基于杨赤中推估法空间插值的三维地质隐式建模

3D geological implicit modelling based on spatial interpolation by Yang Chizhong estimation method

杨赤中推估法是一种对空间域复合变量通过连续的几何滤波过程来建立核函数的最小二乘推估法,建模过程简便且能基于少量已知数据点取得好的建模效果。针对地质勘查中离散、稀疏而不规则分布的地质特征点数据难以构建地质体三维模型的难点问题,提出了一种基于杨赤中推估法的三维地质空间插值与模型建立的自动化方法。该方法首先以地质特征点数据库为基础,选用负幂指数函数模型建立适合三维地质空间插值的杨赤中推估法估值数学模型;在此基础上,构建一套基于杨赤中推估法的三维地质空间插值计算和地质体隐式建模的自动化实现流程与程序;最后以实例矿化插值数据为基础,采用基于移动立方体算法的三维隐式建模方法,快速构建实例矿体三维模型。与人工交互圈定地质体边界和进行矿体推断的三维地质显式建模相比,这种方法能快速直观地分析地质特征并处理样品分析数据,方法可行且高效。

Yang Chizhong estimation method is a kind of least-squares estimation method with the kernel function constructed by successive geometrical filtering in the spatial-domain compound variable. Its process of modelling is simple and can achieve good results with only a few known data points. To solve the problem of constructing the 3D model hindered by discrete and sparse spatial-data points within the geological body,it is proposed to implement the 3D geological implicit modelling based on spatial interpolation by Yang Chizhong estimation method. Firstly,on the basis of geological feature database,Yang Chizhong estimation model is altered suitable for the spatial interpolation in the 3D geological body by using negative exponent function model. Secondly,automatic flow and program are designed to facilitate the 3D geological spatial interpolation calculation and geological body modelling based on the Yang Chizhong estimation model. Finally,based on the practical mineralized interpolation data,3D model of practical ore body is built by using 3D implicit modelling with marching cubes algorithm. Compared with delineating geological body boundary by human-machine interaction and ore body estimation with explicit 3D modeling,this method is feasible to efficiently provide a visual way for the geologist to analyze and deal with large number of sample data.