一种重力异常向下延拓的球谐分析迭代方法研究  

Analytical downward continuation of gravity anomaly based on global spherical harmonic expansion iteration

作　　者：丁子凡 李建成[1] 徐新禹[1] DING Zifan;LI Jiancheng;XU Xinyu(School of Geodsy and Geomatics,Wuhan University,Wuhan 430079,China)

机构地区：[1]武汉大学测绘学院,武汉430079

出　　处：《测绘科学》2022年第10期8-14,共7页Science of Surveying and Mapping

摘　　要：针对物理大地测量学中经典的向下延拓问题,该文尝试全球球谐分析和泰勒级数展开的思路实现航空重力异常的向下解析延拓。首先使用泰勒公式构建向下延拓的迭代结构,随后使用球谐分析方法分析了重力异常数据,并据此求解了其各阶导数,从而实现向下延拓的迭代计算。模拟实验的结果表明,在延拓高度为8000 m,且加入了标准差为2 mGal白噪声的情况下,模拟重力异常的向下延拓误差的均方差为5.58 mGal,证明了该方法的可行性与有效性;使用该方法将台湾地区5156 m高度处实测航空重力异常数据向下延拓至地面重力数据点处,向下延拓误差的均方差为9.37 mGal,该结果与加入地形改正的最小二乘配置法延拓结果的精度相当。Aiming at the downward continuation problem which is a classical problem in physical geodesy,this paper tried a method based on the global spherical harmonic expansion and Taylor expansion,for analytic downward continuation of the airborne gravity anomaly.Firstly,Taylor’s formula was used to build an iterative structure for downward continuation.Then the gravity anomaly data was analysed by global spherical harmonic expansion,and accordingly its derivations was solved to realize the iterative computation of downward continuation.The result of the numerical simulated experiment showed that when the continuation height was 8000 m and the standard deviation of the white noise was 2 mGal,the root mean square of downward continuation error of the simulated gravity anomaly was 5.58 mGal,which proved that the method was feasible and effective.The measured airborne gravity anomaly at 5156 m in Taiwan district was downward continued to the position of the land gravity data points by this method.The root mean square of continuation error was 9.37 mGal,which was close to the result by least square collocation method with terrain correction.

关 键 词：球谐函数 向下延拓 泰勒展开 垂直梯度 

分 类 号：P223.4[天文地球—大地测量学与测量工程]