基于球谐函数的重力异常和垂线偏差误差匹配关系

摘要

Gravity anomalies and vertical deflections are important products of altimetry satellites.The precision indexes of them are essential for the design of future altimetry satellites.In this paper, the spherical harmonic function is used to discuss the precisions of gravity anomaly and vertical deflections.Firstly, the approximate matching relationship between gravity anomaly and vertical deflection error is deduced theoretically.Then, six ultra-high degree gravity field models are used to verify the correctness of the conclusions.The results of numerical experiments show that the errors of vertical defections and gravity anomaly satisfy the approximate proportional relation, that is, if the precision of vertical deflection is 1μrad, the precision of gravity anomaly is about 1.4mGal.Conversely, if the precision of the gravity anomaly is 1mGal, the precision of the corresponding vertical deflection is about 0.7μrad.%重力异常和垂线偏差是测高卫星非常重要的产品.二者的精度指标对于未来的测高卫星方案设计至关重要.本文利用球谐函数来对重力异常和垂线偏差的精度指标进行讨论,首先从理论上推导了重力异常和垂线偏差误差的近似匹配关系,然后通过6个超高阶重力场模型验证了有关结论的正确性.数值试验表明:垂线偏差误差和重力异常误差满足近似的比例关系,即若垂线偏差各方位向等精度测量,且假定精度均为1μrad,则所对应的重力异常精度约为1.4mGal;反之,若重力异常的精度为1mGal,则所对应的垂线偏差的精度约为0.7μrad.