测高重力异常中央区奇异积分数值求积公式

Some numerical quadrature for singular integral of the altimetry gravity in the innermost area

为简化逆Stokes法和逆Vening-Meinesz法反演中央区重力异常计算过程,提高计算效率,本文采用数值求积公式,分别利用Simpson公式和Cotes公式对逆Stokes法和逆Vening-Meinesz法中的奇异积分问题进行了新的研究,系统地推导出了中央区重力异常普适数值积分计算公式。在大地水准面高和垂线偏差理论模型下的分析表明,此公式可直接利用格网节点处的大地水准面高和垂线偏差计算重力异常值,形式简单,计算效率高,计算精度与解析法计算结果精度相当,可以满足实际应用。研究结果可为高精度卫星测高反演重力异常提供基础理论依据。

In order to simplify the calculation process and improve the calculation efficiency of inverse Stokes formula method and the inverse Vening-Meinesz formula method to invert the gravity anomaly,the numerical quadrature method is adopted.A new study on the investigation of singular integral of inverse Stokes formula and inverse Vening-Meinesz formula based on Simpson formula and Cotes formula is done and the formula of gravity anomaly in innermost area are derived systematically.The analysis based on the theoretical model of geoidal height and vertical deflections shows that the formula can directly use the geoid height and vertical deviation at the grid node to calculate the gravity anomaly which have simple form,high precision and high calculation efficiency.These research results can provide theoretical basis for high-precision satellite altimetry inversion of gravity anomalies.