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Analysis of radial basis function interpolation approach
Authors:You-Long Zou  Fa-Long Hu  Can-Can Zhou  Chao-Liu Li  Keh-Jim Dunn
Institution:1. Research Institute of Petroleum Exploration and Development, Beijing, 100083, China
2. China University of Petroleum, Beijing, 102249, China
Abstract:The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman’s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.
Keywords:Inverse problems  radial basis function interpolation  new approach
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