基于后向递推与扩展指数的球谐域高斯滤波系数高精度计算方法  

A Precise Calculation Method of Gaussian Filtering Coefficients in Spherical Harmonic Domain by Backward Recursion and Exponent Extension

作　　者：钱博浩 杜劲松 王林松 张攀 彭桢燃 QIAN Bohao;DU Jinsong;WANG Linsong;ZHANG Pan;PENG Zhenran(School of Geophysics and Geomatics,China University of Geosciences,388 Lumo Road,Wuhan 430074,China;Hubei Subsurface Multi-Scale Imaging Key Laboratory,388 Lumo Road,Wuhan 430074,China;State Key Laboratory of Geological Processes and Mineral Resources,388 Lumo Road,Wuhan 430074,China)

机构地区：[1]中国地质大学(武汉)地球物理与空间信息学院,武汉市430074 [2]地球内部多尺度成像湖北省重点实验室,武汉市430074 [3]地质过程与矿产资源国家重点实验室,武汉市430074

出　　处：《大地测量与地球动力学》2023年第9期963-969,共7页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(42174090);地质过程与矿产资源国家重点实验室科技部专项(MSFGPMR2022-4)。

摘　　要：针对滤波半径较大、参考球面半径较小、球谐阶数较高时,传统高斯滤波球谐系数计算存在不稳定性的问题,将扩展指数法应用于高斯滤波球谐系数的后向递推计算。数值计算和实际应用均表明,该方法基本可实现在任何半径大小球面上、任意滤波半径的超高阶高斯滤波高精度计算。For the traditional calculation method for Gaussian filtering coefficient,when the filtering radius is large,the reference spherical radius is small,and the spherical harmonic order is high,there is often computational instability.In order to solve this problem,the extended exponential method is applied to the backward recursive calculation of the spherical harmonic coefficient of Gaussian filtering.The numerical calculation and practical applications show that,the method proposed in this paper realizes the high-precision computation of ultra-high-degree Gaussian filtering with arbitrary radius on any radius sphere.

关 键 词：球谐分析 高斯滤波 高斯平滑 后向递推 扩展指数 

分 类 号：P223[天文地球—大地测量学与测量工程]