5. Regional Gravity Field Modeling: Theory and Practical Results

Geodesy, with its three core areas positioning and reference systems, Earth rotation determination, and gravity field modeling, is striving for a relative accuracy of at least 10⁻⁹ for all relevant quantities, and to a great extent this goal has already been reached (10⁻⁹ corresponds to about 6 mm relative to the Earth’s radius and \( 10^{ - 8} \,{\text{ms}}^{ - 2} = 1\,\upmu {\text{Gal}} \) in terms of gravity). Regarding gravity field modeling, the highest accuracy demands are from geodesy, especially Global Navigation Satellite System (GNNS) positioning, oceanography, and geophysics. In this context, the geoid and quasigeoid are of major interest; e.g., these quantities are required for the transformation between the purely geometric GNSS (ellipsoidal) heights and gravity field related heights as well as for the modeling of the (mean) dynamic ocean topography (DOT), requiring accuracies at the level of about 1 cm or even below. In this way, the importance of geoid and quasigeoid modelling has increased considerably—also for economic reasons—and as early as 1982 Torge (1982) postulated a “renaissance of the geoid.”