函数进行地下三维建模并不一定能获得平滑曲面。研究结果对如何选择合理的空间采样密度进行古地形DEM重建具有重要的指导意义。

Effect of Outcrop Sampling Density on the Underlying Terrain Reconstruction

The Pre-Quaternary underlying terrain profoundly controls the evolution and formation of loess landform. Obvious relationships, i.e. the geomorphological inheritance, could be found between the underlying terrain and the modern terrain. As a consequence, the Pre-Quaternary underlying terrain in the Loess Plateau should be regarded as the key factor for the understanding of the loess landform evolution. Among numerous numerical calculation methods, spatial interpolation has been regarded as an important method to reconstruct the DEM of underlying terrain by using the sampled bedrock outcrop points selected from a geological map. However, the sampling density has a great impact on the accuracy of the reconstructed underlying terrain. In this paper, the Suide geological map area (1:200 000) was selected as the study area, and then the influence of sampling density on the accuracy of the reconstructed underlying terrain was investigated using spline method. By adopting cross-validation method to evaluate reconstructed underlying terrain, the result shows that, different interpolation methods cause uncertainties to different degrees during the reconstruction of underlying terrain, particularly the spline method. On a basis of high density outcrop points and spline function interpolation process, the morphology of underlying terrain exhibits a typical “Runge phenomenon”. This phenomenon was always resulted from a polynomial interpolation process. With an increased sampling density, the error in underlying terrain appears a slowly decrease tendency firstly, and then it keeps stable. Meanwhile, the number of the extracted features has a linear upward trend. The result also shows that the sampling density of 1.7-2.0 points per square kilometer could achieve a good balance between the accuracy and underlying terrain feature reservation. The aforementioned results adjust our previous understandings that spline function could smooth the interpolated surface to some extent. And the result also provides guidance for the selection of a reasonable spatial sampling density.