The 1964 Prince William Sound Earthquake Joint Inversion of Tsunami and Geodetic Data

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. BI, PAGES 523-532, JANUARY 10, 1996

The 1964 Prince William Sound earthquake: Joint inversion of tsunami and geodetic data

JeanM. Johnsonand Kenji Satake • Departmentof GeologicalSciences, University of Michigan,Ann Arbor

Sanford R. Holdahl NationalGeodetic Survey, Coast and Geodetic Survey, National Ocean Services, NOAA, SilverSpring, Maryland

Jeanne Sauber GeodynamicsBranch, Dab for TerrestrialPhysics, NASA GoddardSpace Flight Center, Greenbelt, Maryland

Abstract. The 1964 PrinceWilliam Sound(Alaska) earthquake, Mw=9.2, ruptured a largearea beneaththe continentalmargin of Alaskafrom PrinceWilliam Soundto Kodiak Island.A joint inversionof tsunamiwaveforms and geodetic data, consisting of verticaldisplacements and horizontalvectors, gives a detailedslip distribution. Two areasof high slip correspondto seismologicallydetermined areas of highmoment release: the PrinceWilliam Soundasperity with averageslip of 18 m andthe Kodiakasperity with averageslip of 10 m. The averageslip on the faultis 8.6 rn andthe seismicmoment is estimatedas 6.3x1022 N m, or over75% of theseismic momentdetermined from long-periodsurface waves.

Introduction subductingYakutat terrane is the Alaskan megathrust,or the plane on which the 1964 earthquakeoccurred. Their work The March 28, 1964 Prince William Sound (Alaska) shows the Yakutat terrane as a low-velocity layer overlying earthquakeruptured an 800-kin-long segmentof the Alaska the higher-velocityPacific oceanic crust. Beneath Prince subductionzone where the Pacific plate is underthrusting William Soundthis lower-velocitylayer extendsto a depthof beneaththe North American plate. The epicenter,61.04øN, approximately 20-25 km, while the Pacific oceanic crust is 147.73øW [Sherburne et al., 1969], is locatedin southcentral deeper,at approximately30 kin. The focal mechanismsof the Alaskaabout half way betweenAnchorage and Valdez, but the 1964 earthquakeand its aftershocks,which show low-angle aftershockarea extends 300 km eastto Cape Yakatagaand 800 thrusting, and the aftershock distribution [Stauder and km southwest to Kodiak Island (Figure 1). The seismic momentof the eventis estimatedas 8.2x1022N m, Mw=9.2 Bollinger, 1966] are compatible with the interpretationof Brocher eta/. [1994]. [Kanamori, 1977], making it one of the largestearthquakes Coseismic crustal deformation occurred throughout the ever recorded, secondonly to the 1960 Chile earthquake, source area, causing extensive damage in Alaska. Soon after Mw=9 .5 . the earthquake,the vertical and horizontaldisplacements were The tectonicsetting of the PrinceWilliam Soundearthquake measuredand compiled by many surveyteams. Vertical uplifts is complex. The Pacific plate is subductingin a north- averaged2 m and reached a maximtun of 11 m on Montague northwestdirection at about 6 cm/yr [DeMets et al., 1990]. Island [Plafker, 1969]. Maximum vertical subsidencewas Microearthquake studies [Page et al., 1989; Pulpan and approximately2 m. Horizontal displacementsof up to 25 m Frohlich, 1985] and reflection and refractionstudies [Brocher were observed in Prince William Sound [Parkin, 1969]. The et al., 1994] havedelineated the structureof the plateinterface vertical deformation of the seafloor in the Gulf of Alaska and the subductingslab. The plate interface, which in the generated a tsunami which devastatedseveral Alaskan towns, Kodiak Island area is dipping about 8ø-10ø , becomesvery causeddamage in Hawaii (4 m maximum run-up) and on the shallowand broad in the PrinceWilliam Soundarea, having a west coast of North America (13 fatalities, average maximum dip of 30-4ø . Furthercomplicating the tectonicsis the presence run-up 2 m, maximum run-up 5 m in CrescentCity, CA), and of severalaccreted terranes [Jones et al., 1987]. The youngest was observedas far away as Australia and Antarctica.It is this of theseis the Yakutat terrane,which is in the final stagesof tsunami and geodetic data which we use to estimate the slip emplacement against southern Alaska. Recent modeling of distributionof the Prince William Soundearthquake. wide angle refraction and reflection data by Brocher et al. [1994] has suggestedthat in PrinceWilliam Soundthe contact between the overlying North American plate and the Previous Seismic Studies

Although the 1964 earthquakeoccurred in the World Wide •Nowat GeologicalSurvey of Japan,Tsukuba. StandardSeismograph Network era and thereforewas recorded Copyright1996 by theAmerican Geophysical Union. on high-quality instruments, the enormous size of the event causedmost instrumentsto go off-scale soon after the first P Paper number95JB02806. wave arrival. This is true of instruments in the teleseismic 0148-0227/96/95JB-02806505.00 distancerange of 30ø-90ø;therefore, there is a lack of body

523 524 JOHNSONET AL.: 1964PRINCE WILLIAM SOUNDEARTHQUAKE

162ø 160ø 158ø 156ø 154ø 152ø 150ø 148ø 146ø 144ø 142ø 140ø 138ø

62 ø b•* .'• PRINCEWILLIAM SOUND EARTHQI•AKE 62 ø I• ßF + + øø * o ...... o • / ß •'•* ß ...... •.•.•,• •,•. . • :.. . 60 ø Ken•me•nsula••• 60 ø • • ••: *'"••f:•"•:•••:::' :* [.•' :Cape Yakataga

58 ø ßß • o•oOo • .o ,. o , . 58 ø

., -0 %.• om• øo

•o ß '

56 ø 56 ø ß '•' ß • , • , • , • 50 0 50100 150 1•0ø 1•8ø 156ø 154ø ld2ø 150ø 148ø 146ø 1• ø 1•2ø 1•0ø

Figure 1. Aftershocksof the 1964Prince William Sound earthquake located between March 28, 1964and December31, 1965(after Algermissen et al., 1969).Hachured area indicates the Prince William Sound asperity asdetermined by Ruff andKanamori [ 1983].

wave data that can be usedto studythe momentdistribution of Sound,one in the Kodiakarea, and a fourthfor the PattonBay the earthquake.Ruff and Kanarnori [1983] overcame this uplift. This inversionis an improvementon the singlefault difficultyby usingP wavesdiffracted by thecore. They were model,but it doesnot give any indicationof slip variationsin able to obtain a source time function for the event and estimate the down dip direction.Most recently,Holdahl and Sauber the location of the main moment release. Their results show a [1994]have used the geodeticdata to invertfor a detailedslip large area of momentrelease covering the entire Prince distribution on 68 subfaults. This inversion shows the Prince WilliamSound area (Figure 1); thisis usuallyreferred to asthe William Soundasperity as a regionwith slip varyingfrom 10 "PrinceWilliam Sound"asperity. Kikuchi and Fukao [1987] to 30 m (Figure 3). Holdahl and Sauber'sresults also show a invertedseveral partially clipped P waveformson horizontal componentsto locateseveral subevents on the rupturesurface. They also found most of the moment releaseto have occurred MARCH 28, 1964 ALASKA EARTHQUAKE in the epicentralarea. Recently, Christensen and Beck[1994] ._Z2'15 have located a secondarea of high moment release in the ß 10 KodiakIsland area (Figure 2). The secondasperity will herebe called the Kodiak asperity. ß 5 E While thesestudies do give a clear indicationof where the o highestmoment release, and by implicationthe highestslip, • 0 600 400 200 0 200 occurred,they give only a minimum estimateof the moment Km Along Fault Strike and a lower bound on the average slip due to the use of March 28, 1964 diffractedor clippedwaveforms. Although Kikuchi and Fukao Mainshock [1987] estimatedthe slip distributionin the down dip Alaska (Mw=9.2) direction,teleseismic body wavesusually have poor depth resolution.To morereliably estimate the moment and the slip 60øN distributionin the down dip direction,we must turn to other sources of data. Prince William Bedng Sea Sound Asperity Previous Geodetic Studies KodiakAsperity 56 ø 1900 Thereis an enormousbase of geodeticdata from the Prince 1854 1844 Gulf of Alaska William Sound earthquake.Much of it was collected and describedby Plafker [1969]. This data, which is describedin the inversionsection, was usedsoon after the earthquaketo 160 ø 150øW estimatethe fault parametersand slip by Savageand Hastie Figure 2. Asperitydistribution determined by Christensen [1966]and Hastie and Savage [1970]. They estimated the slip and Beck [1994]. The upperfigure showsthe along-strike on a singlefault plane as approximately 10 m. Theyincluded a momentdensity in unitsof 1026 dyne-cm/km.The lower figure small secondaryfault to explain the Patton Bay uplift. shows the map view of the asperitiesdetermined from the Miyashitaand Matsu'ura[1978] invertedthe geodeticdata to upper figure. The datesof historic earthquakesin the Kodiak determinethe slip on four fault planes'two in PrinceWilliam segment are listed. JOHNSONET AL.: 1964PRINCE WILI•AM SOUND EARTHQUAKE 525

158øW 138øW earthquake,the tsunamidata cannotprovide any constrainton Fairbanks 66ON estimatesof the slip which occurredon the landwardpart of the fault.

Joint Inversion

The limitations discussed previously for each of the inversion methods demonstrate the necessity for a more comprehensiveapproach if we wish to determine the slip distribution on the entire 1964 fault zone. Satake [1993] introduceda method for inverting tsunami and geodeticdata simultaneously for the complete down dip slip distribution, usingthe 1944 Tonankaiand 1946 Nankaidoearthquakes as an example. This method is eminently suitable for earthquakes '...•Anch, which occur in subduction zones adjacent to continental margins.As long as sufficient geodeticand tsunamidata exist, ß Tide Gauge the entire slip distribution of the earthquake can be - Leveling determined. This approach is different than HoldaM and • Triangulation Sauber's [1994] using geodeticdata and a priori information 56ON from tsunamis.In the joint inversion, all the data must be satisfied simultaneously. Slip in meters I 1 Data 0-5 5-10 10-15 15-20 20-25 25-30 The tsunami generated by the Prince William Sound earthquakewas recorded on analog tide gaugesat points all Figure 3. Slip distributiondetermined from geodeticdata aroundthe Pacific, at stationswhich are a part of the Seismic (from HoldaM and Sauber, 1994). Sea Wave Warning System (now Pacific Tsunami Warning System). We chose a wide distribution of these records from Alaska, North America, the Pacific Islands,and Japan(Figure regionof high slip east of Kodiak Island, but this slip is not a 4). Many have been publishedin a report on the tsunamiby resultof the geodeticinversion, as will be explainedbelow. Spaeth and Berkman [1972]. We obtained the original tide There is a serious limitation to using geodetic data to estimate the slip distribution. Geodetic data gives very good gauge records and digitized them at 1 min intervals. We controlon slip occurringon the landwardpart of the fault, but, removed the tidal component and applied clock corrections as is typicalof subductionzone earthquakes, a greatpart of the where necessary. slip occurson the oceanicpart of the fault plane. The fact that There are a wide variety of geodeticdata in the form of point observations taken all over southern Alaska, the islands in a large tsunami was generatedshows that significant slip occurred beneath the continental shelf in the Gulf of Alaska. Prince William Sound, and Kodiak. In this study, we used a subsetof the data used by HoldaM and Sauber [1994]. This Geodeticdata is unableto constrainthe estimatesfor this slip. in thestudy of Holdahland Sauber, the slip on over a thirdof includestwo data types, verticaldisplacements and horizontal the subfaultscannot be determinedsolely from the geodetic vectors. The vertical data include (1) displacementsof tide data. Holdahl and Sauber used slip estimatesprovided by gauges, (2) repeated leveling surveys, and (3) geologic data preliminary tsunamimodeling by Johnsonand Satake [1993a] including changesin growth limits of coastalmarine species, as a priori information. Without this information, there would beach markers, and bathymetric surveys. The horizontal have been no constrainton the slip valuesnear the trench. vectors are computed from preseismic and postseismic triangulationsurveys. A completedescription of the geodetic data and a reference list can be found in HoldaM and Sauber Previous Tsunami Studies [1994]. The source area of the 1964 tsunami has been estimated Fault Model previouslyby Pararas-Carayannis[1967] andHatori [ 1981]by backwardpropagation of the tsunami travel times from tide The subfault model used in the joint inversion is a gauge stationswhere the tsunami was recorded. Their estimates simplified version of the model used by Holdahl and Sauber show that the major tsunamiwhich swept the Pacific was [1994]. They used a mosaic of 68 small (-50 by 50 kin) generatedmainly from uplift of the continental shelf in the subfaults, 28 spanning the area from Kodiak to the Kenai Gulf of Alaska. No one, however, has previously used the Peninsulaand 39 coveringPrince William Soundand the Gulf tsunamiwaveforms to estimatethe slip distribution.Johnson of Alaska out to the Alaskan trench. One additional subfault is and Satake [1993a] did a preliminaryinversion of the data to includedto representthe PattonBay fault on MontagueIsland. estimatethe offshoreslip, and the resultsshow large slip near We modified this subfault model in several ways. First, we the trench in the Gulf of Alaska off the Kenai Peninsula and merged sets of four subfaultsinto a single subfault to reduce near Kodiak Island. Althoughfar-field tsunamidata have been the computational effort needed to generate the tsunami used to estimate the slip distribution of other Alaskan- Green's functions.The presentmodel includeseight subfaults Aleutianearthquakes which had no landwardextension of slip in the Kodiak area and nine in the Prince William Sound/Gulf [Johnson and $atake, 1993b, 1994], in the case of the 1964 of Alaska area. We also includedthe PattonBay subfault.The 526 JOHNSONET AL.: 1964PRINCE WILLIAM SOUND EARTHQUAKE

ComputationArea andTide GaugesUsed in Inversion

220'W 200'W 180'W 160'W 140'W 120'W

60'N ' 60'N

,•IJnalaska

,' ß Neah Bay PACIFIC OCEAN

Miyako nO'N Fort Rincon Is anta a Joll: ,

20'N ß Wake •'• Hilo 20'N

ß' Guam I I ' I NawiliwiliI HonoluluI I ] 220'W 200'W 180'W 160'W 140'W 120'W

Figure 4. Computationarea for 1964 tsunamiand locationsof tide gaugestations used in this study. subfault locationscan be seen in Figure 9, and the fault have more variable mechanisms; therefore, the subfaults in parametersare listedin Table 1. Next, we modifiedthe depths this area have motion aligned with the direction of Pacific of the subfaults. Holdahl and Sauber'spreferred model is plate motion, approximatelyN17*W in PrinceWilliam Sound. consistent with rupture between the North American and This means that the motion is mainly dip-slip, with a small Pacific plates in Prince William Sound, hencethe subfaultsare (<20%) left-lateral strike-slip component. deeperand dipping more steeplythan the inferredrupture plane This modelexplicitly assumes that underwaterlandslides or suggested by Brocher et al. [1994], described earlier. slumpingwere not importantfactors in the generationof the Therefore, we chosethe depth and dip of the subfaultsto be major tsunamiwhich sweptthe Pacific. It is well established consistentwith ruptureon the Yakutat terrane-NorthAmerican that several submarine landslides caused devastating local plate interface. The faults in the Kodiak area (a-d and h-k) are tsunamis in several locations in southern Alaska, most 100 km by 100 km and dip 8*. The faults in the PrinceWilliam notablyin Valdez Arm and ResurrectionBay [Plafker, 1969], Sound area are approximately 100 km by 100 km, but are but theprincipal trans-Pacific tsunami was caused by themajor slightly smallernear the trench and slightly larger along the tectonicuplifts associatedwith faulting. coast.Subfaults e, f, and g dip 8*, therest dip 3*. Green*s Functions The directionof slip for each subfaultis determinedby one of two methods. The aftershocks in the Kodiak area have Given the abovefault model, we specifyunit displacement almost pure dip-slip mechanisms [Stauder and Bollinger, on each subfault. The vertical and horizontal deformations are 1966]; therefore,the subfaultsin this area have pure dip-slip calculatedusing the equationsof Okada [1985]. For the motion. The aftershocks in the Prince William Sound area geodetic Green's functions, we compute the vertical and

Table 1. Fault Plane Parameters

Subfault Latitude, Longitude, Depth, Length, Width, Strike, Dip, Rake, øN øW km km km deg deg deg

a 56.43 150.95 3 100 100 218 8 90 b 56.97 150.13 3 100 100 218 8 90 c 57.67 149.10 3 100 100 218 8 90 d 58.38 148.05 3 lO0 100 218 8 90 e 58.58 146.63 2 90 100 230 8 62.87 f 58.95 145.45 I 90 100 242 8 75.02 g 59.17 144.12 1 90 100 256 8 87.44 h 56.98 152.50 17 100 100 218 9 90 i 57.52 151.33 17 100 100 218 9 90 j 58.22 150.30 17 100 100 218 9 90 k 58.93 149.28 17 100 100 218 3 90 I 59.32 147.62 16 120 100 229 3 64.16 m 59.77 146.13 15 120 100 241 3 74.15 n 60.03 144.40 15 120 100 256 3 86.38 o 60.35 148.92 21 130 100 219 3 65.92 p 60.57 146.73 20 130 100 241 3 73.33 q 60.92 144.65 20 130 100 256 3 85.56 r 60.05 147.33 0.1 72 30 219 60 90

The latitude,longitude, and depthare given for the referencepoint at the top cornerof the fault. In this case,the referencepoint is the easternmostof the subfaultcorners. The lengthis alongstrike, the width is down-dip.The strike direction is measured from north. JOHNSONET AL.: 1964PRINCE Wll J IAM SOUND EARTHQUAKE 527

horizontal displacementdue to each subfault at each point be determined by minimizing the weighted sum of the (latitude and longitude) where there is a geodeticobservation. residuals, that is, For the tsunami Green's functions, we use the vertical deformation due to each subfault as the initial condition for ßx- + .x- -->rain tsunamipropagation. The equationof motion and equationof IIAT bTI 2%In G continuityfor a small amplitude,linear long wave are where A is the matrix of Green's functions, either a vertical or horizontaldisplacement for the geodeticdata or a waveform 312=-gdVh and 3h for the tsunami data, b is the matrix of observations,and x is the matrixof unknownslip values.The superscriptsG andT where g is the accelerationof gravity, h is the water height refer to geodetic and tsunami, respectively,and )• is a displacedfrom the equilibrium position, d is the water depth, weighting factor. This weighting factor has the effect of and {• is the flow rate vector. Using digital bathymetryof the normalizingthe power of the different data sets,preventing Pacific Ocean, we solve the equationof motion and equationof one or other of the datasets from entirely controlling the continuity by a finite difference computationon a staggered solution. In this case, two different weighting factors were grid systemusing a 5'x5' (-10 kin) grid. To ensurean accurate appliedto the geodeticdata, one for the verticaldata and one syntheticwaveform, we switch to a l'xl' (<2 kin) grid system for the horizontal data. The vertical weighting factor was 65, along the westerncoast of North America, aroundthe Hawaiian the horizontal weighting factor was 28. and Alaskan-Aleutianislands, and aroundJapan. Several tide We inverted23 tsunamiwaveforms with an averageduration gauges, such as the Canadian, Mexican, and Pacific Island of 100 min, 188 vertical and 292 horizontal geodetic stations, are in the 5'x5' grid system. An example of the observations.The total number of data points is 2797. The synthetic waveforms from each of the subfaults for the tide slip valuesobtained are listed in Table 2. We also applieda gauge at Sitka can be seen in Figure 5. The subfaultsnearest nonnegativityconstraint on the inversion.The resultingslip the trench (a-g) have the largest amplitudes for the tsunami values are also listed in Table 2. The variance reduction of the Green's functions. least squaresinversion is 60%. The only major difference As it was difficult to separatethe deformationdue to the between the least squares and nonnegativeleast squares major underthrustingfrom the local deformation due to the inversionsis the slip value for subfaulta, which is on the edge Patton Bay fault, we inverted only for the 17 major subfaults of the subfaultarray. The observedand computedwaveforms on the megathrust.To remove the effect of the subsidiary are shown in Figure 6. Figure 7 showsthe observedand faulting, we assumeda slip of 8.5 m from Holdahl and Sauber residual vertical deformations.Figure 8 shows the observed [1994] as the slip amount on the Patton Bay fault, calculated and computedhorizontal vectors. the deformationdue to this slip, and subtractedit from all the If we examinethe observedand syntheticdata, or residuals geodetic observations. The contribution of this fault to the in the case of the vertical data, we can see how well the model tsunamiwaveforms was small enoughto be neglected. explainsthe data.In the caseof the verticaldata, the residuals

Inversion Results Table 2. Slip Distributionof 1964 PrinceWilliam Sound We assumethat the observedgeodetic data and the tsunami Earthquake waveforms are a linear superpositionof the Green's functions, so the least squaressolution for the slip on each subfaultcan SUp SUp Subfault NonnegativeLS, Errors, LeastSquares, Errors, m m m m

GREEN'S FUNCTIONS FOR SITKA, ALASKA a 0.0 0.0 -6.5 2.9 Subfault a b 5.5 1.3 9.7 3.6 c 14.5 2.4 13.3 4.1 d 0.7 1.1 1.1 2.7 e 18.5 2.7 20.5 3.4 f 10.8 2.7 10.3 3.5 f g 4.1 1.1 4.1 5.8 g h 4.1 0.0 3.2 9.4 h i i 0.0 0.7 -1.3 2.9 J j 4.6 0.7 5.7 4.3 k k 8.0 2.0 8.2 3.7 I I 22.1 4.6 22.1 4.4

m m 17.9 1.8 17.7 1.8 n n 5.7 1.3 5.6 1.2 o o 0.7 0.9 0.6 1.2 p p 20.9 1.1 20.1 1.1 q 7.9 0.4 7.9 0.4 r r 8.5* 8.5* I i I z I i I i I [ I [ I i I • I time, hour 0 2 4 6 8 Average 8.6 8.4

Figure 5. Synthetictsunami waveforms for each subfaultfor *Value derivedfrom inversionof geodeticdata only [fromHoldaM Sitka, Alaska tide gaugestation. and Sauber, 1994]. 528 JOHNSONET AL.:1964 PRINCE WILLIAM SOUND EARTHQUAKE

100[Unalaaka 100- Wake 100 _ Torino,B.C. o 0•__ , '••.'•.,, 0 ...... 0 100-0 ....Silk& AK•;..•, '.• 100 O-•,;•v'•.Nawiliwili,HI ß 1000 NeahBa;.:,y.• 100"""N••' •]•'•:'•100kEnsenada .A 100FridayHarbor,WA

i i i i ß " .øtß ß ß , '-:',-':I'f.,i I i i i o......

time, min

0 ....

100 AlarnitosBay, CA

lOO La Jolla lOO Miyako,Japan 0 ...... -

100 Santa Monica lOO

0 2 608•) 1201 0 20 60801 120140 0 2040 6080 100 120 140 time, min

Figure6. Observedand synthetic waveforms from nonnegative least squares joint inversion of tsunamiand geodeticdata. The start time for each waveform is different.

showthat the extremely large uplifts have been matched to a of therupture area. Slip values in theKodiak area are generally certainextent, but thatlarge residuals remain, mostly near smaller,but thereis a patchof highslip on subfaultsb andc. PrinceWilliam Sound. There are several reasons for this.First, We performeda secondinversion using a subfaultmodel theextent of thePatton Bay fault is notwell known; therefore, basedon the depthsand dips of the originalHoldaM and the subfaultparameters may havebeen inaccurate. Also, it is $auber[1994] model. The results are very similar to theresults difficultto separatethe upliftsthat occurred due to the Patton of the above inversion, but the residuals for the vertical Bayfault from the general uplift associated with the faulting deformationinland on the Kenai Peninsulaand alongthe on the megathrust.Last, the subfaultsused in the inversioll levelingline in interiorAlaska are largerby a factorof about may be largerthan the scaleof slip variability,leading to 2. This indicatesthat the shallower,less steeplydipping incompatibilitybetween observations as seenon the scaleof subfaultsare a bettermodel of the earthquakefault plane and the subfaultsin this model. The horizontal observationsare supportsthe hypothesisthat the 1964 earthquakewas also well matched, althoughthere are some differences underthrustingon the North America•akutat terraneinterface. betweenthe directions of theobserved and synthetic vectors. The averageslip on the entire fault area is 8.6 m. If we Thismay be dueto the fact thatthe slip directionof the consider the Kodiak subfaults as one tectonic block, the subfaultsin ourmodel was determined by platemotions rather averageslip on this block is 4.7 m. The averageslip on the than the slip vectorof the earthquake,which is not well Prince William Sound block is 12.1 m. If we consider subfaults known. The main featuresof the tsunamiwaveforms, e, f, 1,m, andp to be thePrince William Sound asperity, then especiallythe longperiod component, are well explained, the averageslip on thisasperity is 18 m. The averageslip on thoughthe amplitudes of the synthetics are generally less than the Kodiak asperity,subfaults b and c, is 10 m. The total fault the observed.The samecauses for mismatchas listedabove for area is approximately184,000 km 2. Usinga rigidityof the geodeticdata can explain the waveformmismatch. 4x101øPa, the seismic moment estimated from this slip model Theslip distribution from the nonnegative least squares is 6.3x1022N m (Mw=9.2),which is 77%of thetotal seismic solutionis shownin Figure9. It is immediatelyobvious that moment estimated from the long-period surface waves thereis anenormous area of highslip concentrated over Prince [Kanamori, 1977]. WilliamSound and extending tothe trench. The slip values are Errors higheston subfaults1 and p withslightly smaller slips on Previousstudies of the slip distribution,particularly the subfaultse,f, andm. The slip values decrease toward the edges geodeticstudies, have includedonly a formal estimateof the JOHNSON ET AL.: 1964 PRINCE WIIJ IAM SOUND EARTHQUAKE $29

156'W 152'W 148'W 144'W 140'W 156'W 152'W 148'W 144'W 140øw 64'N 64'N ß[ I I I 64'N 64'N [ • I Obs'd:VerticalMovements Obse'rved Vertictil M0veme'nts

(a) GeologicData (c) TidGaugesand Line -•..,;.••,.. .. • .. •'• ,.. ...- , ..,. • -;/;'...... :.. ..,.•7• •,

60'N 60'N 60'N 60'N

oO 56'N 56•N 56'N 56øN 156'W 152'W 148'W 144'W 140'W 156'W 152'W 148'W 144'W 140øW

140'W 64'N

60øN

56'N 141)øW

Figure 7. (a) Observedvertical geodetic data from geologicsources. (b) Residualvertical geodetic data from geologic sources.(c) Observedvertical geodeticdata showingtide gauge displacementsand changesin repeatedleveling measurements. (d) Residualvertical geodetic data for tide gaugesand leveling line.

errorsin the solutions.This studygives the first rigorouserror unconstrained and nonnegative least squares inversions are analysis.To estimatethe errors of the slip distribution,we listed in Table 2. The errorsfor the least squaresinversion are employeda modifiedjackknifing technique,similar to that of the orderof a few metersand are slightlyless for the describedin Tichelaarand Ruff [19891.As thereare two quite nonnegativeinversion. The errors clearly show that the areas distinct data types involved in the inversion, we chose a of high slip determined from the joint inversion are real "delete-half' jackknife as the most reliable method. In this features.The large asperityin Prince William Sound and the method, half the data is deleted and the remainder reinverted for smallerasperity off Kodiak Island are well resolvedfeatures of a new slip distribution.To be a true delete-halfjackknife, all the coseismicrupture of the 1964 earthquake. possiblecombinations must be tried to give the true errors.As Comparison with PreviousStudies the numberof possiblecombinations was too large to be computationallyreasonable, we did 25 different reinversions. We can comparethe resultsof the joint inversionwith the For eachjackknife inversion,we randomlychose one half of results of previous works, particularly the recent works of the geodetic data and 12 of the 23 waveforms, always HoldaM and Sauber[1994] and Christensenand Beck [1994]. attemptingto maintain a semblanceof the completestation Thesestudies represent the mostdetailed geodetic and seismic distribution. The standard deviation of the values for each work to date..Theresults of Christensenand Beck give only a subfault of the these 25 inversions is the error for the general idea of the locations of high moment release. The inversion using all the data. The errors for both the Prince William Sound asperityis an unquestionablefeature. 530 JOHNSON ET AL.: 1964PRINCE WILLIAM SOUND EARTHQUAKE

Horizontal Movements that the Prince William Sound and Kodiak blocks are separate plate segmentswith differing ruptureprobabilities [Nishenko, 1991; Bufe et al., 1994]. Indeed, the historicrecord suggests that the Kodiak segmenthas ruptured both independentlyand together with segmentsfurther to the west along the Alaska Peninsula [Davies et al., 1981]. The resultsof the joint inversiondo supportthe division of the 1964 rupturezone into two differentsegments. The Kodiak

62'N - 62'N block has, on average, much lower slip than the Prince William Sound block. The difference could be due to several factors or a combination of them. First, the geometry of subduction in the Gulf of Alaska "comer" causes the slab to fiattenunder Prince William Sound[Creager and Chiao, 1992]. This causes the plate interface to have a larger surface area 61'N 61'N [Davies and House, 1979], and this may be responsiblefor highercoupling in the Prince William Soundblock. A second importantfactor is the presenceof the Yakutat terrane.As less dense continental crust [Brocher et al., 1994], it would resist subductionand produce higher coupling with the overlying plate. In contrast,in the Kodiak segment,the plate interfaceis 60'N 60'N narrowerand typical oceaniccrust is subducting. From these results, it is necessaryto assessthe seismic hazards for the Kodiak and Prince William Sound block separately.While all estimatesof the recurrenceinterval for Prince William Sound suggestthat anotherearthquake similar to the 1964 earthquakemust be unlikely for several centuries [Nishenko, 1991], the same is not true of the Kodiak segment. Estimates for the recurrence interval are as low as 60 years [Nishenko, 1991]. If this is so, a large or even great Figure 8. Observedand synthetichorizontal vectors. earthquakecould be likely within the next 50 years. Tsunami hazards must also be considered.Coseismic slip during subduction zone earthquakes has been previously Christensenand Beck, however, have identified a second area characterized as having a seismic and aseismic component, of high moment release centered on Kodiak Island and extending to the trench. This feature is similar to the smaller 138øW area of high slip derived from the joint inversion, but its 66øN locationdiffers. The Kodiak asperityas determinedby the Fairbanks joint inversion lies to the east of Kodiak and closer to the trench. The difference in the location may be due to the uncertaintiesin the rupturevelocity used by Christensenand Beck. ALASKA It is difficult to view the geodetic inversion results of HoldaMand Sauber[1994] independentof thejoint inversion results, particularly since the geodeticinversion relies on Anchorage information obtained from tsunami studies. The joint inversionresults are clearly very similar to the geodetic inversion results. Both show the Prince William Sound asperityas a region of high, but variable,slip. The slip in bothmodels is low alongthe easternand southwesternedges of the aftershockzone (though the model of Holdahl and Saubershows a small areaof high slip at the easternterminus of rupture),and bothmodels show low slip betweenthe Prince William Soundand Kodiakasperities. The Kodiakasperity, however,is a featurederived entirely from thetsunami data and "Kodiak"Asperity would go unresolvedin an inversionusing the geodeticdata 56oN alone. Slip in meters Discussion 1 0-5 5-10 10-15 15-20 20-25 A consideration of seismic and tsunami hazards in Alaska requiresthat we examineclosely the slip distributionof the Figure 9. Slip distribution of the 1964 Prince. William 1964 earthquake.Recent analysesof seismicityand seismic Sound earthquake from nonnegative least squares joint recurrence along the Alaska-Aleutian subductionzone show inversion.The subfaultletters correspond to thosein Table 1. JOItNSONET AL.: 1964PRINCE XVILI_.IAM SOUND EARTHQUAKE 531

1964 Alaska earthquakes.Even if large near-trenchslip is commonfor the largest earthquakes,this may not be the case with smaller Prince William Sound Asperity events.Near-trench slip may not have any physicalsimilarity to the mechanismof tsunami earthquakes.Without detailed studiesof the mechanismof tsunamiearthquakes, it will not be possibleto tell if tsunamiearthquakes are simply a special caseof a phenomenoncommon in large and greatearthquakes 15-16 such as the 1964 Prince William Sound earthquakeor if they 20-21---• are totally dissimilar. This information is necessary to determine the tsunami hazards of the Alaska-Aleutian 24-25--• subduction zone. km Acknowldgments.This studywas supportedby the U.S. Geological Survey (1434-92-G-2187) and the NationalScience Foundation (EAR- 9117800). We thank Doug Christensen,Bob Paige, and GeorgePlafker k Asperity for reviewingthis manuscriptand offering helpful suggestions.

References

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