Spherical gravitational curvature boundary value problem
Values of scalar, vector and second order tensor parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and well understood. On the other hand, new sensors for observing gravitational curvatures, i.e. components of the third order gravitational tensor, are currently under development. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, the gravitational curvature tensor is decomposed into six parts which are expanded in terms of third order tensor spherical harmonics. Secondly, gravitational curvature boundary value problems defined for four combinations of the gravitational curvatures are formulated and solved in spectral and spatial domains. Thirdly, properties of the corresponding sub integral kernels are investigated. The presented mathematical formulations reveal some important properties of the gravitational curvatures and extend the so called Meissl scheme, i.e. an important theoretical framework that relates various parameters of the Earth's gravitational field.
Journal of Geodesy