The initial analysis done by this group involved the processing of GPS data from survey-mode (``campaign'') measurements, using the GAMIT GPS processing software to estimate daily station positions and atmospheric parameters; resolving ambiguities whenever possible. For 1993 and after, we used, along with the survey-mode data, data from a few permanent stations in southern California, and loosely-constrained initial orbits from the daily analysis computed by the Scripps Orbit and Permanent Array Center (SOPAC). Prior to 1993, we included the regional and global data in a single GAMIT analysis. The result was daily sets of loosely-constrained station and orbital parameters.
We used the GLOBK software to combine the daily solutions for up to a month using both our own solutions and (from 1993 on) an appropriate set of global and regional solutions from SOPAC. We estimated both orbital and station parameters daily; for data before 1992 we determined multi-day orbits and allowed the orbital parameters to vary stochastically according to the level of unmodeled accelerations of the satellites and the strength of the global tracking data. The final combined file contained (loosely constrained) estimates of station positions for all surveys within a span of up to a month, with orbital and troposphere parameters suppressed.
The next step was to use the QOCA and GLOBK softwares (in parallel) to independently estimate, from these combined files, positions, velocities, and coseismic displacements for all stations, keeping the solution well-conditioned by applying loose a priori constraints for positions, vertical velocities, and coseismic displacements. In order to accommodate temporally correlated errors (such as those associated with orbital and atmospheric disturbances), we also allowed a random-walk perturbation to station positions in the Kalman filtering process, assigning 1, 1, and 10 (mm squared per year) for the variances of the north, east, and up components of all the sites.
The VLBI data, which help to constrain the reference frame prior to the availability of a large global GPS tracking network, were processed using the the CALC/SOLVK software to analyze group delay observations, producing for each day station position estimates and their covariances similar to those from the GPS analysis. For the EDM data (individual line lengths) we used the FONDA software to estimate station positions and velocities from the data, again applying loose a priori constraints to construct a solution and covariance file.
The final step was to use QOCA to combine the GPS, VLBI, and EDM results, constraining the velocities at 54 EDM sites to be close to the GPS velocities for the same sites. To define the reference frame for our solution we minimized the velocities of 12 North American GPS stations:
YELL 62.480895 -114.480699 180.86 Yellowknife [IGS] VLBI tie PIE1 34.301506 -108.118926 2347.73 Pietown VLBA [IGS] VLBI tie MDO1 30.680511 -104.014992 2004.51 McDonald VLBA [IGS] CHUR 58.759078 -94.088727 -19.37 Churchill [IGS] NLIB 41.771591 -91.574894 207.04 N. Liberty VLBA [IGS] RICM 25.613822 -80.384182 -16.53 Richmond VLBI tie ALGO 45.955800 -78.071367 200.89 Algonquin [IGS] VLBI tie GODE 39.021727 -76.826829 14.53 GGAO (Greenbelt) [IGS] WES2 42.613335 -71.493326 85.02 Westford [IGS] VLBI tie THU1 76.537337 -68.788007 55.02 Thule AFB [IGS] STJO 47.595239 -52.677749 152.84 St. John's [IGS] KELY 66.987418 -50.944837 229.81 Kellyville [IGS]
The covariance matrices for the input GPS and EDM data have both been scaled so that the post-fit residual variance is about equal to the number of degrees of freedom in each dataset. Thus the total residual variance of the combined datasets is also about equal to the number of degrees of freedom, and the uncertainties reported correspond to one standard deviation in each parameter. The error estimates capture explicitly only those errors that contribute to residuals, but there is sufficient diversity and redundancy in the measurements that we think it unlikely that there is any large undetected systematic error in relative velocities within southern California. For regions in which crustal velocities are smoothly varying or can be fit by an Okada model for a locked fault, the scatters in the residual velocities are mostly consistent with our estimated uncertainties.
A part of our analysis testing was to perform parallel estimation of velocities from the original monthly combined covariance files; this involved independent choices of what data to leave in, and completely independent software (QOCA runs at UCLA, GLOBK at MIT). The figure below shows a comparison of the resulting velocity estimates. The systematic differences are small; though there are some large differences at a few sites, most of these are for poorly-determined velocities; only one of these differences (for SAND_GPS) exceeds two standard deviations of error.
Co-seismic displacements are a potential source of error in estimating interseismic velocities. We have minimized this error by constraining (conservatively) the allowed departures of displacements from values predicted by our a priori models, which were taken from Bennett et al. (1995) for the Joshua Tree earthquake; Hudnut et al. (1994) for the Landers earthquake, Hudnut et al. (1996) for the Northridge earthquake, and Ji et al. (2002) for the Hector Mine earthquake. The a priori uncertainty for each displacement component was taken to be the root sum of squares of 0.6 times the a priori value of that component, plus 0.3 times the a priori values of the other two components at the site.
We have assumed that the interseismic velocity is the same before and after an earthquake, except for sites nearest the Landers and Northridge epicenters. At our level of uncertainty, rate changes are only statistically significant near the 1992 Landers earthquake; smaller rate changes may exist, but would not be significant in our current analysis. Stations with separate velocities are indicated by different suffixes in the station name for the same 4-character ID (e.g., PIN1_GPS and PIN1_GLA. The 2-character codes are LA for Landers, NR for Northridge, and JP for a separate post-post-Northridge rate at JPLM.
For the Landers earthquake,
a transient signal was clearly apparent on a number of time series
through at least mid-1993.
We therefore did not use data from the period after the earthquake,
through 1993.9, for the following sites:
6052 6056 7000 7001 F726 HECT LAE1 LAE2 LAE3 LAE4The figure below shows the postseismic transient at some of these sites, and the period excluded from the final analysis.
LAW1 LAW2 LAW3 LAW4 LAZY LUC2 MEEK OLDD OLDW ONYX PAXU
PBB4 SAND SIBE TROY WIDC
R. A. Bennett, R. E. Reilinger, W. Rodi, and Y. P. Li (1995) Coseismic fault slip associated with the 1992 Mw 6.1 Joshua Tree, California, earthquake: implications for the Joshua Tree-Landers earthquake sequence, J. Geophys. Res. 100, 6443-6461.
K. W. Hudnut, Y. Bock, M. Cline, P. Fang, Y. Feng, J. Freymueller, X. Ge, W. K. Gross, D. D. Jackson, M. Kim, N. E. King, J. O. Langbein, S. C. Larsen, M. Lisowski, Z.-K. Shen, J. L. Svarc, and J. Zhang (1994). Coseismic displacements of the 1992 Landers earthquake sequence Bull. Seismol. Soc. Amer. 84, 625-645.
K. W. Hudnut, Z. Shen, M. Murray, S. McClusky, R. W. King, T. Herring, B. Hager, Y. Feng, P. Fang, A. Donnellan, and Y. Bock (1996) Coseismic displacements of the 1994 Northridge, California, earthquake Bull. Seismol. Soc. Amer. 86, S19-S36.
C. Ji, D. J. Wald, and D. V. Helmberger (2002). Source description of the 1999 Hector Mine, California, earthquake: II. Complexity of slip history, Bull. Seismol. Soc. Amer. 92, 1208-1226.