Abstract.
A very efficient approach for computing spherical harmonic coefficients from satellite gravity gradiometry (SGG) data has been developed. The core of the proposed approach is a combination of the method of conjugate gradients with preconditioning on the one hand and an extremely fast algorithm for synthesis (application of the design matrix to a vector) and co-synthesis (application of the transposed design matrix to a vector) on the other. The high performance of the synthesis and co-synthesis is achieved by introducing an intermediate step, where computations are made on a regular three-dimensional (3-D) spherical grid. As a result, the Legendre functions can be computed for all the points at a given latitude only once and 1-D fast-Fourier techniques can be fully exploited. Transition to the true observation points is carried out by means of a 3-D spline interpolation. It is expected that the technique will be able to invert the full set of SGG data from the GOCE satellite mission (12-month data, four tensor components, 1-s sampling) in only a few hours on an SGI Origin 3800 computer with 16 processing elements. This corresponds approximately to 1 or 2 days of computation on a Pentium-IV PC. The choice of a relatively coarse 3-D spherical grid improves the efficiency even further, at the cost of minor errors in the solution. In this mode, the proposed approach can be used for quick-look data analysis.
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Received: 21 February 2002 / Accepted: 20 September 2002
Correspondence to: P. Ditmar
Acknowledgments. The research was financially supported by the Netherlands Space Research Organization SRON (grant eo-028). This support is gratefully acknowledged. The authors are very thankful to E. Schrama and J. Kusche for numerous valuable discussions and to J. van den IJssel for computing the realistic GOCE orbits that were used in simulations. They would like also to thank the official reviewers of the article – Prof. Schuh, Dipl.-Ing. Mayer-Gürr, and Prof. Tscherning – for many valuable remarks and suggestions. Computing resources were provided by Stichting Nationale Computerfaciliteiten NCF (grant SG-027) and by the Center for High Performance applied Computing (HPαC) at Delft University of Technology.
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Ditmar, P., Klees, R. & Kostenko, F. Fast and accurate computation of spherical harmonic coefficients from satellite gravity gradiometry data. Journal of Geodesy 76, 690–705 (2003). https://doi.org/10.1007/s00190-002-0298-x
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DOI: https://doi.org/10.1007/s00190-002-0298-x