earthquake rate, slip rate, and the effective seismic...

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Earthquake rate, slip rate, and the effective seismic thickness for oceanic transformfaults of the Juan de Fuca plate system

E. C. Willoughby1 and R. D. Hyndman1 & 2

1. Pacific Geoscience Centre, Geological Survey of Canada, P.O. Box 6000 Sidney,B.C. V8M 1S4, Canada

2. SEOS, University of Victoria, Victoria, B.C., V8W 3P6, CanadaSubmitted to Geophysical Journal International 17/02/04

SummaryThe earthquake rate, average fault slip rate, and the effective seismic thickness have beenexamined for the Revere-Dellwood-Wilson, Sovanco, Nootka, Blanco and Mendocinotransform faults, bordering the Juan de Fuca plate system. Seismicity statistics are relatedto the rate of slip along a given fault from earthquakes, using the concept of seismicmoment. There are significant sources of uncertainty, including: the incompleteness andlimited history of the earthquake catalog, the variety of magnitude definitions which canonly be related empirically, empirical moment-magnitude relations (and the effect oftheir stochasticity), uncertainty in fault lengths and the effective seismic thickness, therecurrence relation, the determination of maximum magnitude and how the recurrencerelation is truncated at maximum magnitude. Nonetheless, this method has been usedsuccessfully to provide estimates of deformation in good agreement with those from platemodels. An agreement between the deformation rate predicted by seismicity statistics forthe fault zones and observed deformation from GPS and other geophysical data is used toshow the soundness of the method and parameters used. The least constrained parameteris the effective seismic thickness, thus the effect of a 2, 3, 6.5 and 10 km thick zone isinvestigated for each fault. The selection of a thin effective seismic layer of about 3 kmcan consistently explain most of the deformation in the region as being seismicallyaccommodated. The upper mantle is inferred to be aseismic, which is consistent withevidence of its serpentinization beneath these faults. The similarity of the deformationestimates based on seismicity and those from plate models, shows a remarkableconsistency in these rates over a significant temporal rangefrom tens to millions ofyears.Key words: seismicity, deformation, oceanic crust, transform faults, Juan de Fuca,Revere-Dellwood-Wilson fault, Sovanco fault, Nootka fault, Blanco fault, Mendocinofault

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Figure 1Bathymetric

map showing plate

boundaries in Cascadia,

for the North America,

Pacific, Juan de Fuca,

Explorer and Gorda

plates. Each of the faults

investigated is shown.

RDW designates the

Revere-Dellwood and

Dellwood-W ilson faults.

Bathymetric data

obtained from

http://topex.ucsd.edu/cg

i-bin/getdata.cgu.

IntroductionIn this article we examine the

seismic and slip behaviour of theoceanic transform faults bounding theJuan de Fuca plate system. Individualseismic moments may be summed butthe statistical uncertainties tend to bevery large. A more stable estimate of thetotal moment rate can be calculated asthe integral over magnitude of themagnitude-frequency of occurrence data,and this rate in turn can be related to therate of fault slip. A previous study, withlimited data, was carried out byHyndman and Weichert (1983).

The shrinking Farallon plate,converging with North America over thelast 150 million years, has becomeincreasing fragmented as the plate andoceanic ridges collide with and havebeen subducted under the continent(Riddihough, 1984; Braunmiller andNáb�lek, 2002). Here, we investigate theseismic slip along oceanic faultsbounding the surviving northernfragments, namely the Explorer, Juan deFuca and Gorda plates, off the coast ofthe Pacific Northwest region of NorthAmerica. The main Juan de Fuca plate is

moving as a coherent block, but both theExplorer and Gorda “plates” appear tobe breaking up and have substantialinternal deformation. From north tosouth, the faults are: the Revere-Dellwood-Wilson faults, marking thesouthwestern boundary of theDellwood/Winona Block, part of theExplorer; the Sovanco Fault Zone,marking the southwestern boundary ofthe Explorer plate; the Nootka FaultZone, the transform fault between theExplorer and Juan de Fuca plates; theBlanco Fault Zone, the southwestboundary of the Juan de Fuca plate andthe Mendocino Fault Zone, to the southof the Gorda plate, as shown in Fig. 1.For each of these faults, deformationsdue to seismic slip can be calculatedfrom earthquake catalog statistics andthese can be compared with estimates ofdeformation based on plate models andother geophysical and geodetic data.

1 Revere-Dellwood-Wilson Fault ZoneAt the northern tip of the

Explorer plate is the Dellwood/Winonablock separated from the Pacific by theDellwood-Wilson and Revere-Dellwoodfaults between Dellwood, Tuzo Wilsonand Explorer ridge spreading centres,designated RDW on Fig. 1 (e.g. Carbotteet al., 1989). This region seems to bemoving very slowly with respect to thecontinent (Davis and Riddihough, 1981)and a fault-slip rate comparable to thePacific-America rate is expected andsome small motion between the blockand the Explorer plate may beaccommodated (Hyndman and Weichert,1983). Though there are competingmodels to explain local tectonics, platemotions inferred from earthquakemechanisms indicate the block ismoving with or nearly with the Explorerplate (Braunmiller and Náb�lek, 2002).

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2 The Sovanco Fault ZoneThe Sovanco Fault Zone (Fig. 1),

extends northwest from the triplejunction between the Pacific, Juan deFuca and Explorer plates to the ExplorerRidge. The zone, in fact, now representstwo different sections in terms oftectonics. The western Sovanco fracturezone and southern Explorer ridge showmarkedly lower seismicity, which issymptomatic of a new developingPacific-Explorer transform boundarycutting through the Explorer plate’ssouthwest corner. FollowingBraunmiller and Náb�lek (2002), we callthis southwest corner, now apparentlytransferred to the Pacific plate, theSouthwestern Assimilated Territory(SAT). To the east, the Eastern SovancoDeformation Zone (ESDZ) shows abroad band of seismicity. Assuming thatall the seismicity in this regionrepresents ongoing deformation betweenthe Pacific and North American plate,regardless of fragmentation of theExplorer plate, we can still useearthquake statistics to predictdeformation. A sufficiently large areamust be selected to encompass thefracture zone and the SAT. GPS datafrom the north end of Vancouver Island,when combined with locked subductionthrust fault models provides anindependent estimate of slip rate forcomparison (Mazzotti et al, 2003a).

3 The Nootka Fault Zone The Nootka Fault Zone extends

from the Juan de Fuca ridge to theVancouver Island margin, where a fault-trench-trench triple junction marks theintersection of the Juan de Fuca,Explorer and North American plates(Fig. 1). The presence of the fault zoneitself was initially inferred from

magnetic anomaly analysis (Riddihough,1977) and substantiated by observationsof focused seismicity, reflection seismicprofiles, gravity and bathymetric data(Hyndman et al, 1979). Magneticanomaly, earthquake and GPS data seemto require the Explorer region to becurrently independent from the Juan deFuca and North American plates (Botrosand Johnson, 1988; Braunmiller andNáb�lek, 2002; Mazzotti et al., 2003a),although this has been subject to debate(Rohr and Furlong, 1995; Kreemer et al.,1998; Gover and Meijer, 2001). Themargin triple junction itself has notpreviously been examined in detail.Available field data at the Nootka faultzone itself is sparse (e.g. Hyndman et al.,1979; Au and Clowes, 1982; Au andClowes, 1984). In fact the preciselocation and trend of the Nootka faultzone is not well confined. It appears tobe a shear zone some tens of km wide.Further study is imperative inpreparation for the NEPTUNE oceanfloor observatory and potential futureIODP drill holes. This was the initialmotivation for this study; weinvestigated the other faults, which aremore readily comparable to plate modelrelative motions as a means ofcalibrating our solution for the Nootkafault zone and determining appropriateparameters, particularly the effectiveseismic thickness

4 Blanco Transform Fault ZoneThe Blanco transform fault zone

(BTFZ), off the coast of Oregon, marksthe southwest boundary of the Juan deFuca plate, between the Juan de Fucaand Gorda ridges (Fig.1). The right-lateral strike-slip oceanic transform faultis segmented, bounded by ridges. Thefault segments are separated by shortextensional basins; the most notable of

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Figure 2 Map of the Explorer plateshowing seismicity, above magnitude3.6, in the regions selected for study.Circle size is proportional to magnitude.The region around the Sovanco FaultZone is delineated with the dashed line.The first region around the Nootka fault,spanning the triple junction to justbeyond the margin, is delineated by adashed line. The extended Nootkaregion, including much more northerlydata and extending to Nootka Island,marked ‘N’, is shown by the dotted line.

which is the Cascadia Depression, wherethere is ongoing active spreading (Dziaket al., 1991). The BTFZ is dominated bythe 150 km high-angle right-lateralstrike slip fault with a small componentof dip-slip motion (where the Juan deFuca is the hanging wall relative to thePacific), called the Blanco Ridge (Dziaket al., 2000) The entire BTFZ isapproximately 350 km long. Thus, thereis potential for much larger earthquakes,than on the nearby faults around theExplorer, provided that the entire fault iscapable of rupturing.

5 Mendocino Fault ZoneThe Mendocino Fault zone

extends from the Mendocino triplejunction at the intersection of thePacific, Gorda and North Americanplates, to the Gorda Ridge (Fig. 1). Thenature of the fault zone and thetectonically complex, anomalouslydeformed area to the north (Riddihough,1980) has been subject to debate. TheGorda plate deformation zone wascreated by the recent clockwise changeof direction of the Juan de Fuca-Pacificrelative motion, which was notaccompanied by reorientation of theMendocino (Wilson, 1989). There arecompeting models to explain: (a) theprecise position, stability and history ofthe margin triple junction (Smith et al.,1993), (b) whether or not the Gordaregion can be truly deemed a separateplate and (c) whether motion along thefault is strike slip or whether there is acomponent of underthrusting, obductionor north-south compression (Wilson,1989; Silver, 1971; Stoddard, 1987). The Gorda is deforming internallyaccording to magnetic and earthquakedata, rather than fragmenting intocoherent pieces like the Explorer whichhas broken off the Juan de Fuca along

the Nootka fault in the north (Goversand Meijer, 2001).

6 Relating Seismicity to DeformationIf we assume, following

Anderson (1979) and Hyndman andWeichert (1983), that seismicity followsthe Gutenberg-Richter recurrencerelation up to an estimated maximummagnitude, we can calculate the totalmoment rate, and thus the deformationrate. This relation in commonly used inseismic hazard assessment. Usingseismicity to estimate deformationimplicitly assumes that most

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deformation occurs seismically over adefined fault cross-sectional area. In anearlier study, Hyndman and Weichert(1983) found good agreement betweenthe deformation rate implied byseismicity and according to platetectonic models for plate boundaries ofwestern North America. The estimate ofboth maximum magnitude Mmax and theform of the truncation of the recurrencerelation near Mmax, have a significantimpact on moment calculation. Anabrupt truncation of the density functionat Mmax results in a smooth fall offtowards Mmax in the cumulativerecurrence function (eg., Weichert,1980). Anderson and Luco (1983)examined the consequences inearthquake statistics and fault slip rate ifsome fraction of the seismic momentoccurs in near-maximum magnitudeearthquakes. Good agreement betweendeformation estimates based onseismicity and those based on geologicand geodetic data, assuming a truncatedcumulative exponential function andlittle to no contribution fromcharacteristic earthquakes, was found byField et al. (1999) for southernCalifornia. Likewise, estimates of thefrequency of large crustal earthquakesbased on geologic and geodetic datamatched those from observed seismicity,with the same assumptions, in thePacific Northwest Cascadia forearc(Hyndman et al., 2003). Here also, weassume an abrupt truncation of theincremental function, althoughrecognizing that it represents anuncertainty in the results. The momentrate and fault slip rate may then becomputed from the recurrence relationparameters (see Hyndman et al., 2003,and references therein).

The density function is given by n(M) = " exp(-$ M), M # Mmax (1)

andn(M) = 0, M > Mmax (2)

where " and $ are the density recurrenceexponential coefficients, as opposed tothe decimal logarithm coefficients a andb, as in

log n(M) = a – b M (3).The Gutenberg-Richter cumulativerecurrence coefficient b is given by

b = $/ ln 10 (4).The moment-magnitude relation is takento be deterministic, and moment Mo isgiven by

Mo = ( exp (* M) (5)or

log Mo = c +d M (6)Where c is of the order of 9.05 and d isof the order 1.5 in S.I. units. The totalmoment rate of the incremental ordensity recurrence function is Mo’ = b 10**[(d-b) Mmax + a + c]/(d-b).

(7) For a single earthquake over a fault ofarea A, the average slip displacement dis related to the seismic moment by

Mo = :Ad, (8)where : is the shear modulus, which weset to a typical value of 3.3 x 1010 N/m2

for crustal rock compositions. The sliprate s is proportional to the rate ofmoment release per unit time per unitfault area such that

s = Mo’/(:A). (9)From this the deformation rate may beestimated,s’ = CMo’/(2:A’) = CMo’/(2:WL), (10)where WL is the effective width timeslength, or effective cross-sectional areaof the effective seismic zone. C is aparameter which depends on theorientation of the faulting with respect toregional motion. Typically, C varies

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from 0.5 to 1.0; if we assume theorientation of these mainly strike-slipfaults is approximately 45o we can set C= 1.0.

7 Earthquake Data Selection: Region,Type of Magnitude and Completeness7.1 Earthquake Catalogs and RegionsInvestigated

All earthquake data offshoreBritish Colombia, for the RDW,Sovanco and Nootka faults, are from theGeological Survey of Canada (GSC)earthquake catalog. Data from theBlanco and Mendocino Faults are fromthe U.S. Geological Survey (USGS), theInternational Seismological Centre (ISC)and the Harvard Centroid MomentTensor catalogs.

The GSC earthquake catalog listsearthquakes in a selected region by date,time, estimated depth, calculatedmagnitude, preferred magnitude (ifseveral are available) and institution atwhich it was measured. The greatmajority of magnitudes are defined bythe local magnitude ML scale, but a fewwere recorded using, in order offrequency, the body-wave magnitude mb,moment magnitude Mw, surface wavemagnitude MS, coda or durationmagnitude MD or other scales. Routineearthquake locations of offshore eventshave been shown to be systematicallybiased by tens of kilometers to thenortheast, relative to bathymetricfeatures. This is because all monitoringstations have been situated on-shore, tothe east of epicenters, as well as aninexact velocity model for the oceaniclithosphere (Hyndman and Rogers,1981; Wahlström and Rogers, 1992;Dziak et al., 2000; Braunmiller andNáb�lek, 2002). Uncertainty in epicentrelocations decreases with time. Prior to1951, uncertainties in epicentre locations

are typically 50 km, and may be as muchas 100 km; more recently uncertaintiesare about 20 km (T. Mulder, GSC,personal communication, 2003). Thereare almost no constraints on eventdepths from routine processing; somedepth estimates come from momenttensor solutions, as discussed below.

Data for the Blanco fault wereretrieved from three USGS databases:the NEIC (1973 onward), USHIS (priorto 1973) and the ANSS (1961 onward).Where the catalogs overlap, their lack ofcompleteness was evident, as there are anumber of events in each catalog whichdo not appear in one or both of theothers. Most of these data are mb, withsome MS, Mw, ML and other magnitudes.Like the data for events off VancouverIsland, these data also suffer from a biasin computed earthquake epicentres; theaccuracy of locations of earthquakessuffers from the distribution of onlyland-based seismic stations, located tothe east, as well as inaccurate velocitymodels (Dziak et al, 1991). Epicentrelocations are routinely 20 to 30 kmoffset to the northeast of the fault zone’sbathymetric expression (Embley andWilson, 1992). Earthquakes locatedacoustically with the SOSUS arraydiffered from NEIC locations bybetween 4 and 71 km to the southwest(Dziak et al., 2000). Cronin andSverdrup (2003) used a joint-relocationprocedure on 120 mb > 5.0 events;recalculated epicentres were relocatedby an average of 34.6 ± 15.2 kmtowards azimuth 196o ± 28o and fell onthe seafloor mapped structural features.

Data for the Mendocino faultwere retrieved from two USGSdatabases: the NEIC (1973 onward) andthe California 1735-1974 catalog, which

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Figure 3 Seismicity, above magnitude3.6, and the regions selected for aroundthe Blanco and Mendocino faults. Circlesize is proportional to magnitude. Theregion around the Blanco is delineatedwith the dotted line. The region linearound the Mendocino fault isdelineated with the dashed line.

were supplemented by data from theHarvard Centroid Moment Tensorcatalog and the InternationalSeismological Centre. Again, there arequestions of catalog completeness as allevents in each catalog are not in everyother catalog. The addition of data fromthe Harvard CMT and ISC catalogsmeant that for many events multiplemagnitude estimates were available. Forthese events, we selected the bestestimate based on the type of magnitudeand proximity of the institution at whichit was measured. We selected Mw,followed by MS for large magnitudesdetermined teleseismically, ML, mb, andMD where no other estimates wereavailable. These data are also subject tobiases in position and apparentlyinconsistent magnitude definitions.

The selected seismicity regionsfor each fault encompass not only thefault under study defined by seafloormapping, but are chosen to be larger toallow for the epicentral uncertainty,known bias, and the scatter in the data.Also, the fault regions selected mustcontain sufficient seismicity data for thestatistics to be significant. For faultsaround the Explorer, the regions selectedare illustrated in Fig. 2. One regionencompasses all of the Dellwood-Wilsonand Revere-Dellwood faults. For theSovanco Fault Zone, a large region wasselected to ensure that all earthquakespertinent to Pacific-Explorer motionwere included, regardless offragmentation of parts of the Explorerplate. Two regions of different lengths,which encompass the Nootka fault, wereinvestigated. The first region spans thedistance from the ridge to the continentalslope. The second region is wider thanand includes most of the first (it issomewhat farther removed from the

ridge) plus the region extending to thecoast as far east as Nootka Island. Anyslip along the fault as it subductsbeneath the margin, would be includedin the second region. Fig. 3 shows theregion selected to encompass the Blancofault and the region for the Mendocinofault. Because of the complex tectonicsin the Gorda plate region and landwardof continental slope on the Mendocinofault, the region was limited to theoffshore fault to exclude seismicity dueto N-S deformation within the Gordaplate and the seismicity of thesubduction zone.

7.2 Magnitude Scales and Magnitude-Moment Relations

To convert different earthquakemagnitudes to seismic moment, anumber of empirical relations wereemployed. These relations differedsignificantly from those found

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previously for land earthquakes;there appears to be a large onshore-offshore amplitude attenuation. Thesecorrections increase the moment rate andcomputed slip rate by up to 68 %.Offshore British Colombia, most of thepreferred earthquake parameter solutionswere calculated by the GSC at thePacific Geoscience Centre (PGC), usingthe local magnitude ML scale. Thesemagnitudes underestimate by at least 0.5magnitude units with respect to themoment magnitude scale. Ristau et al.(2003) show that the ML values for theregion offshore Vancouver Island aresystematically less by 0.62 ± 0.08magnitude units than the more robustmoment magnitude (Mw) values derivedfrom moment tensor analysis. Wetherefore corrected the ML magnitudesaccording to

Mw = ML + 0.62 (11)Similarly, Braunmiller and Náb�lek(2002) found that for the Explorerregion, that the body-wave magnitudesmb underestimate Mw by 0.46 magnitudeunits and that for surface wavemagnitudes MS <5.8,

Mw = 2.8 + 0.5 MS (12)but for MS $ 5.8 they are equal to Mw.Thus, in the Explorer region, all ML, mb,and MS values were converted to Mw

according to these empirical relations. Asmall minority of the data was onlyavailable in MD (coda or duration) orother scales. These data were not altered.For the Blanco fault, we have processedthe data with original magnitudes andusing

Mw = 1.29 + 0.82 mb(13)and

Mw = 2.40 + 0.62 MS,(14)provided by Braunmiller (1998). Thoughcomparable corrections may be neededin the vicinity of the Mendocino fault,

no such comparisons of magnitudescales were found in the literature.

By supplementing the USGScatalogs by the Harvard CMT and ISCcatalog data, we were able to deriverelations between ML, MS, mb, MD andMw. Fig. 4 shows plots of Mw versuseach of ML, MS, mb and MD, as well as aplot of ML versus MD for events in thecombined catalogs for which estimateswere available of multiple types ofmagnitudes. For least-square fits to thedata, we found that Mw = (1.01± 0.031) ML + (0.15 ± 0.14)

(15)or if the slope was assumed to be 1, that

Mw = ML + (0.21 ± 0.079), (16)where the uncertainties quoted representone standard deviation. Likewise, wefound that:Mw = (0.72 ± 0.032) MS + (1.79 ± .158),

(17) or, with the slope set to 1,

Mw = MS + (0.46 ± 0.149), (18)Mw = (0.94 ± 0.042) mb + (0.72 ± 0.194),


Mw = mb + (0.44 ± 0.087), (20)Mw = (0.94 ± 0.060) MD + (0.62 ± 0.26),


Mw = MD + (0.36 ± 0.48). (22)Since there were not a large number ofevents for which there were both Mw and MD estimates available, we also foundthat:ML = (0.99 ± 0.037) MD + (0.12 ± 0.13),


ML = MD + (0.07 ± 0.055). (24)With the exception of MS the data can besufficiently well fit by setting the slopeto 1 and adding a constant to convert toMw or ML. We have fit MD by assumingthe relations (16) and (24) between Mw

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Figure 4 The panels show the relationship between types ofmagnitudes (Mw versus ML, MS, mb, and MD, as well as ML versusMD) on the Mendocino fault for earthquakes where multipleestimates of magnitude are available. Each plot shows a blackline with slope of 1, which goes through the origin. The dashedline also has a slope of 1, but has an intercept equal to theaverage difference between the types of magnitude. The dottedline is the best fit in the least-squares sense. The plot of Mw

versus MD also shows a gray line (based on Mw versus ML andML versus MD fits).

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and ML and ML and MD respectively,which gives us:

Mw = MD + (0.28 ± 0.55). (25)Thus, we have applied equations (16),(19), (20) and (25) to the data for theMendocino fault.

7.3 Completeness PeriodsAccurate calculation of moment

rate and fault slip rate requires that forany given increment of magnitude, databe included only for time periods duringwhich all events within that incrementwere recorded. The dates for completedetection vary with magnitude andregion. Most of the seismic moment andslip on a fault is due to the largestmagnitude earthquakes. Theseearthquakes occur the least frequently,but have been measurable for the longesttime. Smaller magnitude earthquakesoccur more frequently but have beenresolvable for less time. If we assumethat the rate at which earthquakes occurin any increment of magnitude isconstant in time, we can combine datagathered over varying durations. Thelowest magnitude for which records arecomplete in any year can be estimatedfrom where the magnitude-frequency ofoccurrence plot deviates from linearity or from knowledge of processinganalysts. We have used quiteconservative completeness limits,although this reduces the number ofearthquakes and increases the statistical

uncertainty in the recurrence relations.For the RDW, Sovanco and Nootkafaults the catalog completeness is takenfrom Hyndman and Weichert, (1983)and T. Mulder (GSC, personalcommunication, 2003). Since themajority of these data were ML

magnitudes, the values quoted wereincreased by 0.62 to create thecompleteness tables. Determining thecompleteness of data offshore Oregonand California is more problematic thanoffshore British Columbia, because thereare multiple catalogs, covering differenttime periods. According to Hyndmanand Weichert (1983), data for the Blancotransform fault is complete to 7.0 since1899, to 5.5 since 1917, to 5.0 since1965, and data for the Mendocino iscomplete to 7.0 from 1899, to 5.5 from1917 and to 4.0 from 1965. Dziak et al.(1991) suggest that the threshold fordetection in the northeast Pacific, since1963, is mb= 4.0. However their databelow 4.5 do not fit the recurrencerelation in either the northwest orsoutheast sections of the Blanco, thoughmagnitudes below 4.5 could be detected,the catalog cannot be complete below (prior to application of equations 6, 9, 10~4.5, from 1963. Braunmiller (1998)claims the catalog is complete to 4.4since 1964. We have therefore used thevalues from Hyndman and Weichert(1983) and determined the year ofcompleteness for magnitude 4.0 on theBlanco, by inspection of the data, to be

Table 1. RDW $ 7.62 – 1899; $ 6.12 – 1917; $ 4.62 – 1965; $ 3.62 – 1985Sovanco $ 7.62 – 1899; $ 6.12 – 1917; $ 5.62 – 1965; $ 3.62 – 1985Nootka $ 7.62 – 1899; $ 6.12 – 1917; $ 5.12 – 1965; $ 3.62 – 1985 Blanco $ 7.00 – 1899; $ 5.50 – 1917; $ 5.00 – 1965; $ 4.00 – 1985Mendocino $ 7.21 – 1899; $ 5.71 – 1917; $ 5.51 – 1965; $ 4.21 – 1985 Table caption: Estimated magnitudes for complete detection as a function of time

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1985. For the Mendocino, we foundsome deviation from linearity if weapplied the Hyndman and Weichert(1983) table on magnitudes as recordedand 15), unless we increased theminimum magnitude for completedetection in 1965 to 5.3 and likewisedetermined the year of completeness formagnitude 4.0, by inspection of the data,to be 1985. Since the vast majority of thedata for this region are ML, whenanalyzing the modified data, we added0.21 to each value to create theapplicable completeness table.

8 Selection of Parameters8.1 Lengths of Oceanic TransformFaults

The moment and slip ratecalculations are applied to specific faultareas, i.e., fault lengths times faultthickness or depth extent. We haveestimated the total length L of the faultsfrom bathymetry and seismicity maps.The Revere-Dellwood and Dellwood-Wilson faults have a combined length ofabout 160 km. From the triple junctionalong the Sovanco fault to the Explorerridge is about 140 km. For the Nootkafault, the length from the continentalslope to the triple junction at theintersection of the Juan de Fuca,Explorer and Pacific plates is about 150km. The length of the second largerregion investigated for the Nootka fault,which extends to Nootka Island, asillustrated in Fig. 2, is about 160 km.The Blanco fault (Fig. 3) spans 350 kmbetween the Juan de Fuca and Gordaridges. The Mendocino fault (Fig. 3)spans 280 km from the Gorda ridge tothe continental margin. 8.2 Effective Seismic Thickness

The effective seismic thicknessof the transform faults is an importantpart of our study, both for the fault area

and maximum magnitude. Thecalculated slip rates are inverselyproportional to the seismic thicknessassumed if the other parameters areunchanged. However, we also use theseismic thickness in our estimate of themaximum magnitude. The twocontributions to the slip rate fromchanges in W partially cancel. Theresult, as discussed below, is that achange in W of a factor of 5 results in achange of only about a factor of 2 in thecomputed seismic slip rate. Analternative approach is to estimate theeffective seismic layer thickness W fromthe seismicity rate, taking the fault sliprates determined independently such asfrom plate models. The effectivethickness may approximate a true nearlyconstant thickness along the fault, withthat area having close to 100% seismicefficiency. Alternatively, it mayrepresent the overall average ofseismogenic patches extending to greaterdepth separated by aseismic portions ofthe faults. As we discuss below, weargue that the former is closer to correctbased on the result that nearly the sameeffective thickness W is found for all ofthe faults. Another useful contribution ofthe earthquake slip rate approach is forthe Nootka fault, which has a poorlyconstrained plate model slip rate. Theeffective seismic thickness W may beassumed to be the same as that for theother faults, where their values of Wwere chosen to give agreement betweenthe seismicity calculated and the platemodel slip rates.

A number of approaches areavailable for estimating the effectiveseismic thickness:

(1) The maximum depth ofseismicity may be taken to be thedepth of brittle failure in theoceanic lithosphere. The limit

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has been associated with the~600 oC isotherm (Abercrombieand Ekstöm, 2001; see alsoDziak et al., 2000). Thisapproach assumes thatearthquakes occur in the mantleso that this mantle compositiontemperature limit applies. Itresults in a thickness that isapproximately related to theaverage age of the oceaniclithosphere on the two sides ofthe fault (e.g., Boettcher andJordan, 2001). This average ageranges from a few Ma for theRDW (Riddihough, 1977) whichis bounded by very younglithosphere, to just over 5 Ma(Wilson, 1989) for theMendocino fault (i.e., little morethan the crust for the RDW to~10 km for the Mendocino fault).

(2) The upper crust has very highporosity and may be sufficientlyfractured such that it cannotsupport significant earthquakes(e.g. discussion by Hyndman andWeichert, 1983). On land, theupper few kilometers of crust arecommonly aseismic ascribed tostable-sliding clay gouge (e.g.,Marone and Scholz, 1988).

(3) The depths of recordedearthquakes can be determinedaccurately only by arrays ofocean-bottom sesimographs(OBS), although some depthconstraints are provided byearthquake moment tensorsolutions. Most OBS arrays havebeen on or near ridges and thedata for transform faults is verylimited. In our study areaHyndman and Rogers (1981)found event depths ranging

between 3 and 6 km in theExplorer region for a W ~ 3 km.They found similar depths for afew events on the Nootka fault.Tréhu and Solomon (1983) foundmost strike-slip earthquakes onthe Orozco transform fault (offthe East Pacific Rise), from theirOBS studies, were confined tothe 4 km thick crust. Wilcock etal. (2003) recorded thousands ofmicroearthquakes in situ on theEndeavour segment of the Juande Fuca Ridge at 2-4 km depth.Golden et al. located thousandsof microearthquakes in MiddleValley, northern Juan de FucaRidge, which were concentratedat 1-2.5 km depth. We expect thedepth of these events on the Juande Fuca Ridge to be thermallylimited, but it is notable thatnone appear to occur in themantle. Furthermore, Golden etal. observed a less well-constrained swarms on faultsoutside their array of OBSsincluding the Nootka, and reportthat hypocentres deepen to ~ 3km away from the vent field.

Some constraint inearthquake depth is availablefrom earthquake moment tensorsolutions determined usingadjacent land station data. Thismethod has low depth resolution,typically of about ±3 km (J.Ristau, personal communication,2004) and is not ideal for shallowearthquakes, which occur near afree surface. Ristau (personalcommunication, 2003; alsoRistau et al., 2003) found depthsin the range 3 to 24 km on theRDW, Sovanco and Nootkatransform faults, with most

13

depths ~ 10 km. Similarly,Braumiller and Náb�lek (2002)found average depths on thetransform faults of the Explorerof ~ 10 km with a standarddeviation of 3.0 km. Since thecrust is some 7 km thick in theregion (Au and Clowes, 1982;Hyndman et al., 1979), this depthestimate suggests mostearthquakes are occurring in theuppermost mantle. Braunmiller(1998) found that most BTFZevents occurred at depths of 4 to6 km and a seismogenic zone ofless than 10 km. However, theearth model used in thesemoment tensor inversions doesnot include the low velocitysediments and upper crust, northe ocean water layer. Theproblem of a velocity structurethat varies along the wave pathsfrom oceanic earthquakes to landstations also has not yet beenaddressed, but the consequence isthat the computed depth frommoment tensor solutions shouldbe biased to being substantiallytoo deep. The lack ofearthquakes at crustal depths alsois puzzling, unless there is a biasto depths that are too great.

(4) Serpentinite occurrences arecommon in oceanic fracturezones and serpentinized mantlerocks are probably aseismic (e.g.,Aumento and Loubat, 1971;Cannat et al., 1992, Thompsonand Melson, 1972; Reinen et al.,1991; Hyndman and Peacock,2003). If the uppermost mantlebeneath the fault zones iscommonly serpentinized, and theupper crust is aseismic asdiscussed above, the effective

seismic zone may be quite thin,i.e., ~ 3km. Londsdale (1986)explained the seismic deficiencyof the Heezen transform fault, inthe Eltanin fault system, as dueto a thin 1 km crust andpervasive serpentinization ofsub-crustal rocks, rather thansuggesting significant aseismicslip. Wilson (1984) explains theuniform positive magneticanomaly over the Mendocinoridge as suggesting a high-susceptibility source such asserpentine. Dziak et al. (2000)explain evidence of uplift (fromgravity, seismic reflection data,and high magnetization frommagnetic data), as suggesting alow-density serpentinite intrusionbeneath the Blanco Ridge. Theysuggest that faulting has led toflow of seawater into andhydrating the mantle, forming aserpentine intrusion along thefault.

Most of the above constraintssuggest an effective seismic thickness of2-5 km, with the possibility of as muchas 10 km. To examine the potential errorintroduced by the uncertainty in theeffective seismic thickness weinvestigate the deformation rate for alloceanic transform faults bounding theJuan de Fuca, Explorer and Gorda platesand search for a single width to matchall available plate model slip rate data. A good agreement between seismic sliprate and plate models is found for allfaults with a 3 km effective seismiczone. Fig. 5, adapted form Dziak et al.(2000), illustrates how a serpentiniteintrusion and fragmented upper crustmight lead to a this, ~ 3km effectiveseismic zone on these oceanic transform

14

Figure 5 Our model of composition andstructure typical of these oceanictransform faults, with thin 3-4 kmeffective seismic zones sandwichedbetween the fragmented upper crust andthe aseismic serpentinite-peridotiteintrusion (adapted from Dziak et al.,2000).

faults. This result supports theconclusion that most of the observeddeformation is seismic and in the lowercrust only. However, we also investigatethe slip rates calculated by setting W to2 km, 6.5 km and 10 km as well, as seenin Table 2.

8.3 Maximum MagnitudesRelating earthquake rate to slip

rate using the recurrence relation alsorequires an estimate of the maximummagnitude for each fault. Since thenumber of earthquakes decreases withincreasing magnitude the seismicitystatistics at the larger magnitudes areinsufficient to resolve the maximummagnitude, from the recurrence relationdeviation from linearity. We must relyon empirical relations between fault areaand magnitude such as

Mmax = 4.07 + 0.98 log A, (26)from Wells and Coppersmith (1994). , IfW = 2 km, 3 km, 6.5 km or 10 km,respectively, this gives a maximummagnitudes of about: 6.5, 6.7, 7.0 and7.2 for the RDW faults; 6.5, 6.7, 7.0 and7.2 for the Nootka fault; 6.5, 6.6, 7.0 and7.2 for the Sovanco fault; 6.9, 7.0, 7.3and 7.5 for the Blanco fault; and 6.8, 6.9,7.3 and 7.4 for the Mendocino fault.Note that increasing Mmax by 0.5magnitude units with no change in otherparameters approximately doubles thedeformation rate calculated. However,because the effective seismic thicknessW is used both directly in the seismicslip rate calculation and in the maximummagnitude calculation, a change of afactor of five in W (from 2 to 10 km)results in only a change ofapproximately a factor of two in seismicslip rate. For these estimates we haveassumed that the largest earthquakesrupture the whole fault length, throughstructural discontinuities and small

offsets. If for example the smallextensional zone in the middle of theBlanco fault stops rupture, the maximummagnitude is reduced by about 0.3 andthe slip rate (on the Blanco Ridge aloneversus the BTFZ) is reduced by about5%.9 Results

Table 2 summarizes therecurrence parameters and fault seismicslip rate values calculated forearthquakes recorded on the RDWfaults, the two extents for the Nootkafault, the Sovanco fault zone, theBlanco, and Mendocino faults. Theeffective seismic thicknesses W arevaried from 2 to 10 km.

15

Table 2. Fa

ult

Even

ts

W x

L

(km

)

-ma

x

$ b a 17N

m/y

r)

(mm

/yr)

Oth

er

estima

tes

(mm

/yr)

RD

W

20

8

160 x 2 4.5 -6 .5 2.4±0.17 1.05±0.072 5.51±0.321 8.8 84 34a, 46b,

56b, 44c,

36e, 55 f160 x 3 4.5 -6 .7 2.4±0.16 1.06±0.069 5.54±0.307 11 68

160 x 6.5 4.5 -7 .0 2.4±0.15 1.06±0.066 5.55±0.293 14 42

160 x 10 4.5 -7 .2 2.5±0.15 1.07±0.065 5.59±0.289 17 33

So

van

co

90

140 x 2 4.0 -6 .5 1.8±0.17 0.78±0.073 3.75±0.288 4.2 45 17a, 49b,

59b, 39c,

38e, 42 f140 x 3 4.0 -6 .6 1.8±0.16 0.79±0.072 3.80±0.283 4.7 34

140 x 6.5 4.0 -7 .0 1.9±0.15 0.81±0.067 3.85±0.263 8.5 28

140 x 10 4.0 -7 .2 1.9±0.15 0.82±0.066 3.89±0.259 11 24

No

otk

a

15

4

150 x 2 3.6 -6 .5 2.2±0.15 0.95±0.065 4.39±0.230 2.2 22 3a, 24b,

25b, 29c,

46d, 20e,

25-35f,

20g

150 x 3 3.6 -6 .7 2.2±0.15 0.96±0.064 4.43±0.227 2.7 18

150 x 6.5 3.6 -7 .0 2.2±0.14 0.97±0.063 4.46±0.223 3.8 12

150 x 10 3.6 -7 .2 2.2±0.14 0.97±0.062 4.47±0.222 4.7 9

No

otk

a

exten

ded 1

38

160 x 2 3.6 -6 .5 1.9±0.14 0.82±0.059 3.86±0.211 3.1 30 15a

160 x 3 3.6 -6 .7 1.9±0.13 0.84±0.058 3.91±0.207 4.0 25

160 x 6.5 3.6 -7 .0 2.0±0.13 0.85±0.057 3.96±0.202 6.0 17

160 x 10 3.6 -7 .2 2.0±0.13 0.86±0.056 3.98±0.200 7.8 14

Blan

co

20

4350 x 2 4.5 -6 .9 2.4±0.13 1.06±0.058 5.56±0.260 14 62 56e, 55 f,

56d, 20h,

(7 & 19)i350 x 3 4.5 -7 .0 2.4±0.13 1.06±0.058 5.58±0.258 16 45

350 x 6.5 4.5 -7 .4 2.5±0.13 1.07±0.057 5.64±0.252 22 30

350 x 10 4.5 -7 .5 2.5±0.13 1.07±0.056 5.65±0.251 25 21

Blan

co

(mo

dified

)

86

350 x 2 5.5 -6 .9 2.8±0.36 1.23±0.156 6.73±0.849 24 104

350 x 3 5.5 -7 .0 2.9±0.35 1.26±0.153 6.86±0.833 26 76

350 x 6.5 5.5 -7 .4 3.0±0.34 1.31±0.146 7.12±0.795 34 46

350 x 10 5.5 -7 .5 3.0±0.33 1.31±0.145 7.15±0.790 36 31

Men

do

cino

28

7

280 x 2 4.0 -6 .8 2.0±0.11 0.89±0.049 4.62±0.203 13 69 56e, 53 f

280 x 3 4.0 -6 .9 2.0±0.11 0.88±0.048 4.60±0.199 15 54

280 x 6.5 4.0 -7 .3 2.0±0.10 0.87±0.045 4.54±0.187 28 47

280 x 10 4.0 -7 .4 2.0±0.10 0.87±0.045 4.55±0.186 32 35

16

Table caption: Parameters used and results of this studyErrors in $ and b are statistical one standard deviation. The preferred seismic slip ratesare shown in bold. Estimates based on plate models are italicized.(a) Rate calculated by summing moments (and using a width W of 10 km) byBraunmiller and Náb�lek (2002). Note that the regions selected for the Nootka fault zonedo not exactly coincide with those discussed here.(b) Rates calculated from the Pacific-Explorer rotation pole based on slip vector azimuthsfor two different models, according to Braunmiller and Náb�lek (2002).(c) Rate calculated according to mean instantaneous rotation poles provided byRiddihough (1984) based on magnetic anomalies.(d) Rate calculated according to mean instantaneous rotation poles provided by Wilson(1993) based on magnetic anomalies.(e) Rate according to Hyndman and Weichert (1980) based on seismicity. Note that theregions selected for both faults do not exactly coincide with those discussed here and ML

values were not modified to match Mw values.(f) Rate used by Hyndman and Weichert (1980) based on plate model results available atthat time.(g) Rate estimated from the difference in margin convergence rate to the north and southof the Nootka fault from continuous GPS measurements, by Mazzotti et al. (2003a),assuming a fully locked subduction thrust on both sides of the fault. (h) Average rate for entire BTFZ calculated by Braunmiller (1998) by summing momentsin four segments of the fault. He also looked at the rate according to seismicity anddeclares that seismicity can account for all of the deformation. He assumed W = 7 kmand µ = 3.5 x 1010 N/m2.(i) Braunmiller’s (1998) corrected estimates for the northwest and southeast sections ofthe BTFZ, respectively, from the Dziak et al. (1991) estimates of moment rate fromseismicity. They assumed W = 10 km and µ = 4 x 1010 N/m2.

Plots of the cumulativefrequency versus magnitude for all ofthe regions investigated are given inFigs. 6-10. The RDW results (Fig.6) arereasonably linear but do stray from astraight line fit. There are two events, M= 6.7 and 6.8, which are larger thanpredicted using the Wells andCoppersmith (1994) relation for athinner effective seismic zone but arewithin the scatter of the data that theyused to define the relation. The resultsfor the Sovanco fault (Fig. 7), are morelinear, although there is a small dipabove 5.5. The thicker effective seismiclayer models (i.e. larger maximummagnitudes Mmax) appear to over-

estimate the data above 5.6. The upperpanel of Fig. 8 shows the results for theshorter region selected for the Nootkafault; the lower panel shows the resultsfor the extended region to the coast. Thetwo regions do give very similardeformation rates. The upper panel ofFig. 9 shows the results for the Blancofault using catalog magnitudes; thelower panel shows the results if themagnitudes are corrected as proposed byBraunmiller (1998). The correctedBlanco data have unusually high b-values, close to 1.5, the point at whichequation 7 becomes undefined (becaused = b), and give rather unstable results,highly sensitive to Mmin the minimum

17

Figure 6 Calculated cumulativerecurrence relation for the Revere-Dellwood and Dellwood-Wilson faultswith truncation at the maximummagnitude. The error bars assume aPoisson distribution. The maximumlikelihood fit for each of Mmax = 6.5 andW = 2 km, Mmax = 6.7 and W = 3 km,Mmax = 7.0 and W = 6.5 km, and Mmax =7.2 and W = 10 km are shown withincreasingly darker shades of gray lines.

magnitude included. Thus, we focus onthe fit to the raw data in the upper panel,which gives a deformation ratecomparable to the expected rate for W=3km. Fig. 10 shows the results for theMendocino fault. The data are quitereasonably linear. The model with W=3km provides the best fit to the data sinceif W is thinner, the largest events at M =6.9 are above the maximum predicted byWells and Coppersmith (1994) and if Wis thicker the models are above errorbars on the data between magnitude 6.0– 6.4. All four models predict slip ratesof the order of that predicted by platemodels, but if W =3 km we get avirtually identical slip rate.

In general, our estimates ofdeformation rates are well within therange of other estimates, based on platemodels, marine magnetic anomaly data,seismic moment and seismicity rates, asshown in Table 2. If the plate motionsare indeed accommodated seismicallywithin a nearly constant thickness layer,the thin effective seismic layer model isrequired to give slip rates similar tovalues derived from plate models.Consider Fig.7, in which the cumulativefrequency for the Sovanco Fault Zone isplotted versus magnitude and the dataare fit with four lines representing thetruncated recurrence relation for W = 2,3, 6.5 and 10 km respectively. Themodel with the thickest effective seismiclayer, resulting in Mmax = 7.2, is the leastconsistent with the available data,(although still just within theuncertainties) and appears to over-estimate the cumulative frequency atmagnitudes greater than 5.5. Since theSovanco region can be used to calibratethe model parameters for the Nootkafault, this encourages the selection of aneffective seismic layer that is thinnerthan 10 km, and suggests that a large

portion of the deformation is actuallyaccommodated seismically.

10. Error Estimation – The Logic TreeApproach

Estimating cumulative error forparameters for which there isconsiderable uncertainty, such as thecompleteness of the earthquake record orthe effective seismic thickness, andpropagating those errors through non-linear equations to calculate an errorestimate for slip rate is far from trivial. An alternative method, commonly usedin seismic hazard models, is the logictree approach. This method involvesselecting a range of reasonable valuesfor each parameter, assigning alikelihood to each value, then

18

Figure 7 Calculated cumulativerecurrence relation for the Sovanco faultwith truncation at the maximummagnitude. The error bars assume aPoisson distribution. The maximumlikelihood fit for each of Mmax = 6.5 andW = 2 km, Mmax = 6.6 and W = 3 km,Mmax = 7.0 and W = 6.5 km, and Mmax =7.2 and W = 10 km are shown withincreasingly darker shades of gray lines.

Figure 8 Each panel illustrates thecalculated cumulative recurrence relationfor the Nootka fault with truncation atthe maximum magnitude. The error barsassume a Poisson distribution. Themaximum likelihood fit for each of Mmax

= 6.5 and W = 2 km, Mmax = 6.7 and W =3 km, Mmax = 7.0 and W = 6.5 km, andMmax = 7.2 and W = 10 km are shownwith increasingly darker shades of graylines. The upper panel is for the marginto the ridge, whereas the lower panel isfor the fault if it extends to NootkaIsland.

calculating the resulting solution forevery possible combination, and itsassociated probability. The map ofcombinations is likened to a tree,wherein each “branch” represents adifferent set of selections of parameters,leading to a “leaf” which is a possiblesolution, for that set of parameters, andits probability. The structure of a logictree, which can be used to assess theprobability of deformation predictedfrom seismicity, is shown in Fig. 11.Following Mazzotti et al. (2003b), theparameters a and b, c and d, shearmodulus, length of faults, and width andassociated Mmax were each allowed anupper, median and lower estimate. Theparameters a and b are well confinedfrom the seismicity data. The median

19

value of each of a and b are the estimatescalculated for a 3 km thick effectiveseismic zone for the RDW, Sovanco,Nootka, Blanco (unmodified) andMendocino faults, as recorded in Table2. The lower and upper estimates are themedian values plus or minus thestandard deviation. The parameters c andd, which were determined empirically(see for instance, Hyndman andWeichert, 1983), were allowed to variedby ±13%, based on the uncertainty in therelation between ML and Mw we appliedin the Explorer plate (Ristau et al.,2003). Previously, the shear modulus µ,was set to the typical value of 3.3 x 1010

Pa. Here, it was allowed to vary by ± 30%. Since we have investigated two areassurrounding the Nootka fault, ofdifferent length, for Nootka, the lengthcould vary from 150, to 155, to 160 km. All other fault lengths were set to thevalues listed in Table 2. The twoparameters, which are the least wellconfined, are the effective width of theseismic zone, W, and the maximummagnitude Mmax. These two parametersare coupled, if we use the Wells andCoppersmith (1994) relation to predictmaximum magnitude based on faultarea. Therefore, these two parameterswere varied from 2 to 3 to 4 km with theassociated calculated Mmax for each fault.Each of these parameters is assigned areasonable probability, as shown in Fig.10, where the numbers above the toparrows are associated with the upperestimate, the numbers above the centrearrows are associated with the medianestimate and the numbers below thelower arrows are associated with thelower estimates. If a parameter is wellconfined the probabilities were set to0.2, 0.6 and 0.2 for the lower, medianand upper values. If the parameter is notwell confined the probabilities were set

to 0.3, 0.4 and 0.3 for the lower, medianand upper values.

What is found, in each case, isthat results tend to cluster, despite thewide range of combinations ofparameters and thus, the range ofallowable solutions can be investigated.The plot of incremental probabilityversus deformation shows the set ofpossible solutions and their calculatedprobabilities. Although the set of allsolutions for each fault includes a widerange of possible deformation rates,those rates which are far from thepredictions listed above in Table 2, arehighly unlikely. The sigmoidal plot ofcumulative probability versus thelogarithm of deformation shows therange of values and the amount ofpotential solutions at or below a givenvalue. The steeper the increase from zeroto one, the better confined is thedeformation estimate. Fig. 12 showsboth the incremental and cumulativeprobability versus motion for each fault.The deformation rates for cumulativeprobabilities of 16%, 50% an 84%, givean estimate of the spread of the solutionsand the sensitivity of predictions to theleast well-constrained parameters. Asummary of results of predicted totalmoment rates and deformations isprovided in Table 3. The deformationrate at 50% cumulative probability iscomparable to, though slightly largerthan our preferred estimates listedabove, in Table 2.With the exception ofthe Revere-Dellwood-Wilson faults, allvalues are slightly lower than thedeformation rates predicted by platemodels. The RDW has two faultsegments, the Revere-Dellwood andDellwood Wilson, and our data setinclude some events which are due tospreading. Nonetheless the estimate iswithin 30% of the deformation rate

20

Figure 9 Calculated cumulative recurrence

relation for the Mendocino fault with truncation

at the maximum magnitude. The error bars

assume a Poisson distribution. The maximum

likelihood fit for each of M max = 6.8 and W = 2

km, M max = 6.9 and W = 3 km, M max = 7.3 and W

= 6.5 km, and Mmax = 7.4 and W = 10 km are

shown with increasingly darker shades of gray

lines.

predicted by plate models. The entire setof solutions, for the Nootka fault,predicts significant deformation. This isinconsistent with the results of Kreemeret al., (1998) who calculated stain ratesfrom seismicity statistics since 1994 andfound little significant deformationalong the Nootka fault, since theircatalog contained no events greater than5.4. This shows the value of using therecurrence relation. The estimate for theBlanco fault is quite close to that fromplate models, despite the fragmentationof the fault and the complexity of thetectonics. The expected deformation iswithin the bounds listed in Table 3 forall faults investigated.

Table 3.Fault 16 % 50 % 84 %RDW 8.7 x 1017 Nm/year

46 mm/year1.1 x 1018 Nm/year71 mm/year

1.4 x 1018 Nm/year110 mm/year

Sovanco 3.9 x 1017 Nm/year25 mm/year



Nootka 2.1 x 1017 Nm/year12 mm/year



Blanco 1.4 x 1018 Nm/year34 mm/year



Mendocino 1.3 x 1018 Nm/year41 mm/year



Table caption: Logic tree results for total moment and slip rates at 16%, 50%, and 84%cumulative probability.

21

Figure 10 Structure of the logic tree isillustrated. Each of a & b, c &d, theshear modulus :, length L and W & Mmax

are allowed three values, an upper,median, and lower value, with theassigned probability denoted by theupper, middle and lower arrows. Theparameters a & b and c& d are deemedwell constrained and hence haveprobabilities 0.20, 0.60 and 0.20,whereas the other parameters are lesswell constrained and have probabilities0.30, 0.40, and 0.40. The variation in Lis only applied to the Nootka fault, andsince we see little evidence thatextending the Nootka fault past themargin is necessary, the probabilitydistribution is asymmetric, favouring150 km over 155 and 160 km. The set ofsolutions and associated likelihood ofeach are calculated for everycombination of parameters.

11 ConclusionsIn this study we have used

seismicity statistics to provide anestimate of the rate of slip due toearthquakes, along all of the oceanictransform faults of the Juan de Fucaplate system: the RDW, Sovanco,Nootka, Blanco and Mendocino faults,using the concept of seismic moment.Rather than summing individual seismicmoments, which is highly sensitive tothe statistics of the small number oflarge earthquakes, the total moment ratecan be calculated as the integral overmagnitude of the magnitude-frequencyof occurrence data. The integral can berelated to the rate of deformation. Thus,the far more frequent smaller magnitudeevents can help constrain the rate for theinfrequent larger magnitudes. Sources ofuncertainty include the incompletenessand limited history of the earthquakecatalog, the completeness table of thecatalog, varied magnitude definitions,empirical moment-magnitude relationsand the effect of their stochasticity,uncertainty in fault lengths and effectiveseismic thicknesses, uncertainties in therecurrence relation, the determination ofmaximum magnitude, and how therecurrence relation is truncated at themaximum magnitude. The leastconstrained parameters are the effectiveeffective vertical thickness of theseismic zone W and the maximummagnitude Mmax possible on a givenfault. We used the empirical equationMmax = 4.07 + 0.98 log A (Wells andCoppersmith, 1994) to predict Mmax, thusthe maximum magnitude is related to Wand the effect of varying W on slip rateestimates partly cancels. Estimates rangefrom a thin effective seismic zone andW = 3 km (Hyndman and Weichert,1984), to a thicker W=10 km zone

(Braunmiller and Náb�lek, 2002; Dziaket al.,1991; Dziak et al., 2000). Theeffect of a 2, 3, 6.5 and 10 km thick zoneis investigated for each fault and thepredicted deformations are comparedwith those based on plate models andother means.

22

Figure 11 For each of the RDW, Sovanco, Nootka, B lanco and M endocino faults, the set of all solutions is

illustrated with the incremental probability versus motion plot and the cumulative probability versus motion

plot. The former plots show all solutions and their calculated likelihood where the most likely deformation

is quite similar to the results shown in Table 2. The latter plot indicate how well constrained the median

solutions are.

For a reasonable range of W andMmax, for each fault, the predicteddeformation rates from seismicity

statistics are comparable to plate modelpredictions and observed deformationfrom GPS and other geophysical data

23

within a factor of two and usually ±25%.This shows the soundness of the method,robustness of the data, and thereasonable selection of parameters. Thesimilarity of the deformation estimatesbased on seismicity and those from platemodels, shows a remarkable consistencyfor time scales ranging over five ordersof magnitude, from decades to millionsof years.

The best agreement betweenseismicity and plate model slip rates isfor a thin effective seismic thickness ofW ~ 3 km. There are two possibleinterpretations. These oceanic transformfaults may have thick (approximately 10km) effective seismic zones andseismicity may only be able to accountfor a fraction (~a to b) of thedeformation. Alternatively, these faultsmay have thin (approximately 3 km)effective seismic zones and most of thedeformation is occurring seismically.The selection of a thick effective seismiczone is based on moment tensorsolutions, but the solutions typicallyhave no more than a 3km resolution andthe largest depths are set equal to theseismic thickness, even though theuppermost crust may not supportsignificant earthquakes. We also arguethat such solutions have significantdepth bias. A thick $10 km effectiveseismic zone for these and other oceanictransform faults is common in theliterature. If such a thick zone isassumed, most of the deformation isdetermined to be aseismic in origin (e.g.Braunmiller and Náb�lek, 2002; Dziak etal.,1991; Dziak et al., 2000, Braunmiller,1998, Abercrombie and Ekström, 2001).Assuming a much thicker seismic zone,in a study of 75 OTFs, Boettcher andJordan (2001) calculated that only ~15%of slip can be accounted for seismicallyand concluded that oceanic transform

faults are fundamentally different fromcontinental transform faults on whichdeformation is generally strictly seismicbelow an upper crust aseismic zone. Ifwe accept that the effective seismic zoneis of the order of 10 km thick the seismicdeformations are 32 mm/yr on the RDW,24 on the Sovanco, 9 on the Nootka, 21on the Blanco and 35 on the Mendocinofaults, which are significantly less thanthe deformation rates of plate models.We therefore favour the thin(approximately 3 km) effective seismiczone model.

W = 3 km may be explained by acombination of an aseismic sedimentand highly porous and fragmenteduppermost crust, probable depth ofhydrothermal cooling of the crust near aspreading centre in young oceanic crust,and pervasive serpentinization in theuppermost mantle. The predictions ofdeformation rate are 68 mm/yr for theRDW, 34 mm/yr for the Sovanco, 18mm/yr for the Nootka, 45 mm/yr for theBlanco and 54 mm/yr for the Mendocinofaults. The estimates for the Sovanco,Nootka and Blanco faults arecomparable to, but slightly less than thepredictions based on plate models,whereas the prediction for theMendocino fault is virtually identical tothe plate model prediction. Theprediction for the RDW overestimatesthe plate model deformation. This is atectonically complex region and someevents in our data set may not associatedwith slip on these faults which mayexplain why the estimate is larger thanexpected. The majority of thedeformation on the RDW, Sovanco,Nootka, Blanco and Mendocino faultscan be explained seismically if theeffective seismic zone is thin.

The uncertainty in thesepredictions (for W= 3 km) is

24

investigated using the logic tree method.This produced a set of solutions,clustered around the preferred solutionsdescribed above. The deformation ratesfor a cumulative probability of 50%,16% and 84%, give an idea of the mostlikely solution and the spread ofsolutions (comparable to ±1F) as well asthe sensitivity of predictions to the leastwell-constrained parameters. Theexpected deformation based on platemodels is well within the range ofsolutions for all five faults.

In order to establish the effectivethickness of the seismic zone and whatproportion of the deformation isoccurring seismically, long term in situseismic studies are needed. OBS recordsof large magnitude events on theseoceanic transform faults coulddistinguish between these models andhave a significant impact on ourunderstanding of the physical slipbehaviour of these faults.AcknowledgementsWe thank Stéphane Mazzotti for accessto software and advice and ourcolleagues John Ristau, Taimi Mulder,Gary Rogers, John Cassidy, Earl Davisand Dieter Weichert, for helpfuldiscussions. Correspondence andrequests for materials should beaddressed to E.C.W.([email protected]). Geol.Surv. Canada Publ. #

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