## ITRF2020

The ITRF2020 solution provides the usual/classical estimates: station positions at a given epoch, station velocities and EOPs, but also Post-Seismic Deformation (PSD) parametric models for stations subject to major earthquakes, as well as annual and semi-annual periodic terms expressed in the Center of Mass (CM – as sensed by SLR) frame, as well as in the Center of Figure (CF) frame.

### Reference epoch

The reference epoch of ITRF2020 is $t_{0}$ = 2015.0

### Station position kinematic model

The tri-dimensional coordinates of a station can be computed as follows:

$$\Large X(t) = X(t_0) + \dot{X}(t-t_0) + \delta X_{PSD}(t) + \delta X_f(t)$$

The station positions $X(t_0)$ and velocities $\dot{X}$ can be found in the SINEX files (ITRF2020-*.SNX.gz or ITRF2020-*.SSC). They are valid at the time intervals provided in the discontinuity files (ITRF2020-soln-*.snx).

### Notes on the post-seismic deformation (PSD) models, $\delta X_{PSD}(t)$

The full equations of the parametric models used in the ITRF2020 generation are supplied in the pdf file “ITRF2020-psd-model-eqs-IGN.pdf”.
The full PSD estimated parameters and their variances are provided in SINEX format (ITRF2020-psd-*.snx) for stations where such terms had to be introduced.
A user who wants to compute the position of a station affected by post-seismic deformation after one or more earthquakes should compute $\delta X_{PSD}(t)$, which is the total sum of the PSD corrections, i.e., the PSD corrections of successive earthquakes are cumulative. The user should read the model parameters (EQ epoch, model type, LOG or/and EXP, amplitude and relaxation time) in one of the following two files:

• SINEX file (ITRF2020-psd*.snx). These files provided per technique contain the full information of the parametric models used in the ITRF2020 generation, including the variance-covariance information. It is strongly recommended to use these SINEX files, especially if the user needs to compute the variance of the estimated corrections. Please refer to the equations in the pdf file “ITRF2020-PSD-model-eqs-IGN.pdf”. A Fortran subroutine called “psdmatc.f” is provided which allows computing the terms of the matrix used in the variance-covariance propagation equations.
• CATREF internal file (ITRF2020-psd.dat). In this case a subroutine called “parametric.f” is provided that allows computing $\delta X_{PSD}(t)$. An example of a subroutine called “psd-example.f” is provided, which shows how to add or subtract the PSD corrections to XYZ coordinates at an epoch t, using CATREF internal files (ITRF2020-psd.dat). It should be adapted by the user to his application (see commentary lines). Note that using CATREF internal files does not allow computing the variance-covariance matrix of $\delta X_{PSD}(t)$.

### Notes on the annual and semi-annual frequencies

The files ITRF2020-Frequencies-XYZ-CM.dat and ITRF2020-Frequencies-ENU-CM.dat provide the cosine and sine terms at the annual and semi-annual frequencies in XYZ and ENU, respectively, expressed in the CM (as sensed by SLR) frame. The files ITRF2020-Frequencies-XYZ-CF.dat and ITRF2020-Frequencies-ENU-CF.dat provide the seasonal terms in the CF frame. The user who wants to make use of the annual and semi-annual signals should compute the sum of both using the following equation and add to the station coordinates at epoch $t$.

$$\Large \delta X_f(t) = \sum^{2}_{i=1} \begin{pmatrix} a^i_x \\ a^i_y \\ a^i_z \end{pmatrix} \cos(2i\pi t) + \begin{pmatrix} b^i_x \\ b^i_y \\ b^i_z \end{pmatrix} \sin(2i\pi t)$$

Where $t$ is the decimal year. The two files list per station and per frequency the 6 coefficients of the above equation: ($a_x,b_x$), ($a_y,b_y$), ($a_z,b_z$) and ($a_E,b_E$), ($a_N,b_N$), ($a_U,b_U$), respectively, together with their uncertainties in mm. The columns of the files are organized as follows: 4-char station ID; PT code; DOMES number; soln; component; $a$; $\sigma_a$; $b$; $\sigma_b$
The annual coefficients are listed first, followed by the semi-annual terms.
The ITRF2020 seasonal terms are additionally provided in SINEX format, in the files ITRF2020-Frequencies-*.snx. Those files do not include the full covariance matrix of all estimated seasonal coefficients, but only their uncertainties. Users possibly interested in the full covariance matrix should send a request to itrf@ign.fr.
Multiple stations within the same site, and multiple segments for stations with discontinuities (see validity period of each “soln” in ITRF2020-soln-*.snx) were constrained to have the same seasonal terms, at a certain sigma level as a function of their agreement. Therefore, for most sites, the same terms are repeated for all multiple points within the same site, even if they are consistent.
Seasonal signals were not estimated for stations with short time span, and so are listed with zero values.