全球及局部海洋扰动重力反演的快速解析方法

从经典边值问题理论及球谐函数理论出发,在空域推导获得了由大地水准面高以及垂线偏差计算扰动重力的解析计算公式,为利用卫星测高数据反演海洋扰动重力提供了理论基础。针对全球海洋区域和局部海洋区域的扰动重力反演,在前人已有工作基础上,提出了改进的基于一维FFT的精确快速算法,保证了计算结果与原解析方法完全一致,且计算速度提高约20倍。该算法在提高计算效率的同时避免了由于引入FFT而产生的混叠、边缘效应问题,而且对观测数据的序列长度没有硬性要求,使得应用更加灵活。利用EGM2008地球重力场模型分别生成了2.5'分辨率大地水准面高数据和垂线偏差数据,按照本文提出的改进方法(采用全球积分计算)分别反演获得了全球及局部海洋区域的扰动重力。经比较分析,由大地水准面和垂线偏差分别反演获得的扰动重力其差异在0.8×10^-5 m/s²以内,这说明两种反演方法是基本一致的,但在数据包含系统误差的情况下,由垂线偏差反演扰动重力具有一定优势。

The Analytical and Quick Computation Method of Disturbing Gravity in Global and Loca l Ocean Area

In order to solve the problem of deriving the disturbing gravity from satellite altimetry data,the analytical formula of disturbing gravity computed from geoid and vertical deflection are derived.The analytical formula can be used to get global ocean disturbing gravity by using altimetry data.Considering the existing achievements,the two improved quick computation methods which are respectively according to the global and local area are also get based on the one dimensional FFT algorithm.The quick computa-tion methods can get the same results as the analytical computation and improve the computation speed of 20 times.The precise,quick computation methods can avoid the problem of aliasing and edge effects and have the flexible application.The 2.5′resolution of geoid and vertical deflection derived from EGM2008 model are used to compute the global and local ocean disturbing gravity.The results show that the difference between two method is about 0.8×10-5 m/s2,so the disturbing gravity respectively derived from geoid and vertical deflection are consistent.Considering the actual situation,the disturbing gravity derived from vertical deflection sti l l has some advantages.