Adaptive Interpolation Method for Generalized Triangular Prism (GTP) Geological Model Based on the Geometric Smoothness Rule

Abstract

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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 is a spatial data model that could retain the internal connection between the three adjacent boreholes and distinguish between the bedding and cross-bedding directions, which is proper for accurate 3D geological modeling. The traditional building method cannot consider two factors: the borehole distance is usually longer than the stratigraphic thickness, and the top and the bottom surface have different accuracy 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, definition and calculation method of the GTP model smoothness are proposed to measure the model smoothness and accuracy degree, which are used to decide whether the GTP voxel requires interpolation. Secondly, the virtual borehole design and calculation method for the GTP voxel subdivision in terms of the GTP geometric smoothness are discussed in detail. Finally, the GTP adaptive interpolation can be performed through the GTP voxel subdivision and the geometric optimization rebuilding. This method could adaptively interpolate the existing GTP model by local updating 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 and reliable interpolation method for the GTP model, and it is also conducive to economic geology related research.

Keywords

• generalized triangular prism
• geological modeling
• adaptive interpolation method
• geometric smoothness
• virtual borehole
• voxel model