Kinematics of the southern Walker Lane Belt and motion of the Sierra

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. Bll, PAGES 27,033-27,049,NOVEMBER 10, 1998

Kinematics

of the southern

Walker

Lane

Belt and motion

of the Sierra Nevada block, California ElizabethHardingHearn andEugeneD. Humphreys Departmentof GeologicalSciences,Universityof Oregon,Eugene

Abstract. Deformationin the southernWalker Lane Belt regionof the southwestern Great Basin accommodates significantportionsof bothPacific-NorthAmerica transformmotion andBasinandRangeextension.Apparentkinematicinconsistencies betweengeodeticand fault slip datain thisregionhavemadeit difficultto understand the natureof the interaction betweenthesedeformationprocessesandto infer the regionalkinematics. We modelthe kinematicsof thisregionin a mannerthatenforceskinematicconsistency andincludesfault geometryandslipratedata,GlobalPositioningSystem(GPS) surveydata,andvery long baselineinterferometry/very longbaselinearray(VLBI/VLBA) sitevelocitydata. A model is foundthatis consistentwith the setof availabledata,andthismodeldifferssignificantly from prior modelsfor the region. Our modelhasthe SierraNevadablock,whichbounds the westernmarginof the GreatBasin,movingN50øW+5ø at 12.7+1.5mm/yr,with only minor amountsof counterclockwise rotation. Left-lateralslip on the westernGarlockFault is a consequence of the relativelygreatwesterlycomponentof SierraNevadavelocity. We also find that the Basin and Rangeextensioneastof our studyareaoccursat a rate of about 2.5 mm/yr, whichis slowerthanthe rate in the centralGreatBasin.

1. Introduction

The Walker Lane Belt (WLB), which comprisesthe greater part of the EasternCalifornia ShearZone (ECSZ), lies -300 km east of the San Andreas Fault, and accommodates about 20-25%

of the Pacific-North America plate relative motion. This shear zone (Plate 1a) extendsnorthwardfrom the Mojave region, incorporatingthe easternGarlock Fault, and continuesalongthe western margin of the Great Basin. Within the westernGreat Basin, continentalcollapseaccommodatedby Basin and Range normal faulting interactswith shearzone strike-slipfaulting in a complex and poorly understoodway. The integratedeffect of faulting in the Great Basin is representedby the motion of the SierraNevada block with respectto stableNorth America. NorthwesterlySierra Nevada motion clearly showsthe dominanceof plate transform interaction over continental collapse, but a component of the Sierra Nevada

motion

should reflect Great Basin dilation

with

respectto stableNorth America and with respectto the nearly inactive southernBasin and Range (as suggestedby left-lateral activity on the Lake Mead seismiczone and the westernGarlock Fault [Davis and Burchfiel,1973]). There are severalpuzzling questionsabout the kinematicsof the southernWLB. Finding a descriptionof WLB kinematics that is consistentwith the geologicinterpretations(basedon the geometryand slip ratesof faults in the region) and geodeticdata has been difficult, and varioussuggestionseven appearcontradictory. These kinematic inconsistencies may be illustratedbest by comparing the very long baseline interferometry (VLBI) predicted motion of the southernSierra Nevada with the patternof faulting in the southernWLB that accommodatesmost of the Copyright1998by the AmericanGeophysical Union. Papernumber 98JB01390. 0148-0227/98/98JB -01390509.00

Sierra Nevada motion with respectto North America. Based on VLBI data [Dixon et al., 1995], we calculate a block motion of the Sierra Nevada with the southernend moving N23øW relative to North America (gray arrow on Plate lb). (If insteadwe used the Argus and Gordon [1991] pole, the orientationwould be slightly more clockwiseat N20øW.) As shownin Plate lb, the faults that separatethe Sierra Nevada from stableNorth America cannotaccommodatethis motion. In particular,(1) the motion of the Mojave block with respectto the Sierra Nevada, as inferred by the trend of the ECSZ or by the motion of the Mojave VLBI station,is suchthat the Garlock Fault would slip in a right-lateral sense (Plate lb), yet the Garlock Fault slips sinistrally at -5 mm/yr, and (2) the southernWLB strike-slip faults average 10ø-20ø more westerly in orientation than the VLBI-inferred southernSierra Nevada motion. This can be seenin Plate lb by comparingthe gray arrow with the orientationof strike-slipfaults in the southernWLB. These relations suggesta more westerly motion

to the southern Sierra Nevada.

The inclusion

of Sierra

Nevada range front faulting and Basin and Range normal faulting to the eastonly increasesthesediscrepancies. Recently,the use of a simultaneouslyoccupiedarray of VLBI siteshasprovidedmore accurategeodeticdata. The existingvery long baselinearray (VLBA) happensto include a site at OVRO (Plate 1a), which is importantbecausethe velocity of this site is /hndamentalto all studiesestimatingSierra Nevada block motion (e.g.,Argusand Gordon[ 1991], Dixon et al. [ 1995], and,to a significant degree, our study). VLBA data suggestthat OVRO is moving more westerly than estimatedby the OVRO VLBI site, consistentwith the faulting patternsin the Mojave and WLB. (NASA no longerpublishesVLBI data summaries,suchasMa et al. [ 1994], but C. Ma and J. Ryan archive the data, which can be accessed via the internet. VLBA

data, and recent VLBI

data,

were downloaded from http://lupus.gsfc.nasa.gov/vlbi.html in March 1997, and are from NASA GoddardSpaceFlight Center's 27,033

27,034

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

(a) km lOO

Sierra

Nevada

Block

Great local info.

Stable North America

Basin

VLBI

Plate

(Almost)

Garlock

(I3

o

{

O O

uj

,

Stable N ' America

(Almost)

Plate 1. Tectonicsettingof the southernWalker Lane Belt. (a) Colored lines show the active faults and open arrowsshowvelocities(relativeto stableNorth America) of the Pacificplate and selectedVLBI and VLBA sitesin the greaterregion. Map projectionis obliqueMercatoraboutthe NUVEL-1 Pacific-NorthAmericaEuler pole [DeMets et al., 1990]. Normal faults are shownin red, right-lateralfaults are shownin light green,left-lateral faults are shownin dark green,andthrustfaultsare shownin blue. The SanAndreasFault (andrelatedfaultsto the south) are shownwith a heavierline. Our studyarea,the southernWalker Lane Belt (highlighted),lies within the Eastern California ShearZone; this deformationzone accommodates both Basin and Rangeextensionand abouta quarterof the Pacific-NorthAmerica transformmotion. (b) SouthernWalker Lane Belt fault patternsand geodeticallydetermined velocitiessuggestthat the southernSierraNevadamovesmore westerlythanpredictedby modelsbasedon VLBI data alone. The arrow labeled "VLBI" showsthe velocity for the southernSierra Nevada block (relative to North America) usinginformationfrom Dixon et al. [1995]. The orientationis more northerlythan the inferred motionof the Mojave Block, eventhoughthisblockis separatedfrom the SierraNevadaby the left-lateralGarlock Fault. Also, strike-slipfaultsin the southernWalker Lane Belt that accommodate EasternCalifornia ShearZone (ECSZ) sheartrend more northwesterlythan the SierraNevadavelocity. Fault name abbreviationsare: DSF, Deep SpringsFault;DVF, DeathValley Fault;E-TPF, Emigrant-Towne PassFaults;EV-SEF,EurekaValley-SalineRidge Faults; FCF, FurnaceCreek Fault; FLVF, Fish Lake Valley Fault; HMF, Hunter Mountain Fault; LLF, Little Lake Fault system;OVF, OwensValley Fault;PVF, PanamintValley Fault;RFF, RangeFrontFault;WMF, White Mountain Fault.

VLBI

terrestrial

reference

frame

solution

number

1067e.

These

data are cited in this manuscriptas Ma and Ryan (1997).) On a more local scale, uncertaintyremainsin understanding how the -10 mm/yr of ECSZ shearpassesthroughthe Mojave region and continuesnorthward. North of the Garlock Fault, mostECSZ shearmustpasseastand/orwest of the PanamintValley Fault-Hunter Mountain Fault system,sinceslip on that system is well constrainedat 2-3 mm/yr (Table 1). The most direct route for the ECSZ is along the Death Valley Fault Zone, but a relatively slow Holocene slip rate hasbeen estimatedfor this fault system[Butler et al., 1988]. The Little Lake Fault Zone, which links the south end of the Owens Valley Fault with the Gafiock

Fault [Roquemoreand Simila, 1993, 1994], may accommodate significantamountsof ECSZ strain. We undertakea studyof the southernWLB regionto address theseissuesin general,and to reconciletectonicprocessesactive in the southernWLB with geodeticobservations.We model the kinematics of southernWLB deformationusing both geodetic and geologic strain constraints(i.e., geodeticvelocity measurementsand fault geometryand slip rates). We first constructa reference model by using velocity boundary conditionsbased on VLBI data and showhow theseboundaryconditionsare inconsistent with the kinematic requirementsof the southernWLB. We then develop a model that satisfiesthe best constrainedgeodetic

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

27,035

Table 1. Fault Slip Rates Fault

OwensValley(OVF)

Rate, mm/yr

0.6-2.2 0.7-2.2 -8

Data Type

Reference

geologic geologic geodetic

Beanlandand Clark [1994] Lubetkinand Clark [ 1988] Savageet al. [ 1990] Dixon et al. [ 1995]

from model

de Polo [1989] Dixon et al. [ 1995]

mid-Holocene

ClarkandGillespie[1993] Gillespie[1982]

north of model

Dixon et al. [1995]

interpolatedat OVRO

geologic geologic geologic

Zhanget al. [ 1990] Burchfielet al. [1987] Zhanget al. [1990]

Holocene, southernPVF past3 m.y., northernPVF past4 m.y.

3.9

White Mountain (WMF)

RangeFront(RFF)

0.5-1.2 3.4

-2.3 0.24 0.2-0.5 -5

geologic geologic geologic

Bryant[ 1989] Reheisand Sawyer[ 1997] P. Guth (personal

Pleistocene

western GF western GF

(plus2.5 mm/yr extension) Deep Springs(DSF)

post-Miocene

communication, 1996)

Little Lake (LLF)

1.5

geologic

Roquemore[1988]

Holocene

Net right-lateral

7-8

geodetic

At OVRO

10.6

Savageet al. [1990] Dixon et al. [ 1995]

ground-based network from model,including 1 mm/yr eastof California

geodetic geologic geodetic

Savageet al. [ 1990] Dokka and Travis [1993] Sauber et al. [1994]

ground-based network post-Miocene ground-based network

latitude

ECSZ in Mojave Desert

-8 6-12 -12

Valuesin parentheses arerangesgivenin originalreference.

and fault slip velocity information. We also addresshow this model resolves the apparent discrepancybetween VLBI data from Mojave and OVRO and the high slip rate on the Garlock Fault, as well as how the ECSZ passesfrom the central Mojave regioninto the southernWLB.

2. Geologic and Geodetic Constraints 2.1. GeologicFault Slip Rate Estimates Table 1 is a compilationof geologicallyand geodeticallyestimated slip rates for faults in the southernWLB; fault locations

are shown on Plate lb. In general, NW trending, right-lateral fault systems(the Fish Lake Valley-FurnaceCreek-DeathValley, White-Mountains-OwensValley, and Hunter Mountain-Panamint Valley systems)have the highest slip rates. In the vicinity of Owens Valley, the summeddisplacementson these right-lateral fault systemsis consistentwith magnitude estimatesof ECSZ shear (8-12 mm/yr [Sauber et al., 1986, 1994; Savage et al., 1990]). In the southernWLB south of Owens Valley and in the northern Mojave, however, summed slip rates on NW oriented right-lateral fault systems(as they are currentlyunderstood)are too low

to account

for ECSZ

strain.

The

left-lateral

Garlock

27,036

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

Fault, which separatesthe northernMojave from the southern WLB, also is an importantfault in the region. The faultswith the lowest estimatedslip rates are normal faults boundingthe Sierra Nevada range front and NNE trending normal faults (e.g., the Deep SpringsFault, and Eureka Valley-SalineRidge Faults). We specifygeologicestimatesof Holoceneor Quaternaryslip rates (or averagesof multiple Holoceneestimates,where available)in our models.

Error bounds for these estimates are used to con-

strainthe range of fault slip ratesallowedin our modeling. The mean late Quaternary-Holocenefault slip rates and error bounds

link to faults north of the Garlock Fault [Dokka and Travis, 1990].

we use in the models are shown in Table 1. 2.2.

zonenow known as the ECSZ. Savageet at. [1990], reportingon resultsfrom severalarrays,find thatthe ECSZ passesthroughthe Mojaveandinto OwensValley,followinga trendalmostparallel to a small circle about the NUVEL-1 pole for Pacific-North Americarelativeplate motion[DeMetset at., 1990] (-N35øW). AlthoughSavageet at. [ 1990] find that 8 mm/yrof NW oriented right-lateralshearpassesthroughtheirarraycenteredon the Garlock Fault, their data do not resolve the questionof how this strainis accommodated throughthe area,giventhat faultsin the northernmostMojave desertsouthof the Gafiock Fault do not

GPS Data

GPS networks

characterize

the deformation

of several limited

regions. The site velocitiesbetweenindividualmonumentsrepresent the integratedelastic (or, if an earthquakeoccurs,seismic) contributionsof all geologicfeaturesin the vicinity of the baseline. Becausethese geodeticnetworksare not tied to a regional

2.3. VLBI

and VLBA

Data

VLBI andVLBA datacanprovidevelocitiesof pointsrelative to a set of far-field reference stations, such as stable North America.

Several

VLBI

stations

and one VLBA

station

are

locatedso as to be useful to our study(Plate l a). VLBI stations reference frame, there is no control on the overall translation or are used in our study to ascertainthe motion relative to stable rotation of these arrays. Analyses of network data from the North America of the Sierra Nevadablock (usingthe OVRO and Mojave Desert and OwensValley showthat sheardominatesover Quincy sites) and the central Great Basin (using the Ely site), dilation in these regions. By placing the Mojave Desert and therebyprovidingvelocity boundaryconditionsfor our model. Owens Valley arraysin a regionaltectoniccontext,a respective We also make use of the VLBI site in the Mojave Desert, which 8-12 and 7-8 mm/yr of NW directedright-lateralshearhas been helps resolve deformationin a critical area and, togetherwith deduced[Sauber et at., 1994; Savageet at., 1990; Savageand OVRO, providesthe only relative motion constraintfor two farLisowski,1995]. Geodeticdata from the centralMojave [Sauber separatedpointswithin the model. Table 2 showsratesreported et at., 1994] indicate that Mojave strain is concentratedin the for VLBI and VLBA sites relevant to the southern WLB model as

Table 2. VLBI

and VLBA

Velocities Relative to North America

Rate,mm/yr

Orientation

Data Type

Reference

Ely

5.4+0.7 4.9+1.3 5.0-•-_0.8

N87.1+5øW N98.0-Z_l.2øW N84.1+10.9øW

VLBI VLBI VLBI

Ma et al. [1994] Dixon et al. [1995] C. Ma and J. Ryan (1997)*

OVRO

11.0-Z-_ 1.0 12.0+0.3 10.1_+0.5 11.8_+0.3 11.3+0.2

N28+3øW N43.8+l.2øW N38+0.7øW N38.3+l.3øW N46.1+I.løW

VLBI VLBI VLBI VLBI VLBA

Argusand Gordon[ 1991] Ma et al. [1994] Dixon et al. [1995] C. Ma and J. Ryan (1997)* C. Ma and J. Ryan (1997)*

11.0-Z-_I.0

12.8_+0.5

N50-Z-_5øW N66+0.8øW N57.3+2.3øW N52.5+2.4øW

VLBI VLBI VLBI VLB I

Argusand Gordon[ 1991] Dixon et al. [1995] Ma et al. [1994] C. Ma andJ. Ryan ( 1997)*

9.9+0.2 8.6+0.4

N37.3+0.9øW N29+0.7øW

10.2_+0.2

N31.7+0.9øW

VLBI VLBI VLBI

Ma et al. [ 1994] Dixon et al. [1995] C. Ma and J. Ryan (1997)*

11.0+1.0 12.8+ 1.5 12.1 + 1.2 11.3+1.2** 13.2+ 1.5 12.7+1.5

N3 l+3øW N47+5 øW N38+5øW N38+5øW ** N42+5øW N50-Z-_5øW

VLBI VLBI VLB I VLBI VLBI VLBA

basedon Argusand Gordon[ 1991] basedon Ma et al. [1994] Dixon et al. [1995] basedon Dixon et al. [1995] basedon C. Ma and J. Ryan (1997)* basedon C. Ma and J. Ryan (1997)*

Quincy

8.9+0.5 12.8_+0.5

Mojave

Sierra Nevada

(near OVRO)

Rate,deg/m.y. Sierra Nevada Rotation

0.61 0.35 0.92 0.40 0.13

EulerPole

DataType

32.0øN, 128.0øW 22.4øN, 132.6øW 32.8øN, 124.7øW 25.4øN, 131.8øW 13.4øS, 154.4øW

VLBI VLBI VLBI VLBI VLBA

Reference Argusand Gordon[1991] basedon Ma et al. [1994] basedon Dixon et al. [1995] basedon C. Ma and J. Ryan (1997)* basedon C. Ma and J. Ryan (1997)*

*Data from internet site, as discussedin the introduction.

**Sierra Nevadavelocitybasedon Quincyvelocityandorientation of SierraNevadavelocitynearOVRO from Dixon et al. [1995] (see text).

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS well as various estimates of Sierra Nevada block motion on VLBI

and VLBA

data.

OVRO

based

is one of the sites used in

VLBA monitoring. Typically, the estimatedvelocitiesof VLBA sites are consistentwith but more precisethan the VLBI sites at the samelocation. However,the OVRO VLBA site velocitydiffers significantly from the OVRO VLBI site velocity (Ma and Ryan, 1997) even though the VLBA site is just 500 m east of nearest OVRO

VLBI

antenna.

2.3.1. The Sierra Nevada block (Quincy and OVRO). The Sierra Nevadablock appearsto behaveas a nondeformingbody, which as the westernboundaryof the WLB, providesa powerful constrainton the deformationof our study area. The motion of the Sierra Nevada block has been estimatedpreviously,relying mainly on datafrom the Quincy and OVRO VLBI stations[Argus and Gordon, 1991; Dixon et al., 1995]. The Quincy VLBI site is essentially on the Sierra Nevada block north of the modeled region, and OVRO lies east of the block, within the OVF-WMF systemand separatedfrom the SierraNevadablockby the Range Front Fault system. The Mammoth Lakes and Hat Creek stations are generallyexcludedfrom theseanalysesbecauseof magmatic (Mammoth Lakes) and tectonicactivity near thesestationswhose contributions

to the station velocities

are not well characterized.

Geologic and combined geologic and geodetic estimatesof Sierra Nevada block motion relative to stable North America

are

availablefor comparison.Theseestimatesfall in the range8.5-10 mm/yr orientedN51-73øW+10ø [Minsterand Jordan,1987; Wernicke et al., 1988; Humphreysand Weldon,1994]. Estimatesof Sierra Nevada velocity based solely on VLBI data are less westerly than estimatesthat includegeologicinformation. Argus and Gordon [1991] describe Sierra Nevada block motion relative to North America with an Euler vector of 0.61ø/m.y. of counterclockwise rotation about a pole at 32øN and 128øW, but this includes some error because they do not correct for relative motion betweenOVRO and the Sierra Nevada block. The Argus and Gordon [1991] pole yields a velocity of 11+1 mm/yr N31+3øW on the Sierra Nevada block immediately west of OVRO. Dixon et al. [1995] considerdeformation between OVRO and the Sierra Nevada block and obtain a more westerlyvelocity for the SierraNevadanear OVRO (12.1 +1.2 mm/yr, N38+5øW), but they do not considerrotation. Given the Quincy VLBI velocity and the correctedOVRO velocityorientationfrom Dixon et al. [1995], the Sierra Nevada block rotates with an Euler vector of 0.92ø/m.y. counterclockwiseabout a pole at 32.8øN, 124.7øW. This predictsvelocitiesof 11.3+1.5 mm/yr, N38+5øW on the Sierra Nevada block near OVRO, and 10.3 mm/yr, N23øW at the southendof this block (the gray arrowin Plate 1b). We consider more recent VLBI Sierra Nevada

block motion.

and VLBA

data to reestimate

The results discussed below

are

tabulatedin Table 2. Our estimatesrely on the velocityat Quincy and the velocity orientation of the Sierra Nevada block near OVRO. The velocity of the Sierra Nevada near OVRO is estimated by adding to the OVRO VLBI velocity the horizontal velocity across Range Front Fault (1.0+0.7 mm/yr, oriented N110øW [Dixon et al., 1995]) and a componentof the velocity for the OVF-WMF.

Because the OVRO

VLBI

and VLBA

sites

are nearly exactly in the center of the OVF-WMF stepover,we use half the Holocene rate estimatedfor this fault zone (i.e., half of 1.5+1 mm/yr [Beanlandand Clark, 1993, 1994]). Using the recent VLBA estimateof OVRO motion (11.3 mm/yr, N46øW, (Ma and Ryan, 1997)), we estimatethat the Sierra Nevada near OVRO moveswith a velocityof 12.7+1.5 mm/yr orientedN50øW +5 ø relative to North America.

The VLBA-based

orientation

of

OVRO and the velocity at Quincy yield Sierra Nevada motion

27,037

describedby rotation rate of 0.13ø/m.y. about an Euler pole at 13.4øS, 154.4øW. For comparison, the Sierra Nevada block velocity near OVRO from the most recent VLBI data (Ma and Ryan, 1997) is 13.2+0.5 mm/yr orientedN41.9øW +1ø. Combined with the VLBI estimate of Quincy velocity, this yields a Sierra Nevada rotation rate of 0.40ø/m.y. about an Euler pole at 25.4øN, 131.8øW. Both of our estimates of Sierra Nevada block

motion at OVRO are slightly less westerly than most geologic estimates,but up to 18ø more westerlythan previousVLBI-based velocity estimates[Argusand Gordon, 1991;Dixon et al., 1995]. Since the VLBA-based Euler vector yields less counterclockwise rotation,it suggestsan increasinglywesterlymotion for the Sierra Nevada southof OVRO relative to existingestimates [Argusand Gordon, 1991; Dixon et al., 1995]. For example, comparethe white andgray arrowson the southernSierraNevadain Plate lb. 2.3.2. The central Great Basin (Ely). To model the southern WLB, we require a velocity boundarycondition on the eastern side of the model, which lies in the southern Great Basin. There is little information relating the velocity of this area to stable North America. In our initial model, we use the velocity of the central Great Basin relative to stable North America to provide this constraint,which is basedon the VLBI stationat Ely, Nevada (Ely, Plate 1a). This approachfollowsthatof Dixon et al. [1995]. Implicit in this assumptionis that no major, active tectonicfeatures separateEly from the southernWLB and that the Great Basin is not rotating significantlywith respectto the WLB. Ely moves nearly due west (N87-98øW) relative to stable North America at a rate of 4.9-5.4 mm/yr [Ma et al., 1994; Ma and Ryan, 1997; Dixon et al., 1995]. This rate mainly reflectsextension acrossthe Wasatch Fault Zone, which is the major tectonic featureseparatingEly from the North Americancraton. The Ely velocity exceedsgeologic slip rate estimatesfor the Wasatch Front (0.5-1.5 mm/yr [Eddington et al., 1987; Lund, 1993; Schwartzand Coppersmith,1984]) andgeodeticdeformationestimates from trilaterationand GPS (1.5-1.8 mm/yr [Savageet al., 1992], 2+2 [Bennettet al., 1998], and 2.7+1.3 mm/yr [Martinez et al., 1998]). 2.3.3. The Mojave block (Mojave). The Mojave block is separatedfrom stableNorth America by the nearly inactivesouthern Basin and Range and by the ECSZ and thereforeprovidesa useful kinematic link between our study area and a stable reference. Geologically inferred deformation east of the Mojave

region sumsto-1 mm/yr [Humphreysand Weldon,1994], and hence the eastern portion of our southernmodel boundary is thought to move little with respect to our reference of stable North America. In the Mojave region, 8-12 mm/yr of N33-39øW oriented right-lateral shear is inferred from GPS networks [Sauber et al., 1986; 1994; Savageet al., 1990], and VLBI data from the Mojave VLBI site (8.6-9.9 mm/yr N29-37øW [Ma et al., 1994; Dixon et al., 1995; Ma and Ryan, 1997]) suggestthat most of this shear strain occurs east of the Mojave station. This locus of shearalso is suggestedby the oroclinal deflectionof the Garlock Fault and by inversionof coseismicand geodeticallydetermined interseismic strain in the Mojave region [Unruh et al., 1996; Savageet al., 1990]. However,geologicallyestimatedfault slip rates in the northernMojave region and the southernWLB immediately north of the Garlock Fault do not sum to the net shear rate thought to occur acrossthe ECSZ [e.g., Dokka and Travis, 1990] (Table 1). To accommodatethe-1 cm/yr of ECSZ shearthroughthe Mojave region, we use slipperynodesto representfaults eastof the Mojave VLBI station. VLBI

data from

the two

sites located

within

the modeled

region (OVRO and Mojave) provide importantkinematicinfor-

27,038

HEARN AND HUMPHREYS:WALKERLANE BELT KINEMATICS

mation becauserelative velocity between sites is not subjectto error associatedwith the choiceof a reference(e.g., the stations chosen to represent stable North America). The velocity of OVRO relative to Mojave, from VLBI data, is 2.1-2.3 mm/yr at N73-78øW [Dixon et al., 1995; Ma et al., 1994; Ma and Ryan, 1997]. Recent VLBA data (Ma and Ryan, 1997) indicate a relative motion of 2.9_+0.3mm/yr at N 106+8øW.

minimizationof strainenergy[Saucierand Humphreys,1993]. It is importantto recognizethat with this kinematicmodeling,stress and straindo not representactuallithosphericvalues;rather,they quantifythe degreeof block misfit that occursin 1 year under the prescribedboundary and fault velocities (given in units of displacementper year). If one were interestedin actuallithospheric stress,an initial (large) stressfield and contributionsresulting from basal tractions and finite fault strengthwould need to be included.

3. Methods 3.1.

Finite

Element

Method

Using the finite element program GAEA [Saucier, 1991; Saucierand Humphreys,1993], we modelthe southernWLB as a two-dimensionalplate broken into blocksby discontinuitiesrepresentingfaults. This model is deformedwith prescribedfault and boundaryvelocities,which are appliedby assigningthe displacementsthat accumulateover a 1 year duration(i.e., our modeling representschanges that occur annually). We prescribe velocities for the NE and SW model boundaries (the NW and SE boundaries are left unconstrained) and include faults in one of

threeways: with slip orientationand rate prescribedCsplit nodes" of Melosh and Raefsky[1981]); with slip orientationprescribed but rate unconstrainedand therefore free to be determinedby modeling("slipperynodes"of Melosh and Williams[1989]); or, at triple junctions, with both slip orientationand rate free to be determined by modeling. Table 3 shows how individual WLB faults are representedin our models. Faults are describedwith piecewise continuousquadratic sections,thereby avoiding the stress concentrations

that would occur at fault kinks if linear fault

sections were used. With boundary and thult velocities prescribed,finite elementmodelingis usedto solvefor the deformation field that minimizes net elastic strain energy of the entire model, where local strain energydensityis given by the tensor dot productof stressand strain. To understandthis modeling approachbetter,recall that stress is linearly related to strain through a material's elastic moduli. One then recognizeselement strain energy densityto be a measure of squaredmisfit, and the model of minimum total strain energycan be viewed as a least squaressolutionto the question: what velocity field best satisfiesthe applied constraints.In this view, the elastic moduli of an elementare the parametersthat

determinethe relativeweightgivento that elementin the global

Table 3. Model

Fault Parameters

Fault

NodeType

OwensValley (OVF) White Mountain(WMF) RangeFront (RFF) PanamintValley (PVF) HunterMountain(HMF) FurnaceCreek(FCF) Death Valley (DVF) FishLake Valley (FLVF) westernGarlock (GF) easternGarlock(GF) Deep Springs(DSF) Little Lake (LLF) ECSZ in Mojave Desert

slippery split slippery slippery split slippery split split split slippery split split slippery

Rate,mm/yr 3.5+2*

As an exampleof kinematicmodeling,considera map cut into pieces(cuts representingfaults) that can be deformedwith a set of displacements so that no overlapor gapsform. Our finite element simulation

and velocities, elements strain to accommodate inconsistencies.

The strain energy is used as a measureof kinematic inconsistency, much like overlap and gap area can be used to measure kinematicinconsistencyin the cut map example. The finite element approachto kinematicmodelingallows for a simultaneous inclusion of information about faults (fault loca-

tion, geometry,faulting style, and slip rate), geodeticdata (i.e., relative point velocities), and far-field velocities (e.g., relative plate velocity). By incorporatingthesedata typessimultaneously, this modeling technique provides significant constraint. The descriptionof the model regionas blocksseparatedby faultshas proven especiallyuseful in incorporatinggeologicinformation into modelsof regionaldeformationbecause,wheredeformation is block-like, importantkinematicconstraintis providedby fault location,orientationand slip velocity. This fault-and-blockmodeling is justified by observationsthat deformationin most places is dominated by slip on major faults: far-field velocities are attainedby summingthe geologicallyinferredslip rateson major faults [Holt and Haines, 1995; Humphreysand Weldon, 1994] and by summing seismic moments [Kostrov, 1974; Hanks and Boore, 1984; Wesnousky,1986]. However, there are regions where deformation

2.5-+2* 5.0+2* 5.5-+2*

0.3_+2* 1.5+2'

* 1erinMonte Carlo sampling;no negativevaluesused.

is known to be distributed on folds and faults

spaced too closely to be representedwell by our model. For instance,the zone of high seismicityin the southernOwens Valley is one placewhere distributeddeformationappearsto occurat significantrates. Where we recognizeor suspectkinematically importantrates of distributeddeformationto be occurring,we handleit in one of two ways. If the regionaleffectsof the deformationcan be representedeffectivelywith a fault, the mostdirect approachis simply to includea fault. This is done,for instance, in the southernOwens Valley (see LLF in Plate l a). The second approach, used where deformation is too complex or poorly understood,is to include low-strengthelementsin those areas. This

2.5+1'

of this case would result in no block deforma-

tion, and stressand strainwould be zero everywhere.If the prescribedfault slip requiresthe creationof overlapand gaps,then one can find a "best"solutionby minimizing the net area of overlap and gap. The generalidea behindthe finite elementmodeling is that where block motion cannotoccurwith the prescribedfaults

allows

deformation

to occur

within

those elements

while

contributinglittle strain energy to the strain energy sum, thereby effectively eliminating the kinematic influenceof the local structures in these areas.

In our modeling,we incorporatetwo weak elements,which are shown in Figure 1. Our elastic constitutive relation is parameterizedwith Poisson'sratio and Young'smodulusE, and E of theseelementsare set at a hundredththe valueusedfor typical elements (Poisson'sratio is 0.25 for all elements). The southern weak elementlies in a portion of the ECSZ where shearappears to be accommodatedby rotatingblocksseparatedby E-W trending faults (including the Garlock Fault) [Schermeret al., 1996],

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

27,039

distribution with a most likely value and a characteristicwidth cr chosento be consistentwith the valuesreportedin the literature, with emphasisgiven to reliable Holoceneslip rate estimates(see Table 3). We do not usea sampledslip rate if it requiresfault slip of a senseoppositeto that known for the fault. In some cases, Holocene slip estimatesare availablefor adjacentintervalsof a continuous fault zone (e.g., the FLVF/FCF/DVF and the WMF/OVF/LLF in Plate 1). For thesesystems,we Monte Carlo samplethe two outsideintervalsand model the middle interval

5OO

4OO

with slippery nodes (Table 3). This is done to preventMonte Carlo samplingfrom wastingcomputertime on casesin which rateson adjoining segmentsare inconsistentwith each other and

3OO

to allow

a smooth transition

in rate from one section of fault to

another.

200

For eachof the two casesdiscussedbelow (and many casesnot shown), we draw 5000 sets of fault velocities and obtain a modeled velocity field for each set (i.e., obtainthe model of minimum

•.

model energy for each particularset of sampledvalues). Of the 5000 setsof fault velocities, our preferred solution (for the case beingmodeled)is the simulationof minimummodelenergy. For the two casesdiscussedbelow (which are distinguishedchiefly by choiceof boundaryconditions),we showthe velocity field of the preferred solution. To representthe model uncertaintiesthat

IO0

result from the data uncertainties, we indicate,/'or each element,

o 0

/ 100

200

300

(km)

Figure 1. Mesh for finite element model. The mesh is oriented with its left and right sides parallel to small circles about the NUVEL-1 Pacific-NorthAmerica pole of rotation[DeMets et al., 1990], as illustratedin Plate 1. The meshis developedwith element boundariescoinciding with fault traces (shown in black, from Jennings[1994]). Matehal propertiesare uniform for all elements except those representingthe Sierra Nevada block (shownwith a patternfill), which are much stiffer than the default stiffness,and elementsin zoneswith complexitiesthat we could not adequatelyrepresentwithout violatingmeshgenerationrules (solid fill). These elements are weaker than the default stiffness.

Seetext for morediscussion.For modeledfault types,seePlate2 and Table 3.

andthenorthernweakelementis locatedwherethe OwensValley Fault transfersslip to the White Mountain Fault Zone acrossa releasingstep. The fact that the OVRO VLBI and VLBA siteslie within a weak elementpreventsus from driving our model with

this geodeticinformation,and we insteadsimply monitorthe motion of the VLBI

and VLBA

sites.

The Sierra Nevada block is maintainedas a rigid entity by assigningto elementsrepresentingit a value of E that is 1000 timesthe valuefor typicalelements.Block motionis prescribed by assigningvelocitiesat two nodeson the block in sucha way that the distance between the two points does not change. Becauseeven minor strain of this block results in large strain energiesand this deformationis irrelevantto our modeling,we excludethis strainenergyfrom the total. 3.2.

Uncertainties

To incorporateuncertaintiesin the fault and boundaryvelocities, we vary eachrate (and, for boundaryconditions,orientation) and run many simulations. Appropriate values for each feature are drawnrandomly(i.e., Monte Carlo sampled)from a Gaussian

the root-mean-squared deviationof the elementvelocityas determined by the set of simulations. These model uncertaintiesdo not includethe effectsof erroneousmodel parameterization(such as incorrectlylocating faults in our finite elementmesh). In any modeling exercise, the effects of this class of uncertaintiesare difficult to assess. In our modeling, we are guided by maps of modeled stress, which indicate the location, magnitude, and nature of modeled

It is from

inconsistencies.

consideration

of modeled

stress in our reference

model that we concludethe previousdescriptionsof WLB kinematicsare in significanterror, and we proceedto improvekinematic consistencythrough trial-and-error modificationsto the boundaryconditions(letting the Monte Carlo samplingcoverthe range of possibleslip rates on faults within the WLB) and by making someminor modificationsto the fault types. The resulting final model is thus attainedthrougha combineduse of rigorous criteria (i.e., minimum model energy) and personaljudgment (guided by intuitive evaluationof modeled stress). To obtain optimal boundary velocities that are independentof personal judgmentandto estimatethemodelsensitivity to boundaryvelocities, we Monte Carlo sampledover the sideboundaryvelocities. We do not include geodetic data explicitly in our modeling. Rather,we prescribeSierraNevadablockmotionbeingawareof the implicationsof its motionon the motionof the VLBI/VLBA sites. The relative motion between OVRO and the Mojave sites are used as an after-the-factmeasureof model quality, and the motion of OVRO relative to the Sierra Nevadablock is compared to thatpredictedby our variousmodels.

3.3.

Mesh

The meshused for modeling (Figure 1) is constructedover an oblique Mercator map of the region, projected about the NUVEL-1 Pacific-NorthAmerica pole of rotation [DeMets et al., 1990] and is oriented with the side boundariesparallel to the small circlesof this projection. The grid coversan areaof 300 by 450 km and is centered

on the southern WLB.

Elements

are

designedwith their boundariesalong faults, whosepositionsare digitizedfrom the Jennings[1994] fault map of California.

27,040

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

Fault geometry is modified from the Jenningsmap in two regions: in the southern Owens Valley (north of the Garlock Fault) and near the Deep SpringsFault. In the southernOwens Valley, we add a right-lateral fault systemforming a southern continuationof the OwensValley Fault. The specificgeometryof this fault zone is constructedusing the seismicity[Roquemore and Simila, 1993, 1994] and the distributionof many minor,NW trending(N20-30øW) right-lateralfaults that have been mapped in this region [Roquemore,1988; Jennings,1994]. One of these, the Little Lake Fault, has a Holocene slip rate of-1.5 mm/yr [Roquemore,1988]). Roquemoreand Simila [1993, 1994] have characterizedthis seismically active region as a throughgoing deformationzone extendingfrom OwensValley southwardto the Garlock Fault, naming it the Little Lake Fault Zone (LLF in Plate lb). A right-lateralLLF slip rate of about 0.75 mm/yr oriented

so as to drive the Garlock Fault left laterallyat a slip rate of 5.5 mm/yr andpermitno rotationof the westernMojave region. Becausefaultsin the northernMojave Desertappearnot to slip at rates high enough to accommodatethe ECSZ [Dokka and Travis, 1990], it is not possibleto assigna locusof ECSZ shear strainthroughthe Mojave region solely on the basisof geologically determinedfault rates. Instead, this strain distributionis basedon kinematic modelsof the region [e.g., Garfunkel, 1974; Luyendyket al., 1980; Carter et al., 1987; Dokka and Travis, 1990; Dokka, 1992; Humphreysand Weldon,1994; Schermeret al., 1996] and geodeticdata [Sauberet al., 1994; Savageet al., 1990]. Our model is constructedto accommodateECSZ deformation through a combinationof slip on NW oriented right-

N20-30øW

northeastMojave [Luyendyket al., 1980; Carter et al., 1987; Schermeret al., 1996]. We do not include slip on NW oriented right-lateralfaults west of the Calico-BlackwaterFault because mostECSZ deformationoccurseastof the VLBI site Mojave and becausethesefaultsappearto havevery low slip ratesor be inac-

is estimated

from moment

tensor data collected from

this region since 1981 (J. Sheridan, personal communication, 1997). During this time, the LLF has been more seismically activethan the Death Valley-FurnaceCreek Fault Zone, the Garlock Fault, and othermajor fault zonesin the area. On the Jennings[1994] map, it is unclearwhere (or whether) the Deep SpringsFault connectswith nearbyNW orientedstrikeslip faults, especiallyto the west. We connectthe Deep Springs Fault at its east and west ends to the Fish Lake Valley and White Mountains-Owens Valley Fault Zones, respectively (following Reheisand Sawyer [1997] and Reheisand Dixon [1996]), and allow the Deep SpringsFault to transferslip betweentheseright-

lateral faults [Dokka and Travis, 1990; Dokka, 1992] and clockwise rotation of east-west oriented, fault bounded blocks in the

tive [Dokka and Travis, 1990]. At the northwest end of the model, we enforce a total shear

rate of 9.6 mm/yr on the White Mountainand Fish Lake Valley Faults. This is the rate Dixon et al. [1995] estimated for these

faults, and with the additional 1 mm/yr assumedby Dixon et al. [1995] to occurto the east(which is incorporatedinto our eastern boundarycondition),the total ECSZ shearrate at this latitude is lateral fault zones. 10.6 mm/yr. For eachMonte Carlo simulation,a Fish Lake Valley Fault slip rate is chosenbasedon its geologicallydetermined rate and uncertainty,and the White Mountain Fault slip rate is determinedby subtractingthe Fish Lake Valley rate from 9.6 4. Kinematic Modeling mm/yr. We developtwo classesof modelsbelow. In the first, a referThroughMonte Carlo samplingover fault rate and orientation, encemodel(M1) is madebasedon the mostcommonlyheld we ran a total of 5000 models. Plate 2a showsthe slip ratesfor ideasabouttheregionandillustrates thekinematicconsequencesmodel M1, which is the best (i.e., minimum strain energy) of of thismodel. We thenmodifyM1 soasto bestsatisfytheavail- thesemodels. Plate 2b showselementstressesfor M1. Virtually able geologic and geodetic data in a self-consistentmanner, the entire model is under compressionnormal to the southern resultingin M2. WLB trend, regardlessof the combinationsof slip ratesthat are tried.

4.1. Reference Model (M1)

This is inconsistent

with the tectonic deformation

in the

region,andit illustratesthat boundaryconditionsrepresenting the

Plate 2a schematicallyillustratesthe boundarycondition Sierra Nevada block or the Great Basin (or both) are wrong. In assignments for M 1. Elementsalongthe southwest modelboundary north of the Garlock Fault representthe SierraNevadablock, whichis modeledas a nondeforming, rotatingblock. For M 1 we assumethat SierraNevadablockmotionis described by therotation pole and rate obtainedfrom the QuincyVLBI velocityand the orientationof the Sierra Nevadavelocitynear OVRO estimated by Dixon et al. [1995] (which includes deformation betweenthe Sierra Nevada block and OVRO). Use of this Euler

vector(32.8øN,124.7øW,0.92ø/m.y.)movestheeastboundaryof the SierraNevadablock near OVRO (37.2øN)at -11 mm/yr, N38øW with respectto North America. This velocityis more westerlythan the estimateof Argus and Gordon [1991] for the samelocation (see Table 2) but is within the error boundsof the

particular, the applied boundary conditions drive shortening across the southern WLB modeled

which cannot be accommodated on the

thults.

Plate 2c shows the velocities of model M1 with respect to North America. The modeled velocity of OVRO relative to Mojave is 4.7 mm/yr, N82øW, comparedwith the velocity estimated by VLBI of 2.1-2.3 mm/yr, N73-78øW [Ma et al., 1994; Dixon et al., 1995]. The estimatedvelocity of Mojave relative to stable North America is not westerly enough; the motion of

Mojave estimatedby M1 is 10.5 mm/yr, N5øW, while the observedmotion is 8.6-9.9 mm/yr, N29-37øW [Dixon et al., 1995; Ma et al., 1994]. These inconsistenciesindicate that M1 describessouthernWLB kinematicsinadequately.

blockvelocityestimateof Dixonet al. [1995]. We imposeSierra Nevada motionby making the two nodesshownon Plate 2a move

as illustrated.The northeastmodel boundaryvelocity is 5.4 mm/yr due west relative to stableNorth America. This is the sum

of therateestimated for a geodetic sitelocatedat Ely (4.9 mm/yr, N98øW [Dixon et al., 1995]) and 1 mm/yr of NUVEL-parallel right-lateral shear accommodatedeast of the southern WLB [Dixon et al., 1995]. Southof the Sierra Nevadablock (in the

4.2. Our Preferred Model (M2)

The principalfailuresof M 1 are a generationof regionalcompression across the model (oriented normal to the NUVEL Pacific-North America direction of motion) and inconsistencies

with the kinematicsof the southernWLB area,especiallythose relatingto slip on the GarlockFault andthemotionof theMojave westernMojaveblock),we movethesouthwest modelboundary VLBI site. We developmodelM2 to reconciletheseissues.

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

(c)

Leaend

FaultType, strike-slipnormal

split nodes { '•- • slippew nodes

-,.,

Model stress

'-

""•(•1

(i.e.,kinematic misfit) ½2 Velocity

model velocity,,,I' mm/yr 13.4 VLBI/VLBA

site velocity standard

deviation

of veloci

...

.

0.2

0.5

1.0

2.0

2.5 mm/yr

Plate 2. Model M 1, representingthe standardview of kinematicsin the southernWalker Lane region. (a) Boundary conditions(boxedvalues)andthe fault slip ratesthat are the mostkinematicallyconsistentwith theseboundary conditions(i.e., M 1 is the lowestenergymodelof 5000 MonteCato simulations, sampledoversplitnodefault slip rates). (b) Element stresses for modelM1. Any stressindicateskinematicinconsistencies in the model. Virtually the entire model is undercompressionnormalto the southernWLB trend,indicatingthat our model boundaryconditionsare incorrect. This compressionoccursbecauseright-lateralmotion on the NW orientedstrike-slipfaults producesan east-westlengtheningthat is inconsistentwith the boundaryconditions.(c) Velocitiesresultingfrom model M1 (relative to stable North America). Shading indicatesthe standarddeviationsof modeled velocities. Velocitiesvary the most near the northwestand southeastmodel boundaries(near free boundaries),indicating poorlyconstrainedslip ratesthere. The modeledvelocityfor the nodeat the OVRO geodeticsitehasbeendisplaced

slightlysothatthemodeledvelocityandgeodeticvelocity(whitearrow)canbe compared.The geodeticvelocityof the Mojave VLBI stationis greaterandmorewesterlythanthe modeledvelocity.

27,041

27,042

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

We determine the NE boundary velocity for M2 by running two setsof 5000 Monte Carlo simulationsin which we vary fault slip velocitiesand the velocityof the NE boundaryand assume one of two motions for the Sierra Nevada block.

•a)Northeast boundary velocity

To be consistent

with the west directed extension of the Basin and Range that occurseast of our model, we sampleover the westwardcomponent of the NE boundaryvelocity. In all models,we also add 1 mm/yr of motionparallel to the NE boundaryto representrightlateral shear inferred to be active in the region just east of our model [Dixon et al., 1995]. In fact, the only importantaspectof thesecontributionson the NE boundaryvelocityis the component of velocitynormalto this boundary;all the otherdetailsproveto

haveinsignificantinfluenceon the modelresults.The first setof modelshas the Sierra Nevadablock moving as describedby the Euler vectorcalculatedusingvelocitiesfrom Dixon et al. [1995], and the secondsethas the SierraNevadablock movingas we calculate using the recent VLBI and VLBA data at Quincy and OVRO, respectively(Ma and Ryan, 1997). With the use of the latter setof boundaryconditions,thereis a classof sampledfault slip velocitiesthatproducemodelsof strainenergyfar lowerthan foundin any of the otherclassesof models,indicatingthe discovery of solutionsthat are kinematicallyconsistentwith the available data. We refine this class of models by holding the NE boundaryfixed at a velocityfoundto be optimal,andthen sample over minor variations in Sierra Nevada velocity. The resulting best simulation

is model M2.

The first set of models (with Sierra Nevada block motion

based on Dixon et al. [1995]) fails to correctly reproducethe Mojave VLBI sitevelocityrelativeto eitherstableNorth America or to OVRO, regardlessof the assumedNE boundaryvelocity. Furthermore,the lowest strainenergymodelswithin this set have the NE boundarymoving with respectto North America so as to require-1 mm/yr of shorteningacrossthe southernGreatBasin eastof our model. The secondgroupof models(with our VLBAbasedSierraNevadablock velocity) doeswell in accommodating fault slip and the boundaryconditionswhen the NE boundary velocityis 2-3 mm/yr to the west (plus the 1 mm/yr to the NW) (Figure 2a). These models also accountfor the Mojave and OVRO velocitieswell (thoughthesesite velocitiesdo not depend stronglyon theNE boundaryvelocity). To determinethe optimalSierraNevadablockmotionfor M2, we set the northeastmodel boundary velocity at 2.5 mrn/yr of westwardmotion(plusthe 1 mm/yr to the NW) relativeto stable North America, and sampleover possibleSierra Nevada block motions.This samplingis doneoverthethreedegreesof freedom inherentin a two-dimensionalblock, which we parameterizewith the velocityof a pointon theblocknearOVRO andblockrotation rate. The pointvelocitysamplingis centeredon theVLBA-based calculatedvelocity for this point of 12.7 mm/yr (samplerr of 2 mm/yr) orientedN50øW (rr = 20ø), and rotationrate is centered on zero (rr= 0.15ø/m.y.). Figures2b and 2c are plotsof minimummodelstrainenergy and minimum OVRO-Mojave relativevelocityerror as a function of SierraNevadablock speedand velocityorientationat the latitude of OVRO. Figure 2b suggeststhat optimumSierra Nevada motion near OVRO is aboutN43-47øW at a rate of 13-14 mm/yr. The OVRO-Mojave relativemotion error plot (Figure 2c) shows that this measure

is less sensitive to variations

in the Sierra

Nevadablock speedand indicatesan optimumblock velocityof 11'-13.5 mm/yr, oriented N52-57øW. Our VLBA-based Sierra Nevada block velocity near OVRO (12.7 mm/yr, N50øW) lies betweenthesetwo velocity estimates.

0

2

'"' 3

4

5

6 mmp

Westwardvelocityrelativeto stableNorthAmerica

Figure 2a. Sensitivityof modelM2 misfitto NE modelboundary velocity. Model strainenergyis usedto quantifymisfit,and strainenergyis normalizedby thatof theminimum-energy model (so that the minimum possiblevalue is one). We assume(1) SierraNevadablock motion as definedby 1997 VLBI andVLBA data (Ma and Ryan, 1997), (2) 1 mm/yr of N35øW oriented motionof the NE boundaryto representNW orientedright-lateral shearoccurringeastof the southernWLB [Dixon et al., 1995], and (3) that Basin and Range extensionin the area to the eastis west directed. We then run 5000 Monte Carlo models, with sam-

pling appliedto NE modelboundaryvelocityandto splitnode fault slip rates. Hence, for each NE boundaryvelocity,many modelswere run with variousimposedfault sliprates;eachtriangle represents oneof 5000 MonteCarlomodels.The mostkinematicallyconsistentmodel is the one with loweststrainenergy. The least-energy modelsat differentboundaryvelocitiesshould definea curvethatis approximately parabolicneartheminimum, which is observed(dashedline). The minimum is well defined for the NE boundarymovingwestwardat a rate of-2.5 mm/yr. This is the NE boundaryvelocityusedin modelM2.

To summarize,the optimal boundaryvelocitiesof model M2 have the NE boundarymoving with respectto North Americaat 3.2 mrn/yr, N72øW (2.5 mm/yr, N85øW plus 1 mm/yr, N35øW, followingDixon et al. [ 1995]) and the SierraNevadablockmoving at 12.7+1.5 mm/yr N50+5øW with a rotation rate of 0.0-0.2ø/m.y. counterclockwise(compared to 0.6ø/m.y. from Argus and Gordon [1991]). The Euler vector for this Sierra Nevadamotionis givenin the last row of Table 3. Plates3a, 3b and 3c showthe fault slip rates,stressfield, and velocity field, respectively,for the optimal model M2. Plate 3b showsthat the pervasivecompressionshownby M1 is absentin M2; any residualmodelmisfit is due to local kinematicinconsistencies. The total strain energy is less than 1/30 that of model M1. The modeled differential velocity between Mojave and OVRO is 2.5 mm/yr N 109øW,which compareswell with the differential velocity of 2.9+0.3 mm/yr oriented N106+8øW estimatedgeodetically(usingthe Mojave VLBI velocityand OVRO VLBA velocityfrom Ma andRyan (1997)). The M2 westernGarlock Fault slip rate (5.5 mm/yr) is within the range of geologicestimatesand declinestowardthe fault's

(b) NormalizedModel Strain Energy

rl

0

v

10

11

v

12

v

v

13

v

ß

14

15 mm/yr

Speed of Sierra Nevada Block •Figure2b, SensJtJ¾ity of modelM2 misfitto SW modelboundaryvelocity,basedon modelenergy. From Monte Carlosampling,we obtaina setof modelstrainenergiesat eachvalueof SierraNevadaspeedandorientation(similar to that shownin Figure 2a). We selectthe minimumof theseenergiesat eachpoint, normalizeall valuesby the globalminimummodel strainenergy,and contourthesevalues. In this figure,the NE boundaryis constrainedto movewestwardat 2.5 mm/yr (from Figure 2a). Under this constraint,modelstrainenergydependson the rate and orientationof Sierra Nevadablock motion near OVRO. The minimum energymodelshave Sierra Nevada block velocitiesof 13-14 mm/yr orientedN43-47øW. The numberof Monte Carlo modelsrun for each SW boundary velocityis shownwith symbols;squares, triangles,plusesanddotsrepresent >20, 10-20,5-10, and1-5 simulations, respectively.

(c) OVRO-Mojave RelativeVelocityDiscrepancy(mm/yr) :

V

V

V

V

V

V

V

V

[]

[]

[]

[]

O

[]

[]

C

O

[]

v

v

O

O

•

O

10

11

12

13

[]

v

v

ß

[]

V

+

+

14

15 mm/yr

Speed of Sierra Nevada Block Figure 2c. Sensitivityof modelM2 misfitto SW modelboundaryvelocity,basedon OVRO-Mojavevelocitydiscrepancy.From Monte Carlo sampling,we obtain a set of velocity discrepancies at each value of Sierra Nevada speedandorientation(similarto that shownin Figure2a). We selectthe minimumof thesevelocitiesat eachpoint andcontourthe values.As in Figure2b, theNE boundaryis constrained to movewestwardat 2.5 mm/yr (fromFigure 2a). Under this constraint,OVRO-Mojave velocity discrepancydependson the rate and orientationof Sierra Nevadablock motion near OVRO. This discrepancyis the magnitudeof the deviationfrom the observedrelative velocityof 2.9 mm/yr at N106øW (basedon 1997 VLBA andVLBI datafrom Ma andRyan (1997)). The symbols are as Figure 2b. The minimum error models indicate a Sierra Nevada block motion of N52-57øW at 11-13.5 mm/yr. The SierraNevadablock velocitynearOVRO estimatedfrom recentVLBA and VLBI data(12.7 mm/yr, N49.6øW (Ma and Ryan (1997)) falls betweenthe minima definedby Figures2b and 2c. Hence we use the value reportedby Ma andRyan (1997) in modelM2 to representthe SierraNevadavelocitynearOVRO.

27,044

HEARN AND HUMPHREYS:WALKERLANE BELTKINEMATICS

(b)

-'-(9.6)

12.7mm/yr

•

N49.6W

\

I

(c)

Leaend

FaultType

strike-slipnormal

split nodes slippew nodes

I

-

I

I.

I

01

Model_ stress.

(i.e., kinematicmisfit)

12.9

Velo•Jt,y model velocity

mm/yr

VLBi/VLBA

site velocity standard deviation of velocit

0.2

0.5

1.0

2.0

2.5 mm/yr

I,

Plate 3. Model M2, representingthe regionalkinematicsbasedon our modeling. All conventionsas in Plate 2. (a) Boundary velocitiesand fault slip rates are estimatedsimultaneouslyby Monte Carlo samplingso as to minimize model strainenergyand reproducedVLBI/VLBA velocitiesrelativeto eachotherand stableNorth America (Figure 2 showsthe boundaryvelocity results). (b) Element stressesindicate the kinematic inconsistenciesof model M2. This model hasno pervasivestressfield (compareto modelM1, Plate 2), indicatingthat any model misfit is due to local kinematic inconsistencies.The net strain energy is less than 1/30 that of model M1. (c) Arrows show the velocitiesfor model M2 (relativeto stableNorth America). Shadingindicatesthe standarddeviationsof modeled velocities. In this model, the Mojave and OVRO velocitiesare close to those observed. The calculatedvelocities for the nodes at OVRO and Mojave geodetic sites have been displacedslightly so that both the calculatedand geodeticvelocitiescan be compared.The differentialvelocitybetweenthesestationsis 2.5 mm/yr, N 109øW (comparableto the measureddifferentialvelocityof 2.9+0.3 mm/yr, N 106øW+8ø (Ma andRyan (1997)).

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

eastwardtermination. M2 requireshigher rateson the NW oriented right-lateral faults of the southernWLB than have been commonlyinferred geologically. For example,the Death Valley Fault Zone slip rate for M2 is 5.8 mm/yr, comparedto geologic andgeodeticestimatesof 2-5 mm/yr [Butleret al., 1988;Bennett et al., 1997]. Such high slip rates are requiredto accommodate the -10 mm/yr of ECSZ activity that passesthroughthe region [Sauber et al., 1994; Savageet al., 1990; Savageand Lisowski, 1995].

Figure 3 showsthe sensitivityof model strainenergyand the OVRO-Mojave relativevelocityto variousfault slip rates. Figure 3a showsthat the westernGarlock slip rate is well constrainedby the OVRO-Mojave relative velocity, though the model strain energyis not sensitiveto the westernGarlock slip rate because thispart of the fault is closeto a free boundary.High DeathValley Fault slip ratescorrelatewith low modelstrainenergyandlow OVRO-Mojave relativevelocity errorsand suggestthat the Death Valley Fault slip rate is at least4 mm/yr (Figure3b). Little Lake Fault slip ratesscaleinverselywith DeathValley Fault rates,and the upper limit for the Little Lake Fault slip rate is -2 mm/yr (Figure 3c). Our model is insensitiveto the choiceof Fish Lake Valley Fault rate becausethis fault is near a free modelboundary (Figure 3d). We assumethat the Fish Lake Valley Fault slip rate must exceedthat of the FurnaceCreek Fault, as requiredby activ-

27,045

ity of the Deep SpringsFault (which transfersright-lateralslip from the Owens Valley Fault to the Fish Lake Valley Fault). Becauseof the insensitivityof model M2 to the Fish Lake Valley Fault rate, we cannotsuggesta rate for the Deep SpringsFault or distinguishhow ECSZ shearis distributedbetweenthe FishLake Valley Fault andthe White MountainFault. 5. Conclusions

and Discussion

5.1. Summary

We have modeled deformationin the WLB region to understand how Basin and Range extension interacts with ECSZ accommodation

of Pacific-North

America

transform

motion and

to resolve existing inconsistenciesin the kinematic data of this region. Our modeling incorporatesfault geometry and slip rate data, GPS surveydata, and VLBI/VLBA site velocitydata, and it enforceskinematic consistency.Within the uncertaintiesof the data, our model is consistentwith all data (geologicand geodetic) exceptthe VLBI estimateof velocityat OVRO. In particular,our model is consistent with the newer VLBA

estimate for OVRO

velocity (Ma and Ryan, 1997), which differs significantlyfrom the VLBI estimate. Prior modelswhich dependedon the OVRO VLBI velocity are found to be inconsistentwith the the faulting patternsin the southernWLB.

4

•>'

(a)Garloc!• Fault

3

(b)De•thValley •Fault Zr•ne

v

•

':•%.V

vv

V

v v

VV

VV

v

.: .......... '

............ :..VV

vv V_v ¾..•:_::::.:..•:-.:¾:..•::::,. ............................ .:.:.:..._,.;: .•::::::.._::• ........................ u.uu

V V

....... -..V V v ......... Y.J. .... ......................................... V::.•.•..,V_ __

,:%

........... o

o:•

[]

O.P

, '":'::'.q:•:,:D:.:a:•:..u::D .D:: ' []

0

2

4

6

8

.......... :::::•:D [][] [] 0' 0

""7:: ::..[! ................ D []mrq 2

Slip rate (mm/yr)

•

4

6

8

Slip rate (mm/yr)

(d) Fish Lake Valley Fault Zone

3 (c) Little Lake Fault Zone -o o

o.•

E>,

>E

-• ._Nr-

>v2

Z•

oøø..:P ............

o:•

v

[]

0=• .,.;.;.;.;.;,; ;:;;;::::

0

1

2

3

Slip rate (mm/yr)

4

2

4

6

8

10

Slip rate (mm/yr)

Figure 3. Sensitivityof model strainenergyand relativeOVRO-Mojave velocitydiscrepancyto fault slip ratesfor model M2. For eachfault sampledby the Monte Carlo algorithm,the minimumOVRO-Mojave velocitydiscrepancy and the corresponding model energyare plotted. Strainenergyis normalizedto the model of minimum net energy,so that the minimum possiblevalue is one. With many samples,theseminima shoulddefine a smooth (parabolic)curvein the vicinity of the global minimum. The gray dashedline representsour visual approximation of this curve. (a) The Garlock slip rate is well constrainedby the OVRO-Mojave relativevelocity. Strainenergyis not sensitiveto the Garlockrate (probablybecausethe westernMojave hasfree boundaries).(b) The Death Valley slip rate is constrainedto be greaterthan about4 mm/yr. (c) The Little Lake Fault Zone slip rate is constrainedto be less than about 2 mm/yr. (d) The Fish Lake Valley Fault Zone slip rate is not well constrainedbecauseof its proximity to the unconstrainedNW model boundary.

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HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

We calculate a velocity (relative to North America) for the

A primary constrainton this is the velocity of the Mojave VLBI

Sierra Nevada block near OVRO of 12.7+1.5 mm/yr at site (8.6-10.2 mm/yr, N29-37øW [Dixon et al., 1995; Ma et al., N50øW+5ø (at 1rr uncertainty).Our modelhasonly0-0.2ø/m.y. 1994]), which requiresmost of the 10-12 mm/yr of ECSZ strain of counterclockwiseSierra Nevada block rotation, and hence the

SierraNevadavelocitynear OVRO is approximately valid over the entire Sierra Nevada block. Our velocity for the southand centralpartsof the SierraNevadablock is more westerlythan

to occur east of this site.

5.2. Implications for Regional Tectonics

Our model provides an accountingfor the distributionand previous estimates. We also find that the southernGreat Basin style of deformationacrossthe southernGreat Basin and across adjacentto our study area (i.e., the southernCalifornia-Nevada the ECSZ. Deformation to the eastof the WLB is dominatedby border)moveswestwardat a rate of about2.5 mm/yr, which is normal faulting, deformationto the south(in the Mojave) is domslowerthanthevelocityof thenorthcentralGreatBasinat Ely. inated by strike-slip faulting, and deformationwithin the WLB The vector diagrams in Figure 4 illustrate the differences involvesboth normal and strike-slipfaulting. Hence, at least in betweenthe more traditional view of Sierra Nevada motion (as our studyregion, the zonesof shearaccommodationand dilation representedby model M1 and illustrated in Plate 2) and our in the southernGreat Basin occur in domainsthat overlap and model (M2, illustratedin Plate 3) by showingthe inferredcontri- have rather abruptboundaries;the zone of shearaccommodation butions to Sierra Nevada block motion at the latitude of OVRO. is largely confinedto the Mojave ECSZ and WLB, whereasthe By incorporating a relatively westerly velocity of the Sierra zone of dilation is largely confinedto the area north of the GarNevada and low extension rate acrossthe southernGreat Basin, lock Fault. The WLB is the overlap area where both styles of model M2 accommodatesa relatively great rate of east-west deformation occur simultaneously. Deformation occurs within lengtheningrequiredacrossthe WLB by the northwesterlystrike the centralWLB on fault systemsthat link strike-slipand normal of strike-slipfaultsin the region. faults togetherin seriesof pull-apart basins(Plate 1) [Burchfiel In our model, ECSZ shear is concentrated on the east side of and Stewart, 1966; Burchfiel et al. [1987] Troxel and Wright, the southern WLB. We have found a kinematic need for the Lit1987], whereasadjacentto the Sierra Nevada, faulting is partitle Lake Fault Zone (in the southwest WLB) but find thatis slips tioned separatelyonto rangeboundingnormal faults and nearby at half the rate of the DeathValley Fault systemor less(Figure4). strike-slipfaults. We find the integratednormal and strike-slip

Velocityof Sierra Nevada near OVRO (relativeto NorthAmerica) Model M1

North

11.3 mm/yr N 38øW

4.9mm/Yr

Model M2

North

"'"•i! 12.7 mm/yr N50øW

West

2.5 mm/yr N 87øW

NA

southern B&R east of California

Figure 4. Vectorsumsshowingcontributions from the southern WalkerLane Belt (WLB) andthe BasinandRange (B&R) eastof California,for modelsM1 andM2. In modelM1, the assumedmotionsof Ely Nevada(seePlate 1) andthe SierraNevada[Dixon et al., 1995] imply strainwithinthe southernWLB consistent with right-lateralshear on planesorientedN12øW. In modelM2, a morewesterlymotionof the SierraNevadaanda lessactiveBasinand Rangeresultin about10.8mm/yrof right-lateralshearresolvedontoplanesorientedN40øW. Thisstrainis consis-

tentwithgeological, geodetic, andseismological data.Tobeconsistent withtheM 1 vectorplot,theM2 plotshows the Basinand Rangevector(not the easternvelocityboundaryconditionvectorof 3.2 mm/yrdue west,which includes1 mm/yrof N35øW orientedright-lateralshearthoughtto occurnearthe Californiaborder[Dixonet al., 1995]). Errorellipsesreflectformalsolutionerrorsfor VLBI andVLBA data[Ma andRyan,1997;Dixonet al., 1995]butdonotreflectthevariability between datafromdifferentsolutions (Table2), whichis greater.

HEARN AND HUMPHREYS: WALKER LANE BELT KINEMATICS

27,047

pull-apart mode of deformation to be the kinematically more important style. The Garlock Fault plays the role of accommodating the dilation of the Great Basin [Davis and Burchild, 1973]; 5-6 mm/yr of left-lateralslip on the westernGarlockFault occursin model M2 as a resultof the more westerlyand largely

North America. If any such regional bias exists in the VLBI/VLBA data, it affectsonly our conclusionsaboutthe deformationrequiredeastandwestof our modelarea. In particular,it would reducethe inferred Basin and Range extensionrate eastof

irrotational

Basedon the distributionof historicalseismicity,Great Basin deformationis concentratednear its westernmargin (the WLB), easternmargin (the intermontaneseismiczone [Smith and Sbar,

Any balancingof the forcesactingon the SierraNevadablock resultsin a conclusionthat a net force is actingon this block with a componentin a directionnormalto the SanAndreasFault (i.e., i• a WSW direction). This is a simpleconsequence of the motion

1974]), and, in the northern Great Basin, in the central Nevada

o_rthe Sierra Nevada block toward the San Andreas Fault (as

seismiczone [Eddingtonet al., 1987]. The geodeticsite at Ely,

accommodated by dilation in the Great Basin and contractionin California). Such a force cannotbe derived from transformplate interaction,which doesnot contributeforcesacting normal to the transform direction. Therefore, unlike passive transform processes(that are driven by plate-guidedforcescreatedfar away), westerndrift of the Sierra Nevada block is evidencefor important

Sierra Nevada block motion.

Nevada, which lies between the intermontane seismic zone and

the centralNevada seismiczone, movesat -5 mm/yr to the west with respectto North America [Dixon et al., 1995]. This velocity representseasternGreat Basin extensionnorth of our studyarea, and it is greater than what can be accommodatedacross the southernGreat Basin east of our study area. This implies that eastern Great Basin extension increases in rate to the north.

The

rapid westerly velocity at Ely appearsto be accommodatedby deformation

across the central Nevada

seismic zone farther north.

It has long been recognizedthat the San Andreas Fault does not accommodate

all of the relative

forces created within

the western United

States that contribute

to

Basin and Range extensionand California CoastRange contraction.

seismic zone that moves

northwesternNevada in a northwesterlydirection,therebymaking the spaceneededfor the northeastern Great Basin (including Ely) to approachthe Sierra Nevada. The relatively northerly motion of crustwest of the centralNevada seismiczone is suggested by normal fault orientationsof relatively northwesterly extensiondirection[Zoback, 1989], a right-lateralcomponentof slip on centralNevada earthquakes[Eddingtonet al., 1987], and the regionalstrainfield inferredby GPS data[Savageet al., 1995; Bennettet al., 1998]. This is to say that the zone of Pacific-North America transform accommodationpenetratesas far east as the California border at the latitudeof our studyand as far eastas the central Nevada

our model and reduce the inferred contraction rate to the west.

motion

between

the Pacific

and North American plates. Any differencebetweenthe relative plate motion and the San Andreas Fault slip velocity has been called the "San Andreasdiscrepancy"[e.g., Minster and Jordan, 1987], and recognitionof the importanceof the ECSZ greatly

reducedthisdiscrepancy [e.g.,Argusand Gordon,1991]. Of particular interest here is the componentof this velocity normal to the San Andreas Fault. Using their estimatedvelocity for the Sierra Nevada block, Argus and Gordon [1991] calculate -2 mm/yr of convergenceat the latitude of the southern Sierra Nevada (36øN). Calculatingthe San Andreasdiscrepancyat the same latitude using our Sierra Nevada block velocity (with respectto North America) and the Pacific plate velocity given by NUVEL-1A [DeMets et al., 1994], we estimatea net shortening rate normalto the San AndreasFault of-6 millimetersper year. Consideringthe uncertaintiesin our modeling and in NUVEL, predictedcontractionrates as low as 1 mm/yr (or as great as 10 mm/yr) are possible. Contraction normal to the San Andreas Fault is expressedgeologically[e.g., Unruh and Moores, 1992; Wentworthand Zoback, 1989], seismically[e.g., Unruh and Lettis, 1998] andperhapsgeodetically(as summarizedby Argusand Gordon[1991]), thoughrate estimatesvary widely. The uncertainties in our estimated Sierra Nevada velocity given abovedo not includethe effectsof any systematicerrorsin the VLBI/VLBA data. There is some suggestionthat western U.S. VLBI and VLBA data are systematicallybiasedwith a westward velocity of a few millimeters per year. The basis for this concernis the -2 mm/yr westerly motion (with respectto stable North America) of stationsin Texas, New Mexico, Arizona, and Colorado that we think shouldbe moving essentiallywith stable

Acknowledgements.We thankChopoMa for supplyingus with new VLBI andVLBA data. We alsothankJudiSheridan,RandyPalmer,Jeff Unruh, and severalattendeesof the 1997 FOP field trip for their assistanceandcomments.This work was supported by grantsfrom the Southern California Earthquake Center (SCEC) and by NSF grant EAR-9405547. SCEC is funded by NSF cooperativeAgreement EAR-8920136 and USGS CooperativeAgreements14-08-0001-A0899 and 1434-HQ-97AG01718. SCEC contribution408.

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E. H. Hearn and E. D. Humphreys,Departmentof Geological Sciences, University of Oregon, Eugene, OR 97403. (e-mail: lizh @@newberry. uoregon.edu; gene@newberry. uoregon.edu) (ReceivedOctober 13, 1997; revisedMarch 17, 1998; acceptedApril 22, 1998.)