Earthquake statistics at Parkfield: 1. Stationarity of …bemlar.ism.ac.jp/zhuang/Refs/Refs/schorlemmer05jgr1.pdfEarthquake statistics at Parkfield: 1. Stationarity of b values D

Earthquake statistics at Parkfield:

1. Stationarity of b values

D. Schorlemmer and S. WiemerSwiss Seismological Service, ETH Zurich, Zurich, Switzerland

M. WyssWorld Agency of Planetary Monitoring and Earthquake Risk Reduction, Geneva, Switzerland

Received 16 June 2004; revised 18 August 2004; accepted 9 September 2004; published 23 December 2004.

[1] In this paper (paper 1), we quantitatively show that the heterogeneous pattern of bvalues (of the Gutenberg-Richter relation) in the Parkfield segment of the San Andreasfault is to a high degree stationary for the past 35 years. This prepares the grounds forpaper 2, where we test the hypothesis that our model of spatially varying b values forecastsfuture seismicity more accurately than the approach in which one assumes a constant bvalue equal to the average regional value. The method we develop to measure stationarityin the presence of spatial heterogeneity consists of the following steps: (1) Determine theoptimal dimensions of the sampling volume by mapping b values with a wide range ofradii and selecting the largest radius that gives the most detailed resolution of the b valueheterogeneity. Along the selected fault segment, the high data density permits thedefinition of the dominant dimensions of the seismotectonic fabric, which is about 8–10 km. (2) Map the difference in b value between two periods, selecting numerouspossible catalog divisions. (3) Identify significant changes of b values by the Utsu test(Utsu, 1992). Along the studied fault segment of 110 km length, only one patch of radius5 km showed a significant increase in b, from below average to above, as a function oftime. This change in b initiates around 1993 and thus correlates in space and time with awell-documented episode of creep at depth. Using the derived spatial variable b valuedistributions, we find that the highest probability for earthquakes with magnitude M � 6 isin the Middle Mountain asperity, where the 1966 Parkfield earthquake nucleated andwhere all M � 4.5 events in the data set occurred. In contrast, if only the regional averageb value of 0.92 is used to predict future seismicity, the creeping segment north of Parkfieldshould produce major earthquakes most frequently, a conclusion that contradicts theobservations. INDEX TERMS: 7215 Seismology: Earthquake parameters; 7223 Seismology: Seismic

hazard assessment and prediction; 7230 Seismology: Seismicity and seismotectonics; 7294 Seismology:

Instruments and techniques; KEYWORDS: earthquake statistics, b value, Parkfield

Citation: Schorlemmer, D., S. Wiemer, and M. Wyss (2004), Earthquake statistics at Parkfield: 1. Stationarity of b values,

J. Geophys. Res., 109, B12307, doi:10.1029/2004JB003234.

1. Introduction

[2] Probabilistic forecasting of earthquakes attempts todeliver the most accurate estimate of future seismicity at agiven location and for a given magnitude range and period.In most cases, this task is attempted by sampling theobserved seismicity of the past and extrapolating it into thefuture, using the assumption that the frequency-magnitudedistribution of earthquakes can be approximated with apower law [Ishimoto and Iida, 1939; Gutenberg and Richter,1944]: log N = a � bM (log denotes the common loga-rithm), where N is the cumulative number of events ofmagnitude M or greater, while a and b are constants. Thisrelationship has been investigated extensively (for an over-

view, see Utsu [1999] and Wiemer and Wyss [2002]) andworks well, in most cases, as a first order approximation. Itis also the backbone of probabilistic seismic hazard assess-ment [Cornell, 1968]. While this forecasting is simple, andhas been used in numerous statistical seismology andhazard related studies, there remain, in our opinion, anumber of fundamental unresolved issues related to spatialheterogeneity and stationarity of b values.[3] The basic questions that we address in this paper can

be stated as follows: (1) For which volume should onedetermine a and b values to obtain a robust and accurateforecast? Is it better to average over large spatial volumes orshould one use small volumes to take into account hetero-geneity in some detail? (2) How can the assumption that thefrequency-magnitude distribution is stationary be verified?[4] The question of the spatial heterogeneity in seismic-

ity parameters is intrinsically linked to the question of

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B12307, doi:10.1029/2004JB003234, 2004

Copyright 2004 by the American Geophysical Union.0148-0227/04/2004JB003234$09.00

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stationarity in these parameters: If temporal changes inseismicity parameters occur, then larger sample volumesmay average out the fluctuations and lead to a reasonableforecast. Spatial heterogeneity in seismicity parameters is bynow a well-established fact. It has long been obvious thatseismicity rates or productivity (a value) varies strongly as afunction of space and time; any map of seismicity revealsthis. Only in the past 10 years, approximately, has it beenfirmly established that the b value, or earthquake sizedistribution, varies also considerably and significantly asa function of space and, possibly to a lesser effect, oftime [e.g., Gerstenberger et al., 2001; Wiemer and Wyss,2002]. One clear example of spatial heterogeneity of bvalues stems from the Parkfield section of the SanAndreas fault [Wiemer and Wyss, 1997]. Volcanic andgeothermal regions also show changes in b values overlength scales of 1 km or less. Significant spatial hetero-geneity of b values can be shown to exist on lengthscales of millimeters in laboratory samples [Amitrano,2003], to thousands of kilometers as in the case of theIndia-Asia collision zone [Wiemer and Wyss, 2002].[5] The issue of how to best resolve spatial heterogeneity

in seismicity parameters, particularly in b value, has twofacets. First of all, it is a question of resolution of theavailable data, which is primarily determined by the samplesize. The uncertainty in estimating model parametersincreases with decreasing sample sizes, resulting in atrade-off between accuracy and resolution. Given a globaldata set of M > 5 events one can hardly expect to resolvevariations in b values of less than tens of kilometers,because in order to establish a reliable b value, one needsa sample size of roughly 50–100 events. The second issuehas to do with scaling of earthquake properties: Differentsize sampling volumes may well measure different intrinsicscaling length in the Earth. A large scale continentalcollision zone and its resulting stress field leaves a largescale imprint on the frequency magnitude distribution, atleast of larger events [Wiemer and Wyss, 2002]. Nestedwithin this regional behavior could be any number ofsmaller scale heterogeneities that reflect local changes inthe earthquake size distribution, for example in the vicinityof volcanic or geothermal systems. However, it is alsoobserved that a given area with seismic activity is charac-terized by a certain size of heterogeneities, due to theseismotectonic fabric [Wyss et al., 2000].[6] The question of the spatial heterogeneity in b values is

closely related to hazard estimates. Even contemporaryhazard mapping projects differ in their approach betweenassuming a constant b value, or a spatially varying one. Italso relates to understanding the underlying physics of thesystem.[7] We choose the Parkfield section of the San Andreas

fault to address these questions, because it is a simple faultsetup with limited interaction between neighboring faultstrands, because it has been extensively studied with variousgeophysical techniques [Roeloffs and Langbein, 1994;Gwyther et al., 1996; Gao et al., 2000; Roeloffs, 2000,2001; Murray and Segall, 2002] and because it has beenmonitored with a dense network of seismographic stationsfor more than 30 years. In addition, we know that herestrong spatial differences in b values have been documentedin 1997, allowing a fully prospective test of the hypothesis

of spatially varying b values that are stationary. There is afinal important aspect to Parkfield: To convince ourselvesthat the spatial heterogeneity in b values are not related toartifacts in catalog properties, we can compare the observedpatterns with an independent data set of moment magni-tudes derived from a network of borehole stations nearParkfield [Karageorgi et al., 1992].

2. Data

[8] We use the NCSN catalog from the Northern Cal-ifornia Earthquake Data Center (NCEDC) spanning theperiod 1967–2003. From this catalog we separated theevents of the Parkfield region, defined as a 5 km widecross section extending from P1: 121�W, 36.4�N to P2:120.2�W, 35.64�N (Figure 1). This cross section has alength of about 110 km and includes the asperity, the lockedsegment, and a large portion of the creeping section. We cutthe catalog at a depth of 16 km, thereby excluding only afew events that may well be erroneous locations.[9] Several processing steps have been performed to

ensure data quality and selection of a reliable data set. Inthe given data set, 451 out of 10673 events are of magnitudeM = 0, indicating events without assigned magnitudes. Weremoved these events from the catalog, thereby deleting theyears 1967 and 1968 which consist only of events withoutmagnitude information. We also rebinned the catalog frommagnitude bins with DM = 0.01 into new magnitude binswith DM = 0.1. This step is necessary because computingmagnitude of completeness is based on the noncumulativefrequency-magnitude distribution [Wiemer and Wyss, 2000].With finer binning, deviations from the assumed Gutenberg-Richter distribution become larger, therefore affecting thecomputation of magnitude of completeness Mc, possiblyresulting in its overestimation.[10] We investigated whether the data set is contaminated

with quarry blasts by mapping the daytime to nighttimeactivity ratio as described by Wiemer and Baer [2000]. Wehave not found any evidence for contamination of the dataset in the selected region.[11] To identify periods of different recording quality and

catalog completeness, we investigated changes in the slopeof the plot of cumulative number of events per time[Habermann and Craig, 1988]. Plotting the cumulativenumber of all events in the catalog shows only minorchanges in the slope at 1981 (see Figure 2b, solid line),but when taking only events with magnitudes M � 1.1, wecan clearly identify periods of lower recording quality (seeFigure 2b, dashed line). The kink in the slope at 1981indicates the well-known improvement in recording qualityat 1981. From 1995 to 2000, recording completenessdropped significantly for small events but was restored in2000 to the same level as in the period before 1995. Whenplotting cumulative events with magnitudes M � 1.5 overtime, we can detect only a slight change of the slope in theperiod from 1995 to 2000. This indicates an overall com-pleteness level of Mc � 1.5 for the catalog in the periodfrom 1981 to 2003.[12] We applied the GENAS algorithm for detecting

magnitude dependent rate changes [Habermann, 1983].We found the aforementioned drop in detected events in1995.06 and increase in 2000.67 (decimal years). Although

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additional increases and decreases are visible in the GENASresult, those cannot be related to changes in recordingquality and are rather reflecting natural rate changes inseismic activity.[13] We also compared rates per magnitude for the two

periods 1990–1995 and 1995–2000, as described byZuniga and Wiemer [1999]. For the first period we detectan overall completeness of Mc = 1.1 ± 0.1, while for thesecond period the completeness is higher with Mc = 1.3 ±0.1 (see Figure 3). This change in completeness can hardlybe seen in the cumulative frequency-magnitude distribution(Figure 3a). In the noncumulative distribution (Figure 3b),however, one can clearly see a higher Mc for the period1995–2000 as a drop in rates for magnitudes M < 1.3. Inthe earlier period, the rates drop for events with magnitudesM < 1.1. This again shows the loss in completeness in theperiod 1995–2000.[14] Computing the magnitude of completeness Mc as a

function of time [Wiemer and Wyss, 2000] using samplesizes of 500 events with a step size of 10 events revealsgradual improvements in completeness from Mc � 1.7 inthe year 1970 to Mc � 1 in the year 1990 (see Figure 2a,gray line). In the years 1995 to 2000, we can detect Mc �1.3, corresponding to the different slope in the cumulativenumber curve for events with M � 1.1. From 2000 onward,completeness improves again to Mc � 1.2. The windowedaverage (50 data points) smoothes the changes in Mc (see

Figure 2a, black line) but also shows the aforementioneddevelopment of Mc.[15] In summary, we use as our primary data source the

period from 1981–2003. We spatially map completenessalong a cross section for this period in order to confirm thatMc does not show strong spatial variability. Having foundno strong spatial variability of Mc, we assume for simplicityand stability reasons a spatially homogeneous completenessof Mc = 1.3. This leaves a total number of 3780 events inour primary catalog. This catalog has an overall b value ofb = 0.92. As a secondary data set, we also analyze theperiod 1967–1981, cut at a higher overall completeness ofMc = 1.7.[16] When bootstrapping to obtain the standard deviation

of b values we have to compute Mc at each node for takinginto account uncertainties in Mc. For this task, we created anadditional catalog cut at magnitude M = 0.8 instead of M =1.3. We have not found Mc values lower than 0.9 in ourspatial mapping. By cutting the catalog at M = 0.8 we allowMc to drop to 0.8 in the bootstrapped samples.[17] For the Parkfield region, an independent data set

exists that allows verification of the results obtained withthe NCSN catalog. This data set was obtained by the High-Resolution Seismic Network (HRSN), established in 1986[Karageorgi et al., 1992], and is superior in locationaccuracy and extends to smaller magnitudes because it isderived from borehole seismometers installed as part of the

Figure 1. Seismicity map of the Parkfield region in central California. Gray dots mark the epicenters ofthe events with M � 1.3 and depth D � 16 km from 1981 to 2003; red lines mark mapped faults. Theinvestigation area (Parkfield segment) along the San Andreas fault is marked by a black rectangle. Thecross section extends from P1 to P2 with a width of 5 km.


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Parkfield earthquake prediction experiment [Bakun andLindh, 1985; Malin et al., 1989; Roeloffs and Langbein,1994; Nadeau and McEvilly, 1997, 1999]. However, thiscatalog spans only the period 1987–1998.5 and covers onlya short stretch of the San Andreas fault near Parkfield. Thecatalog provides moments which have been converted tomagnitudes with 3 significant digits by Wyss et al. [2004].We rebinned this catalog to magnitude bins of DM = 0.1.We applied the aforementioned quality analysis to thiscatalog also. We found no indication of artificially intro-duced rate changes or magnitude shifts. Because of itslimited spatial and temporal extent, we are using this catalogonly for comparing b values with the NCSN catalog.

3. Method

[18] To investigate the heterogeneity of b values along theParkfield segment of the San Andreas fault, we map in crosssection a and b values along the fault segment shown inFigure 1. We are applying the gridding technique [Wiemerand Wyss, 2002] using the software package ZMAP[Wiemer, 2001]. We compute maximum-likelihood b valuesusing the equation [Utsu, 1965; Aki, 1965; Bender, 1983]

b ¼ 1

M �Mmin

log e: ð1Þ

M denotes the mean magnitude and Mmin the minimummagnitude of the given sample. The sample is consideredcomplete down to the minimum magnitude Mmin. Mc has tobe corrected by DM/2 to compensate the bias of roundedmagnitudes to the nearest DM bin, thus Mmin = Mc � DM/2

[Utsu, 1965; Guo and Ogata, 1997]. The confidence limitof this estimation is given by [Shi and Bolt, 1982]

s bð Þ ¼ 2:30b2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

Mi �M� �2

=n n� 1ð Þs

; ð2Þ

where n is the total number of events of the given sample.This s(b) tends to underestimate the true standard deviationof the b value due to its assumption of a complete catalogand a correctly determined magnitude of completeness Mc.Therefore we compute the standard deviation of b valuesusing the bootstrap approach as described by Schorlemmeret al. [2003].[19] For computing b values, the knowledge of complete-

ness of a sample is important. Mc has to be computed eitherfor every sample or defined assuming a homogeneousrecording quality for the entire volume. Here we assume ahomogeneous overall Mc = 1.3 and do not compute Mc ateach node. However, we confirm that our results are notdependent on this choice.[20] For sampling of earthquakes, we use cylindrical

volumes perpendicular to the cross-sectional plane andcentered at the nodes spaced at 0.5 km � 0.5 km. Thelength of these cylindrical volumes is defined by the widthof the volume along the cross section, which is 5 km. Ineach sample, we also require a minimum number of eventswith M � Mc, Nmin, in order to determine a reliable b value.For samples containing fewer than Nmin events, we do notcompute b values. Here, we arbitrarily set Nmin = 50,because below this value the uncertainty in b increasesrapidly. To estimate the largest radius for sampling, which isnot obscuring the b value contrasts and anomalies, therefore

Figure 2. (a) Magnitude of completeness Mc as a functionof time. The gray line is computed using sample sizes of500 events and a step size of 10 events; the black line is thewindowed average of 50 data points. (b) Cumulativenumber of events. The solid line (left Y axis) representsall events; the dashed line (right Y axis) represents eventswith M � 1.1.

Figure 3. (a) Cumulative frequency-magnitude distribu-tions for the periods 1990–1995 (dashed line) and 1995–2000 (solid line). (b) Noncumulative frequency-magnitudedistributions for the periods 1990–1995 (dashed line) and1995–2000 (solid line).


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providing the highest possible coverage, we computed bvalue cross sections using different radii, varying thembetween r = 2 km and r = 20 km.[21] On the basis of a and b values, one can compute the

probabilistic recurrence time Tr for an earthquake withmagnitude equal or greater than a chosen M0, given as

Tr ¼DT

10a�bM 0 : ð3Þ

[22] Here DT denotes the length of the recording periodfrom which the a value is derived. When spatially mappingthe probabilistic recurrence time Tr, we denote Tr at eachnode as ‘‘local recurrence time’’ TL. Giving the rate l forevents of magnitude M0 as l = 1/Tr, we can compute theprobability Pr of occurrence of one or more events ofmagnitude M0 using the cumulative Poissonian distribution:

Pr lð Þ ¼ 1� e�lX0i¼0

li

i!¼ 1� e�l: ð4Þ

[23] For testing stationarity of b values, we divide thecatalog in two abutting periods at different divisions in timeand spatially map b values for both periods. If in bothperiods the sample size is greater or equal Nmin and thus bcan be computed, we also compute the probability Pb of thehypothesis that the b values of the two periods are comingfrom the same population, i.e., exhibit stationary behavior.This probability Pb is derived from the Akaike InformationCriterion (AIC) [Akaike, 1974]. Comparing the AIC0 forboth periods having the same b value b0 and the AIC12 forboth periods having two different b values b1 and b2 leads tothe difference DAIC of these two AIC scores as given byUtsu [1992]:

DAIC ¼� 2 N1 þ N2ð Þ ln N1 þ N2ð Þ þ 2N1 ln N1 þ N2b1=b2ð Þþ 2N2 ln N1b2=b1 þ N2ð Þ � 2: ð5Þ

The probability Pb that the b values are not different is givenby

Pb ¼ e�DAIC

2�2: ð6Þ

Following Utsu [1999], we consider the difference in bvalues not significant if DAIC < 2. If DAIC > 2, thedifference is significant. DAIC = 2 corresponds to Pb �0.05. The difference is considered highly significant ifDAIC > 5. This value corresponds to Pb � 0.01. Applyingthe logarithm leads to log-probabilities of log Pb � �1.3 forsignificantly different b values and log Pb � �1.9 for highlysignificant differences in b values.

4. Results

4.1. Mapping b Values

[24] To find the appropriate radius for resolving b valuecontrasts at Parkfield, we mapped b values with samplingradii varying between 2 km and 20 km (Figure 4). Samplingwith radii from 2 km to 5 km (frames A–D) showsessentially the same pattern but with different coverage.The smaller the radius, the fewer volumes match the

requirement of at least Nmin = 50 events for computing bvalues. Radii smaller than 5 km resolve additional detail inonly few locations. At the southern end of the creepingsection (at a distance of 50–60 km from P1) we see thatthe samples at a depth of approximately 4 km loose theirhigh b values when computed with a radius of 5 kmcompared to 2 km. When sampling these shallow volumeswith small radii, events with small magnitudes are predom-inant, increasing the b value. Sampling with larger radiitends to mix the shallow volumes with deeper ones andresults in average b values.[25] The observation of a nearly identical pattern of

b values when sampled with radii from 2 km to 5 kmsuggests that using smaller radii than 5 km is not revealingdetails which are obscured when sampling with larger radii,but it only reduces coverage. The selection of the optimalradius for Parkfield is not applicable to other areas becauseit depends on the local seismotectonic fabric and dataavailability.[26] Sampling with radii greater than 5 km (frames E–I)

results in smoothed b values. Using a radius of r � 10 km isobscuring any b value contrast at Parkfield. We can also seethat the low b value zone (at a distance of 70 km from P1)looses its crispness with sampling radii of r � 6 km andmoves toward southeast (to the right). This is because thesmall volume containing the information about the very lowb value is located at the edge of the active volume. Earth-quakes have not been recorded below or in the southeasternvicinity of it. Therefore, with increasing radii the center ofthe cylindrical volumes has to move southeast to remaindominated by the low b value distribution. At the locus ofthe b value anomaly, the sample becomes a mixture ofdifferent distributions when increasing the radius and theanomaly vanishes.[27] Thus the optimal radius for sampling events to map

b values at the Parkfield segment is in the range of 4–5 km.Sampling with smaller radii reduces the coverage whilesampling with larger radii obscures the anomalies andcontrasts. For this study, we decided to sample events atthe Parkfield segment using a radius of r = 5 km.[28] Figure 5b shows the high-resolution mapping of

b values along the Parkfield segment of the San Andreasfault based on the NCSN catalog of the period 1981–2003. At every node (grid spacing: 0.5 km � 0.5 km) wecomputed the b value, using all events within a cylindricalvolume of radius r = 5 km. If a volume contained less thanthe minimum number of Nmin = 50 events, no b value wascomputed.[29] The b value distribution (Figure 5b) shows strong

spatial variations. Different anomalous patches along thissegment can be distinguished: At a distance from point P1 ofabout 70 km, the Middle Mountain asperity, the ruptureinitiation point of the 1966 Parkfield event, correlates with apatch of very low b value (b � 0.5). The low b value zoneextends from the asperity about 25 km southeastward andmatches the locked part of the fault (Figure 5).[30] The southern end of the creeping zone (distance

from point P1: 30–60 km) shows high b values. Theseb values range from b � 1 up to b � 2. At a distance frompoint P1 of 15 km we can identify a volume with highb values extending to a depth of 10 km. In accordancewith Gerstenberger et al. [2001] and Wiemer and Wyss


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Figure 4. Distribution of b values in the Parkfield segment of the San Andreas fault computed with theNCSN catalog from 1981 to 2003 using different radii r and Nmin = 50. (a) r = 2 km. (b) r = 3 km. (c) r =4 km. (d) r = 5 km. (e) r = 6 km. (f ) r = 7 km. (g) r = 8 km. (h) r = 10 km. (i) r = 20 km.


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[1997], shallower parts show in general higher b valueswhile deeper parts exhibit lower b values.[31] The independently derived HRSN catalog shows

approximately the same pattern (Figure 5c), although onlyfor a shorter stretch of the fault. In the part covered by theHRSN data, the Middle Mountain asperity again correlateswith low b values (b � 0.5). The b values in the barelycovered creeping section show similar values as in theNCSN catalog (b � 1.1). To take advantage of the superiorlocations and considering the fact that this catalog containsmore earthquakes per unit volume, we mapped b valuesusing radii of r = 3 km. Using the same radius r = 5 km asin the NCSN catalog smoothes the b value contrast. Wefound strong variations in completeness, ranging from Mc =0.4 to Mc = 0.9; therefore we computed Mc in this casefor every node separately. We also constrained the magni-tude of completeness to the range of Mc 2 [0.4, 0.9] tocompensate for occasionally instability of the Mc compu-tation algorithm.[32] As a third data set, we analyze the NCSN catalog for

the period 1967–1981. We cut the catalog at the overallcompleteness level of Mc = 1.7 (see Figure 2a) and againuse a spatially homogeneous Mc. The resulting b value map(Figure 5d) shows the same general pattern with almost the

same absolute b values. Because of the higher Mc thresholdand the shorter period, we actually resolve fewer nodes withNmin � 50 than in the 1981–2003 period.[33] The frequency-magnitude distributions based on

these three catalogs (Figure 6) for the asperity and southernend of the creeping section (marked volumes in Figure 5)illustrate the large b value contrast between these twovolumes. Even though the b values of the asperity and thecreeping section are not identical in the three samples, theyare remarkably similar and convey the same information. Inthe asperity, the b values are in the range of b 2 [0.46, 0.60],indicating very low b values. Because the observationperiods are different between the three sets, the a valuesalso differ. The lowest b value is detected in the HRSNcatalog with a sampling radius of r = 3 km. Using a radiusof r = 5 km would increase the b value to 0.57, slightlysmoothing the large contrast. In the creeping section, weobserve relatively high b values in the range of b 2 [1.04,1.12]. Consequently, the Utsu test establishes that it isstatistically highly unlikely that the frequency-magnitudedistributions of the creeping and asperity section come fromthe same population (log Pb � �5).[34] The probability of a future earthquake of a given

magnitude at any location along the fault segment investi-

Figure 5. Distribution of b values in the Parkfield segment of the San Andreas fault. The circles markvolumes for which frequency-magnitude distributions are shown in Figure 6. The radii correspond to thesampling radii. The red circles mark the asperity (distance from P1: 70 km, depth: 10 km); the blackcircles mark a part of the creeping section (distance from P1: 63.5 km, depth: 3 km). The bars at the topmark the extension of the creeping section, Middle Mountain asperity, and the locked part of the fault.(a) Seismicity distribution of the years 1981–2003. All earthquakes withM � 1 and depth D � 16 km areplotted; (b) b values of the NCSN catalog from 1981 to 2003; (c) b values of the HRSN catalog from1987 to 1998.5; (d) b values of the NCSN catalog from 1969 to 1981.


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gated can be estimated according to equations (3) and (4). InFigure 7, we compare the resulting earthquake probabilitiesfor an M � 6 event given the assumption of a spatiallyvarying b value, and the assumption of a regionally constantb = 0.92, as it is often used in seismic hazard assessment.The forecasts issued by these two approaches are strikinglydifferent: The volume of the asperity at a distance frompoint P1 of 70 km shows a high probability Pr � 0.025 forone or more events of magnitude M � 6, when computedwith local b values. This observation has previously beendocumented by Wiemer and Wyss [1997] as a Tr minimum.When computing the Pr with the constant overall b value,the location of the highest probability is in the creepingsection, because here the activity of microearthquakes ishighest. The probability is with Pr � 0.004 overall lower.

4.2. Stationarity of b Values

[35] The stationarity of b values and the stationarity of theaforementioned strong spatial variations in b is the nextquestion we address. Our method to detect local temporal

changes in b is based on mapping Db, the differencebetween the values in two periods [Wiemer et al., 1998].If Db is statistically significant at some locations, we plot bas a function of time for those volumes to further investigatethe cause of change. As a first test of stationarity, wecompare b values by simply subdividing the data set intotwo periods of equal length, obtaining two 11-year periods(1981–1992 and 1992–2003). In Figure 8, frames A and Bshow the b value cross sections for these two periods.Overall, both periods show the same pattern. The differ-ences Db = b1992–2003 � b1981–1992 are small (frame C).They range from Db = �0.49 to Db = 0.36, while 90% ofthe values are in the interval Db 2 [�0.1, 0.2].[36] We do not consider changes in b value significant if

they do not exceed the standard deviation s (obtained bybootstrapping) of the b values, shown in frame D and E. Thestandard deviation of the first period’s b value (frame D) ison average s = 0.116 and 90% of the values are smaller than0.187. For the second period (frame E), the average stan-dard deviation is s = 0.122 while 90% of the values are

Figure 6. Frequency-magnitude distributions of the two selected volumes marked in Figure 5. Redcrosses mark the frequency-magnitude distributions of the Middle Mountain asperity; black squares markthe frequency-magnitude distributions of the creeping section. (a) NCSN catalog from 1981 to 2003 (r =5 km), frame B in Figure 5. (b) HRSN catalog (r = 3 km), frame C in Figure 5. (c) NCSN catalog from1969 to 1981 (r = 5 km), frame D in Figure 5.

Figure 7. Annual probabilities Pr for one or more events of magnitude M = 6 at the Parkfield segment.(a) Pr computed using the overall b value of b = 0.92 and spatially varying a values. (b) Pr computedusing spatially varying a and b values.


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smaller than 0.209. Comparing the values of Db with sshows that the differences in b values mostly equal thestandard deviation. Therefore we can say that except for afew samples, the b values remain stationary in the bounds oftheir standard deviation s. This statement is further quan-tified by applying at each node the test proposed by Utsu[1992] (frame F). Log probabilities of Pb � �1.3 (auburncolors) indicate significant changes in b value. Only 34 of2950 computed samples show significant changes in bvalue, equivalent to less than 1.2%.[37] The result of this stationarity investigation depends

on the two periods selected. A second sensible division ofthe data is at 1996, because this allows us a prospective testof the b value distribution at Parkfield published by Wiemerand Wyss [1997]. Figure 9, analyzing the periods 1981–1996 and 1996–2003, reveals a different picture from theprevious division in 1992. We again plot the b values in thetwo respective periods, their standard deviation, the differ-

ence and finally the result of the Utsu test. While most ofthe fault segment shows stationary behavior, we can identifyseveral volumes with significant b value changes accordingto the Utsu test. The largest changes are located at distancesfrom P1 of 15 km, 25 km and 90 km (frame C). At adistance of 15 km, the b value dropped by a maximum ofDb = �0.37. The largest change in this area happened atdepth of D � 5 km. Even though the standard deviation s israther large at this depth (frames D and E), the Utsu testshows significant changes in b value (frame F). In thevolume at a distance of 25 km, the change in b value showssimilar values (Db � 0.2–0.4) but the standard deviation sis smaller (frame D), about 0.1 or less. The Utsu test showshighly significant changes in b values for these volumes. Ata distance of 65 km, we can detect changes in b value ofDb � 0.2, while the standard deviation shows smallervalues. The Utsu test shows significant changes in b valuesfor this volume also. While in the previous volume the

Figure 8. Results from the stationarity test comparing the periods 1981–1992 and 1992–2003:(a) b values from 1981 to 1992; (b) b values from 1992 to 2003; (c) differences in b values between theperiods 1981–1992 and 1992–2003; (d) standard deviation s of b values of the period 1981–1992;(e) standard deviation s of b values of the period 1992–2003; (f ) log-probability of b values havingnonstationary behavior according to Utsu [1992].


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seismicity rate stayed constant, we can detect a higher ratein the last years of the second period for this volume. Anextreme change in b values can be detected in the volume ata distance of 90 km with changes up to Db � 1. In thisvolume, we also found a change in seismicity rates, in-creasing in the second period. In total, 488 of 2580computed nodes show significant changes in b value,corresponding to 18.9%.[38] Although both stationarity tests (Figures 8 and 9)

cover in total the same period (1981–2003), the results aredifferent. In the first test, almost no volumes showedsignificant b value changes, in the second test, the portionof volumes with significant changes in b values amounts to18.9%. To explore this difference in more detail we inspectthe frequency-magnitude distributions of the different peri-ods and the development of b values as a function of time atnodes that showed a change. The b value for the volume at adistance from P1 of 25 km (volume 1) remains stationary

and below the regional average b value during 1981–1995,but it increases from 1996 on (Figure 10 frames 1A and1B). It reaches a maximum in the period 2000–2003. Whenselecting 1992 for dividing the data set into two periods, theb value of the second period of the catalog (1992–2003) isthe average of the observed development during that time;thus the difference of b values between the two periods isinsignificant. The green indicators in the figure show the bvalues of the two periods and their difference.[39] The same effect can be seen in the volumes at

distances of 65 km (volume 3 and frames 3A and 3B) and90 km (volume 4 and frames 4A and 4B). In the latter case,no b value for the pre-1992 period can be computed but thedevelopment of the b value with time shows a clearincrease, starting about 1995. Volume 3 shows a dip in blimited to the years 1990–1995. During other times, the bvalue remains stationary with values b � 0.8. Although thisvolume exhibits fluctuations in b, these values are at all

Figure 9. Results from the stationarity test comparing the periods 1981–1996 and 1996–2003:(a) b values from 1981 to 1996; (b) b values from 1996 to 2003; (c) differences in b values between theperiods 1981–1996 and 1996–2003; (d) standard deviation s of b values of the period 1981–1996;(e) standard deviation s of b values of the period 1996–2003; (f) log-probability of b values havingnonstationary behavior according to Utsu [1992].


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Figure 10. Stationarity test comparing the periods 1981–1996 and 1996–2003. Center frame: Log-probability of b values having nonstationary behavior according to Utsu [1992]. Circles mark volumes1–4 (location of volumes in distance from point P1/depth. Volume 1: 26 km/7 km. Volume 2: 50 km/5 km.Volume 3: 64 km/8 km. Volume 4: 92 km/7 km.). CRR1 indicates the location of the creep meter at theCarr Ranch site [Roeloffs, 2001]. A frames: b value with time of volumes 1–4. For volumes 1–3 asample size of 100 events is used; for volume 4 a sample size of 50 events is used. The green indicatorbars indicate the b value changes between both the periods 1981–1992 and 1992–2003 and the periods1981–1996 and 1996–2003. In frame 4B, only the latter change is indicated. B frames: Cumulativefrequency-magnitude distributions of both periods of volumes 1–4. Red squares mark the distribution ofthe period 1981–1996; green squares mark those of the period 1996–2003. The b values of both periodsare marked by the accordingly colored lines.


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times smaller than the average value of b = 0.92, preservingthe information of comparatively low recurrence time. Incontrast, the volume at a distance of 50 km (volume 2 andframes 2A and 2B) shows perfect stationary behavior with bvalues around 1, which is above the regional average of b =0.92.[40] Examining the results for volume 3 in Figure 10,

frames 3A and 3B, we see only slight variations in b values.Considering the changes in completeness over the period ofinvestigation and errors in magnitude estimates, we interpretthis b value pattern as nearly stationary. Also, the b valueover time keeps presenting the information that it is lowerthan 1 and is not scattering around the overall b value of b =0.92.[41] In contrast, in volume 4, we see a larger b value

difference accompanied by a probability in the range of logPb 2 [�4, �2.5]. This volume shows clearly a significantchange in b values, as demonstrated by the green bar for theyear 1996 in frame 4A. We conclude that, even blurred byscattering, the b value distribution in most volumes containsinformation about low or high b values.

4.3. Analysis of Stationarity for Different Periods

[42] To systematically assess the stationarity of b, werepeat the above analysis for seven midpoints, starting in1986 and moving in two year steps (1986, 1988, 1990,1992, 1994, 1996, and 1998, requiring at least 5 years ineach period). We only show the final results of the Utsu test,because in the maps of probabilities Pb, the nodes where b isstationary can be readily identified (Figure 11). We canclearly see that no significant change in b values occurreduntil 1992 (frame D). From 1994 (frame E) on, threepatches where significant changes in b values can bedetected. Two patches (at a distance from point P1 of65 km and 90 km, volumes 1 and 3) show an increase inactivity of events with smaller magnitudes (M � 2) startingaround 1996–1998. This caused a higher b value in thesevolumes. Catalog subdivision at 1998 again shows fewsignificant deviations from stationarity. This shows that bvariations are averaged out when longer periods are used forthe calculation of b.[43] We also applied this test on changes of b values as a

function of time using a moving window technique. Wetook five year periods before and after the dividing date tocompute b values. Using periods of fewer than five yearsleft too few events in most of the volumes for computing bvalues. This test showed similar results to those shown inFigure 11.

5. Discussion and Conclusions

[44] The b values along the Parkfield segment of the SanAndreas fault vary significantly. The asperity region be-neath Middle Mountain exhibits an anomalously low bvalue of b � 0.5 (Figures 5 and 6). The neighboringsouthernmost part of the creeping section at shallower depthis characterized by values of b > 1.1. Using the HRSN dataset based on borehole instruments gives the rare opportunityto independently confirm a seismicity pattern (Figures 5cand 6b). This data set has superior location accuracy,confirming that location errors cannot be the cause for thespatial differences in b. It also is based on magnitudes

derived from moments [Wyss et al., 2004], confirming thatsystematic biases in magnitudes cannot explain the spatialvariations in b. Finally, by analyzing the period 1996–2003(Figure 9b), data collected after the hypothesis that b valuesat Parkfield vary spatially has been proposed, we confirmthe basic pattern in b also in a prospective test mode.Prospective testing is considered the ultimate test of ahypothesis, because only in this way inadvertently biasingthe analysis can be excluded [Jackson, 1996; Mulargia,2001]. In summary, we cannot think of any possible artifactthat may create the strong spatial heterogeneity at Parkfield,and thus must accept that it is a natural phenomenon. Theassertion that b value computations are mainly influencedby the corner magnitude mc [Kagan, 2002], but are essen-tially everywhere the same, cannot hold for the Parkfieldsegment.[45] When mapping spatial variability in b one has to

strive for a suitable balance between available resolution,uncertainty of the estimate and the size of the seismotec-tonic feature under investigation. We illustrate this impor-tant yet sometimes neglected point in Figure 4, where weimage b using sampling radii ranging from 2–20 km.Sampling with r > 5 km mixes populations of dissimilarfrequency-magnitude distributions and thus cannot resolvethe apparent intrinsic structure, or seismotectonic fabricat Parkfield, resulting in average values of b � 0.9. Forr < 5 km no significant additional heterogeneity of b valueswas detected. Thus we strengthen the conclusion of Wiemerand Wyss [1997] that a radius in the range of 4–5 km is thebest choice for this fault segment and data set for identifyingand resolving contrasts in b values.[46] Establishing the optimal sampling dimensions is the

first step in the method we propose here to test forstationarity of b. The optimal radius varies from region toregion, depending on the seismotectonic target and thedensity of catalog information. In a worldwide study whereMc might be 5.5, the minimum dimensions of volumescontaining enough events for analysis are often 100 km,which means that details like asperities of earthquakes ofmagnitude M = 6 cannot be resolved, even if such asperitiesexisted. Thus studies in which it cannot be demonstratedthat smaller radii than a certain optimal value yield noadditional information have only limited value because theydo not penetrate to the depth appropriate for the dimensionsof the local seismotectonic fabric. Nevertheless, the amountof data is constraining the targeted dimensions of seismo-tectonic fabric which can be resolved.

5.1. Investigating Stationarity of b Values at Parkfield

[47] We have performed in this paper for the first time anin depth investigation of stationarity of b in the Parkfieldregion. This question is important because it relates to thephysical understanding of b values and transients in theEarth’s crust, and is also highly relevant for the probabi-listic forecasting of seismicity. It is complicated by theintrinsic coupling of stationarity and spatial heterogeneity.Stationarity can only be established relative to a givenspatial volume. We use as our reference framework theaforementioned 5 km sample radii, as they are the upperlimit that resolve the spatial b value contrasts.[48] As a second step in b value analyses, we recommend

that one tests the stationarity of b value patterns that may


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exist as a function of space. The method we propose here isoutlined in Figures 8–11. Because one looses informationby mixing samples with different magnitude distributions,mixing must be identified and avoided if possible. Thisapplies to both, mixing dissimilar samples in space andtime. Thus we propose that mapping of Db (comparing datafrom two periods) and judging its significance by Utsu’s test(Figures 8 and 9) is a way to find possible changes of b atthe time selected for the comparison. The amount and exacttime of change can then be determined by plots of b value asa function of time (Figure 10) for the locations where mapsof Utsu probabilities have shown a change. Because not allchanges are identifiable by a single cut in time, one needs to

plot the probabilities Pb according to the Utsu test for allpossible divisions of the data set in time (Figure 11).[49] Only a minute percentage of the nodes (1.2%)

showed temporal changes when subdividing the data in half(Figure 8). When analyzing the data for the periods 1981–1996 and 1996–2003 (Figure 9), a larger percentage(18.6%) of nodes displays a change in b. The analysis ofstationarity for different periods (Figure 11) essentiallyleads to the same conclusions, but it establishes in additionthat the change in b values initiates between 1992 and 1994.[50] The test proposed by Utsu [1992] assumes that the

frequency-magnitude relationship perfectly obeys a powerlaw. Thus it may interpret two earthquake populations as

Figure 11. Maps of log-probabilities Pb of the stationarity test for different catalog divisions: (a) catalogdivision at 1986; (b) catalog division at 1988; (c) catalog division at 1990; (d) catalog division at 1992;(e) catalog division at 1994; (f ) catalog division at 1996; (g) catalog division at 1998.


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having significantly different b values, when in reality thedifference may stem from errors, not from a real differencein mean magnitude. The problem with this test is that it doesnot allow for errors in magnitudes and completeness andthus underestimates the probability Pb.[51] Figure 12 shows clearly that the observed changes in

b value are not an effect of random scattering of b valuesaround the regional average. Each cross in one of the framesof Figure 12 represents the two b values (first and secondperiod) of a single node and their standard deviation. For thestationarity test with periods 1981–1992 and 1992–2003(frame A) most data points are aligned along the stationarityline (gray line in Figure 12). Performing the stationarity testwith periods 1981–1996 and 1996–2003 still shows amajority of data points aligned along the stationarity line,although 18.9% of the nodes showed significant changes inb values. If these changes would indicate random scatteringaround the regional average, the crosses in Figure 12 wouldhave shape a circular cloud with its center at the regionalaverage b value.[52] A number of other geophysical transient changes

around 1993 have been detected and described in theParkfield region. The change in b value in volume 4(Figure 10) correlates with the region of increased creepat the Carr Ranch site (location of creep meter CRR1,Figure 10), as detected by EDM and creep meter data. Thisgeodetic transient has been investigated at length by Gao etal. [2000] and Roeloffs [2001], their conclusion is that itrepresents most likely a tectonic signal rather than a rainfallinduced artifact. Our observation of increasing b values inthis location after 1993 corroborates this interpretation. Themost viable interpretation to us is that a transient decrease inlocking strength started around 1993 in this fault segment,increasing the creep at depth. The seismicity reacts to this

strain transient by producing relatively more small eventsand fewer large events (Figure 10, frame 4A), or a b valueincrease from b � 0.7 to b � 1.2.[53] Transients in b that are established with high signif-

icance and correlate with other geophysical signals are rareand important in order to enhance the physical understand-ing of the frequency-magnitude distribution. Increases in bvalue have been reported in volcanic regions [Wyss et al.,1997; Wiemer et al., 1998] where magma or fluids arebelieved to have migrated and caused these changes. In arecent study in the Tokai region of Japan, S. Wiemer et al.(Correlating seismicity and subsidence in the Tokai region,Central Japan, submitted to Journal of Geophysical Re-search, 2004) were able to show a clear correlation of bvalue and subsidence measure by leveling data. Additionalevidence for understanding b value changes is based on theobservation that b decreases significantly with depth inCalifornia [Mori and Abercrombie, 1997; Wiemer and Wyss,1997; Gerstenberger et al., 2001]. This observation isconsistent with laboratory experiments by Amitrano[2003], who suggests that the increase in confining pressureat greater depth is the reason for lower b values.[54] We feel that the increase of b at Parkfield is consis-

tent with the conceptual model of the striking spatialdifferences in b between the asperity and creeping sectionof the fault (Figure 5): A largely locked fault is character-ized by low b values, and this fact can be used to mapasperities [Wiemer and Wyss, 1997; Wyss et al., 2000; Onceland Wyss, 2000; Zuniga and Wyss, 2001; Wyss andMatsumura, 2002]. Creeping sections of faults on the otherhand display the opposite kind of behavior, relatively higherb values [Wiemer and Wyss, 1997; Amelung and King,1997]. When the southern part of the locked section(volume 4 in Figure 10) started to creep, a corresponding

Figure 12. Changes in b values in the Parkfield segment of the San Andreas fault. Each cross representsone sample of the cross section. The position of each cross indicates the b values of the first and secondperiod. The crossbars indicate the error in b values for both periods. The color of each cross correspondsto log Pb of the test proposed by Utsu [1992]. The gray line marks the stationary behavior. (a) Changes inb values for the periods 1981–1992 and 1992–2003. (b) Changes in b value for the periods 1981–1996and 1996–2003.


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change in b value occurred. An important conclusion fromthis observation is that the governing factor that determinesthe b value cannot be material heterogeneity engrained inthe volume under investigation, because this could not bechanged readily. To be able to change the b value so readilyafter a comparatively minor creep episode suggests that thelocal stress/strain environment and/or fluid interaction arethe main causes. However, the ultimate physical reasons forthe difference of b values between the asperity and thecreeping section is not known. The SAFOD drilling holemight help to open new perspectives on processes at thefault. Unfortunately, this hole will only be drilled to a depthof 4 km, it will only reach the high b value zone in thecreeping part of the fault not the more interesting asperity ata depth of approximately 10 km, Figure 13.[55] The frequent occurrence of events in the asperity

(1857, 1881, 1901, 1922, 1934, and 1966 [Bakun andLindh, 1985]) suggests that the properties of the asperityremain stationary over decades to centuries. Taking the bvalue as a quantity related to the stress level, the stationarityof b values along the Parkfield segment, and especiallyaround the asperity and the locked segment, supports theconcept of the asperity being the nucleation zone of largerearthquakes which propagate southeastward. A preferredsoutheastward propagation of moderate and large earth-quakes in the Parkfield area is expected from the knownvelocity contrast across the San Andreas fault there [Ben-Zion, 2001]. We have shown that the b values remainedstationary, although in one fault patch a significant changehas been observed (volume 4 in Figure 10). We concludethat in most (90%) of the fault surface mapped the pattern ofdisproportionately higher/lesser production of small earth-quakes in the unlocked/locked segments, respectively,remains stable for more than 30 years, and therefore shouldbe considered stationary. However, transient changes insubvolumes do occur if significant changes in the environ-mental conditions take place.[56] We want to elaborate on the question how one should

sample a data set of earthquakes that contains variations of bas a function of space and time. If one uses the entire dataset to calculate b, the result is usually near b = 1, and onegains no information. One can even argue that such aselection makes no sense because dissimilar groups ofearthquakes are arbitrarily mixed. The same is true forany subset of the data that is strongly heterogeneous. It

follows that, ideally, one wishes to subdivide the data setinto all subsets that are homogeneous and stationary. Al-though it is difficult to detect local changes of b as afunction of time in the presence of strong spatial heteroge-neity, it is possible by maps of Db and probabilities Pb

(Figures 8 and 9). Also, variations of b with time are usuallynot frequent, thus it is not necessary to subdivide intosamples of short periods (Figure 10, A frames). Thereforewe recommend that the following steps should be used in adetailed analysis of the mean magnitude, or b: (1) Map (incross section or in normal map view) variations of b as afunction of sampling radius (as in Figure 4) to establish themost suitable sampling radius. (2) Using this samplingradius, map Db and Pb, comparing the data from twoperiods, for a suite of separation dates. (3) Select sampleswith homogeneous and stationary distribution of earthquakesizes for tectonic analysis. This suggested procedure isidealized and approximations have to be exercised in datasets that usually are complex.

5.2. Implications for Earthquake Hazard andProbabilistic Forecasting

[57] The pattern of probability of future earthquakes alongthe fault is strikingly different in our model (varying b values)and the approach of applying the overall b value to alllocations, asperity and creeping segments, alike (Figure 7).Our model predicts that major earthquakes are most likely toinitiate in the Middle Mountain asperity, whereas a modelwith b = const. predicts that major ruptures are most likelyin the seismically highly active, creeping segment of thefault. On the basis of the facts that the Middle Mountainsegment is recognized as an asperity and that low b valuesare linked to high-stress environments [Scholz, 1968; Wyss,1973;Urbancic et al., 1992], we believe that our model takesaccount of physical conditions along the fault, and is moreappropriate for forecasting seismicity. This expectation hasbeen tested in paper 2 [Schorlemmer et al., 2004].[58] The low b values in the asperity and the locked

segment together with their stationarity strongly support ourhypothesis that the asperity is the nucleation zone of earth-quakes which ruptured the locked part of the fault. Theasperity matches the Middle Mountain alert box (markedwith 2 in Figure 13) by Michael and Jones [1998]. TheSmall Middle Mountain alert box (marked with 1) is notspecially characterized by b value features compared to the

Figure 13. Distribution of b values in the Parkfield segment of the San Andreas fault computed with theNCSN catalog from 1981 to 2003 (r = 5 km, Nmin = 50). Earthquakes with M � 1 are plotted as circles.Events with M > 4.5 are marked by red stars. The boxes denoted with 1, 2, and 3 are the small MiddleMountain alert box, the Middle Mountain alert box, and the Parkfield alert box, respectively [Michaeland Jones, 1998]. The surface break of the 1966 event is marked by an arrow. The SAFOD drilling holeis marked by a vertical black line with a derrick on top.


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Middle Mountain alert box but is also located in theasperity. The event on 14 November 1993 of magnitudeM = 5 occurred in this alert box while all three events withM > 4.5 are located in the Middle Mountain alert box (redstars in Figure 13). This low b value zone continues about25 km southeast and corresponds to the 1966 rupture zoneaccording to Segall and Du [1993] and matches perfectlythe Parkfield alert box by Michael and Jones [1998]. Theobserved postseismic surface break (Figure 13, arrow)according to Smith and Wyss [1968] extends from theasperity over the locked part into a high b value volumewhere it stopped.[59] When computing the probabilistic recurrence time

Tr of the entire Parkfield volume for a magnitude M =6 event, we get Tr = 116.6 years. This is a clear overestimatebased on the proposed Parkfield earthquake cycle of about22 years [Bakun and McEvilly, 1979, 1984]. In contrast, thelocal recurrence time of the asperity volume, TL � 30 yearsagrees well with the observed recurrence times of theearthquake cycle.[60] The local recurrence time is not simply another

representation of the b value. It takes into account the bvalue as well as the a value of a particular volume. The lowb value zone extents from the asperity (distance about 70 kmin Figure 13) southeast along the rupture zone (to a distancepoint about 90 km). However, only the nucleation point ofthe Parkfield earthquakes shows the low values of localrecurrence time or high values of probabilities Pr. Only asuitable combination of a and b values produces low localrecurrence times TL. On the other hand, using the regionalaverage b value when computing the probability Pr of oneor more magnitude M = 6 events, selects the creepingsection as the locus with the highest probability (Figure 7a).In this case, the probability is proportional to the a value.This result contradicts the observation of the Parkfieldearthquake cycle and also the observation that the threeevents with magnitudeM > 4.5 which occurred in the period1981–2003 are located in the Middle Mountain alert box(Figure 13). Computing the probability Pr for one or moreevents of magnitude M = 6 using spatially varying b valuesshows the highest probability in the Middle Mountain alertbox. This result again emphasizes the concept of the asperitybeing the nucleation point of larger earthquakes at Parkfield.

[61] Acknowledgments. We would like to thank the Northern Cal-ifornia Earthquake Data Center (NCEDC) for providing us with catalogdata, the Northern California Seismic Network, U. S. Geological Survey,Menlo Park for the NCSN catalog, and the Berkeley SeismologicalLaboratory, University of California, Berkeley for the HRSN catalog.We profited from discussions with M. Gerstenberger, D. Jackson, andR. Zuniga. We also want to thank J. Woessner, J. Ripperger, G. Hillers, andY. Ben-Zion for their useful hints. This paper is contribution 1370 of theGeophysical Institute, ETH Zurich. This research was supported by theSouthern California Earthquake Center. SCEC is funded by NSF Cooper-ative Agreement EAR-0106924 and USGS Cooperative Agreement02HQAG0008. The SCEC contribution number for this paper is 786.

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Wyss, M., C. G. Sammis, R. M. Nadeau, and S. Wiemer (2004), Fractaldimension and b-value on creeping and locked patches of the SanAndreas fault near Parkfield, California, Bull. Seismol. Soc. Am.,94(2), 410–421.

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��D. Schorlemmer and S. Wiemer, Swiss Seismological Service, ETH

Zurich, HPP P5, 8093 Zurich, Switzerland. ([email protected])M. Wyss, World Agency of Planetary Monitoring and Earthquake Risk

Reduction, Route de Malagnou 36A, Geneva, 1208, Switzerland.


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Earthquake statistics at Parkfield: 1. Stationarity of …bemlar.ism.ac.jp/zhuang/Refs/Refs/schorlemmer05jgr1.pdfEarthquake statistics at Parkfield: 1. Stationarity of b values D