Reading a 400,000-year record of earthquakefrequency for an intraplate faultRandolph T. Williamsa,1, Laurel B. Goodwina, Warren D. Sharpb, and Peter S. Mozleyc

aDepartment of Geoscience, University of Wisconsin–Madison, Madison, WI 53706; bBerkeley Geochronology Center, Berkeley, CA 94709; and cEarth andEnvironmental Science, New Mexico Institute of Mining and Technology, Socorro, NM 87801

Edited by Barbara A. Romanowicz, University of California, Berkeley, CA, and approved March 21, 2017 (received for review October 31, 2016)

Our understanding of the frequency of large earthquakes attimescales longer than instrumental and historical records is basedmostly on paleoseismic studies of fast-moving plate-boundaryfaults. Similar study of intraplate faults has been limited until now,because intraplate earthquake recurrence intervals are generallylong (10s to 100s of thousands of years) relative to conventionalpaleoseismic records determined by trenching. Long-term varia-tions in the earthquake recurrence intervals of intraplate faultstherefore are poorly understood. Longer paleoseismic records forintraplate faults are required both to better quantify their earth-quake recurrence intervals and to test competing models of earth-quake frequency (e.g., time-dependent, time-independent, andclustered). We present the results of U-Th dating of calcite veinsin the Loma Blanca normal fault zone, Rio Grande rift, New Mex-ico, United States, that constrain earthquake recurrence intervalsover much of the past ∼550 ka—the longest direct record of seis-mic frequency documented for any fault to date. The 13 distinctseismic events delineated by this effort demonstrate thatfor >400 ka, the Loma Blanca fault produced periodic large earth-quakes, consistent with a time-dependent model of earthquakerecurrence. However, this time-dependent series was interruptedby a cluster of earthquakes at ∼430 ka. The carbon isotope com-position of calcite formed during this seismic cluster records rapiddegassing of CO2, suggesting an interval of anomalous fluidsource. In concert with U-Th dates recording decreased recurrenceintervals, we infer seismicity during this interval records fault-valve behavior. These data provide insight into the long-term seis-mic behavior of the Loma Blanca fault and, by inference, otherintraplate faults.

earthquake | fault | geochronology | seismic | hazard

Recent increases in the rate of seismicity associated withsubsurface wastewater injection have generated substantial

interest in the seismic cycles of intraplate faults (1–4). Un-fortunately, increasing seismicity in the continental interior hasoutpaced our understanding of the processes that govern naturalearthquake recurrence on these faults. The seismic cycles ofplate boundary faults are much better known, although the exactnature of their earthquake recurrence distributions remainsmuch debated (5, 6). At the heart of this debate lies a funda-mental question: Are seismogenic faults ever controlled by astress-renewal process that can be approximated by elastic re-bound theory? The latter states that stress buildup will be ac-commodated elastically until shear stress on the fault reaches athreshold value that will allow failure.If seismogenic faults are governed by a renewal process, then

elastic rebound theory predicts that earthquakes will be pro-duced quasiperiodically (7) (i.e., occur at regular intervals andtherefore be “time-dependent”) with steady tectonic loading.However, an alternative view posits that spatial and temporalvariations in fault strength and/or mechanical interactions be-tween adjacent faults can lead to either a random or a clustereddistribution of seismic events for a given fault (8–13). This view hasled to greater use of “time-independent” and clustered earth-quake recurrence models. Although an increasingly large body of

research has shown that many seismogenic plate-boundary faultsaround the world exhibit quasiperiodic failure (14–17), compara-tively slow recurrence rates in conjunction with short paleoseismicrecords have until now prevented robust assessment of earthquakerecurrence intervals for intraplate faults. We address this fun-damental knowledge gap by using a significantly different ap-proach; direct dating of coseismic veins preserved as part of thelong-term rock record.We studied an exhumed section of the Loma Blanca normal

fault, which juxtaposes <2.6 Ma sediments and sandstonesagainst 5.3- to 1.8-Ma fluvial sands in the Socorro Basin of the RioGrande rift of New Mexico (18) (Fig. 1). Maximum displacementacross the Loma Blanca fault is ∼500 m (21). Fault-scarp mor-phology and offset Pleistocene terrace deposits preserved in otherlocations along the fault record a history of recurrent, surface-rupturing earthquakes (18). Assuming rupture of the entire23-km-long fault trace, earthquake magnitudes estimated for theLoma Blanca fault are ∼6.2–6.9 (22). This magnitude is a min-imum estimate, because it neglects possible multifault events,which may produce larger earthquakes (23).Within the exhumed section of the fault, sand injectites and

calcite veins are largely restricted to the hanging wall damagezone near and within a relay zone between two fault segments(Fig. 1, “South Fracture Zone”) (20). Sand injectites in this arearecord early, coseismic fluid overpressure and/or liquefaction,which occurred during ground shaking before lithification. Cal-cite veins postdate cementation of the sand injectites. They occurin dominant fault-strike-subparallel and subordinate fault-strike-subperpendicular sets. The veins are hosted by extension frac-tures, exhibit crack-seal microstructures, and commonly contain

Significance

U-Th dating of coseismic calcite veins in the Loma Blanca fault,New Mexico, quantifies an earthquake history spanning morethan 400,000 years, the longest paleoseismic record everdocumented for any fault. Data show that earthquakes on theLoma Blanca fault generally occurred at regular intervals,rather than aperiodically as previously hypothesized for faultsin similar tectonic environments. However, periodic earth-quake slip was interrupted by a relatively brief interval of in-creased earthquake frequency. Stable isotope data indicativeof rapid CO2 degassing suggest this interval was associatedwith elevated pore-fluid pressure. The Loma Blanca fault thusprovides a record of “naturally induced” seismicity duringwhich fault-valve behavior is inferred to have reduced earth-quake recurrence intervals.

Author contributions: R.T.W. designed research; R.T.W., L.B.G., and P.S.M. performed research;R.T.W. and W.D.S. contributed new reagents/analytic tools; R.T.W., L.B.G., W.D.S., andP.S.M. analyzed data; and R.T.W., L.B.G., W.D.S., and P.S.M. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: rtwilliams@wisc.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1617945114/-/DCSupplemental.

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multiple generations of calcite cement (Fig. 2). Both vein densityand cumulative aperture increase with proximity to the relay.The dominant vein set is perpendicular to the minimum stressshown by numerical modeling to develop in relay zones duringfailure (24). Collectively, the distribution, orientation, and mi-crostructure of the veins suggest they record failure in responseto coseismic fluid overpressure during dynamic rupture acrossthe relay (Fig. 2A) (20). Vein sealing thus records precipitationof calcite during postseismic fluid migration.Postseismic fluid flow along faults is a well-documented phe-

nomenon (25). This effect appears to be most pronounced inseismogenic normal faults like the Loma Blanca, in which docu-mented postseismic fluid discharge volumes are up to 10 timesthose resulting from similarly sized earthquakes on strike-slip orreverse faults (25). Several conceptual models have been proposedto explain postseismic fluid migration from depth along normalfaults. For example, where faults transect overpressured reser-voirs, coseismic increases in fault permeability may provide amechanism for pressure release via the upward migration of fluids(26, 27). Alternatively, postseismic increases in the least com-pressive horizontal stress around normal faults may promote pore

collapse at depth, also driving the upward migration of fluids (25,28). Although the exact mechanism responsible for fluid migrationand vein formation in the Loma Blanca fault zone remains un-known, previous research has shown that fluids precipitating cal-cite cements in this and other basin-margin faults of the RioGrande rift likely originated from several kilometers beneath thecurrent exposures (29). Because postseismic fluid flow has beenshown to begin as little as a few days after normal fault rupture(25), the timing of calcite precipitation is a reasonable proxy forthe timing of individual earthquakes.The timing of vein precipitation can be accurately determined

using U-Th geochronology if the calcite (i) has favorable U andcommon Th (232Th) concentrations and (ii) formed in the past∼600,000 years. We used this approach to determine the ages ofthe first calcite deposited at the base of each distinct generationof calcite in veins to constrain the timing of coseismic fractureopening—a proxy for the timing of seismic failure (Fig. 2). Byconstraining the timing of individual earthquakes, we can cal-culate recurrence intervals between successive earthquakes. Veinsamples obtained from the South Fracture Zone of the LomaBlanca fault (Fig. 1) had undergone previous microstructural andstable isotope analyses (20). We resampled these veins for U-Thgeochronology using the scheme shown in Fig. 2B. In rare caseswhere samples of different veins showed temporal overlap withinanalytical uncertainty, stable isotope values were compared.Ages were considered distinct if carbon or oxygen isotope (δ13Cand δ18O) values differed by >1.5‰ or if the samples werecollected from two distinct generations of crack-seal calcite fromthe same vein. Otherwise, veins of overlapping age were inferredto have formed at the same time and an error-weighted meanage was calculated.

ResultsU-Th dates for 20 samples of calcite (including replicates ofselected samples) from veins in the Loma Blanca fault zonedocument 13 distinct earthquakes since ∼550 ka (Fig. 3A). Fourof these events define a pronounced cluster recording increasedearthquake frequency at ∼430 ka. Two of the veins formedduring the earthquake cluster exhibit markedly higher δ13C valuesrelative to older and younger veins (Fig. 3C). These high δ13Cvalues are consistent with rapid, postseismic fluid flow anddegassing of CO2-rich fluids (22). We calculate a long-term re-currence interval for background earthquake activity of 40 ± 7 kaover the ∼390- to 150-ka period and a shorter recurrence intervalof 5–11 ka for the earthquake cluster near ∼430 ka. Because agesof events associated with the cluster cannot be distinguishedwithin analytical uncertainty, the range given represents the ap-parent recurrence interval and also a maximum possible re-currence interval that incorporates the uncertainties of the oldestand youngest events in the cluster. To further evaluate the validityof the long-term recurrence interval calculated for the periodfrom ∼390–150 ka, we calculated a recurrence interval for theentire record using the average age of events in the earthquakecluster (Fig. 3B). The latter recurrence interval is 46 ± 6 ka,within error of the recurrence interval calculated for the periodfrom ∼390–150 ka.To provide a quantitative measure of periodicity, we calculated

the coefficient of variation (COV) for the long-term recurrenceinterval from ∼390–150 ka as well as for the entire dataset usingthe average age of the clustered events. Perfectly periodicearthquakes would yield a COV of 0, whereas random or clus-tered earthquakes would yield values of 1 and >1, respectively(9). The COVs calculated for the period of ∼390–150 ka and forthe entire record (using the average age of cluster events) are0.43 and 0.40, respectively, indicating quasiperiodic earthquakeactivity. The measured recurrence intervals therefore support atime-dependent model of earthquake recurrence for the LomaBlanca fault.

QTsa

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BlancaFault

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Fig. 1. Simplified geologic map of an exhumed section of the Loma Blancafault overlain on satellite imagery (map data: Google, Landsat/Copernicus).Fault is dashed where inferred. (Inset) Location of detailed map in NewMexico. Geologic units: Qac (yellow), Quaternary alluvium; QSa (brown),Quaternary unit A; Qss (uncolored), stabilized Holocene deposits; QTsa(blue), axial stream deposits; Tpl (gray), Popotosa Formation; Tsp (green),piedmont slope and alluvial fan deposits. The box outlines the South Frac-ture Zone of ref. 20, within which dated veins were collected. Geologic dataare from ref. 19.

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We note that the age of event 13 represents the error-weightedmean of two distinct veins, whose carbon isotope values differed byvalues near our threshold of >1.5‰. If treated as distinct events,the recurrence intervals for the period from ∼390–150 ka and forthe entire record (using the average age of cluster events) become34 ± 8 ka and 41 ± 7 ka, respectively, within error of our originalestimates. The COVs then become 0.59 and 0.52, respectively.

DiscussionSources of Uncertainty.Our analysis assumes that the dated calciteveins were formed in response to seismic fault slip. It is, however,conceivable that damage zone fracturing was slip related butsubsequent calcite precipitation was controlled by other factors,such as climatic variations associated with glacial cycling. Wehave tested this hypothesis by comparing our U-Th dates withthe Devil’s Hole climate record, which provides a continuousrecord of glacial cycling over the last ∼500 ka (30). This com-parison shows no correlation between the timing of vein for-mation and glacial/interglacial cycles. This result is consistentwith previous work showing that calcite in the Loma Blanca faultzone was controlled by upward migrating, endogenic fluids ratherthan shallow, meteorically derived fluids (20, 29).Uncertainty in our quantification of the Loma Blanca record

arises from the fact that we could not sample all of the numerousveins in the damage zone. As we have no means of estimatingexactly how many events are recorded in the fault zone, it ispossible that some were not sampled. It is also possible that onlyseismic events above a particular magnitude resulted in damagezone fracturing and vein formation, such that not all events wererecorded. Finally, missing events may result from erroneously

combining distinct events where U-Th ages and stable isotopecompositions are similar. Any of these scenarios would lead toerrors in earthquake recurrence intervals and COV calculatedfrom our U-Th data.To evaluate our interpretation that earthquake recurrence was

largely time-dependent in light of the fact that we might havemissed events, we constructed simple Monte Carlo simulationsto test the hypothesis that our calculated COV reflects incom-plete, random sampling of a record of time-independent (COV =1) or clustered (COV > 1) earthquake recurrence (Methods).These simulations allow us to conclude at the 95% confidencelevel that the time-dependent COVs calculated from the LomaBlanca earthquake record cannot result from random sampling ofa time-independent or clustered record (Fig. 4). This result holdseven if the two ages comprised by our event 13 are treated asdistinct events, albeit at the 90% confidence level for the intervalfrom ∼390–150 ka. In summary, although we cannot be certainhow missing events may alter the absolute value of the COVcalculated for the Loma Blanca fault, we can conclude based onthe apparent COV that the underlying recurrence on the fault wastime-dependent. Even if only the largest earthquakes on the LomaBlanca fault were recorded by veins, then those largest earth-quakes must have occurred quasiperiodically through time.

Implications for the Seismic Cycle of Intraplate Faults. The pro-nounced cluster of earthquakes at ∼430 ka shows that long-termperiodic (time-dependent) fault failure may be interrupted bytransient increases in earthquake frequency of nearly 1 order ofmagnitude (Fig. 3B). Moreover, the average age of the clusteredevents fits in the long-term earthquake history of the LomaBlanca fault, indicating that such substantial increases in the rate of

FluidInfiltration

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Fig. 2. (A) Outcrop photo of cross-cutting relationship between two largely sealed calcite veins in the hanging wall damage zone. Numbers denote order offormation of cross-cutting veins. Open and closed arrows show open and sealed sections of the vein, respectively. Arrow head on card is 5 cm long. Photofrom ref. 20. (B) Plane light photomicrograph showing composite calcite vein with two generations of cement. Dashed line highlights boundary betweencement generations and arrows show the inferred calcite growth direction. Each generation of calcite cement corresponds to a distinct earthquake event asshown in C. Subsamples were collected from the base of each generation of calcite (F1 and F2) for U-Th analyses. A and B are modified from ref. 20. (C)Schematic illustration of spatial and temporal relationships between fault slip, fracture opening, and sealing recorded in calcite veins. F1 and F2 denote theearliest cements precipitated following successive fault slip events, and therefore record the approximate timing of coseismic fracture opening.

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seismicity can occur within the expected interseismic period of anotherwise time-dependent cycle (Fig. 3B). We note that clusterspreviously documented on plate-bounding faults are generallyseparated by pronounced periods of quiescence (8–12). In contrast,our results show that an earthquake cluster may be an anomaly inan otherwise quasiperiodic record, at least on intraplate faults.The time-dependent nature of the Loma Blanca earthquakes

is consistent with recent work that documents quasiperiodic

earthquake recurrence intervals on some plate-boundary faults(14–17). However, other plate-boundary faults exhibit randomor clustered earthquakes over time scales of thousands of years(8–13). Previous work has hypothesized that a continuum ofearthquake recurrence behavior may exist, with quasiperiodicbehavior exhibited by high slip rate, isolated structures withsimple geometries and aperiodic behavior characteristic of lowslip rate, networked fault systems with complex geometries (15).An appealing aspect of this interpretation is that it would allowappropriate statistical models of earthquake recurrence to beapplied to individual faults based on their geometry and geologicsetting in the absence of robust paleoseismic records. However,our results do not support this conceptual model. As a low slip-rate fault that is just one of many locally linked and commonlysegmented structures (19), the Loma Blanca should, per thismodel, exhibit aperiodic failure. However, it records periodicseismicity over most of the 400 ka we can constrain.In the absence of changes in regional strain rates, variations in

Loma Blanca earthquake frequency must fundamentally reflectchanges in processes driving fault slip. It is likely that the ca.40 ka periodicity of the long-term Loma Blanca record repre-sents a background rate of failure during intraplate extension, assimilar rates have been documented for other normal faults inthe Rio Grande rift (31, 32). The dominantly time-dependentnature of our earthquake chronology suggests that this back-ground fault rupture was driven principally by a stress-renewalprocess. The interruption of this time-dependent series by clus-tered seismicity near 430 ka therefore must record a change inthe process driving failure. Stable isotope evidence of rapid CO2degassing during postseismic fluid flow and vein precipitationsuggests that the clustered earthquakes occurred during an in-terval of anomalous fluid source. We infer that the pronouncedincrease in earthquake frequency recorded by these veins reflectsa source that increased both CO2 concentration and pore-fluid

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Fig. 3. Results of U-Th and δ13C analyses of calcite veins. (A) Earthquake ageversus relative position within the total earthquake sequence record. Lines inthe lower left of the graph show the length of the seismic instrument recordand the length of previous paleoseismic studies. Error bars represent 95%(2σ) confidence intervals. Error bars are not shown where uncertainties areless than symbol size. Trend lines show linear regression analyses of theplotted age ranges where slope is proportional to earthquake frequency.The COV provides an estimate of earthquake periodicity (0, perfectly peri-odic; 1, random). The gray box shows the time interval associated withclustered seismicity on the Loma Blanca fault. (B) Similar to A but showing amean age calculated from the clustered events. (C) Vein δ13C [Vienna Peedeebelemnite standard (VPDB)] is shown as a function of calcite age. Uncer-tainties in δ13C analysis are less than 0.1‰. Two dated veins were destroyedduring sample collection before δ13C analyses could be conducted. Carbonisotope data were sourced in part from ref. 22.

Number of Samples6 7 8 9 10 11 12 13 14 15

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Fig. 4. Results of Monte Carlo simulation testing the hypothesis that theCOVs calculated from our U-Th data are the result of incomplete, randomsampling of a time-independent (i.e., random) earthquake record. For anyCOV (vertical axis) calculated from a particular sample size (horizontal axis),points falling outside the shaded area allow rejection of the null hypothesisthat a calculated COV could be the result of random sampling of a time-independent record at the 95% confidence level. Because the COVs calcu-lated from our U-Th data plot outside of the shaded region, we reject thehypothesis that the underlying earthquake recurrence behavior of the LomaBlanca fault was time-independent. See SI Appendix for model source codeand results of the clustered recurrence test.

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volume, and thereby pressure, at depth. This inferred increase inpore-fluid pressure is interpreted to have decreased effectivefault strength, leading to more frequent seismic rupture, con-sistent with fault-valve behavior (26).The geometry of normal faults and the associated stress field

makes it difficult to sustain large fluid overpressures over longtime scales (27). However, previous work has shown that fault-valve behavior can occur in extensional settings where basinstratigraphy includes low-permeability horizons at depth, as isthe case in the Socorro Basin beneath the Loma Blanca fault(33). We hypothesize that the inferred increase in CO2 contentof pore fluids may record input of volatiles exsolved from rift-related magma. Such volatiles could be trapped where the faulttransects low-permeability sediment. We note that there is con-siderable evidence suggesting that overpressured CO2-rich fluidsmay have been responsible for modern normal-fault ruptures inthe Apennines (27). In the case of the Loma Blanca fault, wespeculate that such volatiles may have been released duringcrystallization of an early (and previously unrecognized) phase ofthe currently active Socorro magma body, which lies beneath thestudy area (34).Our longer earthquake chronology indicates that the inferred

period of fault-valve behavior was a transient episode in theLoma Blanca fault history. Although our record contains onlytwo events older than the earthquake cluster, the interval be-tween them is consistent with those observed in the youngerrecord of periodic recurrence. For this reason, and because thelong-term periodicity of earthquakes on the Loma Blanca fault issimilar to that of other normal faults in the Rio Grande rift, weconclude that failure on the Loma Blanca fault was driven by astress-renewal process for most of the recorded history. We in-terpret the seismic cluster as a record of enhanced seismicitycaused by naturally elevated pore-fluid pressure, which drovefault failure for a relatively short period.

MethodsGeochemical Methodology.Powder sampling. Powders were collected from vein samples that were pol-ished flat in a plane perpendicular to the fracture wall. A variable speed drillwith a carbide bit (head diameter: 100 μm) was used to collect ∼30 mg ofsample powder in a fracture-wall-parallel trench at the base of each gen-eration of cement. Sample trenches were kept 0.5–1 mm from the fracturewall to avoid contamination from sandstone calcite cements. Following eachdrill pass, sample powders were collected with a hypodermic needle andplaced into static-free sample vials. All sample collection tools were thor-oughly rinsed with ethanol and dried between samples.U-Th analytical methods. Analyses were carried out at the Berkeley Geo-chronology Center. Samples were totally dissolved in 7 M HNO3 and equili-brated with a mixed spike containing 229Th, 233U, and 236U. The spike wascalibrated using New Brunswick National Lab CRM145 uranium solution andsolutions prepared from a 69-Ma U ore from Schwartzwalder Mine, Colo-rado, United States, that has been demonstrated to yield concordant U-Pbages (35) and sample-to-sample agreement of 234U/238U and 230Th/238U ra-tios. U and Th were separated from sample matrix using two stages ofHNO3–HCl cation exchange chemistry followed by reaction with HNO3 andHClO4 to remove any residual organic material. Procedural backgrounds forU and Th were measured with each batch of samples and corrections forbackground 230Th were applied. Procedural backgrounds for 238U, 234U, and232Th were negligible relative to sample amounts.

Analyses were performed using a Thermo-Fisher NEPTUNE Plus multi-collector inductively coupled plasma mass spectrometer. Purified U and Thfractions were analyzed simultaneously. Analyses were carried out in auto-mated sequences, with each analysis consisting of a preanalysis washout, aninstrumental background measurement, a sample measurement, and ameasurement of peak-tails. All measurements are normalized to simulta-neous measurements of 238U to cancel intensity fluctuations. Instrumentalbackgrounds at each U and Th mass, along with Faraday collector baselinesand ion counter dark noise, were measured while aspirating the same diluteHNO3–HF solution used to introduce samples. Sample measurements werecarried out in peak-jumping mode with all masses measured on Faradaycollectors except 230Th and 234U, which were measured with an ion counter.

Sample measurements incorporated within-run mass bias corrections usingthe known 233U/236U ratio of the spike. Faraday amplifier gains were cali-brated weekly using the Neptune’s constant current source and switchingsystem. Ion counter yields (relative to Faraday collectors) were determinedduring each sample measurement by cycling 229Th and 233U signals betweenthe ion counter and the L1 Faraday collector. Peak tails were monitored atseven half-mass positions from m/e = 229.5–241.5 while aspirating samplesolutions, the sum of tails from all peaks was modeled at each U and Th massposition, and the result subtracted from the measured intensities. Measuredpeak heights were corrected for Faraday baselines/ion counter dark noise,instrumental backgrounds, Faraday gains, ion counter yields, mass frac-tionation, peak-tails, procedural blanks, and interfering spike isotopes.

Activity ratios and ages were calculated using the half-lives of ref. 36 for 238U,ref. 37 for 232Th, and ref. 38 for 230Th and 234U. Correction for U and Th fromdetritus was made assuming detritus with activity ratios of (232Th/238U) = 1.2 ±0.5, (230Th/238U) = 1.0 ± 0.1, and (234U/238U) = 1.0 ± 0.1. Errors for corrected agesare 2σ and include contributions from measurement errors and the assigneduncertainties in detritus composition but not decay constant error.

Monte Carlo Simulation. We used a Monte Carlo simulation (MATLAB sourcecode included in SI Appendix) to test the hypothesis that the periodic distri-bution of earthquakes we have documented does not reflect time-dependentseismicity, but instead was produced by random sampling of either a random(i.e., time-independent) or clustered earthquake distribution. Our model takesas input an assumed mean earthquake recurrence interval and a COV, fromwhich it randomly generates 10,000 synthetic earthquake records fitting theseparameters. We tested the above hypothesis by randomly sampling eachsynthetic earthquake record to assess the variability of the calculated COVs fora range of sample sizes. For example, incomplete, random sampling of a time-independent earthquake record with a COV = 1 would frequently produceapparent COVs that are either greater or less than one. In essence, our modeldetermines the lowest (more time-dependent in appearance) COV that is likelyto be produced through random sampling of a time-independent or clusteredearthquake distribution.

We used this approach to assess the variability of COVs calculated fromrandom samples of synthetic time-independent and clustered recurrencerecords. The model assumes a mean recurrence interval of 40 ka, COVs of1 and 1.5 for time-independent and clustered tests, respectively, and a recordof 15 earthquakes. To evaluate each sample size (we tested 6–15), 10,000synthetic earthquake records were randomly sampled and the COV of theapparent interseismic periods in each subsample was calculated and stored.Sensitivity analyses demonstrate that model results are not affected by vari-ations in either the assumed mean recurrence interval or the total number ofsynthetic earthquakes in each record (SI Appendix, Fig. S1).

We define a ‘critical COV threshold’ as the fifth percentile of the 10,000calculated COVs from each model run of a given sample size. Thus, if thecritical COV threshold for a given sample size is greater than that calculatedusing our U-Th dates for the same sample size, we can reject (at the 95%confidence level) the null hypothesis that the latter COV could result fromrandom sampling of a time-independent or clustered record. In the maintext, we consider the COV of both the time period from ∼390–150 ka andthe entire Loma Blanca record using the average age of the clustered events.For the time-independent test, these COVs (0.43 and 0.40, respectively) areboth less than the critical COV thresholds (0.54 and 0.68, respectively) for thesame sample sizes, allowing us to reject the null hypothesis that COVs cal-culated using our U-Th dates could be the result of random sampling of atime-independent record (Fig. 4). Similarly, the clustered recurrence testyields critical COV thresholds of 0.69 and 0.88 for sample sizes of 7 and 10,respectively, which also allows us to reject the hypothesis that our calculatedCOVs could result from random sampling of a clustered record (SI Appendix,Fig. S2).

ACKNOWLEDGMENTS. We thank Christine Gopon for assistance with fieldwork and Brian Goodman for statistical advice. We are grateful to theSevilleta National Wildlife Refuge for access to study sites. We also thanktwo anonymous reviewers for providing constructive reviews of themanuscript, which greatly improved its quality. This work was supportedby grants from the Geological Society of America, the American Associationof Petroleum Geologists, and the GDL Foundation (to R.T.W.) and a grantfrom the Wisconsin Alumni Research Fund (to L.B.G.). Acknowledgment ismade to the donors of the American Chemical Society Petroleum ResearchFund for partial support of this research. Partial support of this work wasprovided by National Science Foundation Grants EAR-1358514, EAR-1358554, EAR-1358401, EAR-1358443, and EAR-1101100 (EarthScope Na-tional Office). We thank the EarthScope Awards for Geochronology StudentResearch Program for its support.

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