Gravity Field

Gravity is a fundamental force, which mirrors mass distribution and mass redistribution in the Earth system, and, as such, is an important source of information used in various Earth sciences. In geophysics, it is used to recover rock densities needed, to build accurate geological models for mineral and hydrocarbon exploration, as well as to improve our knowledge of the Earth’s behavior and evolution at the global scale. In oceanography and hydrology, gravity is used to observe variations in ocean currents, the melting of ice sheets, and variations of continental water storage, all of which are important for global climate studies. In geodesy, surfaces of constant gravity potential serve as reference surfaces for national height systems. Finally, gravity governs the motion of satellites around the Earth and, therefore, is a key quantity in precise orbit determination of satellites. 

The interrelation between gravity/temporal gravity variations and mass distribution/transport (from Ilk et al. 2005).


The main goal of this subprogram is to develop and apply new methodologies and algorithms for gravity field modelling, in particular based on data from the dedicated satellite gravity missions CHAMP (launched in 2000), GRACE (launched in 2002), and GOCE (launched in 2008). An important step towards achieving this goal is the combination of these satellite data with each other and with terrestrial and airborne gravity observations. Our ultimate goal is to promote the development of innovative final (so-called “level 3”) products of highest quality for applications in Earth sciences and engineering. This requires complete insight into all steps of the data analysis, ranging from the physical-mathematical and stochastic modelling to parameter estimation and error propagation.

Global gravity field modelling

The dedicated satellite gravity missions CHAMP, GRACE, and GOCE provide information about the Earth’s static gravity field with unprecedented accuracy and spatial resolution. Furthermore, GRACE enables for the first time studies of the time-variable gravity field on medium-range spatial scales and monthly temporal scales. These dedicated missions open up various new application areas and, consequently, play a key role in this theme.

The highest priority is given to the development of innovative, tailored strategies, which provide the
 highest accuracy and spatial-temporal resolution. At the same time, our developments also help improving the traditional approach of integrated orbit and gravity field determination based on the solution of the so-called variational equations. The research comprises 1) the proper choice of the functional and stochastic model; 2) the development of efficient data retrieval algorithms (e.g., data-driven weighting and regularization schemes based on statistical theory, variance component estimation); 3) the implementation of the developed algorithms on multi-processor platforms for real data processing; 4) the description of the quality, reliability and information content of global gravity field models and of the contribution of individual data groups to combined solutions;  5) the calibration and cross-validation of satellite observations in terms of the functional and stochastic model as well as the calibration and validation of derived global gravity field models.

A new model of the mean gravity field of the Earth 'DEOS_CHAMP-01C_70' displayed in terms of geoid height differences with respect to the EGM96 model (truncated at spherical harmonic degree 70). The model has been computed by PSG from a one-year set of CHAMP data. The largest deviations are observed at remote continental areas, which were not covered by gravimetric measurements at the time when the EGM96 model was compiled.

Regional gravity field modelling

Regional gravity field modelling refers to the combination of satellite data with terrestrial and/or airborne data to achieve an improved spatial resolution for limited areas. Wavelengths > 100 km are more accurately determined from CHAMP, GRACE and GOCE satellite gravity data, because of the higher accuracy and homogeneous distribution compared to terrestrial and airborne data. Therefore, a regional inversion of the satellite data is investigated in an attempt, to obtain a better signal-to-noise ratio for some specific areas, e.g. the polar regions. Moreover, satellite data can be easily
 combined in this case with terrestrial and airborne data. Research will be initiated towards the development of alternatives to the traditional remove-restore technique, which is so far the standard approach to data combination. The focus will be on the stochastic properties of the individual data sets, the proper weighting, and the numerical efficiency of the algorithms. These efforts will help in dealing with the huge amount of data, including available variance-covariance information, and to mitigate potential instabilities in the solutions without compromising the accuracy.  

Additionally, the research comprises the development of strategies to combine gravity data with geometric data provided by global navigation satellite systems (e.g. GPS) and spirit leveling as well as the development of new methodologies for regional (quasi-) geoid modelling and height reference surface realization.

In our philosophy, global and regional gravity field modelling are seen as two closely inter-related tasks, which share a number of research activities. Moreover, recent developments in spherical radial base function theory (e.g., spherical wavelets) suggest a unified parameterization of global and regional fields by a combination of spherical harmonics and radial base functions with zoom-in and zoom-out capabilities.

Water storage variations in the Zambezi river basin observed by GRACE for October 2004 relative to a yearly mean. PSG regional solution using spherical radial basis functions (left), PSG global solution (middle), and GFZ global solution (right) (400 km Gaussian smoothing).