Research On3D Interpolation Approaches Based On Kriging With Anisotropic Spatial Structures

In order to establish an effective and reliable model, spatial field reconstruction must take spatial structure and anisotropy of geographic phenomena into account, which is based on three dimensional spatial interpolation approaches, because three dimensional geographical phenomena have spatial structure and anisotropy. Due to the influence of a variety of environmental factors, distribution and variation of geographic phenomena has its own inherent tendency. It also exists some different characteristic directions in which the spatial structure characteristics presented are different. Variogram in Geostatistics is an effective means to describe the spatial structure, which reflects phenomena anisotropy to different directions.3D spatial interpolation approaches must analyze variation directions of sampled data of geographical phenomena in a three dimensional space. As a result, space coordinate axis will be consistent with the dominant characteristic direction of geographic property.Traditional interpolation approaches fail to combine structural analysis with the dominant characteristic direction of geographic property. In response to the problems mentioned above, an improved Kriging method is proposed in this paper to combine the Kriging method with the directional characteristics analysis of the geographical attribute. To take the advantage of considering spatial correlation and anisotropy of three-dimensional Kriging spatial interpolation, we will achieve a goal of only relying on the observation to implement effective and reliable reconstruction of three dimensional spatial fields with anisotropic spatial structures. The main research work and achievements including:(1) Based on the principle of principal hessian direction method (PHD) method, we could analyze characteristic directions of geographic phenomena in the three dimensional space. Then the characteristic directions of the observed properties of geographical phenomena are extracted by PHD method. By this way, real geographical space is converted to a standardized three-dimensional space. It provides space basis for structural analysis of geographic phenomena.(2) To implement structural analysis of geographical phenomena in the standardized three-dimensional space. We could separate variogram fitting in different characteristic directions. Then, a unified anisotropic variogram, which reflect geographical phenomenon anisotropy in the standardized three-dimensional space, can be generated by nested overlap of anisotropic variograms in different directions.(3) The spatial structure parameters in different directions provide a reference for spatial elliptical definition in the standardized three-dimensional space. In this paper, a new Kriging method considering anisotropy is demonstrated. The feasibility of this method is testified by a case study about spatial distribution of sediment content in Taihu.