格林样条插值算法及其应用

Green's function-based interpolator and its application

新近发展起来了一种基于双调和算子格林函数计算的数据插值方法———格林样条插值法,这是用中心点位于各观测数据点的多个格林函数进行加权叠加而解析地计算出插值曲面(曲线)的全局插值方法.本文介绍了该方法的基本原理、插值方法和实用程序的发展概况及使用中可能出现的问题.利用格林样条插值法和另两种常用插值法处理了某地布格重力异常的实测数据,对比插值结果说明,格林样条法在抑制虚假异常、稳定显示局部异常和消除奇异边缘效应等方面,具有一定的优越性.

A recently developed interpolator, the greenspline, is based on the application o{ green＇s functions of the biharmonic operator. The interpolated surface is constructed by globally summing the weighted Green＇s functions centered at every data point. The basic mathematic principle of the interpolation, it＇s developing state and possible problems in application of this technique are reviewed in this paper. The greenspline interpolator and the surface interpolating program in GMT tool were used to test a 2D interpolation of a set of GTOPO30 data. The result indicates that the greenspline acquired a more accurate interpolated topography pattern than the surface did. The greenspline and other two traditional interpolators were also applied to processing the Bouguer gravity anomaly observations obtained somewhere. Comparison of the interpolated results indicates that the greenspline interpolator is superior to the other two in suppressing false anomalies, stably displaying local anomalies and removing singular boundary effect.