Satellite Gravitational Gradiometry: Methodological Foundation and Geomathematical Advances/ Satellitengradiometrie: Met
S atellite G ravitational G radiometry (SGG) is an observational technique of globally establishing the fine structure and the characteristics of the external Earth’s gravitational field. The “G ravity field and steady-state O cean C irculation E xplorer”
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W. Freeden () Department of Mathematics, TU Kaiserslautern, Kaiserslautern, Germany E-Mail: [email protected]; [email protected] H. Nutz CBM – Gesellschaft für Consulting, Business und Management mbH, Bexbach, Germany E-Mail: [email protected] R. Rummel Astronomical and Physical Geodesy, TU Munich, Munich, Germany E-Mail: [email protected] M. Schreiner Institute for Computational Engineering, University of Applied Sciences of Technology NTB, Buchs, Switzerland E-Mail: [email protected] © Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019 W. Freeden, R. Rummel (Hrsg.), Handbuch der Geodäsie, Springer Reference Naturwissenschaften, https://doi.org/10.1007/978-3-662-46900-2_111-1
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4.2 Pseudodifferential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Multiscale Frequency Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 SGG in Space-Based Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Fredholm Integral Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Space Solution in Preparatory Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Space Solution in Multiscale Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Abstract
Satellite Gravitational Gradiometry (SGG) is an observational technique of globally establishing the fine structure and the characteristics of the external Earth’s gravitational field. The “Gravity field and steady-state Ocean Circulation Explorer” GOCE (2009–2013) was the first satellite of ESA’s satellite programme intended to realize the principle of SGG and to deliver useful SGG-data sets. In fact, GOCE was capable to provide suitable data material of homogeneous quality and high data density. Mathematically, SGG demands the determination of the gravitational potential in the exterior of the Earth including its surface from given data of the gravitational Hesse tensor along the satellite orbit. For purposes of modeling we are led to invert the “upward continuation”-operator resulting from the Abel–Poisson integral formula of potential theory. This approach requires the solution of a tensorial Fredholm integral equation of the first kind relating the desired Earth’s gravitational potential to the measured orbital gravitational gradient acceleration. The integral equation constitutes an exponentially illposed problem of the theory of inverse problems, which inevitably needs two regularization processes, namely “downward co
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