Mapping Earth’s Gravitation Using GRACE Data

Summary

This article describes an approach for global mapping of the Earth’s gravitational field developed, tested and successfully implemented at the Geodetic Institute of the Stuttgart University. The method is based on the Newtonian equation of motion that relates satellite-to-satellite tracking (SST) data observed by the two satellites of the Gravity Recovery And Climate Experiment (GRACE) directly to unknown spherical harmonic coefficients of the Earth’s gravitational potential (geopotential). Observed values include SST data observed both in the low-low (inter-satellite range, velocity and acceleration) and the high-low (satellites’ positions) mode. The low-low SST data specific for the time being to the GRACE mission are available through a very sensitive K-band ranging system. The high-low SST data are then provided by on-board Global Positioning System (GPS) receivers. The article describes how the mathematical model can be modified. The geopotential is approximated by a truncated series of spherical harmonic functions. An alternative approach based on integral inversion of the GRACE data into the geopotential is also formulated and discussed. The article also presents sample numerical results obtained by testing the model using both simulated and observed data. Simulation studies suggest that the model has a potential for recovery of the Stokes coefficients up to degree and order 120. Intermediate results from the analysis of actual data have a lower resolution.