离散光滑插值方法在地球物理位场中的快速实现

研究并探讨了1种新的插值方法-离散光滑插值方法及其在地球物理位场中的快速实现。首先由待插值点与巳知点之间的拓扑关系建立线性约束，进一步结合场满足Laplace方程，建立离散光滑插值联立方程组，采用预条件共轭梯度求解该方程组。为更好地提高计算效率，在求解过程中采用螺旋坐标系和Wilson-Burg谱分解，将二维数据转换到一维空间处理。通过理论模型和实际资料计算，该方法适合地球物理位场特征，插值效果好，速度快。

THE FAST REALIZATION OF DISCRETE SMOOTH INTERPOLATION IN THE INTERPOLATION OF POTENTIAL DATA

This paper presents a new method Discrete Smooth Interpolation method (DSI) and its fast realization in geophysical potential data gridding. First the topological relations between the unknown points and known points are built as a linear constrain, then the DSI equation group is formulated by combining Laplace equation with the linear constrain equation. The preconditioning conjugate direction descend method is used to seek the solution and speed up the solving. To improve the efficiency of the computation, the theory of the helical coordinate system is used to convert the two dimensional data to one dimensional data and deal with them in one dimensional space. In addition, the method of Wilson Burg spectral factorization is employed to solve the linear algebraic equation derived from DSI. Through the application of theoretical model and the real raw data, it is shown that the method in this paper is suitable for the features of geophysical potential field, the effects of interpolation is satisfactory and the convergence rate is very high.