1) model also fits the data and suggests that the velocity uncertainties should be 3-6 times larger than for the white noise model. We cannot adequately distinguish between these two noise models, nor can we rule out the possibility of a random walk signal at the lowest frequencies; these questions await the analysis of longer time series. In any case, reducing the magnitude of low-frequency colored noise is critical and appears to be best accomplished by building sites with deeply anchored and braced monuments. Otherwise, rate uncertainties estimated from continuous GPS measurements may not be improved significantly compared to those estimated from infrequent campaign-mode measurements.

Abstract. Analysis of frequent trilateration observations from the two-color electronic distance measuring networks in California demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power law behavior at lower frequencies. In contrast, Earth scientists typically have assumed that only white noise is present in a geodetic time series, since a combination of infrequent measurements and low precision usually preclude identifying the time-correlated signature in such data. After removing a linear trend from the two-color data, it becomes evident that there are primarily two recognizable types of time-correlated noise present in the residuals. The first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall; this noise is significant only for a small fraction of the sites analyzed. The second type of correlated noise becomes evident only after spectral analysis of line length changes and shows a functional relation at long periods between power and frequency of 1/f •, where f is frequency and a • 2. With a = 2, this type of correlated noise is termed random-walk noise, and its source is mainly thought to be small random motions of geodetic monuments with respect to the Earth's crust, though other sources are possible. Because the line length changes in the two-color networks are measured at irregular intervals, power spectral techniques cannot reliably estimate the level of 1/f • noise. Rather, we also use here a maximum likelihood estimation technique which assumes that there are only two sources of noise in the residual time series (white noise and randomwalk noise) and estimates the amount of each. From this analysis we find that the random-walk noise level averages about 1.3 mm/X/yr and that our estimates of the white noise component confirm theoretical limitations of the measurement technique. In addition, the seasonal noise can be as large as 3 mm in amplitude but typically is less than 0.5 mm. Because of the presence of random-walk noise in these time series, modeling and interpretation of the geodetic data must account for this source of error. By way of example we show that estimating the time-varying strain tensor (a form of spatial averaging) from geodetic data having both random-walk and white noise error components results in seemingly significant variations in the rate of strain accumulation; spatial averaging does reduce the size of both noise components but not their relative influence on the resulting strain accumulation model.

It is usually assumed in geodetic studies that measurement errors are independent from one measurement to the next and that the rate of deformation (velocity) is constant over the duration of the experiment. Any temporal correlation between measurements can substantially affect the uncertainty in this velocity estimate when it is determined from the time series of measurements. One source of possible long‐term correlation is motion of the geodetic monument with respect to the “deep” crust. Available measurements suggest that this motion introduces errors that have the form of a random walk process. We show how such errors affect the uncertainty of velocity estimates. For a geodetic experiment of set duration we calculate the velocity uncertainty as a function of the number of observations and of the relative amount of correlated and uncorrelated noise. We find that 1) neglecting long‐term temporal correlations makes the uncertainty in the estimated velocities much too small, and that 2) when the correlated and independent noise sources are of similar magnitude, the expected improvement in uncertainty from having more measurement is not realized; there is almost no improvement in some cases. We have also examined the effect of outliers (“blunders”) on the velocity uncertainty; for a frequency of outliers typical of geodetic field campaigns, the previous two conclusions remain unchanged. These results suggest that long‐term correlations have a large effect on estimating deformation rates; unless these correlations are small, frequent observations give little advantage. If frequent observations are planned, the amount of correlated noise due to monument instability must be kept small if the full capabilities of the measurement technique are to be realized.

Abstract. The southern California Permanent GPS Geodetic Array (PGGA) was established in 1990 across the Pacific-North America plate boundary to continuously monitor crustal deformation. We describe the development of the array and the time series of daily positions estimated for its first 10 sites in the 19-month period between the June 28, 1992 (Mw=7.3), Landers and January 17, 1994 (Mw=6.7), Northridge earthquakes. We compare displacement rates at four site locations with those reported by Feigl et al. [1993], which were derived from an independent set of Global Positioning System (GPS) and very long baseline interferometry (VLBI) measurements collected over nearly a decade prior to the Landers earthquake. The velocity differences for three sites 65-100 km from the earthquake's epicenter are of order of 3-5 mm/yr and are systematically coupled with the corresponding directions of coseismic displacement. The fourth site, 300 km from the epicenter, shows no significant velocity difference. These observations suggest large-scale postseismic deformation with a relaxation time of at least 800 days. The statistical significance of our observations is complicated by our incomplete knowledge of the noise properties of the two data sets; two possible noise models fit the PGGA data equally well as described in the companion paper by Zhang et al. [this issue]; the pre-Landers data are too sparse and heterogeneous to derive a reliable noise model. Under a fractal white noise model for the PGGA data we find that the velocity differences for all three sites are statistically different at the 99% significance level. A white noise plus flicker noise model results in significance levels of only 94%, 43%, and 88%. Additional investigations of the pre-Landers data, and analysis of longer spans of PGGA data, could have an important effect on the significance of these results and will be addressed in future work.