Devising stable geometrical reference frames for use in geodetic studies of vertical crustal motion

We present a method for constructing and assessing the stability of a geometrical reference frame for use in vertical crustal motion studies. Our approach exploits the fact that when we transform GPS velocity solutions from one reference frame (RF) to another one using a Helmert transformation, only the frame translation rate parameters produce significant changes in the vertical station velocities expressed in the final RF. Loosely speaking, one can select and impose a 'vertical RF' from an ensemble of candidate frames, without any reference to the 'horizontal RF' (which can be selected and imposed afterwards), by seeing how the frame translation rates vary as one moves across the ensemble of frames. We order this ensemble according to the number of stations, N, incorporated into the set VREF whose RMS vertical motion is minimized in order to realize each frame. The value of N controls the level of scatter in, and hence the degree of similarity between the vertical velocities of the stations composing VREF. We characterize a specific vertical RF as stable if all of the frames located in a large neighborhood of the ensemble which includes the specific frame are characterized by very small relative frame translation rates. In this case, the expression of vertical GPS station velocities in any of these frames would lead to very similar results. We present a case study using a very large global time series in which we find a large RF neighborhood in which vertical station velocities are globally stable at the 0.2 mm/year level, and a slightly smaller neighborhood in which vertical stability improves to 0.1 mm/year level in polar regions.