John Langbein

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.

Implications for prediction and hazard assessment from the 2004 Parkfield earthquake

Obtaining high-quality measurements close to a large earthquake is not easy: one has to be in the right place at the right time with the right instruments. Such a convergence happened, for the first time, when the 28 September 2004 Parkfield, California, earthquake occurred on the San Andreas fault in the middle of a dense network of instruments designed to record it. The resulting data reveal aspects of the earthquake process never before seen. Here we show what these data, when combined with data from earlier Parkfield earthquakes, tell us about earthquake physics and earthquake prediction. The 2004 Parkfield earthquake, with its lack of obvious precursors, demonstrates that reliable short-term earthquake prediction still is not achievable. To reduce the societal impact of earthquakes now, we should focus on developing the next generation of models that can provide better predictions of the strength and location of damaging ground shaking.

Slip on the San Andreas Fault at Parkfield, California, over Two Earthquake Cycles, and the Implications for Seismic Hazard

Parkfield, California, which experienced M 6.0 earthquakes in 1934, 1966, and 2004, is one of the few locales for which geodetic observations span multiple earthquake cycles. We undertake a comprehensive study of deformation over the most recent earthquake cycle and explore the results in the context of geodetic data collected prior to the 1966 event. Through joint inversion of the variety of Parkfield geodetic measurements (trilateration, two-color laser, and Global Positioning System), including previously unpublished two-color data, we estimate the spatial distribution of slip and slip rate along the San Andreas using a fault geometry based on precisely relocated seismicity. Although the three most recent Parkfield earthquakes appear complementary in their along-strike distributions of slip, they do not produce uniform strain release along strike over multiple seismic cycles. Since the 1934 earthquake, more than 1 m of slip deficit has accumulated on portions of the fault that slipped in the 1966 and 2004 earthquakes, and an average of 2 m of slip deficit exists on the 33 km of the fault southeast of Gold Hill to be released in a future, perhaps larger, earthquake. It appears that the fault is capable of partially releasing stored strain in moderate earthquakes, maintaining a disequilibrium through multiple earthquake cycles. This complicates the application of simple earthquake recurrence models that assume only the strain accumulated since the most recent event is relevant to the size or timing of an upcoming earthquake. Our findings further emphasize that accumulated slip deficit is not sufficient for earthquake nucleation. Online material : Model fault geometry, fit to the data for the inversions, and model resolution.

Noise in two‐color electronic distance meter measurements revisited

[1] Frequent, high-precision geodetic data have temporally correlated errors. Temporal correlations directly affect both the estimate of rate and its standard error; the rate of deformation is a key product from geodetic measurements made in tectonically active areas. Various models of temporally correlated errors are developed and these provide relations between the power spectral density and the data covariance matrix. These relations are applied to two-color electronic distance meter (EDM) measurements made frequently in California over the past 15-20 years. Previous analysis indicated that these data have significant random walk error. Analysis using the noise models developed here indicates that the random walk model is valid for about 30% of the data. A second 30% of the data can be better modeled with power law noise with a spectral index between 1 and 2, while another 30% of the data can be modeled with a combination of band-pass-filtered plus random walk noise. The remaining 10% of the data can be best modeled as a combination of band-pass-filtered plus power law noise. This band-pass-filtered noise is a product of an annual cycle that leaks into adjacent frequency bands. For time spans of more than 1 year these more complex noise models indicate that the precision in rate estimates is better than that inferred by just the simpler, random walk model of noise.

Coseismic and Initial Postseismic Deformation from the 2004 Parkfield, California, Earthquake, Observed by Global Positioning System, Electronic Distance Meter, Creepmeters, and Borehole Strainmeters

Global Positioning System (gps), electronic distance meter, creepmeter, and strainmeter measurements spanning the M 6.0 Parkfield, California, earthquake are examined. Using these data from 100 sec through 9 months following the mainshock, the Omori’s law, with rate inversely related to time, 1/ t p and p ranging between 0.7 and 1.3, characterizes the time-dependent deformation during the postseismic period; these results are consistent with creep models for elastic solids. With an accurate function of postseismic response, the coseismic displacements can be estimated from the high-rate, 1-min sampling gps; and the coseismic displacements are approximately 75% of those estimated from the daily solutions. Consequently, fault-slip models using daily solutions overestimate coseismic slip. In addition, at 2 months and at 8 months following the mainshock, postseismic displacements are modeled as slip on the San Andreas fault with a lower bound on the moment exceeding that of the coseismic moment. Online material: Data description and supplementary figures, tables, and data used in models and time-series analysis.

Response of Long Valley Caldera to the Mw = 7.3 Landers, California, Earthquake

Of the many sites in the western United States responding to the June 28, 1992, Landers earthquake (M w = 7.3) with remotely triggered seismicity, only Long Valley caldera is monitored by both seismic and continuous deformation networks. A transient strain pulse and surge in seismicity recorded by these networks began within tens of seconds following arrival of the shear pulse from Landers. The cumulative strain and number of triggered earthquakes followed the same exponentially decaying growth rate (time constant 1.8 days) during the first 6 days following Landers. The strain transient, which was recorded on a borehole dilatometer at the west margin of the caldera and a long-base tiltmeter 20 km to the east, peaked on the sixth day at =0.25 ppm and gradually decayed over the next 15-20 days. The absence of a clear strain signal exceeding 0.4 ppm in data from the two-color geodimeter deformation lines, which span the central section of the caldera, indicates that the strain transient cannot be due solely to pressure changes in the concentrated pressure source 7 km beneath the central part of the caldera that accounts for most of the uplift of the resurgent dome since 1980. The triggered seismicity occupied the entire seismogenic volume beneath the caldera. The focal mechanisms, the frequency-magnitude distribution, and the spatial distribution of the triggered earthquakes are typical of other swarms in Long Valley caldera. The cumulative seismic moment of the triggered earthquakes through the first 2 weeks after the Landers earthquake corresponds to a single M = 3.8 earthquake, which is too small by nearly 2 orders of magnitude to account for the 0.25-ppm peak amplitude of the observed strain transients. Evidently, the strain transient represents the dominant response mode, which precludes direct triggering of local earthquakes by the large dynamic stresses from Landers as the dominant process. Conditionally viable models for the triggering process beneath the caldera include (1) the transient pressurization of magma bodies beneath the resurgent dome and Mammoth Mountain by the advective overpressure of rising bubbles, (2) a surge in fluid pressure within the seismogenic zone due to upward cascading failure of isolated compartments containing superhydrostatic pore fluids, (3) relaxation (fluidization) of a partially crystallized magma body or dike intrusion in the deep crustal roots of Long Valley magmatic system, or (4) aseismic slip on midcrustal faults. Either the deep, relaxing-magma body or lower crustal dike intrusion satisfy all the strain observations with a single deformation source. The latter model admits the possibility that large, regional earthquakes can trigger the episodic recharge of the deep roots of crustal magmatic systems.

Shallow and peripheral volcanic sources of inflation revealed by modeling two-color geodimeter and leveling data from Long Valley caldera, California, 1988-1992

We refined the model for inflation of the Long Valley caldera near Mammoth Lakes, California, by combining both geodetic measurements of baseline length and elevation changes. Baseline length changes measured using a two-color geodimeter with submillimeter precision revealed that the resurgent dome started to reinflate in late 1989. Measurements between late 1989 and mid-1992 revealed nearly 13 cm of extension across the resurgent dome. Geodetic leveling surveys with approximately 2-mm precision made in late 1988 and in mid-1992 revealed a maximum of about 8 cm of uplift of the resurgent dome. Two ellipsoidal sources satisfy both the leveling and two-color measurements, whereas spherical point sources could not. The models primary inflation source is located 5.5 km beneath the resurgent dome with the two horizontal axes being nearly equal in size and the vertical axis being 4 times the length of the horizontal axes. A second ellipsoidal source was added to improve the fit to the two-color measurements. This secondary source is located at a depth between 10 and 20 km beneath the south moat of the caldera and has the geometry of an elongated ellipsoid or pipe that dips down to the northeast. In addition, the leveling data suggest dike intrusion beneath Mammoth Mountain during the 1988-1992 interval, which is likely associated with an intense swarm of small earthquakes during the summer of 1989 at that location. Our analysis shows the dike intrusion to be the shallowest of the three sources with a depth range of 1-3 km below the surface to the top of the intrusion.

An episode of reinflation of the Long Valley Caldera, eastern California: 1989–1991

Following the episodes of inflation of the resurgent dome associated with the May 1980 earthquake sequence (four M 6 earthquakes) and the January 1983 earthquake swarm (two M 5.2 events), 7 years of frequently repeated two-color geodimeter measurements spanning the Long Valley caldera document gradually decreasing extensional strain rates from 5 ppm/yr in mid-1983, when the measurements began, to near zero in mid-1989. The corresponding seismic activity within the caldera persisted at a low rate of fewer than 10 M ≥ 1.2 earthquakes per week from 1985 through November 1989 with no events exceeding M 3.0. Early October 1989 marked a change in activity when measurements of the two-color geodimeter network showed a significant increase in extensional strain rate (9 ppm/yr) across the caldera. The seismic activity began exceeding 10 M ≥ 1.2 per week in early December 1989 and rapidly increased to a sustained level of tens of M ≥ 1.2 per week with bursts having hundreds of events per day. Many events exceeded M 3.0 and the largest event was M ≈ 4. The 1989–1991 inflation episode is the first time that we have sufficient geodetic measurements in Long Valley to define the temporal relation between onset of an inflation episode and onset of brittle failure (earthquake swarm within the caldera). Here, the onset of deformation preceded the onset of increased earthquake activity by more than 2 months. The seismicity rate began to decrease in mid-July 1990, consistent with a gradually slowing of extension across the caldera as measured by the two-color geodimeter. The recent episode of inflation can be modeled by a single Mogi point source located about 7 km beneath the center of the resurgent dome. In contrast, the deformation pattern observed between mid-1983 and mid-1989 is best reproduced by fault slip in the south moat, inflation at 6.5 km depth near Casa Diablo Hot Springs and inflation beneath the resurgent dome. It appears that the 7-km source beneath the resurgent dome that was active for the earlier episodes is the primary source for the more recent episode. The model used to satisfy the line length observations predicts 7.5 cm of uplift along leveling route along highway 395 from mid-1983 to mid-1989 and an additional 11 cm through the end of 1991. To comp are with the energy release from seismicity, the modeled inflation from late 1989 through the end of 1991 has a moment that is a factor of 40 more than the cumulative seismic moment from earthquakes located within the caldera from the same period. Thus the recent inflation episode represents a significant portion of the observed geodetic deformation with only little seismic energy release.

High‐rate real‐time GPS network at Parkfield: Utility for detecting fault slip and seismic displacements

[1] A network of 13 continuous GPS stations near Parkfield, California has been converted from 30 second to 1 second sampling with positions of the stations estimated in real-time relative to a master station. Most stations are near the trace of the San Andreas fault, which exhibits creep. The noise spectra of the instantaneous 1 Hz positions show flicker noise at high frequencies and change to frequency independence at low frequencies; the change in character occurs between 6 to 8 hours. Our analysis indicates that 1-second sampled GPS can estimate horizontal displacements of order 6 mm at the 99% confidence level from a few seconds to a few hours. High frequency GPS can augment existing measurements in capturing large creep events and postseismic slip that would exceed the range of existing creepmeters, and can detect large seismic displacements.

The Earthquake Prediction Experiment at Parkfield, California

Since 1985, a focused earthquake prediction experiment has been in progress along the San Andreas fault near the town of Parkfield in central California. Parkfield has experienced six moderate earthquakes since 1857 at average intervals of 22 years, the most recent a magnitude 6 event in 1966. The probability of another moderate earthquake soon appears high, but studies assigning it a 95% chance of occurring before 1993 now appear to have been over-simplified. The identification of a Parkfield fault “segment” was initially based on geometric features in the surface trace of the San Andreas fault, but more recent microearthquake studies have demonstrated that those features do not extend to seismogenic depths. On the other hand, geodetic measurements are consistent with the existence of a “locked” patch on the fault beneath Parkfield that has presently accumulated a slip deficit equal to the slip in the 1966 earthquake. A magnitude 4.7 earthquake in October 1992 brought the Parkfield experiment to its highest level of alert, with a 72-hour public warning that there was a 37% chance of a magnitude 6 event. However, this warning proved to be a false alarm. Most data collected at Parkfield indicate that strain is accumulating at a constant rate on this part of the San Andreas fault, but some interesting departures from this behavior have been recorded. Here we outline the scientific arguments bearing on when the next Parkfield earthquake is likely to occur and summarize geophysical observations to date.