Deducing Paleoearthquake Timing and Recurrence …pangea.stanford.edu/~hilley/REPRINTS/HilleyandYoung_B...ern San Andreas fault that seeks to establish the timing, recurrence, and

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Deducing Paleoearthquake Timing and Recurrence from Paleoseismic

Data, Part II: Analysis of Paleoseismic Excavation Data and Earthquake

Behavior along the Central and Southern San Andreas Fault

by G. E. Hilley and J. J. Young

Abstract We present an analysis of paleoseismic data along the central and south-ern San Andreas fault that seeks to establish the timing, recurrence, and along-faultcorrelation of paleoearthquakes. We use Bayesian methods to compute a series ofprobability density functions (PDFs) that cast paleoearthquake timing in the contextof yearly probabilities. To quantify the uncertainties present in the paleoseismic data-set based on stratigraphic interpretations, we use a scenario-based approach in whichdifferent, viable, stratigraphic interpretations are used to infer paleoearthquake timing.Using these PDFs, we attempt to correlate earthquakes along the fault through time toimage a time series of past fault ruptures. We find that site-to-site correlation is oftendifficult due to significant uncertainties. Nonetheless, some ruptures could be corre-lated from site to site. Assuming the paleoseismic record is complete, these inferencesmay indicate that ruptures begin and terminate more or less randomly in space. Theresults of our analysis may prove beneficial to future probabalistic seismic hazardassessments of this area and may serve as inputs to studies that seek to quantitativelytest rupture models against data in the paleoseismic record.

Online Material: Scenario probability density functions and associated data.

Introduction

Earthquake-generating ruptures may recur in their ap-proximate extent and magnitude along a particular lengthof a fault (e.g., Schwartz and Coppersmith, 1984), occur ran-domly over a fault’s length throughout time (e.g., Gardnerand Knopoff, 1974), or oscillate between several ruptureextents and magnitudes over time to accommodate thelong-term slip budget along the fault. Each of these differentbehaviors may have different implications for future earth-quake forecasting, may influence hazard assessments, andmay reveal important information about changes in geometryand/or mechanical properties along the fault length (e.g.,Graymer et al., 2005). With the exception of a few rare seriesof earthquake ruptures (e.g., Stein et al., 1997), the databaseof historical ruptures along a particular fault is often insuffi-cient to discern between these different modes of rupture.Thus, imaging a time series of ancient ruptures along a faultprovides one way to test different models of long-term rup-ture behavior. This imaging is often carried out by excavatingthe near-surface fault-zone stratigraphy at sites along a faultand by analyzing the cross-cutting relationships betweenfault-generated offsets in the sediments with radiocarbonor thermoluminescence dating of the strata to deduce therelative sequence and absolute ages of ancient surface-

rupturing earthquakes (McCalpin, 1996, and referencestherein). Finally, by estimating the timing of earthquakesat a number of sites along a fault, the extent of ancient rup-tures can be estimated and used to determine the long-termrupture behavior of the fault.

The San Andreas fault (SAF) in central and southernCalifornia is one of the most well-studied plate-boundingstrike-slip faults in the world. Extensive resources have beendedicated to understanding the timing of ancient earthquakesalong this fault because of the devastating past earthquakesthat it has generated (e.g., the 1857 Fort Tejón earthquakeand the 1906 San Francisco earthquake) and the future haz-ard that it poses to a heavily populated area of the UnitedStates (Working Group on California Earthquake Probabil-ities [WGCEP], 1988, 1995, 2003). In particular, betweenParkfield, California, and Indio, California (Fig. 1), thereare eight sites reported in the peer-reviewed literature atwhich the timing of ancient earthquakes has been deduced.Thus, the relatively dense distribution of paleoseismic sitesalong this portion of the SAF may provide information aboutthe long-term rupture behavior of this fault. In addition, thereare a number of other sites in this area that have not yetemerged in the peer-reviewed literature, and the future

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Bulletin of the Seismological Society of America, Vol. 98, No. 1, pp. 407–439, February 2008, doi: 10.1785/0120070012

evaluation of these sites may help refine our inferences of therupture behavior of this fault. Surprisingly, there has not yetbeen a consistent analysis of the timing of earthquakes be-tween all of these sites that might clearly image the time ser-ies of ancient ruptures in this area. The development of thistype of time series was attempted using a smaller subset ofsites by Grant and Sieh (1994) and Sieh (1996) that wereavailable when these studies were undertaken. However,these previous studies necessarily did not take advantageof newly developed Bayesian statistical methods that rigor-ously estimate the age of ancient earthquakes based on radio-metric and paleoseismic excavation data. Thus, it appearstimely that the available peer-reviewed paleoseismic excava-tion data be analyzed using these new methods to estimatethe ages, recurrence, and correlation of earthquakes along thecentral and southern SAF.

This article is the second in a study that seeks to under-stand the timing, recurrence, and behavior of ancient rupturesalong the central SAF. In the first article (Hilley and Young,2008), we presented new Bayesian statistical methods thatimprove statistical inference of the ages and recurrence ofearthquakes based on paleoseismic excavation data. Wetested these methods against similar, previously developedmethods used to analyze the ages and recurrence of earth-quakes at two sites in this area. In this contribution, weuse our Bayesian methods to reanalyze paleoseismic dataalong the central and southern SAF that are reported inthe peer-reviewed literature. In particular, we consider a total

of eight paleoseismic sites (Sieh et al., 1989; Fumal et al.,1993; Grant and Sieh, 1994; Seitz et al., 2000; Fumal, Wel-don, et al., 2002; Lindvall et al., 2002; McGill et al., 2002;Weldon et al., 2002; Young et al., 2002) (Fig. 1) and calcu-late the probability density functions (PDFs) for the timing ofpast earthquakes observed in the geologic record and theirrecurrence. We propose some metrics for assessing thecorrelation of earthquakes between each site, and presentrupture scenarios that are most consistent with the paleo-seismic and radiometric data from all of the sites. While theseresults will certainly change as new and higher quality paleo-seismic data become available from this area, our results con-stitute an attempt to use PDFs derived from Bayesian analysisof paleoseismic data from the area to understand the possiblepatterns of ruptures through time that characterize this por-tion of the SAF.

Study Area

We chose the central and southern SAF (Fig. 1) as ourfocus area because of the extensive documentation of thetiming of ancient earthquakes in the area (Sieh, 1978b; Fu-mal et al., 1993; Grant and Sieh, 1994; Fumal, Weldon, et al.,2002; Lindvall et al., 2002; McGill et al., 2002; Weldonet al., 2002; Young et al., 2002), and because many paleo-seismic techniques for strike-slip faults were developed here(Sieh, 1978a). Parkfield (PF, Fig. 1) and the Mission Creekpaleoseismic site (MC, Fig. 1) bound the study area to thenorthwest and southeast, respectively (Fig. 1). In the northern

Figure 1. The SAF in central and southern California. White text refers to excavation sites, while yellow text denotes landmarks referredto in the text. The map is labeled as follows: San Andreas Fault, SAF; Garlock Fault, GF; Red arrows denote the sense of motion along faults.The excavation sites, shown in yellow italic symbols, are from northwest to southeast: Las Yeguas, LY; Bidart Fan, BF; Frazier Mountain, FM;Pallett Creek, PC; Wrightwood, WW; Pitman Canyon, Pit; Plunge Creek, Plunge; and Mission Creek, MC. Landmarks are Parkfield, PF;Cholame, CH; Carrizo Plain, CPl; Tejón Pass, TP; and Cajón Pass, CP.

408 G. E. Hilley and J. J. Young

and central portions of the study area, the fault consists oftwo roughly linear traces between PF and the Carrizo Plain(CPl, Fig. 1), and Tejón and Cajón Passes (TP and CP, respec-tively, Fig. 1). The former trace strikes approximately 345°,undergoes an ∼30° restraining bend between the southernCarrizo Plain and TP, and continues ∼315° southeast ofTP. In the vicinity of CP, the fault bifurcates into the southern,oblique-slip Banning fault segment and the northern SAFsegment. In the southern portion of the study area, the Ban-ning fault once again merges with the SAF and undergoes an∼30° bend in the vicinity of the MC site (Fig. 1) and con-tinues ∼345° toward its southern termination in southernCalifornia.

Eight sites that have been documented in the peer-reviewed literature exist along this portion of the SAF, andso this area constitutes one of the highest quality paleo-seismic datasets in the world. The quality of the paleoseismicsites varies from site to site due to changing depositional con-ditions and the prevalence of datable material containedwithin the stratigraphy. At the Wrightwood site, fourteenearthquakes are documented within the published stratigra-phy; most sites image significantly fewer surface-rupturingearthquakes. Sites used in this study are shown in Figure 1and include, from northwest to southeast, Las Yeguas (LY,Young et al., 2002), Bidart Fan (BF, Grant and Sieh,1994), Frazier Mountain (FM, Lindvall et al., 2002), PallettCreek (PC, Sieh, 1978b; Sieh et al., 1989), Wrightwood(WW, Fumal et al., 1993; Fumal, Reymer, et al., 2002), Pit-man Canyon (Pit, Seitz et al., 2000), Plunge Creek (Plunge,McGill et al., 2002), and Mission Creek (Fumal, Weldon,et al., 2002). In addition, historical events have ruptured vari-ous portions of the SAF in the study area. Seven historicalearthquakes around Ms ∼6 have ruptured the portion ofthe fault restricted to the PF area; however, ruptures appar-ently have not propagated as far south as Cholame (CH,Fig. 1). In 1857, the Fort Tejón earthquake likely rupturedthe portion of the fault from CH towards CP (Agnew andSieh, 1978; Sieh, 1978a). Prior to this event, a smaller eventin 1812 apparently ruptured the region of the fault includingthe PC, WW, and Pit sites. It is worth noting that there areseveral sites that were not included in this study, includinga site southeast of MC (Indio site, Sieh, 1986), one betweenPit and Plunge (City Creek, McGill et al., 1998), and twosites between Plunge and MC (Burro Flats, Yule and How-land, 2001, and Cabazon, Yule et al., 2001). We chose not toinclude these sites in our analysis, either because they havenot yet had the chance to be peer reviewed in the literature, orbecause they are active working sites whose results maychange as new data emerges.

Methods

In this study, we use Markov-chain Monte Carlo(MCMC) simulation methods to estimate, in a probabilisticsense, the ages of earthquake and their recurrence at eachof the paleoseismic sites considered. These simulation meth-

ods are used to approximate Bayes’s theorem (Bayes, 1763),which can be used to assimilate geologic information intoradiometrically determined estimates of stratal ages. Themethods employed in this study represent an extension ofpreviously developed Bayesian strategies for estimatingearthquake timing and recurrence, and the details of ourmethod are documented in a companion article (Hilleyand Young, 2008). Here, we briefly summarize the key im-provements implemented in our new Bayesian simulationmethod that are particularly tailored to paleoseismic appli-cations.

The Bayesian methodology used in this work allowsgeologic information, such as relative ordering of strataand information provided by peat growth in paleoseismic ex-cavations, to be used in concert with radiometric age controlto estimate PDFs of earthquake ages and their recurrence.Two general classes of Bayesian algorithms have been usedin the past by the paleoseismologic community to infer thesePDFs. The first class was developed by Biasi and Weldon(1994) and Biasi et al. (2002) and uses explicit evaluationof Bayes’s rule using a limited subset of data from a paleo-seismic site to calculate these PDFs. In their method, Biasiand Weldon (1994) and Biasi et al. (2002) used geologic in-formation on the relative ordering of strata in excavations, aswell as the time that separates each layer that is representedby peat growth to refine initial estimates of stratal ages. Incontrast, the second class of Bayesian algorithms, developedby the archeological community, uses simulation rather thanexplicit evaluation to estimate earthquake ages (e.g., Bronk-Ramsey, 1995; Buck et al., 1996). The relative ordering ofstrata and the minimum time separating the layers repre-sented by peat growth can likewise be used to constrainearthquake ages in this method.

In our previous work, Hilley and Young, 2008 foundthat systematic biases may arise in the estimation of the PDFsof stratal and earthquake ages when simulation was used incases where minimum time separation between strata repre-sented by peat growth was considered. Thus, the use of cur-rently available Bayesian simulation methods, which allowall data from a paleoseismic excavation to be simultaneouslyconsidered when calculating stratal and earthquake ages, andrecurrence interval PDFs seemed incompatible with sites atwhich peat growth should be used as constraints on thesePDFs. This problem arose due to the idealization that peatgrowth represents a minimum time that separates differentstrata in a paleoseismic excavation. In reality, if the accumu-lation rate is assumed constant (e.g., Biasi et al., 2002) thestratigraphic position reveals the age at any given peat thick-ness rather than the time that separates individual samples.Our improved Bayesian method has three key benefits overeach of these two methods: (1) We revise the idealization ofpeat growth to take advantage of benefits of MCMC simula-tion while properly treating the accumulation of peat growthin paleoseismic excavations. This allows all radiometric agecontrol and geologic information to be incorporated rigor-ously into the estimates of stratal and earthquake age, and

Deducing Paleoearthquake Timing and Recurrence from Paleoseismic Data, Part II 409

recurrence interval PDFs. (2) Our simulation methods allowthe approximation of the full joint distribution of stratal andearthquake ages, and recurrence intervals. (3) Our formula-tion ensures that the covariation between stratal agesthroughout the paleoseismic excavation is taken into consid-eration when calculating the earthquake age and recurrenceinterval PDFs. More importantly, the approximation of thejoint PDF allows us to explicitly track how specific choicesfor layer ages affect the earthquake age PDFs and how thesein turn affect the recurrence interval PDFs. Thus, our newmethod represents a hybrid between explicit methods thatmust consider only a subset of strata when calculating theconditional-stratal-age PDFs (Biasi and Weldon, 1994; Biasiet al., 2002), and the previously used MCMC simulationmethods (e.g., Bronk-Ramsey, 1995; Buck et al., 1996).

In this work, we use two measures of earthquake corre-lation as a guide for identifying contemporaneous ruptures.We use the mean event overlap and weighted range overlapmethods, shown schematically in Figure 2a,b, respectively.In the former method, we select two different earthquakesfrom adjacent sites and find the time at which the cumulativeprobability for each PDF is 2.5% and 97.5% (times are re-presented by dashed vertical lines in Fig. 2a). We then cal-culate the degree of overlap of these times by computing thecumulative probability of each PDF that falls within the 95%range of the other. These ranges are normalized to the entire95% range of each PDF. Finally, the degree of overlap is theaverage of these two values and is expressed as a percentage.

The second parameter we computed to assess earth-quake rupture correlation between sites was the weightedrange overlap (Biasi et al., 2003), shown schematically inFigure 2b. In this method, we consider two events at adjacenttrenches (PDFs shown as event at site A and event at site B inFig. 2b). We compute the weighted event overlap as

W �Xt�∞

t��∞min�EA�t�; EB�t��; (1)

where W is the degree of overlap, EA�t� and EB�t� are theevent PDFs of event A and B, respectively, and the functionmin denotes that we determine the minimum yearly probabil-ity value of EA�t� and EB�t� for each time t. Graphically, thevalue of W is represented by the area of the shaded zoneshown in the right-hand column of Figure 2b and is boundedby the minimum value of the two PDFs. Higher overlap be-tween PDFs yields higher values of the parameters deter-mined by both of these methods.

These parameters are not formal statistical tests and soonly serve to guide interpretations of correlations along thefault length. We acknowledge that PDFs with large uncertain-ties generally yield higher values for these parameters thantheir low-uncertainty counterparts. Because these twoparameters provide only a qualitative measure of potentialcorrelation of events, we have used these parameters in con-junction with careful study of the data to identify potentialcorrelations between events recorded at adjacent paleoseis-

mic sites. We calculated correlation metrics for earthquakesbetween all sites, and when correlating multiple sites, we re-quired that correlation metrics between adjacent sites be qua-litatively high enough to justify a correlation. However, wedid encounter several cases where correlation of events be-tween adjacent sites was low but correlation between distantsites was high. In most of these cases, we stopped the ruptureat adjacent sites where correlation was low.

Results

Earthquake Timing and Recurrenceat Paleoseismic Sites

Las Yeguas Site. The LY paleoseismic site is thenorthwestern-most site analyzed in this study and is located∼40 km southeast of the Cholame Valley along the SAF(Stone et al., 2002; Young et al., 2002). Excavations wereseated on the distal edge of an alluvial fan that crossesthe SAF. Sediments consist of a sequence of moderatelyto heavily bioturbated laminated sands, silts, gravels, anddebris flows that document three ground-rupturing earth-quakes (events in Young et al. [2002] are their L2 and L1events; Stone et al. [2002]’s C1/C2 event lies between Younget al. [2002]’s L2 and L1 events) and one ground-fracturingevent (L0 event in Young et al. [2002]). Importantly, theheavily bioturbated soils exposed at the site may have con-founded the identification of earthquakes at the site, and sothe paleoseismic record here is likely incomplete. For exam-ple, a previous study at the site (Stone et al., 2002) foundthree ground-rupturing earthquakes, whereas heavy biotur-bation of sediments at a closely located trench prohibitedthe identification of all three of these events (Young et al.,2002). Analysis of pollen within the sediments that constrainthe age of the L0 event indicate that the ground-fracturingepisode occurred after the 1857 Fort Tejón earthquake,and field estimates of offsets along the fractures suggest thatthere was less than 0.5 cm of vertical displacement of unitsduring this event (Young et al., 2002). Based on these data,Young et al. (2002) interpret L0 as a triggered-slip event thatmay have been related to the 1877 or 1881 earthquakes in thevicinity of Parkfield, California.

Sample ages for all sites used in this analysis are shownin Ⓔ Table A1 in the electronic edition of BSSA and thestratigraphy of the site is summarized in Ⓔ Table A2 inthe electronic edition of BSSA. Summary statistics for layerages at the site are given in Table 1. In our analysis, we ac-cepted the Young et al. (2002) interpretation that the L0event was triggered-slip related to a post-1857 earthquake,and so we did not calculate a PDF for this event. The heavilybioturbated sediments exposed in the excavations reportedby Young et al. (2002) likely masked the identification ofan additional event revealed in a previous study of the site(Stone et al., 2002). Thus, in this study, we attempt to synthe-size the two studies reported from the LY site by reintro-ducing an additional event prior to the 1857 Fort Tejón earth-quake (assumed to be event L1 at the site). Young et al.


(2002) report that their deepest event (LY2) is contempora-neous with event C2 identified by Stone et al. (2002). Theage of the intermediate event identified by Stone et al. (2002)(C1/C2) is bracketed by layers 5 and 13 by stratigraphic cor-

relations between the two trench locations. Thus, we renameLY2 of Young et al. (2002) as LY3, and introduce the LY2event of this study, which is bracketed by the same strata.Because our LY3 and LY2 events are bracketed by the same

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Figure 2. (a) Bayesian refinement of layer-age PDF due to known layer-age bounding constraints (left-hand panel) and upper- and lower-bounding radiocarbon ages (right-hand panel). (b) Bayesian inference of event-age PDFs when upper- and lower-bounding ages for the eventare known (left-hand panel), and event timing is constrained by upper- and lower-bounding radiocarbon ages (right-hand panel). Y-axis scaleis truncated to show posterior PDFs; however, the a priori bounding ages in the left column have a probability of yearly occurrence of one,since these ages are known.


stratal ages, it is only their relative ordering in the trench thatcreates differences between each earthquake age PDF.

We show the stratal, earthquake, and recurrence PDFs forthe LY site in Figure 3 and report the summary statistics forearthquake ages in Table 2. In Figure 3, and subsequent fig-ures that report PDFs at each site, we plot the marginal stratalPDFs in the left-hand column, while earthquake and recur-rence interval marginal PDFs are arranged to the right-handside in an order that shows the stratigraphic relationships thatwere used to estimate each. For example, the statigraphicallylowest layer (13) is shown at the bottom, while the highest(5) is shown at the top of the first column of the figure. Be-cause L2 and L3 are bracketed by these two ages, we plottheir marginal PDFs to the right, and between units 13and 5. Finally, the recurrence interval marginal PDFs areplotted in the third column, and their position between eachof the earthquake marginal PDFs denotes the bounding earth-quake ages that were used to produce the PDFs.

Our calculated mean ages for L2 and L1 fall within therange of A.D. 1050–1460 and A.D. 1460–1860 estimated byYoung et al. (2002). However, the differing earthquake stra-tigraphy that we used (the inclusion of the additional eventreported by Stone et al. [2002]) caused the total range en-compassed by L3 and L2 to decrease relative to Young et al.’s(2002) estimates of the age of their L2. The age range of eachof our L3 and L2 earthquakes likewise decreased. Based onthe close proximity of the L1 rupture to the surface and post-settlement pollen-bearing sediments, Young et al. (2002) in-terpreted L1 to be the 1857 Fort Tejón earthquake. This ageexceeds the 95% age range of the L1 earthquake (Table 2). Inreality, the 1857 earthquake certainly ruptured ground in thevicinity of the LY site (Sieh, 1978a; Lienkaemper and Sturm,1989), and so earthquake L1 likely represents the 1857 earth-quake because no younger pre-1857 events were observed atthe LY site. However, this example highlights the difficulty ofdefinitively correlating the 1857 earthquake with L1 becauseof the poor age control that exists at the site. Finally, Younget al. (2002) claim that the site likely experiences groundrupture every 290–410 yr. This estimation assumes that

the L1 event was indeed the 1857 Fort Tejón earthquake.The recurrence interval summary statistics calculated in thisstudy are reported in Table 3. If we do not assume that L1was the 1857 Fort Tejón earthquake, but instead regard itsearthquake age PDF as representing its true age, then theaverage recurrence interval between events L3 and L1 is183 yr, and plausibly may lie within the range of 55–314 yr (95% bounds). If instead, we regard L1 as the1857 earthquake as did Young et al. (2002), the mean recur-rence interval is 289 yr, and may plausibly lie within therange of 228–370 yr. Our shorter recurrence intervals atthe site reflects our inclusion of the additional event reportedby Stone et al. (2002).

Bidart Fan Site. The BF site (Grant and Sieh, 1994) islocated ∼35 km southeast of the LY site along the SAF(Fig. 1). The site is seated in the vicinity of an alluvialfan and channel that is offset by motion along the SAF. Sedi-ments within four excavations consist of bioturbated, lami-nated silts to gravels and paleosols, which recorded sevenevents. The upper five events (events A–E, labeled fromyoungest to oldest, Grant and Sieh [1994]) are observedin a total of two trenches, with the uppermost event (eventA) representing the 1857 Fort Tejón earthquake (Grant andSieh, 1994). The lower two events (events F–G, Grant andSieh [1994]) have poor age control and so are not consideredin this analysis. The timing of earthquakes B–E is bracketedby a total of four nondetrital radiocarbon ages (Ⓔ see Ta-bles A3 and A4 in the electronic edition of BSSA). In addi-tion, Grant and Sieh (1994) argue that the age of event Boccurred approximately contemporaneously with the forma-tion of a paleosol (their layer 8) that is disrupted by ground-fracturing associated with the event.

In our analysis of the BF site, we consider two scenariosfor the timing of earthquakes recorded in the area. In the firstscenario, referred to hereafter as scenario 1, we use the inter-pretation of Grant and Sieh (1994) in which event A is the1857 Fort Tejón event, the age of event B is represented bythe age of a paleosol that it disrupts, and the ages of eventsC–E are constrained by the additional nondetrital radio-carbon samples taken from the strata (Ⓔ see Tables A3and A4 in the electronic edition of BSSA). Finally, Grantand Sieh (1994) report that the timing of earthquake E is re-presented by a layer that is either cut by or draped into afissure created by this earthquake. Given this information,earthquake B bounds the ages of the earthquake that pre-ceded it (earthquakes C–E), and we use the additional radio-carbon ages to constrain the ages of the events. Unlike Grant

Table 1Summary Statistics for LY Layer Ages

LayerID

Mean PriorAge

Prior 95%Bounds

Mean PosteriorAge

Posterior 95%Bounds

W13 1197 1049–1278 1201.7 1053–1278W5 1432 1347–1477 1432.5 1404–1474

Table 2Summary Statistics for Earthquakes at LY Site

Earthquake ID Mean Age 95% Age Bounds

L1 1645 1438–1846L2 1356 1210–1442L3 1279 1116–1401

Table 3Summary Statistics of Recurrence Intervals at the LY Site

Recurrence Interval Mean Recurrence 95% Recurrence Bounds

L2–L1 289 49–543L3–L2 77 2–222


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and Sieh (1994), in both of our scenarios we take a moreconservative interpretation of the stratigraphic relationshipsthat constrain the timing of event E, and use the lowermostdisrupted dated unit that constrains its timing as a lower-bounding age of the event, rather than the age of the eventitself.

In a second scenario, referred to hereafter as scenario 2,we consider an alternate interpretation of the relationshipsthat constrain the timing of events B–E. As stated in the pre-ceding paragraph, Grant and Sieh (1994) assert that the ageof a paleosol layer (their layer 8;Ⓔ see Tables A3 and A4 inthe electronic edition of BSSA) represents the timing of eventB based on the supposition that paleosols at the site form inapproximately 20 yr. However, the use of paleosol formationas an absolute dating tool requires extensive local calibrationand analysis of systematic changes in soil chemistry overtime (e.g., Rockwell, 2000); neither of these were reportedfor this site. We analyze the sensitivity of the timing of earth-quakes at the site to a differing interpretation of this singlelayer by using the paleosol as a lower-bounding age for eventB, rather than a direct measure of the timing of the earth-quake. In this revised scenario, lower and upper boundson the timing of event B are constrained by the age of thepaleosol layer and the 1857 Fort Tejón event, respectively.

Summary statistics for layer ages are reported in Table 4.Considering scenario 1 (Fig. 4), our mean event ages forevents B–D (A.D. 1452, 1415, and 1378, respectively) (Ta-ble 5) agree with the range of A.D. 1405–1510, 1277–1510,and 1277–1510 reported for these events (Grant and Sieh,1994). However, our use of the lowermost dated stratumas a lower-bounding age of event E causes us to estimatea younger mean age of event E (A.D. 1293) relative to thepublished range of A.D. 1218–1275 (Grant and Sieh,1994). In any case, our 95% ranges in the estimate of thetiming of this event (Table 5) encompass the range estimatedby Grant and Sieh (1994). Our calculated mean recurrenceinterval RIs in this case are 400, 37, 37, and 85 for the eventintervals (from youngest to oldest event intervals) (Table 6).The youngest recurrence interval analyzed, which is con-strained by the age of the paleosol (layer 8), agrees well withthat of Grant and Sieh (1994) (350–450 yr); however, ourmean recurrence estimate (Table 6) systematically under-estimates that posited by Grant and Sieh (1994) (73, 73,and 146 yr). However, when considering the 95% boundson the recurrence intervals, our ranges agree well with thosereported by Grant and Sieh (1994) (Table 6).

Next, we considered scenario 2 (Fig. 4), which wasdesigned to test the sensitivity of earthquake ages and recur-rence intervals to interpretations of stratigraphic relation-ships at the site. When using the paleosol layer (layer 8)as a lower-bounding age for event B instead of its age,and bounding the upper age of the earthquake using the1857 Fort Tejón earthquake, all earthquake ages at the sitewere altered (Table 5). In particular, the mean earthquakeages for events B–D increased substantially to A.D. 16631559, and 1456. Only the lowermost event (event E) was re-latively unaffected by this change (Table 5). This resultedbecause independent radiocarbon samples define the agesof layers that bound this event, and so the timing of this pa-leoearthquake is relatively insensitive to the ages of the over-lying layers. Importantly, even the ranges in the earthquakes’timing are shifted to younger ages, emphasizing the potentialimpact that even a single interpretation within a trench’s stra-tigraphy may have on the inferred earthquake ages.

These large differences in earthquake ages also createsubstantial differences in the recurrence intervals betweenearthquakes at the site (Table 6). In particular, relative to sce-nario 1, the scenario 2 mean recurrence intervals are moreconstant through time, and range between 103–203 yr. None-theless, the ranges in the earthquake recurrence intervals arelarge (2–401 yr, depending on the recurrence interval consid-ered) (Table 6). Thus, these data imply either temporallyclustered earthquake behavior (e.g., scenario 1; Grant andSieh, 1994), or a fairly uniform recurrence (e.g., scenario 2),depending on the treatment of a single layer within the stra-tigraphy. Further excavations are ongoing at the BF site (J R.Arrowsmith, personal comm., 2006), and so in the future,more robust age control and tightly constrained stratigraphicmodels may shed light on the appropriateness of either ofthese two scenarios.

Frazier Mountain Site. The FM site (Lindvall et al., 2002)is located ∼80 km southeast of the BF Site (Fig. 1). The ex-cavations were located within a closed depression interpretedto result from a right step in the SAF (Lindvall et al., 2002).Units exposed at the site consist of bedded sand, silt, andclayey silt that form unbioturbated, laterally continuous unitsin the excavations (Lindvall et al., 2002). Shallow ground-water conditions at the site prohibit exposure and analysis ofunits below several meters. Therefore, only two paleoearth-quakes are recorded in the exposed strata, the youngest of

Table 4Summary Statistics for BF Layer Ages

LayerID

Mean PriorAge

Prior 95%Bounds

Mean PosteriorAge

Posterior 95%Bounds

150 1244 1162–1295 1245 1175–1290100 1345 1291–1391 1341 1290–13908 1462 1415–1608 1458 1415–1588

Table 5Summary Statistics for Earthquakes at BF Site

Scenario 1: Paleosol RepresentsEQ Age

Scenario 2: Paleosol Bounds EQAge

Earthquake ID Mean Age 95% Age Bounds Mean Age 95% Age Bounds

B 1452 1415–1502 1663 1456–1848C 1415 1338–1473 1559 1383–1788D 1378 1306–1443 1456 1321–1677E 1293 1217–1369 1300 1220–1373


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Figure4.


PDFs

fortheBidartFan(B

F)site.SeeFigure

3foran

explanationof

thefeatures

ofthis

figure.


which is interpreted to be the 1857 Fort Tejón event by Lind-vall et al. (2002). A total of eight samples, two of whichlikely had a detrital component, constrain the ages of layersin the area. In our analysis, we bracket both earthquake agesusing radiocarbon age determinations. The radiocarbon agesused to date layers in the FM excavation are reported in ⒺTable A5 in the electronic edition of BSSA, and the relation-ship between these layers and earthquakes that were reportedby Lindvall et al. (2002) are reported in Ⓔ Table A6 in theelectronic edition of BSSA. We use an upper bound for event1 of A.D. 1857 due to the fact that no earthquakes have beenhistorically observed in this area. Summary statistics forlayer-age PDFs are reported in Table 7.

The layer age, earthquake age, and recurrence intervalPDFs derived from our analysis are shown in Figure 5,and summary statistics for earthquake age and recurrenceare reported in Tables 8 and 9. Based on the ages and strati-graphy at the site, we estimate mean earthquake ages of A.D.1724 and 1513 for event 1 and event 2 (event notation afterLindvall et al. [2002]), respectively (Fig. 5; Table 8). Lind-vall et al. (2002) inferred that the stratigraphically highestearthquake (event 1) represents the 1857 Fort Tejón earth-quake. Our age range for this event (A.D. 1571–1851) is con-sistent with this conclusion; however, the poor age control inthis portion of the site precludes demonstration of this asso-ciation based solely on the radiocarbon age constraints. Ourmean earthquake age for event 2 lies near the reported maxi-mum probability reported by Lindvall et al. (2002) (A.D.1510), and our 95% limits of the earthquake age are similarto their reported 2σ age range for the event (A.D. 1460–1600). Using Lindvall et al. (2002)’s conclusion that themost recent event recorded at the site represents the 1857Fort Tejón earthquake, we calculate a mean RI of 344 yr, witha 95% range between 262 and 398 yr (Fig. 5; Table 9).

Pallett Creek Site. PC is located ∼110 km east–southeastalong the SAF from the FM site (Fig. 1). Excavations atthe site expose a >8-m-thick section of peat-rich and clasticsediments that constrain the timing of eight prehistoric events(Sieh, 1978b; Sieh et al., 1989). Rapid accumulation ofsediments at the site provides a near-continuous record ofdeposition, and recent entrenchment of PC has loweredthe water table in the area. This entrenchment has formeda ∼10-m-deep, 50–170-m-wide canyon within the older ter-race deposits (Sieh, 1978b). Radiocarbon samples collectedduring several periods of work (Ⓔ see Table A7 in the elec-tronic edition of BSSA) constrain many of the layer ages andresolve the values of peat accumulation rates at the site(Fig. 6) (Ⓔ see Table A8 in the electronic edition of BSSA).

Our analysis uses the radiocarbon ages, peat accumula-tion rates, and inferred stratigraphic relationships reported inBiasi et al. (2002) and Biasi and Weldon (1994). We chose touse the inferences of this previous work due to the fact thatwe have no direct experience with the sediments exposed atthe site, while several members participating in the Biasi et al.(2002) study have excellent knowledge of the stratigraphicrelationships at the site. Thus, we feel that the geologic re-lationships and radiocarbon ages reported in Biasi et al.(2002) provide an excellent basis for evaluation of event tim-ing at the site. As in the analysis of Biasi et al. (2002), weaccept the assertion that the stratigraphically youngest eventrecorded at the site represents the 1857 earthquake, and usethis event to limit the upper ages for layer and earthquakesrecorded at the site. The radiocarbon ages used to constrainlayer ages are reported in Ⓔ Table A7 in the electronic edi-tion of BSSA, and the stratigraphic relationships used to inferearthquake ages are reported inⒺ Table A8 in the electronicedition of BSSA. Summary statistics of layer-age PDFs arereported in Table 10.

Table 6Summary Statistics of Recurrence Intervals at the BF Site

Scenario 1: Paleosol Represents EQ Age Scenario 2: Paleosol Bounds EQ Age

Recurrence Interval Mean Recurrence 95% Recurrence Bounds Mean Recurrence 95% Recurrence Bounds

B–1857 400 255–441 203 9–401C–B 37 0–116 103 2–327D–C 37 0–116 103 2–326E–D 85 13–181 156 23–386

Table 7Summary Statistics for FM Layer Ages

Layer ID Mean Prior Age Prior 95% Bounds Mean Posterior Age Posterior 95% Bounds

FM9 1447 1399–1602 1428 1335–1467FM7 1511 1436–1624 1462 1434–1506FM5b 1495 1431–1619 1487 1446–1587FM5a 1555 1454–1645 1542 1472–1617FM4 1520 1438–1627 1591 1497–1636


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fortheFrazierMountain(FM)site.SeeFigure

3foran

explanationof

thefeatures

ofthis

figure.


The peat-rich layers exposed in the PC stratigraphyallow further constraints to be place on the layer and earth-quake ages. As discussed in Biasi and Weldon (1994), insome cases the accumulation of peat may occur at an ap-proximately constant rate, and so the thickness of peat layersmay be used to further refine the layer ages. However, asdocumented in our companion article, the supposition of Bia-si and Weldon (1994) that the peat ages provide a minimumamount of time that separates radiocarbon ages may stronglybias layers to older ages when all constraints are adhered tousing the MCMC simulation methods. In addition, at the PCsite, it appears that the accumulation rate of peat dramaticallychanges throughout the trench stratigraphy. To provide aninternally consistent means of using peat accumulation tobetter constrain layer ages, we developed a method that sam-ples selected points in the trench stratigraphy between which

peat accumulation rates remain approximately constant. Theintervening layer ages are then calculated based on ages ofsamples contained within them as well as the relative strati-graphic distance within each constant-accumulation-rate in-terval. While Biasi et al. (2002) also adjusted their peataccumulation rates throughout the stratigraphic column toaccommodate the nonuniform accumulation periods seenin Figure 6, a single value for accumulation rate for eachof their accumulation intervals was selected based on thedata. Our method uses the layer-age PDFs themselves to cal-culate the peat accumulation rates for each defined interval,and then uses these rates with the sample depth to calculatelayer and event ages recorded in the stratigraphy. This newanalysis method represents an important difference betweenour work and that of Biasi et al. (2002), who also evaluatedthe PC site using Bayesian methods.

Table 8Summary Statistics for Earthquakes at the FM Site


FM1 1724 1571–1851FM2 1514 1459–1601

Table 9Summary Statistics of Recurrence Intervals at the FM

Site


FM2–FM1 210 52–359

Calendar Year (yrs)

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tal P

eat

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ickn

ess

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0 P88uP81u

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P68l2

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P26Nl

P9Nc

Figure 6. The distribution of peat-bearing layer ages at the Pallett Creek (PC) site. Those layers labeled in bold were used to define thepeat accumulation rate for each interval as described in our companion article (Hilley and Young, 2008). Those layers lying within eachinterval spanned by the noted bounding layer ages are assumed to have formed under a constant peat accumulation rate. Note that there issignificant variation in the peat accumulation rate over time.


We show the relationship between peat thickness andsample ages for the PC site in Figure 6. Ages of peat layersare calculated by refining initial radiocarbon estimates oftheir ages using only stratigraphic ordering constraints (e.g., Biasi et al., 2002). Error bars show the 95% bounds ofthe peat layers. In this plot, intervals along which pointslie along a line of constant slope indicate that peat accumu-lation rates are approximately constant, while deviations inthis linear relationship document changes in peat accumula-tion rates through time. In this study, we define 11 intervalsover which we felt that peat accumulation rates could be re-garded as constant. The bounding layers to these intervals areshown in Figure 6 by the large hollow circles, and these layer

names are reported next to the symbols. These layers aresampled using the methods described in Hilley and Young,2008 to estimate peat accumulation rates and refine the in-tervening layer ages.

Finally, we emphasize that based on our previous ana-lysis of the WW site, layer, and earthquake age PDFs may besensitive to the supposition that peat accumulation rates re-main constant over a given interval (Hilley and Young,2008). In this article, we present layer and earthquake ageand recurrence interval PDFs for the case that peat accumula-tion is used to refine these estimates, as well as the case inwhich only relative stratigraphic ordering is used to constrainthese PDFs.

Table 10Summary Statistics for PC Layer Ages

Order-Only Constraints Used Peat Growth Used

Layer ID Mean Prior Age Prior 95% Bounds Mean Posterior Age Posterior 95% Bounds Mean Posterior Age Posterior 95% Bounds

P9Sl 82 �91–241 34 �122–135 9 �136–126P9Nc 263 �226–601 144 �47–363 88 �30–215P17u 124 �23–290 204 60–378 142 50–238P19c 324 87–603 300 156–503 214 102–307P26Nl 227 19–426 373 257–549 281 141–405P26Nm 650 639–658 648 638–657 651 642–658P26Nu 520 289–682 659 644–681 671 664–677P26Nu3 685 663–757 679 663–707 678 671–683P26Suu 691 603–800 696 671–736 685 678–690P26Nuu 733 691–773 719 691–763 695 688–700P31 714 565–881 740 699–792 701 695–707P33m 737 693–776 763 718–805 732 722–740P33u 652 449–862 785 735–845 745 733–755P33uu 725 683–768 811 793–856 758 745–770P36 600 388–844 850 799–893 794 754–845P38 996 725–1215 905 847–931 815 777–859P38u 817 733–876 930 923–938 842 800–880P41 834 691–1040 941 926–964 901 844–932P43 819 691–959 953 931–977 914 853–946P43u 748 417–1078 968 941–992 938 869–973P45u 945 716–1147 985 962–1011 952 877–990P47 1115 906–1580 1003 981–1026 979 891–1024P49 915 721–1129 1022 988–1092 1004 901–1057P51 1178 895–1410 1054 1006–1117 1136 1104–1156P53 1033 705–1260 1089 1031–1158 1160 1140–1175P59fl 1102 1045–1178 1127 1058–1180 1172 1156–1186P59fu 1192 1162–1217 1185 1162–1213 1184 1165–1199P59u 1086 909–1232 1207 1171–1242 1194 1176–1209P61ll 1168 908–1257 1234 1211–1257 1224 1209–1237P61l 1211 1028–1388 1261 1222–1306 1265 1253–1274P61 1341 1136–1575 1304 1248–1370 1295 1285–1303P61u 1349 1287–1412 1345 1297–1396 1345 1338–1351P61uu 1358 1310–1405 1371 1320–1406 1366 1359–1371P68ll 1403 1333–1421 1410 1400–1421 1406 1398–1413P68l2 1473 1263–1795 1458 1408–1546 1492 1411–1619P68u2 1442 1226–1756 1508 1427–1602 1511 1441–1623P68u3 1588 1460–1799 1583 1484–1778 1527 1464–1626P68uu 1590 1469–1880 1639 1503–1785 1620 1603–1644P75 1647 1545–1660 1786 1781–1792 1648 1637–1658P77 1548 1436–1664 1793 1784–1806 1693 1679–1710P81m 1771 1532–1945 1812 1789–1847 1745 1719–1773P81u 1788 1669–1945 1837 1798–1855 1768 1736–1802P88u 1827 1696–1923 1846 1817–1856 1830 1812–1854


Layer and earthquake age PDFs and recurrence intervalPDFs are shown in Figure 7 for cases in which we considerpeat accumulation with relative stratigraphic ordering andstratigraphic ordering only, respectively. We report the sum-mary statistics for earthquake ages and recurrence intervalsin Tables 11 and 12, respectively. In addition, we show theearthquake age and recurrence interval PDFs from Biasi et al.(2002) in Tables 11 and 12 to provide a comparison betweenour different methods. When considering the uncertaintiesreported in our study and those of Biasi et al. (2002), wefind broad agreement between our two estimates with somenoteworthy exceptions. First, mean earthquake ages appearto differ by up to ∼115 years. However, there is no consistentover- or underestimation of mean earthquake ages whencomparing one method to the other. The most striking differ-ences between mean ages occur for events V and F whenonly ordering constraints are used to estimate earthquakeages. We suspect that these discrepancies arise from the dis-cretization of time intervals into 5-yr bins by Biasi et al.(2002) (versus 1-yr bins used in this study), the use of up-dated radiocarbon calibration data used herein, and the factthat we use simulation rather than explicit evaluationof Bayes’s rule to estimate the earthquake age PDFs (e.g.,

Hilley and Young, 2008). When considering the 95% boundson estimated earthquake ages, our results appear consistent.

Similar to the mean earthquake ages, mean recurrenceintervals may differ by up to ∼148 years between our methodand that of Biasi et al. (2002). In addition, there does notappear to be a consistent bias when comparing the resultsof the two methods (Table 12). Considering the 95% boundsreported by our study and Biasi et al. (2002), these two meth-ods are in broad agreement. For the case that we considerpeat accumulation and stratigraphic ordering, use the 1857earthquake as an upper-bounding earthquake age, and notethat there are nine chronicled earthquakes prior to the 1857event, we estimate a mean recurrence interval of 132 yr atthe site with 95% bounds on this interval between 131and 133 yr.

Wrightwood Site. The WW paleoseismic site is located∼23:5 km from the PC site east–southeast along the SAF(Fig. 1). This site was used to evaluate our Bayesian refine-ment methods and to compare them to other methodsemployed in the past (Hilley and Young, 2008). Our compa-nion article contains a description of the site, the joint poster-ior PDFs, and a lengthy comparison of our results with thoseof Biasi et al. (2002), and so we refer the reader to this pre-

Table 11Summary Statistics for Earthquakes at the PC Site

Peat Growth Used* Order-Only Constraints Used* Peat Growth Used† Order-Only Constraints Used†

Earthquake ID Mean Age 95% Age Bounds Mean Age 95% Age Bounds Mean Age 95% Age Bounds Mean Age 95% Age Bounds

X 1978 1756–1838 1842 1804–1855 1804 1758–1837 1799 1746–1836V 1596 1541–1641 1713 1571–1788 1562 1496–1599 1600 1508–1641T 1373 1366–1379 1391 1338–1414 1360 1343–1370 1381 1331–1410R 1158 1132–1181 1108 1044–1169 1084 1046–1113 1110 1041–1165N 1143 1122–1165 1071 1020–1134 1067 1031–1096 1075 1014–1137I 896 811–984 994 971–1019 956 914–986 972 914–1003F 838 792–897 936 924–954 842 803–868 827 788–860D 759 742–786 830 795–877 764 749–775 760 713–799C 671 664–677 669 650–694 645 614–666 647 610–674

*This study.†Biasi et al. (2002).

Table 12Summary Statistics of Recurrence Intervals at the PC Site


RecurrenceInterval

MeanRecurrence

95% RecurrenceBounds

MeanRecurrence


MeanRecurrence


MeanRecurrence


X–1857 57 17–100 161 116–213 53 15–94 58 16–106V–X 180 133–223 129 50–260 242 176–314 198 121–299T–V 248 228–272 322 185–409 202 134–243 220 115–290R–T 205 183–232 283 222–349 276 240–311 270 193–346N–R 12 0–33 37 1–104 27 10–63 54 10–122I–N 191 144–266 77 25–141 111 61–160 103 30–182F–I 92 31–149 59 32–86 114 60–162 145 78–195D–F 102 53–142 105 56–145 79 37–108 68 15–121C–D 98 77–119 161 116–213 119 90–146 112 58–163



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Figure7.


PDFs

forthe

PallettCreek

(PC)site,using

bothpeataccumulationandlayer-ordering

constraints(thick

solid

lines)and

usingonlylayer-ordering

constraints(thinsolid

lines).SeeFigure

3forfurtherexplanationof

thefeatures

ofthis

figure.

(Contin

ued)


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vious work for a complete exposition of the evaluation of theWW site. For completeness, in this article we present thelayer and earthquake age PDFs and recurrence interval PDFsin a form similar to the other sites analyzed in this study. Theform of these PDFs differs from that presented in Hilley andYoung, 2008 in that our previous work normalized the PDFsto the maximum yearly probability to facilitate comparisonwith the results of Biasi et al. (2002), rather than normalizingto ensure unit area as we have done in this study.

Layer and earthquake age PDFs and recurrence intervalPDFs calculated using both peat accumulation and strati-graphic ordering constraints, as well as the case when onlystratigraphic ordering was used to refine these PDFs, areshown in Figure 8. The radiocarbon samples used to calcu-late layer ages are presented inⒺ Table A9 in the electronicedition of BSSA, the stratigraphic relationships that define theearthquakes are shown inⒺ Table A10 in the electronic edi-tion of BSSA, and the layer ages used to define constant peataccumulation rates are noted in figure 3 of Hilley and Young,2008. Layer-age summary statistics are reported in Table 13.Summary statistics for earthquake ages and recurrence inter-vals are reported in Tables 14 and 15, respectively. Again, fora complete discussion of the layer and earthquake ages, thereader is referred to Hilley and Young, 2008. As discussed inHilley and Young, 2008, layer and earthquake ages are con-sistent between our methods and those of Biasi et al. (2002),

with important exceptions towards the tops of the strati-graphic column. In addition, our uncertainties in earthquaketiming tend to be smaller than those of Biasi et al. (2002),and this results in a slightly smaller range in the recurrenceinterval PDFs (Fig. 8; Table 15).

Pitman Canyon Site. Pit is located ∼25 km southeast of theWW paleoseismic site along the SAF and ∼10 km north ofSan Bernardino, California (Seitz et al., 2000; Fig. 1). Herea >7 m section of gravels, sands, and peats is disrupted bythe SAF. The fault zone consists of ∼10 m long, an echelon,left-stepping patches (Seitz et al., 2000). Interbedded peatlayers provide in situ estimates of layer ages at the sitesand reported peat thicknesses and accumulation rates; thesepeats allow further refinement of layer, event, and recurrencePDFs at the site. Unfortunately, Seitz et al. (2000) did notreport peat thickness data in their study, and so we matchedtheir tabulated calendar year ages (their table 1) with the ca-lendar years reported on their plot of peat thickness versuscalendar year age (their figure 3) to reconstruct this informa-tion. This process likely produced some error, as the numberof reported calendar year ages in their figure 3 does notmatch the total number of dated strata in their study. Our re-constructed peat thickness and ordered layer-age estimatesfor the site are shown in Figure 9. Importantly, there wereseveral layers for which peat thickness is not reported in

Table 13Summary Statistics for WW Layer Ages



W97 263 120–398 217 117–313 237 133–353W100a 294 163–389 288 189–371 293 234–371W100b 307 146–425 342 259–427 369 278–436W100c 723 548–975 620 539–680 565 522–608W105 748 664–884 680 651–721 712 665–762W105d 737 664–863 698 667–747 719 677–764W110a 724 666–797 717 678–760 727 684–766W110b 720 661–805 735 688–770 742 691–773W110c 720 661–805 758 709–806 749 693–779W110d 822 700–948 810 759–881 757 695–796W115 892 731–1097 847 780–945 915 779–1011W120a 858 689–994 891 803–986 961 878–1018W120b 919 770–1144 936 827–1022 976 908–1021W120c 974 781–1148 985 892–1039 991 937–1034W122 1063 904–1203 1028 969–1114 1014 977–1076W125a 1051 995–1154 1062 1003–1147 1030 1001–1107W125b 1122 1025–1259 1122 1029–1210 1060 1024–1169W125c 1177 1044–1273 1211 1107–1276 1234 1207–1272W130L 1352 1297–1415 1340 1294–1400 1321 1290–1358W130 1398 1301–1612 1380 1315–1460 1356 1312–1578W130u 1449 1334–1613 1439 1402–1520 1441 1409–1602W135a 1533 1430–1640 1498 1436–1606 1477 1450–1612W135b 1548 1444–1633 1558 1478–1631 1513 1489–1621W135d 1593 1489–1796 1613 1523–1666 1561 1539–1635W135e 1774 1536–1943 1705 1543–1782 1597 1575–1645W135f 1606 1495–1790 1784 1744–1798 1645 1621–1666W135g 1811 1675–1943 1801 1767–1811 1693 1663–1718


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the Seitz et al. (2000) study including the uppermost layer(unlabeled; sample T1-1), and the stratigraphic unit labeled“below 30” (sample S-34-T6). These layer ages were calcu-lated by using the ages of the surrounding peat layers to es-timate the layers’ ages using only stratigraphic ordering.Thus, we used a hybrid of the peat accumulation and strati-graphic ordering methods at this particular site due to a lackof information about the trench stratigraphy. In addition, thesporadic nature of peat deposition at the PC site made it dif-ficult for us to be convinced that peat deposition was constantthroughout the exposed stratigraphy (Fig. 9). This stands incontrast to the analysis of Seitz et al. (2000), in which peatdeposition rates were assumed constant between the 10upper unit and unit 33. For this reason, in our analysis, onlytwo strata (layers 16 and 20) were actually refined by the peataccumulation constraints (Fig. 9).

A total of six events were recorded within the strata atthe site, whose ages range from A.D. >900 to the present

(Seitz et al., 2000). The most recent event recorded at thesite appears to be the 1812 rupture also seen at the WWand PC sites to the northwest. In our calculations, we use thisearthquake as a maximum age constraint to refine the ages ofunderlying layers. Radiocarbon ages used to determine layerages at the site are reported inⒺ Table A11 in the electronicedition of BSSA, whereas statigraphic relationships used torefine these layer ages and infer earthquake and recurrencePDFs are reported inⒺ Table A12 in the electronic edition ofBSSA. PDFs for layer and event ages and recurrence intervalsare reported for the case that peat accumulation and orderingconstraints were used and for the case that only ordering con-straints were used (Fig. 10). Summary statistics for layer-agePDFs, earthquake age PDFs, and recurrence intervals are re-ported in Tables 16, 17, and 18, respectively. Comparisonsbetween the results of our analysis and those of Seitz et al.(2000) are complicated by the fact that they do not reportmean earthquake ages or ranges. Our mean event age esti-

Table 14Summary Statistics for Earthquakes at the WW Site


Earthquake ID Mean Age 95% Age Bounds Mean Age 95% Age Bounds Mean Age 95% Age Bounds Mean Age 95% Age Bounds

W3 1659 1633–1681 1793 1755–1808 1685 1647–1717 1665 1616–1796W4 1527 1502–1625 1585 1500–1648 1536 1508–1569 1569 1482–1632W5 1453 1423–1605 1469 1416–1574 1487 1448–1518 1490 1409–1546W6 1277 1250–1308 1275 1174–1367 1263 1191–1305 1264 1158–1355W7 1045 1014–1138 1092 1018–1178 1116 1047–1181 1090 1016–1194W8 995 943–1042 982 870–1075 1016 957–1056 979 864–1083W9 915 779–1011 855 782–956 850 800–881 855 768–944W10 757 695–796 798 735–880 781 736–811 812 731–894W11 734 689–770 726 683–764 722 695–740 729 687–758W12 719 677–764 699 664–746 697 657–722 728 664–743W13 663 622–706 652 574–700 634 551–681 697 565–704W14 565 522–608 497 320–659 534 407–628 529 329–676


Table 15Summary Statistics of Recurrence Intervals at the WW Site


RecurrenceInterval

MeanRecurrence


MeanRecurrence


MeanRecurrence


MeanRecurrence


W3–1812 153 130–178 19.3 6–341 130 88–158 109 10–189W4–W3 132 37–158 207.3 135–293 150 98–188 146 31–266W5–W4 74 21–89 116.6 27–203 49 10–89 102 12–191W6–W5 175 142–315 193.5 87–333 224 159–294 193 83–319W7–W6 233 143–279 183.0 56–310 148 49–226 175 39–290W8–W7 50 6–116 110.0 20–241 101 16–186 126 12–264W9–W8 80 10–185 127.7 36–227 165 94–226 137 15–261W10–W9 158 13–278 56.7 2–157 70 13–118 72 10–168W11–W10 23 0–59 72.4 14–157 60 12–96 79 10–172W12–W11 15 0–39 27.1 27–203 31 10–63 36 10–75W13–W12 57 41–72 46.7 4–129 65 10–140 60 10–143W14–W13 98 70–132 155.1 6–341 110 10–231 153 10–329



mates (Table 18) agree well with the range we might quali-tatively infer from the results presented in Seitz et al. (2000)with two important exceptions. First, the PDFs presented bySeitz et al. (2000) for earthquakes Pit-3 and Pit-4 (their Ev-3and Ev-4) are significantly younger than those we deter-mined (Fig. 10) for both peat accumulation and order-onlyscenarios. This arises from the assertion by Seitz et al. (2000)that peat accumulation rates throughout the trench strati-graphy have been uniform; the ages that bound these earth-quakes (units 16, 20, and 30) are clearly older than would beexpected by using a constant average peat accumulation rate.Thus, the imposition of a constant peat accumulation ratewhere this may be unwarranted forces these earthquake agesto be systematically younger than they actually may be.Mean recurrence intervals vary between 45 and 345 yr atthe site. If we take the uppermost earthquake recorded atthe site to be the 1812 earthquake, the mean recurrence inter-val and 95% bounds are 134 yr (115–155 yr) for the case thatpeat accumulation is considered and 136 yr (113–159 yr)when only ordering constraints are used. These results areon the order of the 144 yr RI estimated by Seitz et al. (2000).

Plunge Creek Site. The Plunge site is located ∼29 kmsoutheast of Pit along the SAF (Fig. 1; McGill et al.,

2002). In the area, the geometry of the SAF is complexand consists of a number of subparallel splays that takeup varying amounts of the fault-generated displacement. Un-fortunately, two strands of the SAF are located to the north-east of the Plunge site in steep terrain that rarely preservesstrata that may be used to document paleoearthquakes(McGill et al., 2002). At the site, nine trenches perpendicularto the San Bernardino strand of the SAF expose gravels, col-luvium, and sand deposits that are locally bioturbated. Twoground-rupturing events are observed within the excavationsat the site (labeled by McGill et al., 2002, as events W and Rfor the youngest and oldest earthquake, respectively). Detri-tal charcoal was recovered from a number of the trenches,and from analyses of these samples, local ecology, and firehistory, McGill et al. (2002) estimate that sample ages maybe between 0–140 yr older than the layers in which they arecontained due to the time radiocarbon may have spent intransport to the ultimate site of deposition. No historic infor-mation exists here that provides an upper bound on layer orearthquake ages.

While detrital carbon was recovered from four of thenine trenches, uncertainties in the correlation of units be-tween trenches and an incomplete record of both earthquakesin all but one of these trenches forced us to limit our analysis

Figure 9. The distribution of peat-bearing layer ages at the Pitman Canyon (Pit) site. Those layers labeled in bold were used to define thepeat accumulation rate for each interval as described in our companion article (Hilley and Young, 2008). Those layers lying within eachinterval spanned by the noted bounding layer ages are assumed to have formed under a constant peat accumulation rate. The irregular peataccumulation rate seen in this figure forced us to define five intervals over which peat accumulation was deemed constant. This left only twolayer ages to be refined using the peat accumulation process described in Hilley and Young, 2008.


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to ages collected within only one of the trenches (trench 7,McGill et al., 2002). We used the 11 radiocarbon samplesrecovered from this trench, the knowledge of the range ofpossible lag times between radiocarbon formation and de-position characterized by detrital times, and the reportedstratigraphic ordering of samples to determine the timingof earthquakes W and R at the site.

At this particular site, we address the possibility that det-rital radiocarbon ages might cause layers to appear older thanthe age provided by radiocarbon measurements. We incorpo-rate the time lag caused by such detrital samples into ouranalysis by adjusting the calibrated radiocarbon age PDFsto account for these lags. Specifically, we assume that thelag between formation of the radiocarbon sample and its de-position is between 0–140 yr, as reported by McGill et al.(2002). For simplicity, we further assume that each lag timeis equally likely to have occurred. Thus, we adjusted the cali-brated calendar year PDFs of the potentially detrital samples

by lagging the entire PDF forward in time, summing each ofthese lagged distributions for lag values between 0–140 yr,and renormalizing the summed distribution to unit area. Theresulting layer-age PDF thus represents the combination ofall possible lags of each detrital radiocarbon sample’s PDF.

We report the radiocarbon ages used in our analysis (Ⓔsee Table A13 in the electronic edition of BSSA), and thestratigraphic ordering constraints (Ⓔ see Table A14 in theelectronic edition of BSSA) used to compute layer age andearthquake, and recurrence interval PDFs for the site (Fig. 11).Summary statistics for the layer-age, earthquake age, andrecurrence interval PDFs are provided in Tables 19, 20,and 21, respectively. Our mean earthquake ages for eventsW and R compare well with those reported for trench 7by McGill et al. (2002), in which they estimated these earth-quakes to have occurred around A.D. 1529 and 1420, respec-tively. Our ordered estimates generally produced narrower95% bounds than those reported by McGill et al. (2002),

Table 16Summary Statistics for Pit Layer Ages



40 727 609–877 702 489–850 714 622–84535 820 690–962 832 696–966 837 710–96733 1091 984–1207 1072 953–1187 1103 1000–120830 1171 1031–1287 1190 1068–1281 1179 1108–125420 1375 1302–1446 1341 1297–1414 1351 1299–142116 1367 1295–1446 1384 1318–1437 1401 1328–144014 1411 1307–1601 1430 1346–1498 1410 1330–1455

10lower 1717 1512–1942 1622 1491–1761 1638 1511–1770? 1770 1567–1944 1725 1645–1793 1731 1647–1795

10upper 1720 1525–1943 1779 1727–1807 1776 1676–1808

Table 17Summary Statistics for Earthquakes at the Pit Site

Peat Growth Used Order-Only Constraints Used

Earthquake ID Mean Age 95% Age Bounds Mean Age 95% Age Bounds

Pit-2 1754 1663–1801 1752 1665–1799Pit-3 1405 1329–1448 1407 1333–1469Pit-4 1376 1314–1429 1363 1307–1424Pit-5 1265 1149–1380 1265 1134–1368Pit-6 1141 1035–1236 1131 1016–1245

Table 18Summary Statistics of Recurrence Intervals at the Pit Site

Peat Growth Used Order-Only Constraints Used

Recurrence Interval Mean Recurrence 95% Recurrence Bounds Mean Recurrence 95% Recurrence Bounds

Pit-2–1812 58 10–148 60 12–146Pit-3–Pit-2 348 249–446 345 246–429Pit-4–Pit-3 30 0–93 45 3–112Pit-5–Pit-4 111 14–238 97 11–233Pit-6–Pit-5 124 21–274 135 21–283


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despite the treatment of detrital radiocarbon ages in thisstudy. McGill et al. (2002) present a range of possibilitiesfor recurrence intervals based on various correlations ofearthquakes between trenches at the site, and because weonly computed recurrence interval PDFs for one of these,we cannot directly compare our results with theirs. However,our mean recurrence interval of 106 yr (23–230 yr within95% bounds) agrees favorably with the value of ∼150 yr re-ported by McGill et al. (2002) for one of their proposed cor-relation scenarios.

Mission Creek Site. The final site we investigated is the MCsite, located ∼85 km southeast of the Plunge site (Fig. 1).Here, seven trenches excavated parallel to the fault expose <3 m of material consisting of gravel, silty sand, and clayinterbedded with rich organic layers (Fumal, Reymer, et al.,2002). The organic layers consist of up to 20-cm-thick finecharcoal horizons, which are interpreted as local fires withinthe area (Fumal, Reymer, et al., 2002). Unfortunately, someof the samples dated at the site appear to have a significantdetrital component, and so Fumal, Reymer, et al. (2002) se-lected a total of 25 samples that appear most likely to providereliable ages of the strata in which they were contained.Based on their interpretation of crosscutting relationshipsin the seven trenches, Fumal, Reymer, et al. (2002) inter-preted five ground-rupturing events that occurred at the site.There is no reliable evidence of historic rupture in the areathat serves to bracket the upper age of the layers and events inthe area, although Fumal, Reymer, et al. (2002) argued thatan event recorded in Indio, occurring around A.D. 1636� 30

possibly corresponds to the youngest event at the MC site. Inour analysis, we take a more conservative approach and donot rely on the assertion that A.D. ∼1636� 30 was the sameas the youngest earthquake recorded at the site (TP-1, whichwas not treated in this analysis due to lack of age control).

We used those samples designated as the least likely tobe detrital (Ⓔ see Table A15 in the electronic edition ofBSSA) and the stratigraphic relationships observed at the site(Ⓔ see Table A16 in the electronic edition of BSSA) to cal-culate the layer and earthquake age, and recurrence intervalPDFs (Fig. 12). Summary statistics for layers, earthquakesand recurrence intervals for this site are reported in Tables 22,23, and 24, respectively. With the exception of the uppermostearthquake recorded in the stratigraphy (TP-2), our earth-quake ages agree well with those presented by Fumal, Rey-mer, et al. (2002a). The TP-2 earthquake in our analysis hasbeen shifted to systematically younger ages due to the factthat we did not use the upper-bounding age constraint of1636� 30 B.P. for the age of the youngest earthquake re-corded at the site, as discussed previously. When consideringthe 95% bounds of our estimate of the age of TP-2 and theirs,we find general agreement between these two values. Ourrecurrence interval estimates for the events analyzed lie be-tween 187–340 yr. Considering the four earthquakes ana-lyzed in this study, the average recurrence intervalbetween events TP-5 and TP-2 lies between 214–302 yr, witha mean value of 255 yr (Table 24).

Correlation of Events between Paleoseismic Sites

We compared the earthquake age PDFs between paleo-seismic sites to identify those earthquakes recorded at a vari-ety of sites that may be contemporaneous. The timing ofearthquakes along the length of the central and southernSAF is shown in Figure 13. The x axis of this plot showsthe distance southeast along the SAF from PF, while the yaxis scales the time of observed earthquakes at the site. Inthis figure, we denote the yearly probability of 0.01 for eachPDF as a solid, vertical line, and so peak values of an earth-quake age PDF that lie close to the site location denote thoseearthquakes whose timing is poorly constrained.

The strength of correlations of earthquakes betweensites is measured by two sets of uncertainties: (1) uncertain-ties associated with known errors in radiocarbon measure-ments and the distribution of datable material in eachexcavation, and (2) uncertainties that stem from differentviable stratigraphic models of the record of ancient earth-quakes at each site. Our Bayesian methods well characterizethe former source of uncertainty. To gauge the strength of thecorrelation of earthquakes between sites based on the uncer-tainty of earthquake ages, we show the mean event overlapand weighted range overlap statistics (described previously)for earthquakes at adjacent sites with the best possible cor-relation as percentages denoted in bold and regular type,

Table 19Summary Statistics for Plunge Layer Ages

LayerID

Mean PriorAge

Prior 95%Bounds

Mean PosteriorAge

Posterior 95%Bounds

E 1395 1270–1511 1386 1269–1497F 1590 1451–1741 1493 1424–1571G 1558 1378–1731 1529 1456–1608Ch 1602 1474–1738 1563 1491–1643J 1500 1352–1688 1594 1520–1701K 1628 1473–1859 1658 1562–1783N 1786 1555–2038 1759 1626–1904P 1867 1683–2047 1869 1735–1994Q 1880 1704–2047 1968 1833–2007

Table 20Summary Statistics for Earthquakes at the Plunge Site


W 1546 1474–1625R 1440 1325–1531

Table 21Summary Statistics of Recurrence Intervals

at the Plunge Site


R–W 106 23–230


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respectively, in Figure 13. To quantify the uncertaintiesassociated with different stratigraphic interpretations andmodels at each of the sites, we show a series of between-siteearthquake correlations that reveal the impact of different in-terpretations of the stratigraphy at the BF site and use of dif-ferent geologic information (i.e., peat growth versus order-only information) when computing earthquake age PDFs.

First, we see that the duration of the earthquake record isfar longer in the southern portion of the study area than thenorth. This results in the fact that earthquakes are more easilycorrelated from site to site in the south relative to the north. Infact, a maximum of three paleoearthquakes may be corre-lated in the north, while the south may record as many asten correlative paleoearthquakes. However, even in thesouthern study area at the most complete, longest, and high-est-resolution paleoseismic sites (i.e., PC and WW), we seethat there are earthquakes recorded at each site that are notimaged at the other and cannot be matched with other paleo-earthquakes recorded to the south. In some cases, relativelylarge uncertainties complicate the correlation of paleoearth-quakes from site to site, leading to a number of plausiblecorrelations that may be made based on the paleoseismic re-

cord. Importantly, the uncertainties in stratigraphic interpre-tation and depositional model (order only versus peataccumulation) play an important role in the correlation ofearthquakes between sites (Fig. 13). For example, in the casethat a single layer age is reinterpreted at the BF site (scenarios1 and 3 versus scenarios 2 and 4), paleoearthquake correla-tions between this site and the adjacent LY and FM siteschange as well. The effect of this uncertainty is also clearlyseen at the PC and WW sites by comparing correlations inwhich peat accumulation is considered as a constraint onpaleoearthquake timing (scenarios 1 and 2; Fig. 13) versuscorrelations that consider only stratigraphic ordering con-straints (scenarios 3 and 4; Fig. 13). In each of these cases,changes in how we interpret the prior geologic informationcan affect correlation of events with the adjacent sites andimpact the correlation metrics used to guide site-to-sitecorrelations.

Given the large uncertainties in correlation that we ob-serve, we focus the remainder of our description of the re-sults on only the robust features observed in all scenariosexplored in Figure 13. First, a paleoearthquake may be re-corded at the LYand BF sites around A.D. 1250 (purple event,Fig. 13). The younger earthquake recorded at LY may cor-relate with either the second- or third-oldest earthquake re-corded at BF, depending on the interpretation of the trench

Table 22Summary Statistics for MC Layer Ages

Layer ID Mean Prior Age Prior 95% Bounds Mean Posterior Age Posterior 95% Bounds

I 371 257–518 363 253–510IIa 815 691–954 739 678–813IIb 864 733–972 791 721–848IIc 836 713–956 816 746–871IId 819 704–936 838 785–888IIe 819 695–951 863 803–941IIf 808 691–943 899 832–974IIIa 1111 1027–1210 1080 1022–1163IIIb 980 709–1230 1137 1045–1216IIIc 1217 1160–1266 1210 1132–1257IIId 1234 1134–1283 1248 1195–1283

IIIe-lower 1316 1223–1394 1303 1244–1382IIIe-upper 1354 1297–1418 1358 1299–1413

IVa 1407 1320–1465 1416 1336–1449IVb 1505 1409–1626 1462 1416–1517IVd 1522 1426–1633 1502 1444–1604IVe 1572 1485–1654 1550 1488–1631Va 1561 1460–1650 1589 1517–1648Vb 1570 1454–1778 1666 1551–1798

Table 23Summary Statistics for Earthquakes at the MC Site

Earthquake IDMeanAge* 95% Age Bounds *

MeanAge† 95%Age Bounds†

TP-2 1569 1502–1638 1502 1450–1555TP-3 1229 1170–1271 1231 1170–1290TP-4 990 874–1111 982 840–1150TP-5 803 733–859 825 770–890

*This study.†Fumal, Reymer, et al. (2002).

Table 24Summary Statistics of Recurrence Intervals at the MC Site


TP-3–TP-2 340 259–431TP-4–TP-3 239 108–365TP-5–TP-4 187 67–318


stratigraphy. None of the earthquakes observed at LY, BF, orFM could be reliably correlated (i.e., had high mean eventoverlap and weighted mean overlap values) to the southernSAF, although the 1857 FT earthquake ruptured from PFthrough the WW site. In many cases, earthquakes betweenPC and WW were difficult to correlate, despite the likelycomplete and high-resolution paleoseismic record containedat the sites. When considering the PC, WW, and Pit sites, noearthquakes could be found to be correlative between all siteswhen considering all scenarios (Fig. 13). This is in part dueto the fact that as earthquake age PDFs become narrower, the

strictness that our correlation parameters demand increases.When viewing all scenarios, an earthquake around A.D. 1550appeared to rupture the WW, Plunge, and MC sites (Fig. 13),although no evidence for this event is found at the Pit site.Thus, either the earthquake record at Pit is incomplete, or twoseparate ruptures occurred approximately coevally with oneanother. The fact that in all scenarios analyzed, the northern-most rupture is not recorded at PC (and hence the rupturelength was necessarily exceedingly small) raises doubt thatthese data record two distinct ruptures. In addition, the lastfour paleoearthquakes recorded at the MC site are associated

Figure 13. Correlation of the timing of paleoearthquakes along the length of the central and southern SAF. The x axis shows the distancesoutheast of Parkfield along the SAF, the y axis denotes the time of paleoearthquakes, and each of the PDFs is scaled such that the yearlyprobability of 0.01 is metered by the vertical line to the right of the base of the PDFs. The mean event overlap and weighted range overlap ofearthquakes at adjacent sites are reported as percentages denoted in regular and bold type, respectively. Each of the panels in this figuredenotes differing combinations of site interpretations and usage of a priori information. (a) and (c) show the case in which the paleosol at theBF site represents the age of the penultimate earthquake, while (b) and (d) show the effect of relaxing this assumption on earthquake ages andcorrelations. Likewise, panels (a) and (b) show the case in which peat accumulation is used as an additional constraint to refine the timing ofearthquakes at the PC, WW, and Pit sites, while (c) and (d) show the effect of using only layer ordering on earthquake timing and site-to-sitecorrelation. (Continued)


with contemporaneous rupture events located at Pit, and insome cases, as far as PC, depending on the scenario consid-ered (Fig. 13). Finally, there are many earthquakes recordedin the older portions of the WW stratigraphy that have nocorresponding event at the PC site.

If we assume that earthquake record is complete at eachof the sites, we see that earthquake ruptures do not appear toinitiate and terminate at fixed points along the SAF as mightbe expected for a segmented fault, whose reaches undergoregular patterns of rupture. Rather, our results paint an ad-mittedly impressionistic picture of rupture timing in whichearthquakes may begin and terminate more or less randomlyin space (Fig. 13). The supposition that a complete earth-quake record exists at each site is undoubtedly incorrect:a partial record of paleoearthquakes likely exists at most,

if not all of the sites. Nonetheless, estimates of earthquaketiming and correlation shown in Figure 13 represent the stateof knowledge of earthquakes along the central and southernSAF, deduced using the state-of-the-art methods developed aspart of this study.

Discussion

This work presents the first statistical evaluation of thetiming and correlation of paleoearthquakes along the centraland southern SAF that analyzes all of the published paleo-seismic sites in a uniform manner. As such, the results repre-sent our most up-to-date view of the paleoseismic historyalong this well-characterized portion of the SAF. It is worthnoting that the relatively high density and the presence of

Figure 13. Continued.


some sites with long earthquake records makes this area anideal place to quantitatively test some of the proposed modelsof rupture behavior for the SAF. While we do not attemptthese types of tests in this study, our results can be usedas direct inputs for such tests, which might be carried outby future studies. In addition, our probabilistic estimatesof earthquake timing and recurrence may be used to improveprobabalistic seismic hazard assessments (PSHA). We envi-sion that similar methods might be applied to other at-riskareas, such as the San Francisco Bay area, once the resultsof the regional-scale Bay Area paleoearthquake experimentproject’s paleoseismic excavations begin to emerge in theliterature.

While our study provides some estimates of the timingand recurrence of specific paleoearthquakes along the centraland southern SAF, perhaps a more interesting aspect of ourwork is the assessment uncertainty in the paleoseismic re-cord. When uncertainties that we could quantify are consid-ered, site-to-site correlation of paleoearthquakes becomestenuous. This situation might be improved by using addi-tional prior information to link ruptures between sites. Forexample, simultaneous consideration of the timing and sur-face offset magnitudes between sites should help to link rup-tures between sites (Biasi et al., 2003), providing a clearerpicture of the temporal and spatial distribution of paleo-seismic ruptures. However, slip-per-event offsets are notori-ously difficult to obtain in the paleoseismic record (e.g.,Weldon et al., 2002), and are absent for all but the most re-cent events in most of the sites studied here.

The large potential uncertainties in the timing and recur-rence of ancient earthquakes found as part of this study makeevaluation of different models of rupture recurrence difficultto test. This raises the question of whether or not the fidelityof the paleoseismic record is sufficient to test such models,especially in cases such as the central and southern SAFwhere earthquake recurrence times are relatively short.Qualitatively, we might expect that as dating uncertaintiesdecrease relative to recurrence times, the fidelity of the paleo-seismic record may be sufficient to test recurrence models.Thus, we believe that similar studies that investigate how thefidelity of the paleoseismic record is affected by earthquakerecurrence time, the rate of deposition of dated strata in ex-cavations, and uncertainties in the radiocarbon dating pro-cess may be timely.

Finally, our results highlight the fact that the density ofpaleoseismic sites is far greater along the southern half of theSAF than along the northern half (Fig. 13). Those sites in thenorth that have been studied also have a relatively shortpaleoseismic record. From our personal experience (Younget al., 2002), sites in these areas may be difficult to find andinterpret, and extensive bioturbation at the sites often ob-scures the paleoseismic record. Nonetheless, our resultshighlight the need to increase the density and quality ofpaleoseismic sites between PF and PC in order to link rup-tures from the central SAF to those to the south.

Conclusions

We report the results of a statistical evaluation of thetiming and recurrence of paleoearthquakes along the centraland southern SAF. We used Bayesian methods to characterizeuncertainties in earthquake timing and recurrence in the areathat arise from intrinsic dating uncertainties and varyinginterpretations of crosscutting relationships exposed inpaleoseismic excavations. We found that correlation ofevents between sites located along the northern SAF werecomplicated by the fact that earthquake records were typi-cally quite short and the spatial density of sites was relativelylow. Along the southern SAF, earthquakes could, in somecases, be correlated from site to site. However, betweenthe two highest quality sites with the longest earthquake re-cords (PC and WW), correlation of earthquakes appeared sen-sitive to the way in which geologic information was used toimprove estimates of earthquake timing. In addition, wefound that uncertainties arising from different, viable alter-native stratigraphic models could impact inferences of earth-quake age and recurrence. As an example, the interpretationof a single paleosol within a trench at the BF site leads tochanges in the inferred temporal distribution of earthquakesalong the central SAF.

The probabilistic estimates of earthquake timing and re-currence, expressed as PDFs, may prove useful for quantify-ing uncertainties in the paleoseismic record when performinga PSHA. In addition, while we do not explicitly test modelsof earthquake recurrence in this study, these PDFs may beused as direct inputs for such tests. Finally, our results high-light two areas of future research in paleoseismology thatmay prove beneficial: (1) studies that assess the factors thatcontrol the resolution of the paleoseismic record may beuseful for planning future excavations and determining theappropriate sets of questions that might plausibly be testedusing paleoseismic data, and (2) paleoseismic excavationsthat increase the spatial and temporal coverage betweenPF and the PC paleoseismic site should be especially usefulin evaluating the rupture history of this area, understandinghow ruptures may be distributed in space and time within thisarea, and understanding if ruptures along the central SAFconsistently rupture the southern SAF as well.

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Department of Geological and Environmental SciencesStanford UniversityStanford, California 94305

(G.E.H.)

Department of Geological SciencesArizona State UniversityTempe, Arizona 85281-1404

(J.J.Y.)

Manuscript received 23 January 2007


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