## 1. Introduction

[2] The earth's crust is subject to tidal phenomena such as earth body tides and ocean tide loading, which result in periodic motion of sites occupied by permanent, continuously operating GPS receivers. The eight principal tidal constituents, M2, S2, N2, K2, O1, K1, P1 and Q1, have either semi-diurnal or diurnal periods and cause unwanted signatures for applications aiming to detect long period crustal motion.

[3] The majority of papers describing GPS data analysis for geophysical applications estimate station positions using a 24 hour processing session [*Larson et al.*, 2001]. Earth body tide and ocean tide loading effects are usually modeled when processing the GPS data, but as no tidal model can perfectly reproduce the true tidal signature, residual tidal errors will always remain.

[4] Unmodeled or residual crustal tides have periods shorter than may be resolved using a 24 hour processing session. The result is that these tidal signatures will appear in the final coordinate time series as aliased signals with longer periods than the original semi-diurnal and diurnal signals. The presence and frequency of these aliased signals is well documented [*Lambert et al.*, 1998; *Dong et al.*, 2002] and is generally assumed to be small since semi-diurnal and diurnal signals average close to zero over a 24 hour processing session [*Dragert et al.*, 2000].

[5] Aliasing of ocean tide harmonics is important in satellite altimetry studies, although not, as with GPS, due to the presence of a residual tidal signature after data averaging over a set time interval. Instead, long period aliased signals result from the sampling of semi-diurnal and diurnal tidal harmonics at an interval equal to the repeat orbit period. Altimetry satellites have repeat orbit periods of the order of several days. For example, TOPEX/POSEIDON has a repeat orbit period of 9.9156 days, resulting in an aliased period of 58.74 days for S2, the pure semi-diurnal constituent. Indeed, the avoidance of certain aliased periods was a major criterion in the orbital specifications of the Geosat, ERS-1 and TOPEX/POSEIDON satellites [*Cartwright*, 1999] and the study of aliased ocean tide signatures is an integral part of the analysis of satellite altimeter data [e.g., *Parke et al.*, 1987; *Cartwright and Ray*, 1990; *Schlax and Chelton*, 1994].

[6] GPS satellites have a repeat orbit period of one sidereal day, which, although considerably shorter than the repeat orbit periods for Geosat, ERS-1 and TOPEX/POSEIDON, is insufficient to adequately sample semi-diurnal and diurnal tidal constituents. It may therefore be hypothesized that the repeat orbit aliasing effect seen in altimeter data due to ocean tides may also be present in GPS data due to unmodeled or residual crustal tides. The basis for this hypothesis can be further explained by considering 24-hour GPS processing sessions and resulting coordinate time series. For each 24-hour session, GPS observations are usually processed at data points defined according to an epoch separation, accumulated and a single set of coordinates obtained using least squares. Due to the GPS repeat orbit period equaling one sidereal day and not 24 hours, the satellite geometric distribution will differ for a data point considered for the same time of (solar) day in two consecutive 24-hour processing sessions. Hence even if the period of the tidal phenomenon were to equal the duration of the processing session, the effect of a crustal tide displacement might affect equivalent data points in successive 24-hour processing sessions differently and propagate to the coordinates derived from the observations accumulated in each 24-hour processing session. Thus it is feasible that the effect of unmodeled crustal tides on a least squares coordinate estimate derived from a GPS processing session will depend on the tidal period, the length of the processing session, and the geometric distribution of the satellites. Now the same satellite distribution will only coincide with the same tidal displacement at certain instances according to the repeat orbit period and tidal period considered. It may therefore be expected that the mitigation of tidal effects in GPS data processing does not simply depend on data averaging, but that a second aliasing effect caused by the repeat period of the satellites may also arise.

[7] This paper tests the hypothesis that not one but two tidal aliasing effects are present in continuous GPS time series derived using a 24-hour processing session. First, the theoretical aliased periods of the eight principal semi-diurnal and diurnal tidal constituents are presented for both the “24-hour processing” and the GPS constellation “repeat orbit” effects. Second, aliased periods are derived from a 10-year span of simulated GPS data for which tidal effects were the only introduced bias. Finally, in the light of the theoretical and simulated results presented, comment is made on some results from previously published work that derive coordinate time series by processing real GPS data in 24-hour sessions.