A Study On Interpolation Method For3D Scattered Potential Field Data

The basic aim of this paper is to present an investigation of different methods for interpolation of3D scattered data to3D scattered data.The first part surveys and introduces a range of widely used methods for filed data interpolation, including radial basis function interpolation, kriging interpolation and natural neighbor interpolation. Those methods are compared in term of accuracy and efficiency. Then in order to introduce a method that has seldom been used in geophysics, the trivariate spline functions based on Delaunay tetrahedralization, theory of barycentric coordinates and the Bernstein are presented. By applying the cubic spline with3D Clough-Tocher split which is generalization of the bivariate Clough-Tocher split on each of the tetrahedron, it could achieve global C1continuity.The results obtained by computing synthetic gravity field data illustrate the exceptional accuracy achieved with piecewise trivariate cubic spline functions based on Clough-Tocher method, as well as advantages like smoothness, efficiency, easiness of using and possibility for parallel computations.