地球物理勘探中几种二维插值方法的误差分析

Error Analysis of Several Two-Dimensional Interpolation Methods in the Geophysical Exploration

为了研究采样和网格化方法对地球物理数据成图精度的影响,为野外数据采集布设提供一定的依据,采用数值模拟确定重力异常场场值,通过不同采样间距和不同插值方法计算重力异常绝对误差均方根值和节点处的绝对误差值,对比不同插值方法的误差,得到了如下认识:1)对于同一插值方法而言,存在小间距绝对误差均方根值小于大间距绝对误差均方根值的关系。2)对不同的插值方法而言:当采样间距小于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、反距离加权插值法、最近邻点法、最小曲率法,并且线性插值三角网法与自然邻点法具有几乎相同的数值;当采样间距大于最小异常地质体尺度时,绝对误差均方根值由小到大的顺序是径向基函数法、改进的谢别德法、克里金插值法、自然邻点法、最小曲率法、最近邻点法、反距离加权插值法,并且线性插值三角网法和自然邻点法具有几乎相同的数值。3)从绝对误差均方值看,径向基函数方法、改进的谢别德方法和克里金方法数值较小,其中径向基函数值绝对误差均方根值最小。4)从节点处绝对误差值来看,径向基函数方法、克里金方法、改进的谢别德方法相对其他插值方法具有更小的误差,不存在局部误差较小或较大的情况,是相对较好的插值方法,并且径向基函数方法是最好的。

In order to study the influence of geophysical sampling and gridding method on mapping accuracy and provide field data collection with theoretical base, we compute a certain gravity anomaly field, and calculate absolute error values（AEV） and absolute error root mean square values（AERMSV） from different sampling intervals and grid interpolation methods. According to the data error, it could conclude= 1）In a single interpolation method, small spacing causes small AERMSV. 2）When sampling interval less than the minimum scale of abnormal geological body, AERMSV will ascend from radial basis function method, modified Shepard method, Kriging interpolation method, natural neighbor method, triangulation with linear interpolation, inverse distance weighted interpolation, nearest neighbor method, to minimum curvature method; when sampling interval exceeds the minimum geological body scale, AERMSV will ascend from radial basis function method, modified Shepard method, Kriging interpolation method, natural neighbor method, triangulation with linear interpolation, minimum curvature method, nearest neighbor method, inverse distance weighted interpolation. 3） Based on AERMSV, radial basis function method, kriging method and modified Shepard＇s method have smaller values, and radial basis function method is best. 4）Based on AEV, radial basis function method, Kriging method and modified Shepard^s method have smaller error.