Gaussian Radial Basis Function interpolation in vertical deformation analysis

Abstract

In many deformation analyses, the partial derivatives at the interpolated scattered data points are required. In this paper, the Gaussian Radial Basis Functions (GRBF) is proposed for the interpolation and differentiation of the scattered data in the vertical deformation analysis. For the optimal selection of the shape parameter, which is crucial in the GRBF interpolation, two methods are used: the Power Gaussian Radial Basis Functions (PGRBF) and Leave One Out Cross Validation (LOOCV) (LGRBF). We compared the PGRBF and LGRBF to the traditional interpolation methods such as the Finite Element Method (FEM), polynomials, Moving Least Squares (MLS), and the usual GRBF in both the simulated and actual Interferometric Synthetic Aperture Radar (InSAR) data. The estimated results showed that the surface interpolation accuracy was greatly improved by LGRBF and PGRBF methods in comparison withFEM, polynomial, and MLS methods. Finally, LGRBF and PGRBF interpolation methods are used to compute invariant vertical deformation parameters, i.e., changes in Gaussian and mean Curvatures in the Groningen area in the North of Netherlands.

Keywords

• Interpolation accuracy
• Gaussian Radial Basis Functions
• Finite Element Method
• InSAR
• Vertical deformation