ORCID Profile
0000-0002-0556-0811
Current Organisation
University of Stuttgart
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Publisher: Springer Science and Business Media LLC
Date: 18-03-2023
DOI: 10.1007/S10712-023-09774-Z
Abstract: The spherical shell and spherical zonal band are two elemental geometries that are often used as benchmarks for gravity field modeling. When applying the spherical shell and spherical zonal band discretized into tesseroids, the errors may be reduced or cancelled for the superposition of the tesseroids due to the spherical symmetry of the spherical shell and spherical zonal band. In previous studies, this superposition error elimination effect (SEEE) of the spherical shell and spherical zonal band has not been taken seriously, and it needs to be investigated carefully. In this contribution, the analytical formulas of the signal of derivatives of the gravitational potential up to third order (e.g., V , $$V_{z}$$ V z , $$V_{zz}$$ V zz , $$V_{xx}$$ V xx , $$V_{yy}$$ V yy , $$V_{zzz}$$ V zzz , $$V_{xxz}$$ V xxz , and $$V_{yyz}$$ V yyz ) of a tesseroid are derived when the computation point is situated on the polar axis. In comparison with prior research, simpler analytical expressions of the gravitational effects of a spherical zonal band are derived from these novel expressions of a tesseroid. In the numerical experiments, the relative errors of the gravitational effects of the in idual tesseroid are compared to those of the spherical zonal band and spherical shell not only with different 3D Gauss–Legendre quadrature orders ranging from (1,1,1) to (7,7,7) but also with different grid sizes (i.e., $$5^{\\circ }\\times 5^{\\circ }$$ 5 ∘ × 5 ∘ , $$2^{\\circ }\\times 2^{\\circ }$$ 2 ∘ × 2 ∘ , $$1^{\\circ }\\times 1^{\\circ }$$ 1 ∘ × 1 ∘ , $$30^{\\prime }\\times 30^{\\prime }$$ 30 ′ × 30 ′ , and $$15^{\\prime }\\times 15^{\\prime }$$ 15 ′ × 15 ′ ) at a satellite altitude of 260 km. Numerical results reveal that the SEEE does not occur for the gravitational components V , $$V_{z}$$ V z , $$V_{zz}$$ V zz , and $$V_{zzz}$$ V zzz of a spherical zonal band discretized into tesseroids. The SEEE can be found for the $$V_{xx}$$ V xx and $$V_{yy}$$ V yy , whereas the superposition error effect exists for the $$V_{xxz}$$ V xxz and $$V_{yyz}$$ V yyz of a spherical zonal band discretized into tesseroids on the overall average. In most instances, the SEEE occurs for a spherical shell discretized into tesseroids. In summary, numerical experiments demonstrate the existence of the SEEE of a spherical zonal band and a spherical shell, and the analytical solutions for a tesseroid can benefit the investigation of the SEEE. The single tesseroid benchmark can be proposed in comparison to the spherical shell and spherical zonal band benchmarks in gravity field modeling based on these new analytical formulas of a tesseroid.
Publisher: American Geophysical Union (AGU)
Date: 2013
DOI: 10.1029/2023JB027157
Publisher: Informa UK Limited
Date: 08-03-2023
Publisher: Springer Science and Business Media LLC
Date: 07-2020
Publisher: Springer Science and Business Media LLC
Date: 22-01-2018
Publisher: Springer Science and Business Media LLC
Date: 07-2019
Publisher: Springer Science and Business Media LLC
Date: 27-09-2022
Publisher: Elsevier BV
Date: 09-2021
Publisher: Springer Science and Business Media LLC
Date: 27-10-2018
Publisher: Springer Science and Business Media LLC
Date: 13-05-2016
Publisher: Springer Science and Business Media LLC
Date: 07-2021
Publisher: Elsevier BV
Date: 07-2021
Publisher: Springer Science and Business Media LLC
Date: 26-08-2021
Publisher: Springer Science and Business Media LLC
Date: 29-06-2016
Publisher: Springer Science and Business Media LLC
Date: 2023
DOI: 10.1007/S00190-022-01673-2
Abstract: An accurate method with conditional split, double exponential quadrature rule, and numerical differentiation has been proposed in the paper “Accurate computation of gravitational field of a tesseroid” (Fukushima in J Geod 92(12):1371–1386, 0.1007/s00190-018-1126-2 , 2018) to compute the gravitational field (i.e. gravitational potential, gravitational acceleration vector, and gravity gradient tensor) of a tesseroid. This study presents the corrections for some formulas in the main paper and electronic supplementary material of Fukushima (J Geod 92(12):1371–1386, 0.1007/s00190-018-1126-2 , 2018). Moreover, the FORTRAN subroutines (or ) and (or ) in the original codes (or ) in double (or quadrature) precision provided by Fukushima (J Geod 92(12):1371–1386, 0.1007/s00190-018-1126-2 , 2018) are revised. The revised parts have impacts on the calculation of these components of the gravitational acceleration vector ( $$g_{\\varPhi }$$ g Φ and $$g_{\\varLambda }$$ g Λ ) and gravity gradient tensor ( $$\\varGamma _{\\varPhi \\varPhi }$$ Γ Φ Φ , $$\\varGamma _{\\varPhi \\varLambda }$$ Γ Φ Λ , $$\\varGamma _{\\varPhi H}$$ Γ Φ H , $$\\varGamma _{\\varLambda \\varLambda }$$ Γ Λ Λ , $$\\varGamma _{\\varLambda H}$$ Γ Λ H , and $$\\varGamma _{H H}$$ Γ HH ). The revised FORTRAN codes and in double and quadrature precision are presented at the GitHub website iaoledeng/xtess-xqtess . These revised FORTRAN codes can accurately compute the gravitational field of a tesseroid in double and quadrature precision no matter the computation point is located outside, near the surface of, on the surface of, or inside the tesseroid. They can be applied to calculate the gravitational field of the different layers (e.g. atmosphere, topography, crust, and mantle) of the Earth or other celestial bodies, which helps investigate the various geoscience applications, e.g. geoid determination in geodesy and gravity interpretation in geophysics.
Publisher: Springer Science and Business Media LLC
Date: 02-2023
DOI: 10.1007/S00190-023-01708-2
Abstract: In recent years, there are research trends from constant to variable density and low-order to high-order gravitational potential gradients in gravity field modeling. Under the research circumstances, this paper focuses on the variable density model for gravitational curvatures (or gravity curvatures, third-order derivatives of gravitational potential) of a tesseroid and spherical shell in the spatial domain of gravity field modeling. In this contribution, the general formula of the gravitational curvatures of a tesseroid with arbitrary-order polynomial density is derived. The general expressions for gravitational effects up to the gravitational curvatures of a spherical shell with arbitrary-order polynomial density are derived when the computation point is located above, inside, and below the spherical shell. When the computation point is located above the spherical shell, the general expressions for the mass of a spherical shell and the relation between the radial gravitational effects up to arbitrary-order and the mass of a spherical shell with arbitrary-order polynomial density are derived. The influence of the computation point’s height and latitude on gravitational curvatures with the polynomial density up to fourth-order is numerically investigated using tesseroids to discretize a spherical shell. Numerical results reveal that the near-zone problem exists for the fourth-order polynomial density of the gravitational curvatures, i.e., relative errors in $$\\log _{10}$$ log 10 scale of gravitational curvatures are large than 0 below the height of about 50 km by a grid size of $$15'\\times 15'$$ 15 ′ × 15 ′ . The polar-singularity problem does not occur for the gravitational curvatures with polynomial density up to fourth-order because of the Cartesian integral kernels of the tesseroid. The density variation can be revealed in the absolute errors as the superposition effects of Laplace parameters of gravitational curvatures other than the relative errors. The derived expressions are ex les of the high-order gravitational potential gradients of the mass body with variable density in the spatial domain, which will provide the theoretical basis for future applications of gravity field modeling in geodesy and geophysics.
Publisher: Springer Science and Business Media LLC
Date: 20-03-2022
Publisher: Springer Science and Business Media LLC
Date: 06-03-2022
Publisher: Copernicus GmbH
Date: 03-03-2021
DOI: 10.5194/EGUSPHERE-EGU21-1886
Abstract: & & We proposed an alternative method to determine the height of Mount Everest (HME) based on the shallow layer method (SLM), which was put forward by Shen (2006). We use the precise external global Earth gravity field model (i.e., EGM2008 and EIGEN-6C4 models) as input information, and the digital topographic model (i.e., DTM2006.0) and crust models (i.e., CRUST2.0 and CRUST1.0 models) to construct the shallow layer model. There are four combined strategies& #65306 (1) EGM2008 and CRUST1.0 models, (2) EGM2008 and CRUST2.0 models, (3) EIGEN-6C4 and CRUST1.0 models, and (4) EIGEN-6C4 and CRUST2.0 models, respectively. We calculate the HME by two approaches: first approach, the HME is directly calculated by combining the geoid undulation (N) and geodetic height (h) second approach, we calculate the HME by the segment summation approach (SSA) using the gravity field inside the shallow layer determined by the SLM. Numerical results show that for four combined strategies, the differences between our results and the authoritatively released value 8848.86 m by the Chinese and Nepalese governments on December 8, 2020 are 0.448 m, -0.009 m, -0.295 m, and -0.741 m using first approach and 0.539 m, 0.083 m, -0.214 m, and -0.647 m using second approach. The combined calculation of the HME by the terrain model and gravity field model is more accurate than that by the gravity field model alone. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228.& &
No related grants have been discovered for Xiao-Le Deng.