Impacts of Using the Rigorous Topographic Gravity Modeling Method and Lateral Density Variation Model on Topographic Reductions and Geoid Modeling: A Case Study in Colorado, USA

• Published in: Surveys in geophysics Vol. 43; no. 5; pp. 1497 - 1538
• Main Authors: Lin, Miao, Li, Xiaopeng
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2022; Springer Nature B.V
• Subjects: Approximation; Astronomy; Benchmarks; Computation; Computational efficiency; Computer applications; Computing time; Density; Earth and Environmental Science; Earth Sciences; Geoid; Geoids; Geophysics/Geodesy; Gravity; Leveling; Mathematical analysis; Methods; Modelling; Observations and Techniques; Reduction; Standard deviation; Terrain models; Topography; Variation; United States > US; Colorado; Residual terrain modeling; Lateral density variation; Parallel computation; Geoid determination; Topographic reduction; Tesseroids
• ISSN: 0169-3298; 1573-0956
• DOI: 10.1007/s10712-022-09708-1

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 .