Temporal changes in attenuation associated with the 2004 M6.0 Parkfield earthquake

Authors


Abstract

[1] Elevated seismic attenuation is often observed in fault zones due to the high degree of fracturing and fluid content. However, temporal changes in attenuation at the time of an earthquake are poorly constrained but can give indications of fracture damage and healing. In this study, spectral ratios between earthquakes within repeating clusters are calculated in an attempt to resolve temporal variations in attenuation at the time of the 2004 M6.0 Parkfield earthquake. A sharp increase in attenuation is observed immediately after the earthquake, which then decays over the next 2 years. Influences of intercluster magnitude variations, time window length and previously reported postseismic velocity changes are investigated. The postseismic decay is fit by a logarithmic function. The timescale of the decay is found to be similar to that in GPS data and ambient seismic noise velocities following the 2004 M6.0 Parkfield earthquake. The amplitude of the attenuation change corresponds to a decrease of approximately 10% in Qp at the time of the earthquake. The greatest changes are recorded on the northeast of the fault trace, consistent with preferential damage in the extensional quadrant behind a north-westerly propagating rupture tip. Our analysis suggests that significant changes in seismic attenuation and hence fracture dilatancy during coseismic rupture are limited to depths of less than about 5 km.

1 Introduction

[2] Fracturing around fault zones is important as it influences the strength and transport properties of the fault zone. How the fracture damage arises and how it evolves temporally over the seismic cycle are the key aspects to understand. Fault zone damage can yield information about the dynamics of rupture and changes to the physical properties of the fault as a result of the earthquake. An understanding of the static properties of fault zones has been built up by studies of their geometry and physical properties (e.g., Chester and Logan, [1986]; Faulkner et al. [2006]; Wibberley and Shimamoto, [2003]). A fault zone can be described by one or more fault cores, where slip is concentrated, surrounded by a damage zone with enhanced permeability due to fracturing (e.g., Caine et al. [1996]). The damage zone has been characterized in terms of the spatial distribution of fracture damage (e.g., Anders and Wiltschko, [1994]; Vermilye and Scholz, 1998; Wilson et al. [2003]) and also in terms of the scaling of the extent of the damage zone with displacement [Mitchell and Faulkner, 2009; Faulkner et al., 2011]. This damaged interior can be imaged seismologically as a low velocity zone (e.g., Cochran et al. [2009]), and the in situ time-dependent evolution of fault damage can potentially be elucidated by changes in the seismic signal.

[3] Studies of the temporal evolution of seismic velocity, InSAR and GPS data within fault zones indicate both pervasive coseismic cracking that heals with time and coseismic redistribution of crustal fluids [Li and Vidale, 2001; Li et al., 2003; Peltzer et al., 1998]. Attenuation is strongly influenced by cracks and fractures, as well as pore fluids and saturation levels (e.g., Winkler and Nur, [1982]). Elevated seismic attenuation is often observed at active faults in the brittle crust (e.g., Rietbrock, [2001]; Lees and Lindley, [1994]). However, there are very few studies of how attenuation evolves over an earthquake cycle. Earlier studies of attenuation changes at the time of large earthquakes have used doublets or earthquake clusters with few repeats (e.g., Got [1990], Aster et al. [1996], Got and Fréchet [1993]). Lower correlation coefficients between repeating events and/or greater interevent distances meant that source variability was of concern. Use of recently determined highly correlated small magnitude clusters, with only small variations in source position minimizes these concerns. More recent studies using such clusters have reported attenuation changes at the time of earthquakes [Allmann and Shearer, 2007; Chun et al., 2004; Chun et al., 2010]. This study uses data from seismometers in boreholes of up to a few hundred meters’ depth. The high signal to noise ratio (SNR) allows smaller magnitude clusters to be used, which have a number of advantages, including more frequent repeats. Also, higher corner frequencies reduce any source influence within the recorded range and allow us to extend our study to high frequencies.

[4] The Parkfield area of the San Andreas fault is an area of great interest as it marks the transition between the creeping section of the fault to the North and the locked section to the South. Earthquakes of M6.0 have occurred on this segment of the fault in 1881, 1901, 1922, 1934, 1966, and most recently in 2004 [Bakun and Lindh, 1985; Bakun et al., 2005]. The 2004 event ruptured approximately the same area as the previous 1966 earthquake, but in contrast to the 1966 and 1934 events, ruptured from the South of the segment mainly toward the North [Johanson et al., 2006]. The hypocenter location of the 2004 earthquake, along with the extent of rupture is shown in Figure 1. The area has been heavily instrumented since 1985 in anticipation of this most recent M6.0 earthquake, including instrumentation for the San Andreas Fault Observatory at Depth (SAFOD) project. A major aim of this instrumentation has been to monitor temporal changes throughout the seismic cycle.

Figure 1.

A map and cross section of the Parkfield area, indicating background seismicity (small grey circles) and locations of the clusters of earthquakes used in this study (black circles). The map also shows the locations of the HRSN stations (triangles). The hypocenter of the 2004 M6.0 earthquake is indicated by the star. The fault trace is shown (latitude and longitude by Jennings [1992]). The extent of the coseismic (solid red) and postseismic (dashed red) slip is also indicated [Johanson et al., 2006]. The inset map indicates the location of the study area shown in the map.

[5] A variety of studies have taken place addressing the temporal evolution of this area at the time of the 2004 M6.0 earthquake. Such studies have included investigation of seismic velocity changes (e.g., Rubinstein and Beroza, [2005]; Li et al. [2006, 2007]; Brenguier et al. [2008])), variations in crustal scattering [Audet, 2010], and variations in the polarization of surface waves [Durand et al., 2011], as well as studies of GPS and InSAR data (e.g., Johanson et al. [2006]; Johnson et al., 2006; Freed, [2007]). Studies have inferred a large amount of afterslip, with moment release after the mainshock similar to the coseismic moment release (e.g., Johanson et al., [2006]; Johnson et al., [2006]; Freed, [2007]). Many observations suggest that shallow coseismic damage occurs at the time of the 2004 M6.0 earthquake, which subsequently heals over time (e.g., Rubinstein and Beroza, [2005]; Li et al. [2006, 2007]; Sleep, [2009]). It is also suggested that there is a redistribution of crustal pore fluids and the breaking of impermeable barriers at middle to lower crustal levels (e.g., Audet [2010]). Increased tremor activity at depths of 15–30 km is observed immediately after the 2004 earthquake for at least 5 years and is possibly influenced by stress perturbations or episodic fluid release at these depths [Nadeau and Guilhem, 2009]. With such coseismic damage and fluid redistribution at this time, a change in attenuation would also be expected.

[6] In Parkfield, attenuation within the fault zone is significantly higher than in the surrounding rocks with fault zone P-wave Quality factor, Qp ≈ 50 [Abercrombie, 2000]. Attenuation across the fault in the surrounding area is highly asymmetric with much higher attenuation to the northeast (Qp ≈ 100) than the southwest (Qp ≈ 200) [Abercrombie, 2000; Bennington et al., 2008]. This reflects the highly contrasting rock types juxtaposed across the fault. The more highly attenuating rocks to the northeast are the Franciscan basement rocks and the Great Valley sequence, which are also of lower seismic velocity than the Salinian granites and arkosic sandstones to the southwest. Antolik et al. [1996] found no evidence of changes in coda attenuation at Parkfield using microearthquake clusters from 1987 to 1994. However, temporal changes in seismic attenuation in Parkfield around the time of the 2004 M6.0 earthquake have been noted by Allmann and Shearer [2007] and Chun et al. [2010]. Here, a systematic study of attenuation values immediately after the 2004 M6.0 earthquake is presented. Clusters of repeating earthquakes are used to resolve changes in attenuation in the Parkfield area. We add spatial resolution and depth resolution to previous studies by using the borehole seismometers of the high resolution seismic network (HRSN). We also investigate how the observed coseismic changes evolve with time after the earthquake. We use the dataset to investigate other possible influences in such a study, i.e., how magnitude variations within a cluster, the length of chosen time window, the chosen bandwidth and coseismic velocity changes may affect results. First, the data used and methods applied are presented. The results and their implications for coseismic fracturing are then discussed.

2 Data

[7] Data used are from the HRSN (see Figure 1). This network of seismometers is deployed in boreholes of depths 63–345 m. Since its upgrade and expansion to 13 stations in March 2001, the HRSN stations have been recording continuous data at 250 samples per second. Seismic activity in the Parkfield area is known to be highly clustered in nature with about half of the microearthquakes recorded occurring within clusters of similar, repeating events [Nadeau et al., 1994, 1995]. Within the clusters, events are effectively colocated, which means that almost identical ray paths are sampled repeatedly, which is ideal for a temporal study. The extremely similar nature and location of events within a cluster are crucial for this study. Events are of similar magnitude and almost identical location and are inferred to have ruptured the same fault patch each time [Nadeau et al., 1995]. Clusters of seismicity at Parkfield are believed to be related to strong heterogeneities (asperities) on the fault [Nadeau and Johnson, 1998]. These strong patches are believed to have high (100 MPa) stress drops [Nadeau and Johnson, 1998]. The corresponding corner frequencies are therefore also very high and often out of the range of the HRSN seismometers (e.g., see Table 1). It has been shown that small differences in rupture kinematics and locations can cause variations in spectral ratio throughout coda, similar to that expected from significant attenuation change [Got and Poupinet, 1990; Got and Fréchet, 1993; Aster et al., 1996]. However, corner frequencies well outside of the range of the recording set up should minimize the source effect when looking for attenuation changes.

Table 1. Summary of Clustersa
ClusterLatLonDepthMin MagnMax MagnAv Magnfc minfc maxMin. Phase Coherency
  1. a

    Locations of clusters used in this study are shown. The range of magnitudes within each cluster, and the corresponding maximum (Δσ = 100 MPa) and minimum (Δσ = 10 MPa) corner frequencies are given, assuming the average cluster magnitude. Minimum phase coherency values for each cluster are also shown.

135.974349–120.5340035.9430.8341.1851.0711002150.96895
235.968176–120.5371285.5310.2000.6170.4612024340.89102
335.964109–120.5278763.3410.5710.8250.6671593420.98890
435.961460–120.5234353.2710.1160.3520.2612545470.98773
535.961889–120.5228173.390-0.675-0.149-0.38853511530.90076
635.955913–120.5180584.1800.5970.8090.6631603440.98774
735.940641–120.5007854.1710.4210.8590.6071703670.96018
835.928252–120.4881764.4000.2981.2870.7821393000.95408
935.958243–120.53872610.8270.8541.4501.221841810.92659

[8] Nine clusters of similar, repeating events with good temporal resolution between 2001 and 2010 are presented in this study (e.g., see Figures 1-4). Events are determined to be within the same cluster based on similarity. Events with a station averaged cross-correlation above 0.8 to an original event are chosen as likely candidates for characteristic repeats of this event. Within this group, events are then characterized by dissimilarity, a weighted statistic based on phase spectrum coherences (weight 1.0), amplitude spectrum similarity (weight 0.8) and double-difference relocation separations (weight 0.3). Once these events are ranked by dissimilarity, those below the first break in the dissimilarity statistics are selected as members of the repeating sequence [Turner et al., 2011]. Including less similar (i.e., more dissimilar) events risks the breakdown of the assumption of similar source. The locations of these clusters along with the station distribution are shown in Figure 1. Eight of these clusters are at 3–6 km depth, with the final cluster at 10.8 km depth. Events are of magnitudes Mp -0.7 to 1.5 where Mp refers to a refined estimate of event magnitude based on low-frequency spectral ratios and the USGS/NCSN preferred magnitude scale [Nadeau and Johnson, 1998; Wyss et al., 2004]. The range of magnitude within clusters is as small as 0.2 to as large as 1.0. Within each cluster, the events have been double-difference relocated with respect to each other, and maximum separation of event locations is typically less than 10–20 m. Details of each cluster used in this study are presented in Table 1.

Figure 2.

Normalized traces from similar earthquakes within a cluster. A high degree of similarity is seen between events. This example shows events from cluster 4 as recorded at station LCCB (see Figure 1). The 850 ms time window used is indicated by the box. The trace shown in black is the event used as the reference event (i.e., the event from this cluster that had the highest signal-to-noise ratio at this station). Event origin time and magnitude are also indicated.

Figure 3.

As in Figure 2 but for cluster 6, as recorded at station VARB.

Figure 4.

As in Figure 2 but for cluster 8, as recorded at station MMNB.

3 Methods

[9] The Fourier velocity spectrum U, of an earthquake i observed at a station j can be represented as

display math(1)

where f is the frequency, S( f) is the source model (the velocity spectrum at the source), B( f) is the attenuation along the ray path, and I( f) is the instrument response function.

[10] The source velocity spectrum, S( f) can be modeled by

display math(2)

[Boatwright, 1978], where f is the frequency, fc is the source corner frequency, n and γ are dependent on the source model and define the high-frequency decay at the source, Ω0 is the long-period plateau value at the source, and

display math(3)

where M0 is the seismic moment, R describes the average radiation pattern (an average of 0.52 for P waves) [Aki and Richards, 1980], ρ is the crustal density, r is the hypocentral distance, and c is the wave velocity. For γ = 2 and n = 1, Si(  f ) (equation (2)) is equivalent to the Brune source model [Brune, 1970, 1971].

[11] The attenuation along the ray path, B(f) is given by

display math(4)

where

display math(5)

with t as the travel time to the station and Q as the quality factor along this path, the inverse of the whole path attenuation (math formula).

[12] By taking the ratio of one velocity spectrum U1, over another U2, recorded at the same station j, where both events have the same corner frequency, and the long-period plateau values vary only due to moment, math formula, the instrument response I( f) and the source S( f) effectively cancel out. It can be shown that

display math(6)

[13] Therefore, in this case, a linear relationship is expected between frequency and the logarithm of the spectral ratio. Using this, a Δt value between the two events can be calculated from the gradient of the straight line. It should be noted that any change in t can be attributed to either a change in travel time t, or a change in attenuation math formula, or a combination of both together.

[14] In this study, spectral ratios are calculated between P arrivals of earthquakes within repeating clusters, to resolve temporal changes in the attenuation operator t and thus in attenuation (math formula). This current study does not extend to S waves. As the S-P time is often very short, the S-wave arrival is often within the P-coda. It is therefore difficult to extract information of S-wave attenuation without contamination from the P-coda.

[15] A window of 850 ms around the P-arrival is extracted, including 150 ms before the P-arrival and 700 ms after. This time window is shown in Figures 2, 3, and 4 for the examples shown. A 850 ms window of noise immediately before the P-arrival is also extracted. The multitaper method [Park, 1987] is used to calculate the Fourier velocity spectra for all three components to capture as much energy as possible from within the time window. Examples using 3, 5, and 7 discrete prolate sequences are calculated (see Figure 5), but these different tapers are shown to have little effect on the calculated Δt values. Results quoted throughout use 7 discrete prolate sequences. Only frequencies with a SNR greater than 3 at 5–30 Hz in all three seismometer components are used. Higher frequencies are also included when the SNR is still good. Frequency spectra from the three components are then stacked. From each cluster, at each station, the event with the highest overall SNR across all frequencies is chosen as the reference event. For a particular cluster-station pair, only events with a frequency range at least 0.7 times the bandwidth of the reference event are used, to ensure a similar bandwidth for comparable data. The spectral ratio is calculated between each event within the cluster and the reference event. A Δt value, relative to the reference event is determined from the gradient of the least squares linear fit of math formula against frequency f (see Figure 6). Error bars are calculated as the 99% confidence intervals of the gradient. In this way, temporal changes in t values are determined around the time of the 2004 Parkfield event.

Figure 5.

Frequency spectra and spectral ratios using 3, 5, and 7 prolate sequences in the spectral calculation. The graphs to the right show the natural logarithm of the spectral ratio as a function of frequency (solid line) and the least squares linear fit to the data (dashed line). The Δt values calculated from the gradient are shown for each calculation. This example is for event of origin time 2007/03/22 00:54:52 from cluster 4, as recorded at LCCB.

Figure 6.

Left shows the three-component-stacked Fourier velocity spectra for an event (solid line), the corresponding reference event (dashed line) and the preceding noise (dash-dot line). Right shows the natural logarithms of the spectral ratios against frequency (solid line). Also shown are the least squares linear fit to the data (dashed line). The gradient of these lines are used to calculate the Δt value between an event and the reference event. Examples are shown from three separate clusters.

4 Analysis and Results

[16] Spectral ratios are calculated between events from 2001 to 2010 within 9 clusters at the 13 HRSN stations. A similar temporal signal in Δt values is seen in data from each cluster. A sharp increase in t is seen directly after the 2004 M6.0 Parkfield earthquake followed initially by a fairly rapid decline and a subsequent gradual decrease over approximately 2 years. Examples of this trend are shown in Figure 7. The perturbation in relative t values after the earthquake is generally of the order of 1 × 10− 3 for each ray path. Other studies have reported postseismic changes in t of similar magnitude (e.g., Chun et al. [2004]). This signal could originate from time-dependent variations in the source or along the travel path. Changes along the travel path that might contribute to such a change in the t signal include changes in seismic velocity, affecting the travel times, or changes in attenuation, math formula. Both these changes might be expected to occur after a large earthquake such as the 2004 M6.0 Parkfield earthquake. We therefore carry out a number of tests to determine the likely origin of the observed signal in t.

Figure 7.

Determined Δt values against time in days relative to the 2004 M6.0 earthquake for three separate ray paths. Determined values are relative to the reference event. Error bars for each data point are calculated from the 99% confidence intervals of the least squares fit to equation (6). Prior to the M6.0 earthquake, a fairly constant Δt is observed. Immediately after the earthquake, an elevated Δt is seen. This perturbation gradually decays to background levels.

4.1 Synthetic Tests

4.1.1 Length of Time Window

[17] A shorter time window, including only 30 ms before the P-arrival and 150 ms after, is tested without significant change to the trend of the results. Shorter time windows allow reflections and P-coda to be excluded from the signal but also mean that the gradient of the linear fit must be calculated over a narrower frequency band. The shorter time window reduces the average t peak by 10% (see Figure 8). The extra signal when the longer time window is used may represent the contribution from the coda which, by their scattered nature, samples a wider path. The time over which the perturbation decays is similar for both lengths of time window.

Figure 8.

Determined Δt values against time, in days, relative to the 2004 M6.0 event for earthquake cluster 4 as recorded at station LCCB, using 850 ms (left) and 180 ms (right) time windows around the P arrival time. The observed perturbation immediately after the 2004 M6.0 earthquake is less in the case of the 180 ms time window, compared to the longer time window. This may represent the contribution from the coda. The time over which the perturbation decays is similar for both lengths of time window.

4.1.2 Bandwidth Used

[18] The effect of the bandwidth used in the spectral ratio calculation is investigated. Fixed bandwidths of 5–30 Hz, 5–45 Hz, 5–60 Hz, and 5–90 Hz are investigated, and the results are compared to those using the variable bandwidth method described. Spectral ratios and values of Δt from each of these bandwidths are shown in Figure 9 for a number of examples. Values are similar across different frequency bands and are generally within error of each other. Values of Δt determined from the 5–30 Hz bandwidth agree less well with those from the other bandwidths. Therefore, a note of caution is needed in comparing data of bandwidth less than 5–30 Hz to data of greater bandwidth. All data used in this study are required to have a minimum bandwidth of 5–30 Hz. Only 11% of ray paths use data with bandwidths shorter than 5–45 Hz. The bandwidths used for each ray path are given in Table 2.

Figure 9.

Spectral ratios and Δt values as calculated over frequency ranges of 5–30 Hz (yellow), 5–45 Hz (dark blue), 5–60 Hz(pink), and 5–90 Hz(light blue), and a frequency range determined by the SNR (red) are shown. The examples shown are from same events as those shown in Figure 6.

Table 2. Bandwidths Used for Each Ray Path
ClusterStationMin Bandwidth (Hz)Max Bandwidth (Hz)ClusterStationMin Bandwidth (Hz)Max Bandwidth (Hz)
1CCRB5–1205–1236FROB5–885–105
1EADB5–375–456JCNB5–745–85
1FROB5–675–906LCCB5–885–91
1JCNB5–695–826MMNB5–565–75
1LCCB5–805–966SCYB5–335–33
1MMNB5–785–926VARB5–685–81
1SCYB5–375–516VCAB5–1205–120
1VARB5–615–717LCCB5–645–80
1VCAB5–1195–1247MMNB5–685–88
2LCCB5–645–807VARB5–725–76
2VCAB5–1135–1218CCRB5–955–112
3CCRB5–1195–1238EADB5–475–58
3FROB5–645–658FROB5–1045–116
3JCNB5–505–558JCNB5–745–94
3LCCB5–735–1028LCCB5–625–78
3MMNB5–755–938MMNB5–495–67
3VARB5–425–458SMNB5–675–72
3VCAB5–825–1128VARB5–685–90
4CCRB5–1225–1238VCAB5–975–115
4JCNB5–605–729EADB5–545–62
4LCCB5–825–1029JCNB5–625–77
4MMNB5–675–809LCCB5–655–82
4SCYB5–335–379MMNB5–535–68
4SMNB5–955–1039RMNB5–385–50
4VARB5–515–519SCYB5–515–51
4VCAB5–815–1079SMNB5–1205–124
5LCCB5–705–889VARB5–505–68
5MMNB5–555–72 

4.1.3 Coseismic Velocity Variations

[19] As changes in t might be caused by changes in travel time or changes in attenuation, calculated Δt values are corrected for observed coseismic velocity changes. Spectral ratios of synthetic Brune spectra are calculated with velocity variations as reported by Brenguier et al. [2008]. The synthetically determined Δt values act as correction factors to our results to account for the observed velocity changes. However, it is shown that this range of velocity perturbation has almost no effect on the determined Δt values.

4.1.4 Magnitude Variations

[20] The spectral ratios method initially assumes that the two spectra involved in the division have the same corner frequency fc and that the long-period plateau values Ω0 vary only due to changes in moment. However, it is debatable whether these conditions are met for repeating clusters of similar earthquakes. From analyzing each of the individual graphs of math formula against frequency, it is observed that they are generally well approximated by a straight line (e.g., see Figure 6). This implies that the assumption that events within a cluster have the same corner frequency is reasonable. However, the magnitudes within a cluster are believed to vary (e.g., see Table 1).

[21] A change in magnitude Mp corresponds to a change in moment by

display math(7)

where moment is in Nm.

[22] Assuming a Brune source model [Brune, 1970]:

display math(8)

where Δσ is the stress drop and r is the radius of rupture, and

display math(9)

where Vp is the P wave velocity and fc is the corner frequency. Therefore, it is seen that the P-wave corner frequency is expected to scale with moment as

display math(10)

[23] Variation of moment within a cluster may therefore cause a variation of corner frequency fc. An attempt is made to quantify how much this change in moment might affect the measured changes in t. Given the range of magnitudes within each cluster, subsequent variations in corner frequency are calculated. Determined moment and corner frequency for each event within each cluster are then used to calculate spectral ratios of synthetic Brune spectra, assuming no changes in along-path attenuation. Values obtained from this synthetic test correspond to changes in t caused solely by magnitude variations within a cluster. This is then used as a correction factor against our original Δt values. From equation (10), it can be seen that the corner frequency used in determining the Brune spectra requires information on stress drop. Some data suggest that stress drops of repeating clusters within the Parkfield area may be unusually high [Nadeau and Johnson, 1998]. The effects of constant stress drops of 10 MPa (0.1 kilobar) and 100 MPa (1 kilobar) are investigated here. It is found that taking these magnitude variations into account generally causes the observed peak in Δt to be reduced (see Figure 10). This effect is greater at smaller stress drops and for larger magnitude events. For a signal corrected for a stress drop of 10 MPa, using the 850 ms time window, the amplitude of the average observed Δt peak is reduced by less than 20%, and the postseismic trend remains similar.

Figure 10.

The spectral ratios method assumes constant corner frequency between events. However, corner frequency is believed to scale as in equation (10). As each cluster of events includes a range of event magnitudes and moments, these differences are taken into account by calculating expected differences using synthetic Brune spectra. Top left shows the original, uncorrected trend of the data, including error bars. Top right shows the data after it has been corrected for magnitude variations assuming a stress drop of 100 MPa (1 kbar). Bottom left shows the data after they have been corrected for magnitude variations assuming a stress drop of 10 MPa (0.1 kbar). Bottom right shows the original, uncorrected data along with corrections assuming stress drops of 100 MPa and 10 MPa. Error bars have been omitted for clarity in this final plot.

[24] Chun et al. [2004, 2010] have previously corrected for magnitude variations in an alternative manner. For each cluster studied, these authors search for a reference ray path along which they believe that no temporal changes in attenuation occur. A correction factor to account for any source differences is calculated from variations in t along this path. This information is used to correct Δt measurements from other ray paths originating at the same cluster. We were unable to utilize this technique for every cluster as it was not always possible to find suitable reference ray paths where every event needed was well recorded at a reference station. However, we are able to compare the corrections that we have applied to those from the method of Chun et al. [2004] for some clusters for which we found adequate reference stations (Figure 11). The corrections required by each method agree well (Figure 11). This adds further confidence that source effects on Δt are removed.

Figure 11.

Source contributions to the Δt signal estimated using a Brune source model, with a 10MPa stress drop are shown in red. The maximum likely source contribution for individual clusters is estimated from the signal at the station that has recorded the least variation in t (the reference station). This is shown in black. Note that not all events are recorded at each reference station. Graphs are to the same scale as those in Figure 7 for easy comparison. The two methods agree well in their estimates of source contribution for these data.

[25] Having corrected the signal for velocity changes and small magnitude variations within clusters and tested the influence of different lengths of time window, these remaining changes in t values appear robust and can be interpreted as changes in attenuation of the material after the 2004 M6.0 event. Values of math formula are calculated from Δt, assuming an average velocity of 4 km/s for the eight shallow clusters. For the deeper cluster (cluster 9), a whole-path average velocity of 4.75 km/s is used. These are the average P-wave velocities to depths of 5 and 10 km from the velocity model of Thurber et al. [2006].

4.2 Amplitude of Perturbation

[26] The value of the attenuation anomaly just after the earthquake, math formula, was investigated. For each ray path, the background math formula was determined from an average of three data points occurring at a time after the 2004 M6.0 earthquake, when the postseismic perturbation had diminished. The math formula was then determined as the maximum departure from this background level. The error in the math formula value was calculated by combining errors from the background level and the maximum departure. Investigating the spatial variability in the attenuation signal allows determination of the areas in which the greatest changes in attenuation occurred. This might correspond to the area of greatest damage in the 2004 M6.0 earthquake or to areas where the greatest saturation changes occurred. The spatial distribution of the variability in the amplitude of perturbation was investigated by comparing signals from different ray paths. The depth dependence of the amplitude of the perturbation was investigated by comparing the signal from the one deep (10 km depth) cluster of earthquakes with the other more shallow (3–6 km depth) clusters.

4.3 Decay Rate

[27] The decay rate informs us on how quickly any earthquake-induced changes return to their pre-earthquake level. Postseismic trends are often described by logarithmic (e.g., Schaff and Beroza [2004]), exponential (e.g., Peltzer et al. [1998]) or power law decays (e.g., Baisch and Bokelmann [2001]). Each of these models was considered in describing the decay of the observed postseismic attenuation signal. The data could adequately be represented by any of these models within error. However, from the fit to the data, we prefer a logarithmic decay. The decay rate was calculated from the gradient of the least squares fit of math formula against log(t) with t as time in days after the earthquake. The data points were weighted by the inverse of the magnitude of their error bars, and the reference data point was excluded. Error bars for the decay rate were calculated from the 68% confidence intervals of the least squares fit. Calculated values are given in table results.

5 Discussion

[28] A range of coseismic and postseismic signals have been observed at the time of the 2004 M6.0 Parkfield earthquake, including changes in seismic velocities [Brenguier et al., 2008; Li et al., 2006, 2007; Rubinstein and Beroza, 2005] and signals in GPS and InSAR data [Freed, 2007; Johanson et al., 2006; Johnson et al., 2006]. Changes in seismic attenuation at this time have previously been noted by Chun et al. [2010] and Allmann and Shearer[ 2007]. In this study, a number of clusters of repeating earthquakes have been used in an attempt to resolve better the amplitude, decay, and location of the observed change in attenuation. Through calculating spectral ratios from clusters of repeating microearthquakes, a temporal change in t is found to occur at the time of the 2004 M6.0 earthquake in Parkfield. A sharp increase in t is observed immediately after the earthquake, and this perturbation subsequently decays with time. After sensitivity tests for effects of source changes and previously reported velocity changes, it is inferred that the changes in t are predominantly caused by changes in attenuation of the fault zone materials, i.e., a coseismic increase in attenuation and postseismic decay of this perturbation.

[29] Commonly accepted causes of attenuation include microcracks and presence of fluids. Pore fluids are observed experimentally to have a very strong effect on attenuation in rocks (e.g., Winkler and Nur, [1982]; Toksoz et al. [1979]). For P waves, it is found that the highest values of attenuation are at partial saturation, with lower values for fully saturated and dry samples [Winkler and Nur, 1982]. The connection between attenuation and fractures is inferred from the increase in Q with confining pressure, presumably due to crack closure (e.g., Toksoz et al. [1979]).

[30] Fault zones are known to be areas of high seismic attenuation due to the large amount of fracturing and high fluid content. Changes in P wave attenuation within a fault zone have also been observed following the 1989 M7.0 Loma Prieta earthquake [Chun et al., 2004]. A large amplitude increase is seen within the first 3 weeks of the main shock, followed by a gradual recovery to preshock levels in the following months [Chun et al., 2004]. These changes were interpreted to be caused by localized coseismic and postseismic changes in fluid saturation along the fault. At shallow depths, the subsurface is fluid-saturated both inside and outside of the fault zone. Coseismically, there is redistribution of fluids, causing temporary partial fluid conditions, but postseismically, these fluids re-equilibrate to fluid-saturated conditions over time. Possible explanations for changes in attenuation following the 1989 M7.0 Loma Prieta and 2004 M6.0 Parkfield earthquakes include an increase in fracture density due to strong shallow ground motion and/or a decrease in fluid saturation in the fault zone. Previously reported changes in seismic velocities have indicated that increased fracture damage occurs at the time of the 2004 M6.0 earthquake [Rubinstein and Beroza, 2005; Li et al., 2006, 2007]. This mechanism is expected to contribute to the observed changes in attenuation occurring over the same period. Fluid-flow expected to occur at the time of the earthquake may also contribute significantly to the signal. These possible mechanisms may also be linked, with an increase in fracture density causing an increase in pore volume and permeability, in turn allowing fluid flow and saturation changes in the area [Rojstaczer et al., 1995]. It seems unlikely that all clusters, located at different parts of the rupture plane would show similar time behavior if the observations were strongly influenced by effects other than path effects, e.g., source variations.

5.1 Amplitude of Signal

[31] Calculated values for coseismic changes in attenuation, math formula, along each ray path, are given in Table 3 and are of the order of 1.0 × 10− 3. Previous studies of time-averaged attenuation in the Parkfield area report a P-wave Quality factor, Qp of approximately 100–200, with lower values of 10–80 within the fault zone itself [Abercrombie, 2000; Bennington et al., 2008]. Given these time-averaged Qp values, simple calculations suggest that an increase in math formula of 1.0 × 10− 3 corresponds to a decrease in Qp of the order of 10%.

Table 3. Summary of Resultsa
ClusterStationDecayErrormath formulaErrorClusterStationDecayErrormath formulaError
  1. a

    For each ray path, the logarithmic decay and the amplitude of the attenuation anomaly are given. The logarithmic decay is the gradient of math formula against log(t) where t is the time in days after the earthquake. The quoted errors are the 68% confidence in the gradient from a least squares linear fit. math formula values are determined by calculating the maximum departure from a background attenuation level. Corrections have been applied for postseismic velocity changes and intercluster magnitude variations assuming a stress drop of 10 MPa. The errors quoted are 99% confidence levels.

1CCRB0.0001830.0001070.0008520.0001216FROB0.0000880.0000290.0003830.000150
1EADB0.0000170.0000590.0002490.0001296JCNB0.0001130.0000390.0003130.000102
1FROB0.0000770.0000690.0005440.0001536LCCB0.0002760.0000490.0006820.000317
1JCNB0.0000900.0000560.0005320.0001016MMNB0.0000850.0000330.0003660.000219
1LCCB0.0003550.0001390.0012260.0001696SCYB0.0000290.0000260.0003590.000276
1MMNB0.0001560.0001260.0010170.0001316VARB0.0001650.0000200.0005050.000092
1SCYB0.0000840.0000640.0005440.0003126VCAB0.0000620.0000160.0002570.000099
1VARB0.0001420.0000710.0006110.0000837LCCB0.0000540.0001120.0009860.000311
1VCAB0.0000400.0000780.0006960.0001047MMNB0.0000890.0001270.0007930.000225
2LCCB0.0005320.0000690.0009170.0002827VARB0.0000640.0000530.0005720.000195
2VCAB0.0000430.0000270.0001170.0000668CCRB0.0002130.0000470.0004940.000151
3CCRB0.0000540.0000230.0002760.0001188EADB0.0003560.0000480.0005830.000181
3FROB0.0000460.0000250.0003350.0002258FROB0.0002230.0000820.0007130.000279
3JCNB0.0000240.0000390.0001390.0001198JCNB0.0002830.0000580.0010630.000205
3LCCB0.0003760.0000390.0012580.0002028LCCB0.0002000.0000170.0005240.000155
3MMNB0.0001860.0000330.0006910.0001258MMNB0.0001460.0000570.0009300.000194
3VARB0.0000970.0000180.0002840.0002128SMNB0.0001470.0000720.0003980.000199
3VCAB0.0000630.0000200.0002960.0000948VARB0.0003060.0000630.0013310.000247
4CCRB0.0003630.0000670.0009950.0000738VCAB0.0001810.0000610.0009000.000157
4JCNB0.0001740.0000490.0006170.0001169EADB0.0002590.0004190.0006660.000151
4LCCB0.0009340.0000830.0023140.0001989JCNB0.0001350.0002440.0004370.000169
4MMNB0.0004640.0000870.0013510.0001799LCCB0.0006940.0002570.0010030.000166
4SCYB0.0004310.0000960.0016090.0007029MMNB0.0006790.0004950.0008320.000306
4SMNB0.0001980.0000410.0006600.0001809RMNB0.0003190.0004960.0008650.000347
4VARB0.0002690.0000850.0009320.0001559SCYB0.0008460.0005080.0007280.000146
4VCAB0.0002040.0000420.0006590.0001239SMNB0.0005690.0006010.0005410.000142
5LCCB0.0003140.0001380.0010830.0003439VARB0.0002240.0003160.0006330.000144
5MMNB0.0000240.0001230.0007430.000368 

[32] From spectral empirical Green's functions, Allmann and Shearer [2007] identified the areas of the largest attenuation changes to be near and between the 2004 M6.0 and 1966 M6.0 hypocenters. We compare signals from different ray paths to add to the resolution of the spatial variation in attenuation changes. The largest amplitude signals were observed from short ray paths, suggesting that the changes were concentrated laterally close to the fault (Figure 12). This suggests that the coseismic crack damage and/or saturation changes at the time of the 2004 M6.0 earthquake were concentrated close to the fault, as might be expected.

Figure 12.

(a) Histograms of math formula values to the northeast and southwest of the fault after corrections have been applied for postseismic velocity changes and intercluster magnitude variations (assuming a stress drop of 10MPa). (b) Map of ray paths, with colors corresponding to the values of math formula as indicated in the key. The focal mechanism represents the 2004 M6.0 Parkfield earthquake. The location of the fault trace is also shown [Jennings, 1992]. It is observed that the largest values of math formula are all recorded to the northeast of the fault.

[33] It is also observed that the largest perturbations in the attenuation signal at this time are recorded on the northeast side of the fault (see Figure 12). Possible explanations for this include lithological control, asymmetric damage, initial asymmetric fluid content or poroelastic flow. Abrupt changes in lithology are seen across the fault at Parkfield, with the more attenuative rocks to the northeast. If the rocks to the northeast of the fault are generally more easily fractured, this would allow larger coseismic changes in attenuation to the northeast. Furthermore, for northwest propagation during right lateral slip, the area immediately behind the rupture tip on the northeast side of the fault is expected to experience higher differential stresses that will promote rock failure, and in some cases, tensional stresses might develop [Rice et al., 2005]. As rocks are weaker in tension than compression, more damage might be expected here (see Figure 13). This would allow another possible explanation for larger changes in attenuation to the northeast. Northeast of the fault is also an area where fluids are believed to be concentrated (e.g., Unsworth and Bedrosian [2004]; Eberhart-Philips and Michael [1993]; Becken et al. [2008]). Therefore, a greater change in saturation might be expected here. Poroelastic flow caused by the earthquake might also contribute to this asymmetry. Pore pressure increase is expected in the crust where compressional strain changes have occurred (e.g., Jonsson et al. [2003]). Conversely, where extensional strain changes have occurred, pore pressure decrease is expected. Hence, to the northeast, a decrease in saturation levels due to poroelastic dilatancy would be expected, which in turn would give an increase in attenuation. To the southwest, an increase in saturation levels would be expected, which would give a decrease in attenuation. As the polarity of the observed changes is positive on both sides of the fault, this cannot be the first-order effect. However, it might act as a second-order effect, altering the observed amplitudes of the attenuation changes, so larger changes are seen to the northeast compared to the southwest. Any or all of these explanations may contribute to the larger amplitude signal being recorded to the northeast of the fault.

Figure 13.

A schematic image of a right-lateral strike-slip fault is shown. The direction of rupture is indicated by the arrow labeled Vr. Along the fault plane, the solid line indicates the area which has slipped, and the dashed line indicates the area which has not yet slipped. Stresses behind the rupture tip are labeled. Greater damage is indicated in the extensional area behind the rupture tip.

[34] The depth extent of the coseismic attenuation signal is also considered. The HRSN stations are deployed in boreholes at depths of 60–350 m. The earthquake clusters that have been used are mainly at 3–5 km in depth, apart from cluster 9, at just over10 km depth. This is therefore the depth range that the seismic waves are sampling. It was found that the amplitudes of the perturbations from the deep cluster were similar to those from shallow clusters. This suggests that the signal from the deep cluster is mainly affected by changes that are occurring in a depth range also sampled by the shallow clusters. As the data from the deepest cluster implies a similar change in whole-path attenuation, the main damage from the 2004 M6.0 earthquake can be constrained to depths shallower than about 5 km.

[35] The areas of greatest attenuation change identified by Allmann and Shearer [2007], near the Middle Mountain asperity and between the hypocenters of the 1966 and 2004 earthquakes, are observed in this study also to undergo significant attenuation change. Li et al. [2006, 2007] report that velocity variations occur close to the fault and to depths of less than 7 km. Results from this study suggest that attenuation changes may be limited to a similar depth range.

[36] Li et al. [2006] report the area of velocity decrease after the 2004 M6.0 Parkfield earthquake to be centered to the southwest of the mapped surface fault trace, rather than the northeast, as observed for attenuation measurements in this study. Li et al. [2006] use a short across-fault surface array which may be more sensitive to local effects than the HRSN borehole seismometers, which give us coverage of a much larger area. Furthermore, the result of Li et al. [2006] may be sensitive to the steep dip of the fault to the southwest, which explains the offset of the seismicity from the mapped surface fault trace [Hole et al., 2001]. If the waves decouple from the low velocity zone at depth, then their signal may represent the location at which this occurs. More work is needed to determine the origin of this signal and its relationship to the signal observed in the attenuation study presented here.

[37] Chun et al. [2010] observe a larger than expected precursory t* at one station to the southwest of the fault trace. They suggest that this may be due to greater damage to the southwest as proposed by Li et al. [2006]. The 2003 San Simeon earthquake may have had an influence on the precursory signal observed by Chun et al. [2010]. Although the distance between the two areas is quite large (65 km), the San Simeon earthquake has clearly been shown to have had a measurable effect on seismic velocity measurements in the Parkfield area [Brenguier et al., 2008].

[38] The studies of Li et al. [2006] and Chun et al. [2010] both use surface stations in their analysis. These studies may therefore be more sensitive to near surface propagation changes occurring in the upper 100 m (e.g., Rubinstein and Beroza [2005]) due to ground shaking from the 2004 M6.0 Parkfield earthquake and changes in near surface due to seasonality and hydrologic effects such as rainfall (e.g., Karageorgi et al. [1992, 1997]). It is also worth noting that Chun et al. [2010], using surface rather than borehole stations, observe postseismic changes in attenuation associated with the 2004 M6.0 Parkfield earthquake, with a time lag occurring before the observed peak attenuation value. Attenuation is observed to be at a maximum at partial saturation (e.g., Winkler and Nur [1982]). Chun et al. [2010] interpret their observation as an initial coseismic decrease in saturation to a level below that where maximum attenuation is observed. As the saturation postseismically increases to pre-earthquake values, attenuation must first increase until it reaches this peak and then will decrease. Such a time-lag before reaching peak attenuation is not observed in this study. This difference might be explained by either a larger change in saturation at depths shallower than HRSN stations (<300 m) or a change in the dominant attenuation mechanism, from fluids at very shallow depths to crack damage at depths greater than the HRSN stations.

5.2 Decay Rates

[39] The postseismic attenuation signals were fitted with logarithmic decay rates. A logarithmic decay is consistent with healing relationships determined from laboratory experiments [Dieterich, 1972; Beeler et al., 1994] and with field observations of postseismic changes in velocity [Schaff and Beroza, 2004] and shear wave splitting [Hiramatsu et al., 2005]. Such a trend is predicted by empirical models of afterslip (e.g., Feigl and Thatcher [2006]).

[40] The attenuation perturbation decays to background levels over approximately 2 years. This is similar to other postseismic observations in Parkfield (Figure 14), e.g., decays in GPS data [Freed, 2007] and in velocity perturbations from ambient seismic noise [Brenguier et al., 2008]. The postseismic decay in the first few days after the 2004 M6.0 earthquake appears much slower in the ambient noise velocity data compared to the attenuation results (see Figure 14). The 30-day stacks required by the ambient seismic noise processing may have caused the initial sharp peak to be averaged out and therefore any initial fast decay to be removed. However, the longer-term decays in the two datasets agree well.

Figure 14.

Signals in different datasets at the time of the 2004 M6.0 Parkfield earthquake. At the top, continuous GPS displacement time series from station HOGS is plotted (http://earthquake.usgs.gov/monitoring/gps/CentralCalifornia/hogs/). Below this, the temporal change in math formula determined from this study is shown (for cluster 4 at station LCCB). At the bottom, the postseismic signal in ambient seismic noise from Brenguier et al. [2008] is shown.

[41] Considering postseismic signals following a variety of different earthquakes, many of the observed perturbations decay over 2–5 years. Coseismic and postseismic velocity changes have also been observed at the time of the 1999 M7.1 Hector Mine earthquake [Li et al., 2003] and the 1992 M7.5 Landers earthquake [Li et al., 1998; Li and Vidale, 2001]. Postseismic signals in GPS data (e.g., Savage and Svarc, 1997) and InSAR data (e.g., Peltzer et al. [1998]) have also been observed following major earthquakes. Changes in the shear wave splitting delay time after the 1997 M5.7 Tokai, Japan, earthquake have been reported [Hiramatsu et al., 2005], and Baisch and Bokelmann [2001] observe changes in coherencies between multiple events immediately after the 1989 Loma Prieta earthquake, which gradually recover over time. These observations have variously been interpreted in terms of increased cracking, afterslip, and poroelastic rebound due to pore-fluid flow. The perturbations in attenuation observed in this study decay over a similar period to these other postseismic observations. The observations of attenuation changes in Parkfield suggest that it takes approximately 2 years for crack closure and fluid re-equlibriation to have completed after the 2004 M6.0 earthquake.

6 Conclusions

[42] A temporal change in attenuation associated with the 2004 M6.0 Parkfield earthquake is observed. An increase in attenuation, math formula of the order of 1 × 10− 3 is observed immediately after the earthquake, and this perturbation then decays over approximately 2 years. The postseismic trend is tested for influences of intercluster magnitude variations, length of time window used, and previously reported velocity changes. Intercluster magnitude variations and time window length are found to affect the amplitude of the perturbation but not the nature of the postseimic trend. Intercluster magnitude variations have a smaller effect for clusters of earthquakes with smaller magnitudes and larger stress drops. The greatest coseismic changes in attenuation are found to occur close to the fault and are recorded to the northeast of the fault trace. Analysis suggests that changes are limited to depths of less than about 5 km. A logarithmic decay is found to fit the trend of the postseismic data well. This agrees with healing relationships determined from laboratory experiments [Dieterich, 1972; Beeler et al., 1994]. The perturbation in attenuation is found to decay in a similar way to postseismic decays from GPS data and ambient seismic noise velocities following the 2004 Parkfield M6.0 earthquake. Changes in attenuation at the time of the 2004 M6.0 Parkfield earthquake imply coseismic cracking and/or fluid redistribution that recover over approximately 2 years.

Acknowledgments

[43] HRSN data were provided by the Berkeley Seismological Laboratory and NCEDC with support from USGS grant G10AC00093. Research support for RMN was provided by NSF grants EAR-0738342 and EAR-0910322. All other research support was provided by NERC grantNE/F019920/1. Dr. Ninfa Bennington and an anonymous reviewer are thanked for their comments which have significantly improved the manuscript.