Dynamic high-speed rupture from the onset of the 2004 Parkfield, California, earthquake



[1] We investigated the 2004 Parkfield earthquake using a multiscale slip inversion. The multiscale approach allows us to both focus on the details of the early stages of the rupture process, and to model the entire earthquake at a larger scale. Our model indicates that the Parkfield earthquake began with bilateral high-speed rupture with fast slip rate, up to 4 m/s, and fast propagation velocity of about 3.0 km/s. Rupture propagation to the southeast was arrested 3 s after onset, while propagation to the northwest continued, generated a large slip patch at ∼5 s, and ceased within 10 s. A similar rapid initiation was observed for the 2004 mid-Niigata Prefecture, Japan, earthquake in a previous study. High-speed initial rupture suggests that large earthquakes may initiate and grow in the same way as small earthquakes, and that the final size is difficult to predict from the early stages of an earthquake.

1. Introduction

[2] How earthquakes initiate has important implications for the feasibility of both earthquake prediction and earthquake early warning. A central question is whether the early stages of large earthquakes differ from the early stages of small earthquakes. To address this question, many authors have focused on the initial portion of seismic waveforms. A weak phase preceding an abrupt increase was found for earthquakes over a wide magnitude range (M1–M8) [Umeda, 1990; Ellsworth and Beroza, 1995; Beroza and Ellsworth, 1996] with the duration of the initial phase proportional to the cube root of the total seismic moment. Gentle rises of observed waveforms, called slow initial phases, following the first arrival were observed for small earthquakes (M–1–M2.6) [Iio, 1992, 1995], and interpreted by Shibazaki and Matsu'ura [1998] as the transition from a nucleation process [Dieterich, 1987; Ohnaka and Kuwahara, 1990] to high-speed rupture.

[3] Uchide and Ide [2007] investigated the early stages of the 2004 mid-Niigata Prefecture, Japan, earthquake using their multiscale slip inversion method, which employs a multiscale source model [e.g., Aochi and Ide, 2004]. They found that, within the first few tenths of a second, high-speed rupture occurs with peak slip rate comparable to or greater than 1 m/s and rupture velocity between 2.5 and 3.0 km/s. This is clearly not a slow/weak initiation process that suddenly transitions to high-speed/energetic rupture. To study the generality of above result, we apply a similar analysis to the 2004 Parkfield earthquake.

[4] Parkfield is well-known as a focus of earthquake studies in California. Many M6 earthquakes have occurred there in the past 150 years [Bakun and McEvilly, 1984]. The events in 1934 and 1966 are similar to each other in terms of their hypocenters and southeastward directivity [Bakun and McEvilly, 1979]. An MW 6.0 earthquake in Parkfield that occurred on September 28, 2004, differed from the previous earthquakes in respect to the hypocenter, which was 20 km southeast of that of previous events, and northwestward directivity [Langbein et al., 2005].

[5] We use a multiscale inversion approach to show that in the 2004 Parkfield earthquake rupture velocity and slip speed were high at the onset of dynamic rupture. As in the 2004 mid-Niigata Prefecture, Japan, earthquake, the initial stages of the Parkfield earthquake were not weak nor slow. This suggests that small and large earthquakes start similarly, and that the final size of an earthquake is difficult to predict from its early stages.

2. Data

[6] We use data from two seismic networks installed in the area (Figure 1a): the General Earthquake Observation System (GEOS) [Borcherdt et al., 1985] operated by USGS and the strong-motion seismic network by California Geological Survey (CGS). Each GEOS station has both a velocity transducer and an accelerometer; however, due to the 16-bit dynamic range of the A/D converter, velocity seismograms for earthquakes (M > 4) are clipped, and accelerograms for small earthquakes (M < 3) have limited resolution. CGS stations have only triggered analog accelerometers and lack both earthquakes of M < 5, and the initial P-wave arrival of the mainshock.

Figure 1.

(a) Map and focal mechanism of the 2004 Parkfield mainshock. Squares and triangles are GEOS and CGS stations, respectively. Stations indicated by closed symbols are used for the analysis, while open ones are not. Star shows mainshock epicenter. Blue thick line is the projection of our fault model. Brown lines show the SAF surface trace. Gray circles mark epicenters of aftershocks relocated by Thurber et al. [2006]. (b) Cross section along the blue dashed line in Figure 1a. Red, green, and blue rectangles indicate extent of scales 1, 2, and 3, respectively, of the multiscale fault model. Gray circles mark aftershock hypocenters. (c) Focal mechanisms of the EGF events estimated using low-frequency amplitudes and polarities at stations as those of Uchide and Ide [2007]. (d) First 2 s of the up-down components of the observed seismograms at the GEOS stations.

3. Multiscale Slip Inversion

[7] We analyze the rupture process from initiation to termination by the multiscale slip inversion method [Uchide and Ide, 2007]. We construct the observation equations at multiple scales, and solve for the slip-rate distributions at each scale simultaneously. This ensures a self-consistent imaging of the slip distribution in detail for the initiation, and at a coarser scale for the entire earthquake.

[8] Table 1 summarizes the assumptions of the analysis. We assume the fault plane has a strike of N141°E and 90° dip. The rupture initiation point is the hypocenter as relocated by Thurber et al. [2006], at 35.815°N, 120.367°W, and at a depth of 8.57 km. The multiscale source model is constructed at three different scales, namely those with different node intervals for basis functions representing the spatiotemporal distribution of the slip-rate on the fault plane. Linear spline functions are used for the basis functions. We call the smallest, intermediate, and largest scales, scales 1, 2, and 3, respectively, and they are nested as shown in Figure 1b. The intervals of the nodes of the basis functions are comparable to the minimum wavelengths of the applied bandpass filters. The fault dimension in scale 3 is selected as the minimum size required for fitting the data. The hypothetical rupture front propagating from the hypocenter, within which fault slip is allowed to occur, was determined to propagate at 3.0 km/s by trial and error modeling. The number of model parameters in the slip-rate distribution is 526.

Table 1. Setup of Multiscale Analysis
 Scale 1Scale 2Scale 3
  • a

    “BF” denotes basis functions.

Fault dimensions
   Length4.0 km7.0 km26.0 km
      # of BF/intervala7/0.5 km6/1.0 km12/2.0 km
   Width4.0 km7.0 km10.0 km
      # of BF/intervala7/0.5 km6/1.0 km4/2.0 km
   Duration0.6 s1.2 s3.0 s
      # of BF/intervala5/0.1 s5/0.2 s5/0.5 s
   Length of data0.55 s1.1 s18.0 s
      Before P/S arrival0.05 s (P)0.1 s (P)1.0 s (S)
   Resampling interval0.01 s0.02 s0.1 s
   Passband of filter2.0–10.0 Hz1.0–5.0 Hz0.16–0.5 Hz
   Stations, Components6 stations7 stations13 stations
 6 comp.9 comp.26 comp.
   Total number of data3304954680
Green's functionEGFEGFTheoretical

[9] We use recordings from the USGS GEOS and CGS strong motion instruments in the analysis. Accelerograms were integrated and bandpass filtered as shown in Table 1, normalized by the maximum amplitude of each component, and time-shifted to align at P (scales 1 and 2) or S arrivals (scale 3). We primarily use the vertical components for scales 1 and 2, and only the horizontal components for scale 3, to focus on the P and S waves, at those scales. The weighting factors (Table 2) are configured to give equal overall weight to the stations on the north and south of the epicenter.

Table 2. Station Lista
Station NameLatitude (°N)Longitude (°W)Weight (UD/NS/EW)
Scale 1Scale 2Scale 3
  • a

    The name and the position (latitude and longitude) of each station, and the weight of each component (UD, NS, and EW) of data in the inversion analysis are shown. The marks “−” indicate unused components in the “weight” column.

M35.958120.496 2/1/1 
V35.923120.534  −/1/1
E35.894120.421 2/−/− 
G35.833120.346  −/1/1
VC2E35.973120.467  −/1/1
FZ1135.896120.398  −/1/1
TF335.886120.350  −/1/1
FZ835.878120.381  −/1/1
GH3E35.870120.334  −/1/1
GH4W35.785120.444  −/1/1
SC3E35.833120.270  −/1/1
CH3E35.770120.247  −/1/1

[10] For scales 1 and 2, we use empirical Green's functions (EGF) [Hartzell, 1978], which are composed of waveforms of small earthquakes (EGF events) whose locations and mechanisms are similar to those of the mainshock. We select six EGF events, EGF1–EGF6 (Table 3), with strike-slip mechanisms similar to the mainshock (Figure 1c). The EGF sets for scales 1 and 2 are constructed by combining the observed waveforms of EGF1–EGF3 (MW 2.4–2.5) and EGF4–EGF6 (MW 2.7–3.7). We account for the finite durations of EGF events, by convolving the mainshock waveforms with triangle functions of duration comparable to that of the EGF events [Ide, 2001; Uchide and Ide, 2007]. The duration of EGF events are roughly estimated by the shortest pulse duration of the displacement waveforms obtained by integrating velocity records, because the pulse duration is possibly lengthened by anelastic attenuation in the crust. Due to the limited dynamic range of the GEOS stations, we use velocity seismograms of small earthquakes as EGFs, and the integral of the acceleration records for the mainshock.

Table 3. Combination of Small Events for the Construction of EGF for Scales 1 and 2a
 Origin Time (yyyy/mm/dd, hh:mm)Distance From the MainshockbDurationcMWDEFJKMRW
  • a

    The waveforms of the EGF events marked as “1” are used as EGF in this study, while those marked as “2” are used in the supplemental analysis. The marks “−” mean that no waveform for that event is available, and the marks “×” indicate that the polarity of the observed waveform is opposite that of the mainshock.

  • b

    The distances between the small events and the mainshock are calculated based on the result of the event relocation by the double-difference tomography [Thurber et al., 2006].

  • c

    Estimated by the pulse duration of displacement waveform obtained by integration of velocity records.

EGF11992/12/11, 22:151.4 km0.10 s2.41,22 2
EGF22004/11/20, 13:142.3 km0.10 s2.4× 21,2
EGF31993/01/14, 04:060.4 km0.10 s2.511,211
EGF41993/01/14, 03:410.4 km0.10 s2.7 21,22
EGF51992/05/29, 17:032.4 km0.15 s3.31,21,22×2
EGF62004/09/28, 17:332.0 km0.20 s3.711×11

[11] For scale 3, we cannot use the EGF method because we lack CGS strong-motion data for small earthquakes, and because the finite extent of the fault will lead to strong variations in the Green's functions. Instead, we use Green's functions obtained using the discrete-wavenumber method [Bouchon, 1981] using reflection and transmission matrices [Kennett and Kerry, 1979] with complex velocities to model anelastic attenuation [Takeo, 1985]. We assume two 1D structures as proposed by Liu et al. [2006] for the stations to the northeast and the southwest of the San Andreas Fault (SAF) to simulate the difference in the seismic velocity structure across the SAF [Eberhart-Phillips and Michael, 1993; Thurber et al., 2006].

[12] To stabilize the analysis, we applied three constraints. First, the model parameters (slip rates) are constrained to be non-negative using the non-negative least square algorithm [Lawson and Hanson, 1995]. Second, we constrained the total seismic moment to be 1.3 × 1018 Nm. Third, we applied a temporal smoothing constraint, with weighting to minimize Akaike's Bayesian information criterion (ABIC) [Akaike, 1980].

4. Results

[13] The final-slip distribution and snapshots of slip rate during rupture are shown in Figure 2. The cumulative seismic moment at 0.5 s and 1 s, corresponding to the effective duration of scales 1 and 2, is 1.8 × 1016 Nm (MW 4.8) and 1.3 × 1017 Nm (MW 5.3), respectively, and the final seismic moment of the earthquake is constrained to be 1.3 × 1018 Nm (MW 6.0). The source model is composed of two major slip areas: one near the hypocenter and another ∼18 km NW of the hypocenter. These two high slip areas were also detected in previous slip inversion analyses using strong-motion data and geodetic data [Langbein et al., 2005; Johanson et al., 2006; Liu et al., 2006; Murray et al., 2006; Custódio and Archuleta, 2007; Kim and Dreger, 2008]. Figure 3 shows the comparison between the observed and synthetic waveforms. The variance reduction (VR), (1 − σr2/σd2) × 100%, where σr2 and σd2 are the variances of the residual and the data, is 68.1%. Assuming the variance of the residual reflects the data errors, the standard deviation of each model parameter is less than 10% of the parameter value.

Figure 2.

Slip-rate distribution history and final slip distribution of our preferred multiscale fault model. The gray circles indicate the hypothetical rupture front propagating at 3.0 km/s from the hypocenter.

Figure 3.

Comparison of the observed (black thin lines) and theoretical (gray thick lines) waveforms. Maximum absolute value of the observed velocity of each component is shown in mm/s.

[14] The earthquake began bilaterally, with a high-speed rupture velocity of ∼3.0 km/s, and slip-rate as high as 4 m/s, during scales 1 and 2. These values are comparable to, or even higher than, those of the main rupture process at scale 3. This may be an effect of the greater potential resolution of the details of slip-rate amplitudes at scales 1 and 2, which can be more concentrated and larger, than at scale 3. To the southeast, rupture was arrested at 3 s after the onset, but the earthquake continued to grow unilaterally to the northwest after that. At 5 s, the second major slip area ruptured, and rupture terminated within ∼10 s.

[15] To verify the validity of the assumed hypothetical rupture front propagation speed, we examine propagation speeds of 2.6, 2.8, and 3.2 km/s. The models with 2.8 and 3.2 km/s explain the data as well as that with 3.0 km/s, with VR = 66.2% and 70.4%, respectively, and show similar location and timing of the high slip-rate areas (Figure S1 of the auxiliary material) to those in the model with 3.0 km/s (Figure 2). Low VR (60.4%) of the model with 2.6 km/s rejects the possibility of such slow propagation. Though we selected 3.0 km/s for the modeling, 2.8 and 3.2 km/s might well be acceptable by the data, and lead to similar conclusions.

[16] The multiscale analysis also depends on the reliability of the EGFs. We found that our model is robust in the sense that analysis with another EGF, shown in Table 3, results in a similar source model (Figure 4), that has similar high slip-rate areas to the preferred model (Figure 2).

Figure 4.

Slip rate history and final slip distribution of the 2004 Parkfield earthquake for the multiscale fault model with the alternative combination of EGF events (marked as “2” in Table 3).

5. Conclusions

[17] Our results indicate that from its very onset, rupture in the Parkfield earthquake was complex with high rupture speed. Rupture began bilaterally, and though our resolution within the first 0.1 s is limited, by 0.2 s the rupture velocity is about 3.0 km/s and slip-rate is as high as 3 m/s, by which time the cumulative seismic moment is equivalent to only a MW 3.9 earthquake, or 10−3 times of the eventual seismic moment. This suggests that any quasi-static nucleation process does not radiate a readily observable signature in the transition to dynamic rupture. The high-speed initial rupture inferred from our model is consistent with that of the 2004 mid-Niigata Prefecture, Japan, earthquake (MW 6.6) [Uchide and Ide, 2007], which implies that such characteristics may hold more generally.

[18] Our results suggest that the early stages of small and large earthquakes may be identical in terms of their cumulative seismic moments, slip rates, and rupture velocities. The observed seismograms (Figure 1d) begin with the sequences of weak phases, and the initial phases [e.g., Umeda, 1990; Ellsworth and Beroza, 1995] might be identified at 0.3 to 0.5 s after the P arrival; however our source model indicates no significant changes corresponding to these apparent initial phases, and is consistent with a cascade of failure [Ellsworth and Beroza, 1995].


[19] We thank Robert J. Geller and two anonymous reviewers for their helpful comments. We used the GEOS data of the USGS and the strong-motion network of CGS. Generic Mapping Tool (GMT) [Wessel and Smith, 1991] was used to draw the figures. This work is supported by Grant-in-Aid for Science Research and Special Project for Earthquake Disaster Mitigation in Tokyo Metropolitan Area of MEXT, Japan. T.U. is a JSPS Research Fellow.