局部地形改正的奇异积分研究

Research on the singular integral of local terrain correction computation

现有的地形改正积分核函数存在奇异现象,使得积分在奇异点处不连续.针对此问题,本文提出了采用高斯积分法与核函数项增加常数因子级数展开法来解决这一难题,并推导了高斯积分法处理奇异积分的公式及含可选小常数的地形改正的严密级数展开式.同时文中采用最新公布的3″×3″高分辨率的SRTM3地形数据代替传统的GTOPO30数据计算地形改正,结合实际算例确定了地形改正数的级数展开式的可选次项和最佳常数以及高斯积分法的最佳内外圈半径,并详细讨论了两种奇异积分处理方法和两种分辨率的地形数据对地形改正的影响.

The existing kernel of terrain correction （TC） computation is singular, which makes the integration discontinuous at the singular points. To solve this problem, Gaussian quadrature and the method of adding a constant factor to the kernel function are adopted to compute TC, and the function of Gaussian quadrature and the rigorous series expansion of the TC with a constant factor to the kernel function are derived in detail. In the paper, the latest SRTM3 data with high resolution （3＂X 3＂） instead of GTOPO30 data are employed to calculate the TC, and a number of numerical examples are used to determine the choices of terms and constant of series expansion and the best inner and outer radii for Gaussian quadrature. Furthermore, the effect of the different singular integral methods and different DTM data on the TC is discussed.