Least-squares modification of extended Stokes' formula and its second-order radial derivative for validation of satellite gravity gradiometry data

The gravity anomalies at sea level can be used to validate the satellite gravity gradiometry data. Validation of such a data is important prior to downward continuation because of amplification of the data errors through this process. In this paper the second-order radial derivative of the extended Stokes' formula is employed and the emphasis is on least-squares modification of this formula to generate the second-order radial gradient at satellite level. Two methods in this respect are proposed: (a) modifying the second-order radial derivative of extended Stokes' formula directly, and (b) modifying extended Stokes' formula prior to taking the second-order radial derivative. Numerical studies show that the former method works well but the latter is very sensitive to the proper choice of the cap size of integration and degree of modification.