LETTERS PUBLISHED ONLINE: 22 NOVEMBER 2009 | DOI: 10.1038/NGEO697 Migration of early aftershocks following the 2004 Parkfield earthquake Zhigang Peng* and Peng Zhao Large shallow earthquakes are immediately followed by numerous aftershocks. A significant portion of these events is missing in existing earthquake catalogues, mainly because seismicity after the mainshock can be masked by overlapping arrivals of waves from the mainshock and aftershocks1���4. How- ever, recovery of the missing early aftershocks is important for understanding the physical mechanisms of earthquake triggering2���4, and for tracking postseismic deformation around the rupture zone associated with the mainshock5���7. Here we use the waveforms of 3,647 relocated earthquakes8 along the Parkfield section of the San Andreas fault as templates9,10 to detect missing aftershocks within three days of the 2004 mag- nitude 6.0 Parkfield earthquake. We identify 11 times more af- tershocks than listed in the standard catalogue of the Northern California Seismic Network. We find that the newly detected af- tershocks migrate in both along-strike and down-dip directions with logarithmic time since the mainshock, consistent with numerical simulations of the expansion of aftershocks caused by propagating afterslip11,12. The cumulative number of early aftershocks increases linearly with postseismic deformation in the first two days, supporting the view that aftershocks are driven primarily by afterslip13,14. The Parkfield section of the San Andreas fault (SAF) straddles the transition between the creeping segment to the northwest and the locked segment to the southeast (Fig. 1). The 28 September 2004 Mw 6.0 Parkfield earthquake nucleated near Gold Hill south of Parkfield, and the rupture propagated predominately in the northwest direction towards Middle Mountain with a total length of ���30 km (ref. 15). The mainshock and its numerous aftershocks were recorded continuously by many near-field seismic instruments, resulting in one of the best recorded earthquake sequences in the world. We use waveforms of 3,647 earthquakes listed in the relocated catalogue8 as templates to detect missing events within three days since 28 September 2004 (see the Methods section). Figure 2 shows an example of a positive detection on 28 September 2004 at 17:17:44, approximately 140 s after the origin time of the mainshock (28 September 2004 17:15:24). Although two more events occurred within 10 s, the matched filter technique is able to uniquely identify the target event with a network-averaged cross-correlation coefficient of 0.79. It is worth noting that none of these newly detected events (in the magnitude range of 2.4���2.6) is listed in the Northern California Seismic Network (NCSN) catalogue. Overall, we have a total of 610,286 positive detections between 28 and 30 September 2004. After removing multiple detections (see the Methods section), we obtain 11,138 individual events. In comparison, only 543 and 933 events were listed in the Thurber et al.8 and the NCSN catalogues, respectively. Hence, our matched filter technique has detected at least 11 times more aftershocks than those in the NCSN catalogue. A detailed School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. *e-mail: zpeng@gatech.edu. comparison of the locations, magnitudes and statistical properties between our detected events and the NCSN catalogue is given in Supplementary Notes S1,S2. Figure 3a shows the locations of the detected aftershocks colour-coded by their occurrence times since the mainshock in a logarithmic timescale. Detailed views of all aftershocks in the first hour and within two days after the mainshock are shown in Sup- plementary Movies. We find that aftershocks within the first hour mainly occurred along a 12-km-long ���streak��� at the depth range of 4���6 km (ref. 8), just above a large patch of high slip 10���20 km north of the epicentre at the depth range of 5���7 km (refs 15���18). In comparison, aftershocks in another seismic ���streak��� at the depth range of 8���10 km were not as active as those in the shallow ���streak��� (Supplementary Fig. S6). Finally, a cluster of deep events at 13 km beneath Middle Mountain and the region north of the San Andreas Fault Observatory at Depth (SAFOD) in the creeping section were not active within the first few hours after the mainshock (Supplementary Figs S6,S7), indicating a possible migration of aftershocks along the SAF strike and the down-dip directions. To investigate this further, Fig. 3b shows the occurrence time since the mainshock against the along-strike distance for all events within 2 km of the SAF. The newly detected events show clear migration with logarithmic time in the creeping section of the SAF. The migration speed is ���3.4 km decade-1 since the mainshock. In comparison, the aftershocks southeast of our study region seem to expand suddenly from 7 to 17 km southeast of the epicentre around 104 s (���3 h) after the mainshock, rather than migrating with time as shown in the creeping section. We also examine the NCSN catalogue, which covers a wider region than the Thurber et al.8 catalogue, and find a similar but weaker migration pattern (Supplementary Fig. S8). Next, we separate all aftershocks into three depth ranges and compare their along-strike migration patterns (Supplementary Fig. S9). A general feature is that aftershocks show clear expansion in the creeping section at three depth ranges. Furthermore, the expansion speed in the top 3 km is faster than those at larger depths. We also examine the temporal evolutions of the hypocentral depths for the detected aftershocks by separating all of the aftershocks according to the seismicity distributions (Supplementary Fig. S10). We find that the aftershocks at shallow depth in the creeping section northwest of Middle Mountain and beneath Middle Mountain seem to migrate in the up-dip direction. In comparison, the down-dip migration at larger depth is best shown in segments beneath and southwest of Middle Mountain. One potential cause of the apparent migration shown in Fig. 3 and Supplementary Figs S9,S10 is an increase in the number of samples by plotting the time axis in a logarithmic scale. We have examined this in detail and found that although such bias does exist in our data, the observed patterns cannot be caused by plotting alone or random occurrence, but rather represent a NATURE GEOSCIENCE | VOL 2 | DECEMBER 2009 | www.nature.com/naturegeoscience 877 �� 2009 Macmillan Publishers Limited. 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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO697 0 5 10 (km) EADB GHIB MMNB 2004 Mw 6.0 San And rea s fault Creeping A A�� SAFOD OcePacific an Cal ifornia Depth (km) Along-strike distance (km) 0 10 20 (cm) EADB GHIB MMNB SAFOD Creeping Locked L ock ed a b ��15 ��10 ��5 0 35�� 48' 36�� 00' 36�� 12' 120�� 24' 120�� 36' 120�� 12' ��50 ��40 ��30 ��20 ��10 0 10 20 Latitude (N) Longitude (W) Figure 1 | Map of the SAF and the 2004 Parkfield earthquake sequence. a, Map of the Parkfield section of the SAF (red line), including the epicentral location of the 2004 Mw 6.0 Parkfield earthquake (green star), and the 3,647 template events listed in the relocated catalogue8 (blue dots). The open triangles represent 13 stations in the HRSN, with selected station names marked. The San Andreas Fault Observatory at Depth (SAFOD) is denoted by the yellow square. b, The cross-section view of the 3,647 template events (blue) along the SAF, and those detected within the first hour after the Parkfield mainshock (red). The size is computed by assuming a circular crack model and a constant stress drop of 3 MPa. The background shading denotes the mainshock slip distribution17. unique combination of space-time migration immediately after the mainshock (see Supplementary Note S6). We also find that other migration functions do not provide a better fit to the propagating seismicity front than the log(t) functions. It has been long recognized that aftershocks often migrate along the fault strike and down-dip directions5,6,19. In some cases, aftershock zones show little expansion5, whereas in other cases, aftershock zones grow rapidly during the first few days following the mainshock, and the expansion slows down at a later time5,6,19. Such spatio-temporal migrations offer important clues on the physical mechanisms of aftershock generation. The temporal decay and spatial expansion of aftershocks could be explained by a delayed response to the coseismic stress changes for populations of faults around the mainshock rupture obeying the laboratory-derived rate���state friction law20. Alternatively, recent observations of aftershocks and postseismic deformation following an Omori-law-type decay with similar relaxation times have led to the suggestion that aftershocks are driven primarily by aseismic afterslip around the mainshock rupture zone13,14. Other possible mechanisms to trigger aftershocks include dynamic stress changes from passing seismic waves21, viscoelastic relaxation in the lower crust and upper mantle, or by fluid flows22. Many previous studies have found that postseismic deformation following the 2004 Parkfield earthquake mostly occurs as afterslip within the aseismic creeping patches of the SAF surrounding the locked asperity16,18,23,24. The cumulative moment release from afterslip in two years after the mainshock is about three times the coseismic moment release18, suggesting that quasi-static stress changes from afterslip may have a more important role in triggering aftershocks than static stress changes from the Parkfield mainshock. Furthermore, the cumulative number of the Parkfield aftershocks and the postseismic deformation seem to be linearly related18,25,26, and the cumulative seismic moment of aftershocks is only ���1% of the geodetic moment owing to afterslip18. These observations imply that both the postseismic relaxation and aftershocks following the 2004 Parkfield mainshock were primarily driven by afterslip. Here we also find that the cumulative number of the newly detected aftershocks with magnitude M 1.5 increases linearly with postseimic deformation in the first two days (see Supplementary Note S7). However, the early aftershocks are too many to match the linear relationship established a few days after the mainshock, consistent with previous findings26. Although the temporal behaviour of cumulative aftershocks seems to be related to postseismic relaxation, their spatial evolutions have not been analysed in detail previously. Recently, Kato12 conducted three-dimensional numerical simulations to investigate the relationships among aftershocks, afterslip, effective normal stress ��eff (that is, the normal stress minus the pore pressure) and frictional parameters a and b of the laboratory-derived rate���state- dependent friction law20. The simulation shows that the radius of the aftershock area expands logarithmically with time since the mainshock, consistent with our observations. Furthermore, the rate of aftershock expansion is inversely proportional to the value of A���B (= (a���b)��eff ref. 12). These results further support the casual link between afterslip and aftershocks, and allow us to draw inference regarding the frictional parameters of the SAF from aftershock migration. As shown in Fig. 3, the aftershock area increases from ���32 km at 100 s to ���48 km at 105 s after the mainshock. Such expansion is roughly compatible with the migration of simulated aftershocks12 in the velocity-strengthening region with the value of A���B in the range of 0.2���0.5 MPa (Supplementary Note S8). Assuming an effective normal stress of 50 MPa (ref. 16), the corresponding value of a���b is in the range of 0.004���0.01, which is close to the value of 0.007 obtained by geodetic inversion of Barbot et al.18, and higher than the value of 0.0001���0.002 obtained by Johnson and colleagues16. We note that the frictional parameters a and b are probably not fixed values, but could vary significantly along the fault strike and depth. Furthermore, the effective normal stress ��eff probably increases with depth. Such a depth-dependent effect could explain the difference in the migration speed for the shallow and deep aftershocks11. If the aftershocks following the 2004 Parkfield mainshock were primarily driven by afterslip18,25,26, an expansion of aftershocks would suggest an outward propagating afterslip from the main- shock rupture area. Recent studies based on kinematic and rate��� state slip inversions have shown that afterslip of the 2004 Parkfield earthquake mainly occurs around the mainshock rupture zone in the top 5 km immediately after the mainshock, and spreads laterally and with depth afterwards16,18. This pattern is largely compatible with our observations of aftershock migration in the along-strike and down-dip directions. We also observed that the shallow seismicity (that is, depth 2 km) in the creeping section and beneath Middle Mountain did not occur until a few hours after the mainshock (Supplementary Figs S9,S10). This is consistent with both field27 and geodetic23 observations of delayed surface slip a 878 NATURE GEOSCIENCE | VOL 2 | DECEMBER 2009 | www.nature.com/naturegeoscience �� 2009 Macmillan Publishers Limited. All rights reserved.