Precise Determination Of The Geopotential With A Low Low Satellite To Satellite Tracking Mission

The error analysis of the global modelling of the geopotential has been carried out up to degree and order 331 of the spherical harmonic expansion, for data from a low-low satellite-to-satellite tracking (SST) mission. The sphericity and the rotation of the Earth have been considered, as well as the discrete nature of the data, assumed to consist of time averages of the measured range-rate sampled at regular intervals. The expansion of the potential has been truncated at degree n = 331, because little information on higher degrees is likely to be present in the data. Two theories have been used: that of least squares adjustment, and that of least squares collocation; above degree n = 200 the accuracies predicted according to collocation are significantly better than those according to least squares. In this report there is also a discussion on how to process SST data to obtain very high resolution models of the gravitational field. Descriptions and listings of computer programs are included. To reduce the computer time and storage needed to set up and to invert the normal matrix, a somewhat simplified orbital geometry and an approximate model of the data have been adopted; no orbit determination errors have been considered. Some arguments are given to justify these shortcuts, which may not affect seriously the validity of the results. An extention of the theory to non-polar orbits is given.

Improved knowledge of the Earth's gravity field was obtained from new and improved satellite measurements such as satellite to satellite tracking and gradiometry. This improvement was examined by estimating the accuracy of the determination of mean anomalies and mean undulations in various size blocks based on an assumed mission. In this report the accuracy is considered through a commission error due to measurement noise propagation and a truncation error due to unobservable higher degree terms in the geopotential. To do this the spectrum of the measurement was related to the spectrum of the disturbing potential of the Earth's gravity field. Equations were derived for a low-low (radial or horizontal separation) mission and a gradiometer mission. For a low-low mission of six month's duration, at an altitude of 160 km, with a data noise of plus or minus 1 micrometers sec for a four second integration time, we would expect to determine 1 deg x 1 deg mean anomalies to an accuracy of plus or minus 2.3 mgals and 1 deg x 1 deg mean geoid undulations to plus or minus 4.3 cm. A very fast Fortran program is available to study various mission configurations and block sizes. Jekeli, C. and Rapp, R. H. Unspecified Center REPT-307 NGR-36-008-161

This symposium continued the tradition of mid-term meetings held between the joint symposia of International Geoid and Gravity Commissions. This time, geodynamics was chosen as the third topic to accompany the traditional topics of gravity and geoid. The symposium thus aimed at bringing together geodesists and geophysicists working in the general areas of gravity, geoid and geodynamics. Besides covering the traditional research areas, special attention was paid to the use of geodetic methods for geodynamics studies, dedicated satellite missions, airborne surveys, geodesy and geodynamics of arctic regions, and the integration of geodetic and geophysical information.

This report is a supplement to a report entitled 3Geopotential Determination From Satellite To Satellite Tracking and Satellite Altimetry3, ETL-CR-74-21, February, 1975. Under appropriate circumstances (as reported in the final report) it has been found that when conservation of energy principles are used in determination of spherical harmonic coefficients of the earth's gravity field, a diagonal set of normal equations is generated. Test results are presented which indicate that perturbations due to extraterrestrial and nonconservative forces may be isolated so that these forces will not contaminate the conservation of energy solution. Uncertainties in gravitational anomalies and deflections of the vertical as a function of uncertainties in the determined spherical harmonic coefficients are given. These uncertainties are given when the spherical harmonic coefficients are determined from conservation of energy principles and from conservation of energy principles augmented with satellite altimetry. In the latter case a reduction by a factor of about thirty in the surface gravity standard deviation is realized when satellite to satellite tracking is augmented with satellite altimetry.

This book provides a sound theoretical basis for the the different gravity field recovery methods and the numerics of satellite-to-satellite tracking data. It represents lectures given at the ‘Wilhelm and Else Heraeus Autumn School’ in Bad Honnef, Germany, October 4-9, 2015. The emphasis of the school was on providing a sound theoretical basis for the different gravity field recovery methods and the numerics of data analysis. The approaches covered here are the variational equations (classical approach), the acceleration approach and the energy balance approach, all of which are used for global gravity field recovery on the basis of satellite observations. The theory of parameter estimation in satellite gravimetry and concepts for orbit determination are also included. The book guides readers through a broad range of topics in satellite gravimetry, supplemented by the necessary theoretical background and numerical examples. While it provides a comprehensive overview for those readers who are already familiar with satellite gravity data processing, it also offers an essential reference guide for graduate and undergraduate students interested in this field.