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ISPRS Int. J. Geo-Inf. 2017, 6(8), 241; doi:10.3390/ijgi6080241

A Triangular Prism Spatial Interpolation Method for Mapping Geological Property Fields

1
Shenzhen Key Laboratory of Spatial Smart Sensing and Services & The Key Laboratory for Geo-Environment Monitoring of Coastal Zone of the Nation al Administration of Surveying, Mapping and GeoInformation, Shenzhen University, Nanhai Road 3688, Shenzhen 518060, China
2
Key Laboratory of Geo-Informatics, Chinese Academy of Surveying & Mapping, Beijing 100830, China
3
Key Laboratory for National Geographic Census and Monitoring, National Administration of Surveying, Mapping and Geoinformation, Beijing 100830, China
4
State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan 430079, China
*
Authors to whom correspondence should be addressed.
Academic Editor: Wolfgang Kainz
Received: 15 May 2017 / Revised: 11 July 2017 / Accepted: 3 August 2017 / Published: 6 August 2017
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Abstract

Abstract: 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 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 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. View Full-Text
Keywords: directivity; linear triangular prism interpolation; triangular prism quadric interpolation; spatial correlation; accuracy evaluation directivity; linear triangular prism interpolation; triangular prism quadric interpolation; spatial correlation; accuracy evaluation
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Cui, Y.; Li, Q.; Li, Q.; Zhu, J.; Wang, C.; Ding, K.; Wang, D.; Yang, B. A Triangular Prism Spatial Interpolation Method for Mapping Geological Property Fields. ISPRS Int. J. Geo-Inf. 2017, 6, 241.

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