利用球谐分析方法构建局部重力场模型的可行性分析  

Feasibility analysis of constructing a regional gravitational model using the method of spherical harmonics analysis

作　　者：李新星 冯进凯[2] 范昊鹏 刘晓刚 范雕[2] 李姗姗 LI XinXing;FENG JinKai;FAN HaoPeng;LIU XiaoGang;FAN Diao;LI ShanShan(State Key Laboratory of Geographic Information Engineering,Xi'an 710054,China;Institude of Geospatial Information,Information Engineering University,Zhengzhou 450001,China;Key Laboratory of Smart Earth,Beijing 100020,China;Xi'an Research Institute of Surveying and Mapping,Xi'an 710054,China)

机构地区：[1]地理信息工程国家重点实验室,西安710054 [2]信息工程大学地理空间信息学院,郑州450001 [3]智慧地球重点实验室,北京100020 [4]西安测绘研究所,西安710054

出　　处：《地球物理学进展》2025年第1期11-24,共14页Progress in Geophysics

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)联合资助.

摘　　要：局部重力场理论相关的技术问题包括大地水准面精化、重力异常向下延拓、局部模型构建等,均会面临着具有较强的边界效应、局部积分代替全球积分、近似计算、积分离散化误差等诸多问题.针对这些问题,本文利用块对角最小二乘方法快速实现超高阶次的球谐分析,并将其引入局部重力场数据的处理及模型的构建,同时使用中低阶卫星重力场模型和GNSS/水准测量数据作为控制,可做到5400阶的全球球谐分析完成2′分辨率的局部重力场的数据处理和建模,算法精度造成的重力异常误差<1 mGal、(似)大地水准面误差<1 cm、垂线偏差误差<0.4″.同时球谐分析还可用于航空重力异常数据的稳定向下延拓,是一种简单易操作的方法,在精度和稳定性方面具有非常好的表现,所以球谐分析方法在局部重力场建模和数据处理中值得推广应用.Technical methods related to the regional gravity fields,include precise geoid determination,downward continuation of gravity anomalies,and construction of regional models,which are greatly faced with challenges,such as low accuracy or efficiency,computation approximations,instability,and lack of criterion.This study introduces the fast implementation technique of ultra-high degree spherical harmonics analysis into the construction of regional gravity field,combined with satellite gravity field models of low to medium frequency spectrum and GNSS/leveling data.By employing a 5400-degree spherical harmonics analysis(SHA),it is possible to achieve a regional gravity field reconstruction with a resolution of 2 arc-minutes and an error less than 1 mGal for gravity anomalies,less than 1 cm for(quasi)geoid,and less than 0.4 arc-seconds for vertical deflection.Meanwhile,SHA can also be used for stable downward continuation of airborne gravity anomalies,which is verified to be more simple,accurate,and stable.Therefore,SHA is worth promoting and applying in the modeling of regional gravity fields and related data processing problems.

关 键 词：球谐分析 球谐综合 向下延拓 局部重力场 大地水准面 正常椭球 

分 类 号：P223[天文地球—大地测量学与测量工程]