The Spectral Analysis and Application of Low-degree Modified Spheroidal Hotine Kernel

doi:10.11947/j.JGGS.2020.0310

Abstract

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 height anomaly in the modified frequency domain. The experimental results show that the accuracy of the quasi-geoid by the cosine or linear low-degree modified kernel is higher than that by the traditional spheroidal kernel. And the accuracy equals the accuracy of the quasi-geoid using the spheroidal kernel with high- and low-degrees modified approximately when the low-degree modification bandwidths of these two kinds of kernels are the same. Since the computational efficiency of the low-degree modified kernel is much higher, the low-degree modified kernel behaves better in constructing the (quasi-) geoid based on Stokes-Helmert or Hotine-Helmert boundary-value theory.

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

Jian MA, Ziqing WEI, Hongfei REN. The Spectral Analysis and Application of Low-degree Modified Spheroidal Hotine Kernel[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(3): 104-114.

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Gravity field model	Cutoff degree
EIGEN- 6C4	360	-1.027	0.869	0.102	0.298	0.282
EIGEN- 6C4	2190	-0.109	0.300	0.106	0.132	0.078
EGM2008	360	-1.649	0.350	-0.304	0.422	0.295
EGM2008	2190	-0.703	-0.115	-0.300	0.318	0.106

Kernel function	Min /m	Max /m	Mean /m	RMS /m	Std /m	Time /min
A	-0.058	0.427	0.126	0.152	0.086	150.0
B	-0.058	0.426	0.126	0.152	0.087	10.5

Spheroidal kernel	High-degree modification band	Min /m	Max /m	Mean /m	RMS /m	Std /m	Time /min
High-and low-degree modified	180	0.008	0.408	0.150	0.166	0.072	156.7
High-and low-degree modified	540	0.008	0.408	0.150	0.166	0.072	166.8
Low-degree modified	—	0.008	0.407	0.150	0.166	0.072	12.3

Low-degree modification bandwidth	Min	Max	Mean	RMS	Std
0 (unmodified)	-0.069	0.349	0.123	0.147	0.082
90	-0.036	0.333	0.131	0.148	0.071
180	-0 007	0.309	0.143	0.157	0.066
270	0.005	0.262	0.141	0.153	0.059
360	-0.022	0.194	0.104	0.115	0.048

Low-degree modification bandwidth	Min	Max	Mean	RMS	Std
90	-0.036	0.333	0.131	0.149	0.071
180	-0.010	0.306	0.142	0.156	0.065
270	-0.006	0.246	0.130	0.141	0.056
360	-0.070	0.158	0.073	0.087	0.048