JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102,NO. B3, PAGES 5029-5041,MARCH 10, 1997
Constraints on Macquarie Ridge tectonics provided by Harvard focal mechanisms and teleseismic earthquake locations
Cliff Frohlich,1 Millard F. Coffin,1 ChristinaMassell,1,2PaulMann,1
Catherine L. Schuur, 1,2ScottD. Davis, 3TrevorJones, 4 and GarryKarner 5 Abstract. In this studywe evaluateteleseismically determinedfocal mechanisms andepicenters for earthquakes alongthe MacquarieRidgeComplex(MRC) from 45øSto 61øSand 155øEto 168øE,a regioncharacterizedby somepreviousinvestigatorsas undergoingsubductioninitiation. From 65 centroidmomenttensorsreportedby Harvard,we developstatisticalguidelinesfor choosing26 whichrepresentbetterdetermined, morereliablefocalmechanisms for tectonic analysis.Althoughthrustmechanisms occurin the north,nearFiordland,elsewherealongthe MRC the betterdeterminedmechanisms virtuallyall indicatethatpresent-daymotionalongmost of the MRC is strike-slip.This is consistentwith sidescansonarandmultichannelreflectiondata collectedbetween50øSand57øSon 1994 and 1996cruises;the activeplateboundar3, zoneappears to be quitenarrow(< 5 km wide),andno activecompressional featurescanbe observedon the seafloor.If we determinea rotationpole for plateboundarymotionusingonly slip vectorsfrom betterdeterminedHarvardmechanismsalongthe MRC, the bestfitting "instantaneous" pole is at 57.4øS,179.4øE,about2.5ø northof theNUVEL-I Australian-Pacific pole,whichaveragesmotion overthe last 3.0 my. If the MRC pole wasformerlyfarthersouththanat present,this could explaintheexistenceof relictfeaturesassociated with crustalshortening, suchasbathymetric highsandtroughs;yet, the absenceof activefeaturessuchasthrustfaults,etc., suggests ongoing compression or subduction initiation.We alsocarefullyreadarrivaltimesfor P phasesfor 53 earthquakes at 16 teleseismic stations, selected to represent a rangeof azimuthssurrounding the earthquakes; we relocatedtheseearthquakes usingstandard joint epicentraldetermination (JED) methods.While mostof the betterqualityrelocationslie on or very closeto the Australia-Pacific boundar3, asdeterminedon the 1994cruise,a few epicenters occurwell awayfrom the boundar3,, apparentlyon Cenozoicfracturezones.Thus,on theMacquarieRidgeComplexandothermajor strike-slipboundaries(e.g.,in California),it appearsthatthe very largestearthquakes occuron the principalplateboundar3, fault but thatotherearthquakes, somequitelarge,may occuraway from the boundaryalongzonesof preexistingweakness. including on May 23, 1989, the largest (Mw = 8.2) strike-slip earthquakeever recorded[Ruff, 1990; Satake and Kanamori, The Macquarie Ridge Complex (MRC) is an anomalous, 1990]. Finally, reported earthquakefocal mechanismsalong shallow(< 1000 m) bathymetricfeatureextendingabout 1500 the MRC are quite diverse(Figure 2); they include strike-slip, km southof New Zealand;it containsa segmentof the Pacific- thrust, and non-double-couplemechanisms[Ruff et al., 1989; Australianplate boundarywhich lie• betweenthe Alpine Fault Frohlich et al., 1989]. and the Australia-Pacific-Antarctictriple junction (Figure 1). One explanation for the simultaneousexistence of large Severalfeaturesof the MRC are puzzling [Jones,1991; Jones earthquakes,diverse mechanisms,and the extreme vertical and McCue, 1988]. First, while the ridge itself is shallow, it relief is that the plate boundary is experiencing tectonic lies adjacentto a seriesof deeperregions,the Puysegurtrench, readjustment;reportedpoles for Pacific-Australiaplate motion the McDougall trough, the Macquarie trough, and the Hjort are situated only about 1200 km distant from the plate trench. Second, in the twentieth century the ridge has boundary [e.g., DeMets et al., 1990], and thus relatively small experiencedan extraordinarynumber of large earthquakes changesin pole location can significantlyaffect the character [Abe, 1981; Anderson, 1990; Frohlich and Apperson, 1992], of interplateinteractionsalong the MRC. For example,Ruff et al. [ 1989] evaluatedearthquakemechanismsand concludedthe lInstitute forGeophysics, University of TexasatAustin. region was experiencing"obliqueconvergenceand subduction Introduction
2Department of Geological Sciences, University of TexasatAustin. 3Cooperative Institute for Research in Environmental Science and
initiation." Also, Das [1992, 1993] relocated more than 1000
epicentersin this region using phasedata reportedin catalogs and concludedthat a significant number did not lie along the 4Australian Geological SurveyOrganisation, Canberra. 5Lamont-Doherty Earth Observatory of ColumbiaUniversity, plate boundary but instead lay well to the west, along a Palisades,New York. Cenozoicfracturezone in the Australianplate.
NationalGeophysical Data Center,NOAA, Boulder,Colorado.
However, new information is now available to us that was
Copyright1997by theAmericanGeophysical Union.
unavailable to the previous investigators;in particular, along
Papernumber96JB03408
the MRC
0148-0227/97/96JB-03408509.00
tensor (CMT) 5029
there are now more than 60 Harvard centroid moment
focal mechanisms (about twice as many
5030
FROHLICH ET AL.: CONSTRAINTS ON MACQUARIE RIDGE TECTONICS 150 ø
155 ø
160 ø
I
I
165 ø i
170 ø
175 ø
180 ø
I
i
Australia
40ø
Australian
•,
40 ø
Plate Tasmania New
Zealand
45 ø
45 ø
Puysegur
Pacific
50 ø
50 ø
Plate
AUS-PAC pole this study
Mocquorie
55 ø
55 ø
60 ø
60 ø Antarctic
DeMe•s
Triple Junction
Plate
I 160 ø
I• 165 ø
et al. [1990]
I
!
170 ø
175 ø
I
180 ø
Figure 1. Locationof the MacquarieRidgeComplex(MRC), whichextendsfrom SouthIsland,New Zealand, to the Pac-Aus-Anttriplejunction.Pacific-Australian plateboundary(thick solidline) is from C. G. Massellet al. (manuscript in preparation,1997).The 4500 m contours(lighterlines)delineatethe Puysegur,McDougall, Macquarie,andHjort bathymetricdeeps.Octagonsindicatelocationsof polesof rotationfor Australian-Pacific plate motionas reportedby DeMets et al. [1990] and as estimatedin this study;ellipsoidsindicateregionof pole locationuncertainty.Box indicatesregiondepictedby subsequent map figures.
mechanismsas were availableto Ruff et al. [1989]) permitting us to be more selectiveabout the quality of the mechanisms that we interpret. To this end, here we develop specific new statistical criteria for choosing the more reliable focal mechanismsfrom the Harvard CMT catalog; then, we use the selected mechanisms to characterize the present-day seismicityalongthe MRC in eachof five differentsubregions definedby distinctchangesin the strikeof the plate boundary (Figure 2). Also, becauseno local seismicstationsconstrained Das's [1993] relocationsusing phaseinformationreportedin catalogs,there is concernthat some of her resultsmight be attributableto misreadphasesor systematicerrorsin location. Thus, for selected earthquakeswe have personally reread phases at specific stations and performed an analysis of reportedepicenteraccuracy. Finally, three recentgeophysicalcruiseshave providednew information to constrain tectonic analysesof the MRC; the R/V L'atlante in 1993, the R/V Rig Seismicin 1994, and the R/V Maurice Ewing in 1996 visited the MRC region and collected side-scan sonar, bathymetry, seismic reflection, gravity, and magnetic data. From analysesof these data, Callat et al. [1995], M. F. Coffin et al. (manuscript in preparation, 1997)and C. G. Massell et al. (manuscriptin preparation, 1997) demonstratedthat (1) the oceanic crust making up the MRC has been thickened along the entire
bathymetricridge, resultingin large positivefree-air gravity anomalies;(2) the Pacific-Australiaplate boundaryalong the MRC is localized and relatively well-defined;between 50øS and 57øS the plate boundary is commonly traceable as a distinctvalley splitting the ridge crest in the bathymetryand seismicreflectiondata; (3) numerousfracturezonesapparent on sidescansonar and bathymetric data intersect the plate boundaryat a low angle and extend hundredsof kilometers away from the MRC; the MRC was thus first a spreading boundaryand subsequently experienced regionalshearingand transpression;and (4) in the north, between 49øS and New Zealand,the natureof faulting observedon seismicreflection data suggeststhat the plate boundary is currently under compression;such faults are not evident between 50øS and 57øS.
Data
and Methods
Analysis of Harvard Catalog
Centraid
Moment
Tensor
Inevitably, earthquake catalogs contain data of varying quality; however, deciding which entries are reliable for tectonic analysis, i.e., "better determined," dependson the specific question of interest. Our specific concernsare the orientationsof the nodal planesand slip vectorsas determined
FROHLICH ET AL.: CONSTRAINTS ON MACQUARIE RIDGE TECTONICS
5031
7.o -a•l 938 •)a 1993 Large Earthquakes Fiordland ••-Macquarie Ridge
46 ø
Hazard M>6'8X
•)b
Ruffet •1.
•5 •
197•
48 ø
48 ø
50 ø
50 ø
52 ø
__
•
1989 52 ø
•
McDougall
54 ø
54 ø
•.•
56 ø
56 ø
•
••• Hjo•
58 ø
60 ø
• MacquaHe 58 ø
-
I
156ø
I
158ø
I
160ø
I
I
I
162ø
164ø
166ø
60 ø
Figure 2. Historical earthquakesalong the Macquarie Ridge with reported magnitudes exceeding 6.8. Locations,magnitudes,and (where available) focal mechanismsare as reportedby Harvard, Ruff et al. [1989], andAbe [1981]. Solid line is Pacific-Australiaplateboundaryas reportedby C. G. Massellet al. (manuscriptin preparation,1997). Boxes labeled "Hjort," Macquarie,"etc., delineategeographicsubregionsevaluatedin this study;lettersbesideepicentersindicatecorresponding focal mechanism.
5032
FROHLICH ET AL.: CONSTRAINTSON MACQUARIE RIDGE TECTONICS
from P, T, andB axesof earthquakefocal mechanisms. We here evaluate focal mechanismsin the Harvard CMT catalog [e.g., Dziewonski et al., 1981; Dziewonski and Woodhouse,1983], utilizing three statisticseasily derivablefrom informationin the catalogto selectbetterdeterminedmechanisms. For eachCMT M reportedby Harvard,the catalogincludes
Fiordlnd 10/12/79
the azimuths(•T,•B,•P) andplunges(OtT,OtB,Ot P) of the T, B, and P axes, along with their associatedprincipalmoments
(/•T,•,•e).
'7,0
An alternatebut equivalentdescription of M is
as a symmetricmatrix, and the catalog also presentsthe six
matrixcomponents roll, m12,m13,m22,m23,andm33,along with
estimates
of the standard error
tensor U,
with
components Ull, u12,u13,u22,u23,andu33. The first statistic we employ is fc•va, which measures whether M is more similar to a double-couplemechanism,as is observed due to slip on a planar fault surface, or to a compensatedlinear vector dipole (CLVD) mechanism.Some
fclvd --- 0.41
nfree = 4
E = 0.24
E = 0.32
Figure 4. Harvard CMT for earthquakesin the Fiordland subregion(Figure 2). Four CMT (top row) are better determined becausethey havefc•vd< 0.2, nfree= 6, and E < 0.15; all are earthquakesclearly do have CLVD components[Frohlich, predominantly thrusts because the T axis is nearest the 1994a]; this may indicate that rupture occurred nearly vertical; two are quite large (magnitudesMw = 7.3 and 7.0). Of simultaneouslyon two or more properlyoriented,nonparallel the remaining four events (bottom row), one had a fault surfaces. For sucha mechanism the principalmoments•,T predominantlyCLVD mechanism(fc•vd= 0.41), one has two and•,p associated withthe T andP axesareof unequalstrength. constrainedmoment tensor components(nfree= 4), and two have large relative errors (E = 0.24 and E = 0.32, We define respectively).
fclvd= IXB/XTI if 1•,•4 > I•,pI= I•,B/3•pI if 1•,•4 < I•,pI;
(1)
fclvd= 0 for a pure double-couple mechanism,andfclvd= 0.5 for a pure CLVD mechanism. As fclvd increases and a mechanismapproaches a CLVD, the orientationsof the B axis and either the T or P axis become indeterminate(Figure 3). Thus, since in this study we are concerned with axial orientations, we select mechanisms with smaller values of
fclvd'
B
P
Couple
to be identically zero; thus we determine nfree simply by
counting thenumber of nonzero uijassociated withthesixmij.
The third statistic we use is the relative error E, which
T
P
determination of M. Whena momenttensorelementmijis constrained, Harvardreports theassociated standard errorsuij There are theoretical reasonswhich cause the ml2 and m•3 componentsof M to be indeterminate as earthquake depth approacheszero; thus, ul2 and u13 are small or zero for very shallow earthquakes.The geometriceffect of theseconstraints is to artificially force one of the three principal axes (T, B, or P) to be oriented vertically (Figure 3). In this study we shall selectmechanismswhich have nfree= 6; thus any of the axes can take any orientationin space.
Double P
The second statistic we employ is nfree, the number of moment tensor elementsthat are not constrainedduring the
comparesthe relative sizes of M and the standarderror tensor U. As definedby Davis and Frohlich [1995]: P
P CLVB
E= Ul 2+u332 22+2u13 2+2u23 2 21 +u22 2+2u12
I 2
roll +m22 2+m33+2m12+2m13 2+2m232
B
Constroined
Figure 3. Limitations of focal mechanismsdeterminedfrom CMT with CLVD components and constrained CMT. To distinguishthrust (top row, left; vertical T axis) and strikeslip (top row, right; vertical B axis) mechanisms,we must know the orientationof the T and B axes; this is not possible
for pure (fclvd= 0.5) CLVD mechanisms (middle row), which have identical radiation patterns regardless of whether the reportedT andB axes are vertical, horizontal,or in between. For shallow and/or poorly recorded earthquakes, Harvard commonly constrainsthe rn12 and rn•3 componentsof the CMT to be zero; this means that the only allowable mechanisms have exactly vertical T, B, or P axis (bottom row).
(2)
Conceptually, E is just the norm or "scalar moment" of U divided by the scalar moment of M. In most cases,E is a numberbetween0 and 1; for CMT in the entireHarvardcatalog its median value is 0.13. When the componentsof M are allowed to vary within the limits fixed by the standarderrorsU [Frohlich, 1995], the orientations of the T, B, and P axes are better constrained
for events with smaller values of E.
In the presentstudy, for a mechanismto qualify as "better determined,"we arbitrarily requirethat it meet three statistical standards:(1) fc]vd < 0.20; (2) nfree= 6; and (3) E < 0.15. Altogether65 earthquakesin the Harvard cataloglie within the geographicregion between45øS and 61øS and between 155øE and 173øE. Of these, 26 meet the three statistical criteria
above and are better determined. Of the remaining 39, ten which were otherwise satisfactoryfail becausefclvd exceeds 0.2, ten possessnfreeless than 6, and 19 have valuesfor E exceeding0.15 (e.g., see Figure 4).
FROHLICH ET AL.: CONSTRAINTS ON MACQUARIE RIDGE TECTONICS
Relocation
of Selected Earthquake
Hypocenters
Routine earthquake locations reported in catalogs may suffer from a variety of related afflictions; these include (1) mispicked phases; (2) a limited range of azimuths for the observingstations;and (3) travel times biased by the Earth's lateral heterogeneity. In this study our strategy was to minimize these problems by assembling a restricted set of epicenters for which (1) we read and graded the phases ourselves;(2) we could obtain data from observingstationsin all available azimuths;and (3) we relocatedthe eventsusing a standardjoint epicenterdetermination(JED) method. Thus we visited the microfiche seismogram library at Lamont-DohertyEarth Observatory(ColumbiaUniversity) and searchedfor phasearrivals from Macquarie Ridge earthquakes at stationsin four different azimuthal sectors(Figure 5): these were
an Antarctic
sector (azimuths
of
160ø-240ø),
an
Australiansector(2800-360ø) which includedstationsin Papua New Guinea and partsof Asia, a New Zealand sector(0ø-60ø),
5033
(for tentative, probably unreliable arrivals). For relocations we only utilized arrivals with confidence ranks of 1, 2, or 3
and weighted the better arrivals higher in the JED process. Generally, we could only obtain good quality arrivals in at least three of the above sectors for earthquakes with magnitudesof about5.4 and larger; thusour restricteddata set comprised53 earthquakesoccurringbetween 1964 and 1987. The format and readabilityof microfichechangedafter 1987, and we couldnot obtaingoodreadingsfor later earthquakes. To relocate earthquakes,we employed a standardJED method [Douglas, 1967; Frohlich, 1979], utilizing the TexFlex programdescribedby Frohlich [1993], and Frohlich et al. [1995]. Because all events of interest were shallow and
because there were insufficient local stations to precisely constrain the depths for the relocations, we fixed the focal depths at 20 km. For relocationswe determined travel times using the iasp91 model, using subroutinesdescribed by Kennett [1991] andKennettand Engdahl [1991].
and a South American sector (90ø-160ø). We also obtained
picks for phase arrivals from three stations operated by the Australian Geological Survey Organisation;these included a station operating on Macquarie Island (MCQ), one in Antarctica, (MAW),
and one in Australia (TOO). Data from
these
were
three
stations
not available
for
the relocations
previouslyreportedby Frohlich [1994b]. For all phase arrivals we subjectivelyassigneda weight or confidencerank between1 (for clear, impulsivearrivals) and 4
270 ø 90 ø
180 ø
Results
Better
Determined
Earthquake
Focal Mechanisms
In the Fiordland subregion (Figure 2), Harvard reports CMTs for eight earthquakes(Figure 4); of these,the four better determined mechanisms are all predominantly thrusting mechanisms with approximately east-west oriented P axes. This includestwo rather large earthquakes(October 12, 1979, Mw = 7.3; August 10, 1993, M = 7.0). Of the four better determined mechanisms, the two more southerly events (~46øS)haveP axesorientedapproximatelyNE-SW. However, P is more nearly E-W to NW-SE for the two northern events
(~45øS); this is quite close to where intermediate-depth earthquakes occurbeneathFiordland,suchas the earthquakeof June 3, 1988 (h = 62 km; Mw = 6.7). Among the non better determinedmechanisms, only one was from an earthquakewith a magnitudeexceeding5.5 (January31, 1985, M w = 6.3); it was disqualified as better determined only becauseit had a CLVD mechanism (fclv•t= 0.41); its P axis was oriented approximately E-W. In the Puysegursubregion(Figure 2) there are CMTs for 15 earthquakes;of these, four qualify as better determined, and two more would qualify except for having large CLVD components(Figure 6). All six earthquakeshave P axes with nearly identical approximatelyE-W orientations;all six have magnitudesof 5.5 or larger, whereasthe nine remainingnon better determinedearthquakesall have magnitudesof 5.5 or less.Two of the four betterdetermined mechanisms are clearly strike-slip,including the largest (M w = 7.6, May 25, 1981). The remainingtwo betterdeterminedmechanisms are midway betweenstrike slip and thrust,as both have T and B axes with dips between35ø and 52ø.
Figure 5. Equal-area projection showing the take off directions for P phasesto the 16 stations used in the JED relocation.On this plot, phasesleaving the earthquakesource region vertically plot at the center, while those leaving horizontally plot at the edges. The station codes are SBA (Scott Base, Antarctica), SPA (South Pole, Antarctica), ADE (Adelaide, Australia), AFI (Afiamalu, Samoa), ANT
(Antofagasta, Chile), CHG (Chiang Mai, Thailand), CTA (Charters Towers, Australia), MAW
(Mawson, Antarctica),
MCQ (Macquarie Island), MUN (Mundaring, Australia), PEL (Peldehue,Chile), PMG (Port Moresby, Papua New Guinea), RIV (Riverview, Australia), TAU (TasmaniaUniversity), TOO (Toolangi, Australia), WEL (Wellington, New Zealand).
There are 24 Harvard CMTs availablein the McDougall subregion(Figure 2); of these,10 qualify as betterdetermined, and three more would qualify exceptfor having large CLVD components (Figure 7). Eight of the better determined mechanismsare strike-slip with P axes orientedwithin 25ø of
E-W; thisincludesall five earthquakes in the subregion having magnitudesof 6.2 or greater.The most anomalousmechanism
was for the relativelysmall(M w = 5.6) earthquake of May 26, 1989; this was an aftershockof the great May 23, 1989 earthquake (M w = 8.2); its mechanismwas dip slip. The remainingbetter determinedmechanism(November 15, 1989) is not clearly strike-slip,thrust,or normal.
5034
FROHLICH ET AL.: CONSTRAINTSON MACQUARIERIDGE TECTONICS
Fi 0 r"t
fclvd '=0.21fclvd =0.25 9/ 3;/87 10/!5/94
6/ 8"/80
fclvd= 0.24
fclvd= 0.21
Figure 6. Harvard mechanisms which are better determinedor nearly better determinedin the Puysegur, Macquarie,andHjort subregions (Figure2). This includesall mechanisms exceptthosewith nfree< 6 andE < 0.15.
In the Macquarie subregion(Figure 2), Harvard reports CMTs for eight earthquakes;of these, four qualify as better determined, and two more would qualify except for having large CLVD components (Figure 6). All six have approximatelyhorizontalP axesorientedwithin 35ø of E-E; three of the better determined mechanismsare dominantly strike-slip, and one is not clearly strike-slip, thrust, or
normal.The CLVD earthquakeof July 21, 1977 is quite large, having Mw of 6.9. In the Hjort subregion(Figure 2) there are 10 CMTs; of these,four qualify as better determined,and two more would qualify exceptfor havinglarge CLVD components (Figure 6). Five of the six have nearly identical NE-SW orientedP axes; the remaining earthquake,which is the northernmostevent,
McDou_qall
5/26/89
ß.;.:' ,//
5/89
4-/22/95
i l:...
5/23:/84 \ r.'.*•.
5/25/89
\ t.:
'
fclvd = 0.20
fclvd ----0.20
fclvd = 0.28
Figure 7. Harvardmechanisms whichare betterdeterminedor nearlybetterdeterminedin the McDougall subregion (Figure2). This includesall mechanisms exceptthosewith nfree< 6 andE < 0.15.
FROHLICH ET AL.: CONSTRAINTS ON MACQUARIE RIDGE TECTONICS
5035
Figure 8. Ternary diagramsfor Harvard CMTs evaluatedin this study.Labelsindicategeographicsubregion of events (Figure 2): F, Fiordland; P, Puysegur;M, McDougall; Q, Macquarie; H, Hjort. (left) The nine earthquakeswith better determined mechanismsand with M w of 6.3 and greater; (middle) the 26 "better determined"mechanisms;(right) data from all 65 Harvard CMT mechanisms.Mechanismsfalling within the curvesnear the three cornersare strike-slip,thrust,or normal mechanisms,as defined by Frohlich [1992].
has an E-W
P
axis.
All
four
of
the
better
determined
57.4øS, 179.4øE, about 2.5 ø northwest of the Australian-
mechanismsare clearly strike-slip. The CLVD earthquakeof Pacific pole determinedby DeMets et al. [1990] (Figures 1 and September3, 1987 is quite large (M w = 7.4, fclvc•= 0.24); it 9). Althoughthe plottedpole (Figure 1) was determinedusing had a somewhatlarge (Mw = 6.8) double-couple aftershock all the better determinedmechanisms,we obtainedessentially with a reportedthrust mechanismwhich occurredon the same the same location when various of the discrepant(e.g., "a", day and which is not shown in Figure 6 becauseit did not "1","s", etc., in Figure 10) slip vectorswere removed. qualify as a betterdeterminedmechanism. While the pole locationso determined(Figure 1) was quite If we consider the mechanismsin all five subregions robust, it was much better constrained in the north-south than together, certain trends emerge. First, in the Fiordland the east-westdirection.When determinedwith slip vectorsfor subregion,all four of the better determinedmechanismsare the entire set of better determinedmechanisms(Figures 4, 6, thrusts(Figure 8, middle); elsewhere,the clear majority (17 of 7, and 9), the mean differencebetweenexpectedand observed 22) are strike-slip. Second,this contrastis even clearer for the slip vector azimuth was 15ø. However, most of this difference larger events(Figure 8, left); all six eventswhich occurredin was attributableto the more anomalousearthquakes;e.g., in the Puysegur,McDougall, Macquarie,and Hjort subregionsare Figure 10, event "1" was the small, anomalousdip-slip May strike-slip,whereasall three in Fiordland are thrusts. 26, 1989, aftershock of the very large event of 1989; earthquakes"e" and "s" had epicenterssignificantly farther Best Fitting AUS-PAC Pole from the plate boundarythan most others;and earthquake"a" To determinethe best fitting pole, we used a grid searchto was a Fiordland thrust in a complex geologic region near find the locationfor which slip vectorsclusteredmost tightly where the subductionfront intersectsthe Alpine Fault.
aroundthe expectedorientation,i.e., perpendicularto a great circle extendingfrom the epicenterto the pole (Figure 10). We did not attempt to calculate a formal error ellipse for the rotationpole becauseof the sparsedata and becausethere was no truly objective way to estimatethe uncertaintiesassociated with each slip vector. Instead, as a measure of pole uncertainty,we determinedthe elliptical regionfor which pole vectors produce mean slip vector root mean square (rms) differences within 10% of the best fit solution (i.e., for best-
fit pole rms difference was 15ø; for elliptical region rms differencewas 16.5ø;seeFigure 1). The orientationsof strike-slipand thrust mechanismsfrom the MRC are consistentwith a rotation pole which lies at
Relocated
Earthquake
Hypocenters
Epicenters determined using the JED method depend stronglyon the exact combinationof stationsand earthquakes used to determine station corrections; for this reason we
performed a series of experiments using different combinationsof stationsand events.The JED processis often unstable when it includes events recorded at only a few stations, or stations recording only a few events; our most stable results came when we determined station corrections at
16 selectedstations(Figure 5) by relocating 14 especially well-recordedearthquakesoccurringbetween49øS and 55øS. Then, keepingthesestationcorrectionsfixed, we relocatedall
5036
FROHLICH ET AL.: CONSTRAINTS ON MACQUARIE RIDGE TECTONICS
53 earthquakesusing standard single-event relocation
slip towards
schemes.
We thengradedtheseepicenters in termsof the azimuthal stationcoverageandrmsresidualof the relocations; A, those havingthe largestazimuthalgap in stationcoverageof 120ø
pole
or less and a residualof 0.8 s or less;B, azimuthalgap of 140ø or less and residuals of 1.0 s or less; C, all others, including
1 x
all events recorded at nine or fewer of the 16 stations,
regardless of gapor residual.Of the 53 epicenters, therewere
156ø
158ø
I
I
160ø
162ø
164ø
I
I
I
46 ø
48 ø
46 ø
Puysegur
///
-
..... 48 ø
-vertical
-" slip 90ø from pole
50 ø
50 ø
Figure 10. Equal-areaplot evaluating fit of slip vector orientationswith respectto best fitting Australian-Pacific rotation pole (57.4øS, 179.40øE; see Figure 1). Crossesare orientationsfor 17 better determined strike-slip mechanisms
/
52ø
/
54ø
/
52ø
_54ø
(thosewith B axisplungeexceeding60ø),andoctagons are for the remainingbetterdeterminedevents(thrusts;seeFigures4, 6, 7, and 9). The plot showsvectororientationswith respect to greatcirclepathbetweenepicenterandpole. If slip vectors were in perfect agreementwith best fitting pole, all slip vectors would be directed horizontally, perpendicularto the pole (lower right vertex of pie figure); the other vertices correspondto orientationswhich are horizontal,toward pole (upper left vertex), and vertical (lower left vertex). Letters adjacentto the mostdiscrepant observations correspond to the labels in Figure 9.
/
56ø
/
56ø
11 of A quality, 19 of B quality, and 23 of C quality.In this paper we only reportthosehaving A and B quality in Table 1 and Figure 11. Note that the quality gradesapply only to the epicenters and not to the focal depths; as mentioned previously,we fixed focal depthsat 20 km for all earthquake relocatedin this study. 58 ø There are systematicdifferencesbetweentheseJED results • Smoll Circles and those of Das [1993], whose relocations utilized phase oround arrivals reportedin the International Seismological Centre (ISC) Bulletin from more stations.Generally, our relocations • BetterDetermined placeindividualepicentersbetween20 and 45 km farthersouth Harvard CMT 60 o _ and somewhatto the west of Das's [1993] epicenters(Figure Hjo• 12); the range of differencesalong the east-westdirectionis somewhat greater, about 80 km, probably caused by the i paucity of recordingstationsin these sectorsin both studies. 156 ø 158 ø 160 ø 162 ø Most of the A and B quality events(Table 1) are situatedon or within a few kilometers of the Pacific-Australia plate Figure 9. Map showing locations (crosses)reported by Harvard for the better determinedmechanisms(Figures 4, 6, boundary;however,between51ø and 56ø, a few are clearly not and 7), Australia-Pacific plate boundary (thick line) as on the boundary.For example,the earthquakeof July 7, 1982, determinedby C. G. Massellet al. (manuscript in preparation, at 51.48Sø and 160.12øE is clearly to the west; it had an rms 1997) and M. F. Coffin et al. (manuscriptin preparation, residual of 0.90 s and an azimuthal gap of 85ø, possessing 1997), and small circles (dashedlines) aroundthe best fitting good quality P arrivals at 14 stations. Similarly, the AUS-PAC pole (seeFigure 1) determinedin this study.Letters earthquakeof June 27, 1982, at 55.61øS and 160.07øE lies
_ /••••' Mocquorie Ridge
beside epicentersindicate corresponding focal mechanism. While
these
focal
mechanisms
are the best
determined
well to the east; it had an rms residual of 0.92 s and an
by Harvardappearto be systematically shiftedwestwardof the
azimuthal gap of 95ø for 13 stations.For both earthquakes, Das [1993] reportedlocations in good agreementwith these
plate boundary.
but situated about 20 km to the north and east of our own.
mechanismsavailable in this region, the epicentersreported
FROHLICH ET AL.: CONSTRAINTS ON MACQUARIE RIDGE TECTONICS
5037
Table 1. RelocatedEpicentersof MRC Earthquakes Redetermined in This Study OriginTime, Date
Latitude
Longitude
RMS,s
UT
ErrorEllipsea a-,
a+,
Angle,
km
km
øE of N
Sept.4, 1964
2207:02.74
49.194øS
164.366øE
0.71
11.1
25.0
341ø
Nov. 8, 1964
0243:54.98
49.501øS
163.777øE
0.86
10.6
18.0
343ø
1157:40.91 1320:56.22
55.158øS 52.928øS
158.486øE 160.216øE
0.61 0.65
6.2 8.5
33.5 19.7
350ø 352ø
April 5, 1966 May 25, 1966 June28, 1967
1434:04.77
47.280øS
165.497øE
0.93
13.0
23.3
329ø
Sept.20, 1967 Sept.20, 1967 Sept.23, 1967 April 21, 1968 Sept.25, 1968 April 1, 1972 April 2, 1972 April 2, 1972
0939:14.86 1030:55.03 0702:06.37 1643:18.01 0702:50.91 2351:23.27 0017:45.25 0039:01.10
49.946øS 49.975øS 49.882øS 56.625øS 46.700øS 49.655øS 49.713øS 49.730øS
163.537øE 163.353øE 163.685øE 157.658øE 166.446øE 163.577øE 163.761øE 163.681øE
0.46 0.78 0.66 0.99 0.77 0.68 0.64 0.65
5.5 9.4 8.9 12.2 12.1 9.9 9.5 9.2
9.8 15.9 16.4 37.9 18.1 18.4 16.6 18.0
343ø 356ø 343ø 354ø 347ø 2ø 357ø 355ø
Dec. 24, 1972 Oct. 19, 1973
2030:57.65 0013:00.77
52.541øS 54.933øS
160.487øE 158.124øE
0.87 0.66
6.2 8.6
15.3 24.5
352ø 352ø
April 6, 1974
1216:23.55
49.183øS
164.366øE
0.93
10.2
16.5
352ø
June 5, 1974
1144:19.93
54.824øS
158.630øE
0.59
7.7
24.9
358ø
Sept.16, 1975 July21, 1977 July,21, 1977 May 24, 1978 April 23, 1979 Aug. 11, 1979
0000:49.87 1153:21.18 1234:31.14 0612:01.84 2154:38.04 0514:38.38
47.472øS 54.101øS 54.068øS 53.258øS 53.257øS 52.147øS
165.097øE 158.678øE 158.247øE 159.131øE 158.902øE 160.997øE
0.73 0.66 0.80 0.87 0.95 0.58
11.3 8.4 9.1 8.3 12.0 3.8
17.9 25.7 29.6 26.6 40.3 9.4
355ø 347ø 340ø 351ø 356ø 345ø
Feb. 7, 1980
1059:12.85
54.458øS
158.645øE
0.77
9.1
29.2
345ø
May 30, 1981
0947:18.79
49.301øS
164.317øE
0.53
6.0
11.0
358ø
June27, 1982
1617:16.84
55.611øS
160.070øE
0.92
12.2
37.5
352ø
July7, 1982 May 23, 1984 Sept.3, 1987 Sept.3, 1987
1043:06.07 0516:36.95 0640:13.24 0801:35.71
51.478øS 52.010øS 58.971øS 59.637øS
160.121øE 160.945øE 158.578øE 158.976øE
0.90 0.85 0.82 0.71
10.0 8.9 9.7 8.8
26.0 20.6 30.1 27.0
350ø 347ø 351ø 352ø
Gapb
94 ø 99 ø 125 ø 89 ø 99 ø 133 ø 132 ø 91 ø 94 ø 85 ø 85 ø 91 ø 91 ø 131 ø 91 ø 133 ø 131 ø 85 ø 90 ø 139 ø 139 ø 88 ø 132 ø 110 ø 133 ø 95 ø 85 ø 94 ø 137 ø 139 ø
C
A B B A B B B A B A A A A B A B B A A B B B B A B B B B B B
aErrorellipseparameters are sizeof minor(a-) andmajor(a+) axis,with azimuthangleof majoraxis.
bGapismaximum azimuthal gapin station coverage. CQis overallqualityof relocatedepicenter(seetext).
Discussion
Present-Day Complex
Tectonics of the Macquarie
Ridge
The principal conclusionof this studyis that the dominant mode of present-day earthquake activity along the central MRC is strike-slip. Only in the north, near Fiordland where earthquakes with focal depths as great as 150 km have occurred,do we find largeor well-determinedthrustearthquakes and other undeniable evidence of ongoing subduction; in Puysegur,morphologicaland geophysicalevidencearguesfor incipient subduction[Christoffeland Van der Linden, 1972; Collot et al., 1995] and there are focal mechanisms which have both strike-slip and thrust components. Otherwise, reported non-strike-slip mechanismsare nearly all small, complex, and/or poorly determined,commonly non-doublecoupleswith uncertainprincipalaxis orientations.Even in the Hjort region all four better determinedmechanismsare strikeslip, although the orientation of the plate boundary suggests there may be ongoingconvergence(Figure 9). In the Puysegur subregionand in all subregionsto the south the focal depths as determinedfrom travel time analysisare poorly determined; thus they do not provide information about whether any hypocentersare deep enough (-50 km) to indicate incipient subduction.However, in all caseswhere accuratelydetermined
focal depths have been obtained from waveform modeling, they havefoundfocal depthsof 30 km or less[Braunmillerand Nabelek, 1990; Ekstrom and Romanwicz, 1990; Tichelaar and
Ruff, 1990]. Nevertheless,our analysisof present-dayfocal mechanisms does not corroborate the suggestionthat the central MRC is undergoing subductioninitiation, at least in the McDougall and Macquarie subregions. Moreover, M. F. Coffin et al. (manuscript in preparation, 1997) and C. G. Massell et al. (manuscriptin preparation, 1997) found that the active plate boundary zone along the central MRC was quite narrow (< 5 km wide), and they observedno active compressionalfeatures on the seafloor in their analysis of side-scan sonar, bathymetric,and seismicreflection data. They do report some evidence of underthrustingin the Hjort region to the south, where Ruff and Cazenave [1985] found evidence for convergencefrom analysis of geoid anomalies and historical earthquakedata. A secondconclusionof this studyis that focal mechanisms between 45øS and 61øS are consistent with an "instantaneous"
rotation pole which is significantlynorthwestof the NUVEL1 Australian-Pacific pole reported by DeMets et al. [1990], determinedby a global inversionof earthquakeand magnetic anomaly data, and producing a pole representingmotion averaged over the past 3 m.y. This conclusion is not new;
5038
FROHLICHET AL.: CONSTRAINTSON MACQUARIERIDGETECTONICS
162ø I
1.64ø
166ø
I
Macquarie Ridge
Fiordland 46 ø
WWSSN
Data
A & B Relocations
,, Puysegur /
This Study X•x• • / /
48 ø
50ø
52 ø
50ø
_
'
52 ø
ugall
54 ø
54 ø
56 ø
56 ø
58 ø
58 ø
60 ø _
Hjo
I
156 ø
60 ø
I
158 ø
I
160 ø
I
I
162 ø
164 ø
166 ø
Figure11. Epicenters of 30 earthquakes relocated in thisstudyusingtheJEDmethod (seeTable1). Map
showsall location(crosses) anderrorellipses for all A andB qualityearthquakes; theauthors personally reread
phases forall phases usedin therelocation. Thinlinesaretraces of fracture zones asdetermined by C. G. Massellet al. (manuscript in preparation, 1997)andCoffinet al. [1996].
bothRuffetal. [1989]andFalconer[1973]foundthatthepole determined from MRC earthquakesdiffered from various
globallydetermined poles.It is tempting to speculate thatthe poleof rotationhasmovedoverthepastfew millionyears;if
the pole did lie near the NUVEL-1 locationin the past,the resultingconvergentplate motioncould producelithospheric shorteningand explain the simultaneouspresenceof both anomalouslyshallowand deep bathymetryalong the MRC,
FROHLICHEr AL.: CONSTRAINTSON MACQUARIERIDGETECTONICS 'A' &
'B'
release along preexisting zones of weakness, old oceanic fracturezones.We generallyagree;our main differenceis that the marine geophysical results of C. G. Massell et al. (manuscript in preparation, 1997) give us a more accurate picture of the location of these fracture zones (Figure 11). While many of the fracture zones cannot be traced into the plate boundary, and while the earthquake locations are not numerousenoughto merit a statisticalanalysis,it does appear that many of the off-boundaryepicentersare situatedalong old
Daha
2O JED-Das
• -20
(Do •
fracture
-40
a• -80 -40
0
5039
40
Diff. in Longitude (km) Figure 12. Difference in epicentrallocationsbetween this
studyand Das [1993] for eventsof A quality (bold symbols) and B quality (light symbols).
zones.
This scenario(comparatively small earthquakesoccurring along zones of weaknessaway from the principal fault trace, where larger earthquakesoccur) is also observed in other strike-slip environments [e.g., see Stein et al., 1992]. For example, in California, the 1857 and 1906 earthquakes,with magnitudesof 8 or more, occurredon the plate boundaryon the San Andreas fault [Wesnousky, 1986]. Yet, of the 12 significant damaging California earthquakes of the 1980s, only one, the 1989 Loma Prieta earthquake,was on the San Andreas [Lay and Wallace, 1995]. Similarly, along the MRC, Das's [1993] relocationplacesthe epicenterof the great 1989 Macquarie earthquakeon the plate boundary;the trend of one nodal plane for this event [e.g., seeAnderson, 1991; Ekstrom and
Romanowicz,
1990; Satake
and
Kanamori,
features such as Macquarie Island as well as the Hjort, McDougall, Macquarie, and Puysegurtroughs.However, it seemsunlikely that a globalchangein Pacific-Australiaplate motion would go unnoticedexcept along the MRC; thus it seemsmore reasonablethat the discrepancymight be caused
1990;
Tichelaar and Ruff, 1990] is identicalto the strike of the plate boundaryas determinedby C. G. Massell et al. (manuscriptin prepration, 1997); we observesmaller earthquakesoccurring away from the plate boundary. One puzzling question about the MRC is: What specific physical or tectonic features of the region permitted the by deformationin the Australianplate west of the MRC [Minster and Jordan, 1978; DeMets, 1993; Valenzuela and century'slargeststrike-slipearthquaketo occur there in 19897 Taken as a group (Table 2), very large strike-slip quakes Wysession, 1993]. In spiteof somedifferencesbetweenthis studyand that of generally occur in one of severalcrustal/tectonicsettings:(1) Das [1993] with respect to the epicenters of individual in continental crust (California, 1906; Irian Jaya, 1938; earthquakes (Figure 12), we essentiallyagreein our overall 1979; Philippines, 1990); (2) in transpressional conclusionsabout the location of seismic activity. That is, environments,commonly at the edges of subductionzones or like Das [1993], we concludethat the majority of well-located near areasof obliquesubduction(Puysegur,1981; Hjort, 1987; earthquakes occuron, or very near to, the Pacific-Australian Gulf of Alaska, 1987; 1988); or (3) in regionscharacterizedas plateboundary(Figure11). However,bothstudiesreportsome intraplate or poorly organized plate boundaries (Prince well-located events which are not situated on the boundary; Edward, 1942; North Atlantic, 1941, 1975; North Fiji Basin, this is significantsince the two studiesutilized somewhat 1990). While the 1989 Macquarie earthquake does not fit perfectly into any of these settings, it has some features in different data and methodsfor obtainingthe relocations. What is the significance of these off-plate-boundary common with each. While MRC crust is not continental, it is earthquakes? Das [1992] suggested that seismicactivityalong thicker than normal for oceanic crust; while the predominant the plate boundary produces stresses in neighboring tectonic regime is not subduction,both the C. G. Massell et lithosphere and the off-fault earthquakesrepresent stress al. (manuscript in preparation, 1997) results and the
Table 2. SomeVery Large EarthquakesWith Strike-SlipMechanisms Date
April 18, 1906 Feb. 1, 1938 Nov. 25, 1941 Nov. 10, 1942 May 26, 1975 Sept.12, 1979 May 25, 1981 Sept.3, 1987 Nov. 30, 1987 March6, 1988 May 23, 1989 March 3, 1990 July16, 1990
Location
GeographicRegion
38.øN,138øW 5.25øS,130.5øE 37.5øN,18.5øW 50.øS,30.øE 36.øN,17.6øW 1.8øS,136.1øE 48.9S,164.4E 59.3S,158.8øE 58.9øN,142.8øW 57.2N, 142.8W 52.2øS,160.4øE 22.1øS,175.4øE 16.0øS,121.2øE
California Irian Jaya? NorthAtlantic PrinceEdwardFZ NorthAtlantic Irian Jaya Puysegur Hjort Gulf of Alaska Gulf of Alaska Macquarie NorthFiji Basin Philippines
Magnitude
MS 8.2 M S 8.2 MS 8.2 M S 7.9 MS 7.9 Mw 7.6 Mw 7.6 Mw 7.4 M w 7.9 M w 7.8 Mw 8.2 M w 7.7 M w 7.7
Reference
Lynnesand Ruff [ 1985] Okal and Stewart [1982] Lynnesand Ruff [1985] Ruff et al. [ 1989] Lahr et al. [1988] Lahr et al. [1988]
5040
FROHLICHET AL.: CONSTRAINTSON MACQUARIERIDGE TECTONICS
In remote areas like the MRC, how reliable are epicentral locationslike thoseof Das [1993], redeterminedusing arrival times taken from the ISC Bulletin? Is it necessary to personallyreread phasearrivals, as we did in this study?To answerthesequestions,it is importantto rememberthat many bulletin phasesare of uncertainquality, and this affects small, poorly recorded earthquakesmore than large events. For example, for the 53 earthquakeswe investigated,there were 585 phase arrivals which, for the stations we were investigating,we were able to read on World-Wide Standard moment release alongtheMRC was188x1019 N m, a factorof SeismographNetwork (WWSSN) microfiche, or which were about30 higherthanthe6x1019N m expected for its 3 cm/yr reportedin the ISC Bulletins [Frohlich, 1994b]. Of these, for relative motion, as determinedfrom an empirical analysis of 49% our readingswere within 1.0 s of thosein the bulletins, for 14% our readingsdiffered by more than 1.0 s, for 14% we strike-slipboundaries.Of this momentrelease,72% was from the 1989 earthquake,8% was from the 1987 Hjort earthquake, found and read phases where none were reported in the and 15% was from the 1981 Puysegurearthquake.Thus three bulletins, and for 23% the bulletins reported phase arrivals which we were unableto find when we carefullyinspectedthe earthquakesaccountedfor nearly all of the discrepancy.In light of the resultsfrom the recent geophysicalcruises(M. F. microfiche seismograms.Clearly, the fact that a significant Coffin et at., manuscriptin preparation,1997; C. G. Massell fraction of the bulletin phaseswere misreador missing will et at., manuscriptin preparation,1997) about the thick crust stronglyinfluence earthquakesrecordedby, say, 30 or fewer and piecewise transpressionatcharacter of the AUS-PAC stations;but it will have a minimal effect on large events boundary along the MRC, it now seems that it was recorded by 100 or more stations, where redundancy inappropriatefor Frohlich and Apperson[1992] to lump the compensates for dataabsences andinadequacies. MRC with other "typical" submarinestrike-slip boundaries. Rather, it may be more analogous to some of the poorly Summary and Conclusions defined plate boundariesand plate boundarysegment"edge" 1. In this study we have developednew, straightforward regions which were specifically excluded in Frohlich and statistical criteria for selecting "better determined" centroid Apperson's [1992] analysis. momenttensorsfrom compilationsof earthquakemechanisms Analysis of Earthquake Catalogs suchas the Harvard catalog. 2. Among better determined Harvard mechanisms for One novel feature of this study is that we propose earthquakes along the Macquarie Ridge Complex, thrust straightforwardstatisticalmethodsfor selectingthe better mechanisms occur predominantly north of 49øS, near determined focal mechanismsfrom the CMT catalog. While thereare variousacceptedtechniquesfor evaluatingthe quality Fiordland;farther southvirtually all mechanismsindicate that of catalogedearthquakelocations[e.g., Cardwell and Isacks, present-daymotion along the plate boundaryis strike-slip. 3. If we use slip vectorsof theseearthquakesto determine 1978; Burbachet al., 1984] and magnitudes[e.g., Habermann, an "instantaneous" local pole of rotation for plate motion, the 1982, 1987], there are no standardmethodsfor evaluating the best fitting pole is at 57.4øS,179.4øE,about 2.5ø northward of quality of cataloguedfocal mechanisms.We submit that selection should be a part of every tectonic analysis using the NUVEL-1 Australian-Pacificpole, which representsplate cataloguedmechanismssince,inevitably, earthquakecatalogs motion averagedover the past 3 m.y. 4. Careful relocationsof 53 earthquakesusing personally contain entries of varying quality. Since different catalog users have different objectives, it is desirable for catalog rereadteteseismictravel timesindicatethat mostlie on or very close to the Australia-Pacificplate boundary;however, a few producersto includeas many eventsas possible;but it is the epicenters do occur well away from the boundary,apparently responsibilityof usersto selectdata which are of sufficient
discrepancybetween the locally determined and NUVEL-I poles suggestthe region has undergoneplate reorganization, possiblyassociatedwith local transpression (Figure 9). Finally, why has post-1977 moment release rate per kilometer of plate boundarybeen so much higher along the MRC than along other submarine strike-slip boundaries? Partly, this is becausethe recenttime periodjust happenedto capture the very large 1989 event, which presumablyhas a centuries-long repeatperiod.However,Frohlich and Apperson [1992] found that between 1977 and 1990 the strike-slip
quality for their particularobjectives. In this paper we select better determinedmechanismsby using three simple statistics.Of these, the relative error E essentiallymeasuresthe signalto noise ratio in the data used
on Cenozoic
fracture zones.
5. Along the centralMacquarieRidge Complex (50øS-57øS) the present-daymodeof deformationappearsto be strike-slip faulting; we find no geophysicalor seismologicalevidence in theinversion, nfree indicates whether theinversion contains suggesting that there is ongoing subduction, incipient subduction,or transpressionin this region. any information about the most nearly vertical principal axis (T, B, or P), and fclvd measuresto what extent the data constrainthe orientation of the two weaker principal axes (B Acknowledgments. Partial supportfor this researchwas provided and T, or B and P). Incidentally, in the Macquarie region, by the Air Force Office of ScientificResearch(contractsF19628-91-Kmagnitudestrongly affected whether mechanismssatisfy our 0026 and F49620-94-0287, and PhillipsLaboratoryTask 2309G2) and arbitraryrequirementsfor E andnfree;all 36 of the earthquakes by the National ScienceFoundation(grantsEAR-91-05069 and OCE-
with E < 0.15 and nfree= 6 had magnitudesof 5.5 or greater, while 24 of the 29 remainingearthquakeshad magnitudesof 5.5 or smaller. Moreover, while the Macquarie region is seismologicallyremote, the proportionsof the 65 available mechanismsthat satisfiedthe E and nfreerequirements(55%) and thefclvdrequirementas well (40%) are not much different than the proportionsfor the 12,414 mechanismsin the entire Harvard catalog,55% and 46%, respectively.
92-16873). We thank Jean-Yves Collot, Shamita Das, Jean-Fred Lebrun, Larry Ruff, and Joanne Stock for their comments and encouragements. University of Texas Institute for Geophysics contribution number 1255.
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