Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: a case study for central Europe

Pitoňák, Martin; Šprlák, Michal; Tenzer, Róbert

doi:10.1093/gji/ggx041

Cited by 12 publications

(3 citation statements)

References 42 publications

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“…in the interpretation of airborne gravity gradients for exploration 14 . Approaches like the use of third-order derivatives yield promising results 15 , but do not reduce the complexity in interpretation. Here, we adopt, therefore, recent advancements in the use of curvature components of the tensor that simplify the interpretation of gravity gradient datasets significantly and are directly making use of the second derivatives of the gravitational potential 16 , 17 .…”

Section: Introductionmentioning

confidence: 99%

Earth tectonics as seen by GOCE - Enhanced satellite gravity gradient imaging

Ebbing

Haas

Ferraccioli

et al. 2018

Sci Rep

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Curvature components derived from satellite gravity gradients provide new global views of Earth’s structure. The satellite gravity gradients are based on the GOCE satellite mission and we illustrate by curvature images how the Earth is seen differently compared to seismic imaging. Tectonic domains with similar seismic characteristic can exhibit distinct differences in satellite gravity gradients maps, which points to differences in the lithospheric build-up. This is particularly apparent for the cratonic regions of the Earth. The comparisons demonstrate that the combination of seismological, and satellite gravity gradient imaging has significant potential to enhance our knowledge of Earth’s structure. In remote frontiers like the Antarctic continent, where even basic knowledge of lithospheric scale features remains incomplete, the curvature images help unveil the heterogeneity in lithospheric structure, e.g. between the composite East Antarctic Craton and the West Antarctic Rift System.

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Section: Introductionmentioning

confidence: 99%

Earth tectonics as seen by GOCE - Enhanced satellite gravity gradient imaging

Ebbing

Haas

Ferraccioli

et al. 2018

Sci Rep

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“…With the first measurement of radial gravitational curvatures (or gravity curvatures, GC, third-order derivatives of the gravitational potential) using the atom interferometry sensors in the laboratory condition (Rosi et al 2015), the subsequent study of the GC was focused on their theory and simulation applications in geodesy and geophysics (Šprlák and Novák 2015(Šprlák and Novák , 2017Hamáčková et al 2016;Sharifi et al 2017;Novák et al 2017;Pitoňák et al 2017Pitoňák et al , 2018Pitoňák et al , 2020Shen 2018a, b, 2019;Novák et al 2019;Du and Qiu 2019;Romeshkani et al 2020Romeshkani et al , 2021. The GC were more sensitive to field sources than the loworder gravitational effects (i.e., GP, GV, and GGT) (Heck 1984;Du and Qiu 2019).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of gravitational curvatures for a tesseroid and spherical shell with arbitrary-order polynomial density

Deng

2023

J Geod

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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 examples 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.

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“…It was designed specifically for gravity measurements and provided highly accurate data. Research such as [8][9][10][11] used GOCE data to estimate regional gravitational field models.…”

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confidence: 99%

Antarctic Time-Variable Regional Gravity Field Model Derived from Satellite Line-of-Sight Gravity Differences and Spherical Cap Harmonic Analysis

2023

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This study focuses on the development of a time-variable regional geo-potential model for Antarctica using the spherical cap harmonic analysis (SCHA) basis functions. The model is derived from line-of-sight gravity difference (LGD) measurements obtained from the GRACE-Follow-On (GFO) mission. The solution of a Laplace equation for the boundary values over a spherical cap is used to expand the geo-potential coefficients in terms of Legendre functions with a real degree and integer order suitable for regional modelling, which is used to constrain the geo-potential coefficients using LGD measurements. To validate the performance of the SCHA, it is first utilized with LGD data derived from a L2 JPL (Level 2 product of the Jet Propulsion Laboratory). The obtained LGD data are used to compute the local geo-potential model up to Kmax = 20, corresponding to the SH degree and order up to 60. The comparison of the radial gravity on the Earth’s surface map across Antarctica with the corresponding radial gravity components of the L2 JPL is carried out using local geo-potential coefficients. The results of this comparison provide evidence that these basis functions for Kmax = 20 are valid across the entirety of Antarctica. Subsequently, the analysis proceeds using LGD data obtained from the Level 1B product of GFO by transforming these LGD data into the SCHA coordinate system and applying them to constrain the SCHA harmonic coefficients up to Kmax = 20. In this case, several independent LGD profiles along the trajectories of the satellites are devised to verify the accuracy of the local model. These LGD profiles are not employed in the inverse problem of determining harmonic coefficients. The results indicate that using regional harmonic basis functions, specifically spherical cap harmonic analysis (SCHA) functions, leads to a close estimation of LGD compared to the L2 JPL. The regional harmonic basis function exhibits a root mean square error (RMSE) of 3.71 × 10−4 mGal. This represents a substantial improvement over the RMSE of the L2 JPL, which is 6.36 × 10−4 mGal. Thus, it can be concluded that the use of local geo-potential coefficients obtained from SCHA is a reliable method for extracting nearly the full gravitational signal within a spherical cap region, after validation of this method. The SCHA model provides significant realistic information as it addresses the mass gain and loss across various regions in Antarctica.

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Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: a case study for central Europe

Cited by 12 publications

References 42 publications

Earth tectonics as seen by GOCE - Enhanced satellite gravity gradient imaging

Earth tectonics as seen by GOCE - Enhanced satellite gravity gradient imaging

Evaluation of gravitational curvatures for a tesseroid and spherical shell with arbitrary-order polynomial density

Antarctic Time-Variable Regional Gravity Field Model Derived from Satellite Line-of-Sight Gravity Differences and Spherical Cap Harmonic Analysis

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