摘要
Abstract
The Poisson integral is usually used to transfer gravity from the topographic surface to the geoid in a so-called downward continuation of gravity. Since it is an inverse problem, numerical techniques, such as discretization of the integral into a system of linear equations, are necessary. Two (point and double mean) discretization schemes of the Poisson integral have been proposed to date. Although the two schemes are mathematically solvable, they produce different gravity on the geoid for the same input data (gravity on topography). This discrepancy arises because of different discretization techniques of the Poisson kernel; still, this problem has not received adequate attention. Actually, the mathematical solvability does not ensure a correct solution. The question is whether the system is well structured, or, whether the discretization is reasonable. Methods to discretize the Poisson integral are investigated in this study. For this purpose, a new single mean scheme is presented to evaluate numerically the Poisson integral. The single mean scheme is basically the same as the double one, but it is numerically simpler since it greatly reduces numerical effort. A comparison between the point and mean schemes shows that, for a limit topographical grid size, the point discretization scheme results in a serious theoretical problem since it greatly underestimates gravity on the geoid, and even gives incorrect results for extreme cases. A careful construction of the coefficient matrix for the discrete system is much more important than using point gravity as input.关键词
重力/向下延拓/泊松积分/离散化方案/大地水准面Key words
gravity/downward continuation/Poisson integral/discretization scheme/geoid分类
天文与地球科学
