复杂地区局部重力场带限SRBF二次逼近法

doi:10.11947/j.AGCS.2024.20230132

摘要/Abstract

摘要：

本文利用基于带限球面径向基函数（SRBF）的重力场二次累积逼近法，对地形复杂地区重力场模型的构建进行了较为详细的数值分析和验证工作。首先，利用带限SRBF将卫星重力场模型（GGM）数据与航空重力数据进行融合，构建了研究地区的初始重力场模型（基于SRBF的重力场第一次逼近）。与仅依赖于航空数据得到的重力场模型相比，初始重力场模型与GPS/水准数据之间的大地水准面差异标准差（STD）在研究区域降低了约0.022 m，表明了融合GGM和航空重力数据进行初始重力场建模的有效性。然后，在移去参考重力场模型、初始重力场模型和残余地形模型效应的基础上，利用残余地面和航空重力数据进行了基于带限SRBF的重力场第二次逼近。与传统的基于SRBF的一次逼近方法相比，二次SRBF逼近方法所得模型在研究区域的大地水准面差异STD和RMS值分别降低了0.036 m和0.024 m，显示了带限SRBF二次累积逼近方法的优越性。此外，研究区域地形属于复杂的山区，可以为复杂地区重力场模型的构建提供一定参考。

关键词: 带限径向基函数, 局部重力场二次累积逼近法, 卫星重力数据, 航空重力数据, 地面重力数据

Abstract:

Utilizing the SRBF-based two-step cumulative approximation method, this study conducted a detailed numerical analysis and validation for the construction of a local gravity field model in complex areas. First, data from the global gravity field model were combined with airborne gravity data to construct the initial SRBF-based gravity field model for the study area (the first gravity field approximation based on band-limited SRBFs). When compared to the airborne-only gravity field model, the standard deviation of geoid height discrepancies between the initial gravity field model and GPS/leveling data decreased by approximately 0.022 m. This suggests the effectiveness of merging GGM and airborne gravity data for initial modeling. Subsequently, after removing the effects of the reference gravity field model, the initial gravity field model and the residual terrain model from the terrestrial and airborne gravity data, a secondary SRBF-based modeling process was conducted (the second gravity field approximation based on band-limited SRBFs). Compared to the one-step SRBF model, the two-step approach yielded reductions of 0.036 m and 0.024 m in terms of STD and RMS, respectively, highlighting the superiority of the SRBF-based two-step cumulative approximation method. Moreover, the study area features a complex mountainous terrain, which can serve as a reference for constructing gravity field model in similar complex regions.

Key words: band-limited spherical radial basis function, two-step cumulative approximation method for local gravity field, GGM gravity data, airborne gravity data, terrestrial gravity data

中图分类号:

P312

马志伟, 边少锋, 徐如一, 陈永冰. 复杂地区局部重力场带限SRBF二次逼近法[J]. 测绘学报, 2024, 53(5): 900-916.

Zhiwei MA, Shaofeng BIAN, Ruyi XU, Yongbing CHEN. Band-limited SRBF quadratic approximation method for local gravity fields in complex regions[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(5): 900-916.

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模型	80阶	120阶	160阶	200阶	240阶	280阶	300阶
GOC6S	0.000	0.001	0.004	0.015	0.049	0.115	0.145
GGC16	0.001	0.002	0.006	0.020	0.058	0.122	-
TJ21S	0.000	0.000	0.001	0.004	0.012	0.026	0.032
WHU22S	0.000	0.001	0.003	0.009	0.025	0.054	0.066
TIM6	0.001	0.003	0.005	0.015	0.049	0.117	0.139
SPW5	0.013	0.021	0.027	0.033	0.061	0.111	0.134

参数类型	参数取值
参考重力场模型(GGM)	GOC6S、GGC16、TJ21S、WHU22S、TIM6、SPW5
核函数类型	Shannon、Blackman、Cubic polynomial (Cup)
航空重力数据的SRBF展开阶次	161～1500
GGM重力数据的SRBF展开阶次	161～280、161～300

展开阶次	GGM	核函数	Mean	STD	GGM	核函数	Mean	STD
280	GOC6S	Shannon	－0.087	0.111	GGC16	Shannon	－0.088	0.112
		Blackman	－0.100	0.115		Blackman	－0.101	0.116
		Cup	－0.099	0.120		Cup	－0.100	0.121
	TJ21S	Shannon	－0.088	0.112	WHU22S	Shannon	－0.093	0.111
		Blackman	－0.101	0.115		Blackman	－0.102	0.114
		Cup	－0.099	0.120		Cup	－0.100	0.120
	TIM6	Shannon	－0.087	0.111	SPW5	Shannon	－0.097	0.105
		Blackman	－0.100	0.115		Blackman	－0.100	0.115
		Cup	－0.099	0.120		Cup	－0.103	0.118
300	GOC6S	Shannon	－0.078	0.120	GGC16	Shannon	—	—
		Blackman	－0.116	0.136		Blackman	—	—
		Cup	－0.120	0.142		Cup	—	—
	TJ21S	Shannon	－0.074	0.121	WHU22S	Shannon	－0.079	0.119
		Blackman	－0.100	0.137		Blackman	－0.109	0.134
		Cup	－0.103	0.147		Cup	－0.113	0.146
	TIM6	Shannon	－0.081	0.120	SPW5	Shannon	－0.084	0.113
		Blackman	－0.118	0.132		Blackman	－0.104	0.128
		Cup	－0.122	0.146		Cup	－0.104	0.133

重力数据	Max	Min	Mean	STD
δg(x_air)	82.65	－80.02	－5.18	29.36
δg_res(x_air)	68.85	－63.48	0.16	20.49
δg(x_SPW5)	53.34	－65.04	－5.16	28.94
δg_res(x_SPW5)	47.63	－47.66	－0.95	18.86

模型	模型构成		Max	Min	Mean	STD
模型	参考场	剩余场	Max	Min	Mean	STD
GCM1	GOC6S(0～160)	Air(161～1500)＋GOC6S (161～280)	0.125	－0.320	－0.087	0.111
GAM1	GOC6S(0～160)	Air(161～1500)	0.196	－0.344	－0.070	0.128
GCM2	GGC16 (0～160)	Air (161～1500)＋GGC16 (161～280)	0.116	－0.312	－0.088	0.112
GAM2	GGC16(0～160)	Air(161～1500)	0.193	－0.346	－0.072	0.127
GCM3	TJ21S (0～160)	Air (161～1500)＋TJ21S (161～280)	0.145	－0.330	－0.088	0.112
GAM3	TJ21S (0～160)	Air(161～1500)	0.196	－0.342	－0.068	0.128
GCM4	WHU22S (0～160)	Air (161～1500)＋WHU22S (161～280)	0.140	－0.350	－0.093	0.111
GAM4	WHU22S (0～160)	Air(161～1500)	0.194	－0.342	0.070	0.127
GCM5	TIM6(0～160)	Air (161～1500)＋TIM6(161～280)	0.117	－0.311	－0.087	0.111
GAM5	TIM6(0～160)	Air(161～1500)	0.196	－0.340	－0.068	0.127
GCM6	SPW5(0～160)	Air (161～1500)＋SPW5(161～280)	0.102	－0.336	－0.097	0.105
GAM6	SPW5(0～160)	Air(161～1500)	0.196	－0.341	－0.068	0.127