6.2 Concepts and Methodologies
6.2.5 Regional Filtering
Coordinate time series derived from daily solutions in regional GPS networks have previ- ously been shown to contain large spatial correlations. Penna(1997) observed correlations in the measurements obtained at UK episodic GPS stations of up to 500 km. Calais(1999) showed that the coordinate time series of three CGPS stations in the Alps were highly correlated and Herring (1999) reported spatial correlations in the order of 60 to 70% for two IGS stations in Australia separated by 300 km. Spatial correlations in BIFROST have been reported to be in the order of 1000 km (Johansson et al.,2002). The characteristic of these correlations suggests a common source for this systematic effect, which has been attributed to reference frame or satellite orbit type biases (Wdowinski et al.,1997;Calais,
1999;Mao et al., 1999; Herring et al., 2002). It is believed that this common mode bias affects GPS observations in regional networks in a similar manner, e.g. by use of a common set of satellites in all regional stations, thus introducing the observed spatial correlations.
Several methods for a spatial filter in order to reduce the amount of correlation can be found in the literature. The method of stacking the daily residual was first introduced by Wdowinski et al. (1997). The coordinate time series of the then Southern California Permanent Geodetic GPS Array (PGGA) (now Southern California Integrated GPS Net- work (SCIGN) see http://www.scign.org) were filtered using this approach and it was possible to improve the signal–to–noise ratio in the data. The reduced RMS scatter of the coordinate time series provided much higher resolution for detecting transient signals on a site–by–site basis without having to fix the position of any site in the regional network.
Chapter 6. Analysis of the Continuous GPS Network 151
This method has previously also been applied by the author to the preliminary height time series of a network of CGPS stations in the UK (Teferle et al.,2002a). A different method for reducing the global scale systematic bias in coordinate time series was presented by
Herring et al. (2002). This approach is based on a local frame realization using stations in a 1200 × 1800 km region in the Tien Shan, Central Asia. In this study, the local frame was matched onto a frame based on Eurasian sites by rotation and translation. This reference frame was in turn defined by minimizing the velocities of these stable Eurasian sitesHerring et al.(2002). The application of a local reference frame definition in order to remove the common mode bias from the GPS coordinate time series of a regional network has also been applied in the analyses of the SCIGN carried out by JPL (Hurst, 2000,
2001).
Using the stacking method (Wdowinski et al., 1997), the common mode bias can be computed as the mean of the coordinate residuals for a selection of stations on a particular day. Here it is important to note that Wdowinski et al. (1997) did not detrend the height time series prior to computing the common mode bias, as they were within their uncertainties. They also applied the algorithm separately for periods before and after an earthquake, and stations that were suspected of experiencing gradual displacements after the event, were not included in the stacking of the daily position components.
In this analysis, the author has applied an updated method for computing the common mode bias. Coordinate offsets, as determined in §6.3.3, have been used to correct for any changes in the coordinate time series and two sets of residual coordinate time series have then been generated, i.e. a trended and a detrended one. Based on the coordinate residuals vi,sof each station s for each day i = 1, . . . , N and the standard errors σi,sof the coordinates, the following equation has been applied to estimate a common mode bias ǫi for each day (Nikolaidis,2002):
ǫi = 0 : Si(ti) < 3 PSi s=1vi,s/σ2i,s PSi s=11/σ2i,s : Si(ti) ≥ 3 (6.1)
with Si being the number of available CGPS stations in the network per day. If Si < 3, then no common mode bias was computed. In a second step, the daily, coordinate specific,
Chapter 6. Analysis of the Continuous GPS Network 152
common mode biases are then subtracted from the raw coordinate time series yi of all stations so that a spatially filtered coordinate time series ˜yi is derived according to
˜
yi = yi− ǫi (6.2)
These filtered coordinate time series then allow the estimation of the best fitting model parameters using least–squares. A new RMS statistic of the residual coordinate time series obtained at this stage can be computed and compared to the RMS statistic of the residual coordinate time series based on the unfiltered data. The amount of change in the RMS scatter can then be expressed in percent of improvement using the following ratio
%Improvement = RMSunf lt− RMSf lt
RMSunf lt
. (6.3)
When computing the common mode bias using this method, several issues have been identified by the author. First, the reduction in the RMS scatter and hence the im- provement of the signal–to–noise ratio is favourable, however care must be taken in order not to introduce signals into individual coordinate time series by inclusion of stations with abnormal behavior in the common mode computation. This may be carried out by selecting a number of representative stations in the regional network on which the common mode computation can be based. Nikolaidis (2002) applied this strategy in the analysis of the SCIGN network, where in order to maintain a consistent setup for the analysis, eight fiducial stations were defined, which have been observed throughout an eleven year period. In Teferle et al. (2002a), the author excluded ABER from the computation of the common mode bias due to the RF interference (see §5.3.3) at that site. Since the re–analysis, additional CGPS stations have been introduced suggesting a need for a more detailed investigation into which of the UK CGPS stations should be included in the stacking process.
A series of thirteen tests were carried out by the author in order to define a set of CGPS stations to be used for the regular computation of the common mode bias. These tests are summarized in Table6.4. In all thirteen tests carried out, the detrended residual
Chapter 6. Analysis of the Continuous GPS Network 153
Table 6.4: Common mode bias tests for the UK CGPS station network. () indicate that only this coordinate component has been excluded in the stacking process.
Test Horizontal Height Stations included in the Components Component stacking process
1 detrended trended all stations included 2 detrended detrended all stations included
3 detrended trended all except for ABERa, ABYWb, MORP, and NSTGc
4 detrended detrended as for Test 3
5 detrended trended all except for ABER, ABYW, BARK(H), BRST(E,H), DUNK(E), LERW(E,H), LIVE(N,E), MORP, NSTG, SHEE(N) and SUNB(E)
6 detrended detrended as for Test 5
7 detrended trended all except for ABERa, ABYW,
BARK(H), LERW(H), MORP, NSTG, SHEE(N) and SUNB(E)
8 detrended detrended as for Test 7 9 trend and annual signals removed all stations included
10 detrended trended ABYW, CAMB, HEMS, LERW, DUNK,
HURN, PERS, and IESG 11 detrended detrended as for Test 10
12 detrended trended BRST, CAMB, NEWL
13 detrended detrended as for Test 12 abefore 30 April 2001 (see §5.3.3)
bsee §5.3.3 csee §5.3.3
coordinate time series for the horizontal components were used, however for the height component the detrended residual height time series were only used in six cases.
In general, the estimation of the common mode bias is assumed to be better if more stations are included in its computation (Wdowinski et al.,1997). Therefore, all stations were included in the initial tests 1 and 2. In tests 3 and 4, four CGPS stations ABER (prior to 30 April 2001), ABYW, MORP and NSTG were excluded from the stacking process, as all have already been identified to be affected by RF interference, multipath or other receiver problems (see §5.3.3and §6.3.1). In tests 5 and 6, all stations with annual amplitudes > 3 mm were also excluded as these were assumed to be due to local effects
Chapter 6. Analysis of the Continuous GPS Network 154
rather than the common mode bias. In tests 7 and 8, only the initial four CGPS stations plus those showing amplitudes larger than two times the standard deviation σaof the mean amplitude of the annual signals computed in §6.2.3 were excluded. Test 9 differs from previous tests in that the residual coordinate time series were computed using a model consisting of a linear and annual term and parameters for coordinate offsets. Whereas these tests tried to use as many stations as possible, tests 10 to 13 used a selection of stations only. In accordance with Nikolaidis(2002), tests 10 and 11 investigated whether a common mode bias representative for all UK CGPS stations could be based on a few stations covering the whole network. As the CGPS stations of the Met Office present themselves as possibly being of higher quality than the CGPS@TG stations (§5.3 and §6.3.1), the author decided to test whether it was possible to base the stacking algorithm on the Met Office and IESG CGPS stations only, purposely excluding the noisier CGPS@TG stations. The final set of tests was only based on the coordinate time series for stations BRST, CAMB and NEWL. As mentioned, these stations are situated in an area with large OTL effects, which have not been modeled correctly as was discovered by the author in the GPS processing (see §6.3.1). Clearly, it cannot be expected that a common mode bias for the whole of network based on these three stations can be computed, however, in this case the emphasis was on whether it was possible to correct the coordinate time series for these stations for the mis–modelling of OTL.