Supplementary Information
Supplementary Text 1: Magnitude Estimates of Parkfield Earthquakes
The seismic moment M_{0} of the 1966 Parkfield earthquake, estimated from analysis of surface waves recorded worldwide, is 1.4x10^{25} dynecm (ref. 1). The corresponding moment magnitude M_{W }(ref._{.} 2) is 6.06. Comparisons of amplitudes written by seismographs recording more than one Parkfield earthquake constrain the relative M_{0} for the 1922, 1934, and 1966 earthquakes. M_{0} for the 1922 and 1934 earthquakes are identical to within a precision of 10% and M_{0} for the 1966 earthquake is 120 ± 20% that of the 1922 and 1934 earthquakes^{3}. Given that M_{W} is 6.06 for the 1966 event, M_{W} is 6.0 for the 1922 and 1934 earthquakes. M_{W} is 6.0 for the 2004 event.
M_{W} can be estimated for other historical earthquakes from Modified Mercalli intensity (MMI) assignments^{4}. We analyze the MMI assignments using a technique^{5} that provides unbiased estimates of M_{W} and location and their uncertainties. Fractures on the trace of the Parkfield section of the San Andreas fault were reported for earthquakes on 2 February 1881, 3 March 1901, 10 March 1922, 8 June 1934, 28 June 1966, and for the 2004 earthquake^{6,7}. Analyses of the intensity assignments for these events are shown in Figure 1. Part of the 2004 rupture length lies within the 1 location region for all six events, which is consistent with the reported cracks on the San Andreas fault there. These six events ruptured the Parkfield section of the San Andreas fault. The intensity magnitude M_{I} for the six events range from 5.9 to 6.1 and M_{W} 6.0 is within the 95% confidence range of M_{W} estimated for each event (Table 1).
Other historical earthquakes have occurred in the Parkfield region. Among these, the magnitude 6.3 earthquake on 16 April 1860^{8}, the magnitude ~5.8 earthquake on 27 April 1908 and the magnitude ~5 ^{1}/_{2} earthquake on 30 May 1877 are of particular interest^{6}. There are no reports of cracking on the trace of the San Andreas fault near Parkfield for these events, or for any other earthquake since 1857. Parkfield was first settled in 1854 and a post office was established at Parkfield in 1884^{9}. The population of Cholame Valley, including the township of Parkfield, peaked in the homesteading years of the late 19^{th} century, but many homesteaders left after the extreme drought of 1898^{9}. Given the reports for the 1881 and 1901 events, it is unlikely that a magnitude 5.8 Parkfield earthquake in 1908 would not have been noticed by the residents of the Cholame Valley; the 1908 earthquake almost certainly occurred elsewhere. However, it is possible that Parkfield earthquakes occuring before 1881 might not be recognized. In particular, earthquakes on 16 April 1860 and on 30 May 1877 may have been at Parkfield.
Supplementary Text 2: Regularity of Timing of Parkfield Earthquakes
We tested the hypothesis that the historical earthquakes at Parkfield have occurred with significant regularity in time, while noting the case against a quasiperiodic recurrence model for Parkfield earthquakes has also been advanced^{10,11}. The basic earthquake sequence is the set of six M_{W }6.0 Parkfield earthquakes since 1857 described in the preceding section. These events were selected based on their magnitude and observations of ground cracking along the San Andreas fault^{3} which allowed a rigorous definition of these events to be made without reference to the regularity in their timing^{12}. Thus, there is no selection bias based on event timing and all events can be used to test their recurrence behavior. Two alternative sequences account for the possibility that M_{W }6 Parkfield earthquakes before 1881 may not have been recognized and that the 20^{th} century list is better known than the 19^{th} century list. In order to account for this epistemic uncertainty associated with the earthquake catalog, we consider three possible sequences of earthquakes: the basic sequence and two alternative sequences. Alternative sequence #1 adds the 30 May 1877 earthquake to the basic sequence, allowing for the possibility that this earthquake was an M_{W }6.0 event on the Parkfield section of the San Andreas fault (although there are no records of cracking along the San Andreas fault which would be required to truly fit the definition of a Parkfield main shock^{12}). Alternative sequence #2 considers earthquakes in the basic sequence since 1881, allowing for the fact that less is known about the 1881 event and other 19^{th} century events than for events in the 20^{th} century.
A reasonable null hypothesis, H_{0}, is that the intervals between Parkfield earthquakes are random. We used a 2sided KolomogorovSmirnov (KS) goodnessoffit test^{13} to determine if H_{0} can be rejected by the data. Application of the KS test to each sequence is illustrated in Figure 2. The KS test is sensitive to the maximum vertical deviation between the observed cumulative distribution function (CDF) and the probability function for, in this case, the exponential distribution.
For the basic sequence (Fig. 2a), H_{0 }is rejected with 98% confidence (p=0.016). The data contain too few short intervals to be random. With the addition of the 1877 event in alternative #1 (Fig. 2b), H_{0 }is rejected with 95% confidence (p=0.038). In alternative #2 (Fig. 2c), H_{0 }is rejected with 90% confidence (p=0.062), again because there are too few short interevent intervals. These statistics are conservative and the pvalues would be lower if other approaches were used^{1315}. All three sequences include fewer short interevent intervals than are expected under the null hypothesis of random occurrence and appear to be quasiperiodic, consistent with the lognormal distributions shown in Figure 2.
From these tests, we conclude that:
1) The interevent times of Parkfield earthquakes are significantly nonrandom.
2) The sequence of M_{W }6.0 Parkfield earthquakes is quasiperiodic, consistent with
a lognormal distribution with a coefficient of variation equal to 0.45.
3) These conclusions are robust with respect to reasonable assumptions about the
epistemic uncertainty in the earthquake catalog.
Supplementary Text 3: Relocation of Earthquakes, 19662004
The aftershocks of the 2004 and 1966 Parkfield earthquakes, along with selected background earthquakes 19692004, were relocated to determine their absolute and relative positions. Pwave arrival times from the Northern California Seismic Network (NCSN) were used for the 2004 aftershocks and the background earthquakes. For the 1966 aftershocks, the Pwave arrival times from 19 USGS and Earthquake Mechanism Laboratory portable stations^{16} and three University of California, Berkeley (UCB) stations were used. In order to better constrain the relative positions of the aftershock sequences, the USGS reoccupied sites of two of the 1966 temporary stations following the 2004 earthquake. The 1966 and 2004 aftershocks sequences are therefore connected directly by two temporary stations (USGS stations 2 and 3)^{16} and one permanent station (PGH at Gold Hill), and indirectly by the three UCB stations (PRI, PRS and LLA) that are common to the 1966 sequence and the early background seismicity.
The absolute earthquake locations were found using the 3D tomography and location program SIMULPS^{17} and a 3D seismic velocity model for the Parkfield region^{18}. We used the station corrections found during the velocity model inversion^{18}, and computed station corrections for additional stations from travel times of selected events and eight calibration shots in 1966^{16}. The entire dataset was then relocated using the original velocity model with the updated set of station corrections.
The relative earthquake locations were then refined using the program HYPODD^{19}. This technique uses the difference in travel times between neighboring events to constrain their relative locations. We require pairs of events to have at least 8 common stations to be linked in the relocation, with the exception that 1966 events may be linked to 2004 or background events with as few as 2 common stations. The linking is restricted to events within 2 km of each other, with the starting locations taken from the 3D results. For most earthquake pairs, differences between catalog arrival times are used. For background events 19842002, highresolution arrival time differences from crosscorrelation^{20} are included. The locations of the 1966 and 2004 aftershocks are very similar to each other, and to the background seismicity (Fig. 4).
