The determination of the geoid from airborne gravity data.

Based on basic principles of potential theory, a proper definition of geodetic boundary-value problems, which are involved in the mathematical model for the determination of the band-limited gravimetric geoid grom airborne gravity, is presented including possible approximations both in gravity and geometric spaces leading to practical solutions. Based on the spherical approximations of the geoid, appropriate integral operators are introduced and their practical evaluations are discussed. The solution of the first and second boundary-value problems is the band-limited disturbing gravity potential at the geoid defined in the Helmert gravity field. It can be transformed using the Bruns theorem into band-limited geoidal heights in the Helmert gravity field. This band-limited co-geoidal height is then added to the reference Helmert spheroid computed from the harmonized spherical harmonic geopotential coefficients yielding the total co-geoid. The co-geoid is transformed back into the real gravity field by applying the indirect topographical and atmospheric effects on the geoid. The mathematical formulations and their computer realization are tested using both simulated and actual airborne gravity data. Results of the tests prove good numerical accuracy and stability of the formulated solutions assuming the characteristics of currently available airborne data. Accuracy at the centimeter level can generally be expected for the band-limited geoid, if errors due to incomplete topographical and atmospheric reduction of gravity and the co-geoid and errors in the geopotential model can be considered negligible.Available from STL Prague, CZ / NTK - National Technical LibrarySIGLECZCzech Republi