MEISSL SCHEME - SPECTRAL CHARACTERISTICS OF PHYSICAL GEODESY

In spherical approximation the gravity disturbance potential, its firs t and its second radial derivative on the Earth's surface and at altit ude are connected by very simple eigenvalue expressions. The complete system of eigenfunctions is the set of spherical harmonics. The result ing scheme of eigenvalue connections between these quantities is denot ed Meissl scheme. Its simplicity results from the fact that the corres ponding integral and differential operators are self-adjoint. However, even for non self-adjoint cases, the operators connecting the disturb ance potential with certain combinations of first and second horizonta l or mixed horizontal-vertical derivatives, similarly simple eigenvalu e expressions exist. In gravity field analysis, after linearization, t he observables become linear functionals of the disturbance potential. Thus the Meissl scheme provides easy insight into their information c ontent and error characteristics and facilitates comparative judgement of current and future measurement concepts.