A Triangular Prism Spatial Interpolation Method for Mapping Geological Property Fields

The spatial interpolation of property fields in 3D, such as the temperature, salinity, and organic content of ocean water, is an active area of research in the applied geosciences. Conventional interpolation methods have not adequately addressed anisotropy in these data. Thus, in our research we considered two interpolation methods based on a triangular prism volume element, as a triangular prism structure best represents directivity, to express the anisotropy inherent in geological property fields. A linear triangular prism interpolation is proposed for layered stratum that achieves a complete C0 continuity based on the volume coordinates of the triangular prism. A triangular prism quadric interpolation (a unit function of a triangular prism spline with 15 nodes) is designed for a smooth transition between adjacent triangular prisms with approximately C1 continuity, expressing the continuity of the entire model. We designed a specific model which accounts for the different spatial correlations in three dimensions. We evaluated the accuracy of our proposed linear and triangular prism quadric interpolation methods with traditional inverse distance weighting (IDW) and kriging interpolation approaches in comparative experiments. The results show that, in 3D geological modeling, the linear and quadric triangular prism interpolations more accurately represent the changes in the property values of the layered strata than the IDW and kriging interpolation methods. Furthermore, the triangular prism quadric interpolation algorithm with 15 nodes outperforms the other methods. This study of triangular prism interpolation algorithms has implications for the expression of data fields with 3D properties. Moreover, our novel approach will contribute to spatial attribute prediction and representation and is applicable to all 3D geographic information; for example, in studies of atmospheric circulation, ocean circulation, water temperature, salinity, and three-dimensional pollutant diffusion.