自然邻点插值方法在三维地质建模中的应用

Application of natural neighbor interpolation method in three-dimensional geological modeling

为了增强三维地质模型的准确性,突出复杂地质体局部相关性较高的特点,避免传统插值方法中存在的计算复杂度高、多依赖人工经验等缺点,在建模过程中引入了自然邻点插值(NNI)方法对三维离散数据进行插值。而现有的NNI方法无法直接应用于有限域的边界插值计算,成为该方法应用于三维地质建模的最大难点问题。依据Voronoi cells和Delaunay triangles的几何性质,采用non-Sibsonian(Laplace)插值方法构造形函数,详细证明了NNI方法在边界处的连续性,实现了边界插值且降低了其计算复杂度,解决了此难点问题。通过构建城市地质模型实例,验证了该方法的正确性和有效性。

To enhance the accuracy of three-dimensional geological model, emphasize the high local relevance characteristics of the complex geological bodies, and avoid complicated calculation and dependence on human experience in traditional interpolation methods, the natural neighbor interpolation （NNI） method was used for three-dimensional discrete data interpolation in the process of modeling. But the existing NNI method could not be applied to the boundary interpolation of finite fields, which was the most difficult problem of its application in three-dimensional geological modeling. Based on the geometry of Voronoi Cells and Delaunay Triangles, the shape function was constructed using non-Sibsonian（Laplace） interpolation method. The continuity of the boundary in NNI method was proven,the boundary interpolation was implemented and the computational complexity was reduced. The accuracy and validity of the method were proven by building the city geological model.