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Distribution of seismicity across strike‐slip faults in California

Peter M. Powers1 and Thomas H. Jordan2

Received 1 December 2008; revised 5 November 2009; accepted 16 December 2009; published 11 May 2010.

[1] The distribution of seismicity about strike‐slip faults provides measurements of faultroughness and damage zone width. In California, seismicity decays with distance fromstrike‐slip faults according to a power law ∼(1 + x2/d2)−

g/2. This scaling relation holds out

to a fault‐normal distance x of 3–6 km and is compatible with a “rough fault loading”model in which the inner scale d measures the half width of a volumetric damage zone andthe roll‐off rate g is governed by stress variations due to fault roughness. According toDieterich and Smith’s 2‐D simulations, g approximates the fractal dimension of along‐strike roughness. Near‐fault seismicity is more localized on faults in northern California(NoCal, d = 60 ± 20 m, g = 1.65 ± .05) than in southern California (SoCal, d = 220 ± 40 m,g = 1.16 ± .05). The Parkfield region has a damage zone half width (d = 120 ± 30 m)consistent with the SAFOD drilling estimate; its high roll‐off rate (g = 2.30 ± .25)indicates a relatively flat roughness spectrum: ∼k−1 versus k−2 for NoCal, k−3 for SoCal.Our damage zone widths (the first direct estimates averaged over the seismogenic layer)can be interpreted in terms of an across‐strike “fault core multiplicity” that is ∼1 in NoCal,∼2 at Parkfield, and ∼3 in SoCal. The localization of seismicity near individual faultscorrelates with cumulative offset, seismic productivity, and aseismic slip, consistent with amodel in which faults originate as branched networks with broad, multicore damage zonesand evolve toward more localized, lineated features with low fault core multiplicity,thinner damage zones, and less seismic coupling. Our results suggest how earthquaketriggering statistics might be modified by the presence of faults.

Citation: Powers, P. M., and T. H. Jordan (2010), Distribution of seismicity across strike‐slip faults in California, J. Geophys.Res., 115, B05305, doi:10.1029/2008JB006234.

1. Introduction

[2] California, with its dense, well‐mapped network offaults and high‐quality earthquake catalogs, is an excellentsetting to investigate seismicity variations in space and time.Earthquake catalogs constructed using improved hypocenterrelocation techniques [Ellsworth et al., 2000; Hauksson andShearer, 2005; Shearer et al., 2005; Thurber et al., 2006]are revealing new details about the 3‐D geometry of faultnetworks [Yule and Sieh, 2003; Carena et al., 2004] andruptures of large earthquakes [Liu et al., 2003], properties ofnascent faults [Bawden et al., 1999], earthquake streaksobserved on creeping sections [Rubin et al., 1999;Waldhauser et al., 1999, 2004; Shearer et al., 2005;Thurber et al., 2006], and the space‐time behavior ofearthquake swarms [Vidale and Shearer, 2006]. Thesestudies, as well as extensive research on the fractal characterof fault systems [Tchalenko, 1970; King, 1983; Okubo andAki, 1987; Hirata, 1989; Robertson et al., 1995; Ouillon etal., 1996; Kagan, 2007], have raised a number of interesting

issues regarding the relationship of small earthquakes tomajor faults. For instance: Are physical properties of a faultzone such as the distribution of secondary faults and frac-tures, damage zone width, and fault roughness captured innear‐fault earthquake rates? Does the rate of small earth-quakes in the vicinity of a major fault zone reflect the long‐term fault slip rate or cumulative offset of the fault? Doother factors such as heat flow and lithology modulateearthquake rate? How might spatial models of near‐faultseismicity improve subsurface fault maps or models ofearthquake triggering?[3] To address these issues, we analyze the variation of

seismicity rate normal to near‐vertical strike‐slip faults inCalifornia and examine its relation to stress heterogeneity,damage zones, and degree of seismic coupling. Strike‐slipfaults were chosen because their locations are constrainedby mapped surface traces and their approximate bilateralsymmetry of seismicity makes their earthquake distributionssimpler to interpret than those of normal and reverse faults.To reveal systematic scaling relationships, we aggregateddata from fault segments in a common class, as defined bygeographic region, fault length, and aftershock activity. Werestricted our analysis to small earthquakes (Mw < 5), whichwe treated as point sources. Examined this way, the near‐fault seismicity shows a power law decay away from the

1Department of Earth Sciences, University of Southern California, LosAngeles, California, USA.

2Southern California Earthquake Center, University of SouthernCalifornia, Los Angeles, California, USA.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2008JB006234

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, B05305, doi:10.1029/2008JB006234, 2010

B05305 1 of 25

http://dx.doi.org/10.1029/2008JB006234

fault surface [Powers and Jordan, 2005, 2007a; Hauksson,2010].[4] We examined regional variations in this fault‐normal

distribution of seismicity by comparing the results fromselected fault segments in northern California, betweenParkfield and the San Francisco Bay (Figure 1), and a moreextensive distribution of faults in southern California(Figure 2). In the northern California region, the fault seg-ments are on or subparallel to the San Andreas master fault,a larger percentage of the faults are creeping [Irwin, 1990],and little seismicity extends below 10 km [Hill et al., 1990]

(Figure 3). In contrast, the southern California segmentshave deeper seismicity [Hauksson, 2000], show little or nocreep [Bodin et al., 1994; Lyons and Sandwell, 2003;Shearer et al., 2005], and often intersect at high angles. Insouthern California, we also investigated the spatial distri-bution of seismicity near smaller faults (e.g., splays of largefaults and unmapped secondary faults) to see how faultlength and along‐fault variations affect the scaling relations.We declustered each data set and incorporated fault seg-ments that ruptured during large (Mw > 6) earthquakes toconstrain how the scaling relations are modified by after-

Figure 1. Map of northern California showing locations of seismicity samples (gray boxes with refer-ence numbers; see Table 3). Black lines delineate large faults, and the heavy black line marks the SanAndreas fault. Dark gray dots mark the locations of 1.5 < M ≤ 2.5 earthquakes (1984–2002). Referencelabel background colors reflect the fault‐normal intercatalog location uncertainty of each segment: sTN

x forthe Parkfield segments (51 and 52); sUN

x for all others.

POWERS AND JORDAN: SEISMICITY RATE NEAR STRIKE‐SLIP FAULTS B05305B05305

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shock activity. To assess the bias and variance in the scalingparameters caused by event mislocation, we supplementedthe errors estimated by the hypocenter location algorithmswith constraints from intercatalog comparisons and statisti-cal simulations.[5] Our results provide measures of shear localization on

faults and indirect evidence that fault damage zones extendthrough the seismogenic crust. We present a model of faultbehavior that incorporates slip on a fractal fault, and discussthe implications of the model on fault evolution using dataon fault width, on‐fault earthquake density, cumulativeoffset, and aseismic slip rate. Through comparisons withstudies of exhumed faults and drilling results, we relate the

structure of a fault damage zone at depth, as defined byseismicity, to near‐surface observations.

2. Fault‐Referenced Seismicity Catalogs

[6] Hypocenters from six earthquake catalogs (three insouthern, two in northern California, and one for the Park-field region (Table 1)) were used to constrain near‐faultseismicity distributions and their uncertainties. The SouthernCalifornia Seismic Network (SCSN) is the southern part ofthe California Integrated Seismic Network (CISN), a regionwithin the Advanced National Seismic System (ANSS). TheSCSN catalog (here abbreviated as “S”; available at http://

Figure 2. Map of southern California showing locations of seismicity samples (with reference numbers;see Table 3). Black lines delineate large faults, and the heavy black line marks the San Andreas fault.Grey boxes with reference numbers in circles (1–15) indicate the limits of seismicity samples about largestrike‐slip faults; reference numbers in squares indicate the locations of samples about small (16–29) andaftershock‐dominated (30–41) fault segments. Dark gray dots mark the locations of 1.5 < M ≤ 2.5earthquakes (1984–2002). Reference label background colors reflect the fault‐normal intercatalog loca-tion uncertainty, sPS

x , of each segment.


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www.data.scec.org) is the standard catalog for southernCalifornia and contains events reported by all networks in theregion. It includes some estimates of hypocentral errors, butall events have a “quality” designation indicative of maxi-mum horizontal and vertical location uncertainties.[7] Hauksson and Shearer [2005] relocated events (cata-

log “H”; available at http://www.data.scec.org) from theSCSN using the double‐difference algorithm of Waldhauserand Ellsworth [2000]. They cross‐correlated waveforms tomeasure traveltime differences and relocated seismicity in athree‐dimensional (3‐D) velocity model. For events lackingsufficient data for double differencing (<10%), they deter-mined hypocenters using Hauksson’s [2000] relocationmethod. They also evaluated errors using this method,because the double‐difference code does not computehypocentral location errors for large data sets.[8] Shearer et al. [2005] relocated events (catalog “P”;

available at http://www.data.scec.org) using a source‐specific station term algorithm [Richards‐Dinger and Shearer,2000] that employs a layered (1‐D) velocity model. Usingevent‐similarity data from a waveform cross‐correlationanalysis, they further refined the locations of spatiallyrelated events (∼60%) via a cluster analysis. Hypocentralerrors reported by Shearer et al. [2005] correspond to therelative locations of events in each cluster.[9] The catalog of the Northern California Seismic Net-

work (NCSN, abbreviated “N”; available at http://www.ncedc.org/ncsn) is the standard catalog for the northern partof the CISN. Ellsworth et al. [2000] relocated a subset of theNCSN events in the San Francisco Bay area (catalog “U”;available at http://pubs.usgs.gov/of/2004/1083) using thedouble‐difference algorithm of Waldhauser and Ellsworth[2000]. The catalog does not include hypocentral locationerrors, but Ellsworth et al. [2000] report average horizontaland vertical location uncertainties of 0.1 and 0.5 km,respectively.

[10] On the creeping section of the San Andreas fault inthe vicinity of Parkfield, relocated events (denoted catalog“T”; available at http://www.seismosoc.org/publications/BSSA_html/bssa_96‐4b/05825‐esupp/) were taken fromThurber et al. [2006]. They constructed an improved 3‐Dwave speed model to first determine station corrections andthen relocated events via double difference using a combi-nation of event cross‐correlation differential times and tra-veltime differences from NCSN phase picks. The catalogdoes not include any hypocentral error information.[11] For each of the six catalogs, we limited our analysis

to events that occurred from the beginning of 1984 until theend of 2002. To allow for intercatalog comparisons, theevents were required to have hypocenters in both northernCalifornia catalogs (N and U or T and U) or in all threesouthern California catalogs (S, P, and H). The northernCalifornia catalogs, T and U, do not overlap geographicallyand may only be compared independently to catalog N,whereas the southern California catalogs span the entirelower half of the state and may be compared collectively.Events identified as quarry blasts or ones with intercatalogseparations greater than 10 km were discarded.[12] We constructed catalogs of earthquakes for five

classes of near‐vertical strike‐slip faults (Tables 2 and 3 and

Figure 3. Depth distributions of relocated earthquakes in the fault segment catalogs. Events from(a) catalog H and (b) catalog P in southern California and (c) catalogs U and T in northern California.The darker shaded bars mark the medial 90% of all events in the catalogs. Note that seismicity is gen-erally shallower in northern California (Figure 3c). The downward bias in catalog H (Figure 3a) is likelyan artifact of the 3‐D velocity model used for earthquake relocation.

Table 1. Earthquake Catalog Sources

Sources by Region IDa Type

Southern CaliforniaSCSN S standardShearer et al. [2005] P relocatedHauksson and Shearer [2005] H relocated

Northern CaliforniaNCSN N standardEllsworth et al. [2000] U relocatedThurber et al. [2006], Parkfield T relocated

aUsed to reference catalog in equations and text.


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Figures 1 and 2): large faults of northern California, the SanAndreas fault at Parkfield, large faults of southern Cali-fornia, small faults of southern California, and fault seg-ments with abundant aftershocks of major southernCalifornia earthquakes. For large faults, we chose relativelystraight segments of named, throughgoing faults (e.g.,Figure 4), eliminated fault segments with earthquake densityof less than one event per km, and avoided fault junctionsand zones of structural complexity. In southern Californiathe SCEC Community Fault Model (CFM, available athttp://structure.harvard.edu/cfm) [Plesch et al., 2007] wasour guide for fault selection; in northern California, wherefaults are well defined by near‐vertical seismicity distribu-tions, we used surface traces. Where the surface trace orseismicity along a particular fault indicates significantchanges in strike or fault‐strand overlap, we restricted ourselection to smaller fault segments; e.g., the Hayward fault(Figure 1; segments 42–43) and Garlock fault (Figure 2;segments 1–3). Large fault lengths, Lk in Table 3, average21 km in northern California and 47 km in southern.[13] We identified small and aftershock‐dominated faults

by sets of earthquakes that define linear structural features ofshorter length (average ∼9 km). The small‐fault class com-prises splays off larger faults and unmapped secondaryfaults. Aftershock‐dominated segments were selected fromfaults activated by the 1992 Joshua Tree (Mw 6.1), 1992Landers (Mw 7.3), or 1999 Hector Mine (Mw 7.1) earth-quakes. Although the seismicity in the aftershock‐dominatedclass spans the entire 19 year length of the source catalogs,it is dominated by aftershocks from these large events. Theseismicity of the small‐fault class is more uniformly dis-tributed in time.[14] We used the most recently updated magnitude data

from catalogs S and N; these were generally reported aslocal magnitude, although there are a few events for whichmagnitudes were computed using other means. The maxi-mum likelihood Gutenberg‐Richter b values [Aki, 1965] forthe northern and southern California catalogs are 0.8 and0.9, respectively (Table 2). Northern California has a lowermagnitude of completeness (Mc = 1.2) than southern Cali-fornia (Mc = 2.0), reflecting its smaller area and higherstation density.

Table 3. Fault Segment Catalogsa

Segment Segment NameSize Nk

(events)Lk(km)

Wkb

(km)

SoCal Large (N0 = 1000, xmax = 6 km)1 Garlock (East) 565 56.3 13.02 Garlock (Central) 566 27.3 8.03 Garlock (West) 534 45.1 8.74 Lenwood‐Lockhart 92 31.9 10.05 San Andreas (Mojave) 742 96.9 10.96 Santa Cruz–Catalina Ridge 70 62.5 15.17 Palos Verdes 115 51.6 14.68 Newport Inglewood (North) 226 34.7 14.49 Newport Inglewood (South) 182 79.0 17.110 Elsinore‐Temecula 554 54.0 13.811 San Jacinto (Anza) 5,027 37.7 17.412 Elsinore–Coyote Mt. 415 23.6 12.013 Cerro Prieto 572 39.4 16.614 Imperial 1,179 21.2 14.115 San Andreas (Coachella) 256 40.7 8.3

Total (NT) 11,095 702.0Length‐weighted average 13.2

SoCal Small (N0 = 700, xmax = 2.5 km)16 Scodie Lineament 1,274 15.0 9.617 San Jacinto (Anza) 1,166 11.0 11.318 San Jacinto (Anza) 1,020 5.8 14.819 San Jacinto (Anza) 978 4.6 14.020 San Jacinto (Coyote Creek) 484 7.0 12.521 San Jacinto (Anza) 326 5.0 10.922 San Jacinto (Coyote Creek) 853 6.8 11.623 San Jacinto (Anza) 359 6.4 9.624 San Jacinto (Borrego) 443 7.5 9.925 Superstition Mt. 258 12.8 12.826 Elmore Ranch 318 19.9 11.227 Elmore Ranch (western ext.) 177 6.8 8.928 Elmore Ranch (western ext.) 382 9.5 10.729 Elsinore 928 7.9 11.2


SoCal Aftershock‐Dominated (N0 = 1500, xmax = 3 km)30 Joshua Tree 1,068 6.6 8.031 Joshua Tree 2,338 7.5 8.032 Joshua Tree 1,815 4.9 8.433 Joshua Tree 861 6.2 9.134 Landers 873 5.5 11.035 Landers 669 10.3 8.736 Landers 1,855 10.7 9.537 Landers 2,539 7.0 7.038 Landers 1,334 5.7 7.939 Hector Mine 984 11.2 8.440 Hector Mine 2,872 14.3 8.841 Hector Mine 2,641 11.2 8.6


NoCal Large (N0 = 1500, xmax = 3 km)42 Hayward (North) 336 44.3 10.743 Hayward (South) 674 45.9 10.844 Calaveras (North) 2,958 13.1 7.145 Calaveras (Central) 508 8.2 5.946 Calaveras (South) 1,200 17.9 7.147 Sargent 1,083 10.9 7.748 San Andreas Creeping (North) 1,229 12.2 7.649 San Andreas Creeping (Central) 3,012 14.9 8.050 San Andreas Creeping (South) 5,881 21.8 8.3


NoCal Parkfield (No Down Weight, xmax = 3 km)51 San Andreas Parkfield (North) 3,417 32.4 8.352 San Andreas Parkfield (South) 480 31.9 10.1


Notes to Table 3:aDown‐weighted level N0, Fitting distance xmax.bFrom relocated catalogs P, U, and T as described in text.

Table 2. Earthquake Catalog Statisitics

NTa (events) b Mc

Southern California (SoCal)SCSN catalog 291,541 0.9 2.0Fault classesLarge 11,095 0.9 1.9Small 8,966 0.8 1.5Aftershock‐dominated 19,849 0.9 1.8

Northern California (NoCal)NCSN catalog 47,711 0.8 1.2Fault classesLarge 16,881 0.7 1.2Parkfield 3,897 0.9 1.2

aAll events common to regional and relocated catalogs in Table 1.


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[15] We filtered the hypocentral depths in each fault cat-alog to focus on the central part of the seismogenic crust.Averaged across all fault segments, 90% of seismicity fallsbetween 2 and 10 km for catalogs U and T and 2.5 and17 km for catalog P (Figure 3). The upper 5% of events tendto occur within 2 km of the free surface, and so we set 2 kmas an upper truncation depth. The lower cutoff shows sig-nificant variation reflecting regional differences in seismo-genic thickness [Hauksson, 2000; Magistrale, 2002]. Wetherefore set the lower truncation depth to exclude the dee-pest 5% of hypocenters in each fault catalog. The differencesbetween the lower and upper truncation depths for the kth

fault segment determined the segment width Wk; values foreach fault segment catalog are listed with the fault lengths Lkin Table 3.[16] For each fault segment, we established a fault‐ori-

ented coordinate system by fitting a plane to the seismicity.An initial estimate of the fault plane was derived from theCFM or, in the absence of a fault model, from a verticalplane that approximated the mapped surface or epicentertrace. All parameters of the plane were perturbed to obtain aleast squares fit to relocated hypocenters from catalogs P, Uor T within 2 km of this initial fault plane. For all faultsegments considered, a 4 km wide swath captures most

Figure 4. Example of intercatalog earthquake location variation. (a) Map of the Elsinore fault (segment10, Figure 2) showing relocated seismicity of catalog P and historic (heavy black lines), Holocene (thinblack lines), and late Quaternary (thin gray lines) faults. (b) Depth section across the map showinglocations of events in the standard catalog S relative to an initial, 3‐D fault model based estimate of the faulttrace (heavy dashed line); earthquakes are the same magnitude ranges as on the map. (c) Fault‐normaldistribution of events. (d) Depth section across the map for relocated catalog P. (e) Fault‐normal seismicitydistribution of relocated events. Note the difference in horizontal bias (black arrow in Figures 4c and 4e) ofpeak seismicity between the standard and relocated catalog.


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near‐fault earthquakes while ignoring off‐fault clusters thatwould contribute to misalignment of the coordinate systemwith the fault plane. Narrower swaths fail to include near‐fault events for fault segments where seismicity exhibits asignificant horizontal shift from the initial estimate, as in thecase of the Elsinore fault (Figure 4). Rotations permitted bythe fitting process further localize events on final, seismic-ity‐based fault planes, as is observed on the Hayward fault(Figure 5).

[17] The hypocenters from the relevant relocated catalogwere transformed into a local Cartesian system defined byan origin at one end of the surface trace of the best fit faultplane, a near‐vertical z axis, a y axis along the fault strike,and an x axis perpendicular to the fault plane. A final, fault‐referenced catalog was then constructed by eliminatingevents with relocated x coordinates greater than ±15 km,relocated y coordinates beyond the ends of the fault seg-ment, and relocated z coordinates outside the depth limits

Figure 5. Example of how a fault‐seismicity‐based coordinate system localizes events on a fault andminimizes artificial fault‐normal dispersion. (a) Map of the southern Hayward fault (segment 43,Figure 1) showing relocated seismicity of catalog U; fault age representations are the same as inFigure 4. The fault strand cutting across the lower right corner of the map is the northern Calaveras fault.(b) Fault‐normal depth section across the fault trace prior to aligning coordinate system to relocatedseismicity; earthquakes are the same magnitude ranges as in the map, and the heavy dashed line marks thedepth projection of the fault surface trace. (c) Fault‐normal distribution of events. (d) Fault‐normal depthsection across the fault trace after aligning coordinate system to a best fit plane to relocated seismicity.(e) Realigned fault‐normal distribution. Note that the fault‐seismicity based coordinate system yields anarrower event distribution in Figure 5e.


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described above. The fault segment catalogs are summarizedin Table 3.

3. Intercatalog Analysis

[18] A proper description of near‐fault seismicity dis-tributions requires careful attention to mislocation errors.Information about such errors can be determined fromcomparisons of hypocenters determined by different meth-ods [e.g., Shearer et al., 2005]. In the present study, we havequantified the intercatalog comparisons on a fault segmentbasis. For the kth fault segment with Nk events common tothe catalog pair A and B, we define the intercatalog fault‐normal bias by

bkxAB ¼ 1

Nk

Xi2k

ðxiA � xiBÞ; ð1Þ

and the fault‐normal variance by

ð�kxABÞ2 ¼

1

Nk � 1

Xi2k

ðxiA � xiB � bkxABÞ2: ð2Þ

Here, xAi is the fault‐normal coordinate of the ith event, and

the summation implied by i 2 k is over all Nk events asso-ciated with the kth fault segment. Similar expressions can bewritten for the fault‐parallel and near‐vertical directions.The intercatalog bias and variance computed for each cat-alog pair (UN and TN in northern California and HS, PS,and HP in southern California) are listed by individual faultsegment in Tables S1–S3 in the auxiliary material.1

[19] For each coordinate of the fault‐oriented referenceframe, the mean intercatalog bias for a fault class wascomputed by taking the absolute values of the segmentbiases, weighting them by the number of events for eachsegment, and averaging over all segments. Likewise, the

mean standard deviation was calculated as the square root ofthe event‐weighted segment variances. These averages aregiven in Table 4. For all classes, the intercatalog biases andstandard deviations are largest for the z coordinate, reflect-ing the uncertainty in estimating hypocentral depth. Nosystematic differences are observed between the two hori-zontal coordinate statistics, x and y. In southern California,the z coordinate statistics are especially large, in part be-cause shallow events in the early part of Catalog S wereoften assigned a default depth of 6 km, and also because thevelocity model used to relocate events in Catalog H tends tobias events downward (Figure 3). Because we are interestedin the fault‐normal distribution of seismicity, we focus ourdiscussion on bAB

x and sABx .

[20] The intercatalog statistics for well‐instrumentedParkfield region are higher than those of the northernCalifornia fault class, particularly the fault‐normal values(e.g., sTN

x = 0.62 km versus sUNx = 0.31 km). These differ-

ences are primarily due to more stations and a greater numberof earthquakes being used in the relocation procedure, aswell as a strong velocity contrast across the San Andreasfault near Parkfield, which is modeled in the Thurber et al.[2006] relocations but not in the standard catalog.[21] The intercatalog statistics for the large faults in

southern California (e.g., sPSx = 1.04 km) are also substan-

tially higher than for the northern California fault class,which we ascribe to several factors. The southern region hasa more heterogeneous crustal structure than the northernregion, such as larger and deeper sedimentary basins, in-creasing the location errors. Moreover, the faults sampled innorthern California were restricted to well‐instrumentedregions of the San Andreas system near the center of theNCSN. In southern California, a number of the large faultsare peripheral to the SCSN, and they invariably show biggerintercatalog variations (Figure 2). For instance, sPS

x for thecoastal Newport‐Inglewood fault (segments 8–9) is 2.1 km,and it reaches 2.7 km for the Cerro Prieto fault (segment 13),which is located in Mexico outside the SCSN. In contrast,the values for the more centrally located San Jacinto fault(segments 17–24) are less than 1 km.[22] In southern California, the large‐fault class has a

higher intercatalog standard deviation than either the small‐fault or aftershock classes (e.g., sPS

x = 1.04, 0.75, 0.55 km,respectively). The fault‐normal biases show a similar or-dering (e.g., bPS

x = 0.54 km, 0.43 km, 0.23 km). The networkgeometry again plays a role, because the latter two classescomprise segments that tend to be more centrally locatedwithin the SCSN. In addition, the estimator given byequation (1) accounts only for a constant translational bias;for long segments, other parameters, such as a rotationalbias, may be needed to represent the catalog differences,especially for faults on the periphery of the network. Theinadequacy of the bias model acts to increase the apparentintercatalog variance.[23] The standard deviations between the two relocated

southern California catalogs (HP) are consistently lowerthan those involving the standard catalog (HS and PS),satisfying the expectation that relocation reduces the hypo-central variance (Table 4). However, histograms of the fault‐normal differences for all three catalog combinations showheavy‐tailed distributions with outliers that dominate thevariance estimates. Most of these outliers can be explained

Table 4. Intercatalog Error Estimates

Catalog Pair(AB)

Bias (km)a Standard Deviation (km)

bxAB byAB bzAB sxAB sxABb syAB szAB

SoCal LargeHS 0.74 0.61 1.36 1.14 0.75 1.23 3.09PS 0.57 0.33 1.36 1.08 0.72 1.16 3.12HP 0.59 0.35 1.06 0.74 0.25 0.77 2.15

SoCal SmallHS 0.47 0.23 1.69 0.80 0.60 0.82 2.62PS 0.43 0.24 0.96 0.75 0.58 0.77 2.41HP 0.24 0.37 0.98 0.40 0.15 0.45 1.52

SoCal Aftershock‐DominatedHS 0.18 0.22 2.06 0.62 0.42 0.70 2.25PS 0.24 0.27 1.09 0.55 0.39 0.63 1.97HP 0.17 0.14 0.97 0.41 0.19 0.44 1.49

NoCalUN (Large) 0.10 0.03 0.15 0.30 0.15 0.24 0.52TN (Parkfield) 0.47 0.13 0.60 0.68 0.42 0.32 0.82

See the auxiliary material for individual fault values.aEvent‐weighted mean absolute values.bThe sxAB estimated by uniform reduction.

1Auxiliary materials are available in the HTML. doi:10.1029/2008JB006234.


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by the way the different location algorithms respond toanomalous travel times (e.g., picking blunders, large pathanomalies). To account for outliers, we applied a method ofuniform reduction [Jeffreys, 1932; Buland, 1986] in whichwe modeled the differences as the superposition of aGaussian distribution and a nearly uniform distribution. Thestandard deviations of the best fit Gaussians are listed inTable 4. The largest reductions, more than 80% in variance,are obtained for the HP intercatalog differences. The re-duced standard deviations were used to characterize theevent mislocations in our subsequent analysis of the errorsin the fault‐normal scaling parameters.[24] If the event location errors from the three southern

California catalogs are assumed to be statistically indepen-dent (possibly a poor assumption) then we can determinecatalog‐specific biases, bA

kx, and standard deviations, sAkx, by

solving the three equations for intercatalog bias:

bkxAB ¼ bkxA � bkxB ; ð3Þ

and the three for intercatalog variance:

�kxAB

� �2¼ �kxA

� �2þ �kxB

� �2; ð4Þ

where AB = {PS, HS, HP}. Equations (3) are not linearlyindependent, and we therefore included the additional con-straint that the biases of the individual catalogs should sumto zero, which minimizes the overall bias. Similar sets ofequations can be solved for the fault‐parallel and depth di-rections. We averaged the event‐weighted absolute values ofthe fault segment biases to obtain the values in Table 5 (seethe auxiliary material for individual fault segment data).

[25] The s values for the relocated catalogs are substan-tially smaller than those for the standard SCSN catalog, asexpected from the intercatalog comparisons, and the s valuesfor the Shearer et al. [2005] catalog are in all cases smallerthan those for the Hauksson and Shearer [2005] catalog. Inparticular, the values of sP

x obtained from the reducedintercatalog standard deviations are only about half the sizeof sH

x , which is consistent with the qualitative observationthat the cluster analysis relocation method used to developthe P catalog provides significantly better localization ofhypocenters into fault‐like structures [Shearer et al., 2005].For this preferred southern California catalog, the fault‐normal standard deviations are less than 0.1 km for all threefault classes. As noted above, our linear removal of bias didnot consider possible intercatalog rotations, which couldskew the intercatalog variance to higher values, whereaspossible correlations in the hypocenter errors between dif-ferent catalogs would skew them to lower values. On thebalance, sP

x ≈ 0.1 km appears to be a good estimate.[26] In Table 5, we compare the results of the intercatalog

error analysis with formal location errors listed in the indi-vidual catalogs. The standard deviations in depth from thelatter sources are always larger than the corresponding meanhorizontal standard deviation, in rough agreement with theintercatalog analysis, but the magnitudes are rather different.The mislocation errors included in the standard networkcatalogs are substantially larger than our computed values.The reverse is generally true for the relocated catalogs,though the agreement is much better. The confidence regionof fault‐normal hypocentral error for the relocated catalogsis 0.05–0.2 km with the high end of the range representedby a few fault segments at the periphery of the southern

Table 5. Catalog‐Specific Error Estimatesa

Catalog (A)

Bias (km)b,c Standard Deviationb (km) Catalog Error (km)

bxA byA bzA sxA sxAd syA szA Horizontal Vertical

SoCal LargeS (standard) 0.37 0.29 0.76 0.98 0.71 1.07 2.71 2.35 4.49P (relocated) 0.28 0.13 0.69 0.45 0.09 0.45 1.55 0.04 0.21H (relocated) 0.40 0.32 0.72 0.58 0.23 0.62 1.50 0.15 0.25

SoCal SmallS (standard) 0.28 0.12 0.88 0.72 0.58 0.73 2.28 1.96 3.52P (relocated) 0.18 0.19 0.30 0.19 0.07 0.24 0.78 0.03 0.13H (relocated) 0.22 0.18 0.82 0.35 0.14 0.38 1.30 0.10 0.17

SoCal Aftershock‐DominatedS (standard) 0.13 0.16 1.05 0.50 0.38 0.59 1.83 1.76 3.26P (relocated) 0.13 0.12 0.16 0.21 0.08 0.22 0.71 0.04 0.25H (relocated) 0.10 0.06 1.01 0.36 0.17 0.38 1.30 0.19 0.33

NoCal LargeN (standard) — — — — — — — 0.30 0.62U (relocated)e — — — — — — — 0.10 0.50

NoCal ParkfieldN (standard) — — — — — — — 0.56 0.95T (relocated) — — — — — — — NR NR

aSee the auxiliary material for individual fault values. NR, not reported.bComputed assuming statistical independence.cEvent‐weighted mean absolute values.dThe sxA estimated by uniform reduction.eCatalog averages as reported by Ellsworth et al. [2000].


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California network. For the most part, location error is<0.1 km, consistent with the intercatalog analysis. Furtherchecks on the mislocation errors from seismicity modeling,described below, support the intercatalog analysis.

4. Fault‐Normal Seismicity Distributions

[27] Because strike‐slip faults in California are nearlyvertical, we developed our scaling relations using the fault‐normal distance ∣x∣ as the independent variable, ignoringbilateral asymmetry in seismicity. We stacked the seismicitydata in each fault group and computed earthquake density asa function of distance ∣x∣ using a nearest‐neighbor method[Silverman, 1986] in which the bins are adjusted to containq neighboring events. For each data set we experimentedwith a range of q values and selected one that yielded anadequate point density for deriving fault‐normal scalingrelations (10 ≤ q ≤ 50).[28] Logarithmic plots of earthquake density versus ∣x∣ for

each regional catalog indicate fault‐normal distributions thathave flat peaks within a few hundred meters of the fault, roll‐off as an inverse power law for about an order of magnitudein distance, and merge with irregular backgrounds at dis-tances less than 10 km (Figures 6–9). Near the fault, the

Figure 6. Fault‐normal earthquake density distributions forlarge faults in southern California. Distributions for (a) relo-cated catalog P, (b) relocated catalog H, and (c) standardcatalog S using a nearest‐neighbor bin interval of q = 50events. The heavy dashed line marks the limit to whichwe fit data, xmax; beyond this limit, background seismicitydominates. The black line is a maximum likelihood fit ofan inverse power law, with asymptotic slope ~�, to observa-tions within that limit. The inner scale of the distribution isdescribed by ~d.

Figure 7. Fault‐normal earthquake density distributions for(a) small faults and (b) aftershock‐dominated fault segmentsin southern California. Both Figures 7a and 7b use eventsfrom relocated catalog P with a bin interval of q = 50 events.Features are the same as in Figure 6.


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observed distributions can be described by the functionalform:

�ðxÞ ¼ �0dm

xj jm þ dm

� ��=m

: ð5Þ

In expression (5), d is an inner scale that removes the powerlaw singularity on the fault, g is the asymptotic roll‐off ofseismicity away from the fault, and the exponent m controlsthe shape of the distribution for x ∼ d, i.e., the sharpness ofthe corner on a logarithmic plot. By varying the latter

parameter, we found that the maximum likelihood fits tothe observed fault‐normal distributions were obtained form ≈ 2. We also experimented with exponential andGaussian distributions but found they were a poor fit to thedata.[29] Assuming m = 2, we obtained a maximum likelihood

fit of equation (5) to the binned data for each fault group outto a maximum fault‐normal distance xmax, chosen such thatthe relative contributions from background seismicity weresmall; the values of xmax for each fault class are listed in

Figure 8. Fault‐normal earthquake density distributions forlarge faults in northern California. Distributions for (a) relo-cated catalog U and (b) standard catalog N using a nearest‐neighbor bin interval of q = 20 events. The heavy dashedline marks the limit to which we fit data, xmax; beyond thislimit, background seismicity dominates. As in Figures 6 and7, the black line is a maximum likelihood fit of an inversepower law to observations within that limit.

Figure 9. Fault‐normal earthquake density distributions forthe Parkfield fault segments. Distributions for (a) relocatedcatalog T and (b) standard catalog N using a nearest‐neighborbin interval of q = 10 events. Features are the same as inFigure 8.


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Table 3. The expected number of events in the jth bin ofwidth Dx is the integral:

nj ¼Zjxjj

jxjj��x

�ðxÞdx: ð6Þ

We assume the observed value, nj, in each bin is Poissondistributed, which yields the log likelihood function [e.g.,Boettcher and Jordan, 2004]:

�ð�0; �; dÞ ¼XJbinsj¼1

nj ln njðxÞ� �� njðxÞ

� �� lnðnj!Þ�

; ð7Þ

Maximizing (7) using a linear approximation to n(x) overeach binning interval (adequate for the small intervals usedhere) yields the estimates ~�0, ~�, and ~d. These estimates havecorrelated errors. However, we note that the maximumlikelihood estimator for ~�0 is Nmax/

R0xmax

(1 + x2/d2)−g/2

dx,where Nmax is the cumulative number of events out to xmax.If Nmax is large, its relative error is small (∼Nmax

−1/2, the stan-dard population error) and uncorrelated with the errors in ~�and ~d. The latter are positively correlated, as shown inFigure 10, which plots the maximum likelihood estimatesand confidence intervals for the various fault groups in the~� − ~d plane.[30] We checked the error estimates from the maximum

likelihood procedure with those derived from jackkniferesampling [Efron, 1979]. Generally speaking, the twowere in agreement, but where they differed, we used thelarger estimate. We experimented with the lower magnitudecutoff and depth ranges and found the results to be robust.We also tested a range of bin widths, q, and found littlevariation in our results.[31] An important issue is the weighting of individual

fault segments in the seismicity stacking. Owing to thevariability in seismicity rates, the number of earthquakes perfault segment ranges from a hundred to several thousand(Table 3), and our results will depend on how each isweighted. In our stacking procedure, we applied a positiveweighting factor wk to each event in the kth fault segmentcatalog, which we computed by

wk ¼ min 1;N0=Nk½ �; ð8Þ

where N0 is a “down‐weighted level” that was held constantfor each fault group. We varied N0 from Nmin, the minimumof all catalog sizes Nk in each fault group, to Nmax, themaximum in each group. The latter bound corresponds to“one‐event‐one‐vote” (wk = 1), whereas the former corre-sponds to “one‐catalog‐one‐vote” (wk ∼ 1/Nk). For inter-mediate values, events from catalogs larger than N0 weredown weighted by the ratio N0/Nk, while those from smallercatalogs received unit weight. We experimented with arange of down weight levels for each structural group andfound that the maximum likelihood estimates for most of theparameters were stable across a wide range between Nmin

and Nmax (Figure 11). Table 3 lists the actual values used inderiving the parameter values discussed below.[32] For all structural groups, there is a well‐defined

scaling region of at least an order of magnitude in fault‐normal distance where the earthquake density shows apower law roll‐off before it merges with the backgroundseismicity (Figures 6–9). In Table 6, we list by fault groupthe maximum likelihood estimates of ~� and ~d. To assess theeffects of earthquake clustering, we declustered the faultsegment catalogs using the algorithm of Reasenberg [1985]with default parameters (rfact = 10, xk = 0.5, xmeff = 1.5, t0 =2 days, tmax = 10 days, p1 = 0.99) and obtained the distri-

Figure 10. Maximum likelihood solutions and errors for~� and ~d. Values for (a) southern California large faults,(b) northern California large faults, and (c) Parkfieldshowing the positive correlation between scaling para-meters. Light gray and black ovals mark the 68% and95% confidence bounds, respectively.


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bution parameters for the declustered catalogs and the eventclusters.[33] Table 6 shows interesting variations across the fault

groups and catalog types. Comparing the relocated catalogsP and U, seismicity decays away from the large faults insouthern California at a significantly lower rate (~� = 0.98 ±0.04) than it decays in northern California (1.60 ± 0.04) orfor the small faults in southern California (1.37 ± 0.08). Insouthern California, clustered events decay more rapidlythan independent events, in agreement with the higher decayrate for aftershocks of large southern California earthquakes(~� = 1.50 ± 0.08).[34] For the larger faults, the apparent inner scale ~d for

relocated catalogs is smaller in northern California (0.08 ±0.01 km) than in southern California (0.23 ± 0.03 km). Theformer is comparable to the relocation uncertainty. Sig-nificantly higher values are obtained for the standard cat-alogs (0.6–0.8 km), consistent with more dispersion due tomislocation.

5. Analysis of Bias

[35] The results in Table 6 are biased by two factors:contributions from background seismicity and hypocentralerror. The former is apparent when we relax the assumptionof bilateral symmetry. We first identified which side of eachfault segment had more events for ∣x∣ ≤ xmax and then re-stacked the data for each of the five fault classes, preservingthis asymmetry in seismic abundance (Figure 12 and theauxiliary material). The estimates of ~� obtained for the lessabundant side were consistently higher than those on themore abundant side. The values of ~d on the less abundantside of each fault class also increased slightly over those ofthe symmeterized distributions owing to the positive corre-lation between ~� and ~d. We did find that, on the side withfewer events, the scaling region extended to greater dis-tances from the fault, in some cases by an order of magni-

Table 6. Apparent Fault‐Normal Scaling Parameters

Catalog

Whole Catalog Declustered Clusters~d (km) ~� ~d (km) ~� ~d (km) ~�

SoCal LargeS (standard) 0.88 ± 0.09 1.19 ± 0.04 0.86 ± 0.09 1.12 ± 0.04 0.95 ± 0.19 1.51 ± 0.12P (relocated) 0.23 ± 0.03 0.98 ± 0.04 0.24 ± 0.03 0.93 ± 0.04 0.24 ± 0.04 1.22 ± 0.05H (relocated) 0.27 ± 0.03 0.98 ± 0.03 0.28 ± 0.05 0.94 ± 0.03 0.27 ± 0.05 1.18 ± 0.05

SoCal SmallS (standard) 0.79 ± 0.11 1.90 ± 0.30 0.86 ± 0.18 1.86 ± 0.44 0.73 ± 0.17 2.17 ± 0.54P (relocated) 0.19 ± 0.02 1.37 ± 0.08 0.19 ± 0.03 1.27 ± 0.08 0.22 ± 0.03 1.62 ± 0.17H (relocated) 0.23 ± 0.02 1.44 ± 0.09 0.22 ± 0.03 1.35 ± 0.10 0.27 ± 0.04 1.71 ± 0.19

SoCal Aftershock‐DominatedS (standard) 0.55 ± 0.04 1.63 ± 0.11 — — — —P (relocated) 0.33 ± 0.02 1.50 ± 0.08 — — — —H (relocated) 0.31 ± 0.02 1.44 ± 0.07 — — — —

NoCal LargeN (standard) 0.16 ± 0.02 1.68 ± 0.06 0.18 ± 0.03 1.73 ± 0.10 0.15 ± 0.02 1.66 ± 0.07U (relocated) 0.08 ± 0.01 1.60 ± 0.04 0.10 ± 0.01 1.62 ± 0.07 0.07 ± 0.01 1.61 ± 0.05

NoCal ParkfieldN (standard) 0.89 ± 0.09 3.86 ± 0.60 0.93 ± 0.12 4.64 ± 0.77 0.85 ± 0.19 5.57 ± 1.60T (relocated) 0.13 ± 0.02 2.52 ± 0.22 0.14 ± 0.02 2.50 ± 0.24 0.10 ± 0.03 2.70 ± 0.78

Figure 11. Down‐weighted analysis results for small faultsin southern California: (a) ~� and (b) ~d vary with downweighted value across the different catalogs. The dashedgray line marks our selected value of N0 = 700. Note thatparameter estimates are largely stable within error for mostdown‐weighted values. Only at low values of N0 do para-meters start to vary as more box catalogs, including thosewith few events, are weighted equally.


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tude, supporting our choice of power law model. Figure 12ashows that exponential and Gaussian distributions are a poorfit to the data. Fault maps show that the truncation of thescaling region on the abundant side can generally be ex-plained by the seismicity increase from another fault branchor splay, proximate to the target fault segment, a commonfeature of the San Andreas system (e.g., Figure 5).[36] Uniform background seismicity associated with

proximate faults significantly alters the shape of a density

distribution close to xmax. We show this by modeling thedistribution in each fault class as the superposition of afault‐normal decay of earthquake rate and a uniform back-ground rate (Figures 12b and 13). Parkfield was excludedfrom the modeling because the background signal is weakand the scaling parameters therefore unbiased. We use theparameters of the low‐abundance side of the fault in eachclass because the contribution frombackground is significantlylower and the scaling only minimally biased. By varyingthe ratio of background to decaying events, we recovered theresults reported in Table 6, as well as the distributions on theevent‐heavy side of the fault for each fault class, suggestingthat the fault‐normal decay of seismicity is similar acrossstrike‐slip faults. Values for background‐corrected scalingparameters are reported in Table 7.[37] We investigated how the results are biased by hypo-

center errors in two ways, theoretically and using MonteCarlo simulations. We assumed that the true fault‐normal

Figure 12. Comparison of fault‐normal earthquake densityfor (a) low‐ and (b) high‐productivity sides of a fault forcatalog P about large, southern California faults using anearest‐neighbor bin interval of q = 20 events. Featuresare the same as in Figures 6–9. Seismicity decays morerapidly on the low productivity side of a fault and spansalmost 2 orders of magnitude. In Figure 12a, maximumlikelihood fits of exponential (dashed) and Gaussian (dotted)distributions are shown for comparison. In Figure 12b, weadditionally fit the data using the parameters from the low‐productivity side (Figure 12a) and include a uniform back-ground rate, nbg. See the auxiliary material for distributionsof other fault classes.

Figure 13. Comparison of fault‐normal earthquake densityfor (a) large faults in southern California (catalog P) with(b) that of a synthetic distribution using bin intervals ofq = 50 events. Features are the same as in Figures 6–9.The synthetic distribution is one realization of a MonteCarlo simulation in which fault‐normal earthquake densityis modeled as the superposition of an unbiased distribution(g = 1.3, d = 0.3 km; compare Figure 12a) that decaysbeyond xmax (dashed gray line) and a uniform background.The maximum likelihood fit to the synthetic distributionout to xmax recovers the scaling parameters determined inthe initial analysis of symmeterized distributions.


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seismicity is governed by the distribution n(x) in equation (5),and that the catalogs have independent, identically distrib-uted mislocation errors approximated by a zero‐meanGaussian probability density function (pdf),

gAðxÞ ¼ 1

�xA

ffiffiffiffiffiffi2�

p exp �x2=2ð�xAÞ2

h i; ð9Þ

where sAx is the standard error for catalog A. The pdf for the

observed seismicity can then be computed as the convolu-tion of the two (normalized) distributions:

pAðxÞ ¼Z 1

�1�ðx� �ÞgAð�Þd�=

Z 1

�1�ð�Þd�: ð10Þ

A little analysis shows that, if sAx /d is not too large (less than

5 or so), pA(x) can be approximated by equation (5) with anasymptotic slope ~� = g and an inner scale ~d computed as theintersection of the small‐x probability density with thelarge‐x asymptote,

d=~d� ��¼ ffiffiffiffiffiffiffiffi

2=�p Z 1

01þ ð�x

A x=dÞm� ��=m

e�x2=2dx: ð11Þ

The bias correction d − ~d derived by solving (11) is onlyweakly dependent on the shape parameter m, so we fixed itat its best fit value (m = 2). We experimented with sA

x valuesspanning the confidence region of 0.05–0.2 km recorded inthe relocated catalogs. Because low values have only aminimal effect and the large values are only applicable to afew fault segments in southern California, the conservativeestimate of sA

x = 0.1 km determined from our intercataloganalysis is appropriate for A = P, U, and T. Figure 14 plots ~dversus d for sA

x = 0.1 km and we see that the correction issmall for d > sA

x and decreases with g.[38] The bias‐corrected estimates of d obtained from (11)

are listed in Table 7. The largest correction, for large‐faultseismicity in northern California, changes the estimated innerscale from 0.09 km to 0.06 km, a difference of only 30 m.Note that the magnitude of bias in this worst case, 0.03 km,is smaller than the quadratic estimator

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid2 þ �2

A

p− d =

0.05 km. We verified the small size of the bias correctionusing a Monte Carlo method in which we generated syntheticcatalogs that satisfied (12), perturbed them with Gaussiannoise (0.05 ≤ sA

x ≤ 0.2 km), and calculated a likelihood scoreof their fit to the distribution curves obtained from the actualdata. The values of d and g that maximized the likelihood formany (∼50) catalog realizations for sA

x = 0.1 km are listed inTable 7; an example of a single realization is presented inFigure 15. The estimates of d are nearly identical to the

theoretically corrected values. Moreover, the simulationsprovided bias corrections for g, which are not zero (as theasymptotic theory predicts) owing to the positive correlationbetween the estimators of d and g arising from a finite rangeof x (see Figure 10). However, the corrections to g are alsosmall, 10% (for catalog T) or less.

6. Rough Fault Loading Model

[39] Our multicatalog analysis of earthquake hypocentersin California reveals that the seismicity in the vicinity ofstrike‐slip faults can be represented by a three‐parameterdistribution:

�ðxÞ ¼ �0d2

x2 þ d2

� ��=2

; jxj � xmax: ð12Þ

The constant n0 describes the fault‐normal seismic intensity(in events/km) on the fault surface. Using the data in Table 3,the intensity n(x) can be normalized by the total faultlength S Lk, as plotted in Figures 6–9, or by the total faultarea S LkWk, which yields a spatial seismic density for thecatalog interval T = 19 years. The inner scale d measures the

Table 7. Bias‐Corrected Scaling Parameters

Fault Class Catalog

Background Correction

Hypocentral Error Correction

Theoreticala d (km)

Simulateda

d (km) g d (km) g

SoCal large P 0.26 ± 0.04 1.23 ± 0.05 0.23 0.22 ± 0.04 1.16 ± 0.05SoCal small P 0.21 ± 0.03 1.44 ± 0.07 0.19 0.18 ± 0.03 1.37 ± 0.10SoCal aftershock‐dominated P 0.39 ± 0.04 1.70 ± 0.06 0.38 0.37 ± 0.03 1.62 ± 0.10NoCal large U 0.09 ± 0.02 1.82 ± 0.05 0.06 0.06 ± 0.02 1.65 ± 0.05NoCal Parkfield T 0.13 ± 0.02 2.52 ± 0.22 0.11 0.12 ± 0.03 2.30 ± 0.25

aBias corrections computed assuming sxA = 0.1 km.

Figure 14. Theoretical relationship between an observedinner scale, ~d, and the true value of d plotted for various g.Theory assumes that an observed fault seismicity scalingdistribution is the product of the true distribution convolvedwith a Gaussian noise function with standard deviation of0.1 km. Only at d < 0.2 km do the observed and true valuesdiverge significantly.


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half width of a near‐fault region where the seismic intensityis flat (∼n0), and the exponent g specifies the power lawroll‐off of seismic intensity in the scaling region d < x ≤xmax.[40] Figure 16 presents a conceptual “rough faulting

loading” (RFL) model that we will use to explain the seis-micity behavior. Our starting point is the observation thatfault surfaces can be described by a self‐affine (fractal)complexity over a large range of spatial scales [Power andTullis, 1995; Lee and Bruhn, 1996; Renard et al., 2006]and evolve in time toward surfaces that are less complex inthe direction of slip [Wesnousky, 1988; Stirling et al., 1996;Sagy et al., 2007; Finzi et al., 2009]. Here “complexity”refers to the fractal branching of faults into multiple surfaces[e.g., King, 1983; Hirata, 1989] as well as the fractalroughness of individual fault surfaces [e.g., Lee and Bruhn,1996; Renard et al., 2006; Sagy et al., 2007]. To build asimple model, we begin by considering a single fault surfacewhose deviations from the planar approximation x = 0 definea fault‐normal topography [Saucier et al., 1992; Chester andChester, 2000; Dieterich and Smith, 2009]. We representan along‐strike (constant z) profile of this topography as therealization of a stationary stochastic process X(y) that haszero expectation, hX(y)i = 0, and a variogram

2�2ð�yÞ ¼ ½X ðyþ�yÞ � X ðyÞ�2D E1=2

: ð13Þ

the surface is self‐affine, then x ∼ DyH, where 0 ≤ H ≤ 1 isthe Hausdorff measure (sometimes referred to as the Hurstexponent) of the along‐strike profile [Feder, 1988; Turcotte,1997]. Assume the self‐affine scaling of fault roughnessbreaks down above some outer scale Dyouter related to the

Figure 16. Schematic representation of the RFL (roughfault loading) model that explains observations of near‐faultseismicity distribution. (a) Tectonic loading of a self‐affinefault generates a heterogeneous stress field that yields apower law decay of seismicity over a scaling region viastress relaxation [Dieterich and Smith, 2009, Figure 3].(b) Toward the fault core, small‐scale stress heterogeneitiesof the rough fault are attenuated by low fracture strengthacross a damage zone of width 2d km. (c) Illustration of howobserved seismicity rates vary with distance from a fault(solid black line). The scaling region likely extends beyondxmax, as indicated by the dashed black line, but is masked byinterference from proximal fault branches.

Figure 15. Sample result from simulation analysis ofparameter bias. In each simulation, synthetic distributionswere perturbed with Gaussian noise (sA

x = 0.1 km) until acombination of g and d was found that maximized the like-lihood score of the fit to the original distribution. The sim-ulation result pictured is for large faults of southernCalifornia and illustrates a good correlation between a per-turbed synthetic distribution (dots) and our observed distri-bution (dashed line) for catalog P.


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characteristic segmentation length hLki. At profile separationslarger than Dyouter, the variogram (13) levels off to 2x∞,where x∞ ≡ hX2(y)i1/2 is the root‐mean‐square (RMS) topo-graphic fluctuation. The power spectrum PX(ky) is then theFourier transform of the autocovariance function CX(Dy) =x∞2 − x2(Dy). PX(ky) plateaus at a value ∼x∞2 below thecharacteristic wave number 1/Dyouter and rolls off as ky

−2H−1

above this characteristic wave number (Figure 17).[41] The widths of the seismicity scaling regions, xmax =

4–10 km, are much smaller than the average segmentationlengths in Table 3, so we do not observe a seismicity cutoffassociated with Dyouter. Instead, the scaling regions arelimited by the background seismicity from proximate faults;that is, the values of xmax are related to fault branching ratherthan fault roughness.[42] In the scaling region Dy < Dyouter, the tectonic

loading of a self‐affine fault will generate near‐fault stressheterogeneity characterized by stress lobes with a power lawsize distribution, as illustrated in Figure 16. Dieterich andSmith [2009] have used two‐dimensional numerical simula-tions based on Dieterich’s [1994] rate‐ and state‐dependentmodel of seismic nucleation to calculate the fault‐normalseismic intensity n(x) from this type of stress loading. Theyobtain a power law decay in seismicity that satisfies n ∼ ∣x∣−D,where D = 2 − H is the fractal dimension of the along‐strikeprofile.[43] If this 2‐D approximation applies to strike‐slip faults

in California, then g ≈ D, and the data from Table 7 yield alow fractal dimension for large‐fault roughness in southernCalifornia:D is close to 1, consistent with self‐similar scaling

(H = 1). For the small‐fault and aftershock‐dominatedclasses in southern California and the large northern Californiafaults, we find D ≈ 3/2, which corresponds to a process withan exponential correlation function (brown noise). Faulttraces and profiles across exposed and laboratory‐generatedfault surfaces typically range between these fractal dimen-sions [Power and Tullis, 1995; Lee and Bruhn, 1996;Renard et al., 2006], as do profiles across other types ofgeologic surfaces [Brown and Scholz, 1985; Goff andJordan, 1988; Brown, 1995]. The seismicity roll‐off ratefor Parkfield is significantly higher, g = 2.3 ± 0.25, con-sistent with H ≈ 0, D ≈ 2. For this type of fault roughness,the power spectrum decays as 1/ky (pink noise). Pink spectrahave been observed on a few normal‐fault scarps in thedirection of slip [Sagy et al., 2007].[44] Of course, the validity of the fractal quantification

can be questioned owing to the simplicity of the calculations(e.g., the Dieterich‐Smith model does not account foraftershock diffusion) and the likely role of 3‐D effects,including fault branching [e.g., King, 1983; Hirata, 1989]and roughness anisotropy [e.g., Lee and Bruhn, 1996;Renard et al., 2006]. Nevertheless, our data do suggest thatthe wave number spectra of large southern California faultsare “redder” than those of northern California; this inferenceagrees with observations that many of the large faults insouthern California are macroscopically complex [Okubo andAki, 1987; Wesnousky, 1988, 1990]. By the same token, ifwe assume the roughness amplitude at short scales (say,Dy ∼ centimeters) is similar for all strike‐slip faults inCalifornia, as depicted in Figure 17, then Parkfield shouldhave the lowest along‐strike roughness amplitude at longscales among the fault classes in Table 7. The Parkfieldsegments of the San Andreas fault are indeed quite straight.Some evolutionary aspects of the RFL model related to faultcomplexity are discussed in section 7.[45] Equally interesting is the interpretation of d. For the

fault classes in Table 7, this inner scale of the seismicitydistribution varies from 50 m to around 300 m. We couldintroduce an inner scale of fault roughness, Dyinner, to theRFL model, as depicted in Figure 18, below which x(Dy)→0. Such a cutoff would cause the stress‐loading amplitudesto level off in a near‐fault region of width d ∼ Dyinner.However, the available data suggest that the self‐affine scalingof fault roughness continues to much smaller dimensionsthan d, perhaps even to microscopic scales [Power andTullis, 1995; Sagy et al., 2007].[46] Rather than relating d to a cutoff in surface rough-

ness, we identify it as the half width of a volumetric“damage zone,” where small‐scale stress heterogeneity isattenuated by low rock strength (Figure 16). Damage zoneswith dimensions of tens to hundreds of meters are widelyrecognized features of exhumed strike‐slip faults [Chesterand Logan, 1986; Chester et al., 1993; Ben‐Zion andSammis, 2003; Chester et al., 2005; Rockwell and Ben‐Zion, 2007], and they have been used to explain verticallow‐velocity zones of comparable dimensions inferred fromfault zone guided waves [Li et al., 1990]; these low‐velocityzones extend at least to several kilometers [Ben‐Zion et al.,2003; Peng et al., 2003; Lewis et al., 2005] and perhapsdeeper [Li et al., 2004;Wu et al., 2008]. Drill samples acrossthe Nojima fault, which ruptured in the 1995 Kobe earth-quake, indicate that shear strength is significantly reduced

Figure 17. Schematic power spectrum, PX (ky), for the RFLmodel as a function of along‐strike wave number. The spec-trum includes upper and lower cutoffs associated with outer,Dyouter

−1 , and inner, Dyinner−1 , scales, as well as a scaling region

with slope −(2H + 1), where H is the Hausdorff measure.The inner and outer scales are beyond the resolution ofour analysis, which only captures the scaling region (graybox). We find that regional variation in seismicity rates cor-relates with different levels of fault roughness, as measuredby H (inset).


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and the permeability increased within a damage zone sur-rounding the fault core [Lockner et al., 1999]. A reduction infracture strength by increased fluid pressures [Unsworth etal., 1997] and the formation of talc and other low‐strength

minerals within the damage zone [Morrow et al., 2000;Moore and Rymer, 2007] is our preferred explanation of thenear‐fault stress homogenization implied by the inner scale d.[47] The best data on damage zone dimensions at seis-

mogenic depths in California come from recent boreholemeasurements near Parkfield by the San Andreas FaultObservatory at Depth (SAFOD) project. In 2007, SAFODdrilling encountered two principal slip surfaces at measureddepths of 3194 m and 3301 m, which were embedded in azone of variably damaged rock approximately 250 m infault‐normal width [Chester et al., 2007; Zoback et al.,2008]. This value, obtained near the top of the seismo-genic zone, is consistent with local studies of fault zoneguided waves, which sample somewhat deeper [Korneev etal., 2003; Li et al., 2004], and it agrees with our Parkfieldvalue of 2d = 240 ± 60 m, which averages over the entireseismogenic zone.[48] For large faults in northern California, the damage

zone width inferred from Table 7 is 120 ± 40 m, in line withgeologic estimates from large exhumed strike‐slip faults[Chester et al., 2004; Frost et al., 2009], faults exposed inmines [Wallace and Morris, 1986], and studies of fault zonetrapped waves elsewhere [Ben‐Zion et al., 2003; Lewis etal., 2005]. The narrow damage zone is consistent with asimple fault geometry comprising a single fault core boun-ded on one or both sides by a variably fractured material(Figure 18a), similar to exposures of the San Gabriel, SanAndreas, and San Jacinto faults [Chester et al., 2004; Dor etal., 2006]. Such a single‐core fault is said to have a “faultcore multiplicity of one.” In this terminology, the double‐core Punchbowl fault [Chester et al., 2004] and the SanAndreas fault at SAFOD have a fault core multiplicity oftwo, which approximately doubles the damage zone width(Figure 18b).[49] The average damage zone width obtained for the

small‐fault class in southern California is significantly largerthan at Parkfield: 2d = 360 ± 60 m, suggesting a fault coremultiplicity greater than two (i.e., wider, more complex faultzones comprising multiply braided fault cores (Figure 18c).We are not aware of observations from southern Californiathat independently confirm this hypothesis, but some strike‐slip faults exposed elsewhere have anastomosing, multicoredamage zones at least several hundred meters in fault‐normalwidth [Wallace and Morris, 1986; Faulkner et al., 2003].[50] The same line of reasoning would attribute an even

higher multiplicity to the large southern California faults, forwhich 2d = 440 ± 80 m. In the case of long faults, however,we must account for an increase in the apparent damagezone width caused by along‐strike variability of the faultcore surfaces. In a self‐similar model (H = 1), the along‐strike RMS topography of the large faults, x(Dyouter) ≈ x∞,should be about 5 times that of the small faults (which areabout one fifth as long; see Table 3). Assuming the fault‐normal topography is approximately Gaussian, we canestimate its contribution to d by replacing sA

x with x(Dy) inequation (11). A calculation shows that the entire differencebetween the large and small faults can be explained if x∞ ≈180 m. Large faults in southern California show at least thismuch variability (e.g., Figure 4). We conclude that a faultcore multiplicity of order 3 can explain the observed d valuesfor both the large‐fault and small‐fault classes in southernCalifornia.

Figure 18. Relationship between fault core multiplicityand damage zone width. Fault cores (heavy black lines)are shown embedded in a damage zone that is surroundedby largely undamaged host rock. Damage intensity is indi-cated [after Chester et al., 2004]. (a) The damage zonewidth about a single fault core is narrow, comparable tonorthern California faults. (b) The width of fault damagezones with a multiplicity of two (paired) is consistent withour observations of the San Andreas fault at Parkfield andfield studies of the exhumed Punchbowl fault [Chester et al.,2004]. (c) Fault damage zones with a fault multiplicitygreater than 2 are comparable to southern California faultsand are manifested as multiple braided or anastamosing faultcores (modified from Faulkner et al. [2003] with permissionfrom Elsevier).


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[51] For aftershock‐dominated faults, 2d = 740 ± 60 m,the highest of all fault classes. Because these fault segmentsare quite short (∼8 km), the RMS topography of the faultsurfaces should not contribute significantly to the apparentdamage zone width. Mislocation errors might be somewhathigher for the aftershock‐dominated faults (e.g., owing tosaturation of network‐processing capabilities during timesof high seismicity), but we can discount enhanced mislo-cation bias as an explanation of higher apparent width,because the subcatalogs of clustered seismicity extracted fromthe other fault classes do not show an increase in ~d relative tounclustered seismicity (Table 6). More likely, the immaturefaults of the Eastern California Shear Zone that were activatedby the Joshua Tree–Landers–Hector Mine sequence are justmore complex than typical southern California faults, assuggested by the broad (∼2 km) compliant zones of induced,and in two cases retrograde, deformation observed followingthe Hector Mine main shock [Fialko et al., 2002].[52] A speculative possibility is that the effective width of

the damage zone increases in response to strong shakingduring large earthquakes and subsequently decreases bylogarithmic healing. This mechanism is consistent with thestudies of fault zone guided waves following the Landersand Hector mine earthquakes, which indicate significanthealing on a decadal time scale [Li et al., 1998, 2003]. Wenote, however, that the fault zone waveguides do not appearto be anomalously wide in the Landers region [Li et al.,2000].

7. Evolutionary Aspects of Near‐Fault Seismicity

[53] The short‐term response of fault zones to shakingduring large earthquakes and the well‐documented long‐term evolution of strike‐slip faults in California [Wesnousky,1988; Stirling et al., 1996; Sagy et al., 2007] and elsewhere[Frost et al., 2009] indicate the RFL model may haveimplications for fault evolution. To augment the geographicvariation observed in our results for the aggregated faultclasses in Table 7, we provide estimates of the seismicityparameters for 10 individual faults with adequate earthquakerates, taken from the large‐fault classes for northern andsouthern California (Table 8). In three cases, the seismicitycatalogs for individual faults correspond to fault segmentslisted in Table 3 and mapped in Figures 1 and 2: segments11 (San Jacinto), 14 (Imperial), and 15 (Coachella segmentof the San Andreas). In the other seven, we aggregated twoor three segments. For instance, the Hayward fault spanstwo segments (42 and 43) with similar geologic historiesand slip rates, and the creeping section of the San Andreasspans three (48–50).[54] The same maximum likelihood procedure was

employed in fitting equation (5) to the individual fault cat-alogs. Because these catalogs comprise fewer events, theestimation uncertainties are larger than in Table 7, and wedid not apply any background or mislocation bias correc-tions, which are small enough to be ignored in the followingcomparisons. The seismicity parameters exhibit interestinginternal correlations. In particular, the seismicity is morelocalized (g is larger and d is smaller) on faults with higherseismic productivity n0/LW (Figures 19a and 19b), and it isless localized where the seismogenic zone, as measured byW, is thicker (Figures 19c and 19d).T

able

8.Dataon

Individu

alFaults

Fault

IDSegment

NT

(events)

~ d(km)

~ �L

(km)

Wa

(km)

n 0/LW

(events/km

3)

Cum

ulative

Offset(km)

Cum

ulativeOffset

References

Aseismicity

Factor

Aseismicity

Factor

References

Garlock

GA

1,2,

316

650.29

1.07

128.7

12.4

1.0

12–64

Pow

ell[199

3]0.0

—Stirlin

get

al.[199

6]New

port‐Ing

lewoo

dNI

8,9

408

0.20

0.84

113.7

18.3

0.16

5±5

Stirlin

get

al.[199

6]0.0

—Elsinore

EL

10,12

969

0.53

0.93

77.7

15.2

0.46

12±3

Stirlin

get

al.[199

6]0.0

—San

Jacinto

SJ

1150

270.25

0.96

37.7

19.4

6.7

28Pow

ell[199

3]0.0

—Im

perial

IM14

1179

0.32

2.53

21.2

7.0

20.0

?to

85Pow

ell[199

3]0.2

Genrich

etal.[199

7]Sh

earer[200

2]San

And

reas

(Coachella)

SAco

1525

60.77

2.95

40.7

10.3

0.62

160–18

5Pow

ell[199

3]0.2

Lyons

andSa

ndwell[200

3]Hayward

HA

42,43

1010

0.21

1.37

90.3

12.8

1.8

100±5

Graym

eret

al.[200

2]0.61

±0.19

WGCEPan

dNSH

MP[200

7]Lienkaemperet

al.[200

1]Calaveras

CA

44,45

,46

4666

0.06

1.73

39.2

8.9

130.0

160±5

Graym

eret

al.[200

2]0.77

±0.24

WGCEPan

dNSH

MP[200

7]Galehou

sean

dLienkaemper[200

3]

San

And

reas

(Creeping)

SAcr

48,49

,50

1012

20.09

1.63

48.9

10.1

120.0

315±10

Mattian

dMorton[199

3]0.62

±0.18

WGCEPan

dNSH

MP[200

7]San

And

reas

(Parkfield)

SApa

51,52

3897

0.14

2.52

64.2

11.2

35.0

315±10

Mattian

dMorton[199

3]0.77

±0.09

WGCEPan

dNSH

MP[200

7]

a Length‐weigh

tedaverage.


19 of 25

[55] Table 8 also lists cumulative offsets on the individualfaults and their aseismicity factors. We aggregated cumu-lative offset values for each fault from the literature, reportinguncertainties and range estimates where available. Follow-ing Wisely et al. [2007], we computed the aseismicity factor(AF) as the ratio of the aseismic slip rate to the long‐termslip rate over the full thickness of the seismogenic zone; thatis, AF = 0 corresponds to a locked fault, and AF = 1 tostable sliding. The AFs in Table 8, which are weighted by Nk,were primarily derived from the slip data compiled byWiselyet al. [2007] for the 2007 Working Group on CaliforniaEarthquake Probabilities [Working Group on CaliforniaEarthquake Probabilities and the USGS National SeismicHazard Mapping Program (WGCEP and NSHMP), 2007],supplemented with a few additional studies. We did notinclude faults that exhibit steady or transient surface creep

thought to be a dynamic (short‐term) or static (long‐term)response to some large, regional event (e.g., SuperstitionHills/Elmore Ranch [McGill et al., 1989]; Landers [Bilhamand Behr, 1992; Bodin et al., 1994]; Loma Prieta[Lienkaemper et al., 1997; Rymer, 2000]; Hector Mine[Rymer et al., 2002]). However, we did assign nonzero AFsto the Coachella Valley [Lyons et al., 2002] and ImperialValley segments of the San Andreas fault, because theyhave exhibited transient creep over the full width of theseismogenic crust. In the case of the Imperial Valley fault,we infer aseismic slip over the seismogenic crust byreevaluating Bilham and Behr’s [1992] fault model in lightof new estimates of seismogenic thickness [Shearer, 2002].[56] Although the scatter is high, we see that the seis-

micity tends to localize with increasing cumulative offset(Figures 20a and 20b), conforming to the notion that faults

Figure 19. Correlations between scaling parameters (a and c) ~� and (b and d) ~d and on‐fault earthquakedensity n0/LW and fault width W for related subsets of faults. Fault names (see Table 8) are indicated asfollows: CA, Calaveras; EL, Elsinore; GA, Garlock; HA, Hayward; NI, Newport‐Inglewood; PA,Parkfield; SAcr, San Andreas–Creeping; SAco, San Andreas–Coachella Valley; IM, Imperial; and SJ, SanJacinto. Note that smaller and more productive faults exhibit greater localization of seismicity (small ~d,large ~�). Solid lines are least square fits to the data with correlation coefficients R. Dashed lines are leastsquare fits with outliers removed; in Figure 19c, SAco and SApa were excluded; in Figure 19d, SAco andIM were excluded.


20 of 25

evolve toward more linear, focused structures. Wesnousky[1988] observed greater localization of surface traces withincreasing cumulative offset on fault length scales ofhundreds of kilometers. Here we observe a similar locali-zation in the seismicity at fault length scales of tens ofkilometers. Seismic localization also correlates with AF(Figures 20c and 20d).[57] Our data and the RFL model are consistent with a

simple narrative for fault evolution. Faults initiate as mul-tiple overlapping strands and coalesce into throughgoingstructures over time. Younger, rougher faults are charac-terized by multiple fault cores (high multiplicity) and cor-respondingly wide damage zones. As offset progresses, afault zone localizes and its roughness spectrum is whitenedby a steady decrease in its low wave number components,which localizes the near‐fault seismicity by increasing theroll‐off rate, g (decreasing H). This localization also reducesthe fault core multiplicity, eventually to a single or paired

core, thus reducing the damage zone width, 2d. Faultlocalization and smoothing promotes aseismic slip. Conse-quently, stressing rates increase markedly at the boundariesbetween steadily slipping and locked patches of a fault,driving up the seismic productivity per unit fault area, n0/LW.[58] In the real world, various combinations of additional

factors may ultimately govern the behavior of a fault. Evenif the geology of a fault at depth were known, the interre-lated factors of pore pressure, frictional strength, and heatflow will produce widely varying conditions for smallearthquake nucleation. Such variability is likely responsiblefor outliers such as the Coachella Valley segment of the SanAndreas fault (SAco in Figures 19 and 20). For example, theCoachella Valley segment is comparable to Parkfield interms of cumulative offset and fault width, but the Parkfieldsegment is known to contain serpentinite [Irwin and Barnes,1975; Zoback et al., 2008] and metamorphic fluids[Unsworth et al., 1997; Bedrosian et al., 2004] that likely

Figure 20. Correlations between scaling parameters (a and c) ~� and (b and d) ~d and cumulative offsetand aseismicity factor (a measure of aseismic slip on a fault) for related subsets of faults. Fault names (seeTable 8) are the same as in Figure 19. High aseismicity factors tend to be associated with more localizedfaults. Localization also increases with cumulative offset reflecting fault evolution toward more linear,focused structures. Solid lines are least square fits to the data with correlation coefficients R. Dashed linesare least square fits with outliers removed; in Figures 20b and 20d, SAco was excluded; in Figure 20c,both SAco and IM were excluded.


21 of 25

encourage aseismic slip along a narrow zone. The CoachellaValley segment, on the other hand, may be dry and thereforehave a larger d, lower seismicity, and less aseismic slip.

8. Discussion

[59] The fault‐normal seismicity distribution for strike‐slip faults in California can be described by an evolutionaryrough fault loading (RFL) model that is consistent withconstraints on fault structure and evolution derived fromother observations. The RFL model predicts no asymmetryin g, yet we observe asymmetry when we partition eachfault class in to groups by low and high seismic abundance.Once we correct for background bias though, the asymmetrydisappears and our results are consistent with the RFLmodel. Asymmetry in d is also of interest as it may correlatewith across‐fault material contrasts [e.g., Weertman, 1980;Cochard and Rice, 2000; Shi and Ben‐Zion, 2006] orasymmetric fault damage [e.g., Dor et al., 2006], propertiesmay be important in controlling rupture directivity. Like-wise, material contrasts are known to cause asymmetricfault‐parallel distributions of aftershocks [Rubin andGillard, 2000; Rubin and Ampuero, 2007] and may there-fore be reflected in fault‐normal earthquake rates. Unfortu-nately, when we initially selected our fault seismicitycatalogs, we allowed the seismicity to guide the choice ofcoordinate system and effectively symmeterized d valuesfrom the start.[60] We are also considering in more detail how the fault‐

normal distribution of seismicity correlates with its depthdistribution. In this paper, we restricted our data to thecentral part of the seismogenic crust and verified that therewas little variability in our results when the truncationdepths were varied. The distribution parameters d and gwere found to correlate with fault width W (Figures 19c and19d), indicating that the fault‐normal seismicity distribu-tions depend on the vertical structure of the fault zones,particularly the geothermal gradient. We have also observedthat the near‐fault seismicity of some segments is highlylocalized in depth, more often than not toward the base ofthe seismogenic zone [Boutwell et al., 2008]. We are inves-tigating what implications depth localization of seismicitymight have for the RFL model.[61] Our results have major implications for earthquake

forecasting and prediction, because they suggest howearthquake triggering statistics might be modified by thepresence of faults. Epidemic‐Type Aftershock Sequence(ETAS) models of triggered seismicity [e.g., Ogata, 1988]are good at predicting the short‐term earthquake rates on aregional scale in California, which are dominated by smallaftershocks, but they are less effective in forecasting the larger,less frequent earthquakes (M > 6) [Helmstetter and Sornette,2002, 2003; Gerstenberger et al., 2005; Helmstetter et al.,2006]. The spatial kernels in ETAS models are usuallyprescribed as an isotropic (radial) power law or exponentialdecay away from an event [Ogata, 1998; Zhuang et al.,2004; Felzer and Brodsky, 2006], so the forecasts incorpo-rate fault structure only through smoothed representations ofthe background seismicity. According to such models, amain shock at, say, 2 km from a fault is equally likely totrigger an aftershock at 4 km from the fault as on the faultitself. An isotropic kernel is not consistent with the observed

sequences of small aftershocks in California, which show anear‐fault bias [e.g., Hauksson et al., 1993], and it is likely tobe an even poorer model for the triggering of larger magni-tude events. We have observed that aftershock sequencesfrom our fault‐referenced catalogs can be described by anETAS spatial kernel modified to include a fault‐normal biasand an strike‐parallel elongation, both proportional to n(x) inequation (5) [Powers and Jordan, 2007b]. This anisotropic,heterogeneous spatial kernel and its consequences forearthquake forecasting will be discussed in a future paper.

[62] Acknowledgments. This research was supported by the South-ern California Earthquake Center. SCEC is funded by NSF CooperativeAgreement EAR‐0106924 and USGS Cooperat ive Agreement02HQAG0008. This is SCEC contribution 1247. We are grateful to BillEllsworth, Egill Hauksson, Peter Shearer, Cliff Thurber, and their respec-tive coauthors for making high‐quality relocated earthquake catalogs avail-able. Efforts on the part of the SCEC Unified Structural Representationgroup are also appreciated, and we thank Jim Dieterich and Deborah Smithfor their insight and opinion.

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T. Jordan, Southern California Earthquake Center, ZHS‐169, Universityof Southern California, 3651 Trousdale Pkwy., Los Angeles, CA 90089‐0742, USA. ([email protected])P. M. Powers, Department of Earth Sciences, ZHS‐117, University of

Southern California, 3651 Trousdale Pkwy., Los Angeles, CA 90089‐0740, USA. ([email protected])


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distribution of seismicity across strike slip faults in...

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