Tsunami early warning using GPS-Shield arrays

Stephan V. Sobolev,1,2 Andrey Y. Babeyko,1 Rongjiang Wang,1 Andreas Hoechner,1

Roman Galas,1 Markus Rothacher,1 Dmitry V. Sein,3 Jens Schroter,3 Joern Lauterjung,1

and Cecep Subarya4

Received 20 July 2006; revised 4 May 2007; accepted 24 April 2007; published 25 August 2007.

[1] The 2004 catastrophic Indian Ocean tsunami has strongly emphasized the need forreliable tsunami early warning systems. Another giant tsunamigenic earthquake may occurwest of Sumatra, close to the large city of Padang. We demonstrate that the presenceof islands between the trench and the Sumatran coast makes earthquake-induced tsunamisespecially sensitive to slip distribution on the rupture plane as wave heights at Padang maydiffer by more than a factor of 5 for earthquakes having the same seismic moment(magnitude) and rupture zone geometry but different slip distribution. Hence reliableprediction of tsunami wave heights for Padang cannot be provided using traditional,earthquake-magnitude-based methods. We show, however, that such a prediction can beissued within 10 minutes of an earthquake by incorporating special types of near-fieldGPS arrays (‘‘GPS-Shield’’). These arrays measure both vertical and horizontaldisplacements and can resolve higher order features of the slip distribution on the faultthan the seismic moment if placed above the rupture zone or are less than 100 km away ofthe rupture zone. Stations in the arrays are located as close as possible to the trench and arealigned perpendicular to the trench, i.e., parallel to the expected gradient of surfacecoseismic displacement. In the case of Sumatra and Java, the GPS-Shield arrays should beplaced at Mentawai Islands, located between the trench and Sumatra and directly at theSumatra and Java western coasts. We demonstrate that the ‘‘GPS-Shield’’ can also beapplied to northern Chile, where giant earthquakes may also occur in the near future.Moreover, this concept may be applied globally to many other tsunamigenic activemargins where the land is located above or close to seismogenic zones.

Citation: Sobolev, S. V., A. Y. Babeyko, R. Wang, A. Hoechner, R. Galas, M. Rothacher, D. V. Sein, J. Schroter, J. Lauterjung, and

C. Subarya (2007), Tsunami early warning using GPS-Shield arrays, J. Geophys. Res., 112, B08415, doi:10.1029/2006JB004640.

1. Introduction

[2] The international community was shocked by thecatastrophic consequences of the great Andaman–NicobarIslands earthquake occurring 26 December 2004 [Stein andOkal, 2005; Ammon et al., 2005; Lay et al., 2005; Krugerand Ohrnberger, 2005; Ishii et al., 2005] in which morethan 250,000 casualties resulted, mostly due to the impactof the induced tsunami waves. This event triggered anumber of international and national initiatives aimed atestablishing modern and robust tsunami early warningsystems. The specific mission of the German Indian OceanTsunami Early Warning System (GITEWS), led by theNational Center of Geosciences (GeoForschungsZentrum)in Potsdam, Germany, is to provide early warning oftsunamis for the Indian Ocean coast of Indonesia, whichis located only 200–300 km from the subduction zone

trench. The proximity of the coast to the potential tsunami-genic source means that a tsunami is expected to arrive only20–30 minutes after an earthquake. This makes earlywarning particularly difficult. Moreover, as we will showbelow, near-field tsunamis are also very sensitive to the slipheterogeneity on the fault [see also Geist, 1998; Geist andDmowska, 1999]. As a consequence, even a very fastderivation of standard earthquake parameters like magni-tude and hypocenter, which are usually sufficient to predictfar-field tsunamis [Okal, 1988], will not solve the problemof local tsunami warning. The key task within GITEWS istherefore to quantify rupture parameters with a degree ofdetail that exceeds the standard set of parameters within10 minutes of the event.[3] In this paper, we suggest a technique for the fast and

reliable determination of the earthquake rupture parameterscontrolling tsunami generation at a subduction zone. First,we discuss the possible location and likely parameters of thenext giant earthquake in the Indonesian region. Next, wecalculate two possible earthquake and tsunami scenarios forthe region of the city of Padang (Sumatra Island). Wedemonstrate that two earthquakes with the same magnitude,location, and fault geometry but different distribution of slipmay generate tsunami waves with drastically different

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, B08415, doi:10.1029/2006JB004640, 2007

1GeoForschungsZentrum, Potsdam, Germany.2Institute of Physics of the Earth, Moscow, Russia.3Alfred Wegener Institute, Bremerhaven, Germany.4BAKOSURTANAL, Jakarta, Indonesia.

Copyright 2007 by the American Geophysical Union.0148-0227/07/2006JB004640$09.00

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impacts on the coast of Padang. We then suggest anobservation system based on a real-time GPS array that isable to distinguish between the two different tsunamiscenarios. We analyze the potential of this observationsystem for resolving rupture parameters and discuss relatedreal-time GPS accuracy issues. Finally, we demonstrate thatthe suggested system, hereafter called ‘‘GPS-Shield,’’ mayalso be applied to the Chilean coast, or even globally in alltsunamigenic regions at active margins where the land islocated above or close to the seismogenic zone.

2. Scenarios of Another Giant Earthquakein Indonesia

2.1. Where Will Another Giant Earthquake Occur?

[4] The 2004 Sumatra earthquake was followed byanother large earthquake in March 2005 with the rupturezone directly continuing the 2004 rupture zone to the southand which approximately repeated the 1861 rupture [Briggset al., 2006] (Figure 1a). Interestingly, this secondearthquake was predicted by the analyses of the regionalCoulomb stress changes caused by the 2004 earthquake[McCloskey et al., 2005]. Another large earthquake in theregion is expected south of the 2005 earthquake rupturezone [Nalbant et al., 2005; Pollitz et al., 2006], and it maywell be similar to the Mw = 8–9 earthquakes that occurredin this region in 1797 and 1833 [Sieh et al., 2004](Figure 1a). The tsunami generated by this future earth-

quake may be very dangerous for the Indonesian city ofPadang, which has a population of more than 750,000 and islocated close to the expected rupture zone. Below weanalyze in detail possible consequences of this particularexpected earthquake for the Sumatra coast and for Padang.Interestingly, Mignan et al. [2006] suggested that thesubduction fault at that location is not yet close to failure,and that it may be still required a few tens of years forpreparation of the earthquake there.[5] The possible coseismic vertical displacements at the

islands during the 1833 earthquake were estimated based ondata from coral reefs [Zachariasen et al., 1999]. We usethese displacements to constrain fault and slip parameters ofa future earthquake. To characterize the rupture, we employthe distributed-slip parameterization [Freund and Barnett,1976; Geist and Dmowska, 1999]. The advantage of thisparticular parameterization is that remaining very simple, itapplies physically justified conditions at the fault ends,which keep finite stress at the crack tips and allowsasymmetrical slip distribution at the fault. Details of thatparameterization are given in Appendix A, where we alsodemonstrate that such parameterization accurately describesslip distribution in natural rupture.[6] Using this parameterization, we invert displacement

data [Zachariasen et al., 1999] for the rupture parametersusing the Nelder and Mead downhill simplex method [Presset al., 1992]. The resulting range of possible solutions is

Figure 1. (a) Location of the rupture zones of the largest earthquakes near Sumatra. The next giantearthquake is expected where the magnitude 8–9 earthquakes occurred in the years 1797 and 1833 [Siehet al., 2004]. (b) Expected static vertical displacement at the surface caused by the expected futureearthquake. The rupture parameters of the earthquake (rupture model 1, solid curve) have been chosen tofit data on island uplift resulting from the 1833 event, which are based on observations of coral reefs(crosses, Zachariasen et al. [1999]). The dashed curve indicates another possible rupture model (rupturemodel 2) having the same seismic moment and fault geometry as model 1, but a deeper slip maximum atthe fault. (c) Horizontal (trench-perpendicular) displacements caused by the possible future earthquakes.Note that the expected displacements and their trench-perpendicular gradients are very large at the islandslocated between the trench and Sumatra.

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very large. We use the solution that has an average downdipslip at the fault of 8.5 m, which can be expected if it isassumed that the seismogenic zone has been locked sincethe 1833 event. The parameters of this solution (hereaftercalled rupture model 1) are presented in Table 1.[7] Very recently, while this paper was in review, Borrero

et al. [2006] have calculated possible tsunami scenarios for1797 and 1833 events at Sumatra and analyzed mostprobable scenarios for the future giant earthquakes andtsunamis in this region. Their preferred models are closeto our rupture model 1.[8] The slip distribution at the fault during a future earth-

quake will not necessarily be the same as for the 1833 event.Therefore we also analyze the consequence of anotherpossible, although perhaps less probable rupture modelhereafter called model 2. Rupture model 2 (see Table 1)has a slip maximum at a greater depth than model 1, with allother parameters being the same. Note that while models 1and 2 have the same seismic moment (in a homogeneouselastic half-space) and fault dimensions, they generate ratherdifferent vertical (Figure 1b) and horizontal (Figure 1c)displacements. Below we demonstrate the dramatic conse-quences of this difference for the induced tsunamis. However,a common feature of both rupture models is that at a distanceof 90–130 km from the trench, where the islands are located,they both generate very large vertical and horizontal displace-ments and displacement gradients (Figure 1b and 1c). Thisfeature is crucial to our study.

2.2. Tsunami Induced by theExpected Sumatra Earthquake

[9] Using the vertical displacements from Figure 1b asthe initial wave heights along the trench in the region ofthe expected future earthquake (Figure 1a), we calculate thepropagation of the tsunami waves for rupture models 1and 2. To do so, we numerically solve nonlinear shallow-water equations in spherical coordinates using an explicit-in-time finite element integration scheme [Hanert et al.,2005] on an unstructured grid and wetting–drying boun-dary condition at the coast. The unstructured grid allowsfor increasing resolution close to the coastal regions,where the maximum accuracy of solution is required [Tintiand Gavagni, 1995]. The node spacing varies from 150 mnear the Sumatra coast to 15 km in the deep ocean. Inour model, we employ 1 arc minute bathymetry data(GEBCO: www.ngdc.noaa.gov/mgg/gebco/) supplementedby recently obtained detailed data for the Sumatra region(E. Fluh, personal communication).[10] The calculated tsunami wavefields are remarkably

different for the considered rupture scenarios. More proba-ble rupture model 1 generates a large tsunami in the seawarddirection from the trench but, due to the screening effect of

the islands, relatively low, but still dangerous, tsunamiwaves at the coast near the city of Padang (Figure 2, uppersection). In contrast, rupture model 2, with the deeper slipmaximum, generates very high tsunami waves at the Padangcoast, but smaller waves traveling into the open ocean(Figure 2, lower section). The resulting maximum heightsof the tsunami in Padang induced by rupture models 1 and 2differ by a factor of more than 5 (Figure 3). We emphasizethat these two rupture scenarios generating such differenttsunamis at Padang have the same magnitude and may becharacterized by the same hypocenter parameters. Thesecalculations therefore demonstrate that in order to correctlypredict near-field tsunami heights, it is not enough to knowmagnitude, epicenter location, and fault geometry of theearthquake, but it is also crucially important to know themain features of the slip distribution at depth. Moreover,due to the presence of the islands in the source, even far-field tsunamis appear to be sensitive to the slip distributionat the fault (note the difference in ocean-ward radiatedtsunamis for rupture models 1 and 2, Figure 2).[11] Even without islands in the source, a tsunami wave is

quite sensitive to the slip distribution at the fault if thedistance to the source is less then several hundred kilo-meters, i.e., so-called local tsunami case [Geist, 1998; Geistand Dmowska, 1999]. In this case, tsunami amplitude iscontrolled by slip (average slip and maximum slip) at thefault rather than by seismic moment. Therefore reliableprediction of the local tsunami amplitude requires know-ledge of higher order features of slip distribution thanseismic moment.

2.3. How to Estimate Fault Parameters Shortly Afterthe Earthquake?

[12] The question is whether it is possible to resolve themain features of the slip distribution at the fault shortly afterthe earthquake. To address this question, we recall recentadvances in using GPS to investigate the great Sumatranearthquakes of 2004 and 2005 [Vigny et al., 2005; Banerjeeet al., 2005; Catherine et al., 2005; Jade et al., 2005; Briggset al., 2006; Gahalaut et al., 2006; Subarya et al., 2006;Meltzner et al., 2006, Chlieh et al., 2007]. These studiesclearly showed that modern GPS techniques allow themeasurement of both horizontal and vertical coseismicdisplacements caused by a giant earthquake, and that thosedisplacements are coherent and very large (meter scale) inthe near-field [Briggs et al., 2006; Subarya et al., 2006;Gahalaut et al., 2006]. Moreover, it was also demonstratedthat GPS measurements could be inverted for the ruptureparameters [Vigny et al., 2005; Banerjee et al., 2005;Catherine et al., 2005; Jade et al., 2005; Briggs et al.,2006; Gahalaut et al., 2006; Subarya et al., 2006; Blewittet al., 2006; Hoechner et al., 2006; Chlieh et al., 2007].[13] However, there are two factors that prevent direct use

of these observations to predict tsunamis close to the source.First, differences in the inversion results [Vigny et al., 2005;Banerjee et al., 2005; Catherine et al., 2005; Jade et al.,2005; Gahalaut et al., 2006; Subarya et al., 2006] indicatethat the solutions are not unique for the case of the currentGPS station distribution, although seismic moment (magni-tude) of the 2004 earthquake can be estimated quite well[Freymueller, 2005; Blewitt et al., 2006]. Second, tsunami

Table 1. Estimated Rupture Parametersa

Model name 8 (�) z1 (km) W (km) Umean(m) q

Rupture model 1 12 1.3 250 8.5 0.34Rupture model 2 12 1.3 250 8.5 0.7Rupture Chile 20 10 150 10 0.5

aFor description of used parameterization [Freund and Barnett, 1976;Geist and Dmowska, 1999] and meaning of parameters, see Appendix A.

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Figure

2.

Maxim

um

tsunam

iheightsaftertheearthquakefrom

rupture

model1(upper

panel)andrupture

model2(lower

panel).

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early warning requires high-accuracy real-time GPS mea-surements, which are still uncommon.[14] To overcome ambiguity in resolving the rupture

parameters, we propose the use of real-time ‘‘GPS-Shield’’arrays, located proximal to the expected future source, at theislands in the Sumatra case, to exploit the expected largedisplacements (both horizontal and vertical) and theirtrench-perpendicular gradients in the source near-field fortsunami prediction (see Figures 1b and 1c). Note that theCaltech/LIPI SuGAR GPS network already has continuousGPS sites in some of the appropriate places, but unfortu-nately none of those sites are equipped to allow for real-timeapplications yet.[15] We first explain the basic functionality of the pro-

posed technique for the simplified two-dimensional caseand then demonstrate a full three-dimensional example insection 4.3. It is worth noting, however, that the two-dimensional approximation is sufficient for determiningthe deformation in the source near-field, which dependsmostly on the rupture process in the closest part of thesubduction zone.[16] In our analysis, we use the following procedure:

(1) we place one or more GPS stations along a trench-perpendicular profile; (2) we calculate the input signal, i.e.,synthetic surface displacements, for given rupture parame-ters using a dislocation model for an elastic homogeneoushalf-space [Okada, 1985] or layered half-space [Wang et al.,2006]; (3) we then define the accuracy for the synthetic‘‘observations’’ of vertical and horizontal displacements,and also for the relative displacements between the stations;(4) we next generate synthetic observations at each stationby randomly perturbing the input signal; (5) the syntheticobservations at all stations are then inverted for the ruptureparameters using parameterization [Geist and Dmowska,1999] and a nonlinear inversion method [Press et al.,1992]; (6) finally, we calculate the distribution of the staticvertical surface displacement (simulating the initial tsunamiwaveform) from the obtained rupture parameters and com-pare the results with the input signal. The above procedureis then repeated for another set of randomly perturbedsynthetic observations. As a result, we obtain a number ofrupture models and the corresponding vertical displacement

curves that may or may not fit the input model, dependingon the resolution of the synthetic GPS array.[17] Let us first place a single GPS station at a distance of

270 km from the trench, which corresponds to the locationof Padang. Now assuming a rather modest accuracy for real-time measurements of horizontal displacements (±5 cm) andvertical displacements (±10 cm) (see discussion below), wegenerate 500 sets of synthetic observations using rupturemodel 1 or 2. Each set is inverted for rupture parameters andthe corresponding prediction for the vertical displacement isshown by the gray (rupture model 1) or black (rupturemodel 2) curves in Figure 4a. It is clear from Figure 4a thatinverting observations from a single station cannot restorethe input signal with sufficient accuracy and thereforecannot issue a reliable prediction for the initial tsunamiwave and distinguish between rupture models 1 and 2.Interestingly, while failing to predict the initial tsunamiwave, the inversion of observations from a single stationstill allows us to estimate the seismic moment of thesynthetic earthquake with accuracy better than 10% inaccordance with estimations by Freymueller [2005] andBlewitt et al. [2006]. This again demonstrates that knowingthe earthquake’s seismic moment (magnitude), even with ahigh precision, is not sufficient to predict the local tsunamiintensity.[18] We repeat the above procedure for two stations

placed 90 km from the trench with a separation of 20 km,i.e., on Siberut Island located between the trench andPadang. The accuracy of absolute displacements at bothstations is assumed to be the same as in the previousexample, but the accuracy of measurements of relativedisplacements between closely spaced (10–30 km) stations(differential GPS) can be much better than that of theabsolute displacements [Bock et al., 2000]. Here weassume the relative accuracy to be ±3 cm for vertical and±1 cm for horizontal displacements (see next section).Using the previously defined GPS array, we performed aset of inversions for both rupture models as input signals(Figure 4b). It becomes clear from Figure 4b that the two-station array at Siberut Island is quite successful in predic-ting the initial tsunami height and in distinguishing betweenrupture models 1 and 2. If the two-station GPS array iscomplemented by an additional station at Padang, the inputsignals are restored even better (Figure 4c).[19] From the above exercises, we conclude that a near-

field array of GPS stations placed on Siberut Island is ableto correctly predict tsunami wave heights and to distinguishbetween more- and less-dangerous tsunami-generating rup-ture scenarios for Padang even if its real-time measuringaccuracy is modest, i.e., several centimeters.

3. Resolving Power of the GPS-Shield Arrays

3.1. Expected Measurement Accuracy of theGPS-Shield Arrays

[20] It is well known that GPS analyses based on long-term observations can attain millimeter scale accuracy in thepositioning of single receivers. However, a number ofproblems, such as ionospheric- and tropospheric-inducederrors, do not yet allow such accuracy to be achieved withsingle-epoch measurements in real time [Bock et al., 2000].Nevertheless, instantaneous GPS positioning techniques

Figure 3. Calculated wave heights close to the city ofPadang. The solid curve corresponds to rupture model 1 andthe dashed curve corresponds to model 2. Note that thetsunami hitting the city of Padang is more than five timeshigher for rupture model 2 than for model 1.

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[Bock et al., 2000; Bock et al., 2004], as well as the PrecisePoint Positioning (PPP) techniques [Zumberge et al., 1997]that are based on a combination of the original absolutepositioning concept and differential positioning techniques,

are rapidly progressing. It has recently been demonstratedthat instantaneous GPS positioning using single-epochmeasurements and a network of four stations is able torecord surface wave displacements with an accuracy of afew mm [Bock et al., 2004]. Based on this result, we inferthat accuracies of a few centimeters can easily be achievedfor single-epoch measurements of relative displacementsbetween stations separated by a few tens of kilometers. Theaccuracy of 30 s moving-window smoothed values, requiredfor our purposes, may be even better, although the actualresult of smoothing will strongly depend on the errorspectrum and needs further analyses.[21] To access accuracy of single-epoch measurements of

absolute displacements, we can use data of a high-rate (1 Hz)GPS station in Yogyakarta (Java) operated for several yearsby the GFZ Potsdam together with Bakosurtanal and GadahMaja University. The station is equipped with a precisegeodetic dual-frequency receiver. The typical RMS ofhorizontal displacements at this station is 1–1.5 cm andthe RMS of vertical displacements is close to 2–3 cm. Thisstation has continuously recorded GPS data during thecatastrophic Yogyakarta earthquake of 26 May 2006(Mw = 6.3), the epicenter of which was located at a distanceof about 30 km from the GPS site. The preliminaryprocessing of the station data clearly shows a horizontalstatic displacement, which is approximately 2 cm in thenorth component (Figure 5). To our knowledge, this was thefirst time that 1-Hz GPS observations were recorded before,during, and after an earthquake in the Indonesian region. Itdemonstrates that the GITEWS real-time GPS observationtechnique is adequate to measure absolute horizontal dis-placements with a precision of about 2 cm. Taking intoaccount observed RMS of the vertical displacements ofabout 2–3 cm, we can also safely assume that the accuracyof ±5 cm can be achieved for the single-epoch measure-ments of vertical displacements using GITEWS technique.[22] Based on the above estimations, we use three sets of

accuracy values in the following resolution tests. In set 1,hereafter called ‘‘realistic,’’ the accuracies for absolutevertical and horizontal displacements are assumed to be±5 and ±2.5 cm, respectively, while accuracies for relativedisplacements at closely spaced stations are assumed to be±1.5 and ±0.5 cm for vertical and horizontal displacements,respectively. In set 2, hereafter called ‘‘conservative,’’ all

Figure 4. (a) Calculated vertical displacements (grey orblack curves) using rupture parameters derived frominversion of the synthetic observations at single GPS stationplaced at Padang (filled triangle) and rupture model 1 or 2(white solid or dashed curves, respectively). Each gray orblack curve corresponds to the inversion using a single set ofsynthetic observations with synthetic random noise. (b, c)The same as Figure 4a, but for an array of two stations placedon Siberut Island (b) and three GPS stations, two on SiberutIsland and one at Padang (c), each shown as filled triangles.

Figure 5. Northern displacement component at the high-rate GPS station JOG2, located near the city of Yogyakarta(Java) with the record of the Yogyakarta earthquake of26 May 2006 (Mw = 6.3).

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errors are doubled. In set 3, hereafter called ‘‘pessimistic,’’all errors are doubled again.

3.2. Resolution Tests

[23] We now address a question of how the resolvingpower of the near-field GPS (GPS-Shield) arrays dependsupon (1) their distance from the trench, (2) the accuracy ofdisplacement measurements at the stations, and (3) uncer-tainty of our knowledge about the fault geometry. To do so,we consider input signal according to rupture model 1 andarray of two stations with 20 km spacing between thestations. Using the multiple inversion procedure as des-cribed above, we analyze how well the particular array canresolve seismic moment, average displacement at the faultand location of displacement maximum at the fault. First weassume that the dipping angle of the fault is known but otherparameters can be varied over a very large range (Table 2).The results of this analysis are presented in Figure 6, whichshows the normalized RMS difference between the invertedvalues of those parameters to their input values versusdistance of the GPS array from the trench. Different curvescorrespond to different assumptions on the accuracy of thedisplacement measurements. As we see from Figure 6, allparameters are resolved best if the array is located justabove the maximum slip at the fault (80–90 km from thetrench). By moving the array landward the resolutiondecreases, but it remains quite good for all parameters untilthe array is moved away from the surface projection of therupture zone. Arrays located still farther from the trenchstrongly decrease their resolution in respect to average slipand location of the slip maximum, and at distances morethan 100 km landward from the downdip limit of the rupturezone, the resolution for these parameters becomes poor,similar to the resolution which can be achieved by asingle GPS station. However, the resolution for the seismicmoment decreases much slower with increasing distance

Figure 6. Root mean square (RMS) of the deviation of theinversion results from the input (rupture model 1) as afunction of the distance from the trench for the two-station GPS array with the station separation of 20 km.(a) Normalized seismic moment; (b) normalized averagedisplacement at the fault; and (c) normalized horizontalcoordinate of the slip maximum at the fault. Differentcurves correspond to different assumptions about theaccuracy of the GPS measurements. Solid curves withsquares correspond to the ‘‘realistic’’ set of accuracynumbers, solid curves with rhombs to the ‘‘conservative’’set and dashed curves with rhombs to the ‘‘pessimistic’’ set(see text for definitions). In the inversion, the dipping angleof the fault is assumed to be known (12�), and the width ofthe rupture zone is assumed to be poorly constrained (lyingbetween 100 and 300 km).

Table 2. Parameter Ranges Assumed in Two-Dimensional

Inversion

Updip depth of a fault (z1) 10.5–15 kmRupture zone width (W) 100–300 or 225–275 kmAverage slip (Umean) 2.5–15.5 mDip angle (8) precise (12�) or 10–15�Asymmetry parameter (q) 0.1–0.9

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and remains quite good even if the GPS array (or singleGPS station) is located by more than 500 km away from thetrench.[24] The major conclusions from Figure 6 are as follows:

(1) an array of closely spaced GPS stations aligned along atrench-perpendicular line can resolve seismic moment(magnitude) of the rupture with very high accuracy evenif it is located several hundred kilometers from the trench;(2) the array can do a much better job than just estimatingseismic moment, i.e., resolve the rupture parameters likeaverage displacement at the fault and location of thedisplacement maximum, with accuracy sufficient for tsu-nami prediction, provided it is located above the rupturezone; (3) if the array is placed less than some 100 km awayfrom the rupture zone, it still can resolve more than just theseismic moment, but the accuracy strongly reduces whilethe array is moved farther away from the rupture zone.[25] The higher the accuracy of the measurements at

single GPS stations, the larger is the distance from thetrench at which GPS array can resolve the rupture para-meters. For instance, at the distance of array from the trenchof 300 km, the resolution of the arrays measuring with‘‘realistic’’ accuracy is by two to three times higher than theresolution of the arrays measuring with ‘‘pessimistic’’accuracy (Figure 6).[26] Now let us assume that some additional data (e.g.,

long-term seismic and GPS observations) constrain thewidth of the rupture zone with relatively high accuracy of±25 km rather than ±100 km as in the previous test. In thiscase, the resolution of the average slip at the fault is greatlyimproved, while location of displacement maximum isresolved only slightly better and resolution of seismicmoment remains the same as in the previous test (compareFigure 7 with Figure 6).[27] It was recently demonstrated [Banerjee et al., 2005]

that slip inversions from GPS data are very sensitive toassumed fault geometry, especially when relying on thenear-field data. That is, the lack of precise dip/geometryinformation may add significantly to the uncertainty in theslip parameters obtained. We test this possibility usingsimilar resolution tests as before but assuming in inversionthat the width of the rupture zone is poorly constrained (asin the first test) and that the angle of subduction zone isunknown and may vary in inversion between 10� and 15�(with actual value of 12�). The results of this test (Figure 8)confirm that uncertainty in subduction zone geometry cansignificantly reduce accuracy of estimating rupture para-meters (especially location of slip maximum) at islands andSumatra–Java coasts (compare Figure 8 with Figure 6).[28] From the above tests, it is clear that the Mentawai

islands in front of Sumatra are the best places to install GPSarrays. The inversion results are particularly good if faultgeometry is also constrained by other observations. TheGPS-Shield arrays at Sumatra and Java coasts (250–300 kmfrom the trench) can be used to precisely estimate theseismic moment of a giant earthquake. In addition, theaverage displacement and location of displacement maxi-mum could be also estimated if the fault geometry is wellknown and the accuracy of real-time GPS measurements isbetter than few centimeters. The precise mapping of theseismogenic-zone geometry can be accomplished with long-term observations using broadband seismometers and

Figure 7. The same as Figure 6 but for the inversion withthe better constrained (±25 km) width of the rupture zone.

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GPS stations, while the few-centimeter accuracy of real-time GPS-Shield arrays measurements is quite realistic, asdiscussed in the previous section.

4. The GPS-Shield Concept forSumatra and Java

4.1. Basic Concept

[29] Key elements of the ‘‘GPS-Shield’’ concept forSumatra are near-field GPS arrays operating in real time.Frontal part of the array consists of two (or more) GPSstations located on the Mentawai islands between theSumatran coast and the trench (Figure 9). Stations in thearray are closely spaced (10–20 km) and aligned perpen-dicular to the trench, i.e., parallel to the expected gradient ofsurface coseismic displacement. One master station andseveral slave stations are all equipped with precise geodeticdual-frequency receivers, a digital meteorological sensor,data processor unit, and radio modems. The array masterstation continuously receives high-rate GPS-observations at1 Hz (and at 10 Hz in the case of an earthquake) from itsslave station(s) and calculates the coordinate differences foreach single measurement epoch in real time, as suggestedby Bock et al. [2000, 2004].[30] The island-hosted parts of arrays are complemented

by GPS stations located directly at the Sumatran coast alongthe same lines. The latter ‘‘control’’ stations, serve toimprove inversion of the rupture parameters and to checkthe internal consistency of a solution. The GPS-Shieldarrays are set along the trench with the spacing appropriateto resolve major trench-parallel slip heterogeneity, which,based on analyses of the 2004 and 2005 events, is expectedto be approximately 100–200 km for the giant earthquake.In the case where there are no islands between the trenchand Sumatra, we suggest the use GPS-Shield arrays at theSumatran coast and ocean buoys equipped with GPSdevices and bottom pressure sensors. The whole system iscompleted with GPS tide gauges on the islands.[31] No islands are located between the trench and

Java (Figure 9). However, as shown in the previous section,GPS-Shield arrays at the Java coast can still be used in thiscase to estimate higher order features of slip distribution atthe fault than seismic moment. Important preconditions toachieve this are that the arrays are placed as close aspossible to the trench and that the geometry of the rupturezone is constrained using long-term seismic and GPSobservations. In the case of Java, the GPS-Shield systemshould consist of several GPS-Shield arrays placed alongthe Java western coast at a distance of about 100–200 km toresolve trench-parallel heterogeneity of the potential rupture(Figure 9). A number of ocean buoys equipped with GPSdevices and bottom pressure sensors should be placed closeto the trench to verify and specify tsunami waveformpredictions derived from the land observations (Figure 9).

4.2. System Functionality Test for the FutureSumatra Earthquake

[32] To examine the functionality of the proposed sys-tem for Sumatra, we performed a three-dimensional simu-lation of the entire rupture process of the earthquakelargely repeating the 1797/1833 events. Synthetic seismo-grams for the scenario earthquake are calculated using the

Figure 8. The same as Figure 6 but for the inversion withthe unknown dip angle of the fault lying between 10–15�.

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deterministic Green’s function method [Wang, 1999] basedon the IASPEI91 elastic layered-Earth model [Kennett andEngdahl, 1991]. In this simulation, the rupture starts in thedeep part of the seismogenic zone northeast of SiberutIsland (star in Figure 9) and propagates updip and south-ward in a trench-parallel direction circularly with a velo-city of 2.5 km/s. The focal parameters and the slipdistribution are listed in Table 1. The ruptured area (692 �250 km) is discretized into about 2600 patches (each of14 km � 5 km size) being treated as point sources. Eachpoint source is composed of a set of Brune’s omega-squaresubevents [Brune, 1970], which are distributed according tothe Gutenberg-Richter law in size and randomly in time. Itis necessary to introduce the randomness into the sourcetime function so that adjacent point sources are reasonablycoherent at low frequency, but incoherent at high frequency[e.g., Irikura, 1983]. The seismic moment of each point

source is released within a time comparable to the risetimeof the entire earthquake. By assuming an average stressdrop of 20 MPa, the risetime of the present scenarioearthquake (Mw �9.1) is estimated to be ca. 100 secondsaccording to the empirical relation of Boore [1983].[33] According to this model, the first seismic signal

arrives at the Siberut and Padang stations less than 20 safter the rupture begins. This signal or much more powerfulS wave signal coming some 10–20 s later (Figure 10) canbe used to switch the observational network into a high-sampling rate mode. At about 30–40 s, the GPS stationsclosest to the rupture zone begin to record large displace-ments simultaneously with arrivals of S waves and firstsurface waves [see also Freymueller, 2005]. After some3 minutes, both vertical and horizontal displacements atGPS stations close to the epicenter almost approach theirstatic values (Figure 11). The displacement oscillations

Figure 9. Concept of the GPS-shield system in the region of Sumatra and Java. Red circles are real-timeGPS stations. Red circles withwhite rings are the sameGPS stations that are also equippedwith a broadbandseismometer and strong motion recorder. The key elements of the system consist of arrays of two (or more)GPS stations (GPS-Shield arrays) located on the islands, immediately above the potential rupture zone andat the Sumatra and Java western coasts. The GPS buoys (red diamonds) are placed where no islands arelocated between the trench and Sumatra and along the Java trench. The zone of possible future earthquake atthe site of the past 1787/1833 earthquakes is indicated. The dashed box and star indicate the rupture zoneand epicenter of the modeled earthquake. Numbers mark the sites where synthetic seismograms werecalculated and which are used for the three-dimensional inversion for rupture parameters.

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with amplitude up to 30–50 cm continue until the rupture ispropagating and generating surface waves, i.e., about 3–5 minutes in our model. Note however that these oscilla-tions can be efficiently smoothed out by 30 s movingaverage. Thus, the first inversion for the rupture parametersusing GPS data can already be carried out at about 3 minutesafter the rupture begins. It is important that even at this earlystage, two scenarios (rupture model 1 and 2) can be clearlydistinguished.[34] After 6–7 minutes, static displacements are fully

established at all stations, and rupture parameters can beresolved (see section 4.3). By this time, the tsunami wavehas already passed the tide gauge at Siberut Island, allowingthe further verification of the estimated rupture parameters.Therefore we expect that the qualified tsunami warning forthe entire Sumatra can be issued 6–7 minutes after therupture begins and even earlier for the region of Padang. Atthat time it will be possible to accurately predict the tsunamiwave heights and thus distinguish between catastrophic andless dangerous scenarios. This leaves more than 18 minutesbefore the tsunami hits the coast at Padang.[35] In addition, we suggest complementing at least some

of the master GPS stations in arrays with broadband

seismometers and strong motion recorders (Figure 9). Thestrong motion recorders can provide additional informationabout the rupture parameters [Ji et al., 2002], while thebroadband seismometers can be used over the long term tomap the seismogenic zone topography. Moreover, the seis-mometers can also provide information about possibleasperities by mapping the distribution of b values [Wyssand Stefansson, 2006]. It would also be useful to installtiltmeters at Sumatra and Java coasts to measure coseismicdeformations where resolution of GPS-Shield arrays isrelatively low.[36] Finally we can compare our synthetic displacement

seismograms with the real data for giant earthquakes. Theraw observations from the December 2004 earthquake atSAMP (Sampali, Sumatra) show about 17 cm peak-to-peakvariation after the earthquake, and this substantial variationcontinues for some 10–15 minutes after the main shock[Freymueller, 2005, see also Figure 1 of Blewitt et al.,2006]. In our model, station 18 (see Figure 9) is at thesimilar distance from the rupture as SAMP. As we see fromFigure 11, the amplitude of synthetic displacement oscil-lations at station 18 is also about 15–20 cm peak-to-peak asat SAMP. Different is only the duration of oscillations,

Figure 10. Calculated synthetic vertical acceleration seismograms (low-pass filtered) at the sitesnumbered in Figure 9.

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Figure 11. Calculated synthetic displacement seismograms at the sites numbered in Figure 9. The x axisis the time in seconds since the time of the origin of the earthquake, and the y axis is the displacement inmeters. The north, east, and vertical (downward positive) components are indicated by letters, N, E, andZ, respectively. Note that amplitude scales are different for different figures. Seismograms at two stationson Siberut Island and in the city of Padang are especially indicated.

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which is about 4 minutes instead of more than 10 minutesat SAMP. This difference is likely due to the differentduration of our model rupture (5 minutes) and rupture of26 December 2007, which is known to be longer than10 minutes.

4.3. Three-Dimensional Inversion of StaticDisplacements for Rupture Parameters

[37] In this section we present results of three-dimensionalinversions for rupture parameters of synthetic observationsat GPS stations marked by numbers in Figure 9. We explore

Figure 12. Input (upper panel) and inverted (lower panel) distributions of slip at a fault for rupturemodel 1 (left column), model 2 (middle column), and model with checkerboard distribution of slip (rightcolumn). Circles mark locations of synthetic GPS stations. See also Animations 1–3 showing results ofreal-time inversions of synthetic displacements.

Figure 13. Comparison of ‘‘predicted’’ (dashed curves) and ‘‘observed’’ (solid curves) wave heights attide gauges located near the cities of Padang and Bengkulu for rupture model 1 (left graph) and model 2(right graph). The ‘‘predicted’’ wavefields are calculated based on the slip distributions derived fromthree-dimensional inversion of synthetic GPS observations (lower section of Figure 12), while the‘‘observed’’ wavefields are calculated based on the input three-dimensional slip distributions (uppersection of Figure 12).

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three rupture models with slip distributions shown in theupper section of Figure 12, i.e., rupture models 1 and 2 and amodel with checkerboard distribution of slip at the fault.Inversion is accomplished for distributions of amplitude ofthe slip vector and for the rake angle in a number of rectangularpatches (subfaults), which cover the potential source regionassuming that dip angle of the rupture plane is known to be12�. We employ a quasi-Newton line search technique tominimize squares of differences of model-predicted and‘‘observed’’ (synthetic) displacements at GPS stations, simul-taneouslyminimizing differences of slipmagnitudes and rakesbetween adjacent subfaults. Displacements are calculatedusing Green’s functions precomputed for the layered Earthmodel using technique by Wang et al. [2006], and the‘‘observed’’ (synthetic) displacements at GPS stations areperturbed with random noise of ±10 cm for vertical displace-ments and ±5 cm for horizontal displacements.[38] As it is demonstrated by the results of inversion

(lower section of Figure 12), observations at GPS-Shieldstations at islands and at the Sumatran coast allow robustestimation of rupture parameters for all tested rupturemodels. Rupture models 1 and 2 can be distinguished very

well, and in accordance with the two-dimensional tests, thebest resolution is achieved where the GPS stations areclosest to the source. See also Animations 1–3 showingresults of real-time inversions of synthetic displacements.[39] Based on the slip distributions derived from three-

dimensional inversion (lower section of Figure 12), wecalculate the propagation of the tsunami waves for rupturemodels 1 and 2 and compare results with ‘‘observed’’ waves,i.e., waves calculated for the input slip distributions (uppersection of Figure 12). Results of this comparison are pre-sented in Figure 13 for synthetic tide gauges located near thecities of Padang and Bengkulu. As one can see, the predictedtsunami waves are quite similar to the ‘‘observed’’ waves. Itis also clear that three-dimensional inversion results allowdistinguishing rupture models 1 and 2 very well.[40] We have also checked the three-dimensional resolu-

tion of GPS-Shield arrays with reduced number of stations.If no stations are installed at the islands, the resolution ofthe array significantly decreases, in accordance with thetwo-dimensional tests of section 2.3. On the other hand, anarray with all island stations in place but no stations at theSumatra coast (subarray A) as well as an array with single,

Figure 14. (a) The expected location of the rupture zone in northern Chile (marked by the white dashedline). (b) Static vertical displacements for the earthquake with parameters similar to those of the GreatChilean Earthquake (upper white solid curve) and an earthquake with a five times smaller average slip atthe fault (lower white solid curve). Black curves are calculated vertical displacements using ruptureparameters derived from the inversion of the synthetic observations at three stations (filled triangles)separated by 10 km, placed at the coast near the city of Arica. Each black curve corresponds to theinversion using a single set of synthetic observations with random noise of ±10 cm and ±5 cm for verticaland horizontal absolute displacements and ±3 cm and ±1 cm for vertical and horizontal relativedisplacements, respectively (‘‘conservative’’ accuracy set). Grey curves show the same but with twice asmuch noise (‘‘pessimistic’’ accuracy set). (c) The same as Figure 14b, but for the city of Antofagasta,which is located closer to the trench than Arica.

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instead of double, stations at the islands and with all stationsat the Sumatra coast (subarray B), have almost the sameresolution as the complete array. Thus, theoretically thesereduced arrays can also be efficiently used for tsunami earlywarning. They, however, strongly lose their resolution if anyof the stations fails. In contrast, the complete GPS-Shieldconfiguration, presented in Figure 9, performs well if anystation fails. Moreover, results of inversion of displace-ments measured by the complete array may be checked forinternal consistency by comparison of independent inver-sions for the subarrays A and B, thus increasing solutionconfidence.

5. The GPS-Shield for Northern Chile andElsewhere

[41] Application of the proposed GPS-Shield concept isnot limited geographically to Sumatra. As we have shownabove, GPS arrays are efficient in resolving tsunami-controlling rupture parameters everywhere, provided theyare placed just above or closer than 100 km to the rupturezone. Other regions where giant earthquakes and tsunamisare expected include Cascadia [Hyndman et al., 1996;Mazzotti et al., 2003; Chlieh et al., 2004] and the coastof Chile, particularly northern Chile where a giant earth-quake may occur in the near future [Chlieh et al., 2004].Using the rupture parameters of the 1960 Great ChileanEarthquake [Barrientos and Ward, 1990] (Table 1), thesame resolution test as before demonstrates that arrays oftwo or three closely spaced GPS stations at the coast canprovide a confident estimate of the initial tsunami height atthe corresponding segment of the subduction zone alongthe entire north-Chilean coastline (Figure 14). Very highresolution can be achieved if the GPS-Shield array isplaced close to the city of Antofagasta that is located onlysome 100 km from the trench. The lowest resolution isexpected for the city of Arica that is located far most fromthe trench. But even in this case, initial tsunami waves canbe estimated reasonably well (Figure 14).[42] Preliminary analysis implies that the GPS-Shield

concept can potentially also be applied to the entire coast

of Chile, the Middle America subduction zone, the PacificNorthwest, Southern Japan, the Aleutian and Kuril Islands,Kamtchatka, and Alaska, as well as to the subduction zonesin the Mediterranean, etc. (Figure 15). Moreover, by pro-viding fast and robust estimation of the initial tsunamiwaveforms, GPS-Shield arrays may also be implementedfor far-field tsunami warnings, thus becoming an importantcomponent of the global tsunami early warning system[Sobolev et al., 2006] (see also Figure 15). It looks likethat the GPS-Shield arrays can be efficiently used at most ofthe tsunamigenic active margins. The best results in pre-dicting tsunami waves within less than 10 minutes of anearthquake can be obtained where the land is located closerthan 100 km to the seismogenic zone (solid curves inFigure 15). If the land is located at larger distances, butstill closer than 500 km from the trench (dashed curves inFigure 15), the GPS-Shield arrays can be used at least forfast and precise estimation of the seismic moment of largeearthquakes. It is also important to mention that the globalGPS-Shield arrays will in fact serve at least two importantpurposes. In addition to their tsunami-warning functiondescribed above, the arrays will also allow long-term defor-mation monitoring in most convergent plate boundaries.This function will provide important data for constrainingglobal geodynamics and, in particular, the processes thatlead to large megathrust earthquakes.

6. Concluding Remarks

[43] We demonstrated that in the presence of massiveislands close to the trench, the tsunami height becomesespecially sensitive to slip distribution at the fault. In thecase of giant earthquakes west of Sumatra, wave heights atPadang may differ by more than a factor of 5 for ruptureshaving the same seismic magnitude but different slipdistribution. Therefore reliable prediction of tsunami waveheights in such cases cannot be provided using traditional,earthquake-magnitude-based methods. This is also true forthe local tsunami in general, as the source near-fieldtsunami height is controlled by the slip at the fault (meanslip and maximum slip) rather than seismic moment of theearthquake.[44] The reliable prediction of tsunami waves can be

issued within less than 10 minutes of an earthquake byincorporating special types of near-field GPS arrays (‘‘GPS-Shield’’), which can resolve higher order features of the slipdistribution at the fault than seismic moment. Frontalstations in the arrays are closely spaced (10–20 km) andall stations are aligned perpendicular to the trench, i.e.,parallel to the expected gradient of surface coseismicdisplacement. In the case of Sumatra and Java, the GPS-Shield arrays should be placed along the trench at MentawaiIslands, located between the trench and Sumatra and directlyin the Sumatra and Java western coasts. In particular, theGPS-Shield array with stations placed on Siberut Island andnear Padang, even with a modest measuring accuracy ofseveral centimeters, is able to correctly predict tsunamiwave heights and to distinguish between more and lessdangerous tsunami-generating rupture scenarios for Padang.[45] The resolution tests show that the GPS-Shield array

or even single GPS station can resolve seismic moment(magnitude) of the rupture with very high accuracy even if it

Figure 15. Global application of the GPS-Shield concept.Solid curves indicate subduction zones where the land islocated closer than 100 km to the seismogenic zone, i.e.,where the real-time GPS-Shield arrays likely can resolvemajor features of slip distribution on the fault. Dashedcurves indicate zones where the GPS-Shield arrays can atleast resolve the seismic moment of the closest largeearthquakes.

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is located several hundred kilometers from the trench. Thearray can do a much better job than just estimating seismicmoment and can resolve average displacement at the faultand location of the displacement maximum with accuracysufficient for tsunami prediction, provided it is locatedabove the rupture zone. If the array is placed less thanapproximately 100 km away from the rupture zone, it stillcan resolve more than just seismic moment, but the accu-racy strongly reduces while the array is moved farther awayfrom the rupture zone.[46] To improve resolution of the GPS-Shield arrays, it is

important to constrain as precise as possible the geometry ofthe possible rupture zone. This can be accomplished withlong-term observations using broadband seismometers andGPS stations.[47] The GPS-Shield concept is not restricted regionally

to Sumatra and Java. We demonstrated that the ‘‘GPS-Shield’’ could also be applied to northern Chile, where agiant earthquake may occur in the near future. Moreover,this concept may be applied globally to many other tsuna-migenic active margins where the land is located above orclose to seismogenic zones.[48] In fact, the global GPS-Shield arrays will serve at

least two important purposes. In addition to their tsunami-warning function described above, the arrays will also allowlong-term deformation monitoring in most convergent plate

boundaries. This function will provide important data forconstraining global geodynamics and, in particular, theprocesses that lead to large megathrust earthquakes.[49] Finally, we summarize benefits of the GPS-Shield

concept for tsunami early warning in comparison to whatcan be achieved by traditional methods based on earthquakemagnitudes.[50] (1) As a minimum, the GPS-Shield arrays placed

along the trench will be able to estimate seismic moment(magnitude) of the corresponding sections of a rupture zone(partial magnitude) within just a few minutes of an earth-quake. Traditional teleseismic methods allow estimation ofthe seismic magnitude for the entire rupture and then onlymore than 10 minutes after an event.[51] (2) If placed above or close to the rupture zone, the

GPS-Shield arrays will be able to resolve major features ofslip distribution not only parallel to the trench, but alsodowndip along the subduction fault, thereby doing a muchbetter job than is possible by just estimating the seismicmoment. This will allow much more reliable prediction oftsunami amplitudes, especially in the case of islands abovethe rupture zone that strongly affect the tsunami-generationprocess.[52] (3) The GPS-Shield is also able to capture relatively

slow (tens of minutes) post-slip at the fault which isundetectable using seismic methods, but may well contri-

Figure A1. (a) Slip distribution in the rupture zone of the Great Sumatra Earthquake of 26 December2004 from three-dimensional inversion of GPS data after Hoechner et al. [2006]. (b) Slip distributionsalong cross-sections shown in Figure A1a. Solid lines present inversion results and dashed curves showtheir approximation using parameterization by Freund and Barnett [1976] and Geist and Dmowska[1999].

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bute to tsunami generation [Lay et al., 2005; Kanamori andStewart, 1979].

Appendix A

[53] The parameterization by Freund and Barnett [1976]and Geist and Dmowska [1999] defines the slip distributionin the local downdip fault coordinate x as

U ¼ 2Umeanx2 �2xþ 3qð Þ=q3; if 0 � x � q

U ¼ 2Umean 2x3 � 3x2 � 3qx2 þ 6qx� 3qþ 1� �

= 1� qð Þ3;if q < x � 1;

where Umean is the average slip at the fault; x is the localcoordinate at the fault, normalized to its width and is 0 at thefault updip edge and 1 at the fault downdip edge; q is thecoordinate at which displacement achieves the maximum. Inthis parameterization, the single fault in two dimensions isdefined by the following parameters: fault azimuth, dipangle (8), updip depth of a fault (z1), width of the rupturezone (W), average slip (Umean), and a parameter q describingthe asymmetry of the slip distribution.[54] As demonstrated in Figure A1, the above paramete-

rization can accurately describe slip distribution at a cross-section through the actual rupture zone (Great SumatranEarthquake of 26 December 2004) derived from inversionof GPS observations by Hoechner et al. [2006], which issimilar to the inversion results by Chlieh et al. [2007].

[55] Acknowledgments. This is publication no. 12 of the GITEWSproject (German Indian ocean Tsunami Early Warning System). The projectis carried out through a large group of scientists and engineers fromGeoForschungsZentrum Potsdam (GFZ) and its partners from the GermanAerospace Centre (DLR), the Alfred Wegener Institute for Polar and MarineResearch (AWI), the GKSS Research Centre, the Leibniz Institute forMarine Sciences (IFM-GEOMAR), the United Nations University (UNU),the Federal Institute for Geosciences and Natural Resources (BGR), theGerman Agency for Technical Cooperation (GTZ), as well as fromIndonesian and other international partners. Funding is provided by theGerman Federal Ministry for Education and Research (BMBF), Grant03TSU01. E. Fluh provided unpublished bathymetry data. We are gratefulto R. Hackney and K. Fleming for carefully reading the manuscript and tothe members of the GITEWS team for useful discussion. Reviews by J.Freymueller, R. Burgmann, and H. Latief were very helpful to improve themanuscript.

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�����������������������A. Y. Babeyko, R. Galas, A. Hoechner, J. Lauterjung, M. Rothacher, S. V.

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