This second version of the Velocity Map is an official SCEC product (approved by the SCEC Board of Directors on 9/30/98).

	Horizontal Deformation Velocity Map Version 2.0 Crustal Deformation Working Group 1 Southern California Earthquake Center July 14, 1998
	The velocity map, presented in the tables and figures of this report, represents an ongoing effort by the Crustal Deformation Working Group of the Southern California Earthquake Center to produce a unified horizontal velocity field that shows the contemporary interseismic deformation across southern California. Geodetic data include observations made with the Global Positioning System (GPS), Very Long Baseline Interferometry (VLBI), and Electro-optical Distance Measurement (EDM) during the past three decades. Steady motion is assumed for most of the sites, except those few that have experienced significant velocity changes after occurrence of large earthquakes in the region. Such velocity changes, whenever estimated, are documented in this release.	click on map to see a larger version

• Figure Index
• Table Index
• References
• Credits

DATA

The GPS data were collected from a series of field surveys performed by many university groups and government agencies between 1986 and 1997 (Tables 1 and 2) and continuous observations by stations of the Permanent GPS Geodetic Array (Bock et al., 1997) and its successor, the Southern California Integrated GPS Network (SCIGN) (Prescott, 1996; Bock and Williams, 1997) between 1991 and 1997. For determining the orbits of the GPS satellites and defining an external reference frame, we also used data collected globally under the auspices of the Cooperative International GPS Network (CIGNET) between 1987 and 1991 (Chin et al., 1987) and the International GPS Service for Geodynamics (IGS) (Beutler et al., 1993) since 1992.

The VLBI data were collected between 1980 and 1994 by NASA and NGS within the US and a number of cooperating groups throughout the world (Clark et al., 1987; Ryan et al., 1993). The data include observations from 13 southern California sites, 10 of which have been tied to our GPS surveys; these are particularly important for constraining the reference frame prior to the availability of a large global GPS tracking network.

The EDM data are from surveys by the California Division of Mines and Geology (CDMG) 1970-79 and the U. S. Geological Survey (USGS) 1970-92 (Lisowski et al., 1991; Dong, 1993). Repeated observations have been made for 127 sites, 18 of which have been tied to our GPS surveys (Table 2).

GPS DATA PROCESSING AND MODELING

The GPS data processing and modeling are performed in three steps:

(1) We used the GAMIT software (King and Bock, 1997) to estimate daily station positions simultaneously with orbital and atmospheric parameters using dual-frequency, doubly differenced GPS phase observations from sites in southern California and global tracking stations. After an initial solution with realistic a priori constraints on orbital and station parameters to resolve integer phase ambiguities (Dong and Bock, 1989; Feigl et al., 1993), we relaxed the constraints to produce daily estimates of station and orbital parameters free of reference-frame assumptions (Herring et al., 1991; Dong et al., 1998). The loosely constrained estimates of station coordinates become "quasi-observations" for combination with those from other surveys. Prior to 1993, we included the regional and global data in the same GAMIT analysis. For most surveys after 1993, we analyzed the field data separately and incorporated SCIGN and global data via quasi-observations, usually from the daily analysis performed by the Scripps Orbit and Permanent Array Center (SOPAC) (Bock et al., 1997).

(2) We use the GLOBK software (Herring, 1997) to combine the daily solutions of each survey. Both orbital and station parameters are estimated, with orbital parameters allowed to vary stochastically according to the level of unmodeled accelerations of the satellites and the strength of the global tracking data. The final solution file contains (loosely constrained) estimates of station positions for each (few-day to several-week) survey, with orbital parameters suppressed.

(3) We use the QOCA (Dong et al., 1998) or GLOBK software to combine the solution files ("quasi-observations") from all of the surveys, estimating station positions, velocities, and coseismic displacements. For the positions and vertical velocities of the stations, we apply only weak (0.2 m, 0.2 m/yr) constraints to condition the solution. Coseismic displacements are constrained to about 100%, 60%, and 60% of the values predicted by the coseismic models given by Bennett et al. (1995) for Joshua Tree, Hudnut et al. (1994) for Landers, and Shen et al. (1996b) for Northridge earthquakes, respectively.

COMBINING GPS, VLBI, and EDM DATA

We used the CALC/SOLVK software (Ryan et al., 1993; Herring et al, 1990; Feigl et al., 1993) to analyze the VLBI group delay observations, producing for each day quasi-observations (station position estimates and their covariances) similar to those from the GPS analysis. We then use QOCA or GLOBK to combine the GPS and VLBI quasi-observations. For our combined solution we defined a North American reference frame by constraining to zero +- 1 mm/yr the the horizontal velocites of the GPS and VLBI stations at Westford (Massachusetts), Algonquin (Ontario), Richmond (Florida), Platteville (Colorado), Penticton (British Columbia),Yellowknife (NW Territories), and Fairbanks (Alaska) and the VLBI stations at Fort Davis (Texas), Los Alamos (New Mexico), Pietown (New Mexico), and Flagstaff (Arizona). Station velocities of about 20 other globally distributed co-located GPS and VLBI stations are tied together at the level of 1 mm/yr.

We used the FONDA software (Dong, 1993; Dong et al., 1998) to estimate station positions from the EDM range measurements, again applying loose a priori constraints. We then use QOCA to combine the GPS, VLBI, and EDM quasi-observations, forcing the horizontal velocities of all monuments within about 1 km area to be equal.

ESTIMATION OF UNCERTAINTIES and DISCUSSION

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 (e.g., Zhang et al., 1997; Savage and Prescott, 1973) that we think it unlikely that there is significant undetected systematic error in relative velocities within southern California.

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. We also have rejected data before or after an earthquake if there are doubts about the adequacy of the co-seismic model. Furthermore, we have assumed that the interseismic velocity is the same before and after an earthquake, except for those sites nearest the Landers and Northridge epicenters.

A regional velocity field change has been observed on the basis of comparing the survey mode GPS and VLBI observations prior to the Landers earthquake (from Feigl et al., 1993), with continuous GPS observations in the first 19 months following it, at three stations (Piñon, Goldstone/Mojave, and JPL) that are 65 to 180 km away from that event (Bock et al., 1997). These observed rate transients are statistically significant at only those stations with the very best histories of precise space geodetic measurements well spanning the times of the Landers and Northridge earthquakes.

It follows that we do not necessarily expect to observe similar rate transients ubiquitously throughout the region in our current analysis. In this study, we are analyzing velocities for many more stations that each have lesser quality space geodetic measurements. Hence, a higher level of error in the velocity estimates of these stations is to be expected, and we have less ability to resolve subtle changes. We have estimated separate velocities for Piñon and Goldstone/Mojave before and after the Landers event, and we have indicated in the velocity map those stations that may be affected by the Landers- induced rate transients. Specifically, because most of the survey-mode GPS observations in the region were made after the Landers earthquake, while EDM measurements were made before, we decompose these two sets of velocities in the eastern Mojave shear zone region and designate the GPS velocities in this region as 'post-seismic' velocities. For a few sites, a co-located preseismic velocity from EDM can be compared to a post-seismic GPS velocity vector, and these estimates differ (e.g., EDOM to edom_2__, PAXU to pax_ncer, VIEW to inspncer). For a few additional campaign-mode GPS stations (HAWE, MDAY, and SAND), the GPS data proved adequate to separately estimate differing pre- and post-Landers velocites in the present study.

At the level of uncertainty of our current analysis, rate changes are only statistically significant in the vicinity of the 1992 Landers earthquake. It is important to note, however, that for almost all of the survey-mode stations, such rate changes as observed by Bock et al. (1997) would likely be insignificant in our current analysis. Clearly, further work is required to minimize the errors inherent in solutions that combine EDM and early space-geodetic measurements with more recent continuous GPS and campaign-mode GPS measurements. Such continuing work will make it possible to investigate more completely the intriguing post-seismic and interseismic phenomena that appear to have been captured by these data.

RESULTS

Our GPS and VLBI solution includes interseismic velocities for 210 stations in southern California with one-sigma uncertainties of both horizontal components less than 5 mm/yr.

Figure 1 shows horizontal velocity vectors (relative to a group of GPS and VLBI stations on the stable North American Plate) and error ellipses for 363 sites after GPS/VLBI and EDM combination. The error ellipses are regions of 95% confidence, computed by

(v-v) ^T C_inv (v-v) = (2.45) ²

where v is a 'statistical expectation' station velocity vector, v is the estimate in Table 3, and C_inv is the inverse of the inter-component covariance matrix for estimation errors.

The velocity components are tabulated in Table 3. For sites where more than one monument has been occupied, we show only the primary station in the table and figure. The magenta arrows in Figure 1 are the velocities resolved from data collected after the Landers earthquake in its epicentral region. The blue arrows are those either for the sites outside of the Landers epicentral region or resolved primarily from data collected prior to the Landers earthquake. The magenta ones may contain postseismic deformation signals. Vertical velocities are not listed because of their large uncertainties. Figure 2 shows the velocity vectors plotted with respect to the station at Palos Verdes, and Figure 3 shows the velocity results for three sub-regions of southern California. Table 4 contains the station velocities along with the lower triangle of the covariance matrix.

REFERENCES

Bennett, R. A., Global Positioning System measurements of crustal deformation across the Pacific-North American plate boundary in southern California and northern Baja, Mexico, Ph. D. thesis, Mass. Inst. of Technol., Cambridge, 1995.

Bennett, R. A., R. E. Reilinger, W. Rodi, Y. Li, M. N. Toksoz, and K. Hudnut, 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, 1995.

Bennett, R. A., W. Rodi, and R. E. Reilinger, Global Positional System constraints on fault slip rates in southern California and northern Baja, Mexico, J. Geophys. Res., 101, 21943-21960, 1996.

Beutler, G., P. J. Morgan, and R. E. Neilan, Geodynamics: Tracking satellites to monitor global change, GPS World, 4, 40, 1993.

Bock, Y. and S. Williams, Integrated satellite interferometry in southern California, Eos Trans. AGU, 78, pp. 293, 299-300, 1997.

Bock, Y., S. Wdowinski, P. Fang, J. Zhang, S. Willians, H. Johnson, J. Behr, J. Genrich, J. Dean, M. van Domselaar, D. Agnew, F. Wyatt, K. Stark, B. Oral, K. Hudnut, R. King, T. Herring, S. Dinardo, W. Young, D. Jackson, and W. Gurner, Southern California permanent GPS geodetic array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes, J. Geophys. Res., 102, 18013-18033, 1997.

Bock. Y., J. Behr, P. Fang, J. Dean, and R. Leigh, Scripps Orbit and Permanent Array Center (SOPAC) and Southern California Permanent GPS Geodetic Array (PGGA), The Global Positioning System for the Geosciences, pp. 55-61, National Academy Press, Washington, D.C., 1997.

Chin, M. M, D. R. Crump, and K. A. Berstis, The status of the NGS GPS orbit tracking network (abstract), Eos Trans AGU, 68, 1239, 1987.

Clark, T. A., D. Gordon, W. E. Himwich, C. Ma, A. Mallama, and J. W. Ryan, Determinations of relative site motions in the western United States using Mark III very long baseline interferometry, J. Geophys. Res., v. 92, 12741-12750, 1987.

Dong, D., and Y. Bock, Global Positioning System network analysis with phase ambiguity resolution applied to crustal deformation studies in California, J. Geophys. Res. 94, 3949-3966, 1989.

Dong, D., The horizontal velocity field in southern California from a combination of terrestrial and space-geodetic data, Ph.D Thesis, Mass. Inst. of Technol., Cambridge, 1993.

Dong, D., T. A. Herring, and R. W. King, Estimating crustal deformation from a combination of terrestrial and space-based data, Journal of Geodesy, 72, No. 4, 200-214, 1998.

Donnellan, A., B. H. Hager, R. W. King, and T. A. Herring, Geodetic measurement of deformation in the Ventura basin region, southern California, J. Geophys. Res., 98, 21,727-21,739, 1993.

Feigl, K. L., R. W. King, and T. H. Jordan, Geodetic measurement of tectonic deformation in the Santa Maria fold and thrust belt, California, J. Geophys. Res., 95, 2679-2699, 1990.

Feigl, K. L., D. C. Agnew, Y. Bock, D. Dong, A. Donnellan, B. H. Hager, T. A. Herring, D. D. Jackson, T. H. Jordan, R. W. King, S. Larsen, K. M. Larson, M. H. Murray, Z. Shen, and F. H. Webb, Space geodetic measurement of crustal deformation in central and southern California, 1984-1992, J. Geophys. Res. 98, 21,677-21712, 1993.

Gonzalez, J., S. McClusky, R. King, R. Reilinger, R. Bennett, Present day tectonic deformation from GPS in northern Baja California, Mexico, (abstract), Eos Trans AGU, v. 78, No. 46, p. F159, 1997.

Herring, T. A., D. Dong, and R. W. King, Sub-milliarcsecond determination of pole position using Global Positioning System data, Geophys. Res. Lett., 18, 1893-1896, 1991.

Herring, T. A., GLOBK: Global Kalman Filter VLBI and GPS analysis program, v.4.1, Mass. Inst. of Technol., Cambridge, 1997.

Hudnut, K. W., Y. Bock, M. Cline, P. Fang, Y. Feng, J. Freymueller, X. Ge, W. K. Gross, D. D. Jackson, M. Kim, N. E. King, J. Langbein, S. C. Larsen, M. Lisowski, Z.-K. Shen, J. Svarc, and J. Zhang, Co-seismic displacements of the 1992 Landers earthquake sequences, Bull. Seismol. Soc. Am., 84, 625-645, 1994.

Hudnut, K. W., Z. Shen, M. Murray, S. McClusky, R. King, T. Herring, B. Hager, Y. Feng, A. Donnellan and Y. Bock, Coseismic displacements of the 1994 Northridge, Calif., earthquake, Bull. Seis. Soc. Amer., v. 86, S19-S36, 1996.

Jackson, D. D., Southern California Earthquake Center geodesy infrastructure progress report, Oct 1, 1991-Sep 30, 1992, Southern California Earthquake Center 1992 Report, I19-I21, 1992.

Jackson, D. D., and D. Agnew, Southern California Earthquake Center crustal deformation working group: Infrastructure, Southern California Earthquake Center 1993 Report, I34-I36, 1993.

Jackson, D. D., S. Salyards, Z. Shen, L. Sung, D. Potter, and M. Kim, Progress Report 1994, Geodesy infrastructure, Southern California Earthquake Center 1994 Annual Report, I31-I35, Vol. II, 1995.

Jackson, D. D., Progress Report Feb 1, 1995 to present, greater L. A. basin field operations, Southern California Earthquake Center 1995 Annual Report, Vol. II, I45-I47, 1996.

King, R. W. and Y. Bock, Documentation for the MIT GPS analysis software: GAMIT, version 9.6, Mass. Inst. of Technol., Cambridge, 1997.

Larsen, S., and R. Reilinger, Global Positioning System Measurements of strain accumulation across the Imperial Valley, California: 1986-1989, J. Geophys. Res., 97, 8865-8876, 1992.

Larson, K. M., and F. H. Webb, Deformation in the Santa Barbara Channel from GPS measurements 1987-1991, Geophys. Res. Lett., 19, 1491-1494, 1992.

Lisowski, M., J. C. Savage, and W. H. Prescott, The velocity field along the San Andreas fault in central and southern California, J. Geophys. Res., 93, 8369-8389, 1991.

Prescott, W. H., Satellites and earthquakes: A new continuous GPS array for Los Angeles, Yes, It will radically improve seismic risk assessment for Los Angeles, Eos Trans. AGU, 77 (43), p. 417, 1996.

Ryan, J. W., C. Ma, and D. S. Caprett, NASA Space Geodesy Program - GSFC Data Analysis-1992: Final report of the Crustal Dynamics Project VLBI Geodetic Results 1979-1991, Report 104572, NASA, Washington, D.C., 1993.

Savage, J. C. and W. H. Prescott, Precision of geodolite distance measurements for determining fault movements, J. Geophys. Res., v. 78, 6001-6008, 1973.

Shen, Z.-K., D. D. Jackson, and X. B. Ge, Crustal deformation across and beyond the Los Angeles basin from geodetic measurements, J. Geophys. Res., 101, 27,957-27,980, 1996a.

Shen, Z.-K., X. B. Ge, D. D. Jackson, D. Potter, M. Cline, and L. Sung, Northridge earthquake rupture models based on the Global Positioning System measurements, Bull. Seismol. Soc. Am., 86, No. 1B, S37-S48, 1996b.

Zhang, J., Y. Bock, H. Johnson, P. Fang, J. Genrich, S. Williams, S. Wdowinski, and J. Behr, "Southern California Permanent GPS Geodetic Array: Error analysis of daily position estimates and site velocities," J. Geophys. Res., 102, 1997 (pp.18,035-18,055).

FIGURE CAPTIONS AND INDEX

Figure 1. Horizontal deformation velocities in southern California with respect to the North American Plate. Error ellipses correspond to 95% confidence. Stars represent recent earthquakes whose coseismic effects are modeled in the velocity map solution. Magenta arrows are the site velocities possibly changed after the Landers and Northridge earthquakes.

Figure 2. Horizontal deformation velocities in southern California with respect to Palos Verdes. Error ellipses correspond to 95% confidence. Magenta arrows have same meaning as in Figure 1.

Figure 3. a) More detailed plot of velocity results for the northwestern portion of the southern California region, b) same for the mid-region, and c) same for the southeastern region. Magenta arrows have same meaning as in Figure 1.

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TABLE INDEX