File: H:\cctwp\champ0103.wpd, 2001-07-10


Gravity field approximation from CHAMP SST

Using collocation.



C.C.Tscherning, F.Sansò, D.Arabelos, R.Forsberg,


Proposal description.

The method of least-squares collocation (LSC) has successfully been used in simulation studies where approximations to the gravity field were determined, (Tscherning, 2001, Arabelos & Tscherning, 1998). A general purpose software package, GRAVSOFT (Tscherning et al., 1994) has been used for this purpose.

We expect that it will be possible to convert the CHAMP SST data and accelerations to velocities or differentiated to represent accelerations. The velocities will be treated like (gravity) potential differences (following ideas by Jekeli) and the accelerations like gravity vector components. Preferably we would like to have the SST data available in the form of orbit state vectors computed kinematically. We hope then that it will be possible to use the accelerations to convert the quantities to "inertial" quantities.

Since LSC requires that a system of equations as large as the number of observations is solved, a preprocessing of the data will be made, also using LSC. Data will be gridded along parallels at satellite altitude, and the new method of Fast Spherical Collocation (Sansò & Tscherning, 2001) will be used to calculate spherical harmonic coefficients and their error-estimates. As a part of the gridding procedure, data will be pre-processed, and gross-errors will be flagged using the same procedures as proposed for COCE (Tscherning et al. 2000).

We will also try to produce a "clean" LSC solution without gridding the data. A data selection will be made, so that the data density is large in areas with strongly varying gravity and the density will be small over smooth areas. In all cases will the product be "corrections" to the best available a-priori estimate of the spherical harmonic coefficients. In this way we also avoid using ground topography for smoothing and the residual field will be (resonably) homogeneous, so that isotropic covariance functions can be used. We will also investigate the feasibility of using finite covariance functions (Moreaux et al., 2000) in the data processing.

If systematic errors are supposed to be present we will try to detect and model these using ground data (Arabelos & Tscherning, 1998). For this purpose KMS has available modern airborne data covering large areas.

The LSC method permits the easy combination with ground or airborne data. Especially combination with ground gravity will be investigated.

The investigation will be carried out as a cooperation between the University of Copenhagen, Politecnico di Milano, Aristotele University of Thessaloniki and the National Survey and Cadastre, Denmark. The Danish participation is funded by a grant from the Danish science research council to the project "Satellite Gravity Data Analysis" (SAGRADA), and the Greek and Italian participation is funded by their Universities. The SAGRADA project ( ) has funds available to support this cooperation. The expertise is documented in the referenced publications. The CV of the principal investigator is available as .

The investigation will last until the data-processing of COCE is completed, probably in 2008.


Arabelos,D. and C.C.Tscherning: Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT. Bulletin Geodesique, Vol. 64, pp. 363-382, 1990.

Arabelos, D. and C.C.Tscherning: Regional recovery of the gravity field from SGG and Gravity Vector data using collocation. J.Geophys. Res., Vol. 100, No. B11, pp. 22009-22015, 1995.

Arabelos, D. & C.C.Tscherning: Calibration of satellite gradiometer data aided by ground gravity data. Journal of Geodesy, Vol. 12, no. 11, pp. 617 - 625, 1998.

Moreaux, G., C.C.Tscherning & F.Sanso': Approximation of Harmonic Covariance Functions by non Harmonic Locally Supported Ones. Journal of Geodesy, Vol. 73, pp. 555 - 567, 1999.

Sanso', F. and C.C.Tscherning: Fast spherical collocation. Paper prepared for IAG2001, Budapest, Sept. 2001.

Tscherning, C.C.: The use of optimal estimation for gross-error detection in databases of spatially correlated data. Bulletin d'Information, no. 68, pp.79-89, Bureau Gravimetrique International, 1991.

Tscherning, C.C.: Computation of spherical harmonic coefficients and their error estimates using Least Squares Collocation. J. of Geodesy, Vol. 75, pp. 14-18, 2001.

Tscherning, C.C., P.Knudsen and R.Forsberg: Description of the GRAVSOFT package. Geophysical Institute, University of Copenhagen, Technical Report, 1991, 2. Ed. 1992, 3. Ed. 1993, 4. ed, 1994.