Harmonic Correction in Regional Gravity Field Determination

The “non-harmonicity” problem, as one of the main problems in the residual terrain modelling (RTM) method, would involve more than 200 mGal errors in the gravity field determination over the Himalaya area. To deal with it, there are five main harmonic correction (HC) methods, i.e., the condensation method, regularized downward continuation method with Taylor series expansions (TS), regularized downward continuation method with spherical harmonics (SH), complete HC method, and Kadlec's method, being provided in previous studies. However, their performances in gravity field determination are not studied nor compared directly yet. In this study, all these five HC methods are completely reviewed and evaluated, especially their performances in regional geoid determination. The expressions of HCs under various approximations are derived, and the Kadlec’s method is proved to be equivalent to the condensation method when adopting the same approximation for Bouguer masses. For the continuation methods, the HC associated with the complete method shows large differences compared to the HC associated with TS and SH methods. This is caused by the fact that the continuation process within the complete method is implemented in the situation of the Earth’s masses being changed. To cope with this problem, we promote a new three-step approach for computing the HC which is proved to be equivalent to the HC using the TS method. Then the HCs with various methods are completely considered and evaluated in the Colorado geoid determination using the remove-compute-restore technique. The best performance is achieved when the SH method is adopted for computing the RTM corrections to gravity anomaly in the removal procedure. The accuracy of the calculated geoid height is ~1.62 cm. Involving HCs for geoid height in the restore procedure would slightly improve the results to an accuracy of ~1.56 cm.