<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The tensor of gravitation is traceless as the gravitational field of the Earth is harmonic outside the Earth’s surface. Therefore, summation of the 2<sup>nd</sup>-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.</p></abstract>

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.

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

Addis Ababa Institute of Technology, School of Civil and Environmental Engineering

Entoto Observatory and Research Centre, Ethiopian Space Science and Technology Institute

Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Published Online: Jun 19, 2018

Page range: 55 - 74

Received: Dec 22, 2017

Accepted: Feb 23, 2018

DOI: https://doi.org/10.2478/arsa-2018-0006

Keywords
Gravitational field, Laplace condition, Regularisation, error estimation

© 2018 Mehdi Eshagh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Jun 19, 2018

Page range: 55 - 74

Received: Dec 22, 2017

Accepted: Feb 23, 2018

DOI: https://doi.org/10.2478/arsa-2018-0006

KeywordsGravitational field, Laplace condition, Regularisation, error estimation

© 2018 Mehdi Eshagh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Gravitational field, Laplace condition, Regularisation, error estimation