泊松积分通常用于把重力值从地球表面转化到大地水准面 (即称之为重力向下延拓 )的过程中。由于这是一个反问题 ,一些数字技术比如将积分离散化为一个线性方程组是必需的。目前 ,已经提出了两种离散化方案(单点和双重平均 )。虽然这两种方案在数学上都是可解的 ,但用它们处理相同的输入地面重力值时 ,却得出不同的大地水准面上的重力值。这种差异的产生是由于对泊松核函数的不同离散化方法造成的 ,而且这一问题尚未引起足够的关注。实际上 ,数学上的可解性并不能保证得到正确的解。问题在于此方程组是否构成得很好 ,或者说 ,离散化是否合理。因而本文研究泊松积分的离散方法。为此目的 ,本文提出一个单点平均的方案来对泊松积分进行估值。单点平均方案基本上与双点平均方案是相同的 ,但它在计量上更为简单 ,因为其计算工作大为减少。比较单点和双点平均方案后表明 ,对于一个有限的地表网格范围情况 ,单点离散方案会带来严重的理论问题 ,因为会相当大地低估大地水准面上的重力值甚至在极端情况时会给出不正确的结果。我们得到 ,仔细构成离散方程组的系数矩阵比应用单点重力值作为输入远为重要 Poisson integrals are commonly used to convert gravitational values ​​from the Earth's surface to the geoid (known as the downward extension of gravity). Since this is an inverse problem, some digital techniques, such as discretizing the integrals into a system of linear equations, are necessary. Currently, two discretization schemes (single point and double averaging) have been proposed. Although both solutions are mathematically solvable, using them to process the same input gravitational values ​​results in different gravimetric values ​​on the geoid. This discrepancy arises due to different discretization methods for the Poisson kernel function, and this issue has not attracted enough attention. In fact, mathematic solvability does not guarantee a correct solution. The question is whether the equations are well-formed, or whether the discretization is reasonable. Therefore, this paper studies the discrete method of Poisson integral. For this purpose, a single-point averaging scheme is proposed to estimate Poisson integrals. The single-point averaging scheme is basically the same as the two-point averaging scheme, but it is much simpler in terms of metrology because its computational effort is greatly reduced. Comparing the single-point and double-point averaging schemes shows that for a limited range of surface grids, the single-point dispersion scheme poses a serious theoretical problem because the gravimetric values ​​on the geoid can be considerably underestimated, even in extreme situations Will give incorrect results. We get that it is far more important to construct the coefficient matrix of a discrete system of equations than to use a single point of gravitation as input