Today repeated GPS measurements are still in use, because we cannot always employ GPS permanent stations due to a variety of limitations. One area of study that uses velocities/deformation rates from repeated GPS measurements is the monitoring of crustal motion. This paper discusses the quality of the velocities derived using repeated GPS measurements for the aim of monitoring crustal motion. From a global network of International GNSS Service (IGS) stations, we processed GPS measurements repeated monthly and annually spanning nearly 15 years and estimated GPS velocities for GPS baseline components latitude, longitude and ellipsoidal height. We used web-based GIPSY for the processing. Assuming true deformation rates can only be determined from the solutions of 24 h observation sessions, we evaluated the accuracy of the deformation rates from 8 and 12 h sessions. We used statistical hypothesis testing to assess the velocities derived from short observation sessions. In addition, as an alternative control method we checked the accuracy of GPS solutions from short observation sessions against those of 24 h sessions referring to statistical criteria that measure the accuracy of regression models. Results indicate that the velocities of the vertical component are completely affected when repeated GPS measurements are used. The results also reveal that only about 30 % of the 8 h solutions and about 40 % of 12 h solutions for the horizontal coordinates are acceptable for velocity estimation. The situation is much worse for the vertical component in which none of the solutions from campaign measurements are acceptable for obtaining reliable deformation rates.

Today GPS is widely used to monitor crustal motion. Methods of continuous GPS have been well established for this purpose (Mao et al., 1999; Williams et al., 2004; Amiri-Simkooei et al., 2007) and are routinely used for monitoring tectonic motion. Researchers are also studying real-time continuous GPS and high-rate GPS from the frequencies of 1 to 50 Hz GPS for the same purpose (Genrich and Bock, 2006; Blewitt et al., 2006, 2009; Larson, 2009; Avallone et al., 2011; Crowell et al., 2012). Such studies aim to use the results for the early prediction of earthquakes, tsunamis and other natural hazards of similar character.

Static GPS measurements have been the tradition for resolving large crustal motion. However, recently scientists have been working on improving the quality of real-time measurements and rapid static GPS based on continuously operating reference stations (Crowell et al., 2012; Hastaoglu and Sanli, 2011; Wang and Soler, 2012). The accuracy of static GPS measurements has been documented well. Researchers have studied the effect of observing session duration, baseline length and the network of reference stations on the accuracy of the static GPS (Eckl et al., 2001; Soler et al., 2006; Sanli and Engin, 2009; Firuzabadì and King, 2012).

Repeated static GPS measurements (also known as GPS campaigns or episodic GPS), which were the desired methods in crustal motion monitoring starting from the end of 1980s, are still in use due especially to financial limitations and various other constraints. Ideal observation session length for a GPS campaign is 24 h. Additionally, carrying out repeated GPS measurements in three different sessions over 3 consecutive days is desired. However, depending on the field work limitations, repeated GPS measurements are sometimes performed with only one session usually lasting 6 h through 12 h. In the literature, it is possible to come across many crustal deformation experiments performed in this way (Miranda et al., 2012; Elliot et al., 2010; Rontogianni et al., 2010; Ashurkov et al., 2011; Ozener et al., 2012; Tran et al., 2012; Catalão et al., 2011).

Time series characteristics of continuous GPS solutions and the quality of velocities estimated from long GPS time series have been studied in detail (Williams, 2003; Amiri-Simkooei et al., 2007; Santamaría-Gómez et al., 2011). The accuracy of GPS static positioning has also been reported thoroughly; however, investigations on the accuracies of static GPS velocities from repeated measurements have not been carried out yet (Eckl et al., 2001; Soler et al., 2006; Sanli and Engin, 2009; Firuzabadì and King, 2012). While bringing rapid static GPS solutions into conformity with static GPS solutions, Hastaoglu and Sanli (2011) noticed that the accuracy of GPS velocities from the repeated measurements is highly correlated with the observing session duration.

In this study, using the continuous data of International GNSS Service (IGS) stations archived by the Scripps Orbit and Permanent Array Center (SOPAC) we studied the accuracy of static GPS velocities from the repeated campaign measurements. The 24 h IGS data were segmented into shorter sessions (i.e., 8 and 12 h) to create the GPS campaigns, and GPS positions were computed for these sub-segmented campaigns. Position time series were formed for all three GPS baseline latitude, longitude and ellipsoidal height using data from the repeated GPS campaigns, which were prepared as explained in the above. The GPS velocities computed from the short GPS campaigns for all three baseline components were then compared with the velocities computed from 24 h data. Based on various statistical methods, conclusions were drawn on the quality of the velocities derived from campaign measurements which are still in use today for monitoring crustal deformation.

GPS data were obtained from IGS through
SOPAC archives at

IGS permanent GPS stations used in the study.

The Automatic Precise Positioning Service (APPS) was used to process the GPS
data. APPS is implemented by the Global Differential GPS System of
NASA's JPL (

A total of 13 IGS sites distributed widely around the globe were selected for the analysis (Fig. 1). We applied two different analysis strategies. First, for each site we selected around 15 days of data observed each year in January from the years 1995 to 2010 inclusive. This was to assess the GPS campaigns that are performed traditionally. Namely, GPS data are collected 1 day per year, usually over 6 to 10 h, and the campaigns are continued for a few years. Secondly, we sampled the data (i.e., densified the time series), taking 1 day from each month of the year corresponding to January, again spanning about 15 years. This was actually to take into account the seasonal variation due to annual and semiannual terms in the vertical component (Blewitt and Lavalleé, 2002). Obviously this would not be achieved with annually sampled data.

Each day's data were subdivided into mutually non-overlapping sessions for
each of 8 and 12 h values of the observing session. For each subset of
data, we computed the positional coordinates using the PPP method described
above. For each day and each unknown point, a position was computed for each
24 h session. The position from each day's 24 h sessions was then adopted as
the “true” position of the point. For the monthly and annually sampled data
spanning 1995 through 2010, true position time series for the geodetic
coordinates latitude, longitude and ellipsoidal height (i.e.,

In this section we describe our analysis procedure for the site KIRU using the annually sampled GPS campaigns, and in the following section we present results and discussions for all 13 sites following the same procedure. Figure 2 depicts the comparison of 8 and 24 h position time series for three GPS baseline components: latitude, longitude and ellipsoidal height.

Comparison of the crustal motion using the results of short sessions and 24 h solutions for the station KIRU.

In Fig. 2, the black discrete line connected through a black diamond indicates
the variation with time from 24 h measurements. The variations of 0–8,
8–16 and 16–24 h are superimposed onto the variation of the 24 h. Note
that for latitude and longitude the variation from sub-segmented 8 h solutions
align well with the variation from 24 h. The difference of the
deformation rates for the longitude values is only slightly worse than those
of the latitude values. This is also the case for the

However, the height component deviations of short sessions in comparison to 24 h solutions are greater. In order to provide a clearer presentation we prepared Table 1.

Comparison of the

In Table 1, we compare crustal motion and

The residual

Note that for the horizontal components in Table 1,

The crustal motion for the height component for KIRU from the annually
sampled data is not clearly linear, and hence

In order to assess the velocities from 8 and 12 h solutions, we applied
hypothesis testing to the velocity values

As an alternative statistical methodology, we formed root mean square
differences (RMSDs) using 24 h solutions as the truth and compared those with
root mean square error of the estimated coordinates (RMSEEs) derived from the
regressions of individual short session solutions. The RMSD between the time
series of 24 h solutions and those of the shorter data spans
(i.e., 8 and 12 h) can be formed with (Pan and Yin, 2012)

In Tables 2 through 4 we represent the statistical hypothesis testing
results outlined in the previous section and the

Hypothesis testing results for latitude: rejections indicated in
bold-faced letters are related to an

Hypothesis testing results for longitude: rejections indicated
in bold-faced letters are related to an

Hypothesis testing results for ellipsoidal height: rejections
indicated in bold-faced letters are related to an

In the tables, if

Note that Table 4 contains results from only five of the GPS stations we used.
This is because we omitted the stations with

As expected, both deformation rates and

Note that

In fact, 11 out of 13 GPS stations include significant annual components in
the height coordinate. However, only five of the stations are affected by the
semiannual component. This has been confirmed by applying Student's
two-sided

Eight hour solutions obviously show poorer results. Only 37 % of latitudinal velocities and 21 % of the longitudinal velocities are significantly comparable to those of the 24 h solutions (Tables 2 and 3). The fact that longitudinal estimates are worse than latitudinal estimates could be ascribed to the ambiguity resolution. At the time of processing version 5.0 of the APPS software was available. However, GIPSY ambiguity resolution released with version 6.0. Bertiger et al. (2010) showed the improvement on the longitudinal component after applying ambiguity resolution in the processing. Eight hour vertical velocity estimates are much worse than those of the horizontal velocity estimates. According to this, all of the estimated velocities from 8 h sessions significantly differ from those of the 24 h solutions (Table 4).

One can infer from the above discussion that the accuracy of the vertical velocities is affected much worse compared to those of the horizontal components. In addition, if one extends the observing session from 8 to 12 h, the accuracy is improved. The reason we prefer to analyze 8 and 12 h is that those session durations approximate the lower and the upper limits to the ones usually applied in practice. In other words, the user prefers about 10 h on average as the observation session for the repeated GPS measurements, and they usually desire to take advantage of the daylight.

Comparison of

The ideal session length for a GPS campaign is obviously 24 h. This is
mainly due to the fact that satellite constellation repeats in 24 h and
hence all the systematic effects such as multipath and mapping-function
errors tend to average out (Blewitt, 1993). If this cannot be managed, one
needs to collect GPS measurements at least for 18 h in order to eliminate
the effect of the semi-diurnal (

Comparison of RMSDs and RMSEEs is given in Tables 6 through 8. In the tables, under the column RMSD, root mean square differences between 24 h solutions and the solutions from shorter data spans, such as 8 and 24 h, are represented according to Eq. (5). The RMSEE column shows root mean square error of estimated coordinates for 8 and 12 h solutions according to Eqs. (6) or (7). The solutions showing agreement between the two measures are presented in bold-faced letters. The comparisons are made for all three GPS baselines latitude, longitude and ellipsoidal height in Tables 6 through 8.

Testing whether RMSEEs from individual latitudinal short session regression models are identical to RMSDs formed using 24 h solutions as the truth (1 mm threshold is used). The identical solutions are shown with bold numbers.

Testing whether RMSEEs from individual longitudinal short session regression models are identical to RMSDs formed using 24 h solutions as the truth (1 mm threshold is used). The identical solutions are shown with bold numbers.

Testing whether RMSEEs from individual vertical short session regression models are identical to RMSDs formed using 24 h solutions as the truth (1 mm threshold is used). The identical solutions are shown with bold numbers.

If we accept the RMSDs as the truth and compare RMSEEs with those, 36 % of 8 h solutions and 38 % of the 12h solutions show agreement around 1 mm for the latitudinal component (Table 6). These are indicated with bold-faced numbers in the tables. Note that these results are comparable with those of the hypothesis testing results, in which 37 % of velocities derived from 8h solutions and 40 % of the velocities derived from 12 h solutions were found to be statistically significant.

For the longitude component, 28 % of 8 h and 38 % of 12 h RMSEE values showed good agreement with RMSD values (Table 7). These are also comparable to those of the hypothesis testing results, in which only 24 % of the velocities derived from 8 h and 43 % of the velocities derived from 12h solutions were found to be useful.

For the vertical component, only one RMSEE value, which corresponds to about 3 % of the total solutions, was found to be comparable to the corresponding RMSD value. This result is also comparable to the hypothesis testing result for the height component, in which none of the vertical velocities were found to be useful from short observation sessions.

In this article, we assessed the accuracy of velocities from repeated GPS measurements. GPS experiments still reporting the results from repeated measurements motivated us to carry out this study. Continuous data of a global network of IGS stations were used to perform the evaluations. This helped us to comprehend the regional differences. Since, in practice, repeated GPS measurements are typically carried out in sessions of about 10 h, we studied observation sessions of 8 and 12 h. Based on the above information our conclusions are as follows.

Accuracy loss for the velocities occurs when using repeated GPS measurements
from short sessions. This is because one does not perform ideal 24 h
observations. 18 h should be sufficient considering that the effect of ocean
tide loading can only be eliminated over 1.5 times the length of the
semi-diurnal M

We used two different statistical methods to assess the quality of our
results. First we assessed whether or not the estimated velocities from short sessions
(i.e., 8 and 12 h) are comparable to those of 24 h sessions
referring to statistical hypothesis testing. Second, we evaluated
whether the accuracy of the regressions (i.e., RMSEE) from shorter sessions are identical to RMSDs formed holding 24 h solutions as the truth. The
comparison of the two led to an independent accuracy evaluation. In both
approaches, we assumed 24 h solutions produce true values and deviation from
24 h solutions should result in accuracy losses. Higher

Our first major conclusion is that the vertical rates produced from repeated GPS campaigns are severely affected. In addition, considering only the annual and the semiannual periodicities for the vertical component was not sufficient to capture the true vertical signal for most of the stations. In 8 out of 13 stations other influences dominated, resulting in greater modeling errors. We noticed low-frequency hidden periodicities in the vertical component; however, these need to be revealed by adopting sophisticated time series analysis procedures in the future. The above-mentioned first method revealed that none of the velocities from shorter GPS sessions were useful for the height component. The second method gave almost a similar result in which only 3 % (i.e., one of the solutions) of the RMSEEs were found to be comparable to the RMSDs. This shows us that the results derived from campaign GPS data using 8–12 h observation sessions are not useful for height determination.

Our horizontal velocity evaluations based on the statistical methods highlighted above showed pretty close results in which only about 30 % of 8 h and 40 % of 12 h solutions were found to be useful. Increasing observation duration from 8 to 12 h did not show much accuracy improvement, i.e., as much as 10 %; however, 60–70 % accuracy loss in the case 24 h data is not really credible. Many research groups considered that at least the horizontal components would not be affected when using repeated GPS campaigns; however, the results of this study contradict with such ideas.

Obviously, these results are essentially related to GIPSY PPP methodology, in which minimum 6 h data are requested for a solution as stated in the literature. However, this is also related to conventional relative positioning (RP) results where regional or global studies are concerned. Many crustal deformation experiments to date were monitored using RP connecting to IGS reference stations which are located on stable tectonic plates hundreds or thousands of kilometers away from study areas.

Mostly the GPS stations from the lower or the equatorial belt suffer from modeling errors and hence accuracy loss, especially for the vertical component. One known error source acting on repeated GPS campaigns and dominating at these regions is ionospheric disturbances due to the magnetic field of the earth.

The data of this study were obtained from the IGS through SOPAC archives. We express our gratitude to both institutions for their excellent service in distributing the GPS data and the other products. Processing of the data was performed using web-based GIPSY (i.e., APPS). We would like to thank NASA for the excellent processing facility that could be used worldwide research community. Last but not least we would like to thank three anonymous reviewers and the editor David Keefer for their constructive reviews. Edited by: O. Katz Reviewed by: A. Dermanis and three anonymous referees