Kinematics of Postseismic Relaxation from Aftershock Focal Mechanisms of the 1994 Northridge, California, Earthquake

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. Bll, PAGES 24,589-24,603, NOVEMBER 10, 1997

Kinematics of postseismic relaxation from aftershock focal mechanisms of the 1994 Northridge, California, earthquake

Jeffrey R. Unruh William Lettis & Associates,Walnut Creek, California

Robert J. Twiss Departmentof Geology,University of California,Davis

Egill Hauksson SeismologicalLaboratory, California Institute of Technology,Pasadena

Abstract. Geodetic observationsof surface deformationassociated with the 1994 Northridge, southernCalifornia, earthquake generally are reproducedby simplemodels of a large-scale elastic dislocation on a blind or buried thrust fault. The smaller-scale aftershocks of the Northridgeearthquake are distributedthroughout much of the volumeof crustthat appearsto have deformedelastically during the mainshock. These aftershocks,averaged over volumes that are large relativeto their ruptureradii, reflect a distributed,permanent deformation that is accommodatedby local brittle fracture. We use a micropolarcontinuum model to invert the aftershocksin suchvolumes for the averageincremental strain, and we comparethat deformation both with the elastic strain from the dislocation model of the mainshock and with geodeticallymeasured strain. Aftershockdeformation that occurredat depthsbelow about 6 km, and which is associatedwith the primary rupturezone, is consistentwith slow continuationof the southwest-side-upreverse slip on the blind Northridgethrust fault. In contrast,aftershock deformation from the upper5-7 km of the hangingwall block directly above the thrust fault can be characterizedby horizontalNE-SW shorteningand horizontal NW-SE (i.e., fault-parallel)extension. This patternof deformationis similar to that associatedwith the mainshock,as observedgeodetically and as calculatedfrom the elastic dislocationmodel. We interpretthat the aftershockactivity in the hangingwall represents the quasi-ductileaccommodation by brittle deformationmechanisms of a permanentstrain distributedthrough the hangingwall block. The aftershocksalong the mainshockrupture zone are interpretedas resultingfrom either (1) the time-dependentrelease along a weakenedfault zone of part of the remainingaccumulated elastic strain in the uppercrust or (2) the continuedslip in the weakenedfault zone driven by the deformationof a ductile-elasticlower crustallayer that relaxesunder the stresstransferred by the coseismicloss of cohesionin the uppercrust. In either case,the aftershockactivity suggeststhat the crustundergoes quasi- ductile flow as a brittle-elastic material, and is not a strictly elastic material.

1. Introduction assumesthat the mainshock rupture can be approximated by a dislocation within an elastic material, and it consists of In this paper we use a generalized continuum model to finding a combinationof elastic strength,fault geometry,and evaluate distributed brittle deformation accommodated by slip distribution that best reproducesthe geodetically aftershocksof the 1994 Northridge earthquake,which occurred determinedsurface displacements. The successof these models on a blind thrust fault beneath the westernTransverse Ranges in reproducingthe first-orderpattern of surfacedeformation in southern California (Figure 1). Patterns of regional [Hudnutet al.; 1996, Wald et al., 1996; Shen et al., 1996] deformation associated with the mainshock have been providesreasonable justification for the assumptionthat the investigatedby severalworkers [Hudnutet al., 1996; Wald et upper crust deformedelastically in the vicinity of the slip al., 1996; Shen et al., 1996], primarily through analysis of dislocation that causedthe earthquake. coseismic surface displacements measured by geodetic Aftershocksof the Northridgeearthquake are not confined techniques.The modeling approachfavored by these workers to a singleplane but ratherare distributedthroughout much of the volume of crust that responded elastically to the Copyright 1997 by the American GeophysicalUnion. mainshock rupture (Figures 2 and 3). Each aftershock representsa discretedisplacement event on a fault surface; Paper number 97JB02157• also, each aftershock is roughly one or more orders of 0148-0227/97/97JB-02157509.00 magnitudesmaller than the mainshock. If we considera

24,589 24,590 UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION

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basementbeneath the Cenozoic cover. Thus the major map- region moved toward each other, accommodatinghorizontal scalecontractional structures in the region (e.g., the Santa shorteningnormal to the strike of the Northridgethrust fault, Monica Mountains and Santa Susana Mountains anticlinoria and stations to the northwest and southeastof the epicentral [Davis and Namson, 1994] probably are best characterizedas region moved away from each other, accommodating basement-involveduplifts or anticlines [Narr and Suppe, horizontal lengthening parallel to the strike of the fault. 1994]. These motions are illustrated by particle displacementpaths sketchedparallel to the displacementdirections of the GPS 3. CoseismicDeformation and Elastic Models stations(Figure 4). Althoughthe fault-normal shortening is not surprising given the dip-slip motion on the Northridge Patterns of surface deformation associated with the thrust, the fault-parallel lengthening is not accountedfor in Northridge earthquakehave been determinedfrom Global two-dimensionalkinematic models for finite growth of Positioning System (GPS) geodesy[Hudnut et al., 1996]. basement-involvedanticlines [e.g., Narr and Suppe,1994]. Thesestudies show an approximatelysymmetrical pattern of The observedpattern of coseismicdisplacements, including coseismicdisplacements in the vicinity of the epicenter: GPS the fault-parallel lengthening, is reproducedby models that stations to the northeast and southwest of the epicentral approximatethe Northridge earthquakeas a dislocation on a

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Figure 4. Displacementof GPS stations during the Northridgeearthquake (from data of Hudnut et al. [1996]). Displacement directions are shown by arrows attached to individual GPS stations. Magnitude of horizontal displacementis indicatedby contour lines. Interpretedparticle displacementpaths are sketchedparallel to the coseismicdisplacement directions to indicate the patternsof crustalflow during the mainshockrupture. 24,594 UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION

A 4. Northridge Earthquake Aftershocks SW SantaSusana NE Mountains Aftershocksof the Northridge earthquake(Figures 2 and 3) "Near-Field" Pin "Far-Field" Pin outline the geometryof the mainshockrupture zone [Hauksson m et al., 1995] and exhibit systematic variations that coincide Hanging FaultTip with the structural segments in the Santa SusanaMountains Wall Block •e identified by Yeats et al. [ 1994]. The Northridge thrust i s relatively well-defined in the Sylmar segment southeastof the 10 km- Chatsworthlateral ramp by a single southwestdipping zone of

- aftershocks(Figure 3, C-C'). The aftershocksextend to a depth - I Footwall of approximately 20 km and can be traced upward as a - relatively planar, 3.5 km wide zone to a depth of - approximately7 km. Above this depth, aftershocksappear to 20 km- ,•t•"Block be more diffuse and the mainshock rupturezone is difficult to identify as a discrete,well-defined structure. In the Placerita segment between the Chatsworth and Gillibrand Canyon lateral ramps, the Northridgethrust appears to be well-defined by aftershocks between approximately 21 B km and 12 km depth, but at shallower depths the seismicity SW NE Direction of Coseismic appearsto be distributedin the hanging wall (Figure 3, B-B'). Displacement Shen et al. [1996] noted that the mainshock rupture zone appearsto steepenabove approximately9-10 km depth in this ,, T-,ast,c(Motion out-of-plane) region, consistent with the observation of Hauksson et al. [1995] that the Gillibrand Canyon and Chatsworth lateral /• I Lengthening ramps bound a "ridge" in the base of the aftershockzone that is

10 km- 3-5 km higher than the surroundingregions to the northwest ShorteningI •x.• •-" and southeast. In the Newhall-Potrerosegment northwest of the Gillibrand Canyon lateral ramp, aftershocks suggest two oppositely dipping zonesbetween approximately 10-17 km depth (Figure 20 km 3, A-A'): a southwest dipping zone to the south, and a northeast dipping zone to the north. It is not clear from Figure 5. Model for the fault-parallel extensional strains patternsof aftershocksif one zone overlaps the other or if indicatedby geodetic measurementsof coseismic deformation both terminateat approximatelythe samedepth. Thereappear (Figure 4). (a) Structuralrelationships prior to the earthquake. to be fewer aftershocks in the upper 9 km of the crust (b) Coseismic slip on the blind Northridge thrust imposes a northwestof the Gillibrand Canyon lateral ramp (Figure3, A- shorteningon the hanging wall block in the direction of slip. A'). The elastic responseof the crust to the fault-normal shortening is a fault-parallel lengthening, which creates components of motion out of the plane that contains the slip vector. 5. Continuum Model for Evaluating Distributed Aftershock Deformation

The majority of the Northridge earthquakeaftershocks are buried or blind fault in an elastic material [Hudnut et al., 1996; small magnitude(M1-M3) events with rupturedimensions of Shen et al., 1996; Wald et al., 1996]. The northeast directed the order of a few tens to a few hundreds of meters. We wish t o motion of the hanging wall block during the earthquakeis the evaluate the average deformation of volumes of crustthat are result of simple shearing along the Northridge thrust fault. much largerthan the ruptureradius of an individual aftershock, Because the fault does not break the surface, however, the so that the small coseismic displacements within a given northeast directedmotion of the hanging wall block must be volume collectively can be assumed to approximate a accommodatedby a shortening strain normal to the strike of continuousdeformation. This assumptionis reasonablegiven the fault (Figure 5). The modeledelastic response of the crust the scattered distribution of most of the Northridge to this shortening is a northwest-southeastelongation parallel aftershocks,especially those that occurredin the hanging wall to the fault, which accountsfor the observedpattern of fault- block above the primary rupture zone (Figure 3). parallel motions (Figure 5). As shown by the coseismic We use a micropolar continuum model [Eringen, 1966, displacement field (Figure 4), the magnitude of the fault- 1967] to evaluate the characteristics of the brittle aftershock parallel extension is comparable to the fault-normal deformation. In contrastto classicalcontinuum theory, which shorteningin the region directly north of the mainshock. The doesnot explicitly accountfor the substructureof a deforming, near-field elastic deformation of the hanging wall block brittle material, the micropolar model assumesthat the crust associated with the mainshock rupture thus can be deformslike a granular material, where the "grains" are rigid, characterizedas an inhomogeneous,approximately horizontal fault-boundedblocks that have dimensions comparableto the pure shear strain; that is, the directions of maximum rupture radii of aftershocks [Twiss et al., 1993]. The shorteningand maximum lengthening are both subhorizontal micropolar theory relates the instantaneousdirection of shear and are directednormal to and parallel to, respectively, the along the boundaries of the "grains" to the larger-scale strike of the fault. deformation of the material and to the local rotation of the UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION 24,595 fault blocks. If the deformation is progressive and can be [Twiss et al., 1991, 1993]. The focal mechanismsprovide smoothedover time, it can be approximatedas a rate of quasi- constraintsonly on the directionsof incremental slip on faults ductile flow and a rate of local block rotation. Any set of but not the actual slip magnitudes. Thus our inversions aftershock data then reflects an increment of that deformatiofi provide solutions only for the orientations of the principal that accumulatesover a geologically small but finite time incremental strain axes and for their relative magnitudes; the period. inversions do not constrain the actual magnitudes of the The kinematics of a "granular" style of deformation are principal strains. The incremental strain tensor, however, can illustratedby the following example. The averagedeformation be converted into the strain rate tensor simply by dividing of a specific volume of crustcan be characterizeduniquely by each of the incremental strain components by the same time the lengths and oi'ientationsof the three principal axes of the increment,which is a scalar quantity. Dividing a tensor by a strain ellipsoid. This average deformation, however, is scalaraffects neither the orientation of the principal axes nor accommodatedat a much smaller scale by the shearing of the ratios (or ratios of differences) of the principal values. crustal blocks (i.e., "grains") past one another along their Thus conclusions about these characteristics of the boundaries. The averagemotion of the block centroids can be incremental strain tensor also apply to the strain rate tensor. describedby a continuumapproximation, and at any given To avoid confusionin discussingthe data, we will refer to the time it definesthe large-scalestrain (i.e., change in shape) of theoretically defined rates as if they were infinitesimal the crustal volume. The relative motion of the block centroids increments in the kinematic vai'iables. To relate the in turn prescribes one component of the local direction of terminology to the theory, it is only necessaryto consider the shearing along the block surfaces. Becausethe blocks are infinitesimal incrementsas incrementsper unit time. rigid and not physically attachedto each other, they also are free to rotateabout their centroidsin a mannerdictated by the 6. Analytical Approach local geometry of the blocks and their interactions with neighboring blocks. This local rotation contributes another To relate the individual aftershocksto a large-scale strain componentof shearingalong the block boundaries,although increment and a small-scale relative rotation increment, we it contributesnothing to the large-scalestrain of the volume. make the explicit assumption that the local coseismic slip To relate the local direction of shear along the block occurs in the direction of the maximum resolved shear boundariesto the large-scale deformation of the volume, we increment on fault surface and that the shear increment is the needto explicitly accountfor the relative displacementof the net result of the large-scale incremental strain tensor and the block centroids as well as the local, small-scale rotations of local incremental relative rotation. Our analytical approach the blocks about their centroids. then consists of two main steps: (1) group the focal There are numerous, well-documented examples in the mechanisms into discrete spatial domains of essentially geologic literature of natural brittle deformations that include homogeneous deformation; and (2) use the micropolar local rotation of fault-bounded blocks (see discussion of Twiss continuum model described above as a basis to invert the focal et al. [1993]). It is reasonable to assume that such mechanisms for the incremental strain and incremental relative deformations may be accommodatedby earthquakes, which block rotation in each domain. representdiscrete slip events along the boundariesof rigid, Data used for the inversions in this study consist of focal fault-bounded blocks. The focal mechanisms that we use as mechanismsfor the Northridge aftershocks. These data were kinematic data for our inversions are essentially data on the recordedby the SouthernCalifornia SeismographicNetwork, a orientation of the two nodal planes, which are the possible joint project of the California Institute of Technology and the shear planes, and the associatedslip direction on each plane. U.S. Geological Survey. The methodology for determining Accordingto the micropolar theory, the slip direction on any focal mechanismsis describedby Hauksson et al. [1995]. given surfaceis determinedby two kinematic components:(1) We grouped the focal mechanismsby spatial domains in the average large-scale deformation rate represented by the order (1) to separateevents on the primary rupturezone from relative motion of the centroids of the rigid blocks, and (2) a aftershocks that were distributed within the hanging wall local independentrotation rate of the individual blocks about block; and (2) to analyze possible variations in seismogenic their centroids [Twiss et al., 1993]. In technical terms, the deformationassociated with distinct structuralsegments of the large scaledeformation rate (i.e., the rate of changein shapeof contractional belt in the Santa Susana mountains. Our initial the crustal volume) is the symmetric part of the velocity approachwas to use the structuralsegments defined by Yeats et gradienttensor (the strainrate) for a continuumdefined by the al. [1994] as a basis for groupingaftershocks (Figure 1). This centroidsof the rigid blocks that constitute the material. The appearsreasonable, given the changesin geometryof the base relative rotation rate (the relative vorticity) is basically the of the aftershock zone associatedwith the Gillibrand Canyon difference between the antisymmetric part of this velocity and Chatsworth lateral ramps [Hauksson et al., 1995]. gradient tensor and the spin tensor that defines the Additional subdivisions of the data were performed as independentlocal rotationrate of the rigid blocks. Thus use of appropriate to isolate volumes of relatively homogeneous the micropolar continuum model to interpret fault-slip data deformation. provides a better constrainton the characteristicsof the strain Seismic P and T axes are unit vectors that conveniently rate, and also permits the extraction of additional kinematic describethe orientationsof the nodal planes and the directions information about the contributions of block rotations to of the first motions. We calculated the P and T axes for the patternsof slip on fault surfaces(see discussionand examples focal mechanism data and plotted them on equal-area,lower of Unruh et al. [1996]). hemisphere, Kamb contour plots. The plots were inspected The micropolar theory is formulated in terms of rates visually to assessthe orientation and distribution of the P and becausethis is the appropriateform for kinematic variables in T axes. If we determined that the P and T axes formed well- the constitutive equations describing ductile deformation defined, single maxima on the Kamb plots, then we concluded 24,596 UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION

Table 1. Inversion Results, Sylmar Segment

Depth, d1 d3 D W MeanCos Cos-1 Number km (Maximum (Maximum (MeanCos) of Data Extension)* Shortening)* 0-3 98, 31 352, 24 0.5 0 0.983 10.616 39 3-6 143, 69 22, 11 0.5 0 0.968 14.419 202 6-8 54, 75 20, - 12 0.5 0.1 0.979 11.756 306 8-10 35, 77 20, - 12 0.5 0 0.987 9.381 181 10-12 310, 52 35, -4 0.5 0 0.988 8.955 158 12-14 295, 47 40, 14 0.5 0 0.987 9.293 142 14-16 172, 69 32, 16 0.6 0 0.982 10.767 85 16-18 312, 83 357,-5 0.5 0.1 0.975 12.778 28 18-20 214, 81 15, 8 0.6 -0.2 0.984 10.176 44

Seetext for completedescriptions of kinematicvariables and misfit values. *Orientationsof d• andd 3 givenas trend, followed by plunge. Positivevalues of plungeare below the horizontal;negative values are above the horizontal.

that the data reflect a homogeneousdeformation within the cosineof the uniquerotation angle that brings the model P and volume of crust containingthose aftershocks. For Kamb plots T axes into coincidence with the observed P and T axes. The that showed multiple concentrations of P and/or T axes, averageof these misfits over all the focal mechanismsin the however, we redefined the boundaries of the crustal volumes as data set defines the mean cosine misfit, and we search for the appropriateuntil the associatedKamb plots showedthat P and model parametersthat minimize this averagemisfit. In Tables T axes clustered in distinct, well-defined maxima and thus 1-3 we report the averagemisfit as the angle whosecosine is reflected a more homogeneousdeformation. the meancosine misfit (i.e., cos'l(meancosine misfit)). The inversion solutionconsists of finding the values of the We use a grid-searchalgorithm to find the parametersof the model parametersfor a micropolar deformationthat minimize best fit micropolar model for each group of P and T axes. A the misfit betweenthe theoreticallycalculated P and T axes and discussionof our grid-searchalgorithm PTGRDSRCHand the the observedaftershock P and T axes. The five parametersof a rationale for the misfit calculation are discussedin detail by micropolarmodel include (1) the three independentparameters Unruh et al. [1996] and will not be repeatedhere. In general, that define the orientationsof the principal axes of the strain we do not search the entire five-dimensional grid rate, or incrementalstrain, tensor (dl, maximumlengthening; systematicallybecause of the large amountsof computertime d3,maximum shortening; d2, intermediateprincipal axis); (2) that wouldbe required. Instead, we generally searcha swath a scalar parameterD (the deformationrate parameter),defined aroundthe path that leadsfrom the starting model to the final by a ratio of the differencesin the principal strain rates, or solution by taking the minimum misfit model in any subgrid incremental strains, which characterizesthe shape of the as the central point in defining the subsequentsubgrid and incremental strain ellipsoid, decreasingthe size of the subgridspacing as we approachthe solution. We ensure that the minimum is bracketed for all D--d--••-3;d2 - (1) parametersin the grid search. The best fit models are dl- d3 determinedwithin grid incrementsof 5ø for the orientation of the principalstrain axes and within grid incrementsof 0.1 for and (3) a scalar parameter W which characterizesthe relative the valuesof D and W. The correspondingprecision of the vorticity (i.e., rate of relative rotation), of rigid, fault-bounded solutionspresented in Tables 1-3 are a grid resolutionof +2.5 ø blocksabout an axis parallelto d2 [Twisset al., 1993] for the orientationsof dl andd 3, and a grid resolutionof +0.05 W-- (tø•3- w•3) (2) for the values of D and W. 0.5(d1 -d 3) 7. Inversion Results where w•3 is a componentof the antisymmetricpart of the large scale velocity gradient tensor which describes the averagelarge-scale rotation rate about d2 and to•3 is an 7.1. SeismogenicDeformation Along the Mainshock Rupture independentcomponent describing the local block rotation Zone rate aboutd2. As discussedpreviously, the parameterW can be interpretedto reflect the incremental relative rotation of fault- The inversion results (Tables 1-3; see Figures 2 and 3 for bounded blocks. As a first approximation, we ignore locations of depth domains cited in the tables) show that the componentsof the relative vorticity about the other principal aftershocks along the main rupture zone generally axes. accommodatenortheast-southwest shortening (i.e., d3 is From any given set of micropolarmodel parameters,we can subhorizontal and oriented NE-SW) and vertical crustal calculatethe orientation of the P and T axes for any given thickening (i.e., the direction of maximum lengtheningdl is orientation of shear plane [Twiss et al., 1993; Unruh et al., steeply plunging to subvertical). This is consistent with 1996]. For eachobserved pair of P and T axes representingan southwest-side(i.e., hanging wall block) up simple shear on aftershock focal mechanism, we find the orientation of the the primary rupture zone. In general, values of the deformation model shearplane for which the model P and T axes are a best parameterD associatedwith the primary rupturezone are 0.5, fit to the observed P and T axes. The misfit is taken to be the which implies, for a constant volume deformation, that there UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION 24,597

Table 2. Inversion Results, Placerita Segment

Depth, d1 d3 D W MeanCos Cos-I Number km (Maximum (Maximum (Mean Cos) of Data Extension)* Shortening)*

Primary RuptureZone 6-12 170, 72 26, 15 0.6 0.1 0.992 7.104 41 12-14 136, 73 7, 11 0.5 -0.1 0.985 9.827 61 14-16 134, 74 13, 8 0.5 -0.1 0.980 11.580 82 16-18 273, 83 18, 2 0.5 0.3 0.989 8.399 41 18-20 149, 82 6, 7 0.5 0 0.991 7.728 71 Hanging Wall 0-6, near the Santa 105, 0 15, 10 0.5 0.1 0.983 10.533 102 Susana fault 0-6, southwestof 109, 51 31, -9 0.5 0.1 0.986 9.542 68 the Santa Susana fault 6-12, above 270, -4 0, -6 0.5 -0.1 0.981 11.101 117 primary rupture 0-4, updipof main 106, -40 20, 5 0.5 0.1 0.993 6.583 38 rupture plane 4-6, updipof main 112, 75 20, 0 0.5 0 0.992 7.163 21 rupture plane

See text for completedescriptions of kinematicvariables and misfit values *Orientationsof dl and d3 given as trend, followedby plunge. Positivevalues of plunge are below the horizontal; negativevalues are abovethe horizontal. is no horizontal extension or contraction parallel to d2 (i.e., (strike=122ø, dip=40ø SW). In essence,this analysisfinds the subparallelto the strike of the fault). The few exceptionsare orientations on the blind Northridge thrust of the maximum from the Sylmar segment(depth intervals 18-20 km and 14-16 resolved incremental shear for the aftershock deformation. km; Table 1) and the Placerita segment (depth interval 6-12 The precision of this orientation is shown on Figure 6 and km; Table 2). Inversion of data from these domains showsthat discussedin the appendix. D = 0.6, which implies that d2 is somewhatcloser in value to Our calculatedmotions of the hanging wall block (Figure 6) dl (maximum lengthening)than to d3 (maximum shortening), indicate up-to-the-northeastshearing on the blind Northridge and thus the deformation within the primary rupture zone thrust, with local components of obliquity. The most probably accommodatesa small component of subhorizontal distinctive departurefrom pure dip-slip motion in our model NW-SE extensionparallel to the strikeof the fault. (Figure 6) is the oppositesense of obliquity on opposite sides Models for the distribution of coseismic slip directions on of the Chatsworthlateral ramp in the depth range of 10-14 km. the Northridge fault have been made by Wald et al. [1996] Specifically, our model predicts left-reverse slip to the using a combinedanalysis of geodetic,teleseismic, and strong southeastof the Chatsworth structureand right-reverse slip to motion data and by Hudnut et al. [1966] and Shen et al. [1966] the northwest. Hudnutet al. [1996] derived a similar upward using inversion of coseismic GPS data. To compare these diverging pattern of mainshock slip on the primary rupture models with our results, we use the characteristics of the plane. Shen et al. [1996] also modeled obliquity on the micropolardeformation (i.e., d i, D, and W) that we found by primary rupture plane, but their best fit model suggests inverting aftershocks from domains along the mainshock predominantly left-reverse displacement on both the Placerita rupture plane, and we calculate the direction of the maximum and Sylmar segmentsduring the mainshock. In contrast, the resolved incremental shear along the best fit rupture plane model of Wald et al. [1996] implies upwardconverging senses

Table 3. Inversion Results, Newhall-Potrero Segment

Depth, dI d3 D W MeanCos Cos-1 Number km (Maximum (Maximum (MeanCos) of Data Extension)* Shortening)* 10-12, noaheast 340, 67 183, 21 0.5 0.2 0.988 8.915 82 dippingevents 12-14, noaheast 302, 73 177, 10 0.5 0.1 0.989 8.516 129 dippingevents 14-16, noaheast 330, 65 198, 17 0.5 0.1 0.991 7.791 52 dippingevents 7-14, southwest 341, 80 20, -8 0.5 0.3 0.984 10.355 69 dippingevents 0-5 (all) 294, 21 17, -18 0.5 0 0.983 10.724 46

See text for completedescriptions of kinematicvariables and misfit values *Orientationsof d• and d3 givenas trend,followed by plunge. Positivevalues of plungeare below the horizontal; negativevalues are above the horizontal. 24,598 UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION

GillibrandCanyon Chatsworth relative vorticity vector is parallel to the d2 axis, this requires Lateral Ramp Lateral Ramp choosing a right-handedcoordinate system wherethe d2 axis also is positive in a subhorizontal, northwest direction (Tables 1-3). With this convention, positive or negative SegmentProtrero Segment Segment 5 km valuesof W in Tables 1-3 imply that the clockwise rotation rate of rigid blocks in the primary blind thrust zone is higher HangingWall • HangingDeformationWall Deformation or lower, respectively, than the averageclockwise rotation rate of material lines in the large-scale top-northeast simple shearing acrossthe zone. The inversion results indicate a range in values of the relative vorticity parameterW between-0.2 and 0.3 (Tables 1- 3). Zero values of W imply no differencebetween the large- lO km scale and small-scale vorticities. Becausethe geometries of the blocks and the seismogenic faults that form their i / boundariesare not visible, however, it is not possible to determine which class of kinematic models is appropriate to account for the nonzero values of W [see Twiss et al., 1993; / Unruh et al., 1996]. Moreover, Unruh et al. [1996] found that valuesof W with an absolute value of 0.2 or less may not be significantly different from zero, based on sensitivity 15 km analysesof inversions using aftershockdata from the 1992 Landersearthquake. If this is true for the Northridgeearthquake aftershocksas well, then only a few of the nonzerovalues of W data) are significant(i.e., 14-16 km interval, Sylmar segment;16- (insufficient• • 18 km interval, Placerita segment;southwest dipping events between 7 and 14 km, Newhall-Potrero segment), and in general, the relative vorticity along most of the primary

20 km rupture zone probably is negligible (Tables 1-3).

Figure 6. Directions of the maximum resolvedincremental shear on the best fit rupture plane of Wald et al. [1996], 7.2. Hanging Wall Deformation From Analysis of Aftershocks determined from micropolar inversion of aftershock data (Tables 1-3). The vectors shown represent the average We groupedaftershocks in the hanging wall block of the direction of slip on the fault associatedwith the aftershocks Northridgethrust fault into depth domainswithin each of the for discrete areas of the mainshock rupture plane. The variation of the rake of the maximum incremental shear three major structural segments identified by Yeats et al. associated with the precision of the inversion results is [1994]. We also identified what appearto be discreteclusters approximately+_7.5 ø and is indicatedby the fan-shapedmarks of aftershocks in the hanging wall from cross sections of on either side of the slip vector. See text for explanation of seismicity (Figures 2 and 3), and we inverted data from these the derived slip directions. See the appendix for derivation of clusters where a sufficient number of focal mechanisms were the precisionin the rake of the slip vector. available to obtain a robust solution. The inversion results (Tables 1-3; see Figures 2 and 3 for locationsof individual domains) generally show that the axis of obliquity (i.e., generally right reverse slip on the Sylmar of maximum lengthening(d i) in the hangingwall for all three segmentand left reverseslip on the Placerita segment)during structuralsegments is subhorizontal horizontal NW-SE, in the mainshock. Although different patterns of obliquity are contrastto the approximatelyvertical orientation of di along associated with the different models, we find that our results for the primaryrupture zone at depth. For both the hanging wall the aftershock deformation generally are consistent with block and the primary rupture zone, the axis of maximum reverseslip on the primary rupture zone. shorteningd 3 is horizontal and orientednortheast-southwest, To interpret the values of the relative vorticity parameterW so the change in deformation style from the primary rupture obtained from the inversion (Tables 1-3), we first adopt a zone to the hanging wall block is characterized by an convention for expressingthe sense of large-scale vorticity exchange in orientation of the d2 and dl axes. Along the associatedwith the southwest-side-upsimple shearing along Sylmar segment, the transition between vertical dl and the southwestdipping Northridge thrust. Looking northwest subverticald2 deformationoccurs at about 3 km depth (Table along the strike of the fault, the senseof shearfor southwest- 1). For the Placerita segment, the domain of subvertical d2 side-upmotion, and the correspondingvorticity viewed in this includes the upper 4 km of the crust updip of the primary direction, is clockwise. Using the right-handrule, a clockwise rupturezone and appearsto extendto the base of the hanging vorticity is representedby an axial vector that lies in the fault wall (Table 2). To the northwest, aftershocks from the plane, is normal to the directionof slip, and is positive in the Newhall-Potrero segment indicate that the transition between northwest direction. The relative vorticity W parallel to d2 subverticald 1 and d2 occursat about3-5 km depth (Table 3). (equation (2)) is proportional to the difference between the This difference in the orientationsof the principal incremental small-scale vorticity of fault-bounded blocks within the strain axes can be seen in equal-areastereograms of dl and d3 primary rupture zone and the large-scale vorticity (equation plottedfor the primary rupturezone (Figure 7), and for events (2); Twiss et al., [1993] refer to these as the microvorticity and that occurredin the hangingwall block or in the upper 4 km of the macrovorticity,respectively). Becausewe assumethat the the crustupdip of the primary rupturezone (Figure 8). UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION 24,599

Equal Area occurring within a tabular zone centered on the Northridge thrustfault. The principal contractionalstrain (d3) within this zone is subhorizontal and normal to the strike of the fault; the principal extensional strain (dl)is subvertical; and the intermediateprincipal strain (d2) is subhorizontaland parallel to strike of the fault. In contrast, aftershock deformation in the upper 3-7 km of the hanging wall block is distributed throughouta large volume of the crust and is characterizedby subhorizontalshortening (d3)directed normal to the strike of the Northridge thrust and subhorizontalextension (dl) parallel to the strike of the Northridge thrust. The intermediate principal strain (d2) in the hanging wall block is subvertical, as opposed to subhorizontal along the mainshock rupture plane. Based on values of the deformation parameter D obtained from the aftershock inversions, the shortening and lengtheningincremental strains in the hanging wall block are approximately equaland opposite in magnitude, and there is negligible vertical thinning or thickening. The different deformation styles of the mainshock rupture zone and the hanging wall are illustratedschematically in a block diagram (Figure 9). N = 16 C.I. = 2.0 sigma

Figure 7. Stereogramshowing the orientations of the principalincremental strain axesobtained from inversionsof Equal Area aftershocksalong the primary rupturezone. Solid dots show the locations (trend and plunge) of individual principal incremental strains in the lower hemisphere; squaresshow principalaxes that plot in the upperhemisphere (results from 16 inversionsplotted; all datataken from Tables 1-3). The Kamb contours of the distribution of the data differentiate the maximumlengthening principal strains (dl, associatedwith the stippledcontours) from the maximumshortening principal strains (d3, associatedwith the striped contours) (contour interval is 2 sigma). Note that for the primary rupture zone, the Kamb contoursshow that dl generally is steeply plunging to subvertical and that d3 generally is subhorizontal and oriented northeast-southwest.

In general,the valueof the deformationrate parameterD for domainsin the hanging wall is 0.5 (Tables 1-3), which for a constant volume deformation, characterizes a plane incrementalstrain suchthat dl (maximumextension) and d3 (maximumshortening) are equal and oppositein value and that there is no length change in the vertical direction (i.e., parallel to d2). An exception to this general result is the N = 7 C.I. = 2.0 sigma hanging wall deformationin the upper6 km of the Placerita segment,southwest of the SantaSusana fault (Table 2). The Figure 8. Stereogram showing the orientations of the inversion resultsindicate that d3 (maximum shortening) is principal incrementalstrain axes obtained from inversions of subhorizontal and directed NE, but that d• (maximum aftershocks in the upper 6 km of the hanging wall block. Solid dots show the locations (trend and plunge) of individual lengthening)is plungingapproximately 51 ø to the SE (Table principal incrementalstrains in the lower hemisphere;squares 2). The moderateplunge of dl for this domain can be show principal axes that plot in the upper hemisphere (results interpretedas reflecting componentsof lengthening both in from seveninversions plotted; all data taken from Tables 1-3). the NW-SE direction and in the vertical direction. Assuming Kamb contours of the distribution of the data differentiate the constant volume, the aftershocks in this domain accommodate maximum lengthening principal strains (d•, associatedwith a componentof vertical thickening of the hanging wall, in the stippledcontours) from the maximum shorteningprincipal addition to northwest-southeast lengthening and northeast- strains (d3, associated with the striped contours) (contour southwest shortening. interval is 2 sigma). The orientations of d3 form a distinct, subhorizontal maximum oriented northeast-southwest, similar to the inversionsof aftershocksfrom the primary rupture zone. 8. Kinematic Model and Interpretation Unlike the primary rupture zone data (Figure 7), however, the directions of maximum lengthening (dl) from inversions of Our inversions indicate that aftershock deformation hanging wall aftershocks form subhorizontal to moderately associatedwith the mainshockrupture is consistentwith slow, plunging maxima, indicating significant componentsof fault- progressive r.everse slip, with most of the aftershocks parallel extension. 24,600 UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION

Figure 9. Schematicblock diagramillustrating geometry of the primaryrupture zone and the kinematicsof uplift and deformationof the hanging wall accommodatedby the Northridgeearthquake aftershocks. Star shows approximate locationof mainshock. Darker shadedarea within the Placeritaand Sylmar segmentsshows area of ruptureplane where most of the coseismicstrain releaseoccurred (from data of Wald et al. [1996]). The variations in geometry of the primaryrupture zone in the diagramare inferredprimarily from cross-sectionsof seismicityand structurecontours of the base of the aftershockzone [Haukssonet al., 1995]. Arrows on the primary rupture zone schematically show the variationsin the averageslip directionas indicatedby the forward modelingof the inversionresults (Figure 6 presentsa detailed model of aftershockslip directions). In particular,note that the aftershockslip directions for the Placerita and Sylmar segmentsdiverge across the Chatsworthlateral ramp boundary. The approximately pure shear, plane strain deformationof the hangingwall block is indicatedby the arrowsshowing the horizontal shortening and lengthening directionsand schematicallyby the upwardflaring of the hanging wall block parallel to the strike of the Northridge thrust,which indicatesa relative increasein fault-parallellengthening with decreasingdepth.

These results generally are consistent with geodetic The mainshock rupture and the associated deformation, observations of postseismic deformation in the epicentral including the fault-parallel lengthening measuredby GPS regionof the Northridgeearthquake. Based on analysisof GPS geodesy,can be successfullymodeled [e.g., Hudnut et al., data, Donnellan and Lyzenga [1996] reportedthat reverseslip 1996] as an elastic dislocation on the blind Northridge thrust on the Northridge thrust fault continuedfor several months fault, which is reflected in the upper crust as an elastic following the mainshock. They further noted geodetic horizontal shorteningnormal to the fault strike and an elastic evidencefor postmainshockdeformation of the upper5 km of lengthening parallel to strike (Figure 5). The distributed the crust,which approximatelycoincides with the depth range aftershock deformation, however, can, at a sufficiently large of most of the aftershocks in the hanging wall block. scale, be viewed as a quasi-continuous"seismic flow" [see According to Donnellan and Lyzenga [1996], the moment Kostrov, 1974], or a quasi-ductiledeformation. Our inversions releaseequivalent of the combinedafterslip on the Northridge of the aftershock focal mechanisms together with the thrust and postmainshockdeformation of the upper crust is postmainshockgeodetic analysis of Donnellan and Lyzenga approximatelyM6.2, which representsapproximately 20% of [1996] show that thrusting motion continued along the the total moment release associated with the M w 6.7 mainshock rupture zone and that the deformation in the mainshock. hanging wall block was characterizedby an inhomogeneous UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION 24,601

pure shear(a plane strain) with shortening normal to the fault Sucha qualitative analysis cannot restrict the rheology of strike and lengtheningparallel to strike. Thus the deformation the crust precisely. Nevertheless, a few conclusions are accommodated by the mainshock continued during the possible. A simpleelastic crustal rheology of the type usedto aftershock sequenceas a quasi-ductileflow with essentially model the surface deformation associated with the mainshock unchangedgeometry. is not sufficient to explain the occurrence,distribution, and This flow can be explained either as a quasi-ductile style of the observedaftershock deformation, either along the continuation of the coseismic deformation or as a relaxation mainshockrupture plane or in the hanging wall block of the phenomenon, as further discussedbelow. The slow reverse Northridge thrust fault. The upper crust must be a brittle- afterslipon the Northridge thrust following the mainshockis elastic material that can deformby quasi-ductileflow; it must not consistent with highly reoriented stressesnear a fault on be a strain-weakening material because the deformation which the stressdrop is assumedto be nearly complete, nor is initiated by the main shock continues after the associated it consistent with elastic rebound following dynamic stress drop; and it must have a fading memory becauseits overshootof fault displacementduring the mainshockrupture. strength must recover with time following the deformation. We proposetwo hypothesesto explain the afterslip along the Finally, a simple relaxation processof converting transient main rupture zone (see Scholz [1990, section5.2.2] for a brief elastic strain into permanent ductile deformation at constant review): total strain is inconsistent with the geodetic evidence of 1. The upper crust, including the depth range of about 10- continuing deformation. There must be greater complexity 20 km wheremost of the coseismicstrain wasreleased during than is implied by such a relaxation model in either the the Northridge mainshock,behaves as a brittle-elastic material constanttotal-strain boundaryconditions or in the theology that can undergo quasi-ductile flow. Both the strain of the material. accumulationprior to the earthquake,as well as the coseismic deformation of the hanging wall block above the blind fault, 9. Implications for Kinematic Models of Basement- can be modeled by adoptingan elastic constitutiverelation for Involved Folding the upper crust. The afterslip and aftershockactivity along the mainshockrupture zone couldrepresent a quasi-ductilerelease The coseismicand postseismicdeformation of the hanging of part of the remaining elastic strain that was not released wall observed during the Northridge earthquake depart during the mainshock. This model implies a strain weakening significantly from the assumptionsof kinematic models for of the material in the fault zone becausethe continuedquasi- basement-involved folding by Narr and Suppe [1994]. These ductile deformation occursin a stress field whose magnitude modelsassume conservation of area in a plane containing the must have decreaseddue to release of strain during the main slip direction and the normal to the thrust fault, and they shock. predict that the horizontal component of motion of material 2. The uppercrust could have layered mechanical properties points in the hanging wall is parallel to the horizontal characterizedby a brittle-elastic layer overlying a ductile- component of slip on the fault at depth. This assumption is elastic layer. The boundary between these two layers could inconsistent with the fault-parallel extension of the hanging coincidewith the local brittle-ductiletransition in this part of wall during the Northridge earthquake. The kinematic models the western Transverse Ranges, with earthquakes and further assumethat deformation of the hanging wall is limited aftershocks primarily confined to the upper layer. In this to rigid body translation, except where material points pass model, assuming constant velocity boundary conditions, the through axial surfaces,which are kink band boundariesthat are progressivelyincreasing displacement on the boundarywould fixed to changesin dip of the fault at depth. As materialpasses have built up elastic stressesin both crustal layers prior to an through these surfaces,it is deformedby localized shearing. earthquake. Presumably the stress would be higher in the Our results clearly show, however, that the pure shear brittle-elastic layer than in the ductile-elastic layer, because deformationis distributedthroughout the hanging wall and is ductileflow in the latter would progressively relax part of the not limited to axial surfacesof the northeast vergent fault stress. The loss of cohesion in the upper brittle-elastic layer propagation fold identified by Davis and Namson [1994] and associatedwith a large earthquakewould have temporarily and Huftile and Yeats [1996] above the blind Northridgethrust. locally decreasedthe stress in the upper layer and thereby As earthquakes occur on different segments of the increasedthe stressin the lower layer. This increaseof stress Northridge thrust fault, it is possible that the fault-parallel in the lower layer would drive an increase in the rate of ductile extensionsmay averageout to zero, and thus the assumptions flow; this in turn would relax the stresses concentrated there of the Narr and Suppe [1994] model may be appropriate for and drive continued reverse slip in the overlying weakened evaluatingfinite deformation. In fact, Narr and Suppe [ 1994] mainshock rupture zone, producing aftershock activity. successfullymodeled the developmentof several basement- Presumably,the mainshockrupture zone and the upper crustal involved anticlines in the southern Rocky Mountains using layer eventually recover all or part of the original elastic the assumptionsdescribed above. If the hanging wall and strength, possibly through a processof static hardening, and primary rupture zone of the Northridge thrust fault were the processof elastic strain accumulationaveraged over both exposed by erosion similar to the basement-involved layers begins again. structuresin the southern Rocky Mountains, however, brittle Above the blind fault tip, the standardCoulomb failure shear sense indicators on small faults in the hanging wall criterion suggeststhat the shallow crust must be relatively would retaina recordof the averagehorizontal pure shearstrain weak and thus would support a relatively small stress before accommodated by the postmainshock deformation. the mainshock event. After the mainshock event, the Presumably,therefore, some recordof the permanent fault- deformationin the shallow crust above the tip of the blind parallel lengtheningwould be retainedin the relatively small thrust stresswould increase and initiate the process of quasi- brittle faults in the hangingwall. This out-of-planemotion or ductile flow. transferof materialmust be accountedfor to developrigorous, 24,602 UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION

area-balancedcross sections, especially if large earthquakes the average direction of postseismic slip on the fault occur repeatedlyon, or are limited to, discreterupture segments associatedwith the aftershockactivity. At present,we cannot in the blind thrust system. evaluatethe statistical uncertainty in the rake of this slip The example of the Northridge earthquake indicates that vector; however, we can evaluate the sensitivity of this vector more general kinematic models for fault-related folding are to the precisionof our inversions. In the following example, needed to account for the coseismic elastic deformation of the we test the sensitivityof modeled aftershock slip direction on hanging wall, and the accumulation of some permanent the Northridgethrust (Figure 6) by systematicallyvarying the distributedbrittle deformationby aftershock activity. For model parametersused in the inversions. example, the trishear model of Erslev [1991] posits that As discussed in the text, the orientations of the best fit localized shearing along the main thrust at depth may be principal strain rate axes are bracketedwithin grid increments distributedupdip in a triangularshear zone. Dependingon the of 5ø, and the best fit values of the parametersD and W are geometry of the shear zone, conservation of volume may bracketedto within 0.1 grid increments. This is equivalentto requireout-of-plane or fault-parallel transfer of material. In a precision of + 2.5ø for the principal strain rate axes and a particular, if the triangular shear zone is primarily containedin precision of + 0.05 for the values of D and W. For the the hanging wall block, mass conservation requires out-of- following analysis,we used the inversion results for the 12-14 plane transfer of material away from the shearzone [see Erslev, km depthrange of the Sylmar segmentof the Northridge thrust 1991, Figure 2a). Thus the trishearmodel potentiallyprovides as a test case. Using our grid-search algorithm PTGRDSRCH, a kinematic explanation for the fault-parallel extension we generateda typical suite of grid models by varying the observedduring the Northridge earthquakethat is consistent orientation of the best fit principal axes by 2.5ø grid with the ductile-elastic model discussed above. increments. Given the precision of our inversion results, a model with a lower misfit value could be found among this suite of models. We then evaluated the direction of resolved 10. Conclusions incremental shear on the best fit fault plane of Wald et al. [1996]; (strike of 122ø , dip of 40øSW) for each of these Based on inversion of aftershock data, deformation that models, holding the values of D and W constant. The results occurred at depthsbelow about 6 km and is associated with the indicate that for a variation of +2.5 ø in the orientation of the primary rupture zone is consistent with slow, progressive, principal strain rate axes, the rake of the maximum postmainshockreverse slip in a southwestdipping thrust fault incrementalshear vector on the Northridgethrust varies by +5 ø zone. In contrast,inversion of aftershocksfrom the upper 5-7 from the rake of the vector for our best fit model. Similarly, km of the hanging wall block directly above the blind thrust we evaluatedthe variationin the rake as a function of varying fault showsthat the seismogenicdeformation can be described D by 0.05 grid increments, holding the orientation of the as an approximately horizontal inhomogeneous pure shear principal strain rate axes and the value of W constant. For a deformation, characterizedby horizontal NE-SW shortening and horizontal NW-SE extension. variation of +0.05 in the value of D, the rake varies by +2 ø. For W, we use _+0.1for the sensitivitytest insteadof +0.05 to Deformation in both regions includes a component of evaluatethe maximumvariation in the rake becauseprevious permanent quasi-ductile flow of a brittle-elastic material. sensitivitytests by Unruh et al. [1996] show that the misfit is Along the fault zone at least, this material must be a strain- less sensitive to variations in W than in d i or D. For a weakeningmaterial with fading memory. A two-layer model of variationof +0.1 in the value of W, the rake varies by +0.5 ø. a brittle-elastic layer overlying a ductile-elastic layer could By conservatively combining the variation in the rake accountfor the observeddeformation, but a simple relaxation associated with the precision of all the individual model processby which transientelastic deformationis convertedby parameters,the minimum precision of the rake on the fault quasi-ductileflow to permanent deformation at constant total plane is +7.5 ø. strain cannot account for the observed progressive accumulation of strain after the main shock event. Acknowledgments. We are indebted to Richard We propose that slip on the blind thrust during the Allmendinger for the use of his program Stereonet 4.9.5, mainshock transferred an inhomogeneous, horizontal pure which we used to plot and contour our orientational data. shear strain to the hanging wall block and that part of this Commentson an earlier draft of this paper by E. Erslev, G. deformationwas accommodatedby slow, quasi-ductile"seismic Huftile, and an anonymous reviewer led to significant flow" which is characterizedby distributed brittle faulting. improvementsin the presentationof the data and analyses. The patternsof mainshockand aftershockdeformation indicate The present paper was improved by critical reviews from K. that kinematic models for incremental fault-relatedfolding in Hudnut, W. Prescott, and J. Gomberg. Support for this crystalline basement terranes must be general enough to research was provided by the National Science Foundation account for the observed three-dimensional deformation (i.e., through grants EAR-9416318 and EAR-9526105 to J.R.U. and fault-parallel extension)of the hanging wall block in order to EAR-9219633 to R.J.T. be useful for predicting patterns of coseismic surface deformation. References

Appendix: Sensitivity of the Derived Slip Davis, T. L., and J. S. Namson, A balanced cross-sectionof the Directions to the Precision of the Inversion Results 1994 Northridge earthquake,southern California, Nature, 372, 167-169, 1994. As discussedin the text, we usethe parametersof the bestfit Donnellan, A., and G. A. Lyzenga, Northridgepostseismic model obtained from the aftershock inversions to evaluate the deformation:inferences from continuousand campaign direction of the maximum incremental shear on the blind GPS observations, Eos Trans. AGU, 77(46), Fall Meet. Northridgethrust (Figure 6). We interpret this vector to show Suppl., F147, 1996. UNRUH ET AL.: KINEMATICS OF POSTSEISMICRELAXATION 24,603

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