Abstract
The “non-harmonicity” problem in residual terrain modelling (RTM) is a challenging issue, causing errors exceeding 200 mGal in the RTM gravity anomaly in rugged areas. Although various methods have been proposed to address this problem, including the condensation method, regularized downward continuation methods with Taylor series expansions (TS) and spherical harmonics (SH), complete harmonic correction (HC) method, closed-form complete HC method, and Kadlec's method, their performances in gravity field determination have not been directly validated. In this study, we reviewed and evaluated these methods, especially for their performance in regional geoid determination. We found that the HC's expression for the closed-form complete method is identical to that under the unlimited Bouguer plate approximation, and Kadlec’s method is equivalent to the condensation method with the same approximation for Bouguer masses. However, the HC associated with the complete HC method shows large differences compared to other methods. This is because the upward and downward continuations in the complete HC method consider an Earth with changing total mass. To address it, we propose a new three-step approach, proved to be equivalent to the HC using the TS method. Then the performance of various HC methods is evaluated in gravity anomaly synthesis and geoid determination over a select region in Colorado, USA. The best result is achieved when using the SH method to compute RTM gravity anomalies, resulting in a geoid accuracy of ~ 1.62 cm. Involving the HC for the height anomaly in the restore procedure slightly improves the accuracy to ~ 1.56 cm.
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Acknowledgements
Meng Yang was supported by the National Natural Science Foundation of China (Grant No. 42104083), and the Natural Science Foundation of Guangdong Province, China (Grant No. 2021A1515011425). Miao Lin was supported by the National Natural Science Foundation of China (Grant No. 42004009). We are grateful for internal and constructive reviews by Prof. Roland Klees, Dr. Dennis Milbert and Dr. Blažej Bucha, and by the anonymous reviewers of the manuscript.
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Yang, M., Li, X., Lin, M. et al. On the harmonic correction in the gravity field determination. J Geod 97, 106 (2023). https://doi.org/10.1007/s00190-023-01794-2
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DOI: https://doi.org/10.1007/s00190-023-01794-2