Review of Reference Frame Representations for a Deformable Earth

Our planet Earth is constantly deforming under the effects of geophysical processes that cause linear and nonlinear displacements of the geodetic stations upon which the International Terrestrial Reference Frame (ITRF) is established. The ITRF has traditionally been defined as a secular (linear) frame in which station coordinates are described by piecewise linear functions of time. Nowadays, some particularly demanding applications however require more elaborate reference frame representations that can accommodate non-linear displacements of the reference stations. Two such types of reference frame representations are reviewed: the usual linear frame enhanced with additional parametric functions such as seasonal sine waves, and non-parametric time series of quasi-instantaneous reference frames. After introducing those two reference frame representations, we briefly review the systematic errors present in geodetic station position time series. We finally discuss the practical issues raised by the existence of these systematic errors for the implementation of both types of non-linear reference frames.