The Earth's shape and gravity field: a report of progress from 1958 to 1982

Summary. A major step forward in geophysics during the last 25 years has been the progress in the determination of the Earth's shape and gravity field, from the halting steps of the first satellite orbit analyses to the global solutions expanded in spherical harmonics up to degree 36, and from painstaking gravity surveys on land to the detailed regional geoids derived from altimeter observations. No other geophysical quantity pertaining to lateral variations in the structure of the crust and mantle is now known with a comparable accuracy and spatial resolution. An increasingly acute problem has been to find ways to validate the global results since differences between individual solutions remain substantial. Absolute tests are not available but statistical comparisons produce some useful insight into the status of the recent gravity field models. A number of recent models are evaluated in this paper. A primary conclusion is that the gravity or geoid anomalies are frequently not as well determined as stated by the authors. We estimate, for example, that the root mean square errors of the geoid heights deduced from models by Lerch et al . and Gaposchkin are about 3 m and that maximum errors may exceed 10 m in some places. A considerable part of this comes from uncertainties in the low degree harmonics, in particular the degree and order 3 coefficients and more generally the odd degree coefficients, for while the signal‐to‐noise ratio of these coefficients is high the power in the spectrum is also high. Most tests developed for evaluating the gravity fields are insensitive to the long wavelength components in the spatial spectrum. Future projects call particular attention to improving the high degree part of the geopotential spectrum but thought should also be given to these low degree harmonics. Considerable progress in determining the gravity field can still be made by using data already available.