Rosborough approach for the determination of regional time variability of the gravity field from satellite gradiometry d
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Rosborough approach for the determination of regional time variability of the gravity field from satellite gradiometry data Wolfgang Keller1 · Rey-Jer You2
Received: 18 May 2015 / Accepted: 25 July 2015 © Springer-Verlag Berlin Heidelberg 2015
Abstract It is well-known that Rosborough approach, based on spherical harmonics, can be efficiently applied to determine the unknown global gravitational field parameters in the framework of the so-called space-wise approach. Usually, for regional gravity field modeling radial basis functions instead of spherical harmonics are used as basis functions. Using the strong relationship between radial basis functions and spherical harmonics, the Rosborough counterparts of radial basis functions are developed. Based on these regionally supported Rosborough basis functions, all components of gravity-gradient tensor are expressed as series in regionally supported Rosborough basis functions. In a simulation study the feasibility of regional static and time-variable gravity field recovery from satellite gradiometry data using regionally supported Rosborough functions is tested. Keywords Gravity field · Gradiometry · GOCE · Rosborough approach · Radial basis functions Mathematics Subject Classification
B
65D10
Wolfgang Keller [email protected] Rey-Jer You [email protected]
1
Institute of Geodesy, Stuttgart University, 24D, Geschwister-Scholl-Straße, 70174 Stuttgart, Germany
2
Department of Geomatics, National Cheng Kung University, University Road 1, Tainan, Taiwan
123
Int J Geomath
1 Introduction Low Earth orbit (LEO) satellite missions, such as GOCE and GRACE, provide a huge amount of data for the determination of the Earth’s gravitational field. The evaluation techniques for the determination of the gravitational field from these satellite data can be distinguished in – the time-wise approach and – the space-wise approach. In the so-called time-wise approach that the data is considered as a time-series and the unknown gravitational field parameters are determined from the time series by standard least-squares techniques. The advantage of the strong flexibility of this approach is counterbalanced by the enormous numerical effort. Furthermore, the timewise approach is not very suitable for regional gravity field determination, because that would mean to cut the time series into pieces, related to the region under investigation. In the so called space-wise approach the observations are not time-tagged but labeled with the respective positions of the observations. This makes a regional evaluation of the observations easy, because only those observations which relate to the region are taken into account, irrespectively of the time of there registration. Rosborough (1986) developed a method to relate the observational time to a specific location on the surface of the Earth. Using this relationship the time-series is converted in a point-set of observations on the surface of the Earth. In this way the Rosborough approach can be seen as a synthesis betwee
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