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In local quasi-geoid modeling, the residual terrain modeling (RTM) method is often used to remove short-wavelength gravity field signals from the measured gravity on the ground in order to obtain a regularized and smooth gravity field that is suited for field interpolation and modeling. Accurate computation of RTM corrections plays a crucial role in computing an accurate local quasi-geoid, and it requires a set of fine-tuned parameters, including the combination of DEMs with different resolutions for suitably representing the real topography, the choice of integration radius for properly defining the extent of the computation zone, and the determination of reference topography to properly describe the RTM-reduced Earth's surface. To our knowledge, this has not been systematically documented, despite its obvious importance. This study aims to systematically investigate the impact of these factors on RTM correction computation and, consequently, on local quasi-geoid modeling to provide practical guidelines for real-world applications. The tesseroid-based gravity forward modeling technique is employed to investigate the following issues existing in the practical use of the RTM method: ① Can the combination of a high-resolution DEM and a DEM with a lower resolution replace the single use of the high-resolution DEM for RTM correction computation while maintaining accuracy and improving efficiency? If it does, how do I properly choose the resolution of this coarse DEM as well as the integration radius r1 for the inner zone and r2 for the outer zone? ② How large would the differences between the RTM corrections computed by three types of reference topographies, which are obtained from the direct averaging (DA) approach, the moving averaging (MA) approach, and the spherical harmonic (SH) approach, be, and how large would their impact on quasi-geoid modeling be? To obtain objective findings, two research regions were selected for this investigation. One is the Colorado test area (USA) with rugged terrain, and the other is the Auvergne test area (France) with moderate terrain. The main numerical findings are: (1) the combination of the 3" resolution DEM (inner zone) and the 30″ resolution DEM (outer zone) is sufficient for accurate and efficient RTM correction computation; (2) if the resolution of the reference topography is 5′ or slightly lower, all three types of reference topographies are able to obtain local quasi-geoid models at a similar accuracy level, while the values of r1 and r2 are preferred to be at least 20 km and 111 km, respectively; (3) if the reference topography has a resolution of 30′ or lower, the MA or SH reference topography is recommended, especially for the latter one, and the values of r1 and r2 are suggested to be at least 20 km and 222 km, respectively. The above numerical findings can be taken as a reference for local quasi-geoid determination in areas with different topographic regimes than the two selected test areas. [ABSTRACT FROM AUTHOR]

Until now, the prismatic mass approximation of the topography and the constant density assumption have been mostly utilized in topographic reductions, which are rough approximations of reality and can be avoided. In this study, the more rigorous tesseroidal mass representation of topographic masses and the global lateral topographic density variation model UNB_TopoDens are considered in topographic reductions. Three tesseroidal modeling methods based on different combinations of numerical tesseroidal approaches are developed for precise topographic gravity modeling. The computational performances of the classic prismatic modeling method and new tesseroidal modeling methods in computing the residual terrain modeling (RTM), terrain correction (TC), full topographic, and Airy-Heiskanen (AH) model-based isostatic effects are tested in the Colorado area with rugged topography. In addition, the improvement of computational efficiency achieved by applying the OpenMP parallelizing technique and the contribution of considering the UNB_TopoDens model are investigated. Then, the RTM effects are applied to local geoid modeling to see the geoid model changes caused by using rigorous tesseroidal modeling methods and by considering lateral density variations. The main numerical findings are: (1) The application of the OpenMP parallelization can significantly reduce the computational time, while the efficiency improvement rate depends on the number of used threads; (2) The modeling method effect on the computation of the RTM, TC, full topographic, and AH isostatic effects is smaller than the lateral density variation effect; (3) In the case of using the RTM reduction, the use of the tesseroidal modeling method instead of the prismatic modeling method can cause geoid model differences at the millimeter level, while almost the same standard deviations are obtained by comparing the geoid models to the GSVS17 and historical GNSS-leveling data; (4) the differences in the geoid height due to lateral density variations can reach a magnitude of about 8 cm when using the RTM reduction scheme, while the validation of geoid models at the GSVS17 GNSS-leveling benchmarks revealed that the geoid considering the UNB_TopoDens model has a slightly larger standard deviation than the one using a constant density of 2.67 g / cm 3 . [ABSTRACT FROM AUTHOR]

"The first author Miao Lin was financially supported by the National Natural Science Foundation of China (Grant No. 42004009)" The Acknowledgements section should be: B Acknowledgements b We thank two anonymous reviewers for their constructive comments that helped to significantly improve the quality of this manuscript. The first author Miao Lin was financially supported by the National Natural Science Foundation of China (Grant No. 42004009). [Extracted from the article]