JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B08309, doi: /2002jb002381, 2004

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2002jb002381, 2004 A multiple time window rupture model for the 1999 Chi-Chi earthquake from a combined inversion of teleseismic, surface wave, strong motion, and GPS data H. K. Thio, R. W. Graves, and P. G. Somerville URS Corporation, Pasadena, California, USA T. Sato and T. Ishii Ohsaki Research Institute, Shimizu Corporation, Tokyo, Japan Received 30 December 2002; revised 4 February 2004; accepted 2 April 2004; published 24 August [1] We present the results of a comprehensive analysis of the rupture process of the 1999 Chi-Chi, Taiwan, earthquake using a broad array of seismic as well as geodetic data, spanning a very wide frequency band. Our results indicate that the rupture was quite smooth, with the slip concentrated in a wide arcuate region north of the epicenter with very little slip to the east or south. We found a moment of dyn cm, which is consistent with the long-period determinations for this earthquake. The rupture velocity is approximately 2.25 km/s and is quite uniform across the fault. We have tested both a single fault plane model as well as a composite fault model with a second E-W striking plane to the north of the rupture to improve the fit of the geodetic data. Overall, the differences in slip distribution between the two models are negligible, but the fit to the GPS data is significantly better for the composite model, which is thus our preferred solution. This model is similar to other rupture models as far as the large-scale features are concerned but differs for the smaller asperities that are present in other models but not as much in ours. These are usually poorly constrained, and with the use of the geodetic data we believe that there is little evidence for a significant amount of slip away from our main slip concentration. INDEX TERMS: 7209 Seismology: Earthquake dynamics and mechanics; 7212 Seismology: Earthquake ground motions and engineering; 7215 Seismology: Earthquake parameters; 7255 Seismology: Surface waves and free oscillations; 8010 Structural Geology: Fractures and faults; KEYWORDS: Taiwan, earthquake, rupture, kinematic, inversion, model Citation: Thio, H. K., R. W. Graves, P. G. Somerville, T. Sato, and T. Ishii (2004), A multiple time window rupture model for the 1999 Chi-Chi earthquake from a combined inversion of teleseismic, surface wave, strong motion, and GPS data, J. Geophys. Res., 109,, doi: /2002jb Introduction [2] The 1999 Chi-Chi earthquake is the largest earthquake on the island of Taiwan (Figure 1) in the 20th century and caused more than 2000 fatalities and extensive damage in the fault area. Estimates of its size range from 6.5 (m b )to 7.7 (M S ), with a local magnitude of 7.2, determined by the Central Weather Bureau (CWB) (Table 1). The earthquake created a fault scarp over a length of 80 km, along the Chelungpu fault (Figure 2), with a maximum displacement of 9 m at the northern end. The island is very densely instrumented with digital strong motion sensors (Figure 2) [Shin et al., 2003], and hundreds of very high quality records have been made available. In addition, a large and densely spaced set of displacement vectors from GPS observations have been published by Yang et al. [2000]. [3] Several studies regarding the rupture process of this earthquake have already appeared in the literature [e.g., Ji Copyright 2004 by the American Geophysical Union /04/2002JB002381$09.00 et al., 2001; Ma et al., 2001; Chi et al., 2001] (see Table 2), and to a first order, these models are consistent. As is to be expected, in the smaller details these models start to diverge, partly due to different data sets that are used, partly due to different methodology and inversion parameters. The tremendous wealth of data that is available for this earthquake means that it will be studied extensively in the future as well, as more sophisticated methods are being developed, for instance to study the dynamics of the fault rupture [e.g., Zhang et al., 2003]. Our aim in this study is to provide a comprehensive and detailed rupture model for this earthquake based on the joint inversion of teleseismic, surface wave, strong motion, and geodetic data. This model will satisfy the widest range of data, but with a simple fault model to avoid overparameterization of the inverse problem. 2. Tectonic Environment [4] Taiwan is located on the boundary between the Philippine Sea plate and the Eurasia plate (Figure 1). Its 1of11

2 Figure 1. Regional tectonic map of Taiwan [from Vitz- Finzi, 2000] showing the major tectonic elements. Indicated are the (a) Coastal Plain, (b) Fold-and-Thrust Zone, (c) the Central Range, and (d) the Coastal Range. LV is the Longitudinal Valley. tectonic environment is quite complex, with the Eurasia plate subducting under the Philippine Sea plate south of Taiwan along the Manila trench and the Philippine Sea plate subducting under the Eurasia plate east of Taiwan along the Ryukyu trench. The location of Taiwan coincides with a 90 change in orientation of the plate boundary. The convergence rate between the Philippine Sea and Eurasia plates is 70 mm/yr [Seno et al., 1993]. [5] Taiwan is often used as a typical example of a thinskinned tectonic environment [e.g., Suppe, 1987], and the fold and thrust belt and the Central Range are generally recognized as an accretionary prism caused by the collision of the two plates. Wu et al. [1997] have argued for a more Table 1. Hypocentral Parameters a Origin Time, UT Longitude, E Latitude, N Depth, km M L m b M S Agency 1747: CWB 1747: NEIC a CWB, Central Weather Bureau, Taiwan; NEIC, National Earthquake Information Center, U.S. Geological Survey. Figure 2. Strong motion stations around the Chi-Chi earthquake, color-coded according to the soil types from Lee et al. [2001]. The soil types follow the general tectonic division of the island with type E in the coastal plain, type D in the fold-and-thrust belt and coastal range, and types B and C in the central range. The major frontal fault (FF) and the Chelungpu Fault (CF) are shown as red dashed and solid lines, respectively. The red boxed area represents the extent of the initial fault model in our inversion. The area in the dashed rectangle is shown in the inset, where all the strong motion stations that were used in the inversion are shown. The blue square represents the epicenter. deep-seated tectonic deformation (lithospheric collision) based on the depth extent of the seismicity in the region, from which they conclude that the deeper crust and even upper mantle are actively participating in the deformation of the Taiwan. Wang et al. [2000] argue in favor of the thin- 2of11

3 Table 2. Focal Mechanism and Moments Strike, deg Dip, deg skinned model based on the limited depth extent of the Chi- Chi earthquake, but Kao and Chen [2000] demonstrate that some of the aftershocks of the Chi-Chi earthquake are as deep as 30 km. [6] The location of this earthquake was not characterized by a high rate of seismicity beforehand. Most earthquakes in Taiwan are concentrated at the eastern side of the island and there is a cluster of events southwest of the current event, where two M = 7 events occurred in the 20th century. The event took place on the Chelungpu (Figure 2) fault, which is one of a series of imbricate thrust faults that cross Taiwan along its length. The convergence between the Philippine Sea and Eurasia plates it distributed among these faults, which are part of the fault and thrust belt and the Central Range (Figure 1) [Vita-Finzi, 2000]. 3. Data Slip, deg Moment, N m Data a Source first motion Chang et al. [2000] TB/SW Harvard SW Caltech 1.7 TB U.S. Geological Survey.5 TB Lee and Ma [2000] TB Ma et al. [2000] 2.3 TB Ma et al. [2001] 4.6 TB/SM/GPS Ma et al. [2001] TB/SM Kikuchi et al. [2000] 1.4 SM Iwata et al. [2000] 4.0 SM Chi et al. [2001] GPS Wang et al. [2001] 5.4 GPS Yoshioka [2001] 2.7 TB/SM/GPS Ji et al. [2003] 3.3 TB/SW/SM/GPS this study a TB, teleseismic body wave; SW, surface waves; SM, strong motion data; GPS; geodetic data. [7] A wealth of very high quality data is available for this earthquake. In this section, we briefly describe data that we used, the processing involved (if any) and the selection criteria used Teleseismic Data [8] We have compiled a large set of teleseismic body wave data and made a selection to achieve a good azimuthal coverage but also a good coverage for takeoff angles (Figure 3). The distances were restricted to within a range of 30 to 90 to prevent complications such as upper mantle triplications (at smaller distances) or scattering and diffraction from DPrime; (at larger distances). We used 34 stations in total, all of which yielded good P as well as SH waveforms, for a total of 68 records. All records were deconvolved to displacement, with a very broadband response ( Hz), and resampled at a rate of 4 Hz Surface Wave Data [9] The surface wave data were also deconvolved to displacement and band-pass-filtered between and Hz. This frequency band is well suited for source studies since the path corrections are relatively simple, and there is contamination from higher modes. The data were windowed using a group velocity window appropriate for the Love and Rayleigh waves. The station distribution is shown in Figure Strong Motion Data [10] In Figure 2 we also show the distribution of strong motion stations in the immediate surroundings of the Chi- Chi fault plane, color-coded according to the soil classification of Lee et al. [2001]. We selected a subset of 19 stations (Figure 2 inset), for a total of 57 records, which are more or less evenly distributed around the fault. We have not used data for stations that are located very close to the fault trace for several reasons. With our current simple parameterization of the fault (as a rectangular plane), stations that are very close to the fault may project on the wrong side of the plane because of the more irregular shape of the real fault plane. It is not clear whether the deformation at the tip of the fault plane is the result of a simple shearing motion or that other processes are involved, e.g., folding at the fault tip or opening of the fault [e.g., Lin et al., 2001], or whether their displacement is more akin to a rigid body motion than elastic behavior. These are important and scientifically interesting issues, and we would like to revisit those later. Also, even if we use the stations that are very close to the fault, we still need to include the farther stations as well since the nearby stations only see the slip in the immediate surroundings. The drop-off of the near-field component with distance practically ensures that slip farther away from those stations is masked by the nearby slip. [11] The amplitudes were corrected according to the documented peak values, which is sometimes different from the nominal values that are given for the different instruments. We checked the timing of the observed data with that Figure 3. Azimuthal distribution of broadband stations that recorded teleseismic data that were included in our inversion. Station names in boldface indicate stations from which we used both surface wave and body wave data, whereas italicized names denote stations for which only body wave data were used. 3of11

4 of synthetic Green s functions computed for a point source at the hypocenter. Several stations (including ILA067) have obvious synchronization problems and have been corrected using simple time shifts to make the initial P wave correspond to the predicted P arrival time from the hypocenter. In fact, even for the other stations we applied small shifts to allow for a mismatch between the synthetic Green s functions and the data. Stations TCU084, TCU074 were originally included but show anomalously high amplitudes which are probably caused by local site responses and have been replaced by two nearby stations. We used all three components of the data, resampled at 10 Hz and windowed to a length of 60 s. The strong motion data were integrated to velocity, and in the inversion we band-pass-filtered the data between 100 and 2.5 s Geodetic Data [12] We used the data that were collected and presented by Yang et al. [2000]. The data coverage is very dense. We have removed a number of GPS stations that are very close to other GPS sites, or stations that have vectors that are very different from nearby observations, and are probably contaminated by very shallow effects. This left us with 219 observation points, with three components each. The geodetic data will be presented in section 5, together with the model vectors for our final slip model. 4. Inversion Method [13] The method for determining the slip distribution and history on a fault that we used is very similar to that developed by Hartzell and Heaton [1983] and is explained in more detail by H. K. Thio et al. (The source process of the 1999 Kocaeli (Turkey) earthquake, submitted to Journal of Geophysical Research, 2004, hereinafter referred to as Thio et al., submitted manuscript, 2004). The fault plane is discretized into a grid of subfaults. We then impose a slip band propagating over the fault plane at a fixed number of time steps to represent the rupture advancing across the fault, starting at the hypocenter. The individual sets of grid points (subfaults) that are contained within a slip band at any time step are combined into one large set that are cast into a normal equation of the form: Ax = b, where A contains the Green s functions from every grid point to every station, x is the vector containing the slip value at every grid point that we are trying to solve for (spatial and temporal), and b is the vector containing all the data. The normal equation is solved using a least squares solver with a positivity constraint, which means that we do not allow for reverse slip [Lawson and Hanson, 1974]. This inverse problem has many degrees of freedom, so we need to apply some regularization of the normal equation to prevent wildly oscillating solutions. This is achieved by imposing a smoothing condition in which the amplitude of slip in one subfault is forced to be equal to its neighbors. Depending on the size of the smoothing constant, this will lead to models of varying complexity, with almost uniform slip for strong smoothing. [14] Our method allows for variable rake, in which case every original rake vector is split into two conjugate vectors where the new rake angles are different from the original by +45 and 45, respectively, so that the same positivity Figure 4. Displacement waveforms for the same azimuth (320 ) and increasing distances (and therefore steeper takeoff angles), lined up along the first arrival (vertical line). The change of the P polarization from down (AAK, BRVK, and ARU) to nodal/up (OBN and GRFO) gives a very good constraint on the orientation of the auxiliary plane. constraint can be used. The final rake vector is the vector summation of the two individual rake vectors. Allowing for variable rake thus leads to a doubling of the number of unknowns, so we need to regularize the two slip vectors to prevent strong, unphysical, variations in rake. This is achieved in a manner analogous to the spatial smoothing, where instead of forcing the amplitude of a slip vector to be equal to its neighbors, we force it to be equal to its conjugate slip vector. In this case, a strong smoothing constraint will cause the two conjugate vectors to become equal, and thus yield the orientation of the initial single rake vector. Many of the inversion parameters including smoothing and weighting are determined by trial and error Fault Model [15] We set up the rupture plane as a single fault, with a strike of 5 and a dip of 32, based on a careful analysis of local and teleseismic data. For a dip-slip event, it is often necessary to obtain a range of takeoff angles to constrain the dip of the fault plane, whereas a strike-slip mechanism can be constrained by good azimuthal coverage alone. In Figure 4 we present waveforms for a small azimuth range but at different distances, and thus different takeoff angles. The switch in polarities is very distinct, and, together with 4of11

5 the other teleseismic data, provides a strong constraint on the dip of the fault plane, at the epicenter. The best fitting rake vector on this 32 dipping plane is 63. This mechanism agrees very well with the mechanism obtained by Chang et al. [2000] based on local first motion data. The long-period Harvard and California Institute of Technology (Caltech) centroid moment tensor (CMT) solutions give a more easterly strike (37 and 20, respectively), which may indicate that the mechanism varied during the rupture. [16] The length of our initial fault plane, as is shown in Figure 5a, is 100 km, with a width of 48 km corresponding to a maximum depth of 25 km. The location determined by the CWB (Table 1) is well constrained [Shin, 2000; Kao et al., 2000; Chang et al., 2000], and we have used it throughout this study as the hypocenter (i.e., starting point of the rupture). Even the depth corresponds well with the one inferred from the dip of the fault plane at that location. Some of the inversion parameters that we varied are: maximum rupture velocity, rupture pulse width and smoothing. We have varied the maximum rupture velocity between 2.0 and 3.5 km/s but found that 2.25 km/s gave the best results (in terms of waveform fits). The maximum rupture pulse width that we can use is 10 s, which is constrained by computer memory considerations. When we use high rupture velocities, the slip tends to be pushed outward toward the edges of the rupture plane, which is to be expected, especially with a narrow slip pulse. [17] For the inversion run that we present here we used 20 time steps with a separation of 1.6 s. This limits the total rupture duration to just over 32 s, but even with longer time window inversions, the source time function rarely exceeded 32 s. The total memory requirement for this inversion is on the order of 2 Gbytes Velocity Model [18] There is a significant variation in seismic structure across the island and, more locally, a sharp contrast in shallow crustal velocities between stations west of the surface rupture, which are located in a sedimentary basin and stations to the east, which tend to be located on stiffer soil or rock. This is also reflected in the distribution of site responses presented in Figure 2. We have computed Green s functions for two different kinds of models, rock and soil, based on the work of Iwata et al. [2000]. We assigned the soil structure only to those stations west of the rupture, i.e., in the basin, which were classified by Lee et al. [2001] as type E. Even though their type D and C might also be considered soil, we have used rock responses in those cases since a simple one-dimensional soil model gives rise to very dominant surface waves that are trapped in the upper soil layer. This is probably an unrealistic model for waves that traverse regions with soil and rock structures. The seismic velocities for the rock and soil models are given in Tables 3 Figure 5. Detailed slip distribution for the three rupture models, showing the slip color-coded as well as in vector representation. (a) Model 1, a single rupture plane obtained using teleseismic body waves and local strong motion data, (b) single plane inversion using all data (including GPS and surface waves), and (c) composite fault model using all data. 5of11

6 Table 3. Rock Velocity Structure Thickness, km V P V S r Q P Q S and 4. The difference between the models is confined to the upper three kilometers. For the teleseismic and surface wave data we used the rock model throughout. 5. Inversion Results 5.1. Results Using Teleseismic Body Waves and Strong Motion Data (Model 1) [19] We present preliminary results of the inversion in Figure 5a. The slip distribution shows a clear northward propagation of the rupture, with the largest asperity 20 km north of the epicenter. The maximum slip amounts to 3.8 m and almost all the slip seems to be confined to the upper 25 km of the fault. Away from the main slip distribution we see some isolated patches of slip, but more analysis is needed to see whether these are significant or merely artifacts of the inversion. The orientation of the rake vectors shows a clear change to a more northerly orientation to the north of the fault which is similar to the geodetic displacements [Yang et al., 2000], although on the average, our results tend to have more westerly orientations. The total moment amounts to dyn cm, corresponding to a moment magnitude of A few representative teleseismic body waves are presented in Figure 6, which show an excellent fit between data and synthetic seismograms. In Figure 6, we also plot the waveform fits for the strong motion data. There is a general good agreement between the data and synthetics, but some problems are also apparent. The greatest mismatch between data and synthetics occurs for stations to the north (e.g., TCU087 and TCU049) Results Using All Data Sets (Model 2) [20] The inversion results based on using all data (Figure 5b) is similar to the previous result in terms of the pattern of slip on the fault, but the overall slip values are significantly higher, by a factor of 1.5, and are also more concentrated in a quarter of an arc pattern to the northwest. Tests have shown that this is primarily due to the addition of the geodetic data, and to a lesser degree to the addition of the surface waves. The slip reaches just over 7.5 m at the northern end of the fault, corresponding to the maximum slip measured at the surface break. There is a clear and consistent rotation of the rake angles going northward from almost 90 to 20 at the northern end of the fault. This explains the difference between the CMT solutions and the first-motion solutions. The teleseismic waveform fits (Figure 6) are again very good, although the data seem to have more high-frequency content than the model synthetics. Overall, the phase and amplitude match are very satisfactory. The same is true for the surface waves (Figure 6), with especially good agreement for the Rayleigh waves. The strong motion data generally which are also presented in Figure 6 show a good agreement with some notable exceptions. The stations on the eastern side of the island (the HWA stations) show a good agreement in terms of amplitude and the more long-period phases. At shorter periods, there is some mismatch, but given the longer distances to these stations, and the complex structure throughout the island, this is not too surprising. To the south, at the CHY stations, the waveform fits are generally very good, which suggests that the absence of slip in our model to the south is well established. The waveform fits at the stations in the TCU series, which are above the fault plane, to the west and north are also good with the exception of the stations to the north, TCU087 and TCU046, which show a good waveform fit for all components except for the north component. We believe that this is an effect of the northern termination of the fault, which may feature a change in the fault plane orientation toward an east-west trending thrust fault. This would also explain a mismatch in of the GPS vectors in that area (Figure 7a). This is a rather localized problem, as can be seen from a comparison of the records at TCU103 and TCU087, which are very close to each other and have very similar waveforms. However, because TCU087 is above the extension of our rupture plane along strike it becomes effectively a hanging wall station, whereas both stations are in fact footwall stations. The effect on the GPS vectors looks more dramatic, since the static displacements in such a case are completely reversed Composite Fault Model (Model 3) [21] To solve for the aforementioned incompatibility of the single fault model and the GPS data, we developed a composite fault model consisting of two intersecting planes: the original fault plane, that was used in the previous inversions (strike/dip/rake: 5 /32 /63 ) and a second plane to the north with a strike 85, a dip of 32 and a rake of 130. The intersection of these two planes surfaces at the NW corner of the original fault plane and plunges in a SE direction (Figure 5c). This geometry changes the area to the north from a hanging wall to a footwall, which, as will be shown later, satisfies the orientation of the displacement vectors. We used the same data that we used for model 2. [22] In Figure 5c, we present a detailed version of the final slip map including the orientation of the slip vectors. A comparison with Figure 5b shows that the slip maps for models 2 and 3 are very similar including the clockwise rotation of the slip orientation toward the north. The teleseismic body waves and surface waves (Figures 6 and 8) are fitted equally well with model 3 as with model 2. The strong motion data are fitted better at almost all stations using the composite model (Figures 6 and 8) but the most significant Table 4. Soil Velocity Structure Thickness, m V P V S r Q P Q S of11

7 Figure 6. Representative waveform comparisons for the different rupture models described in the text. The observed data are in black, and the model waveforms in red. improvement is with the GPS data (Figure 7b), especially to the north where in some cases the model vectors have rotated with respect to the previous model by almost 180, consistent with the change from hanging wall to footwall, an are now consistent with the observed vectors. The surface slip distribution (Figure 9) along the rupture front shows little change, except for the gap of 60 km in the previous model, which is not seen in this model. Other rupture parameters, like time history, slip velocities, duration and rupture velocity are plotted in Figure 10. The highest slip velocities (both average as well as peak) tend to correlate with the amount of slip but this might be an artifact from the limits that are placed on the risetime in the inversion. On the other hand, they are consistent with the large slip velocities that are observed by stations that are located on the hanging wall near the rupture front. The rupture velocities range from 1 to 2 km/s, with lower velocities in the epicentral region, and the highest velocities on the second plane to the north. 6. Discussion and Conclusion [23] We have obtained a detailed slip model for the Chi- Chi earthquake that satisfies a wide variety of data over a very broad frequency range. The best fitting model consists of two planes, a main fault with a strike of 5 and a second plane to the north with a strike 85. Both planes have a dip of 32, although it should be noted that the dip of the second 7of11

8 Figure 7. Displacement vectors from GPS observations (dark arrows, from Yang et al. [2000]) and model displacements (white arrows) model 2 (single rupture plane) and model 3 (composite rupture plane). The fit for model 2 is generally very good, except at the northern end of the fault where the GPS observations show evidence for a southward dipping termination of the main fault plane. Model 3 includes the southward dipping plane and provides a better fit for the northern observations. plane is not as well constrained as the first plane since the slip on that plane occurred late in the earthquake. [24] Our final inversion results share some overall similarities to the results of other studies based on the inversion of seismic data. Starting with some first-order parameters, the moments that were obtained for this earthquake range from 0.5 to dyn cm from seismic or seismic and GPS combined studies, although the initial low estimate of 0.5 [Lee and Ma, 2000] has been superseded by more recent work [Ma et al., 2000], and dyn cm from GPS data only [Wang et al., 2001; Yoshioka, 2001]. Ma et al. [2001] obtained a moment of 2.3 to dyn cm when they added strong motion data as well as GPS data, respectively. Iwata et al. s [2000] value of dyn cm is based on the inversion of 31 strong motion stations (90 records) but band-limited between 20 and 2 s. Their moment seems to be particularly low, compared to the longperiod global moment determinations (3.4, Harvard, and 2.7, Caltech), which may be due to the narrow frequency band of the data that they used, especially at the long-period end. Another possibility is that they used a damped inversion, which tends to minimize the moment. It is interesting to compare these results with those of Chi et al. [2001], whose model is also based on strong motion data only, but found a high moment ( dyn cm). They used 41 records from 21 stations and therefore do not have as good a coverage, especially at the eastern end of the fault where they find two minor asperities which are poorly resolved. Without these asperities, their final moment would be more on the order of dyn cm. Without the use of the long-period data and geodetic data, our moment is on the order of dyn cm, and including geodetic and long-period data it is dyn cm, comparable to the result without GPS of Ma et al. [2001], Zeng and Chen [2001] with only strong motion data, Wu et al. [2001] using strong motion and geodetic data, and Kikuchi et al. [2000], who used both teleseismic body waves and strong motion data. The larger value of dyn cm may thus reflect the contribution of long-period energy, to which the teleseismic body waves and the strong motion data are not very sensitive. It is also consistent with the tendency for the GPS studies [Wang et al., 2001; Yoshioka, 2001], and Ma et al. s [2001] result including the GPS data, to yield larger moments. Our current inversion is based on a window length of 10 s, and with the current parameterization, it is not possible to increase this window length without increasing the length of the time steps, and thus the source time of the individual point sources, thereby loosing temporal resolution. [25] The slip patterns from the various studies all show the largest amount of slip to the north of the epicenter. Also, some studies show a similar clockwise rotation of the slip vectors going north. The differences are more pronounced for the smaller asperities. For instance, Iwata et al. [2000] and Chi et al. [2001] both have smaller asperities to the south of the fault plane and at greater depths to the east. We believe that these asperities are poorly resolved, and are inconsistent with the geodetic vectors in those regions. In fact, our slip distribution is very similar to the model of Ji et al. [2001], which is primarily based on GPS observations with some additional displacement records from the strong motion network. [26] Our model is characterized by a rather smooth slip distribution, in terms of slip amplitudes as well as slip orientations, with an exception of the northwest corner where the two fault planes meet. There, we find a patch of slip, extending over both fault planes, where the slip vectors are more westerly oriented compared to the sur- 8of11

9 Figure 8. Observed (black) and synthetic (red) waveforms for the final composite slip model (model 3). 9of11

10 Figure 9. Surface slip distribution of the first fault plane of the final composite slip model (model 3). rounding fault plane. Since these orientations are found on both fault planes, it seems unlikely to be an artifact of the composite fault model but may indicate that the deformation is more complex due to the proximity to the free surface and the intersection of the two planes. [27] A number of studies, including Ma et al. [2001] and Wang et al. [2001] show very abrupt nonsystematic changes in slip orientation, which we believe is unrealistic and may explain the very high moments that they obtained. Other studies use complex fault models [Zeng and Chen, 2001; Wang et al., 2001], with the complexity of the surface trace extended toward the entire fault surface at depth. This level of complexity is probably not warranted with the current data set, and risks the introduction of artifacts in the slip pattern related to the imposed fault complexity. In both cases, the extra complexity, beyond the second fault plane to the north, does not lead to a significantly improved fit of the data over other studies. Although it seems reasonable to suggest that the exclusively geodetic studies yield higher moments since they contain data at much longer timescales than the seismic data, we do believe that the estimates of more than dyn cm are higher than necessary, since our work and that of Ji et al. [2001] give equally good fits to the observations at moments that are consistent with the long-period seismic moments. The very high moments of Wang et al. [2001] could be the result of the complexity of their slip model, especially in terms of variability of the slip orientation. [28] The dynamic parameters for this earthquake remain difficult to interpret, due to potential artifacts introduced by the parameterization of the rupture. The slip velocities are the highest at the northern end of the fault, where we find most slip (Figure 10a). These average slip velocities are consistent with the results of Ji et al. [2003] but seem to be in contrast with the work of Ma et al. [2003], who concluded that the southern end of the fault experienced higher accelerations than the northern end. This may be due to the fact that they studied stations that are very close to the actual surface rupture, and are observing very shallow effects that are not resolved in our study, since we avoided these stations to concentrate on the overall rupture model. [29] The observation that the slip velocities are highest at the surface are in contrast with our conclusions for the 1999 Kocaeli earthquake (Thio et al., submitted manuscript, Figure 10. (a) Average slip velocities, (b) rupture front, (c) peak slip velocities, and (d) rupture velocity for the final composite slip model (model 3). 10 of 11

11 2004), where the surface slip velocities tended to be lower. This is not necessarily inconsistent, since the modes of deformation for the two events are quite different, one being a long strike-slip fault and the other a wide thrust event. Our rupture model for the Taiwan earthquake is also much smoother than for, for instance, the Kocaeli earthquake, which may be due to a combination of fault geometry and local geology. The additional complexity introduced by adding the second plane has a very limited effect on most of the seismic data but is crucial for the modeling of the geodetic data. The changing fault orientation, and the systematic variation in slip angles suggests that the strain in the overriding plate has a strong three-dimensional character. References Chang, C.-H., Y.-M. Wu, T.-C. Shin, and C.-Y. Wang (2000), Relocation of the 1999 Chi-Chi earthquake in Taiwan, Terr. Atmos. Oceanic Sci., 11, Chi, W.-C., D. Dreger, and A. 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Res., 108(B5), 2232, doi: /2002jb R. W. Graves, P. G. Somerville, and H. K. Thio, URS Corporation, 566 El Dorado Street, Pasadena, CA 91101, USA. (robert_graves@urscorp. com; paul_somerville@urscorp.com; hong_kie_thio@urscorp.com) T. Ishii and T. Sato, Ohsaki Research Institute, Shimizu Corporation, Uchisaiwai-cho, Chiyoda-ku, Tokyo , Japan. (satom@ori.shimz. co.jp; toshiaki.sato@shimz.co.jp) 11 of 11