Dec 10, 2000 - slip history along the central part of the Sumatran fault. The arc-parallel .... widely differing measurement epochs and scenâ¢ios is important for two ..... and GLORG version 4.04 [Herring, 1997] to estimate site coordinates and ...
JOURNAL OFGEOPHYSICAL RESEARCH, VOL. 105, NO.B12, PAGES 28,343-28,361, DECEMBER 10,2000
Onecenturyof tectonicdeformation alongtheSumatranfault
from triangulation andGlobalPositioning System surveys L.Prawirodirdjo, Y. Bock, andJ. F. Genrich
Cecil H.and IdaM.Green Institute ofGeophysics and Planetary Physics, Scripps Inslitution ofOceanography
University of California,SanDiego
$.$. O. Puntodewo, J. Rais,C. Subarya,andS. Sutisna National Coordination AgencyforSurveying andMapping, Cibinong, Indonesia
Abstract. Ananalysis combining historical triangulation andrecent Global Positioning
System (GPS)survey measurements in westandnorthSumatra, indonesia, reveals a detailed
slip history along thecentral partoftheSumatran fault.Thearc-parallel components ofthe combined velocity fieldareconsistent withsliprates inferred fromGPSdata, ranging from 23to24mm/yr. Between 1.0øS and1.3øN theSumatran faultappears tobecharacterized by deep locking depths, oftheorder of20km,andtheoccurrence oflarge (M,•, ~ 7)
earthquakes. Thelong-term (1883-1993) strains showsimple right-lateral shear, withrates similar to GPS-measured,1989-1993strainrates.Coseismicdeformationdueto the 1892
Tapanuli and1926Padang Panjang earthquakes, estimated fromtriangulation measurements taken before andaftertheevents, indicates thatthemainshocks weresignificantly larger
than previously reported. The1892earthquake hadalikelymagnitude ofMw--7.6,while
the1926events appear tobecomparable in sizetothesubsequent (M - 7) 1943events and
anorderof magnitude higherthanpreviously reported. 1. Introduction
the vicinity of the SF inferred from triangulationand GPS data spanninga period of over 100 years. The triangulation
Thefirstgeodeticmeasurements of coseismicdeformation data were available
to
us from
historical
archives
and
were madebyserendipity ontheislandof Sumatra duringthe provided the intriguing opportunityto test whether recent
course of a triangulation survey[M•itler, 1895].Thesedata, GPS-measured deformationratesare consistentwith longerwhichindicatedright-lateralmotionin a NW-SE direction, term rates if we could reoccupysome of the triangulation werelater referencedby Reid [1913] as evidencefor his pillars with GPS. Many of the triangulationmonumentsare
elasticreboundtheory of the earthquakecycle. The in remote areasthat even with modem logisticsrepresenta triangulation surveywas part of an extensivegeodetic formidable challenge for state-of-the-art, space-based network established by theDutchcolonialgovernment in the geodeticsurveys.Furthermore,as we discoveredduring the 1880s and1890s.Theentiretriangulation networkconsisted reconnaissance phaseof the project,the stateof preservation ofmorethan2000 primary,secondary, andtertiarysites, of the triangulationpillars usuallycorrelatedinverselywith coveting mostof the island[TrianguIatiebrigade van den accessibility. ropographischen Dienst, 1916; War ResearchInstitute, The GPS network on Sumatra came to include 22 1944].Construction of a concretepillar and subsequent historical triangulationsites,and was surveyedfrom 1989 to initial surveys oftentookseveralweeksat eachsite.Because
triangulation involvedpoint-to-point optical direction 1993
[see also Genrich et aI., this issue]. The subset of triangulation sites we call the "west Sumatra" network readings througha theodolite, moststationsweresituatedon (Figure 2 and Table l a), establishedbetween1883 and 1896 mountain tops.The Sumatranfault (SF) extendsover the at 1.5øS to 2øN latitude,is especiallyusefulfor comparing entire lengthof the island(-1600 km) through theBukit Barisan Mountains andthevolcanic chain(Figure 1)andwas crustal deformationrates becausemany of its sites were thus conveniently well-spanned bythetriangulation network. surveyedat more than one epochwith triangulationand were Weinitiated GlobalPositioning System (GPS)geodetic also surveyedduring the 1989-1993 GPS campaigns.In
surveys in Sumatra in 1989[Bocket aI., 1990;McCaffreyet
addition, we used several sites from the "north Sumatra"
Copyright 2000 bytheAmerican Geophysical Union.
terrestrialsurvey data to derive an unambiguousvelocity field. Dong [1993] and Dong et aI. [1998] subsequently developeda theoreticallyrigorousmethod for combining heterogeneous geodeticdata setsbasedon the work of Hein
al.,1990]aspartof a largercampaign whichincluded the network (north of 2øN, Figure 2 and Table lb), established entire Indonesian archipelago [Puntodewo et al., 1994; between1907 and 1918, which were reoccupiedwith GPS. Several studies[e.g., Shay and Drew, 1989; Grant, 1990] Genrich etaI., 1996;Prawirodirdjo et al., 1997;Stevens et have shown it feasible to combine space geodetic and al.,1999]. In thispaper, wedescribe crustal deformation in
Paper number 2000JB900150.
0148-0227/00/2000JB900150509.00
[1986] and Collier et al. [1988]. This mett•od, which we 28,343
28,344
PRAWIRODIRDJO ET AL.' TRIANGULATION
AND GPS ON SUMATRAN FAULT 4øN
"' ..:..: • ..d-•, tl•2.'•'m/•r" .'.: •:. " '"• • lio•'sEm-..•s Plate [ ß:
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ß
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nggano .J
,' 95øE
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I
I
(-
98øE
99øE
100øE
--
I
101øE
•
I
I
107E
103øE
6os 104øE
Figure 1. Map of the westand northSumatraregionwith bathymetry (500-mcontourintervals),tectonic features,andinsetshowinggeographic location. TheSumarran faulttraceis basedondatacollected by Sieh and Natcm'idjaja[this issue],andfault segmcnts discussed in the text are labeledin bold italicswith names and dates of earthquakeoccurrences.Arrows in the Indian Ocean and at the trenchshow the direction and
ratesof convergence of theAustralian platerelativeto Southeast Asia.Openarrowsshowsliporientation on theSumarranfault,with slipratesfromGPSmeasurements reported by Gertrichet al. [thisissue].
appliedhere, was implemented in the softwarepackage triangulation and GPS data to obtain an averaged FONDA developedby Dong [1993]. The ability to combine heterogeneous data sets with widely differing measurementepochs and scen•ios is importantfor two reasons.First, it allows us to extend the
relativelyshorttemporal coverage of spacegeodetic databy combiningthem with terrestrialgeodeticdata, which in
deformationfield over the last 100 yem's,whichwe then compareto the short-term (4-year)GPS-derived deformation. We examinedwhether our combinedvelocity field is consistent with slip ratesand lockingdepthsinferred from
GPSmeasurements andgeological observations. In addition, we estimated thecoseismic deformation causedby the1892
Sumatradate as early as the late nineteenthcentury. [Reid,1913],1926(Ms= 6.5and6.8[Gutenberg andRichter,
Furthermore,the addition of space geodeticdata lets us
1954]),and1943(Ms = 7.1 and7.4 [Pacheco w•dSvl, es,
eliminatetherankdeficiencies inherentin terrestrial geodetic 1992])earthquakes. We discuss ourresults in thecontext ofa datawithoutapplyingarbitraryexternalconstraints, suchas,
recent, comprehensive geological study oftheSFbySieh
for example,the "innercoordinate" constraint [Segcdl and Natawidjaja [thisissue],andcompare themto results from Matthews, 1988].
theGPSsurveys reported byGertrich etal. [thisissue] with
We performed a network adjustmentof the combined furtheranalysisby McCaffreyet al. [thisissue].
PRAWIRODIRDJO
ET AL.: TRIANGULATION
AND GPS ON SUMATRAN
FAULT
28,345
i- 4øN
14
Plll
P 109/DSIM
Lake Toba P065 P1
)63
2øN
O Pt P062
P055/BINA
1892 )63
West Sumatra
Network
0
)43
PO42/PAUH
P0,•( P017
Sianok
P027/AJUN P023
6 5
P022/TANJ P014
P021
SUmani P032
1926,1943 PO02
÷13
PO03, P033
P026
2øS
150 km
98OE
100øE
102øE
Figure 2. Historical triangulation andGPS networks inSumatra. Sites connected bysolid lines indicate triangulation sites used inthis study. Solid crosses indicate triangulation sites with more than oneepoch of observation. Circles indicate GPSsurvey sites. Shaded areas arerupture zones ofthe1892,1926, and1943
earthquakes. Sites discussed inthetextarelabeled with site names. Some ofthetriangulation sites which were resurveyed with GPS were renamed intheprocess (see Table 2).These sites arelabeled withboth triangulation andGPS sitecodes, separated bya slash. Sites belonging tothe"north Sumatra" and"west Sumatra" networks arelistedin Table1.Subnetworks arelabeled in bold.
2. Sumatra Tectonics
0.677 + 0.016ø/Myr.Thus,southwest of Sumatra,the
convergence oftheAustralian plate occurs obliquely, ranging
at (6øS,102øE), to 52 Sumatraexperiencesactive deformationand large from60 mm/yr,N17øEazimuth
mm/yr, N10øEazimuth at (2øN,95øE)(Figure 1). The oblique convergence is p•titioned into subduction at the Southeast Asia[e.g.,Newcomb andMcCa/m,1987].From
earthquakes dueto subduction of theAustralianplatebeneath
to the •c, and arcvelocityvectors derived t¾om regional GPS data trenchwhichis nearlyperpendicular
motion of theforearc along theSF[Fitch, 1972' [Prawirodirdjo, 2000]thepoleof rotation fortheAustralianparallel plate relativeto Southeast Asia is locatedin EastAfrica (9.64
McCaffrey, 1991 ]. McCaffrey [1991 ] further demonstrated
slip vectordeflections and plate +-1.44øN, 51.38+ 2.03øE),withan angularrotationrateof from earthquake
28,346
Table la. WestSumatraTriangulation Network:StationCoordinates (WGS84)and CalendarYearsof Survey SiteCode
Lat.,øN
Lon.,øE 100.5337 100.2308 100.4293 100.7504 100.7037 100.4582 100.6731 100.3311
Triangulation SurveyYears
GPSSurveyYears
1883,1884,1885,1927,1930 1883,1884,1885,1927,1930 1883,1884,1885,1927,1930 1885,1886,1887,1927,1930 1883,1885,1886,1927,1930
1991,1993 1991,1993 1990,1993 1991,1993 1991,1993
P001 P002 P003 P004 P005
-0.8992 -0.9560 -1.1166 -1.1769 -0.7159
P006 P007 P008 P009 P010 P011 P012 P0!3 P014 P015 P016
-0.7256 -0.3245 -0.3899 -0.5724 -1.3677 -1.2777 - 1.2465 -0.9879 -0.5861 -0.3612 -0.2323
P017
-0.0075
P018 P019 P020 P021 P022
0.0753 -0.2452 -0.4112 -0.5959 -0.4444
101.0131 101.0827 100.9833 100.8985 100.7850 100.6538 100.3893 100.1309 100.1794 100.0748 99.9867
P023 P024 P025 P026 P027
-0.2662 -1.5980 -1.6079 -I.8474 -0.1584
99.8846 101.0098 100.6414 100.8503 99.7655
1885,1886,1930 1887,1888,1889,1917,1918 1885,1887,1888 1887,1888,1889,1890,1918 1885,1886,1890
P028 P030 P031 P032 P033 P034 P035 P036 P037 a P038 P039 P040
0.0787 -1.9006 -1.0189 -0.7751 -1.3242 -1.6778 0.3093 0.7364 0.7018 -2.1010 -2.1604 0.2226
99.9839 101.1387 101.2732 101.2399 101.3418 101.4280 100.1904 100.2429 99.8199 101.2631 101.1209 99.3879
1885,1886,1888,1890 1887,1888,1889,1890,1917,1918 1886,1887,1888 1886,1917 1886,1887,1888,1917 1887,1888, 1917,1918 1887,1888,1891 1887,1888,1891 1888,1890,1891, 1892 1889,1890,1904 1888,1889,1890,1904 1885, 1890,189 !
P041a P042
0.4770 0.2372
99.6513 100.8324
1885,1888,1890,1891,1892,1893 1886,1887
P043 P047 P049a P050
0.4097 -2.5413 0.7562 1.4782
100.6978 101.4393 99.2753 99.2096
1887,1888,1891 1890, 1904 1890,1891,1892,1893,1894 1893,1894,1895
P051a
0.9439
99.6261
1890,1891,1892,1893,1894
P052 P053 P054
0.3439 0.8388 1.7859
99.1288 98.9818 98.8779
1890,1891,1893 1891,1893,1894 1894,1895
P055
1.4489
99.7553
1894,1895
P056
1.9599
98.9682
1894,1895,1908,1913
P057 P058 P059 P060 P061 P062 P063 P104
1.2710 1.7572 1.8756 2.0830 2.1770 1.6480 2.0605 -2.2277
98.8258 99.5604 99.1724 99.5083 99.1364 99.8344 99.7981 101.4272
S059a
0.6861
99.5393
100.2368 100.6090 100.8021
1883,1885,1927,1928 1885,1886,1887,1928 1885,1886,1928 1884,1885,1927 1885,1887 1885,1887 1886,1887,1888, 1885,1886,1917,1930 1886,1930 1885,1886,1887,1928 1885,1886,1887,1928
1885,1887,1928 1885,1886,1887,1888,1928 1885,1886,1930 1885,1886,1930 1885,1930 I885,1886, I930
1893,1894 1894, I895,1930 1894,1895, 1894,1895,1930 1895,1908,1912 1894,1895,1930 1894,1895,1930 1890,1917,1918
1890,1891,1892,1893
-
1991,1993 1991,1993 -
1991,1993 1991,1993 1990,1993 (as DING) 1989,1990,1991, 1993 (as TANJ) 1989,1990,1991, 1993 (as AJUN) 1989,1990,1991, 1993 (as AIRB) 1993 (data are bad) I989,1990,1991, 1993 (as PAUH) 1991,1993 1990,1993 (as GADI) 1989,1990,1991, 1993 (as BINA)
1989,1990,1993 -
1990,1993 (as MERA)
S063a S080a S174
0.8605 0.7686 -1.8980
99.7678 99.6401 101.7749
1891,I892,1893 1891,1892,1893 1887,1917,1918
-
aSitescomprisingMtiller's surveynetworkthatspanned the 1892Tapanuliearthquake.
PRAWIRODIRDJO ET AL.: TRIANGULATION
AND GPS ON SUMATRAN FAULT
28,347
Table lb. NorthSumatraTriangulation Network:StationCoordinates (WGS84)and CalendarYears of Survey SiteCode Lat.,øN
Lon.,øE
Triangulation SurveyYears GPSSurveyYears
P064
2.3782
99.6871
1895,1913,1930
-
P065
2.5083
99.5534
1913
-
P066
2.4524
99.3570
1912,1913
P106
2.4622
98.7463
1908,1912
1989,1990,1993(asDOLO)
P107 PI08 P109 P110 Pill Pl12 P121
2.5982 2.6854 3.0130 2.9259 3.2474 3.1376 2.1958
99.0654 98.6090 98.9036 98.5354 98.5006 98.!267 98.5976
1908,1909 1908,1909 1908,1909 1908,1909 1909,1910,1914,1915 1909,1910 1908,1913
1990, 1993 (as DSIM) -
S103
2.1726
99.3616
1913
S104
2.0763
98.8257
1908,1913
S200
2.0922
98.6153
1908,1913
-
-
-
1990.1991,1993 (as SIGL)
observations suchas thosemadeby Sieh and convergence vectorsthat the forearcsliverplatelocated geological thispaper,in referring between the trench and the SF is not rigid but instead Natawidjaja[thisissue].Throughout to various regions along the SF, we usethe fault segment undergoes arc-parallel stretching, requiring a northwestward increase in slipratealongthe SF. Slip ratesestimated at two locations by Siehet al. [1991]fromstreamoffsetsincisedin
Quaternary volcanic tuffs,andat several locations by BeIlier
namesproposed by SiehandNatawidjaja[thisissue]. 3. Data
andSgbrier[1995] from SPOT satelliteimagesof stream 3.1. Triangulation Data
offsets, support an increase in slip ratesfromSE to NW.
The original triangulationmonumentsconsistedof However, recentGPS surveys[Gertrichet al., this issue] concrete pillars- 1.5m high,withembedded bronzemarkers show onlya marginalincrease.
angles froma centralstation to a setof The spatialand temporalvariationsin slip rate and (Plate1). Horizontal stations weremeasured usingmicrotheodolites, seismicity alongthe SF are still only poorlyknown.The surrounding spatial variationsare just beginningto be revealedby from Pistorand MartinsandWegenerand Wanschaff,and placed onthepillarswiththeiraxesin theplumb geodetic andgeologicobservations. While it is confirmed heliotropes thatthe obliqueconvergence is generallypartitioned into line of the bronzemarkers[War ResearchInstitute,1944]. We used 391 horizontalangle measurements from the subruction at the trenchand transcurrent shearalongthe SF, west and north Sumatra networks, defining 106, roughly modeling of geodetic datashowsthatthissimplescenario is complicated by manyintriguingdetails.Thereappears tobea north-south segmentationin the pattern of strain accumulation alongthe subructionzone [Prawirodirdjo et aL,1997].The southern half of theforearcis movingroughly in the same direction as the convergencebetween the Australian plateandSoutheast Asia,whilethenorthern half ismoving in a direction morecloselyparallelto thearc.The division of the forearcvelocity field coincideswith the boundary between therupturezonesof the 1833and 1861
equilateral triangles (Figure 2), withsidesmeasuring 20to70 km long.For eachnetwork,therewerealsoavailable one
seaward of the Mentawai Islands[McCaffreyet al., this issue]. Ourgoalin thisstudy,together with thosepresented by Genrich etal. [thisissue]andMcCaffreyet aI. [thisissue],is
(IøN latitude, Figure2), an earthquake occurred in 1892
distance measurement and one azimuth measurement, intendedto fix the scale and orientationof the network.The
distance measurements werenotpreciseenough,however,to constrainthe scale to within less than severalhundredparts
permillion(ppm). Noraretheazimuth measurements useful
to us,sincetheyweretakenat siteswherewe donotknow the coordinates precisely.Instead,we fixed scaleand orientation by linking GPS and triangulation horizontal (Mw> 8) thrustearthquakes postulated by Newcomb and and velocities at well-determined, collocated McCann[1987] and is thus probablyrelated to the positions subruction zone'srupturekinematics. Also,theinferred slip stations,as describedin section5.1. Theinitialsurveyof thewestSumatra network beganin rateon the SF is about 1/3 less than the full arc-parallel in 1896.ThenorthSumatra network component of platemotion[McCaffrey et al., thisissue].To !883andwascompleted in 1907-1916. Afterthe1926Padang Panjang account for 20 km of offset on the SF since the Oligocene wassurveyed earthquake (Figure 2), sites around the rupture area were [Sieh andNatawidjaja, thisissue], anadditional 20mm/yrof resurveyed in 1927-1930. At the Angkola segment of the SF strike-slip isrequired westof theSFandprobably takesplace
whilea second-order surveywasunderway, displacing the
triangulation monuments [M•iIter,1895;Reid,1913].Sites neartherupture areawerelatersurveyed again overthenext
unknownto us, repeat togainsomeinsight intothespatialandtemporal detailsof 2 years(1892-1894).For reasons werealsoperformed in 1917and1918at a thedynamics along the SF. Moreover,sincerupture measurements few sites in the west Sumatra network (Figure2) andin 1930 kinematics alongthe SF andin the forearcare strongly network (Figure 2). TableI summarizes correlated with structuralfeatures,it is importantthat we in thenorthSumatra sitesandtheirdatesof survey. formulate interpretations of ourgeodetic dataconsistent with thetriangulation
28,348
(A)
PRAWIRODIRDJO
ET AL.' TRIANGULATION
ß ':.
AND GPS ON SUMATRAN
FAULT
(D) S58
P106
PI09
?.lBg' ' (E) Poe5
(c) S200
Plate 1. Photographsshowingdifferenttypesof Sumatratriangulationmonumentssurveyedwith GPS. (a) and (b) Primary pillars (P106 and P I09) that have remainedintact since the 1880s, including their brass surveymarkers.Shapeand heightof the pillarsoften requiredmetal extensionrods(shownin Plate l a) lbr the survey tripodsin order to centerthe antennaaccuratelyabovethe survey mark. (c) A well-preserved secondarypillar (S200). (d) At other sites like S58, pillar still erect but damaged,with no trace of bronze marker. We placedstainlesssteel pins at the centerot' the top surfaceto serve as the GPS survey mark. (e) Monument P005 which sufferedheavy damageover the years.In suchcasestt new concretemonumentwas reconstructed over the still recognizablel:oundation of the originalpillar. Horizontal locationof the original surveymarker could often be identified and "recovered"to within tensof centimeters.
PRAWIRODIRDJO ETAL.:TRIANGULATION ANDGPSONSUMATRAN FAULT The originalraw data were reducedby one of us (S.
28,349
2. At monuments which were still erect but had sustained
Sutisna) toonemeasurement foreachangleandthenusedas somedamage,includingremovalof the bronzemarker,the GPS antennawas set up overthe remainsof the monument input to a leastsquares adjustment of station coordinates the locationof the triangulation using thesoftware package CHAOS(School of Surveying,(Plate l d), approximating University of NewSouthWales).Theancillary distance and marker to within a few tens of centimeters. 3. Monumentswhichhadsustainedheavydamageor had azimuthmeasurements mentionedabove were used to of a new nominally constrain thescaleandorientation of thenetwork. beencompletelydestroyedrequiredconstruction Theresultof thisadjustment wasa setof stationcoordinatesmonumentoverthe likely locationof the originalmark. GPS referenced to theGRS67ellipsoid. We usedtheseasa priori reoccupationwas performed within ! m of the estimated triangulation sitecoordinates. TheGRS67is basedon the originalmark (Plate l e).
geocentric equipotential ellipsoid, withellipsoid parameters In addition,in an attemptto tie in eight moretriangulation (ellipticity f = 1/298.2472and semiaxislengtha =
sites,we established new monumentsplacedas closeto the
6,378,160.00 m [h•ternationalAssociatio/iof Geodesy, originalsitesas local logisticspermitted(up to severalkm). 1971]) significantly differentfromtheWGS84ellipsoid0r = Although GPS vectors were measured from these eight 1/298.257223563, a = 6,378,137.00 m [DefenseMapping eccentric sites to the respectivetriangulationsites, the
Agency, 1987]),to whichourGPSgeodetic coordinates are measurementswere, unfortunately,not precise enough to referenced.Hence, before combining the data we transformed the triangulationcoordinatesinto the WGS84
serveas ties in our analysis.We usedone of theseeccentric sites (DEMU) to establisha referenceframe in the northern system by convertingthem into geocentric Cartesian part of the networkby linking its horizontalvelocityto that coordinatesand converting them back to geodetic of its corresponding triangulationmonument(P065).Table 2 coordinates usingthe WGS84 ellipsoidparameters. summarizes therelationships betweenthe triangulation and GPS stations.
3.2. GPS Data
The triangulation stationswhich were resurveyed with GPS were usedto updatethe a prioritriangulation site
Ouranalysisis basedon GPSdatafromgeodeticsurveys coordinates.Using FONDA, we used the GPS-measured performed in Sumatrain 1989, 1990, 1991, and 1993. Some ve!ocities of thecollocated stations to propagate backin time sitesin southand east Sumatrawere surveyedin 1994, but to estimate coordinates of thecollocated stations duringthe thesemeasurements are not usedin this analysis.Neither did
triangulation epochsand usedthe anglemeasurements to
weusedatafromthe near-fieldarrays,discussed by Genrich estimatecoordinates for all othertriangulation stationsnot eta!. [this issue], which were part of the Sumatra GPS resurveyed with GPS.This process,describedin moredetail surveys. A detaileddescriptionof the GPS campaignsin in section4.2, yielded improvedcoordinates for all the Sumatra is givenby Prawirodirdjo[2000], andthecomplete triangulation stations and allowed us to assume, in GPSvelocityfield is documentedby Genrich et al. [this subsequentanalyses,that the coordinatesfor most of the issue]. triangulationstationsare well determined.In this manner, Dual-frequencycarrier phase and pseudorangeinformation from the GPS measurements allowed us to observations werecombinedwith improvedorbits[Fanga•d eliminatetherankdeficiencies of thetriangulation data. Bock,1996] to computedaily solutionsconsisting of site coordinates, satellitestatevectors,tropospheric zenithdelay 4. Analysis parameters, andphaseambiguities by weightedleastsquares using GAMIT version9.40 [KingandBock,1995].Thedaily Our analysisof the triangulation and GPS measurements solutions werethen combinedusingGLOBK version4.12 was basedon the methoddevelopedby Dong [1993] and
andGLORGversion4.04 [Herring,1997]to estimate site Dong et al. [1998] to analyzetrilaterationand GPS data in coordinates and velocities. North and east velocity southernCalifornia. This method is implementedin the components have a typical formal one standarddeviation softwarepackageFONDA [Dong, 1993], a sequential least (assuming a white noisestochasticmodel for the estimated squares (Kalmanfilter)estimation in whichstationpositions sitecoordinates [seeZhanget aI., 1997])of 1-2 and 3-4 are estimatedas a function of time, taking into account mm/yr, respectively. secular velocities and, where appropriate,episodic and Ofthemorethan70 GPSsitessurveyed, 22 werelocated stochasticstation displacements.The method is briefly on triangulation sites. A 4-day GPS surveyof a well- reviewed here. preserved sitetypicallyrequireda 1-dayvehicledriveto the First,looselyconstrained estimates of geodeticparameters to nearest village, assemblyof a team of local guidesand are obtainedfrom an analysisof individualexperiments porters, a 1-3 day ascentto the siteon previouslynonexisting serve as "quasi-observations"for the combined solution. orbarelyestablished narrowmountaintrails,severalhoursof Here we derived loosely constrainedestimatesof site
siteperimeter clearing to gainreasonable satellite visibility, positions from the 1989-1993 GPS observationsand the theactual 4-dayGPSsurvey, anda 1-2dayreturn triptothe angle measurements f¾omtriangulationsurveys.The quasi village.
observationsare then combinedusing FONDA. Unknown
Thetriangulation sitesthatwerereoccupied duringthe episodic (coseismic)site displacementsat a subset of GPS campaigns fallroughly intothreecategories: specified sites are modeled as step functionsin the site 1. Monuments which were sufficientlyintactwere positions.Generalconstraintson positionand site velocity resurveyed directlyover the originalbronzemm'ker(Plates were imposedon the solutionto removethe rankdeficiency la-!c). At least four sites, P106/DOLO,P109/DSIM, in the triangulationdata and to define a uniform reference S059/MERA, andS200/SIGL (Figure 2 andTable2), fall frame throughwell-determinedstationscommonto all data within thiscategory. Werefertothese asthe"core" sites. sets.Includingdatafrom a globalnetworkin the analysisof
28,350
PRAWIRODIRDJO ET AL.: TRIANGULATION AND GPS ON SUMATRAN FAULT
Table 2. North andWestSumatraHistoricalTriangulation SitesResurveyed with GPSin 19891993 Estimated Offset Between
SiteCode Triangu-GPS
Relation ofGPSSurvey Uncertainty ofGPS Triangulation andEccentric Site b Mark to Original TriangulationMark
SurveyMark Relative to Triangulation
lation
P001 c P002 c P003 ½ P004 c P005 ½
P001 P002 P003 P004 P005
Mark a,cm
monument reconstructed monument reconstructed monument reconstructed monument reconstructed new monument
Azimuth, Distance, km deg
10 10 10 10 100
reconstructed over center of foundation' s remains
P007 c
P007
monument reconstructed
P008c
P008
originalmonument, no
P015 c P016 P017 ½
P015 P016 DING
monument reconstructed monument reconstructed monument reconstructed
ULUA
eccentricpoint to P017
P022
P027 ½
TANJ AJUN
monument reconstructed monument reconstructed on foundation remains
10 10
P037 P035
P37E PETO
eccentricpoint to P037 eccentricpoint to P035
AIRB
monument
PAUH SIBI
original monument eccentricpoint to P050
10 10
bronze marker
P040 c P042 c P050 P051 P054
!0 20 10
reconstructed
P051
monument reconstructed
GADI
original monumentfound
297
5
10 5 -
327 124 225
8.75 10 4
l0
-
-
125 1!6
13.75 14
~
-
291
8
-
tilted
P059
PANT
eccentricpointto P059
50 -
P061 e
P061
monument reconstructed
10
P065
over original foundation DEMU original monument destroyed- eccentricpoint
PISA
eccentricpoint to P054
P055 c
BINA
monument reconstructed
constructed to P065
P 106 ½ P 109 c S059 c S200 c
DOLO MART DSIM MERA SIGL
_
original monument eccentricpoint to P!06 original monument original monument original monument
5
141 -
12.25
5 5
-
-
aForcollocatedsites;notapplicableto eccentricsites.
bOnlyapplicable to eccentric sites. cSiteswhichwereusedto estimate transformation parameters betweenthetriangulation andGPScoordinates.
primary GPS observations renders the GPS solution using the GPS measurements).To estimate long-term
unambiguous on the regionalscale.Thus, by linkingGPS interseismic strain, we used the first-epochtriangulation
measurements and GPS data, accountingfor coseismic displacements by applyingcorrectionsbased on the of the and rotationambiguityinherentin the triangulation surveys coseismicestimation.More detaileddescriptions [Dong et al., 1998]. procedures usedat eachsteparegivenin sections 4.1and and triangulationestimatesof horizontalvelocitiesof well-
determined, collocated stations we removed the dilatation
FONDA's estimation procedureyields site coordinates, velocities, and episodic (in this case, coseismic) displacementssimultaneously.However, we chose not to estimate all the desired parameters in one large solution involving all the triangulation and GPS data. We opted insteadfor a slightly distributedapproach,with the goal of minimizing the effect of any systematic shifts on the displacementand velocity estimates. For example, to
4.2.
4.1. Assessment of TriangulationData Quality
To estimatethe error in the triangulation (angle) measurements, we invertedthe triangulation datasetfor
station coordinates only.Holdingfixedthecoordinates of
two arbitrarilychosensites,P037 and P042 (Figure2), eliminates therankdeficiency duetoscaleandorientation. h estimatecoseismic displacements spanned by triangulation.thisinversionwe did not includemeasurements takenby surveys, we usedonlysubsets of anglemeasurements from MiiIler[1895]in theepicentral areaimmediately afterBe beforeandaftertheearthquake (andsitecoordinates updated 1892earthquake, sincewe expected themto contain lax'g,
PRAWIRODIRDJO ET AL.:TRIANGULATION AND GPSONSUMATRANFAULT
28,3>1
140
120
•
1oo
80
z
60
4O
20
0 -3
-2
-1
0
1
2
•
Residuals (arc seconds)
Figure 3. Histogram of residuals from adjustmentof 374 horizontal angles in the 1883-1896 survey, calculatedwith P037 and P042 fixed (see text). Solid line representsa normaldistributionwith zero mean and standard deviation
of 0.4 arc sec.
contributions from the earthquake. Figure 3 shows the adjustment,the positionsand velocities of the four core sites distribution of angle residualsfi'om this adjustmentof 374 (Pi06, PI09, S059 and S200) are tightly constrainedto their angle measurements from 82 sites.We foundthatrepeating GPS-determined values. In addition, velocities (but not thisadjustment while holdingcoordinates o1'differentpairs positions) of triangulation sites where the GPS rcsurveys ofsitesfixed did not significantlyaffect the distributionof were within tens of centimetersof the original mark were
residuals. With the exceptionof angles measuredfrom constrainedto their GPS-determinedvalues. Beginning with station P009,theroofmean-square (rms)residuals of angles strict outlier identification criteria, we repeated the measured from each station all fall below 0.5 arc sec. The standard deviation of the residuals is 0.4 arc sec. This
adjustmenta few times, updatingcoordinatesand loosening
corresponds to - 2 ppm in trianglemisclosure[Davieset al.,
final adjustmentwe constrainedthe horizontal coordinatesof the GPS-resurveyedtriangulationsitesto within 20 cm and of
the outlier
identification
criteria
after each iteration.
In the
1997],the differencebetweenthe sumof threeanglesin a given triangleand 180ø plusthespherical excess[Bomford, the four core sites to within I cm of their GPS-determined 1980;Yu and Segall,1996]. This level oi' precision is positions(the coordinateconstraintswere loosenedup again adequate to detectregionalstrains,whichareexpected to be when we beganestimatingdeformationrates).By thus using a fewtenso1'ppm over 100 years(the intervalbetween the GPS-measured velocities of the collocated stations, triangulation andGPSsurveys) or severalppmover---45 FONDA propagatesback in time to estimatecoordinatesof years (the
interval between repeated triangulation the collocatedstationsduring the triangulationepochs,and
measurementsin the region of the 1926 and 1943
uses the angle measurementsto estimate coordinatesfor all
earthquakes, Figure2).
other triangulationstationsnot resurveyedwith GPS. This process yieldedimprovedcoordinates for all thetriangulation sitesto be usedin the velocity field estimation. Our final adjustmentincluded357 angle measurements 87 stations. All angle measurementswere given equal weight. We did not estimatevertical velocities,and vertical positions(heights)were given tight constraints.After the final iteration the postfit nns of the angle measurementswas
4.2.UpdatingSiteCoordinates
First,weestimated fourtransformation parameters (threedimensional translation androtation aboutoneaxis)based on the collocatedsites indicated in Table 2. A coordinate
transformation was then performed to align the a priori
triangulation site coordinateswith the GPS coordinate system. This first stepservesas a large-scalecorrectionto 0.9 arc sec.This level of error, higher than the 0.4-0.5 arc sec
obtainedfi'om our initial adjustmentof angle measurements, suggeststhat somestationsmay have experiencecoseismic Next,we usedFONDAto adjustthe triangulation site as well as secular motion. Nevertheless, these updated coordinates, usingall the angle measurements. In this coordinatesm'e sufficient in quality to be used as a priori
thea priori triangulation site coordinates, while still disregarding thetemporal variations insitepositions.
28,352
PRAW!RODIRDJO
ET AL.: TRIANGULATION
values in the studies that follow. Three measurements, all
taken from site S080, were discardeddue to large angle residuals.
AND GPS ON SUMATRAN FAULT
FollowingDong's[1993]approach, we firstcombined the triangulation and GPS observations in a looselyconstrained solution. We thenappliedconstraints to P042 andP065.We
constrained the position andhorizontal velocityof P042, whichis locatedon the backarc, to theirGPS-derived,
5. Results and Discussion
ITRF96 values.As mentionedabove,we also constrained P065 to have the same velocity as DEMU but did not 5.1. Interseismic Deformation Rates Obtained by constrainits position.The constraints on P042 andP065 Combining Triangulation and GPS Measurements placedtheestimated velocityfield in the ITRF96reference between By performing a solution combining first-epoch frame and allowedus to make a direct comparison velocitiesderivedhereandthe GPS-measured triangulationmeasurementsfor the west and north Sumatra the long-term the only assumptions we madeare networks with GPS measurements,we estimatedthe long- velocities.In thisprocess, that two sites(DEMU and P042/PAUH) locatedon theback ReferenceFrame 1996 (ITRF96) [SilIard et al., 1998] -based arc havehad a constant velocity(as measured by GPS) locationsservedas a prioricoordinatesfor the GPS sites,and duringtheperiodbetween thetriangulation andGPSsurveys the set of updatedcoordinatesdescribedabove servedas and that P065 movesat the same (constant)velocityas thosefor the triangulationsites.Since the intervalbetween DEMU. The velocity field for 1883-1993 obtained from the the triangulation and GPS surveysalsospansthe 1943 is earthquake,we solvedfor coseismicdisplacements at sites combinedsolutionof triangulationandGPS measurements near the 1943 rupture zone along with the interseismic shownin Figure4, plottedrelativeto theEurasianplatepole of rotation. This does not include the measurementsmadein deformationrates (see section5.3.3). As quasi-observations for the GPS-reoccupied sites(listed 1927-1930. For comparison,the short-term GPS-derived in Table2), we usedlooselyconstrained coordinates obtained velocities have also been included. At sitesP005, P015, P017, P106 and P109, long-term and from analysisof the entire GPS data set. For sitessurveyed both by triangulationand GPS, our goal was to obtainthe short-termrates agreewithin their 95% confidenceregions long-term (1880s to 1990s) velocities from the a priori (Figure4). The long-termvelocitiessouthof the equator triangulationcoordinates,angle measurements, and current clearlyshowright-lateralshearacrossthe SF. Siteslocated GPS positions.To minimize dependenceon the short-term aroundthe Suliti and Siulak segments(southof 1.5øS)are (GPS-measured)velocity signal, we did not want to include only weakly connectedto the rest of the west Sumatra GPS-measuredvelocities as quasi-observations (although network,yet the velocity field in this area clearlyshows note that the GPS velocitieshave been used to updatethe fight-lateralshear acrossthe SF. The velocitiesin the triangulationsite coordinates).However, we included the northernback arc (north of 1.5øN) have large uncertainties, GPS-measuredvelocity for one site, DEMU, as a quasi- but the uniformityof the vectorssuggestslack of internal observationin our adjustment.This site is eccentricto P065, deformationin thatregionof the backarc. Genrichet al. [this issue]inferredslip ratesand locking and we constrainedP065 to have the same velocity as term interseismic
DEMU
deformation
rates. International
Terrestrial
to install a frame of reference for velocities in the
northernpart of the triangulationnetwork.Both sites,only 8 km apart,are locatedin the back arc basin,where strainrates are very small (- 0.01 gstrain/yr [McCaffrey et aI., this issue],Table 3). As input from the triangulationsurveys,we used all available first-epoch angle measurementsfor the
depthsalongthe SF by fitting GPS-measured velocities to Savageand Burford's[1973] 1-D elasticdislocation model for a lockedstrike-slipfault.In thismodel,velocities located far (>100 km) from the fault tracelargelyconstrain theslip rate, while velocities near the fault constrainthe locking
depth.Vectorsfrom the combined triangulation andGPS
west and north Sumatra networks. This included several sites
solution all lie within 150 km of the SF, are sparsely
which were surveyed only once, which are needed for triangleclosure(we did not estimatetheirvelocities).
distributed, and havelargeuncertainties; hencetheyonly looselyconstrain sliprateandlockingdepth.Therefore we
Table
3. Horizontal
Region
•;11,
Interseismic Strain Rates
•22,
10'6yr-1 10'6yr-1
0,
deg
10'6yr-1
10-6yr-1
Sumani
-0. i0+0.04
0.09_+0.07
24.8_+10.9
0.13-+0.09
-0.15_+0.08
Sumani
-0.09_+0.03
0.14+0.03
32.4+2.9
0.09_+0.02
-0.3+_0.02
N
Source of Estimate
16 1989-1993GPS McCa.ffrey et al. [this issue] 9
1883-1885
to 1989-1993
triangulationandGPS Sumani
Back arc Northern Back are
-
-0.01+0.03 -
-
31.0-+ 12.9
0.08-+0.08
-0.15-+0.07
21
1883-1885
to 1927-1930
0.02-+0.08
168.1+12.6
0.03-+0.07
0.014_+0.06
triangulation 8 1989-1993 GPS McCa.ffrey et al. [this issue]
-
not well determined
0.03_+0.12
0.06_+0.09
6
1893-1895 to 1930
triangulation
Strainratesareexpressed in termsof theaxesof maximum compression ( •l• ) andextension ( •;22) andthe engineering shearstrainrates'iq and •/2; 0 is theazimuthof maximum contraction; N is thenumberof sites usedin the stxainestimation.Quoteduncertaintiesare forrnalstandarderrors.
PRAWIRODIRDJOET AL.: TRIANGULATIONAND GPSON SUMATRANFAULT
•......
.:.....
.:
28,353
63
2øN -
D957 u..'.....
(••
.......... ':'. PAND
BINT
BLMS ¸ ;P055 DUR•
IøN
,
3
•PASI
SIKA """•"D952
;E
RUMB
ß . (•PO42
P( D947
0ø-
D94
P027
P016
:..
•2 P0(
P00'
-
P003
D937.• 2ø$-
P039 P038
30 mm/yr 150 km
3øS
•
•
97øE
98øE
99øE
I
•
100øE
101 øE
102øE
Figure 4. Interseismicvelocity field (solid arrows)derivedfi'oma combinationof triangulationand GPS observations. Open arrowsare 1989-1993GPS-derivedvelocitiesfrom Ge/•richet al. [thisissue],shownfor comparison. Ellipsesindicate95% confidencelevels
didnotattempt to inferslipratesor lockingdepths fromour combined velocities, butin Figure5 we comparethemto the slip rates andlocking depths estimated byGertrich et al. [this issue]. Because convergence between the Australian plate andtheforearcis nearlyperpendicular to thetrench,strain
2ø to 3.5øN) are consistentwith a slip rate of 24 mm/yr and a lockingdepthof 9 km reportedby Getsrich et al. [thisissue] for this region (Figure 5a). Between 0ø and 1.8øN, the SF splits into two major strands(the Barumunand Angkola segments,Figure 1), and thus cannot be modeled by a simple fit to Savage and
accumulation on the subductionzone mainly afi:ectsthe arcnormalcomponents of the vectors,while the arc-parallel Butford's[1973] model.Assuminglockingdepthsof 10-20 components reflect slip along the SF [Prawirodirdjoet al., km andtreatingthe vectorsasthe sumof surfacedeformation Gertrichet al. [thisissue] 1997]. Henceweplotted (Figure5) thearc-parallel velocities dueto slipon bothfault branches, fortburregions across the SF corresponding to segmentsestimatedslip ratesof 2-4 mm/yr on the eastern(Barumun) reported by Sieh and Namwidjaja [this issue],with curves branchand 19-2! mm/yr on the western(Angkola) branch.In
vectorshavelargeuncertainties. reflecting slipratesandlocking depths estimated byGertrich thisregion,all ourcombined
etal. [thisissue]fromGPSdataat theappropriate latitudes. Within the 95% confidencelevel the arc-pm'allelcomponents of our vectors at P040 Our combined velocities attheTorusegment (approximately
and S059 are consistent with either the
28,354
PRAWlRODIRDJO
ET AL.: TRIANGULATION
AND GPS ON SUMATRAN Barumun/Angkola
Tom
50
......
50
,
,
.
,
b
Slip rate---24 mm/yr Lockingdepth= 9 km
40
FAULT
Sliprates= 20 and3 mm/yr Lockingdepths= 20 km
40
30
20
20
10
-10 -!5o
-lOO
-50
0
50
113o
150
-10 -150
-lO0
-50
0
100
150
Sumani
Sianok 50
,
Slip rate= 23 mm/yr Lockingdepth= 24 km
Sliprate= 23 mm/yr Lockingdepth= 22 km
40
•
40
•
30
30
.• 20
20
•
50
lO
I
