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Fast 3D Kriging Interpolation using Delaunay Tetrahedron with CUDA-Enabled GPU
Yao, Xingmiao (University of Electronic Science and Technology of China) | Wang, Qian (University of Electronic Science and Technology of China) | Liu, Zhining (University of Electronic Science and Technology of China) | Hu, Guangmin (University of Electronic Science and Technology of China) | Huang, Dongshan (CNPC Chuanqing Drilling Engineering Company Limited Geophysical Exploration Company) | Zou, Wen (CNPC Chuanqing Drilling Engineering Company Limited Geophysical Exploration Company)
Summary Kriging interpolation algorithm is a kind of optimal linear unbiased interpolation method and applied to many fields, especially in geological field. As a kind of regional algorithm, how to choose the neighbor points is an important part of kriging algorithm. Moreover, in recent years, with the wide use of kriging interpolation technology, higher efficiency of kriging interpolation is required and traditional kriging interpolation algorithm has not been able to meet the current requirement for efficiency. For kriging is an algorithm defined in the limited space domain, it has to select the calculation area, which is completed by selecting neighbor known points as input for interpolating unknown points. But the existing kriging interpolation method could not consider neighbor points. Instead, it uses all the known points as the input. And if all the known points are used as the input, the scheme will be infeasible. Considering these problems, this paper puts forward a fast kriging interpolation algorithm based on Delaunay tetrahedron with CUDA-enabled GPU, which establishes a spatial index for 3D Delaunay tetrahedron to quickly search neighbor points. Meanwhile, based on CUDA platform, an effective parallel interpolation strategy is proposed by using powerful computing capability of GPU to improve the efficiency of interpolation. Introduction Kriging algorithm (D. G. Krige) is an important interpolation method, which provides optimal linear unbiased estimation for the discrete points. In recent decades, kriging method has been extensively applied to the field of geological research. As an algorithm defined in the limited space domain, kriging inevitably will meet problems of the selection of the calculation area. Especially when there is a large scale of known points data, the algorithm needs to select neighbor known points as input instead of choosing all of the known points, considering computational complexity or feasibility. At present, in 2D kriging interpolation, Masoud Hessami et al. (2001) used Delaunay triangle implementation to improve kriging computing efficiency. But most of the 3D Kriging interpolation usually use all known points to the interpolation calculation, and there are few studies about the search of neighbor points in 3D Kriging interpolation, which resulting in a low-accuracy interpolation or heavy computational workload. As an optimized triangle subdivision, 3D Delaunay tetrahedron provides a good solution for this problem. Therefore, this paper uses 3D Delaunay tetrahedron as the rule of searching neighbor points to realize a fast search for neighbor known points.
- Information Technology > Hardware (0.90)
- Information Technology > Graphics (0.90)
Smooth Complex Geological Surface Reconstruction Based on Partial Differential Equations
Yao, Xingmiao (University of Electronic Science and Technology of China) | Deng, Shiwu (University of Electronic Science and Technology of China) | Liu, Zhining (University of Electronic Science and Technology of China) | Hu, Guangmin (University of Electronic Science and Technology of China) | Jia, Yu (Chengdu University of Technology) | Chen, Xiaoer (CNPC Chuanqing Drilling Engineering Company Limited Geophysical Exploration Company) | Zou, Wen (CNPC Chuanqing Drilling Engineering Company Limited Geophysical Exploration Company)
Summary Reconstruction of geological surface is an important foundation of 3D geological modeling, and has important application in geological and geophysical fields. Methods commonly used include Kriging interpolation method, Triangulation method, the weighted least square fitting method, etc. Because of the particularity of geological conditions, there are some difficulties for these methods to deal with complex geological faults and to reconstruct surface with certain smoothness. In this paper, we propose a smooth complex geological surface reconstruction method with partial differential equations. Regarding geological fault constraints as internal boundary conditions, this method uses finite difference method to solve property value of the grid points with discrete partial differential equations, which make the surface reconstruction reaches the requested smoothness rapidly. Meanwhile, we build triangulation at fault constraints to adapt to fault polygon topology and solve the attribute values of fault polygon through the triangular mesh difference format, constructing a smooth surface at fault. Application examples show that the method, which fully considers various faults in the geological surfaces and rapidly reconstructs complex fault constraints geological surface with G1 continuity. Introduction Geological surface reconstruction has an important application in geological field, and can be seen as scattered point cloud reconstruction problem, witch is also a hot topic in computational geometry, computer graphics, reverse engineering and other fields. Generally, methods of interpolation and fitting are used to reconstruct geological surface, which are realized by distance-weighted average, Kriging interpolation, cubic spline function fitting, trend surface fitting, etc. However, because geological data possesses characteristics of large number, irregular distribution and containing fault information (normal fault, reverse fault and vertical fault), the surfaces reconstructed by conventional methods may not represent the real geological surfaces and cannot reach specified smoothness. In the late 1980s, Bloor and Wilson first proposed surface modeling method based on geometric partial differential equations (Bloor et al., 1989). Since then, many scholars started to explore the basic theory and application of this method in surface reconstruction filed. It is found that this method can easily construct a large number of practical surface forms and plays a huge role in the construction of transition surface (Zheng C,2005), free-form surface design (Du H et al., 2007) and the filling of N boundary domain.
- Banking & Finance (0.36)
- Energy > Oil & Gas > Upstream (0.35)