The main emphasis of the GPSVEL project is to attach regional permanent and campaign GPS solutions into a global frame. The approach will be modular, regional velocity solutions will be attached to a "core" global frame in the most rigorous way possible. The procedure will loosely follow the procedures developed within the IGS densification project.

IGS Densification project

The IGS densification project was initiated in September 1995 [Blewitt et al., 1995; Zumberge and Liu, 1995] and produces consistent weekly station coordinate solutions. The project was designed to produce a high quality reference frame while reducing the processing burden by "distributed processing" [Blewitt et al., 1995; Davies and Blewitt, 2000; Zumberge and Liu, 1995]. In this scheme the IGS Global Analysis Centers (AC) process sufficient global sites to estimate (amongst other GPS products) precise orbits which are combined to give the IGS official orbit and coordinates. The IGS Regional Network ACs (RNAACs) then estimate denser regional site coordinate solutions, fixing the IGS orbit. The Global Network Associate Analysis Centers (GNAACs) then combine these global and regional solutions to produce the IGS "polyhedron". A key factor in this approach has been the use of Solution Independent Exchange (SINEX) format files which records station coordinates, both full a priori and a posteriori variance-covariance information and all site equipment information

Core solution

The GPSVEL "core" global velocity solution will be a kinematic combination of weekly solutions from the IGS GNAAC at the University of Newcastle upon Tyne (NCL). The methods used by the NCL GNAAC to produce weekly GPS solutions are described by Davies and Blewitt [2000]. The NCL GNAAC combines coordinate solutions from the 7 IGS Global ACs and 3 RNAACs using a free-network approach with outlier detection and an evolving variance component procedure [Davies and Blewitt, 2000]. Site coordinates are classified as Global (G) when they have been estimated by at least 3 Global AC's and subjected to outlier detection, Regional (R) when they have been estimated by a Regional AC and A-R when they fail the 3 estimate requirement to become G points.

Free-networks are created by (i) removing any a priori constraints from AC SINEX and (ii) augmenting the de-constrained estimate covariance matrices so that the standard errors of the unobserved reference frame parameters become large. Only G-network rotation parameters are augmented since with global coverage the average offset of the polyhedron relative to the Earth systems center of mass is estimable. For R-networks both rotation and translation are augmented since the origin is non-estimable. This loose minimal constraints approach avoids introducing reference system parameters into the combination functional model. The free-networks are then combined using a modified Helmert blocking procedure where the R-networks are "attached" to the G solution via at least 3 junction stations [Davies and Blewitt, 2000]. Junction stations in R-networks are back substituted with G network estimates and in this way the R-networks are not allowed to perturb the primary G reference frame.

An initial step in producing velocities has been to correct errors in applied antenna hgt in all weekly AC SINEX solutions reproducing the NCL SINEX for the early part of the IGS densification project (GPS weeks 0815-1022). During this early part of the project site information was updated by email and often inconsistent/unreliable. In this manner 2522 inconsistencies were corrected improving site precision and reliability since (i) less outliers were rejected and (ii) the most up to date AC SINEX was used when resubmissions occurred.

IGS weekly RNAAC solutions often include stations that are not "official" IGS sites and are not included in the weekly NCL combination. These sites are often important from a plate tectonic perspective so to include these sites in GPSVEL 0.1 an alternative procedure to estimating velocities to that described by Davies and Blewitt [2000] is adopted. To avoid re-estimating the entire NCL SINEX series, R sites are rejected from the NCL series and velocity solutions are estimated for each RNAAC including the additional sites.

These velocity solutions are then attached to the global velocity solution (which includes both G and AR points) using the same modified Helmert-Wolf blocking procedure used in the weekly combination [Davies and Blewitt, 2000] but extended to 6 parameters (xyz position and velocity).

The core solution is aligned to ITRF2000 using by estimating a 14 parameter Helmert transformation and applying 12 parameters (scale excluded), 14 parameters are estimated since scale parameters are correlated with rotation and translation parameters.

Velocities are estimated from the free-networks using the following criteria:

(i) To be included a site must have at least 104 observations over a minimum 2.5 year data-span.

(ii) Both annual and semi-annual periodic terms are estimated.

(iii) Time series offsets due to equipment changes, earthquakes etc. are estimated where necessary.

It has been shown that a minimum data-span for reliable GPS velocity estimates is 2.5 years [Blewitt and Lavallee, 2001]. Significant annual variation is induced by hydrological and atmospheric loading [Van Dam et al., 2001], significant periodic variation is also seen in GPS time series [Blewitt and Lavallee, 2001] typically at the 2 and 4 mm level in the horizontal and vertical respectively. [Blewitt and Lavallee, 2001] show that for data-spans less than 2.5 years such periodic signals cause significant velocity bias when not accounted for. Annual and semi-annual periodic terms are therefore accounted for in the functional model (ii) however only for sites not requiring offsets (iii). At shorter data spans and when estimating additional time series offsets (iii) the increase in velocity formal error due to the extra parameters is unacceptable. A minimum data span of 2.5 years is therefore chosen to counter both these issues. The data span of sites in the solution is 2..5- 5..5 years with a mean data-span of 4.2 years and over 50% of site velocities estimated from greater than 5 years of data.

Extra position offsets are often estimated in GPS time series to account for co-seismic displacements and changes in equipment setup such as antenna and radome changes. In GPSVEL 0.1 for example 61 sites require between them 102 such offsets, of these 11% are correlated with nearby earthquakes, 54% with equipment changes and 35% are for unknown reasons. Furthermore 24 of these sites are amongst the 107 sites that could be considered within stable plate interiors. The velocity formal error when estimating offsets depends on the length of the segments, it can be shown that the largest formal error occurs when the data segments are the same length. When n data segments of the same length are used to estimate the velocity the formal error is n times larger than if no offsets were estimated.

Amongst the 61 core sites in GPSVEL 0.1 (37% of total) requiring extra offsets each site requires a mean of 1.7 extra offsets (i.e. n ~ 3) with the most being 7 (radome changes). The velocities of these sites are strongly affected by this procedure. It is also not possible to estimate the periodic signals as well as the offsets since the data segments are generally too short. The sites requiring offsets are therefore included in separate solutions and attached to the primary global solution in the same way as the regional networks. This prevents such errors affecting the whole solution.

Velocity Error scaling

Velocity formal errors are scaled by the Unit variance of the estimation procedure. Velocity formal errors are additionally scaled according to a colored noise model [Zhang et al., 1997]. Coloured noise amplitudes for spectral index -0.6 are estimated using a straight line fit to the log-log periodogram of the time series. Velocity formal errors are updated accordingly and a 2mm/sqrtyear random walk noise is also added. SINEX full covariance velocity errors are only updated along the diagonal. For sites requiring offsets where a periodic signal could not be estimated velocity formal errors are updated using an expression for an assumed periodic signal of 5mm amplitude in the up and 2 mm in the horizontal [Blewitt and Lavallee, 2001].

References

Blewitt, G., Y. Bock, and J. Kouba, Constructing the IGS Polyhedron by distributed processing in Densification of the IERS Terrestrial Reference Frame through regional GPS networks, edited by J. F. Zumberge and R. Liu, Int. GPS. Serv. Cent. Bur., 21-38, 1995.

Blewitt, G., and Lavallee. D., Effect of Annual signals on Geodetic velocity, Geophysical Research-Solid Earth, in press, 2001.

Davies, P., and G. Blewitt, Methodology for global geodetic time series estimation: A new tool for geodynamics, Journal of Geophysical Research-Solid Earth, 105 (B5), 11083-11100, 2000.

Van Dam, T., J. Wahr, P.C.D. Milly, A.B. Shmakin, G. Blewitt, D. Lavallee, and K.M. Larson, Crustal displacements due to continental water loading, Geophysical Research Letters, 28 (4), 651-654, 2001.

Zhang, J., Y. Bock, H. Johnson, P. Fang, S. Williams, J. Genrich, S. Wdowinski, and J. Behr, Southern California Permanent GPS Geodetic Array: Error analysis of daily position estimates and site velocities, Journal of Geophysical Research-Solid Earth, 102 (B8), 18035-18055, 1997.

Zumberge, J., and R. Liu, IGS Workshop Proceedings: Densification of IERS Terrestrial Reference Frame through regional GPS networks, Pasadena, California, November 30 - December2, 1994, Int. GPS. Serv. Cent. Bur., 1995.

Last modified Friday, 28-Jan-2011 21:10:25 UTC