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超高阶全球地形球谐系数模型的构建方法与实现

Design and implementation of ultra-high-degree spherical harmonic model of earth topography
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摘要 针对10800阶地形球谐系数模型构建的计算精度、计算稳定性及超大规模运算量等问题,本文首先通过比较分析矩形离散积分方法、Gauss-Legendre积分方法和Driscoll/Healy积分方法,验证了Driscoll/Healy积分方法具有更高的计算精度。然后,给出了改进的Belikov公式,将完全正常化缔和勒让德函数在全球范围内以优于10^(-12)精度高效、稳定递推至10800阶;提出了联合FFT和基于OpenMP的多核并行方法求解超高阶球谐系数的优化策略,显著提高了球谐系数模型构建的计算效率。最后,利用Earth2014_TBI与全球海底地形模型STO_IEU2020格网数据建立了全球10800阶地形球谐系数模型sph.10800_IEU,总体精度与Earth2014_TBI2014.shc相当,在试验海域的相对精度略优于模型Earth2014_TBI2014.shc。 Aiming at solving the problems of calculation accuracy,stability and the large scale operations in the construction of 10800 degree spherical harmonic of topography,the experiments were carried out.For the first part,Driscoll/Healy quadrature was proved to have higher computational accuracy by comparing and analyzing rectangular discrete quadrature,Gauss-Legendre quadrature and Driscoll/Healy quadrature.For the second part,a modified Belikov formula was given,which could make sure that fnALF is recursed to order 10800 with better accuracy than 10^(-12) in the full latitude range.Also,an optimization strategy was proposed for computing ultra-high-degree spherical harmonic coefficients by combining FFT and multi-core parallel technology based on OpenMP,which significantly improved the computational efficiency.For the last part,the 10800 degree spherical harmonic model of topography,sph.10800_IEU,whose overall accuracy was similar to Earth2014_TBI2014.shc,was established by using the grid data of model Earth2014_TBI and model STO_IEU2020,however,its relative precision in the experimental areas was proved slightly better than that of model Earth2014_TBI2014.shc.
作者 单建晨 李姗姗 范雕 李新星 黄炎 邢志斌 SHAN Jianchen;LI Shanshan;FAN Diao;LI Xinxing;HUANG Yan;XING Zhibin(Information Engineering University,Zhengzhou 450001,China;Troops 31201,Guangzhou 510080,China;University of Aerospace Engineering,Beijing 102200,China)
出处 《测绘学报》 EI CSCD 北大核心 2023年第5期748-759,共12页 Acta Geodaetica et Cartographica Sinica
基金 国家自然科学基金(42174007,42204009)。
关键词 地形球谐系数模型 Gauss-Legendre积分法 Driscoll/Healy积分法 矩形离散积分法 FFT OPENMP spherical harmonic model of topography Gauss Legendre quadrature Driscoll/Healy quadrature rectangular discrete quadrature FFT OpenMP
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