低阶修正的Hotine截断核函数的频谱分析与应用

The spectral analysis and application of low-degree modified spheroidal Hotine kernel

传统截断核函数存在谱泄露问题,且实测数据在移去恢复频段的利用率低。本文以Hotine核函数为例引入了一种高低阶均修正的截断核函数,在其基础上进一步提出了仅低阶修正的截断核函数,具体包含余弦修正和线型修正两种类型。修正核函数能够有效地控制截断核函数存在的谱泄露问题,并且增大了实测数据在修正频段对高程异常的贡献率。试验结果表明,当低阶修正带宽一定时,低阶修正核函数计算的似大地水准面精度优于传统截断核函数计算的似大地水准面精度,并且与高低阶均修正的核函数的解算精度相当。但在计算效率上,低阶修正核函数明显优于高低阶均修正的核函数。本文的试验证实了在基于Helmert第二压缩法的边值问题(Stokes-Helmert或Hotine-Helmert边值问题)中低阶修正核函数是一种比较有效的核函数。

The traditional spheroidal kernel results in the spectrum leakage, and the utilization rate of the removed degrees of the measured data is low. Hence, a kind of spheroidal kernel whose high and low degrees are both modified is introduced in this research, which is exampled by the Hotine kernel. In addition, the low-degree modified spheroidal kernel is proposed. Either cosine or linear modification factors can be utilized. The modified kernel functions can effectively control the spectrum leakage compared with the traditional spheroidal kernel. Furthermore, the modified kernel augments the contribution rate of the measured data to the height anomaly in the modified frequency domain. The experimental results show that the accuracies of the quasi- geoids using the cosine and linear low-degree modified kernels are higher than the traditional spheroidal kernel, and differ little from the accuracies of the quasi-geoids using the kernel whose high and low degrees are both modified when the low-degree modification widths of these two kinds of kernels are the same. Since the computational efficiency of the low-degree modified kernel is improved obviously, the low-degree modified kernel behaves better in constructing the (quasi-) geoid based on Stokes-Helmert or Hotine-Helmert boundary value theory.