Department of Earth and Space Sciences, University of California, s:

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1 PostScript le created: September 22, 2005 CHARACTERISTIC EARTHQUAKES AND THE PARKFIELD PREDICTION Jackson, D. D., and Y. Y. Kagan Department of Earth and Space Sciences, University of California, Los Angeles, California , USA s: Abstract. The ocial Parkeld earthquake prediction was too vague to meet the generally accepted denition of a prediction, yet it still failed when time expired. The 2004 event failed to satisfy many features predicted unocially. Yet the 2004 event is widely viewed as at least a partial success. Why? The recent event did satisfy two features predicted by the\characteristic earthquake" model: the general location of the rupture zone and the magnitude. The rupture zone was not predicted precisely, and various predictions diered, but the 2004 rupture did overlap the 1966 rupture to a signicant extent. That overlap provides important constraints on rupture propagation at Parkeld. Whether the lesson can be exported to other areas is still an open question. The magnitude of the 2004 event agrees with both the characteristic model and a simple Gutenberg-Richter null hypothesis, thus it provides no support for characteristic earthquakes. The characteristic model does not explain the slip rate on the San Andreas Fault at Parkeld, while the Gutenberg-Richter model could. Furthermore, all earthquakes at Park- eld since the 1966 earthquake, which dened the prediction zone, t the Gutenberg-Richter distribution well. 1

2 The apparent uniformity of magnitudes (about 6) and the apparent quasi-periodicity of moderate Parkeld earthquakes are only evident in specially selected data. Globally, the same hypotheses have agreed with selected data but not with independent data. The 2004 earthquake did little to conrm the characteristic model, but it might serve as an inducement to formulate a testable version of that hypothesis. Short running title: Characteristic earthquakes and Parkfield 1 Introduction The characteristic model, rst proposed more than 20 years ago, is at the heart of many recent estimates of U.S. earthquake probability and seismic hazard (Frankel et al., 2000 Working Group (WGCEP), 2003, Stein and Newman, 2004 Stein et al., 2005). Without doubt it inuences earthquake hazard assessment eorts in other countries as well. The characteristic model was also the basis of the long-term earthquake prediction for Parkeld. Parkeld has become in many ways the archetypical example of a place where characteristic earthquakes predominate, in part because it had apparently experienced ve or perhaps six very similar earthquakes as of the end of Therefore, Parkeld has been closely watched, especially for evidence for or against another characteristic event. A search inthe\isiweb of Science" under topic \characteristic earthquake*" yields 15 publications for the year 2004 alone. These papers consider application of the characteristic earthquake model in the United States, Japan, France, Russia, New Zealand, India, Turkey, and other countries. These and earlier papers either assume that the characteristic earthquake model is correct, or they nd that the model does agree with some aspect of the data. These papers do not test the model by examining whether all of its predictions 2

3 are conrmed. A successful scientic theory should not just explain phenomena it should also be able to predict results that can be tested with independent data. Stein and Newman (2004) show that artifacts are common in the interpretation of seismic data. 2 Seismic gaps and characteristic earthquakes The seismic gap hypothesis has enjoyed intuitive appeal since the early work of Reid (1910). He suggested that a large earthquake releases most of the stress on a given part of a fault and that further earthquakes could be expected when that stress has been re-accumulated by tectonic motion. The acceptance of plate tectonics in the 1960s as a believable mechanism for re-supplying stress added intuitive arguments for the seismic gap hypothesis. The standard explanation for quasi-periodicity is that the stresses which cause earthquakes are slowly building up by plate movements after one event (Nishenko and McCann, 1981, p. 21) a new, strong earthquake is less probable until the stress or deformational energy reaches a critical value (Shimazaki and Nakata, 1980). The classical seismic gap models (Fedotov, 1968 McCann et al., 1979 Nishenko, 1991) further assume that plate boundaries are divided into segments, and that for each segment there is a \characteristic earthquake" (Schwartz and Coppersmith, 1984) large enough to dominate the seismic moment release and so reduce the probability of large earthquakes within the segment. The characteristic earthquake assumption has profound consequences. First, the multidimensional earthquake process is simplied immensely. Instead of having dimensions of latitude, longitude, magnitude and time, characteristic earthquake processes require only a specication of the size of the characteristic earthquake, and its frequency. Second, if characteristic earthquakes dominate the moment release, their frequency must 3

4 exceed substantially the frequency predicted by the Gutenberg-Richter distribution. Smaller quakes would then contribute little because their momentcontributions are so small, and larger earthquakes would be very infrequent compared to the Gutenberg-Richter model. Because the frequency of characteristic earthquakes is assumed so high, it should be easy to estimate their magnitude the largest known earthquake on a particular fault is likely to be close to the characteristic magnitude, because larger ones are so rare. Many other properties are ascribed in one form or another to characteristic earthquakes. If the earthquake size is controlled by segmentation of a fault, then the rupture length and even the slip distribution is hypothetically common to successive characteristic earthquakes on a fault. Their frequency is easily computed as the ratio of the tectonic moment rate to the moment released in a characteristic quake. Given a nearly constant characteristic moment, and a nearly constant tectonic moment rate from plate tectonics, it follows that characteristic earthquakes should be nearly periodic, and the time interval between any two events should be a good estimate of their period. Given their similar slip distributions, successive characteristic events might alsohave similar hypocenters, rupture histories and even similar seismograms. How could such anobvious, intuitive model not be true? Consider the list of assumptions that have been made. First, the segmentation assumption is crucial. If successive earthquakes aren't conned between the same segment boundaries, there is no reason to expect similar rupture lengths, magnitudes, etc. Second, we must assume that the average displacement is similar for successive events, else the magnitudes won't be similar. Third, we must assume that earthquake initiation and termination depend only on processes on the given fault segment stresses from earthquakes on other segments, or other faults, would likely ruin the similarity of successive quakes. If the assumption of identical events is maintained it is possible to estimate the eect of larger o-segment earthquakes on the timing of 4

5 characteristic events (Cornell et al., 1993 WGCEP, 1990), but the required assumption is a big one. Finally, to use this simplifying model, we must be able to recognize the size of the characteristic earthquake with little ambiguity. Ifwe should be fooled by a sequence of earthquakes smaller than the characteristic magnitude, and assume that they were characteristic, then we would seriously overestimate their frequency. 3 The Parkeld Prediction 3.1 History of the Parkeld prediction The Parkeld prediction is often referred to as the only earthquake prediction reviewed and approved by the U. S. government. Here we review several of the descriptions of the predicted event and compare them with the generally accepted denition of earthquake prediction. In 1976 a National Academy panel on earthquake prediction wrote \An earthquake prediction must specify the expected magnitude range, the geographical area within which it will occur, and the time interval within which it will happen with sucient precision so that the ultimate success or failure of the prediction can readily be judged (National Academy of Sciences, 1976). The sequence of \characteristic earthquakes" at Parkeld was described by Bakun and McEvilly (1984). They referred to the \20- to 30-km long section of the fault." They estimate the local magnitude ML of the 1934 and 1966 earthquakes to be 5.6 each. The National Earthquake Prediction Evaluation Council (NEPEC) met in November of 1984 to consider the implications of the apparent characteristic sequence at Parkeld. They concluded that earthquakes in 1881, 1901, 1922, 1934, and 1966 were nearly identical, and that another like it could be expected soon. They also concluded that there was a \signicant 5

6 potential of a larger earthquake (M7.0 to 7.5) growing out of (in conjunction with) a seismic event inparkeld, and which may break to the southeast for as much as 25 miles." Bakun and Lindh (1985, p. 623) propose that the Parkeld earthquake maycontinue southeast, resulting in an earthquake with \a rupture length of about 90 km." Prof. Lynn Sykes, Chair of the National Earthquake Prediction Evaluation Council (NEPEC) reported NEPEC's conclusions in a letter to Dallas Peck, the Director of the U. S. Geological Survey. The letter, dated 10 July 1985, is included as pages 167 to 171 of USGS Open File report (Shearer et al., 1985). It described an expected earthquake on \the Parkeld segment of the San Andreas Fault" with a \magnitude near 6, similar to that of 1966, within 4 years of 1988." The ocial prediction was expressed in a letter dated April 4, 1985 by Dallas Peck, Director of the U. S. Geological Survey, to William Medigovich, Director of the California Oce of Emergency Services. Peckmentions \another magnitude 6 earthquake" on the \San Andreas fault near Parkeld." with a 95% chance of occurring in the interval. He goes on to state that \an earthquake larger than magnitude 6 is possible in the Parkeld area, with the fault breaking up to 25 miles further south than it did in 1966." Donovan Kelly, Public Aairs Ocer of the USGS, announced the forecast in a public announcement on April 5, That letter referred to \an earthquake of magnitude 5.5 to 6"...\ in the Parkeld, Calif., area within the next several years ( )." In a letter included with a document entitled \Parkeld earthquake prediction scenarios and response plans" (Bakun et al., 1986), Sykes writes that NEPEC \concurred with the general aspects of the USGS prediction." The introduction to that document refers to the \25-km-long Parkeld segment" of the San Andreas Fault. Michael and Jones (1998, p. 125) dene the Parkeld earthquake asmw > 5:7 event with the surface rupture \between 36 N and N [degrees] and within 5 km of the mapped 6

7 trace". This assumes the total rupture length of about 37 km. Their Figure 1 shows several polygons surrounding the main shock and foreshocks of the 1966 event none is clearly identied as that box in which the next Parkeld earthquake was expected to occur, but from the context the \mainshock box" seems the best candidate. From the statements above, it appears that the Parkeld prediction could have been satised by a timely earthquakehaving a magnitude anywhere from 5.5 to 7.5, with a rupture length anywhere from 20-km to 90-km. Not until the Michael and Jones paper of 1998 was the Parkeld area dened in terms of a polygon. Even that description was ambiguous, because the requirement of surface rupture could be read to mean (a) any surface rupture within the latitude limits (b) surface rupture entirely contained within the latitude limits, or (c) surface rupture spanning the latitude limits. Thus the simple requirements for an earthquake prediction expressed by the National Academy report in 1976 have still not been met. In spite of the ambiguity in denition, the Parkeld prediction carried some amazingly specic expectations. According to Bakun and McEvilly (1984) the next characteristic Park- eld earthquake should have several properties in common with the previous ones, including the \same epicenter, magnitude, seismic moment, rupture area, and southeast direction of rupture expansion." Bakun and Lindh (1985, p. 620) add that the \Characteristic Park- eld Earthquake" should have magnitude 5.1 foreshocks preceding each main shock by17 minutes, based on the quakes in 1934 and Prediction Scorecard Langbein et al. (2005) and Bakun et al. (2005) review the observations concerning the 2004 event. Its magnitude (6.0) was certainly within the predicted range. The northern termination of the rupture zone was within a few km of that of the 1966 earthquake, while 7

8 the southern termination was about 5 km short (North) compared to that of the 1966 event. Using interpretation (b) of the rupture zone criterion of Michael and Jones, the 2004 event met that part of the prediction. However, it came about 12 years too late, and it clearly missed the predictions concerning epicenter, rupture area, southeast propagation, and magnitude 5.1 foreshocks. 3.3 Magnitude distribution of Parkeld earthquakes Since the great earthquake of 1857 there have been six earthquakes near Parkeld with magnitudes of about 6. The great event had a magnitude of about 7.9, and it too may have ruptured the San Andreas Fault at Parkeld. Since then there have been no earthquakes with epicenters in the prediction zone with reported surface wave magnitudes between 5.2 and 5.6, nor greater than 6.3. This leaves a cluster of magnitudes around 6.0 generally taken to be evidence of characteristic behavior at Parkeld. There are two problems with interpreting the sequence of \magnitude 6" earthquakes as characteristic. First is that the data come from rather diverse sources. The magnitudes and locations of the 1857, 1881, and 1901 earthquakes were determined from qualitative commentsby residents and travelers, who had little prior experience with earthquakes. Given the sparse population and the lack of a consistent set of standards for judging shaking, the estimated magnitudes and locations must have large uncertainties. The second problem comes from the fact that the spatial, temporal, and magnitude limits employed in selecting those quakes were not set before the data were selected. The rst six of the Parkeld characteristic events were selected from a much larger set of California earthquakes, and the freedom to draw boundaries after looking at the data invite selection bias. A feature that might be an expectable coincidence in a large set of data can appear quite non-random when the sample is narrowed to a small number of events. It is impossible 8

9 in retrospect to know what were in fact the selection criteria, unless they are specied before the data themselves are available for selection. For this reason we conclude that it is invalid to infer a magnitude distribution from the magnitudes of the presumed characteristic earthquakes at Parkeld. Another view comes from the catalog of instrumentally recorded earthquakes, selected to avoid bias. Figure 1 shows the cumulative magnitude distribution for earthquakes within the \mainshock zone" dened by Michael and Jones (1998). We assume that the mainshockzone was dened solely by the rupture zone of the 1966 Parkeld earthquake, so that earthquakes after that time have no impact on the zone boundaries. We considered earthquakes above magnitude 3, safely above the completeness threshold, since The beginning date was chosen to be as early as possible, without including aftershocks of the 1966 event that might have inuenced the boundary selection. Figure 1a shows the cumulative earthquake count for earthquakes in the mainshock zone from the beginning of 1967 through the end of 2003, before the recent earthquake. This information was available to assess the probability of an earthquake meeting the description of a characteristic event, according to a \null hypothesis" that forgoes the characteristic assumptions. The gure shows that the magnitude distribution is fully consistent with the Gutenberg-Richter magnitude distribution, with a b-value of We approximate the observational curve by the Gutenberg-Richter distribution. The displayed 95% condence limits for b-value (Aki, 1965) are conditioned by the total number of earthquakes observed. To calculate full uncertainty bounds, it is necessary to convolve the b-errors with the event number distribution. We make the simplest assumption that this distribution is Poisson. For the number N of samples in the Poisson distribution greater than 30, one can use the Gaussian approximation with the variance equal to N. To make the calculations easy for this illustrative diagram, we extend this approximation down to 9

10 N = 1. For the upper limit, the resulting uncertainties shown by the upper dashed curvein the plot are smaller than the actual Poisson bounds, so our limit is an under-estimate of the actual uncertainty spread. For the lower limit, the opposite is true, so that the real lower limit should be between the b (solid) line and the dashed line shown in the plot. Given the magnitude distribution in Figure 1a, should one be surprised that a \characteristic" magnitude 6 earthquake occurred in the prediction zone? Using the description given in Michael and Jones (1998), any earthquake over magnitude 5.7 with some rupture in the prediction zone might becounted as a successful prediction. The magnitude distribution says nothing, by itself, about surface rupture, and Michael and Jones don't dene what is a \characteristic" earthquake, but for discussion let's assume that a characteristic eventisa shallow earthquake with its epicenter in the prediction zone and a magnitude in the range 5.7 to 6.3. What is the chance that the next earthquake over 5.7 in the prediction zone after 1966 is a characteristic one? It is just (R-S)/R, where R is the rate of magnitude 5.7 and above, and S is the rate of magnitude 6.3 and above, in the prediction zone. From the maximum-likelihood Gutenberg-Richter line in Figure 1a, R =.0128/yr and S =.0039/yr. Thus the probability that the next event would be \characteristic" is 70%. Given Figure 1a, what is the probability that an earthquake of magnitude 5.7 or larger would occur before the end of 2004? Assuming a Poisson process, that probability is 1 ; exp(;r T ), where T is 2004 ; 1967 = 37 years. The probability is 38%. The corresponding probability for a \characteristic" earthquake is 28%, and that for an earthquake of 6.0 or larger is 23%. Thus neither the size nor the timing of the 2004 event would be a surprise, according to a simple null hypothesis of Poissonian, Gutenberg-Richter earthquakes at Parkeld. Figure 1b shows the magnitude distribution when the recent earthquake and its aftershocks are included. The overall seismicity increases modestly, butthechange in b-value is 10

11 negligible, and the earthquake count is within the 95% condence limits for all magnitudes. Thus objective evidence, using instrumental magnitudes and selection criteria independent of the catalog itself, are consistentwiththenull hypothesis. There is nothing in the earthquake data since 1967 that suggests earthquakes won't exceed magnitude 6. While the historic earthquake data since 1857 don't include any suggestion of larger earthquakes there, the errors in magnitude would allow nineteenth century earthquakes to be substantially larger. 3.4 Moment release at Parkeld The tectonic moment rate and its release by Parkeld earthquakes have been discussed thoroughly in papers by Kagan (1997), Murray and Segall (2002) and Murray et al. (2004) We concur with the conclusions of those papers, so we will just summarize the arguments here. Assuming that the rigidity is N/m 2, and that the Parkeld segment is35km long, 15 km wide measured down-dip, and slips at 35 mm/yr, the tectonic moment rate for the segmentis0: Nm/yr. In the 148 years since 1857, a tectonic momentof Nm would have accumulated. A magnitude 6 earthquake releases about Nm of seismic moment. Thus the six Parkeld earthquakes since 1857 would have released about Nm, leaving Nm unexplained. Any of the assumed parameters might be questioned, and it may be that some fraction of the tectonic moment is released aseismically. However, the discrepancy is so large that reasonable adjustments won't resolve it. Remember that one of the primary features of the characteristic earthquake model is that the characteristic events explain most of the tectonic moment release. If the primary mechanism for moment relief were magnitude 6 earthquakes, they would need to occur about every two years on average. A more likely scenario is that the moment isrelieved by earthquakes with a Gutenberg-Richter magnitude distribution, tapered at a corner magnitude 11

12 of about 8.0 (Kagan, 1997). That corner magnitude would be consistent with the value of 8.0 suggested by Bird and Kagan (2004) for continental transform fault regions around the globe. The Gutenberg-Richter model, with b = 0:87 and corner magnitude 8.0, is consistent with the total moment rate and the instrumental earthquake catalog. The great 1857 earthquake, with magnitude about 7.9, ts into that picture nicely. Earthquakes between magnitude 6 and 8 most likely occur too, but their frequency would be such that absence of any during the period of instrumental seismology would not be surprising. 3.5 Are Parkeld earthquakes periodic? A major justication for the Parkeld prediction and for the quasi-periodic characteristic earthquake hypothesis to a signicant degree was earthquake temporal statistics: the 22 year recurrence interval and 95% prediction (Bakun and Lindh, 1985) all result from the statistical analysis of seismicity. It is doubtful that if earthquakes did not exhibit seeming quasi-periodicity, the experimentwould have been proposed. Bakun et al. (2005) report that the six moderate Parkeld earthquakes since 1857 have occurred with statically signicant regularity in time. However, judging the temporal statistics from hand-picked data raises the same problem we discussed above concerning the magnitude distribution: the spatial, temporal, and magnitude limits employed in selecting those quakes were not set before the data were selected. The freedom to draw boundaries after looking at the data invites selection bias, and an expectable coincidence can appear deterministic after selection. Thus it is invalid to infer a temporal distribution, whether quasi-periodic or otherwise, from the selected data. While the 2004 earthquake was not hand-picked, the previous 5 were, and the time interval between the 1966 and 2004 events has little eect on the inferred regularity of the sequence. 12

13 3.6 Is Parkeld special? The part of the characteristic model best t by the 2004 event is the fact that its rupture zone resembled that of earlier moderate events. This would have important implications for earthquakes elsewhere if the conditions that conned the rupture to the prediction zone also exist, and can be recognized, elsewhere. It would be especially convenient if those conditions were intrinsic rock properties, or features of the fault geometry,thatwould persist for geologic time periods and be recognizable with available technology. A less convenient, but still useful condition would be that earthquakes in general are controlled by stress conditions or other extrinsic properties that nevertheless prevail for centuries or longer. Earthquakes during the nineteenth century suggest that the general picture we have of the seismicityatparkeld, and the creeping zone north of it that presumably prevents earthquake from propagating further north, may not be permanent. Figure 2, using data from Toppozada et al.'s (2000) statewide earthquake catalog, suggest that the creeping zone experienced moderate earthquakes where today we see only small ones. Figure 2a shows in map form the locations of earthquakes over magnitude 5 since The size of the symbol denotes magnitude. Circles indicate the epicenters of earthquakes within 20 km of the San Andreas Fault, while diamonds indicate the others. Figure 2b shows the times and latitudes of those same earthquakes. Several earthquakes above magnitude 5 occurred before 1900 near Parkeld and in the creeping zone north of latitude 36. This activity apparently ceased at around 1900, possibly because of the \stress shadow" of the 1906 San Francisco earthquake. The magnitudes and locations of the early events are quite uncertain. Nevertheless, the results imply that earthquake occurrence near Parkeld is variable, and the predominance of magnitude 6 events there may not be a permanent feature. Whether the rupture at Parkeld is controlled by intrinsic or extrinsic conditions, the 13

14 usefulness of any observations at Parkeld depend strongly on how commonly those conditions occur elsewhere. If Parkeld is too special, the results of investigation there may not be exportable to other situations. If Parkeld is typical, then the lessons there may apply elsewhere. Such a judgment cannot be made by examining Parkeld in isolation. A program that might lead to success is to identify the specic conditions that make Parkeld earthquakes cluster in the magnitude and space domains, identify other places where similar conditions apply, and test for magnitude and temporal clustering there. In other words, Parkeld should be viewed as an experiment to develop a hypothesis for testing elsewhere. 4 Parkeld and other seismic gaps The seismic gap idea has been applied to long-term forecasting of earthquakes in many regions. Rong et al. (2003) give a summary (see also Kagan and Jackson, 1991 Nishenko and Sykes, 1993 Jackson and Kagan, 1993 Kagan and Jackson, 1995). McCann et al. (1979) and Nishenko (1991) gave long-term earthquake forecasts for the most of the Pacic Rim. The dierence between these two papers is that McCann et al. specied ranked categories of earthquake potential based on the time since the last large earthquake, while Nishenko went further and estimated a probability of a specied characteristic earthquake based on the elapsed time and the estimated mean recurrence time. Nishenko's list of 125 seismic regions (including Parkeld), was dened, likeparkeld, by previous earthquake ruptures zones. Rong et al. compared the forecasts made in 1979 and 1991 with earthquakes that occurred later. Neither of the forecasts was consistent with the later earthquake record. Earthquakes meeting the specied magnitude threshold occurred more frequently in the zones identied by McCann et al. as having lower earthquake potential than they did in the zones identied as 14

15 having higher potential. The rate of earthquakes meeting the \characteristic" threshold was signicantly less than the number predicted by Nishenko (1991): nineteen were predicted, and only 5 occurred, for the period Had the 2004 Parkeld event occurred before the end of 2001, which would be more favorable to the seismic gap model, there would be just one more \success," but the hypothesis would still fail at the 95% condence level. Figure 3 illustrates one reason why the Nishenko forecast of 1991 mayhaveover-predicted the rate of characteristic earthquakes. We compiled earthquake sub-catalogs, using the PDE earthquake reports, for each of the 125 zones, computed magnitudes relative to the estimated characteristic magnitude for each zone, and stacked all the data. If the earthquake magnitude distribution in each zone were compatible with the characteristic model, then the magnitude distribution should exhibit a strong concentration at zero (relativetothecharacteristic magnitude). The red curve in Figure 3 shows the expected concentration, based on a literal interpretation of the curve in Figure 15 of Schwartz and Coppersmith (1984). The curve connecting blue dots shows the stacked magnitude distribution in the Nishenko zones, for earthquakes occurring before Earthquakes in that time interval were the ones used to set the zones, characteristic magnitudes, and frequencies used in the 1991 paper. The curve shows a noticeable kink at about the characteristic magnitude, but not nearly as extreme as depicted in the Schwartz and Coppersmith paper. The curve connecting red x's shows the distribution of magnitudes after Earthquakes in that time period were independent of the forecast in the 1991 paper. In that time interval, the magnitude distribution agrees well with the Gutenberg Richter distribution, and the rate of earthquakes at about the characteristic magnitude is substantially lower, by a factor of about 2, than it was before Why the dierence? The explanation lies, surely, in the dierence between specially selected data and data collected under controlled circumstances. At the time the zones were dened, the investigator had the opportunity to select regions on the map with two or more 15

16 large events, a condition necessary to estimate the recurrence interval. Earthquakes occur with some randomness, and those regions with higher than average numbers of earthquakes, by chance, satised the selection criterion. Zones with lower numbers, by chance, were preferentially not chosen. After the zones were dened, in about 1989, data selection was no longer possible. Again, some zones had more, and some zone had fewer earthquakes than their average, but the total for all zones was about average. 5 Discussion The fundamental requirement of any scientic method is the testability or falsiability of its hypotheses (Popper, 1980). The prediction experiment of an individual earthquake could in principle have only two outcomes: success or failure. In the latter case, there is no practical possibility to learn from experience: there is no updated or revised prediction for \the next Parkeld earthquake". In eect, the prediction of individual earthquake with almost exact specication of the future event transforms after a prediction failure into its opposite: no new prediction ideas or modications and improvement of original model are proposed in et al. (2005). The lack of falsiability and inability to construct an improved hypothesis contradicts the fundamental requirements of a modern scientic method (Kuhn, 1965 Popper, 1980). We challenge the supporters of the characteristic earthquake model to demonstrate that such earthquakes can be identied in most of seismic regions and then prove that these earthquakes behavior conrms the model. How, for instance, would the defenders of the characteristic earthquake model subdivide the focal area of the recent two (M9.3 and M8.7) Sumatra earthquakes (Bilham, 2005, Lay et al., 2005) into characteristic segments? These earthquakes ruptured over previously identied rupture areas of several high M7 { low M8 16

17 earthquakes of 19th and 20th centuries, putting all fault segmentation ideas (McCann et al., 1979) into doubt. The more important question is why there is still no strategy for a rigorous test. Such a strategy must include a denition, a description of the conditions under which the model should apply, and specic values for end points, magnitudes, etc. 6 Conclusions Before 2004 many claims were made about the nature of an earthquake predicted to occur at Parkeld (Jackson and Kagan, 1998 Roelos, 2000). Some of those claims were too vague to be tested by the 2004 Parkeld earthquake. Examples include the presumed similarity to the 1966 and earlier Parkeld earthquakes, and the predicted surface rupture. Other predictions, such as the expected rupture length, were given dierent values by dierent authors. As a result, there was not a clear, testable denition of the expected event before the 2004 earthquake. The 2004 event failed to satisfy most of those predictions that were specic enough to test. Examples included the time of the event, the location of the hypocenter, the direction of rupture propagation, and the presence of sizable foreshocks within minutes before the event. The 2004 quake did have a magnitude within the range usually predicted, but such agreement says little about the magnitude distribution of earthquakes there. Large earthquakes anywhere are less frequent than small ones, and earthquakes smaller than 5.7 would not in 2004 be considered as \Parkeld earthquakes," so the next earthquake above the threshold magnitude was likely to be very near the threshold magnitude. The 2004 event did rupture a part of the San Andreas Fault that had been ruptured previously in 1966, probably in 1934 as well and perhaps in 1922, 1901, 1881, and/or

18 This repeated rupture, stated very generally, was successfully predicted and it may carry important information about what controls rupture initiation and termination at Parkeld. The common claim that the sequence of moderate Parkeld earthquakes is quasi-periodic, with a relative small aperiodicity, is baseless. The earthquakes chosen for study were selected from a much larger sample, and their apparent periodicity mayhave been a factor in their choice. When data are examined before dening the sample specication, subjective choice mayinvalidate any amount of statistics. If the magnitude threshold for inclusion were raised or lowered a modest amount, the sampled catalog would be much less periodic. The 2004 event adds little support to the characteristic earthquake hypothesis, which has many attributed properties but generally is taken to mean that earthquakes within a narrow magnitude range account for most of the moment accumulation on a fault or segment. The string of moderate earthquakes at Parkeld does not explain the moment accumulation on the fault segment, and the seismic record is way too short to conclude that substantially larger earthquakes haven't contributed to the secular moment accumulation. The magnitude distribution of Parkeld earthquakes, examined prospectively, resembles the Gutenberg-Richter distribution more than a characteristic magnitude distribution, as it also does for many \seismic gaps" around the globe. The apparent similarity of the rupture zones of moderate earthquakes may indicate a special feature of the tectonic regime at Parkeld. Whether this similarity results from permanentintrinsic physical properties of the crust, or from a transient condition, is an open question. The historical earthquake record suggests the latter interpretation. Even if intrinsic properties control to some extent the rupture at Parkeld, this control would not provide evidence of general validity of the characteristic earthquake hypothesis. If Parkeld is special, the magnitude similaritymay not apply to other regions. To evaluate the general validity of the characteristic earthquake hypothesis, one must treat Parkeld as but one example in 18

19 a much larger collection of hypothesized fault segments or plate boundary segments. The characteristic hypothesis has so far failed badly in tests on larger samples, and the Parkeld event won't change that substantially. Acknowledgements The authors appreciate support from the National Science Foundation through grant EAR and from the Southern California Earthquake Center (SCEC). SCEC is funded by NSF Cooperative Agreement EAR and USGS Cooperative Agreement 02HQAG0008. Publication 0000, SCEC. 19

20 References Aki, K., Maximum likelihood estimate of b in the formula log N = a ; bm and its condence limits, Bull. Earthquake Res. Inst. Tokyo Univ., 43, Bakun, W. H., B. Aagaard, B. Dost, W. L. Ellsworth, J. L. Hardebeck, R. A. Harris, C. Ji, M. J. S. Johnston, J. Langbein, J. J. Lienkaemper, A. J. Michael, J. R. Murray, R.M. Nadeau, P. A. Reasenberg, M. S. Reichle, E. A. Roelos, A. Shakal, R. W. Simpson, and F. Waldhauser, The 2004 Parkeld, California, Earthquake: Implications for Earthquake Prediction, Nature, in press. Bakun, W. H. et al., Parkeld Earthquake Prediction Scenarios and Response Plans, USGS Open-le report Bakun, W. H., and A. G. Lindh, The Parkeld, California, earthquake prediction experiment, Science, 229, Bakun, W. H., and T. V. McEvilly, Recurrence models and Parkeld, California, earthquakes, J. Geophys. Res., 89, Bilham, R., A Flying Start, Then a Slow Slip, Science, 308, Bird, P., and Y. Y. Kagan, Plate-tectonic analysis of shallow seismicity: apparent boundary width, beta, corner magnitude, coupled lithosphere thickness, and coupling in seven tectonic settings, Bull. Seismol. Soc. Amer., 94(6), Cornell, CA, Wu, SC, Winterstein, SR, Dieterich, JH, Simpson, RW, Seismic hazard induced by mechanically interactive fault segments, Bull. Seismol. Soc. Amer., 83, Fedotov, S. A. (1968). On the seismic cycle, feasibility of quantitative seismic zoning and long-term seismic prediction, in: Seismic zoning of the USSR, pp , Nauka, Moscow, (in Russian) English translation: Israel program for scientic translations, 20

21 Jerusalem (1976). Jackson, D. D., and Y. Y. Kagan, Reply [to Nishenko & Sykes], J. Geophys. Res., 98, Jackson, D. D., and Y. Y. Kagan, Parkeld earthquake: Not likely this year, Seismological Research Letters, 69(2), p Kagan, Y. Y., Statistical aspects of Parkeld earthquake sequence and Parkeld prediction experiment, Tectonophysics, 270, Kagan, Y. Y., and D. D. Jackson, Seismic gap hypothesis: Ten years after, J. Geophys. Res., 96, 21,419-21,431. Kagan, Y. Y., and D. D. Jackson, New seismic gap hypothesis: Five years after, J. Geophys. Res., 100, Kuhn, T. S., Logic of discovery or psychology of research?, In Criticism and the Growth of Knowledge, eds. I. Lakatos and A. Musgrave, pp. 1-23, Cambr. Univ. Press, Cambrigde. Langbein, J., et al., Preliminary report on the 28 September 2004, M6.0 Parkeld, California, earthquake, Seismol. Res. Lett., 76, Lay, T., et al., The Great Sumatra-Andaman Earthquake of26december 2004, Science, 308, McCann, W. R., S. P. Nishenko, L. R. Sykes, and J. Krause, Seismic gaps and plate tectonics: seismic potential for major boundaries, Pure Appl. Geophys. (PAGEOPH), 117, Michael, A. J., and L. M. Jones, Seismicity alert probabilities at Parkeld, California, revisited, Bull. Seismol. Soc. Amer., 88, Murray, J., and P. Segall, Testing time-predictable earthquake recurrence by direct 21

22 measurement of strain accumulation and release, Nature, 419(6904), Murray, J. R., Segall, P., and Svarc, J., Slip in the 2004 Parkeld M6 Earthquake: Comparison With Previous Events and Implications for Earthquake Recurrence Models, Eos Trans. AGU, 85(47), Fall Meet. Suppl., Abstract S54B-03 National Academy of Sciences, Predicting Earthquakes, A scientic and technical evaluation { with implications for society, Panel on Earthquake Prediction of the Committee on Seismology, Washington, DC. Nishenko, S. P., Circum-Pacic seismic potential { , Pure Appl. Geophys. (PAGEOPH), 135, Nishenko, S. P., and McCann, W. R., Seismic potential for the world's major plate boundaries: 1981, in: Earthquake Prediction, An International Review, Maurice Ewing Volume 4, D. W. Simpson and P. G. Richards, eds., AGU, Washington, D.C., Nishenko, S. P., and L. R. Sykes, Comment on \Seismic gap hypothesis: Ten years after" by Y. Y. Kagan and D. D. Jackson, J. Geophys. Res., 98, Popper, K. R., Logic of Scientic Discovery, 2nd ed., London, Hutchinson, 479 pp. Reid, H. F., Elastic rebound theory, Univ. Calif. Publ. Bull. Dept. Geol. Sci., 6, , Roelos, E., The Parkeld, California earthquake experiment: An update in 2000, Current Science, 79(9), Rong, Y.-F., D. D. Jackson and Y. Y. Kagan, Seismic gaps and earthquakes, J. Geophys. Res., 108(B10), 2471, ESE-6, pp. 1-14, doi: /2002jb Schwartz, D. P., and K. J. Coppersmith, Fault behavior and characteristic earthquakes: Examples from Wasatch and San Andreas fault zones, J. Geophys. Res., 89, ,

23 Shearer, Minutes of the National Earthquake Prediction Evaluation Council (NEPEC), USGS Open-le report Shimazaki, K., and Nakata, T., Time-predictable recurrence model for large earthquakes, Geophys. Res. Lett., 7, Stein, S., and A. Newman, Characteristic and uncharacteristic earthquakes as possible artifacts: Application to the New Madrid and Wabash seismic zones, Seismol. Res. Lett., 75(2), Stein, S., A. Friedrich, and A. Newman, Dependence of possible characteristic earthquakes on spatial sampling: Illustration for the Wasatch seismic zone, Utah, Seismol. Res. Lett., 76(4), Toppozada, T., D. Branum, M. Petersen, C. Hallstrom, C. Cramer, and M. Reichle, Epicenters of and Areas Damaged by M 5 California Earthquakes, , Map sheet 49, Div. Mines Geology, California. Working Group on California Earthquake Probabilities (WGCEP), Probabilities of large earthquakes in the San Francisco Bay Region, California, USGS Circular 1053, 51 pp. Working Group on California Earthquake Probabilities (WGCEP), Earthquakes probabilities in the San Francisco Bay region: 2002 to 2031, USGS, Open-le Rept

24 Figure 1: Magnitude-frequency relation for the Parkeld earthquakes. ANSS catalog is used ( Earthquakes are selected in the Parkeld box proposed by Michael and Jones (1998), its corners are: 35:971 N, 120:598 W, 36:029 N, 120:512 W, 35:788 N, 120:262 W, 35:729 N, 120:347 W. (a) Time period (before the 2004 Parkeld earthquake). (b) Time period (after the 2004 Parkeld earthquake). Figure 2: (a) Spatial pattern of earthquakes along the San Andreas fault according to Toppozada et al. (2000). The symbol size is proportional to event magnitude, earthquakes along the fault trace are shown as circles, outside the San Andreas as diamonds. (b) Temporal pattern for earthquakes along the fault trace. Figure 3: Distribution of PDE magnitude dierences for two time periods: July 1, 1968 { January 1, 1989 and January 1, 1989 { January 1, 2003, calculated relative tothecharacteristic magnitude (Nishenko, 1991). Asterisks, time interval July 1, 1968 { January 1, 1989 crosses, time interval January 1, 1989 { January 1, 2003 dash-dot line, the G-R relation dashed line, the predicted distribution of characteristic magnitudes. 24

25 10 3 Fig. 1a Cumulative earthquake numbers N = 106; b = 0.87+/ 0.08 M t = Magnitude

26 10 3 Fig. 1b Cumulative earthquake numbers N = 152; b = 0.83+/ 0.07 M t = Magnitude

27 37 Fig. 2a Latitude, degrees Longitude, degrees

28 37 Fig. 2b Latitude, degrees Time, years

29 10 2 Fig. 3 Zones Magnitude difference rate eqs/year Zones Characteristic Gutenberg Richter Magnitude difference (M S M CHAR )