This supplement is divided into there parts; One being more description of the processing of the GPS, EDM, creepmeter, and strainmeter data; Two being supplementary figures and tables to those presented in the main manuscript; and Three being the data used in the fault modeling and the time-series data used in curve fitting.
For most of the figures and tables, two links will be given for each; there will be links to png and pdf files for the figures and, there will be links to png and text files for the tables. The pdf files provide better resolution than the png files while the text files allow the reader to obtain the numerical results.
Because of the importance of the GPS data to the results presented in this paper, we describe below the additional processing carried out to improve the precision of these measurements.
CGPSAlthough most of the CGPS sites are recording both phase and pseudo range data once per second, we obtain the position observations by processing 24 hours of the 30 second measurements using standard point-position techniques [Zumberge et al., 1997] called GIPSY. However, the time series of position changes (displacements) show significant common mode signals that are probably non-tectonic in origin and are assumed to be due to fluctuations of the reference frame used to process GPS data. The common mode signals are estimated using a similar method suggested by Wdowinski et al. [1997]. However, rather than using stations outside of the Parkfield network to estimate the common mode signal, the high frequency fluctuations of displacements are averaged over all of the Parkfield sites and these averages are used to adjust the east, north, and vertical components for the common mode signal. Several steps are required. For each time series, the parameters of equation 1 are estimated. Because of the possible influence of the 23 December 2003, M6.5 San Simeon Earthquake [Hardebeck et al., 2004], which was located 70 km west of Parkfield, an additional offset is included as a parameter. Outliers tagged as being four times the interquartile distance in the residual time-series are removed. Then for each component, east, north, and vertical, the residuals are averaged as a function of time and identified as the common-mode signal. The common-mode is removed from each of the residual time series and the temporal model of equation 1 (main manuscript) is added back to the residuals to create a clean, more precise, set of data for further analysis. By removing the common-mode signal, the variance of the high frequency fluctuations is typically reduced more than 75%.
In processing the GPS data, the position changes are relative to holding the North American Plate fixed. However, to compare the daily solutions of the CGPS network with the high-rate solutions described below which measure displacements relative to the station CRBT, the displacements of the CRBT site are subtracted from the other time series.
Temporal errors affect GPS measurements and these have been quantified by Williams et al. [2004]. Although Williams et al. [2004] did not examine the Parkfield GPS data, they found that most GPS measurements have at least two types of noise, consisting of white noise and power law noise, with an index between -1 and -2, with a tendency that the index is closer to -1 indicating a flicker noise process. Here, we've assume that the noise process is actually a summation of three components, white, flicker, and random walk (which has an index of -2). The assumption is that the power law process found by Williams et al. [2004] is actually a summation of flicker noise associated with the GPS measurement and its processing, and that the random walk is due to monument instability similar to that found by Langbein and Johnson [1997] and Langbein [2004] for EDM using shallow monuments. Thus, this allows the CGPS to have less noise than SGPS because of their better monuments. In much of our analysis that estimates the parameters of equation 1, we also estimate simultaneously the amplitudes of the noise components using the methods of Langbein [2004]. Typically, the estimates of noise for the CGPS in the horizontal components is 1mm white noise, 1mm/yr0.25 flicker, and 1mm/yr0.5 random walk. Often, the value of random walk is in-determinant because of the limited time-span of the data. However, because of infrequent sampling, the noise components of the SGPS data are not estimated but are assumed to be twice that of CGPS.
CGPS-PBO sites
In response to the Parkfield earthquake, PBO installed 5 CGPS sites in the Parkfield region. Initial measurements at two sites started about one month following the mainshock and the others became operational within two months of the mainshock. In principle, these sites could be folded into the common-mode processing of the Parkfield CGPS network. Instead, the RMS scatter in these measurements is reduced by subtracting from the PBO data the common mode signal determined for the CGPS data.
CGPS; high rate solutions
Since the Parkfield network also records 1-second data [Langbein and Bock, 2004], these are processed using the method of Bock et al. [2000] to estimate the position once per second of each site relative to station POMM, which lies adjacent to the fault (Figure 1; main manuscript). A limitation of Bock's method is that, unlike point-positioning, it cannot estimate absolute displacements. In order to better observe both the coseismic and the postseismic deformation, the displacements are re-estimated relative to the Parkfield CGPS site farthest from the fault, CRBT, using simple subtraction rather than re-processing the raw phase and pseudo range data.
The raw 1-Hz displacements are further processed to remove outliers, to improve precision, and to decimate. The goal is to create two subsets of data for further analysis. One data set consists of one minute samples and spans two days on either side of the time of the Parkfield mainshock. The second set consists of 30-minute samples and spans a 10-day interval on either side of the mainshock. Initially, the first 100 seconds of the 1-Hz solutions following the time of the 2004 mainshock are deleted since a significant portion of those observations contain the seismic waveform of displacement. Then, the 1-second sampled data are decimated to 1-minute and 30 minute samples. To extract the common mode signals from this network of GPS stations, the slow changes in the displacement time series are removed by fitting time-dependent model of equation 1 to the data and high-pass filtering the residuals of that model. Because of the short time-window, the rate, R, and the sinusoidal terms, C and S, are not estimated. The output of the high-pass filter is a residual time series from a running median with a one day window. In each of the residual time series, outliers greater than four interquartile distance are identified and removed. The common-mode algorithm described previously for the CGPS data is used and this resulted in better than a 50% reduction in the variance of the residual data set. Then, both the terms of the running median and parameters of the time-dependent model of equation 1 are added back to the residual time series that had been corrected for the common-mode signal.
With the 1-minute samples, another iteration is used to improve its precision. The time-dependent model of equation 1 is fit to the adjusted data from the first iteration. The parameters of that model are used to remove the coseismic and the immediate postseismic signal from the raw 1-Hz data. The residuals to a running median filter are examined and outliers are removed. From these cleaner, 1-Hz data, a sidereal filter [Langbein and Bock, 2004] is applied. The output of the sidereal filter are decimated into 1-minute samples. Finally, the common-mode signal is removed from each of the time-series and the model of equation 1 is added back to the 1-minute samples. With four days of 1-minute data, this yielded approximately 5700 points. To ease the computational load in analyzing these data, this data set is reduced to one minute samples over 12 hours centered on the time of the mainshock and three minute samples out to two days on either side of the time of the mainshock.
SGPS
SGPS (Survey or campaign mode GPS) observations were started within two days following the Parkfield mainshock to spatially augment the CGPS sites. Over the next two months of SGPS observations, the receivers were left at their sites for periods of approximately one week. To reduce the RMS scatter in these measurements, the common mode signal determined for the CGPS data is subtracted from the SGPS data.
EDM
Although the two-color EDM has a precision of approximately 1 mm, its long-term precision is compromised because the monuments used are either piers that only extend to 1.5 meters depth or steel pipe driven to refusal. Only two of the EDM monuments have deeply braced monuments [Langbein et al., 1995] that are typically used with CGPS. A full discussion of two-color precision is found in Langbein and Johnson [1997] and Langbein [2004].
With the intermittent measurements of EDM baselines, during which significant deformation occurred, one of the difficulties with these measurements is that the displacements exceeded the 5 cm wavelength of its modulation frequency. Because this EDM is setup to measure distance changes, large changes are difficult to reconcile because the actual observable has a 5 cm ambiguity. For most cases with the EDM data, these were easy to reconcile because the baseline is redundant with CGPS; there is a CGPS station, CARH, within 50 meters of the central EDM site CARR on top of Carr Hill. Many of the reflector sites are also locations of CGPS. However, when there is no CGPS data available, the EDM ambiguity is resolved using predicted length changes based upon preliminary modeling of the coseismic and postseismic period using GPS. In one case, the baseline MIDD, modeling may not be applicable. As pointed out by Langbein et al. [1991], the site MIDD might be within the fault zone, which is suggested by its inter-seismic rate. Thus, if the modeling of coseismic and postseismic slip does not include the possibility that MIDD is within the fault zone, a prediction of its length change due to the earthquake could be spurious.
Creepmeter
The creepmeter XMM1 appears to be disturbed by near explosions. Figure 1 shows the response of the XMM1 creepmeter to two, nearby explosions used for seismic tomography experiments in 2002 and 2004. The times of the explosions are shown with a dashed line. These explosions were set off within 100 meters of the creepmeter. In both cases, the creepmeter registered a displacement. With the 2004 Parkfield mainshock, the XMM1 creepmeter registered a displacement within five minutes of the mainshock. It is possible, based upon the observation of displacement of the creepmeter coincident with nearby explosions, that the coseismic offset recorded at XMM1 might be spurious; the sudden, momentary shaking either from a nearby explosion or the passage of seismic waves could cause the creepmeter to displace.
[ Top ]In this section, plots of all of the CGPS, creepmeter and strainmeter data are shown along with the curves for the simplified Omori law, the modified Omori law and the model of Perfettini and Avouac [2004].
CGPS; initial fit
The plots shown in this section are the results of fitting Omori's law to the CGPS data. For each component at each site, a simple form of Omori's law is fit to the observations. This fit is carried out separately for the 1-minute sampled data, shown in blue in the figures, the 30-minute sampled data data shown in green, and the 1-day sampled data shown in red. Written in the color of each subset of data is the estimate of t for Omori's law. The thin lines are the predicted values from Omori's law that is fit to each subset of the data.
The estimated values of τ from equation 1 (main manuscript) for Omori's law are listed Table 1 (text).
The parameters of a noise model are estimated simultaneously with the parameters in equation 1. For the 1 minute and 30 minute data, that noise model is a combination of Gauss-Markov and flicker noise; the index of the power law part of the Gauss-Markov component is assumed to be -1. Therefore, the noise model written in the frequency domain is: P(f)= P1/(fo + f) + P2/f. Table 2a (1-minute data) (text) and Table 2b (30-minute data) (text) list estimates of the noise parameters for the high rate data. However, the amplitudes for power law noise in the data covariance matrix, P'1, and P'2, are related to amplitudes in the frequency domain, P1 and P2. See equation 11 in Langbein [2004]
In reading the tables of noise estimates, there are a few caveats. In particular, if the two amplitudes of power law noise are roughly equivalent, then the Gauss-Markov frequency is meaningless; the model is actually flicker noise. And, for low Gauss-Markov frequencies, fo 1/(time span of data set), then it should be considered as zero and contributions from the second power law should be neglected; again, this noise model is actually flicker noise.
For the daily sampled CGPS data, we assumed a noise model composed of white noise, flicker noise (1/f), and random-walk noise; the amplitudes of the noise estimates are in Table 2c (text).
The plots shown in this section are the results of fitting the modified Omori's law and the equation of Perfettini and Avouac [2004] to the CGPS data. The colors represent the 3 subsets of data; 1 minute, 30 minute, and daily observations. The 3 subsets of data from each component are combined into a single regression to estimate the parameters of the modified Omori's law. Temporal covariance of each subset of data is set to the best noise model found with the initial fit of Omori's law described above. The thin, black line is the predicted curve of the modified Omori law; The corresponding value of p and τ are shown with each component. The dashed, black line is the fit of Perfettini and Avouac [2004] model to the observations. The corresponding values of tr and the ratio, δ/tr are shown. Finally, the value, MS_diff, indicates the difference in sum of the squares of the residual of the Omori model from the Perfettini and Avouac model; a positive number indicates that the modified Omori law fits the data better than the Perfettini and Avouac model. Finally, the light, dashed line is the fit of an exponential function, 1- exp( -t/τ) to the observations.
The comparison of the misfits of the three functions to the data are listed int Table 3a (text) . The parameters of these three functions are found in Table 3b (text) . The fits shown in the "sum of misfits" Table 3a (text) are calculated by rt C-1r where r is the residual, defined as the vector comprised of the data minus the calculated values, and C is the data covariance matrix. A model that fits the data would has a sum of misfits close to the number of observations.
The plots shown in this section are the results of fitting the modified Omori's law, the equation of Perfettini and Avouac [2004], and an exponential to the creepmeter data. The colors represent the two subsets of data; 10-minute, 6-hour observations. The two subsets of data from each component are combined into a single regression to estimate the parameters of the modified Omori's law. Temporal covariance of each subset of data was set to the best noise model found with the initial fit of Omori's law. The thin, black line is the predicted curve of the modified Omori law; The corresponding value of p and τ are shown with each component. This line is hard to see since it overlays the data in many cases. The magenta line is the fit of Perfettini and Avouac [2004] to the observations. The corresponding values of tr and δ are shown. Finally, the light blue line is the fit of an exponential function, 1-exp( -t/τ) to the observations.
The noise models estimated for both the 10-minute and 6-hour data for the creepmeters are listed in Table 4a (text). These noise models are based upon fitting a combination of Omori's law, a coseismic displacement, and a rate to each time-series and adjusting the parameters of the noise models to maximize the log-likelihood [Langbein, 2004] Using the estimates of noise, three different functions representing postseismic slip are fit simultaneously to both the 10-minute and 6-hour sampled data from each creepmeter. The three functions are the modified Omori law, the model of Perfettini and Avouac [2004], and a exponential. The values of the misfits are listed in the Table 4b (text). The fits shown in the "sum of misfits" tables are calculated by rt C-1r where r is the residual, defined as the vector comprised of the data minus the calculated values, and C is the data covariance matrix. A model that fits the data would has a sum of misfits close to the number of observations. However, many of the sums of misfits are much less than the number of observations; this suggests that the noise model used might be much too conservative. The estimates of temporal parameters to functions of postseismic deformation are listed in Table 4c (text).
The plots shown in this section are the results of fitting the modified Omori's law, the equation of Perfettini and Avouac [2004], and an exponential to the strainmeter data data. The colors represent the two subsets of data; 10-minute, 3-hour observations. The data are plotted twice with an offset. The upper traces are the data and predictions from models of postseismic deformation that is a combination of Omori's law and an exponential. This model is fit to the two subset separately.
In the bottom traces, the two subsets of data from each component are combined into a single regression to estimate the parameters of the modified Omori's law. Temporal covariance of each subset of data is set to the best noise model found with the initial fit of Omori's law. The thin, black line is the predicted curve of the modified Omori law; The corresponding value of p and τ are shown with each component. This line is hard to see since it overlays the data in many cases. The magenta line is the fit of Perfettini and Avouac [2004] to the observations. The corresponding values of tr and δ are shown. Finally, the light blue line is the fit of an exponential function, 1- exp( -t/τ) to the observations.
The coseismic strain offset plotted for VC is not correct since, just after the the passage of seismic waves, this instrument automatically reset itself thus loosing its zero reference [Borcherdt et al., this volume].
The noise models for both the "full sampled" and 6-hour sampled strainmeter data are shown in the Table 5a (text). By "full sampled", that means either 10 minute sampling for the dilatometers (volumetric strainmeters), or 18 or 30 minute sampling for the tensor strainmeters. These models are base upon fitting a combination of Omori's law, an exponential, a coseismic offset, and a rate to each time-series and adjusting the parameters of the noise models to maximize the log-likelihood [Langbein, 2004]
Using the estimates of noise, three different functions representing postseismic slip are fit simultaneously to both the fully sampled and 3-hour sampled data from each strainmeter. The three functions are the modified Omori law, the model of Perfettini and Avouac [2004], and a exponential. The values of the misfits are listed in the Table 5b (text). The fits shown in the "sum of misfits" tables are calculated by rtC-1r where r is the residual, defined as the vector comprised of the data minus the calculated values, and C is the data covariance matrix. A model that fits the data would has a sum of misfits close to the number of observations. The estimates of parameters to functions of postseismic deformation are shown in Table 5c (text). For the strain data, the value of the index, p, for the modified Omori's law has been constrained to be less than or equal to two.
A color plot (Figure 6a) of the estimated distribution of slip during the coseismic and postseismic intervals; model is same as Figure 8 in the main manuscript. The measured displacements of the Parkfield sites and the predicted displacements using the model in (Figure 6a) are plotted in Figure 7 of the manuscript. These vectors of displacements use the model coordinate system proposed by Segall and Matthew [1988]. The vectors are listed in (Table 6a), (Table 6b), (Table 6c), (Table 6d), (Table 6 text), In addition, the slip model where we have forced the slip at a point beneath Gold Hill to be close to that estimated by Liu ea al. (this volume) is shown in (Figure 6b)
The resolution of slip at depth is determined for a few different patches of slip. To examine resolution, a simple model of fault slip is used. Specifically, using the fault plane partitioned into patches described in the main manuscript, slip on a single patch is simulated. With that one meter of slip on the single patch, the displacements of the GPS sites and lengthening of EDM baselines are calculated. Using the same errors in the simulated data as the real data, the same smoothing constraints, the positivity constraint on slip, and the same parameter that balances smoothing against fitting the data, a distribution of slip is estimated using the simulated data. The results of the spatial distribution of slip are plotted and compared to the unit, one meter of slip used to create the data. That way, one can gage that actual spatial averaging of slip that is accomplished with the modeling and the limitation of the data used.
In the figures that follow, if slip on a partition is perfectly resolved, then its estimated value would be 1000 mm with a corresponding color of red. None of the examples show perfect resolution; instead, usually 200 mm of slip is estimated for the partition being examined and its neighboring partitions.
[ Top ]Format is station name (pair), displacement or position change in meters, the standard error in meters, and the RMS (data misfit to equation 1 normalized to the data covariance and number of degrees of freedom).
GPS data; similar format but data are in column of north, east, and up position changes; (station name (pair), north disp., error in disp, RMS misfit; east disp., error in disp., RMS misfit; vertical disp., error in disp., RMS misfit.
Please note that this supplement contains many tar files of the time-series data used in the published report. The data in these tar files are derrived results which are based upon many assumptions that have been stated above. For the actual data, one should go to the source. These sources are either web pages and/or the principal investigator which are listed below.
GPS data
The daily solutions of positions of the GPS sites processed using GIPSY can be found by following these links:
Two color EDM data. Format is year, day of year, and length change in mm. Measurements have ceased for this network. More information is found by following the link to http://quake.wr.usgs.gov/research/deformation/twocolor/parkfield.html. The raw EDM data is also provided here.
Creepmeter data. The format of these data are year, Day of year, and creep in units of mm. More information can be found by following the link to: http://quake.wr.usgs.gov/research/deformation/monitoring/downloadcreep.html
Dilatometer data. The format of these data are year, day of year, strain in units of nano-strain. Ignore the last column. The dilatometer data given here have been adjusted for changes in atmospheric pressure. The Earth tide signal remains in these data. These processed data are courtesy of Malcolm Johnston, USGS
Tensor Strainmeter data can be found through the following link: http://www.gtsmtechnologies.com/NEHRP/strain_download/strain_form.html Data is archived and periodically updated by Micheal Gladwin of GTSM Technology.
[ Top ]Langbein, J. and H. Johnson, Correlated errors in geodetic time series: Implications for time-dependent deformation, J. Geophys. Res., 102, 591-604, 1997.
Creepmeter data:
<http://quake.wr.usgs.gov/research/deformation/monitoring/downloadcreep.html>.
Data is archived and periodically updated.
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