Geodetic Observables and Their Mathematical Treatment in Multiscale Framework

For the determination of the Earth’s gravitational field various types of observations are available nowadays, e.g., from terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gravity gradiometry, etc. The mathematical relation between these observables on the one hand and the gravitational field and the shape of the Earth on the other hand is called the integrated concept of physical geodesy. In this paper, an integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are Runge–Walsh type integration formulas relating an integral over an internal sphere to suitable linear combinations of observational functionals, i.e., linear functionals representing the geodetic observables in terms of gravitational quantities on and outside the Earth. A scale discrete version of multiresolution is described for approximating the gravitational potential on and outside the Earth’s surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of bandlimited wavelets. A method for combined global outer harmonic and local harmonic wavelet modeling is proposed corresponding to realistic Earth’s models.