Adaptive Interpolation Method for Generalized Triangular Prism (GTP) Geological Model Based on the Geometric Smoothness Rule - Sun, Liming; Wei, Yingqi; Cai, Hong; Xiao, Jianzhang; Yan, Jun; Wu, Shuaifeng (Frontiers in Earth Science, 2022)
Three dimensional (3D) geological model is frequently used to represent the geological conditions of the subsurface. The generalized triangular prism (GTP) model designed for borehole sampling data are spatial data models, it could retain the internal connection between the three adjacent boreholes and distinguish between the bedding and cross-bedding directions, which is proper for 3D geological modeling. The traditional building method cannot consider two factors: The borehole distance is usually longer than the stratigraphic thickness, and the accuracy difference of the top surface and the bottom surface at the same time. In this study, we describe the new interpolation method for the GTP 3D geological model to improve the model accuracy with sparse borehole data. Firstly, the GTP model smoothness definition and calculation method are proposed to measure the model smoothness and accuracy degree, which is used to decide whether the GTP voxel requires interpolation. Secondly, the virtual borehole design and calculation method are discussed in detail for the GTP voxel subdivision according to the GTP geometric smoothness. Finally, the GTP adaptive interpolation can be performed through the GTP voxel subdivision and the geometric optimization rebuilding. This method could interpolate the existing GTP model by local updating adaptively without changing the GTP model structure, it has high efficiency compared to the classical method. In addition, the feasibility and accuracy of this method could be proven by the actual case. The study will provide a new reliable interpolation method for the GTP model.