缔合Legendre函数的快速插值计算及其在六边形网格模型重力异常计算中的应用  

A fast method for interpolation of the associated Legendre functions and its application to the calculation of local hexagonal grid point gravity anomalies using an ultra-high-degree gravity field model

作　　者：李新星[1,2,3] 范昊鹏 万宏发 范雕 冯进凯 LI Xinxing;FAN Haopeng;WAN Hongfa;FAN Diao;FENG Jinkai(Institute of Geospatial Information,Information Engineering University,Zhengzhou 450001,China;State Key Laboratory of Geo-information Engineering,Xi an 710054,China;Key Laboratory of Smart Earth,Beijing 100020,China)

机构地区：[1]信息工程大学地理空间信息学院,河南郑州450001 [2]地理信息工程国家重点实验室,陕西西安710054 [3]智慧地球重点实验室,北京100020

出　　处：《测绘学报》2024年第9期1737-1747,共11页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(U23A2028,41404020,42174007,42074013);地理信息工程国家重点实验室基金(SKLGIE2023-Z-1-1);中国地质大学(武汉)中央高校基本科研业务费(2024XLB13)。

摘　　要：鉴于局部区域非等纬度分布点的超高阶次球谐综合计算效率较低,本文深入研究了缔合Legendre函数的插值算法,结合模型重力异常求解的展开式,提出了超高阶模型空间重力异常插值快速计算方法,为了验证本文方法在东西狭长分布的点集更具有应用优势,采用球谐旋转变换技术进一步提升了计算效率。试验结果表明,利用2160阶次EGM2008模型计算日本地区同一高度的30303个非等纬度分布的六边形网格点处模型重力异常,插值快速计算方法相比逐点计算,在误差不超±0.005 mGal水平下,计算耗时从3669.41 s缩减到98.05 s,同时经过球谐旋转变换,将南北狭长的日本区域点集旋转为东西狭长分布,使得上述相应计算内容的耗时进一步由98.05 s缩减到19.06 s,计算效率相比最初方法提速比达到近200倍,有效解决了非等纬度分布点的超高阶模型重力异常快速解算的效率难题,且验证了该方法在东西狭长分布的情况下具有更高的提速比。In view of the low efficiency of the calculation of ultra-high-degree spherical harmonic synthesis for non-equal latitude distributed points of regional area,this article has conducted a deep research on the interpolation algorithm of associated Legendre functions.Combined with the harmonic expansion of the model gravity anomaly,a fast calculation method using interpolation was proposed for ultra-high-degree model free-air gravity anomaly.In order to verify the advantages of this new method over point sets with narrow distribution from east to west,the efficiency of the new method was further improved by adopting the spherical harmonic rotation(SHR)technology.The experimental results showed that the proposed method using interpolation reduced the calculation time from 3669.41 s to 98.05 s compared with point-by-point approaches,with errors not exceeding±0.005 mGal,when we used EGM2008 model up to 2160 degree and order to achieve the model free-air gravity anomalies of 30303 hexagonal grid points at the same height level in Japan with non-equal latitude distribution.Meanwhile,by applying SHR and rotating these points distributed in the north-south direction to the east-west direction,the time consumption for the corresponding solution was further reduced from 98.05 s to 19.06 s,with a speed-up ratio of nearly 200 times to the original method.The method proposed in this article effectively solves the problem of low efficiency in solving ultra-high-degree model free-air gravity anomalies for regional non-equal latitude distributed points,and has a higher computing speed-up effect in the case of east-west elongated distribution.

关 键 词：地球重力场模型 球谐综合 勒让德函数 六边形网格 球谐旋转变换 插值方法 

分 类 号：P223[天文地球—大地测量学与测量工程]