Convergence and optimal truncation of binomial expansions used in isostatic compensations and terrain corrections
Convergence and optimal truncation of binomial expansions used in isostatic compensations and terrain corrections
复制标题
用于均衡补偿和地形校正的二项展开式的收敛和最优截断
DOI：
10.1007/s001900000125
复制
发表时间：
2001
影响因子：
4.4
通讯作者：
L. Sjöberg
中科院分区：
文献类型：
--
作者：
Wenke Sun;L. Sjöberg
摘要：在大地测量研究中，二项式展开是一种强有力的工具。 它常用于地形校正和均衡补偿。研究了二项式展开式的性质、收敛性和截断性。通过理论分析和数值计算，讨论了地形高度H（或补偿深度）、球谐次数n和二项式级数项m之间的关系。根据该关系式，确定了一个截断数M，以获得1%的精度，即可以找到在实际计算中应该使用多少项（或地形的幂数）。
Abstract. A binomial expansion is a powerful tool in geodetic research. It is often used in terrain correction and isostatic compensation. The behaviour, convergence and truncation of the binomial expansion are investigated. The relation of the topographic height H (or the compensation depth), spherical harmonic degree n and the binomial series term m is discussed using theoretical and numerical results. According to the relation, a truncation number M is determined for obtaining an accuracy of 1%, i.e. it can be found how many terms (or power numbers of the topography) should be used in practical calculations.