局部地形改正快速计算的GPU并行的棱柱法

doi:10.11947/j.AGCS.2020.20190403

摘要/Abstract

摘要： 在重力归算中，局部地形改正在重力勘探、地壳结构分析和大地水准面计算等领域有着重要意义，但严格棱柱体积分公式计算效率低，而快速计算公式则会降低计算精度。本文利用CUDA并行编程平台，提出一种地形格网重新编码和严格棱柱体积分八分量拆解方法，实现了基于CPU+GPU异构并行技术的严格棱柱体积分计算地形改正快速并行算法，克服了GPU各个线程计算任务分配和线程计算超载问题，解决了局部地形改正的高分辨率、高精度严密公式的快速计算难题。通过试验，在显卡型号为Tesla V100的计算机上进行4°×6°范围，积分半径40'和分辨率1'的局部地形改正计算仅需1.5 s；分辨率10″的局部地形改正计算仅需14.6 min；进行分辨率3″的地形改正计算耗时45.7 h，而传统串行算法则难以完成计算。在保证微伽级以上计算精度的条件下，计算加速比最高达到850倍以上，有效缩短了计算耗时，提高了计算效率。本文还依据上述并行算法对全国范围地形改正量进行计算。结果表明，我国地形改正量普遍低于80 mGal（1 Gal=10^-2 m/s²），平均值1.83 mGal，最大值达到196 mGal。

关键词: 地球重力场, 局部地形改正, GPU, CUDA, 严格棱柱体积分, 加速比

Abstract: In gravity reduction, local topographic correction is of great significance in the fields of gravity exploration, crustal structure analysis and geoid calculation. However, the calculation efficiency of strict prism formula is low, while the calculation accuracy of fast formula will be reduced. In this study, it is proposed that a method of topographic grid re-encoding and an eight-component strict prism integral disassembly using a CUDA parallel programming platform which realizes a fast parallel algorithm of topographic correction based on CPU+GPU heterogeneous parallel technology. The problem of task allocation and thread overload in each thread of GPU is effectively solved. And the high score of local topographic correction is solved. The results of this study provide a rigorous, fast, and accurate solution for high-resolution and high-precision topographic correction. Experimental verification shows that it takes only 1.5 s to calculate the local topographic correction in the range of 4°×6°, with the integral radius of 40' and the resolution of 1' using Tesla V100, and only 14.6 min to calculate the local topographic correction with 10″ resolution and 40 minute integral radius. It takes 45.7 h to calculate the 3″ resolution, while the traditional serial algorithm is difficult to complete the calculation. Under the condition of guaranteeing the accuracy above the micro-Gal level, the acceleration ratio of calculation can reach more than 850 times, which effectively shortens the calculation time and improves the calculation efficiency. Based on the parallel algorithm mentioned above, the topographic correction in China is calculated. The result shows that the topographic correction in China is generally lower than 80 mGal (1 Gal=10^-2 m/s²), with an average of 1.83 mGal and a maximum of 196 mGal.

Key words: earth's gravity field, local topographic correction, GPU, CUDA, rigorous prism integration, acceleration ratio

中图分类号:

P228

黄炎, 王庆宾, 冯进凯, 邢志斌, 范雕, 谭勖立, 吕明昊. 局部地形改正快速计算的GPU并行的棱柱法[J]. 测绘学报, 2020, 49(11): 1430-1437.

HUANG Yan, WANG Qingbin, FENG Jinkai, XING Zhibin, FAN Diao, TAN Xuli, LÜ Minghao. Rapid calculation of local topographic correction based on GPU parallel prism method[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(11): 1430-1437.

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