Hadley O. Johnson

Correlated errors in geodetic time series: Implications for time‐dependent deformation

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/ƒα, where ƒ is frequency and α≈2. With α=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 Earths 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/ƒα 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 random-walk noise) and estimates the amount of each. From this analysis we find that the random-walk noise level averages about 1.3 mm/√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.

Southern California Permanent GPS Geodetic Array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes

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 earthquakes 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.

Monument motion and measurements of crustal velocities

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.

Improved stability of a deeply anchored geodetic monument for deformation monitoring

A test of two different monument designs used in geodetic networks shows that monuments installed to depths of 5 to 10 meters, and laterally braced, exhibit less environmentally caused displacement than those installed to 2 meters depth. At Parkfield, California, we have been monitoring the lengths of 17 baselines over the past decade with a 2 to 3 day interval between measurements using a two-color geodimeter with a nominal precision of 0.5 mm over 5 km long baselines. Significant variations are observed on many of these baselines which appear to be related to the seasonally occurring rainfall, with the larger variations approaching 10 mm over the past decade. To test whether we could improve upon the measurements on some of the more susceptible lines, at two sites we installed new monuments within about 30 meters of the original monuments. After 1.5 years of measurements it is evident that the new monuments significantly attenuate the seasonal displacements to less than 1 mm. The use of deeply anchored monuments should improve the ability of fault-scale geodetic monitoring arrays to detect small tectonic displacements.

Present-day crustal deformation in southern California

The effects of laterally homogeneous mantle electrical conductivity have been included in steady. Using an extensive set of precise geodetic measurements, we have developed a detailed picture of present-day deformation rates in southern California. This large set of measurements, amounting to nearly 2000 repeated distance measurements over the period 1973 to 1991, comes from the U.S. Geological Surveys Geodolite trilateration program, involving their combined Anza, Joshua Tree, and Salton networks. Building on previous results from these data, we are able to present the deformation field as estimates of the rate of horizontal strain accumulation in small four-station subnetworks of the overall 89-station network. Using this technique, the spatial details of the 18-year average strain rate field can be determined. By correlating these spatial details with the tectonics of the region we are able to understand better how deformation is partitioned across this highly complex margin between the Pacific and North American tectonic plates. Some of the more interesting findings of this study are that (1) the vast majority of strain rate estimates show a pattern of nearly pure shear as would be expected in a transcurrent environment, (2) the fastest accumulation of surface strain in southern California is along the San Jacinto Fault west of the Salton Sea, not along the San Andreas Fault, (3) strain accumulation rate along the length of the San Jacinto Fault increases toward the southeast as the fault enters the Imperial Valley, (4) a large area near the southern end of the Salton Sea, where the San Andreas Fault meets the Brawley Seismic Zone, is undergoing areal dilatation, which is in part consistent with the formation of crust at a spreading center, and (5) deformation at the transition zone between the San Andreas Fault and the Eastern California Shear Zone also appears to be the result of crustal spreading.

A new statistical test for static stress triggering: Application to the 1987 Superstition Hills earthquake sequence

Over the past several years, many investigators have argued that static stress changes caused by large earthquakes influence the spatial and temporal distributions of subsequent regional seismicity, with earthquakes occurring preferentially in areas of stress increase and reduced seismicity where stress decreases. Some workers have developed quantitative methods to test for the existence of such static stress triggering, but no firm consensus has yet been reached as to the significance of these effects. We have developed a new test for static stress triggering in which we compute the change in Coulomb stress on the focal mechanism nodal planes of a set of events spanning the occurrence of a large earthquake. We compare the statistical distributions of these stress changes for events before and after the mainshock to decide if we can reject the hypothesis that these distributions are the same. Such rejection would be evidence for stress triggering. We have applied this test to the November 24, 1987, Elmore Ranch/Superstition Hills earthquake sequence and find that those post-mainshock events that experienced stress increases of at least 0.01–0.03 MPa (0.1–0.3 bar) or that occurred from 1.4 to 2.8 years after the mainshocks are consistent with having been triggered by mainshock-generated static stress changes.

Early Postseismic Deformation from the 16 October 1999 Mw 7.1 Hector Mine, California, Earthquake as Measured by Survey-Mode GPS

The 16 October 1999 ( M w 7.1) Hector Mine earthquake was the largest earthquake in California since the 1992 ( M w 7.3) Landers event. The Hector Mine earthquake occurred in the eastern Mojave Desert, where the density of permanent Global Positioning System (GPS) stations is relatively low. Since the earthquake, groups from the United States Geological Survey, University of Southern California, University of California, Los Angeles, University of California, San Diego, and Massachusetts Institute of Technology have made postseismic survey-mode observations to increase the spatial coverage of deformation measurements. A total of 55 sites were surveyed, with markers from a few meters to 100 km from the surface rupture. We present velocity estimates for the 32 sites that had enough repeated observations between 17 October 1999 and 26 March 2000 to provide reliable results; these survey-mode data complement the temporal and spatial coverage provided by newly installed Southern California Integrated Geodetic Network permanent GPS stations and future Interferometric Synthetic Aperture Radar postseismic results. We then use the postseismic velocity estimates to compute a simple afterslip model. Results of inversions show that the observed velocities are consistent with deep afterslip occuring underneath the coseismic rupture area.

Coseismic Displacements from the Hector Mine, California, Earthquake: Results from Survey-Mode Global Positioning System Measurements

We describe the collection and processing of Global Positioning System (GPS) data from 77 locations around the Hector Mine earthquake, which we use to estimate coseismic displacements related to this shock. The existence of pre-event GPS data, some collected to monitor postseismic displacements from the 1992 Landers earthquake and some to establish survey control in the meizoseismal area, provided a relatively dense coverage close to the rupture zone. The data available were collected mostly within the 2 years prior to the 1999 earthquake; we reobserved many points within a few days after the shock, and all within 6 months after. We include corrections for interseismic motion to provide the best value possible for coseismic motion caused by this earthquake. The displacements in general display the pattern expected for a strike-slip fault, though a few show significant vertical motion. The maximum horizontal displacement observed was 2 m; one station between fault ruptures showed little horizontal motion, but significant uplift.

Salton Trough Regional Deformation Estimated from Combined Trilateration and Survey-Mode GPS Data

The Salton Trough in southeastern California, United States, has one of the highest seismicity and deformation rates in southern California, including 20 earthquakes M 6 or larger since 1892. From 1972 through 1987, the U.S. Geological Survey (USGS) measured a 41-station trilateration network in this region. We re-measured 37 of the USGS baselines using survey-mode Global Positioning System methods from 1995 through 1999. We estimate the Salton Trough deformation field over a nearly 30-year period through combined analysis of baseline length time series from these two datasets. Our primary result is that strain accumulation has been steady over our observation span, at a resolution of about 0.05 μstrain/yr at 95% confidence, with no evidence for significant long-term strain transients despite the occurrence of seven large regional earthquakes during our observation period. Similar to earlier studies, we find that the regional strain field is consistent with 0.5 ± 0.03 μstrain/yr total engineering shear strain along an axis oriented 311.6° ± 23° east of north, approximately parallel to the strike of the major regional faults, the San Andreas and San Jacinto (all uncertainties in the text and tables are standard deviations unless otherwise noted). We also find that (1) the shear strain rate near the San Jacinto fault is at least as high as it is near the San Andreas fault, (2) the areal dilatation near the southeastern Salton Sea is significant, and (3) one station near the southeastern Salton Sea moved anomalously during the period 1987.95-1995.11. Online material: Tables of stations used in this study and of estimated strain fields. Manuscript received 8 January 2003.

Stabilized laser for long base-line interferometry

A helium--neon laser is described which employs an easily-replacable Melles Griot plasma tube, and stable operation is achieved in its use in an optical interferometer. (AIP)