Spectral Combination of Spherical Gradiometric Boundary-Value Problems: A Theoretical Study

Eshagh, Mehdi

doi:10.1007/s00024-012-0504-6

Cited by 13 publications

(4 citation statements)

References 36 publications

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“…The spectral combination of solutions to the spherical gravitational curvature BVP for estimation of the gravitational potential was investigated by Pitoňák et al (2018). The method can be used not only for combination of various data types but it can also continue observables from an observation level down to the irregular Earth's surface (or elsewhere as long as the harmonicity of the gravitational potential is guaranteed) and transform them to corresponding gravitational field quantity, e.g., Sjöberg and Eshagh (2012), Eshagh (2012) or Pitoňák et al (2018). Despite DWC being an inverse problem, the method does not need any matrix inversion and the signal-to-noise ratio of results is controlled by spectral weights.…”

Section: Spectral Combinationmentioning

confidence: 99%

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Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Pitoňák

Šprlák

Novák

2023

International Association of Geodesy Symposia

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In this study, we apply a spectral combination method for estimation of height anomalies from gradients of the gravitational potential measured by satellites. The spectral combination method is used for solving over-determined problems within gravity field modelling when multiple types of gravity data are collected and used for recovery of unobservable quantities (typically the gravitational potential). The method applies solutions to geodetic boundary-value problems formulated in spherical approximation for gradients of the gravitational potential of up to the third order. Spectral forms of the solutions are combined using spectral weights defined under the condition of minimizing the global mean-square error of the estimators. Mathematical models are implemented and tested using gradients synthesized from a global geopotential model which allows for closed-loop testing of the estimators. The tests reveal among others that horizontal derivatives of the gravitational potential influence recovered values more than their vertical counterparts.

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Section: Spectral Combinationmentioning

confidence: 99%

“…which is obtained from spherical harmonics T i;n derived by spherical analysis of the gradient group T i . Spectral weights a i;n are defined as follows (Eshagh 2012;Pitoňák et al 2020):…”

Section: Spectral Combinationmentioning

confidence: 99%

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Pitoňák

Šprlák

Novák

2023

International Association of Geodesy Symposia

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“…the works done by Arabelos and Tscherning (1990, 1993and 1995, Tscherning (1988Tscherning ( , 1989, Tscherning et al (1990) and Yildiz (2012). Also, the gravity field can be recovered using a direct integral method, which in fact does two separate computations in one step, integrating the satellite over the mean orbital sphere and continuing them downward to sea level; see Tscherning et al (1990), Eshagh (2011a), Eshagh (2012) and Sjöberg and Eshagh (2012). Another approach is to determine gravity field from the inversion of integral equations.…”

Section: 2478/arsa-2018-0006mentioning

confidence: 99%

Regional Recovery of Gravity Anomaly from the Inversion of Diagonal Components of GOCE Gravitational Tensor: A Case Study in Ethiopia

Eshagh

Gedamu

Bedada

2018

Artificial Satellites

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The tensor of gravitation is traceless as the gravitational field of the Earth is harmonic outside the Earth’s surface. Therefore, summation of the 2nd-order horizontal derivatives on its diagonal components should be equal to the radial one but with the opposite sign. The gravity field can be recovered locally from either of them, or even their combination. Here, we use the in-orbit diagonal components of the gravitational tensor measured by the gravity field and steady state ocean circulation explorer (GOCE) mission for recovering gravity anomaly with a resolution of 1°×1° at sea level in Ethiopia. In order to solve the system of equations, derived after discretisation of integral equations, the Tikhonov regularisation is applied and the bias of this regularisation is estimated and removed from the estimated gravity anomalies. The errors of the anomalies are estimated and their significance of recovery from these diagonal components is investigated. Statistically, the difference between the recovered anomalies from each scenario is not significant comparing to their errors. However, their joint inversion of the diagonal components improved the solution by about 1 mGal. Furthermore, the inversion processes are better stabilised when using errors of the input data compared with its exclusion, but at the penalty of degradation in accuracy of the estimates.

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“…Later on Sjöberg and Eshagh () developed this theory for combining satellite gravity gradiometry and terrestrial data with EGMs for geoid determination purposes. Spectral combination was applied by Eshagh (, ) for combining the solutions of vector gravimetric and gradiometric boundary‐value problems.…”

Section: Introductionmentioning

confidence: 99%

A theoretical study on terrestrial gravimetric data refinement by Earth gravity models

Eshagh

2013

Geophysical Prospecting

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A B S T R A C TThe idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models and produce a high-quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point-wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady-state ocean circulation explorer mission. Numerical results show that the integral estimators have smaller global root mean square errors than the point-wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point-wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high-degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2 • for numerical integration and a maximum degree of 2500 for generation of band-limited kernels are found suitable for the integral estimators.

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Spectral Combination of Spherical Gradiometric Boundary-Value Problems: A Theoretical Study

Cited by 13 publications

References 36 publications

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

Regional Recovery of Gravity Anomaly from the Inversion of Diagonal Components of GOCE Gravitational Tensor: A Case Study in Ethiopia

A theoretical study on terrestrial gravimetric data refinement by Earth gravity models

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