Boundary value problems and invariants of the gravitational tensor in satellite gradiometry

Holota, Petr

doi:10.1007/bfb0010559

Cited by 11 publications

(4 citation statements)

References 2 publications

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“…Methodology and use of the invariants in satellite gradiometry is discussed, e.g., by Baur et al [21]. In order to find "geometrical meaning" of the invariants and/or to show a deeper relationship of the invariants to the geometry of the gravitational field, Holota [22], see his equations 3.15 -3.16 and 4.12 -4.13, derived that the invariants I 1 and I 2 depend on curvatures of the equipotential surface and on the curvature vector of the line of force. For the simplest model of geopotential (gravity point source, monopole) I 1 = -3 (GM) 2 r -6 and I 2 = -2 (GM) 3 r -9 , indicating a relation to volume of shallow subsurface masses [7].…”

Section: Theory Data and Computationsmentioning

confidence: 99%

Gravity Disturbances, Marussi Tensor, Invariants and Other Functions of the Geopotential Represented by EGM 2008

Klokočník¹,

Kostelecký

Kalvoda

et al. 2014

JESR

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Gravity disturbances, the Marussi tensor, invariants of the gravity field, their certain ratio and other functions of the geopotential (including newly defined "virtual deformations") are computed based on the harmonic coefficients of the global gravitational field model EGM 2008. Regional examples of correlations of large-scale morphotectonic and landform patterns with some aspects of the geopotential as computed from the EGM 2008 are presented. It is suggested that morphotectonic and landform patterns with very conspicuous combinations of significantly high positive or negative values of Γ 33 are under the strong influence of rapid and/or intensive geomorphic processes. These geophysical signatures supported by values of the strike angle θ S and virtual dilatations or compressions of the ellipse of deformation reflect the regional dynamics of Earth surface evolution as characterised by very effective integration of tectonic and climate-driven morphogenetic processes.

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Section: Theory Data and Computationsmentioning

confidence: 99%

Gravity Disturbances, Marussi Tensor, Invariants and Other Functions of the Geopotential Represented by EGM 2008

Klokočník¹,

Kostelecký

Kalvoda

et al. 2014

JESR

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“…In view of this challenging problem, Rummel and Colombo (1985) began to investigate how to use the IGGT to build gravity field models. Holota (1989) discussed how to use the theory of boundary value problems for partial differential equations in satellite gradiometry. Then Sacerdote and Sansò (1989) analyzed the effects of orbit and attitude errors on GGs, and they found that using a reference gravity field including the J 2 term is preferable.…”

Section: Introductionmentioning

confidence: 99%

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

Luo

Zhong

et al. 2017

J Geod

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Based on tensor theory, three Invariants of the Gravitational Gradient Tensor (IGGT) are independent of the Gradiometer Reference Frame (GRF). Compared to traditional methods for calculation of gravity field models based on the Gravity field and steady-state Ocean Circulation Explorer (GOCE) data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. The IGGT approach as studied in this paper is a quadratic function of the gravity field model's spherical harmonic coefficients. The linearized observation equations for the least squares method is obtained using a Taylor expansion, and the weighting equation is derived using the law of error propagation. We also investigate the linearization errors using existing gravity field models and find that this error can be ignored since the used a-priori model EIGEN-5C is sufficiently accurate. One problem when using this approach is that it needs all six independent Gravitational Gradients (GGs), but the components V xy and V yz of GOCE are worse due to the non-sensitive axes of the GOCE gradiometer. Therefore we use synthetic GGs for both inaccurate gravitational gradient components derived from the a-priori gravity field model EIGEN-5C. Another problem is that the GOCE GGs are measured in a band-limited manner. Therefore, a forward and backward finite impulse response band-pass filter is applied to the data, which can also eliminate filter caused phase change. The Spherical Cap Regularization Approach (SCRA) and the Kaula rule are then applied to solve the polar gap problem caused by GOCE's inclination of 96.7 0. With the techniques described above, a degree/order 240 gravity field model called IGGT R1 is computed. Since the synthetic components of V xy and V yz are not band-pass filtered, the signals outside the measurement bandwidth are replaced by the a-priori model EIGEN-5C. Therefore this model is practically a combined gravity field model which contains GOCE GGs signals and long wavelength signals from the a-priori model EIGEN-5C. Finally, IGGT R1's accuracy is evaluated by comparison with other gravity field models in terms of difference degree amplitudes, the geostrophic velocity in the Agulhas current area, gravity anomaly differences as well as by comparison to GNSS/Leveling data.

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“…Hence, the gravitational gradient tensor's invariants are introduced. Around 1990, Holota [3], Sacerdote and Sanso [4], and Vermeer [5] discussed potential uses of invariants in GOCE, but their discussions mainly focus on Christoffel's signs, which are all geometric invariants and not suitable for GOCE data. Recently, Baur et al [6] introduced the gravitational gradient tensor's invariants, established some linearized models based on them, and analyzed accuracies of the models by computations.…”

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confidence: 99%

The gravitational gradient tensor’s invariants and the related boundary conditions

Zhao

2010

Sci. China Earth Sci.

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Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor's invariants. Our results only depend on GOCE satellite's position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite's orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J 2 -term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to 2 2 ( ), O J T ⋅ which is approximately equivalent to O(T 2 ). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10 −7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J 2 -term have accuracies of 10 −8 and the order can reach up to 280. the Earth's gravitational field, gravitational gravidiometry, tensor's invariant Citation: Yu J H, Zhao D M. The gravitational gradient tensor's invariants and the related boundary conditions.

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Boundary value problems and invariants of the gravitational tensor in satellite gradiometry

Cited by 11 publications

References 2 publications

Gravity Disturbances, Marussi Tensor, Invariants and Other Functions of the Geopotential Represented by EGM 2008

Gravity Disturbances, Marussi Tensor, Invariants and Other Functions of the Geopotential Represented by EGM 2008

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

The gravitational gradient tensor’s invariants and the related boundary conditions

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