Analysis of radial basis function interpolation approach

径向基函数插值方法分析(英文)

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.

Freedman提出了径向基函数插值方法用于解决测井和其它岩石物理问题中遇到的反问题。该方法利用一组测量数据集来预测物理性质。然而,该方法仍有一些问题需要研究,如刻度数据集的空间分布对插值效果的影响。本文提出了一种新的径向基函数插值方法,在输入参数空间域中均匀填充单位基函数,并且利用地层因子、粘度、渗透性和分子组成的数据集对这两种方法做了分析和比较。两种插值方法效果相当,新方法的基函数操作更为灵活。当数据库较大时,新方法可适当减少基函数个数,从而简化插值函数表达式。考察数据集空间分布对插值效果的影响,发现当数据集群相距甚远时,中部数据的预测效果不是很理想。