自然邻点插值方法在三维地质建模中的应用

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.

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

To enhance the accuracy of thr ee-dimensional geolo gical model, emphasize the hig h local relevance characterist ics of the complex g eo logical bodies, and avoid complicated calculat ion and dependence on human ex perience in t radit ional interpo lation metho ds, the natural neighbor interpo lation ( NNI ) metho d w as used fo r three-dimensional discrete data interpolat ion in the process of modeling . But the exist ing NNI metho d could not be applied to the bo undary interpolat ion of finite f ields, w hich w as the most dif ficult pr oblem of it s application in three-dimensional g eo logical modeling. Based o n the geomet ry of Voronoi Cell s and Delaunay T riang les, the shape funct io n w as const ructed using non-Sibso nian( Laplace) interpolatio n metho d. T he co nt inuity of the boundary in NNI metho d w as pr oven, the bo undary interpolat ion w as implemented and the computatio nal complex ity w as reduced. The accuracy and validity o f the method were pr oven by building the city geolo gical model .