The ULR7a GPS solution is a preliminary version of the reanalysis of 21 years of GPS data from 2000 to 2020 that has been undertaken within the framework of the 3rd data reprocessing campaign of the International GNSS Service (IGS). Its associated vertical velocity field is expressed in ITRF2014.

Double-differenced ionosphere-free GPS carrier phase observations from daily regional (plus one global) networks of 546 stations were reanalyzed using a free-network strategy (station positions, Earth Orientation parameters, satellite orbits and zenith tropospheric delays adjusted simultaneously using GAMIT software. The daily subnetworks were then combined into daily global network of stations using GLOBK software. The data analysis strategy (models, corrections...) was compliant with the specifications adopted by the IGS for this reanalysis (more information here).

Position time series expressed in ITRF2014 were then computed using CATREF software using a time-dependent functional model that includes station positions at reference epoch, velocities, semi-annual and annual seasonal signals and transformation parameters (translation, rotation, scale, and their velocities) between the daily undetermined frames and the ITRF2014 for a subset of IGS core stations. Where appropriate, station position offsets (mostly due to equipment changes or earthquakes), velocity changes and post-seismic displacement signals were added.

After the substraction of non-tidal atmospheric loading displacements in the time series (provided by the Earth System Modelling team of the German research center for geosciences at Potsdam), both a functional and a stochastic model were adjusted including long-term linear trends, position offset discontinuities, and periodic signals, following the equation:

$$ \begin{align} x(t) = & x_{ref}+ v_{x}(t-t_{ref}) & \textit{reference position and velocity}\\ & + \sum_{i=1}^{N_{O}} a_{i}H(t-t_{i}) & \textit{position offsets}\\ & + \sum_{j=1}^3 s_{j}\sin(\frac{2\pi}{\tau_{j}}t)) + c_{j}\cos(\frac{2\pi}{\tau_{j}}t)) & \textit{seasonnal signals} \\ & + \sum_{d=1}^8 s_{d}\sin(\frac{2\pi}{\tau_{d}}t)) + c_{d}\cos(\frac{2\pi}{\tau_{d}}t)) & \textit{draconitic signals}\\ & + \sum_{f=1}^3 s_{f}\sin(\frac{2\pi}{\tau_{f}}t)) + c_{f}\cos(\frac{2\pi}{\tau_{f}}t)) & \textit{fortnightly signals} \\ & + \sum_{k=1}^{N_{PSD}}PSD_{k}(t) & \textit{post-seismic deformation signals} \end{align} $$


$$ \begin{align} x_{ref} & \text{ is the position at the reference epoch} t_{ref} \\ v_{x} & \text{ is the linear velocity} \\ H(t-t_{i}) = & \begin{cases} 0 & \text{if } t \lt t_{i}\\ \\ 1 & \text{if } t \geq t_{i} \end{cases} \\ \tau_{j} = & \frac{1}{j} \text{ years} \\ \tau_{d} = & \frac{P_{D}}{365.25} \text{ years}, P_{D} \text{ being the period in days of the draconitics} \\ \tau_{f} = & \frac{P_{F}}{365.25} \text{ years}, P_{F} \text{ being the period in days of the fortnightly signals}\\ PSD_{k}(t) = & \begin{cases} a_{k} \log(1+ \frac{t-t_{k}}{\tau_{k}}) \text{ if PSD model is log} \\ \\ a_{k}(1- \exp(-\frac{t-t_{k}}{\tau_{k}})) \text{ if PSD model is exp} \\ \\ a_{1k} \log(1+ \frac{t-t_{k}}{\tau_{1k}}) + a_{2k}(1- \exp(-\frac{t-t_{k}}{\tau_{2k}})) \text{ if PSD model is log+exp} \\ \\ a_{1k} \log(1+ \frac{t-t_{k}}{\tau_{1k}}) + a_{2k} \log(1+ \frac{t-t_{k}}{\tau_{2k}}) \text{ if PSD model is log+log} \\ \\ a_{1k}(1- \exp(-\frac{t-t_{k}}{\tau_{1k}})) + a_{2k}(1- \exp(-\frac{t-t_{k}}{\tau_{2k}})) \text{ if PSD model is exp+exp} \end{cases} \end{align} $$