Regional gravity fields

The goal is to determine high resolution regional gravity fields by combining all available gravity data. In the framework of a multi-scale representation (MSR) the gravitational potential can be decomposed in a number of detail signals, which mean series expansions in terms of wavelet functions and imply a band pass filtering of the potential. The series coefficients of the different detail signals are connected with another through a pyramidal algorithm. The scaling coefficients are determined from the observations in "zeroth" step of the algorithm using parameter estimation. Geodetic measurements allow the determination of the unknown coefficients using a combined solution. This method is being realized in the context of a project together with the Bundeswehr Geoinformation Office (“Amt für Geoinfomationswesen der Bundeswehr”, AGeoBw). The figure below schematically shows a possible combination strategy.

The input data for the combination are for example measurements of the satellite gravity missions GRACE and GOCE. These data are combined with satellite altimeter measurements, terrestrial gravity data and measurements from airborne gravimetry. In general the dynamic ocean topography should be co-estimated with the gravity field when altimeter data are used in the combination.

: Combination of data from modern satellite missions and terrestrial measurements

The successful satellite mission GRACE puts the focus of geodetic work on the representation of the time-variable gravity field. At DGFI, over the last years different strategies have been developed to include time-variations in the gravity field modelling. An adequate approach describes the series coefficients in one-dimensional series of time-dependent base functions, e.g. B-splines. These are time localising functions, by means of which a four-dimensional MSR can be developed. Time-dependency is dealt with in a submitted project of ESA.

Selected publications

Bouman J., Bosch W., Goebel G., Müller H., Sanchez L., Schmidt M., Sebera J.: Das Schwerefeld der Erde - Messen, Darstellen und Auswerten. Zeitschrift für Vermessungswesen, 135, Heft 2, 2010

Schmidt M., Fabert O., Shum C.K.: On the estimation of a multi resolution representation of the gravity field based on spherical harmonics and wavelets. J. Geodynamics (39), 512-526, 2005

Schmidt M., Fengler M., Mayer-Gürr T., Eicker A., Kusche J., Sanchez L., Han S.-C.: Regional Gravity Modelling in Terms of Spherical Base Functions. J Geod, 81, 17-38, doi: 10.1007/s00190-006-0101-5, 2007

Schmidt M., Han S.-C., Kusche J., Sanchez L., Shum C.K.: Regional high-resolution spatio-temporal gravity modeling from GRACE data using spherical wavelets. Geophys. Res. Lett., 33, L08403, doi:10.1029/2005GL025509, 2006