Some numerical quadrature for singular integral of the altimetry gravity in the innermost area - ZONG Jingwen (Surveying and Mapping Press, 2021)
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.