航空重力梯度地形改正

doi:10.11947/j.AGCS.2024.20230342

摘要/Abstract

摘要：

地形改正是航空重力梯度数据处理的重要环节，其改正精度不仅取决于地形精度和分辨率，还与改正模型有关。本文基于棱柱积分公式研究了地形精度和分辨率、观测点高程误差对地形改正的影响，导出了一种量化评估模型。为了在不降低改正精度的前提下提高计算效率，设计了一种基于CUDA的棱柱积分并行算法，在GPU端实现了地形改正分量的快速计算。分别在地形起伏平缓和剧烈区域进行模型验证，结果表明，当测量高度大于40 m时，精度优于0.5 m的10 m分辨率地形数据可使地形改正精度优于1 E，验证了本文量化评估模型的有效性。棱柱积分并行算法在普通GPU显卡上实现了15倍以上的效率提升，在NVIDIA TiTan V专业计算显卡上效率提升了150倍以上，完全能够满足大范围高精度地形改正应用需求。本文的量化评估模型和并行算法可为航空重力梯度测量任务设计和数据处理提供参考。

关键词: 航空重力梯度, 地形改正, 高程精度, 量化评估模型, GPU并行计算

Abstract:

Terrain correction is a critical part for airborne gravity gradient data processing, the quality of which is not only depends on elevation resolution and accuracy, but also related to the correction model. Based on the prism integration method, this paper studies the effects of terrain accuracy and resolution, and survey height error on the terrain correction results, then derived an evaluation model. To accelerating calculation of terrain correction without any approximations that may lead to a loss of accuracy, the prism method was parallelized on Nvidia's GPU card based on CUDA interface. Our model and paralleled algorithm were validated in both moderate and rugged terrain. The result shows that a 10 m resolution terrain dataset with accuracy better than 0.5 m can guarantee the terrain correction accuracy better than 1 E when survey altitude is higher than 40 m. Meanwhile, the parallel algorithm achieves speedup of a factor of 15 on consumer GPU and a factor of 150 on professional GPU, which helps to quickly accomplish terrain corrections even in large survey areas. We confirm that our model, a simple analytic formula, presents a clear guideline for both position and terrain requirements in gravity gradient survey, our parallel algorithm proves to be practical and dramatically reduce the calculation cost while retaining the accuracy.

Key words: airborne gravity gradiometry, terrain corrections, elevation accuracy, evaluation model, GPU parallel computing

中图分类号:

P223

黄佳喜, 边少锋, 纪兵. 航空重力梯度地形改正[J]. 测绘学报, 2024, 53(8): 1540-1551.

Jiaxi HUANG, Shaofeng BIAN, Bing JI. Terrain corrections for airborne gravity gradiometry[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(8): 1540-1551.

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t	N	δT_xx	δT_xy	δT_xz	δT_zz
1	1000	57.12kδh/H_min	28.47kδh/H_min	55.81kδh/H_min	93.35kδh/H_min
1/2	2000	29.87kδh/H_min	17.21kδh/H_min	34.4kδh/H_min	48.78kδh/H_min
2/5	2500	24.29kδh/H_min	14.02kδh/H_min	28.04kδh/H_min	39.66kδh/H_min
1/3	3000	20.44kδh/H_min	11.8kδh/H_min	23.6kδh/H_min	33.37kδh/H_min
1/4	4000	15.48kδh/H_min	8.94kδh/H_min	17.87kδh/H_min	25.28kδh/H_min
1/5	5000	12.44kδh/H_min	7.18kδh/H_min	14.36kδh/H_min	20.31kδh/H_min

研究区域	地形高程/m				飞行高度/m				观测点数量
研究区域	max	min	mean	std	max	min	mean	std	观测点数量
Kauring	358	202	263	29	173	41	66	12	394 893
Great Sand_A	2995	2351	2522	102	225	41	81	13	28 4571
Great Sand_B	2994	2360	2451	89	287	24	46	21	20 3540

高程精度/m	Kauring(内、中、外区半径：1.6、4、10 km)			Great Sand A(内、中、外区半径：2、6、15 km)			Great Sand B(内、中、外区半径：1.6、6、12 km)
高程精度/m	min	max	RMS	min	max	RMS	min	max	RMS
0	－1.08	0.60	0.33	－2.78	1.19	0.18	－1.19	1.75	0.22
0.25	－1.40	1.36	0.37	－2.81	1.14	0.21	－2.52	2.38	0.46
0.50	－2.44	2.23	0.48	－2.82	1.90	0.29	－4.47	4.95	0.84

研究区域	观测点数	平台1(CPU：i9－9900k@3.6 GHzGPU: NVIDIA TITAN V)			平台2(CPU：i7－10750H@2.6 GHzGPU: NVIDIA GTX 1650Ti)
研究区域	观测点数	CPU串行	GPU并行	加速比	CPU串行	GPU并行	加速比
Kauring	5000	650.6 s	3.7 s	175.8	757.0 s	47.1	16.1
Kauring	全部	约14 h	4.3 min	—	约16 h	约1 h	—
Great Sand_A	5000	963.2 s	4.8 s	200.1	1 406.0 s	92.7 s	15.2
Great Sand_A	全部	约15 h	4.3 min	—	约22 h	约1.4 h	—
Great Sand_B	5000	831.7 s	4.7 s	177	1 255.7 s	80.1 s	15.7
Great Sand_B	全部	约9 h	2.9 min	—	约14 h	约0.9 h	—