Earth Deformation Effect

Fundamentals
Title	Earth Deformation Effect
Author(s)	J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level	Basic
Year of Publication	2011

The receiver station coordinates are affected by tidal motions that must be accounted for when high accuracy is required. It is important to point out that these effects do not affect GNSS signals, but if the tidal effects were not considered the station coordinates would oscillate with relation to a mean value as a consequence of these effects.

The main reasons for the earth's crust to vary and modify the receiver location coordinates are summarised in:

• Solid Tides
• Ocean loading
• Pole Tide

The vector of tidal displacements for each one of such effects is labelled [math]\displaystyle{ \Delta {\mathbf r}_{sol} }[/math] , [math]\displaystyle{ \Delta {\mathbf r}_{ocn} }[/math] and [math]\displaystyle{ \Delta {\mathbf r}_{pol} }[/math], respectively. After computing each tidal displacement, the receiver location is given by:

[math]\displaystyle{ {\mathbf r}_M ={\mathbf r}_{M_0}+\Delta {\mathbf r}_{sol}+\Delta {\mathbf r}_{ocn}+\Delta {\mathbf r}_{pol} \qquad\mbox{(1}) }[/math]

where [math]\displaystyle{ {\mathbf r}_{M_0} }[/math] are the MM coordinates free of tidal displacements and [math]\displaystyle{ {\mathbf r}_M }[/math] is given by equation (2).

[math]\displaystyle{ {\mathbf r}={\mathbf r}_M+{\boldsymbol \Delta}_{ARP}+{\boldsymbol \Delta}_{APC} \qquad\mbox{(2}) }[/math]

where [math]\displaystyle{ {\mathbf r}_{M} }[/math] is the position of Monument Marker in a ECEF reference frame. [math]\displaystyle{ {\boldsymbol \Delta}_{ARP} }[/math] is the offset vector defining the ARP position relative to the Monument Marker, and [math]\displaystyle{ {\boldsymbol \Delta}_{APC} }[/math] the offset vector defining the APC position relative to the ARP (see Receiver Antenna Phase Centre).