The enigma of the Arthur's Pass, New Zealand, earthquake

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. B7, PAGES 16,139-16,150, JULY 10, 2000 The enigma f the Arthur's Pass, New Zealand, earthquake 2. The aftershck distributin and its relatin t reginal and induced stress fields Russell Rbinsn and Peter J. McGinty Institute f Gelgical and Nuclear Sciences, Lwer Hurt, New Zealand Abstract. The aftershck distributin f the 1994 Arthur's Pass earthquake, Mw6.7, is unusual fr a reverse faulting event in that it extends 12 km NNW and 30 km SSE f the actual fault plane, which strikes NE-SW. We have used several methds t infer the reginal stress field in the regin, including gedetic results, earthquake mechanisms, and inversin f P wave plarity data fr the stress tensr rientatin. The inversin methd is new and des nt require the fcal mechanisms f the events used. It als incrprates the Culmb failure criterin. All results pint t a stress field favring strike-slip faulting, nt thrusting, with near-hrizntal cvl and cv3 principal axe striking at 298 ø and 28 ø. Using dislcatin thery, we calculate the stress induced by the Arthur's Pass earthquake and its largest aftershck (a strike-slip event) and add this t the reginal field. There is a fair crrespndence between the hypcenters f aftershcks away frm the mainshck fault plane and regins f high induced Culmb Failure Stress (CFS) n ptimally riented fault planes. Hwever, there are regins f high induced CFS that are devid f aftershcks. It appears that earthquake slip in this regin f blique (19 ø ) plate cnvergence is, as bserved elsewhere, partitined int cmpnents parallel and perpendicular t the plate margin. Mst f the slip is parallel, as ccurs n the nearby dextral Alpine fault, the bundary between the Pacific and Australian plates. Hwever, ccasinal reverse events, such as the Arthur's Pass earthquake, accunt fr at least sme f the perpendicular cmpnent f slip and the uplift that prduced the Suthern Alps. 1. Intrductin prcedure, aftershck statistics, and implicatins fr seismic hazard estimatin in New Zealand are discussed in a The Arthur's Pass earthquake, Mw6.7, June 18, 1994, cmpanin paper [Abercrmbiet al, this issue]. Our apprach ccurred in the Suthern Alps, Suth Island, New Zealand, a t understanding the Arthur's Pass aftershck distributin is regin f blique cntinental cllisin (Figure 1). Althugh similar t that in several ther studies [e.g., King et al., 1994] aftershcks range in depth frm-1 t 10 km, there was n (als see the review by Harris, [1998] and accmpanying surface rupture. The aftershcks have an unusual spatial papers). The hypthesis is that aftershck smeway ff the distributin with respect t the mainshck fault plane and fault plane will preferentially ccur in regins where the stresses mechanism. The mainshck was primarily a reverse event (rake induced by the mainshck have increased the Culmb failure = 112 ø) centered at-6 km depth n a fault striking NE-SW stress (CFS) n small faults ptimally riented in the cmbined (221 ø) and dipping t the NW (47ø). Hwever, the numerus reginal and induced stress field. The reasning is that in aftershcks (largest ML6.0) define an elngate regin extending tectnically active regins there are numerus small faults with --12 km NNW and 30 km SSE f the mainshck epicenter a wide range f rientatins. Given sme change in stress due t (Figure 2), well away frm the presumed mainshck fault plane slip in the mainshck, there will usually exist sme faults which is nt well defined by the aftershcks. This is in cntrast riented such that the maximum ptential CFS is realized, r t the case fr sme ther reverse events f similar size, such as nearly s, and they will fail in preference t ther less favrably the Nrthridge, Califrnia, event f 1994, Mw6.7. Fr the riented faults. Aftershcks n the mainshck fault plane will Nrthridg event mst aftershcks fall within a few kilmeters mstly have mechanisms similar t the mainshck and arise f the fault plane, althugh there is significant diffuse activity in because f variatins in the amunt f slip during the the hanging wall [Mri et al., 1995]. It is the purpse f this mainshck. A clear example f this situatin is that f the nstudy t explain why the Arthur's Pass aftershcks are fault and ff-fault aftershcks f the 1984 Mrgan Hill distributed as they are. The answer prbably has significant earthquake in Califrnia [Oppenheimer et al., 1988]. implicatins fr the lcal tectnics. S, if we wish t explain the distributin f ff-fault Details f hw the mainshck mechanism was determined aftershcks fr the Arthur's Pass earthquake, we first need t and hw it relates t knwn faults, mdeling f Glbal knw the rientatins f the reginal stress principal axes. The Psitining System (GPS gedetic data, aftershck lcatin data frm backgrund seismicity in the regin are nt sufficient t infer the reginal stress via inversin f fcal mechanisms, s Cpyright 2000 by the American Gephysical Unin. we use instead gedetic results and mechanisms r P wave plarities fr ff-fault aftershcks t infer the reginal stress Paper number 2000JB tensr. The latter assumes that the stress perturbatins due t the /00/2000JB mainshck are small and variable in rientatin thrughuthe 16,139

2 16,14 ROBINSON AND MCGINTY: THE ARTHUR'S PASS EARTHQUAKE, 2 Figure 1. The reginal setting f the Arthur's Pass earthquake in the central Suthern Alps f the Suth Island, New Zealand. Backgrund seismicity, magnitude , in the decade preceding the Arthur's Pass event is shwn by circles. Als shwn are the psitins and mechanisms (upper hemisphere) f the Arthur's Pass earthquake and its largest aftershck and f the Cass earthquake (1.5 years later). regin f the ff-fault aftershcks. Once the reginal stress tensr is defined, we then add the induced stress changes due t the Arthur's Pass mainshck, calculated using dislcatin thery, and cmpare the spatial distributin f the aftershcks t the regins experiencing increased CFS n ptimally riented faults. We als calculate the CFS induced by the Arthur's Pass event n the fault plane f the Mw Cass earthquake [Gledhill et al., 2000], 30 km t the west, t see if the Arthur's Pass event culd have acted as a trigger. 2. Reginal Stress Tensr 2.1 Gedetic Results Pearsn et al. [1995] reprt n analyses f gedetic results alng a 60-km prfile acrss the central Suth Island that passes thrugh the Arthur's Pass regin. Their data cnsist f GPS bservatins made in 1992 and first-rder triangulatin/trilateratin data frm abut The azimuth (degrees east f nrth) f the axis f maximum hrizntal cntractin in the western and eastern halves f the prfile are 107 ø +/- 6 ø and 116 ø +/- 9 ø. The Arthur's Pass earthquake lies near the bundary, s we take ø as an apprpriate value. This is very clse t the value (110 ø) they btain frm a 25 km t the NW f the Arthur's Pass epicenter, is the dminant active fault in the Suth Island, with cumulative strike-slip ffsets f--480 km and paleseismic evidence f large earthquakes within the last 500 years [Berryman et al., 1992; Bull and Brandn, 1998], the last being in circa 1717 (K. R. Berryman, persnal cmmunicatin., 1998). If we assume, as is cmmnly dne, that ne principal axis f stress is vertical and the ther tw are hrizntal, and if we take the azimuth f the mst cmpressive principal axis f stress (cyl) t be the same as that fr the axis f maximum hrizntal cntractin (111.5ø), then the stress tensr rientatin is still ambiguus: the vertical principal axis culd be either 02 r 03. Mst f the active faults in the regin, including the Alpine fault, are dminantly strike slip, suggesting 02 is vertical. On the ther hand, the presence f the Suthern Alps suggests uplift by reverse faulting, implying that 03 is vertical as wuld be apprpriate fr a reverse event such as the Arthur's Pass earthquake. 2.2 Aftershck Fcal Mechanisms All aftershck data used in this study are frm the relcatin f the Arthur's Pass aftershcks using a three-dimensinal (3-D) velcity mdel, as described by Abercrmbie et al. [this issue]. dislcatin mdel in which the Nuvel-lA plate cnvergence; Because the permanent New Zealand Natinal Seismgraph velcity is reslved nt a 50 ø dipping Alpine fault lcked t a Netwrk is sparse, we nly cnsider events during the perid f depth f 12 km and freely slipping belw that. The Alpine fault, best cverage with temprary prtable statins, June 22 thrugh

3 ROBINSON AND MCGINTY: TI ARTHUR'S PASS EARTHQUAKE, 2 16,141 ( õ r 0 O0 ß 17114øE 171'.1 øe Figure 2. Map view f aftershck lcatins fr the Arthur's Pass earthquake, quality A and B slutins. The rectangle represents the surface prjectin f the mainshck fault plane. Depths f these aftershcks range frm ~2 t 9 km. July 2, Fcal mechanisms f all such events with (fr T). Fr example, a pint in Figure 5a with azimuth 100 ø and magnitudes 3.1 r mre and lcatin quality A r B (78 events) dip 10 ø wuld be cnverted t the equivalent pint with azimuth were btained (Figure 3). The quality criteria are mre fully 280 ø and dip -10 ø. The mean directin f P then crrespnds t explained by Abercrmbiet al. but quality A and B events an azimuth (clckwise frm nrth) f ø and a dip f 7.8 ø. shuld have hypcenter errrs f less than -1 km. The methd The mean directin fr T crrespnds t an azimuth f ø used t btain mechanisms makes use f P wave plarities and and a dip f 5.6 ø. The standardeviatins fr P and T are 24.0 ø the amplitude ratis f lw-pass-filtered P and S envelpes as and 23.1 ø. Alternatively, we can find the lines arund which the described by Rbinsn and Webb [1996] and Reyners et al. mments f inertia f the set f P r T axes are minimum: this [1997], making use f the riginal idea f Schwartz [1995]. The requires n "flipping" as befre. These lines have azimuths and use f amplitude ratis can ften reslve ambiguities in dips f ø and 7.4 ø fr P and 201.8ø and 6.2 ø fr T. mechanisms based n plarities when the number f The average P axis azimuth is very clse t that f the l bservatins is small, as is the case here (the average number f stress axis inferred frm gedetic results. Althugh the P, B, plarity bservatins fr the events used is 13.3). An example is and T axes f an individual fcal mechanism are nt equivalent shwn in Figure 4. All P wave plarities were rechecked, and a t the stress principal axes, when averaged ver many diverse few new readings were added. events, they shuld be similar. This suggests that a reginal Cnsidering the 57 events mre than 2 km away frm the stress tensr with a hrizntal l axis, azimuth 115 ø, a inferred fault plane, there are a wide variety f aftershck hrizntal 3 axis, azimuth 25 ø, and a vertical 2 axis wuld be mechanisms (Figure 5). Hwever, there are regularities: the? apprpriate (all must be rthgnal). axes tend t be subhrizntal and striking ESE r WNW, and the T axes tend t be subhrizntal and striking NNE r SSW. 2.3 Inversin f Plarity Data This pattern implies predminantly strike-slip faulting. We can There are several methds fr inverting fcal mechanisms fr be mre quantitative if we cnsider the P and T axes as vectrs the stress tensr [e.g., Gephart and Frsyth, 1984; Michael, rather than lines s that spherical means can be calculated 1987a; Rivera and Cisternas, 1990; Hriuchi et al., 1995]. Fr [Davis, 1986]. T d this, we chse as the vectr that endpint several reasns we have used ur wn inversin methd, f the axis which has an azimuth clsest t 300 ø (fr P) and 30 ø described belw, which uses first mtins directly rather than

4 16,142 ROBINSON AND MCGINTY: THE ARTHUR'S PASS EARTHQUAKE, 2 i 110 km 171'.2'E 17.4' 17.6' 17.8' Figure 3. Fcal mechanisms (upper hemisphere) fr the Arthur's Pass aftershcks. All events, quality A r B, f magnitude 3.1 r mre during the perid f gd cverage with prtable seismgraphs (June 22 thrugh July 2, 1994) are included. The secnd reasn is that we wuld prefer a methd that makes use f the numerus smaller aftershcks (which we will in sectin 3 cmpare t the induced stresses) rather than the mre limited set f larger aftershcks fr which we have fcal mechanisms. The third reasn is that the step f ging frm plarity data t fcal mechanisms must intrduce nise int the data since mechanisms are rarely very tightly cnstrained and s include an interpretatin f the data. Finally, the estimatin f cnfidence limits in mst existing methds is via the resampling technique [Michael, 1987b], which can be very time cnsuming. Fr the methd f Hriuchi et al. [1995] we estimate mnths f cmputer time fr ur data set and 95% cnfidence limits; see the wrk f Zha et al. [1997]. Other methds require significantly less, but still cnsiderable, cmputer time. Fr these reasns we have develped ur wn inversin methd, althugh we will als use the resampling technique t estimate cnfidence limits. We will cmpare ur results with thse frm the fcal mechanism inversin methd f Michael [1987b], keeping in mind the different data sets used. In ur methd we cnsider all plarity bservatins tgether, regardless f whether r nt they are sufficient t define singleevent fcal mechanisms. We search ver a range f stress axes' rientatins defined by l azimuth and dip and 3 azimuth. These parameters are sufficient define the tw planes with maximum Culmb failure stress and the directin f maximum shear stress n them, assuming a cefficient f frictin. These planes are independent f the shape f the stress ellipsid [Harmsenand and Rgers, 1986] and f the pre pressure. We assume that the aftershcks will ccur mstly n faults with rientatins clustered abut ne r ther f these ptimal planes and that slip will be in the directin f maximum shear stress. While it is prbable that the reginal stress tensr varies smewhat frm place t place and that ptimally riented faults may nt ccur everywhere, ur methd assumes that the "average" stress tensr can still be btained by cnsidering a large number f events, an assumptin supprted by the test results belw. via the intermediate step f fcal mechanisms. The first reasn Fr all events tgether, we simply cunt the number f is that nne f the abve methds invke the Culmb failure plarities fr which bservatin and predictin are the same, fr criterin, which will be the underpinning assumptin we use in each pssible stress tensr, and take as the best stress sectin 3 t (hpefully) explain the distributin f aftershcks. rientatin that which maximizes this cunt. The search Figure 4. An example f the use f P/S amplitude ratis in cnstraining a fcal mechanism when there are few P wave plarity bservatins. (left) Allwable P (crsses) and T (circles) axes fr mechanisms that satisfy all the plarity bservatins (first mtins). The ndal planes shwn are thse that are maximally distant frm the bservatins. (middle) P and T axes fr mechanisms that fit all the plarity and fit the amplitude ratis fairly well (first mtins and amplitudes). The ndal planes are thse that fit all plarity bservatins and best fit the amplitude ratis. (fight) The ndal planes frm the center plt plus the actual plarity bservatins (slid circles indicate cmpressin, and pen circles indicate dilatin)

5 ROBINSON AND MCGINTY: THeE ARTHUR'S PASS EARTHQUAKE, 2 16,143 q- q- q- q Figure 5. (a) P axes fr the mechanisms in Figure 3, if the event is mre than 2 km frm the mainshck fault plane. (b) Same as Figure 5a but fr T axes. Slid circles are the P and T axes f the ptimal mechanisms as determined frm the stress inversin methd. prcedure is dne in tw steps: the first with a carse reslutin Mrgan Hill, Califrnia, earthquake. It may seem that a value f (10 ø) and the secnd with a finer reslutin (2 ø) centered arund 0.75 is high, but recall that this is the dry cefficient: a lw the result f the first step and with a maximum deviatin in effective cefficient due t pre pressure is nt a factr in the the l and 3 azimuths and dips f +/-20 ø. Errr estimates inversin. It may be that fr well-develped majr faults, like (95% cnfidence limits) fr ur inversin technique are the San Andreas fault in Califrnia, the cefficient f frictin btained by the resampling methd. We find that fr a data set wuld be lwer, but we feel that 0.75 is apprpriate fr the f 1000 r mre plarities, 500 resamples are sufficient fr the Arthur's Pass mainshck and aftershcks. In any case, the tests cnfidence limits t be stable t within 2 ø (see belw). This belw shw that mderate variatins in the cefficient d nt number f resamples cnsumes abut -3 hurs f cmputer greatly change the inversin results. time fr 1000 bservatins. It might seem that ur inversin methd is little mre than As mentined abve, it is necessary t assume a cefficient the ld practice f "cmpsite mechanisms," but it differs in f frictin (Ix) which defines the angle between the principal that we are slving fr the stress axes (nt strain), that the cmpressive stress (51 and the tw planes with maximum CFS. Culmb failure criterin is incrprated, and that the tw fault Hwever, Ix cannt be included as a parameter in the inversin, planes are nnrthgnal. If Ix were taken as 0.0, then the because as Ix becmes large, the cmpressin (r dilatin) methds wuld be essentially the same, but that seems quadrants f the tw pssible fcal mechanisms have less and unreasnable. less area in cmmn (i.e., it becmes mre likely that if a The ability f ur methd t retrieve the reginal stress plarity cannt be reprduced by ne fcal plane, then it will be tensr has been tested in several ways with sets f artificial data. reprduced by the ther). S, if Ix is included the inversin, We set the "real" reginal (51 azimuth and dip t 116 ø and 10ø; then large values are unreasnably favred. In all ur wrk we the 3 azimuth and dip were 206 ø and 0 ø. Given these, the tw have taken Ix as 0.75, midway between the value f 0.7 in the ptimal fault planes and ra!:es are determined fr a cefficient Kntinentales Tiefbhrprgramm der Bundesrepublik f frictin f Fr realism, all sets f test data make use f Deutschland (KTB) ultradeep brehle [Brudy et al., 1997] and real Arthur's Pass hypcenters, statin lcatins, and which the value f 0.8 fund frm induced seismicity studies in statin recrded a plarity fr which event. There were 460 Clrad [Raleigh et al., 1972]. Oppenheimer et al. [1988] als events and 4012 plarities. Fr all tests the fault plane fr a used a value f 0.75 t explain the aftershck distributin f the given event was ne f the tw ptimal planes, chsen Table 1. Tests f the Stress Tensr Inversin Methd l Azimuth, deg l Dip, deg 03 Azimuth, deg 03 Dip, deg Percent Crrect Real Nise gee / / / / Nisy / / / / Nisy, g wrng / / / / Nisy, variable / / / / Errrs (95% cnfidence limits) are based n 500 resamples f the 4012 bservatins.

6 16,144 ROBINSON AND MCGINTY: THE ARTHUR'S PASS EARTHQUAKE, 2 Figure 6. (a) P axes f the 4012 earthquakes used t test ur stress inversin methd. (b) Same as Figure 6a but fr T axes. randmly, and the expected plarities were calculated frm that. The test was then t see if the inversin methd culd find the crrect c l and c 3 rientatins fr this nise-free data. The result (Table 1) was that it culd, with n errr. All resamples prduced the same "best" c l and c 3 axes. The secnd test was t add three types f nise: (1) fault planes deviate frm the ptimal (deviatins in strike, dip, and rake chsen randmly frm a Gaussian distributin with zer mean and 15 ø standard deviatin); (2) events culd be mislcated, resulting in incrrect azimuths and take-ff angles (latitude and lngitude errrs chsen randmly frm a Gaussian distributin with standard deviatin 0.5 km; similarly fr depth but with a standard deviatin f 1.0 km); and (3) 5% f the plarities were reversed. The distributin f event mechanism P and T axes fr this artificial data (Figure 6) is similar t that fr the 57 real fcal mechanisms (events mre than 2 km frm the mainshck fault plane), except that the few real axes with dips tending tward vertical are nt reprduced. The retrieved c l and c 3 axes fr this nisy artificial data (Table 1) were quite clse t the "real" c l and c 3 axes. The best stress tensr explains 90.6% f the plarities; the wrst scre fr any stress tensr is 48.4% crrect plarities. The next test was t assume an incrrect cefficient f frictin (0.60 rather than 0.75) in the inversin f the nisy data. Again (Table 1), the retrieved parameters are clse t the "real" values. The next test was t use a reginal stress that varied frm nrth t suth, the( l and c 3 azimuths rtating 20 ø clckwise frm 15 km nrth f the mainshck epicenter t 30 km suth f it. Other nise surces were intrduced as abve, except that the cefficient f frictin was crrect. The result is again quite gd ( Table 1). We have als redne the "nisy data" test fr smaller F Figure 7. Cnfidence limits (95%) fr the c l (pluses) and c 3 (circles) axes frm nisy test data. (a) Using all 4012 bservatins. (b) Using 3000 bservatins. (c) Using 2000 bservatins. (d) Using 1000 bservatins. (e) Using 500 bservatins. (f) Using 250 bservatins.

7 ROBINSON AND MCGINTY: TI ARTHUR'S PASS EARTHQUAKE, 2 16,145 Table 2. Test Results With Varying Number f Observatins Number f Observatins l Azimuth, deg cj1 Dip, deg Azimuth, deg Dip, deg / / / / / / /-8 0,20/ / / / / / / / / / / / /-65 The real values fr s 1 azimuth, 1 dip, 3 azimuth, and 3 dip are 116 ø, 110 ø, 206 ø, and 0 ø. numbers f data, taking the first 250, 500, 1000, 2000, and 3000 bservatins. The results (Figure 7 and Table 2) indicate that -500 bservatins are required fr a minimally useful result, ne that distinguishes between stress tensrs fr predminantly reverse, nrmal, r strike-slip faulting. We expect that this result depends n a fairly gd distributin in azimuth and take-ff angle. In Figure 7 the 95% cnfidence limits are indicated by pltting the l and 3 axes resulting frm the 95% best resamples (best equals the clsest t the riginal result); they are usually nt symmetric abut the riginal result. The number f resamples fr a stable (within 2 ø) 95 % cnfidence estimate is -500 fr 1000 r mre bservatins but increases fr fewer bservatins. Fr 500 bservatins the number is Fr 250 bservatins it des nt seem pssible t get a stable estimate f the cnfidence limits; thse shwn in Figure 7 are frm 1000 resamples. T apply ur inversin methd t the real data we have used P wave plarities fr aftershcks during the perid f best cverage with prtable instruments, restricting the events t quality A lcatins (see Abercrmbie et al. [this issue] fr infrmatin n quality assessment) with eight r mre plarity bservatins. We have excluded events within 2 km f the inferred mainshck fault plane. This results in 3808 bservatins frm 385 events. Because the seismgraph statins surrund and verlie the aftershck zne [Abercrmbie et al., this issue], the distributin f azimuths and take-ff angles is very gd. The results (Figure 8 and Table 3) indicate hrizntal, r nearly s, 1 and 3 axes. The best stress tensr explains 93.4% f the plarity bservatins. This rientatin f the reginal stress tensr is quite clse t that inferred abve frm gedetic and fcal mechanism data. The P and T axes fr the tw ptimal fcal mechanisms crrespnding t the best stress tensr are similar t the actual P and T axes fr the larger aftershcks (shwn in Figure 5). Fr cmparisn, we have used the methd f Michael [1987a] t invert fr the stress tensr using all 57 fcal mechanisms fr which the hypcenter is mre than 2 km frm the mainshck fault plane. The results (Table 3 and Figure 8) are in gd agreement with thse frm ur new methd: althugh the best 1 and 3 azimuths and dips are up t 16 ø different, the 95% cnfidence limits verlap. Differences in the best results culd be due t a magnitude bias (smaller versus N ' Slazi=298.0 Sldip=80.0 S3azi=28.0 S3dip=90.0 best scre = 93.4% f 3297; wrst = 41.7% cnfidence limit = 95.0% Figure 8. c l (pluses) and c 3 (circles) axes frm the inversin f 3808 plarities frm 385 events, quality A and with eight r mre plarity bservatins. The 95% cnfidence limits are indicated by the areas defined by the symbls, with the actual result being blder stars. Als shwn, by the dashed lines, are the 95% cnfidence limits fr 1 and 3 using the methd f Michael [1987b] n 57 aftershck fcal mechanisms. The "beach balls" shw the fcal mechanisms (upper hemisphere) crrespnding t the tw ptimal faults, the asterisk indicating that the upper mechanism the preferred mechanism because it has smewhat fewer plarity mismatches.

8 16,146 ROBINSON AND MCGIN Y: MRTHUR'S PASS EARTHQUAKE, 2 Table 3. Results f the Stress Inversin Azimuth, deg Dip, deg l First value is fr ur inversin methd, and secnd is fr the methd f Michael [ 1987a]. are psitive, but we retain the cmmn usage f "pressure" (cmpressin is psitive). The change in shear stress is psitive if its directin is within +/- 90 ø f the rake in an "ptimum event"; therwise, it is negative. Als, we weight it by the csine f the difference between the ptimum rake and the directin f the induced shear stress. This avids sharp psitive t negative transitins. In sme studies, (1) is replaced by tr2fs = t Tshea r + Jr- (t Tii) (3) where/.t ~ =/.t (1-,8). This assumes that & i is the same fr all i, larger aftershcks), r t the larger uncertainties fr Michael's which may be the case very near majr faults like the San methd because f the much smaller amunt f data used, r t Andreas [Rice, 1992]. Hwever, we d nt believe it is an effect f different assumptins. apprpriate fr the small faults respnsible fr mst f the Arthur's Pass aftershcks, and we retain equatin (1). Our 2.4 Magnitude f the Stresses preferred values arett = 0.75 and[ =0.5, althugh we In additin t the rientatin f the stress tensr, we als investigate the effect f thers. need t knw the magnitude f the deviatric stress, at least The mainshck mment was taken as that given by rughly. This determines hw much the stresses induced by the Abercrmbie et al. [this issue], i.e., 1.3x1019 Nm (Mw6.7). The mainshck can alter the reginal stress tensr rientatin. One average slip was calculated frm this and the fault dimensins, way t estimate this wuld be t calculate the deviatric stress which gives a stress drp f-10 MPa, 10% f the assumed required fr slip in the mainshck, given the rientatin f the reginal deviatfic stress. In ur preferred mdel we applied a fault plane. This requires estimates f the lithstatic and pre linear taper frm a maximum slip at the center t zer at the pressures as well as a cefficient f (dry) frictin. Taking edges, as this seems mre physically realistic; the real reasnable values fr these (frm a density f 2.65 x 103 kg/m, distributin unknwn. We als present results fr unifrm a hydrstatic pre pressure, and a cefficient f frictin f slip. The tapering ur preferred mdel was dne by 0.75), we get a value f 2530 MPa (25,300 bars) at 5-km depth, subdividing the fault int 20 x 20 equally sized patches. The and that seems much t high. This is because the mainshck average slip ver the fault plane is 2.85 m, as is implied by the fault plane is prly riented fr reverse slip in the reginal mment, and the maximum is 3.80 m. These are smewhat high stress field (a pint we will discuss in sectin 4). Instead we fr an event f magnitude 6.7, but we cannt reasnably take have adpted the values f deviatric stress bserved in the the fault plane any larger. The mainshck fault plane rientatin KTB ultradeep brehle, i.e., 100 MPa (1000 bars) at 5-km and sense f slip used were thse adpted by Abercrmbie et al. depth [Brudy et al., 1997]. This is clse t the theretical value [this issue], i.e., strike 221 ø, dip 47 ø (NW), and rake 112 ø. The assuming the crust is at a near-critical level f stress. It is reginal stress field used was that btained by ur inversin sufficiently high that the strike, dip, r rake f ptimally methd, as given in Table 3. Because the largest aftershck riented fault planes is rtated by nly -5 ø t 10 ø at a distance (Figure 1) was fairly large (M 6.0), situated in the suthern part f 2 km frm the Arthur's Pass fault plane, given the amunt f f the aftershck zne, and ccurred befre the installatin f slip inferred by Abercrmbie et al. [this issue]. prtable seismgraphs, we have als included its induced stress field using the mechanism determined by inversin f 3.0 Induced Changes in Culmb Failure Stress teleseismic bdy waves [Abercrmbie et al., this issue]. It was a strike-slip event (mre cnsistent with the reginal stress field We have used the methd f Okada [1992] t calculate the than the mainshck itself was), and we have chsen the ENE strains and their derivatives in a hmgeneus half-space due t striking ndal plane as the fault plane, in accrd with the strike slip n a rectangular fault. These strains can be cnverted t f nearby mapped faults. The fault plane was taken as 8 x 8 km. stresses (using a rigidity f 2.68 x 10 ø N/m 2) and rtated t The distributin f induced changes in CFS fr pfimally whatever crdinate system required. Once the induced stresses riented faults is first cmpated 5-km depth (Plate la) using are knwn, we can add them t the reginal stress tensr. Then ur "standard" mdel. By "standard" we mean using It = 0.75,/3 we calculate the ptimally riented fault planes in that = 0.5, tapered slip, the mechanisms frm Abercr nbie et al. cmbined stress field. Then we can rtate the induced stress [this issue] and cnsidering nly events mre than 2.0 km away nt thse faults, calculate the induced Culmb failure stress, frm the fault planes f the mainshck and largest aftershck. and examine its spatial variatins. The induced Culmb failure The aftershcks superimpsed in Plate l a are thse that fall stress (5CFS) is given by within the 4 t 6 km depth range. Mcst f the ff-fault t CFS = Tshea r + ].t(t T n + t) P) (1) aftershcks ccurred in regins f psitive induced CFS and few ccurred in negative regins: 91.4% in psitive regins where/.t is the cefficient f frictin, ts h r is the induced versus 48.3 % fr randm lcatins. Hwever, there are smaller change in shear stress, t Vn is the induced change in nrmal psitive lbes extending west and east withut aftershcks in stress, and ty, P is the induced change in pre pressure. The last is them. given by We have als cmputed the induced changes in CFS in tw vertical crssectins: the first perpendicular t the mainshck ep = -(] ] 3),t ii (2) fault plane (azimuth 131 ø, Plate lb) and the secnd aligned where,b is Skemptn's cefficient and we assume an istrpic alng the majr psitive lbeseen in Plate la (i.e., azimuth pr-elastic medium. Our sign cnventin is thatensile stresses 170 ø, Plate l c). In these views there is als a reasnable

9 ROBINSON AND MCGINTY: THE ARTHUR'S PASS EARTHQUAKE, 2 16,147 A B KM K 15 BARS +2. BARS +Z c 0 OO ' - / 15 K! 50 0 KI ß 3 BARS +Z -.4 BARS +.4 Plate 1. Induced changes in Culmb failure stress (tcfs) due t the Arthur's Pass mainshck and largest aftershck. (a) Changes at 5-km depth, n planes with ptimal rientatins in the reginal plus induced stress field. The black rectangle and linc arc the surface prjectins f the faults. Black circles arc higher-quality aftershck spicenter fr svsnts in the 4 t 6 km depth range and mre than 2 km away frm the fault planes. Nts that the clrs saturate well belw the maximum / minimum values. The center f the Plats la is at ø latitude, ø lngitude, which is the center f the Arthur' s Pass fault plans as determined by Abercrmbie et al. [this issue]. (b) Sams as in Plats l a except n a vertical crss sectin passing thrugh the center f the Arthur's Pass mainshck fault plans at an azimuth f 136 ø, perpendicular t the fault plans. Aftershcks within 2 km f the sectin are shwn if they are mre than 2 km frm either fault plane. Nte the vertical exaggeratin. (c) Same as in Plate lb except fr a sectin azimuth f 170 ø. (d) Same as in Plate la except that SCFS is fr faults f the same rientatin and sense f slip as that fr the Cass earthquake. The black rectangle is the surface prjectin f the Cass fault plane. Nte the change in scale frm that in Plates 1 a-lc.

10 16,148 ROBINSON AND MCGINTY: TffE ARTHUR'S PASS EARTHQUAKE, 2 Table 4. The Effect f Different Parameter Values n the Percentage f Aftershck Hypcentres That Fall in Regins f Psitive Induced CFS Percent Psitive Percent Psitive if Number f Events Randm Hypcentres Standard Values g = g = g = = = Near = 0.0 km Near = 4.0 km Near = 6.0 km Near km Slip = Unifrm Standard values are as fllws: g = 0.75, = 0.5, near = 2.0 km, slip = tapered. CFS, Culmb failure stress. crrelatin between aftershck hypcenters within 2 km f the plane f sectin and areas f psitive induced CFS: 69.6 and 90.7% f the hypcenters in psitive regins versus 24.0 and 73.9% fr randm psitins. Hwever, recall that events within 2 km f the fault planes are nt shwn and nly quality A events are used, which precludes very shallw events whse depths are less well cnstrained. increased 15CFS, with a maximum value f MPa (0.4 bars). Finally, we have calculated the induced CFS n the Alpine fault t the NW. The surface trace f the Alpine fault is 25 km away (Figure 1), but it d ps at 45 ø t the SW despite the predminantly strike-slip mtin. The induced CFS n the nearest part f the Alpine fault was psitive (mre than 0.05 The results s far (Plates la-lc) suggest a psitive crrelatin MPa r 0.5 bars) but becmes negative by abut half that farther between ff-fault aftershcks and regins f psitive induced t the NE alng strike. CFS, but we have als cmputed the CFS value at the hypcenter f each aftershck individually in rder t get a glbal statistic. Using ur standard mdel, we find that 77.4% f the aftershcks ccur where the induced CFS is psitive. If 4. Discussin We think that the unusual distributin f aftershcks fr the the aftershcks were distributed randmly within a 50 x 50 x 10 Arthur's Pass earthquake can be explained by the cmbinatin km regin centered n the mainshck, then the expected f the mainshck mechanism and the reginal stress field, under percentage wuld be 47.6%. We have examined the effect f different values fr/t,/3, the "nearness" criterin, and slip distributin n the glbal crrelatin f aftershcks and psitive CFS (Table 4). In the assumptin that ff-fault aftershcks will preferentially ccur where the induced CFS n ptimally riented planes is psitive. The parameters in ur standard mdel were chsen withut reference t the end results (i.e., they were ur best additin t ur standard values, we als take/t as 0.85, 0.50, guess befrehand). Since the results suggest that the assumptin and 0.25 (0.75 standard), /3 as 0.0 and 1.0 (0.5 standard), is valid, the results f the tests with a variety f different "nearness" as 0, 4, 6, and 8 km frm the mainshck fault plane parameter values suggesthat ur standard values may nt be (2 km standard), and unifrm slip (tapered slip standard). In all cases there is still a psitive crrelatin, smetimes better and smetimes wrse than that fr ur standard mdel. While these ptimum. In particular, we see (Table 4) that the crrelatin imprves as the "nearness" criterin (distance t the mainshck fault planes) is increased, althugh care is needed since the tests are nt exhaustive (we nly vary ne parameter at a time), number f events decreases with distance. Als, high values f we think that the bservatin f a strng psitive crrelatin the cefficient f dry frictin (/0, and Skemptn's cefficient between aftershck hypcenters and psitive induced CFS is (13) are favred. The increase in crrelatin with distance well funded. Fr ur standard mdel the percentage f aftershcks that fall within regins f psitive induced CFS can suggests that slip during the mainshck was nt as simple as we assume: hetergeneuslip wuld prduce "nise" in the be increased t 85.1% by small changes in the mainshck induced stress field that becmes prgressively smthed ut mechanism (within the quted errrs f Abercrmbiet al. [this issue]): strike frm 221 ø t 226 ø, dip frm 47 ø t 50 ø, and rake frm 112 ø t 102 ø. This alternate mechanism increases the percentages fr ther mdels by abut the same amunt. We have als calculated the induced 6CFS n the faults f with distance. Abercrmbie et al. [this issue] cnsider the pssibility that the Arthur's Pass mainshck cnsisted f tw subevents with very different mechanisms: the first mainly thrusting (as mdeled here), but the secnd, 2 s later, being strike slip n a the same rientatin as that fr the 1995 Cass earthquake, NW striking fault. This pssibility is cnsidered because f the ML6.2, 30 km east f the Arthur's Pass event. We have used the Cass fcal mechanism given by Gledhill et al. [2000]: strike 176 ø, dip 46 ø, and rake 44 ø. The results, at a depth f 5 km (Plate l d), shw that the Cass fault plane lies within a lbe f differences between the bdy wave inversin mechanism and varius CMT mechanisms, with the latter having a large nnduble-cuple cmpnent, and because f the aftershck distributin. Hwever, frm the results presented here there is

11 ROBINSON AND MCGINTY: THE ARTHUR'S PASS EARTHQUAKE, 2 16,149 n need fr a secnd event t explain the aftershck relatin t the stress drp (-5 MPa r 50 bars), but changes distributin. This, cmbined with the lack f any evidence fr a in 6CFS as small as 0.1 bar have been fund t prduce secnd event in the bdy waves, leads us t suggesthat the bservable changes in lw-level seismicity [Reasenberg and cmplex lcal velcity structure (e.g., the rt f the Suthern Simpsn, 1992] and t affect aftershck distributins [King et Alps) may be respnsible fr the discrepancies in mechanisms. al., 1994]. Hwever, this des nt mean that the Cass A remaining questin is why the rientatin f the earthquake culd have been frecast, since the 6CFS depends mainshck fault plane and slip directin are seemingly n the fault rientatin and sense f slip, which were nt knwn incnsistent with the reginal stress field. In fact, the predicted ahead f time. Als, the preexisting stress wuld have had t be rake fr a preexisting fault with the strike and dip f that fr the fairly high fr such a small change t act as a trigger. If the Arthur's Pass mainshck is 130 ø, cmpared t the bserved mechanism f future events is assumed, then it is pssible t 112ø; nt a great difference. Hwever, as pinted ut abve, the calculate the cumulative effect f the stresses induced by large differential stress required fr slip t ccur, given the reginal past earthquakes (if their mechanisms are knwn) and lk fr stress field and ur standard parameters and hydrstatic pre regins where the CFS is high. This apprach has prduced pressure, is 2530 MPa (25,300 bars), which is very high. If the gd results in suthern Califrnia, at least in retrspect [Deng cefficient f frictin were as lw as 0.25, then the required and Sykes, 1997], and we hpe t apply it t the Arthur's Pass differential stress is mre reasnable, 109 MPa (1090 bars). and ther New Zealand regins in future wrk. Hwever, such a lw value f the cefficient f frictin reduces The Arthur's Pass earthquake induced stress changes n the the crrelatin between aftershck hypcenters and induced nearby Alpine fault that wuld encurage fight-lateral strike-slip CFS. The fault respnsible fr the Arthur's Pass mainshck is faulting, the maximum change in CFS being MPa (0.5 nt well develped, judging by the lack f any surfac expsure bars). Hwever, smewhat lesser (because f distance) negative r tpgraphic expressin, s it seems unlikely that it wuld be CFS was induced farther NE alng strike. The last majr event very weak befre the effect f pre pressure is cnsidered. An n that fault was in circa 1717, magnitude-7.9. Gelgic and alternative wuld be that the pre pressure is higher than gedetic bservatins indicate that sufficient strain has hydrstatic while the cefficient f frictin is nrmal. This accumulated fr anther such event (K. Berryman and J. wuld nt affect the cerrelatin f aftershcks and psitive Beavan, persnal cmmunicatin, 1998). Hwever, the Arthur's induced CFS r ur inversin prcedure. Hwever, pre Pass event did nt serve as an immediate trigger. Nt enugh is pressures near lithstatic wuld be required. knwn abut the time dependence f the triggering mechanism Aside frm the bservatin that the Suthern Alps were [Gmberg et al., 1998] r abut the likely initiatin pints f created by vertical mtin, it is ften bserved in regins f large Alpine fault events t make much use f this bservatin blique plate cnvergence that se, ismic slip is partitined int at present. We just present it fr future reference. events with slip parallel t the plate bundary and with slip The interactive cmputer prgram used in this study t derive perpendicular t that [Fitch, 1972; McCaffrey 1992; Yu et al., the induced changes in CFS is available via ftp frm 1993]. The resultanttal slip is in the directin f cnvergence. ftp.gns.cri.nz, directry pub/rbinsn, as a self-extracting and This is the case fr the subductin margin f the east cast f self-installing file GNSetup.exe. The prgram is fr Windws the Nrth Island, New Zealand [Webb and Andersn, 1998]. PCs nly. The parameters used in this study are in file ap.par Pearsn et al. [1995] attempted t mdel their gedetic which can be imprted int the prgram. Aftershck bservatins in the central Suthern Alps with a dislcatin hypcenters (ap.hyp) are als available fr thse wh may wish mdel in which the Nuvel-lA plate cnvergence velcity is t experiment. The cmputer prgram used t invert plarity reslved nt a 50 ø dipping Alpine fault lcked t a depth f 12 data t a reginal stress tensr is als available as GetStress.exe km and freely slipping belw that. They fund that the predicted (with a Windws interface but relatively slw) r as genetic shear strain parallel t the Alpine fault agreed with their Frtran surce cde GetStress.fr (n interface but relatively bservatins but that the predicted shear strain perpendicular t fast). the fault did nt agree, even rughly. They inferred that the Alpine fault takes up a large fractin f the cmpnent f plate Acknwledgments. We thank S. Hriuchi, Y. Okada, and A. cnvergence parallel t the plate bundary (i.e., t the Alpine Michael fr making their cmputer prgrams available t us. Rachel Abercrmbie, Martin Reyners, Terry Webb, Jhn Beavan, and Kathleen fault) but that the cmpnent nrmal t the bundary must be Hdgkinsn have reviewed an early versin f the text and made useful taken up elsewhere. It seems that the fault respnsible fr the suggestins fr imprving it. Rachel Abercrmbie prvided many ther Arthur's Pass earthquake is part f that "elsewhere." Since the helpful suggestins thrughut this research. S. Schwartz, R. Simpsn, bliqueness is nt large (18ø), we wuld expect earthquakes like and ne annymus reviewer all made imprtant suggestins fr imprving this paper. This wrk was made pssible by grants frm the the Arthur's Pass event t be relatively rare. New Zealand Earthquake Cmmissin and the New Zealand The near equivalence f the average P and T axes f the Fundatin fr Research, Science and Technlgy. individual event fcal mechanisms with the c51 and c53 stress axes derived via ur inversin methd is cnsistent with the assumptins in that methd, i.e., that slip will ccur n either f References the tw ptimally riented planes chsen mre r less randmly Abercrmbie, R. E., T. H. Webb, R. Rbinsn, P.J. McGinty, J. J. Mri, and with randm deviatins. The tw ptimal planes are and R. J. Beavan, The enigma f the Arthur's Pass, New Zealand, symmetric abut the c51 axis, s an average P axis wuld be earthquake, 1, Recnciling a variety f data fr an unusual expected t be clse t the c51 axis. If ne ptimum plane was earthquake sequence, J. Gephys. Res, This issue. greatly favred ver anther, this wuld nt be the case. Berryman, K. R., S. Beanland, A.F. Cper, H. N. Cutten, R. J. Nrris, and P. R. Wd, The Alpine fault, New Zealand: variatin in It is reasnable t say that the Cass earthquake was triggered Quaternary structural style and gemrphic expressin, Ann. by the Arthur's Pass event (Plate l d). The maximum Tectn., VI, suppl. 5, , induced 6CFS was MPa (0.4 bars), which seems small in Brudy, M., M.D. Zback, K. Fuchs, F. Rummel, and J. Baumgartner,

12 16,150 ROBINSON AND MCGINTY: ARTHUR'S PASS EARTHQUAKE, 2 Estimatin f the cmplete stae, s tensr t 8 km depth in the KTB slutins Ibr the 1984 Mrgan Hill, Califrnia, earthquake scientific drill hles: Implicatins fr crustal strength, J. Gephys. sequence: Evidence fr the state f stress n the Calaveras Fault, J. Res., 102, 18,453-18,475, Gephys. Res., 93, , Bull, W. B., and M. T. Brandn, Lichen dating f earthquake generated Pearsn, C. F., J. Beavan, D. J. Darby, G. H. Blick, and R. I. Walctt, reginal rckfall events, Suthern Alps, New Zealand, Gel. Sc. Strain distributin acrss the Australian-Pacific plate bundary in Am. Bull., 110, 60-84, the central Suth Island, New Zealand, frm 1992 GPS and earlier Davis, J. C., Statistics and Data Analysis in Gelgy. Jhn Wiley, New terrestrial bservatins, J. Gephys. Res., 100, 22,071-22,081, Yrk, Raleigh, C. B., J. H. Healy, and J. D. Bredeheft, Faulting and crustal Deng, J., and L. R. Sykes, Evlutin f the stress field in suthern strength at Rangely, Clrad, in Flw and Fracture f Rck, Califrnia and triggering f mderate-sizearthquakes: A 200-year Gephys. Mngra. Ser., vl. 16, edited by H. C. Heard et al., pp perspective, J. Gephys. Res., 102, , , AGU, Washingtn, D.C., Fitch, T. J., Plate cnvergence, transcurrent faults, and internal Reasenberg, P. A., and R. W. Simpsn, Respnse f reginal seismicity defrmatin adjacent Sutheast Asia and the Western Pacific, J. t the static stress changes prduced by the Lma Prieta earthquake, Gephys. Res., 77, , Science, 255, , Gephart, J. W. and D. W. Frsyth, An imprved methd fr Reyners, M. E., R. Rbinsn, and P. J. McC inty, Plate cupling in the determining the reginal stress tensr using earthquake fcal nrthern Suth Island and suthernmst Nrth Island, New Zealand, mechanism data: Applicatin t the San Fernand earthquake as illuminated by earthquake fcal mechanisms, J. Gephys. Res., sequence, J. Gephys. Res., 89, , , 15,197-15,210, Gledhill, K., R. Rbinsn, T. Webb, R. Abercrmbie, D. Eberhart- Rice, J. R., Fault stress states, pre pressure distributins, and the Phillips, J. Beavan, and J. Cusins, The Mw6.2 Cass, New Zealand, weakness f the San Andreas fault, in Evans, B. and T. F. Wng, earthquake f 24 Nvember, 1995: Reverse faulting in a strike-slip editrs, Fault Mechanics and Transprt Prperties f Rck: a regin, N.Z.J. Gel. Gephys., in press, Festschrift in Hnr f W.F. Brace, edited by B. Evans and T. F. Gmberg, J., N.M. Beeler, L. B lanpied, and P. Bdin, Earthquake Wng, pp , Academic, San Dieg, Calif., triggering by transient and static defrmatin, J. Gephys. Res., 103, Rivera, L., and A. Cisternas, Stress tensr and fatfit plane slutins fr a 24,411-24,426, ppulatin f earthquakes, Bull. Seisml. Sc. Am., 80, , Harmsen, S.C., and A.M. Rgers, Inferences abuthe lcal stress field frm fcal mechanisms: Applicatins t earthquakes in the suthern Rbinsn, R. and T. Webb, AMPRAT and MECHTOOL: Prgrams fr Great Basin f Nevada, Bull. Seisml. Sc. Am., 76, , determining fcal mechanisms f lcal earthquakes, Sci. Rep. 96/7, Inst. f Gel. and Nucl. Sci., Wellingtn, New Zealand, Harris, R. A., Intrductin t special sectin: Stress triggers, stress Schwartz, S.Y., Surce parameters f aftershcks f the 1991 Csta shadws, and implicatins fr seismic hazard, J. Gephys. Res., Rica and 1992 Cape Mendcin, Califrnia, earthquakes frm 103, 24,347-24,358, inversin f lcal amplitude ratis and bradband wavefrms, Bull. Hriuchi, S., G. Russ, and A. Hasegawa, Discriminatin f fault Seisml. Sc. Am., 85, , planes frm auxiliary planes based n simultaneus determinatin f Webb, T., and H. Andersn, Fcal mechanisms f large earthquakes in stress tensr and a large number f fault plane slutins, J. Gephys. the Nrth Island f New Zealand: Slip partitining at an blique Res., I00, , active margin, Gephys. J. Int., 134, 40-86, King, G. C. P., R. Stein, and J. Lin, Static stress changes and the Yu, G., S. G. Wesnusky, and G. Ekstrm, Slip partitining alng triggering f earthquakes, Bull. Seisml. Sc. Am., 84, , majr cnvergent plate bundaries, Pure Appl. Gephys., 140, , McCaffrey, R., Oblique plate cnvergent c, slip vectrs, and frearc Zha, D., H. Kanamri, and D. Wiens, State f stress befre and after defrmatin, J. Gephys. Res., 97, , the 1994 Nrthridgearthquake, Gephys. Res. Lett., 24, , Michael, A. J., Use f fcal mechanisms t determine stress: A cntrl study, J. Gephys. Res., 92, , 1987a. Michael, A. J., Stress rtatin during the Calinga aftershck sequence, J. Gephys. Res., 92, , 1987b. P. J. McGinty and R. Rbinsn, Institute f Gelgical and Nuclear Mri, J. J., D. Wald, and R. Wessn, Overlapping fault planes f the Sciences, P.O. Bx , Lwer Hurt, New Zealand. (r.rbinsn@ 1971 San Fernand and 1994 Nrthridge, Califrnia, earthquakes, gns.cri.nz) Gephys. Res. Lett., 22, , Okada, Y., Internal defrmatin due t shear and tensile faults in a halfspace, Bull. Seisml. Sc. Am., 82, , (Received January 29, 1999; revised July 7, 1999; Oppenheimer, D. H., P. A. Reasenberg, and R. W. Simpsn, Fault plane accepted Nvember 10, 1999.)