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For the current GSRM, 6739 velocities were derived from position time-series obtained from the analysis of RINEX data that was either freely available or made available to us specifically for this project. All but 34 of these velocities were used in the modeling. We added 15,710 velocities from 233 studies in the published literature (or from personal communications) to achieve a grand total of 22,415 velocities at 18,356 unique locations used in the modeling. Of all velocities, 17,567 are in plate boundary zones (as defined by us) and the remaining 4848 velocities are for points on, predefined, rigid tectonic plates.

UNR GPS Analysis

We use GIPSY-OASIS II software for the data analysis package from the Jet Propulsion Laboratory (JPL). Station coordinates were estimated every 24 hours using the Precise Point Positioning method [Zumberge et al.,1997]. Ionosphere-free combinations of carrier phase and pseudorange were processed every 5 minutes. The observable model includes ocean tidal loading and companion tides [Scherneck,1991] using the FES2004 ocean tidal model [Lyard et al.,2006], estimation of wet zenith troposphere and two gradient parameters as a random walk process [Bar-Sever et al.,1998] using the GMF mapping function [Boehm et al.,2006], and antenna calibrations for ground receivers and satellite transmitters [Schmid et al.,2007], and station clocks estimated as a white-noise process. We applied JPL's single receiver ambiguity resolution [Bertiger et al.,2010], which significantly reduces the scatter in the East component time-series. Satellite orbit and clock parameters were provided by JPL, who determine them in a global fiducial-free analysis using a subset of the available IGS core stations as tracking sites. The fiducial-free daily GPS solutions are aligned to IGS08 [Rebischung et al.,2012] by applying a seven parameter Helmert transformation (3 rotations, 3 translations and a scale component) obtained from JPL [Bertiger et al.,2010].

We consider all data between January 01, 1996, and December 31, 2013, but only derive velocities from time-series that are at least 2.5 years long, so as to best account for seasonal cycles [Blewitt and Lavallée,2002]. In some cases, time-series for (near) collocated stations are concatenated to extend their length and/or to derive a single velocity for two stations that operated consecutively. Because we are interested in capturing the “secular”, or interseismic, velocity, we exclude parts of the time-series that show significant transient motion. These transients are often due to postseismic deformation or slow-slip events (where the excluded part of the time-series is replaced with an offset). In the extreme, the exclusion could be for periods >10 years, sometimes at stations as far as several thousands kilometers from the largest earthquakes [Baek et al.,2012; Tregoning et al.,2013]. We model the time-series as an offset + trend (i.e., velocity) + annual cycle + semi-annual cycle + offsets. Offsets could come from equipment changes, earthquakes, or unknown reasons discovered in the analysis. Some stations only have intermittent data limiting our ability to model the seasonal terms, which could bias the velocity estimate. We therefore apply a damped inversion, which ensures that the amplitude of the seasonal cycles remains at bay in those cases where data is only available for short periods year(s) apart. The velocities uncertainties are not adopted from this inversion, because it is well-known that those are too small due to the time-correlation of the errors. Instead we use the CATS software to calculate velocity uncertainties under the assumption that the error model consists of flicker-noise plus white-noise. We then multiplied the standard deviations with a factor of 2.0 so that the reduced chi-squared for fitting rigid-body rotations to velocities on stable plates is closer to 1.0.

Stations for which the time-series indicated rapid subsidence, unexplained transient, or for which the velocities were significantly different than nearby stations, were excluded. We also excluded any station near volcanic activity.

For the strain rate modeling we removed 34 velocities for stations within 22 km of the creeping section of the San Andreas Fault . The reason for this that the velocity profile across this fault is a step-function, which causes artifacts in the model, i.e., the spline function that we fit to the data will contain “overshoots” [Kreemer et al.,2012]. Removal of the data points close to the fault allows us to model the step-function as close as possible without creating “overshoots”.

Synthesis of Published Velocities

The majority of geodetic velocities are derived from campaign-style measurements and are typically published in the literature. In other cases, publications report velocities for CGPS stations for which data is not publicly available. A very small minority of publications also report velocities derived from non-GPS techniques, such as DORIS, VLBI, or trilateration. For several studies did researchers supply us with additional information such as station coordinates or velocities at nearby IGS sites. Six investigators sent us unpublished results. For the first time, we included a handful of velocity estimates from submarine markers, off shore Peru and Japan.

We applied the following criteria to decide whether data should be included:

a) studies were excluded when the velocity field was entirely based on publicly available data from (semi-)CGPS stations already analyzed for the core solution.

b) if study a clearly superseded study b,then only results from study b were used. When in doubt both were included;

c) clear outlier velocities were removed, including those affected by volcanic deformation;

d) results reflecting postseismic deformation were not included;

e) velocities derived from <2.5 year (or sometimes <2 year) time-series were excluded;

f) any station that was also excluded from the core solution;

g) velocities for 64 stations near the creeping portion of the San Andreas Fault.

Next, we performed one large inversion in which we solve for, and apply, a translation rate and rotation rate that would minimize velocity differences at collocated sites (within ~1km) and transform all results into the IGS08 reference frame of our core solution. This is done for all studies simultaneously, because study a may, for example, not have any collocated sites with the core solution, but has them with study b,which does have collocated sites with the core solution. Any velocity for a site collocated with the core solution will be removed, under the assumption that the velocity of the core solution is superior (e.g., it is typically derived from longer time-series and we checked offsets ourselves). At least three collocated sites are needed to solve for a translation and rotation rate. If only two collocated sites are present, we only solve for a rotation rate. To avoid solving for a large translation rate when the geographic footprint is small (in which case there may be a trade-off between translation and rotation rate), we damp the inversion in favor of the rotation parameters. In the few cases where study a mostly supersedes study b,but some velocities from study b are not in study a,we first translate study b onto study a before we perform the global transformation. In those cases do we not duplicate the velocities at the collocated sites.

In the end, we included 15,710 velocities from the literature. Together with the core solution, there are 22,415 velocity data at 18,356 unique locations available for the modeling.

map of sites

Figure 1. Gray shading is outline of all areas allowed to deform. White areas comprised of 50 assumed rigid plates. Purple and green dots are for GPS stations on rigid plates or in deforming zones, respectively, for which we derived a velocity. Yellow and blue dots are for GPS stations on rigid plates or in deforming zones, respectively, for which we took the velocity from the literature.


Of the 50 plates, 36 angular velocities were estimated from the GPS velocities by this project, 6 were taken from PB2002 [Bird,2003] and 8 were taken from MORVEL [DeMets et al.,2010]. A table with angular velocities relative to the Pacific plate, can be found here.

We chose to not use every GPS velocity on each rigid plate to estimate the angular velocities. Typically we would only use the best-behaved, longest running stations from our own analysis. In some cases, there were insufficient stations from our own analysis (or a sufficient number was not well distributed across the plate) to estimate the angular velocity. In those cases we also used velocities from the literature synthesis. In general, we would omit stations near plate boundaries, as those may be affected by elastic strain accumulation.


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Bar-Sever, Y. E., P. M. Kroger, and J. A. Borjesson (1998), Estimating horizontal gradients of tropospheric path delay with a single GPS receiver, J. Geophys. Res.,103(B3), 5019–5035,

Bertiger, W., S. D. Desai, B. Haines, N. Harvey, A. W. Moore, S. Owen, and J. P. Weiss (2010), Single receiver phase ambiguity resolution with GPS data, J Geod,84(5), 327–337,

Bird, P. (2003), An updated digital model of plate boundaries, Geochemistry, Geophysics, Geosystems,4(3), 1027,

Blewitt, G., and D. Lavallée (2002), Effect of annual signals on geodetic velocity, J. Geophys. Res.,107(B7), B72145,

Boehm, J., A. Niell, P. Tregoning, and H. Schuh (2006), Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data, Geophys. res. Lett.,33(7), L07304,

DeMets, C., R. G. Gordon, and D. F. Argus (2010), Geologically current plate motions, Geophys. J. Int.,181(1), 1–80,

Gan, W., P. Zhang, Z.-K. Shen, Z. Niu, M. Wang, Y. Wan, D. Zhou, and J. Cheng (2007), Present-day crustal motion within the Tibetan Plateau inferred from GPS measurements, J. Geophys. Res.,112(B8), B08416,

Lyard, F., F. Lefevre, T. Letellier, and O. Francis (2006), Modelling the global ocean tides: modern insights from FES2004, Ocean Dynamics,56(5-6), 394–415,

Rebischung, P., J. Griffiths, J. Ray, R. Schmid, X. Collilieux, and B. Garayt (2012), IGS08: the IGS realization of ITRF2008, GPS Solut.,16(4), 483–494,

Scherneck, H.-G. (1991), A parametrized solid earth tide model and ocean tide loading effects for global geodetic baseline measurements, Geophys. J. Int.,106(3), 677–694,

Schmid, R., P. Steigenberger, G. Gendt, M. Ge, and M. Rothacher (2007), Generation of a consistent absolute phase-center correction model for GPS receiver and satellite antennas, J. Geod.,81(12), 781–798,

Shen, Z.-K., C. Zhao, A. Yin, Y. Li, D. D. Jackson, P. Fang, and D. Dong (2000), Contemporary crustal deformation in east Asia constrained by Global Positioning System measurements, J. Geophys. Res.,105(B3), 5721–5734,

Shen, Z.-K., M. Wang, Y. Li, D. D. Jackson, A. Yin, D. Dong, and P. Fang (2001), Crustal deformation along the Altyn Tagh fault system, western China, from GPS, J. Geophys. Res.,106(B12), 30,607–30,621,

Shen, Z.-K., J. Lü, M. Wang, and R. Bürgmann (2005), Contemporary crustal deformation around the southeast borderland of the Tibetan Plateau, J. Geophys. Res.,110(B11), B11409,

Tregoning, P., R. Burgette, S. c. McClusky, S. Lejeune, C. s. Watson, and H. McQueen (2013), A decade of horizontal deformation from great earthquakes, J. Geophys. Res.,in press,

Wang, Q. et al. (2001), Present-Day Crustal Deformation in China Constrained by Global Positioning System Measurements, Science,294(5542), 574–577,

Zhang, P.-Z. et al. (2004), Continuous deformation of the Tibetan Plateau from global positioning system data, Geology,32(9), 809–812,

Zumberge, J. F., M. B. Heflin, D. C. Jefferson, M. M. Watkins, and F. H. Webb (1997), Precise point positioning for the efficient and robust analysis of GPS data from large networks, J. Geophys. Res.,102(B3), 5005–5017,

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