关键词: Hotine截断核函数, 余弦低阶修正, 线型低阶修正, 频谱分析, 谱泄露, 贡献率

Abstract: 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.

Key words: spheroidal Hotine kernel, cosine low-degree modification, linear low-degree modification, spectral analysis, spectrum leakage, contribution rate