Source model of an earthquake doublet that occurred in a pull-apart basin along the Sumatran fault, Indonesia

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1 Geophys. J. Int. (2010) 181, doi: /j X x Source model of an earthquake doublet that occurred in a pull-apart basin along the Sumatran fault, Indonesia M. Nakano, 1 H. Kumagai, 1 S. Toda, 2 R. Ando, 2 T. Yamashina, 1 H. Inoue 1 and Sunarjo 3 1 National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Ibaraki , Japan. mnakano@bosai.go.jp 2 Active Fault and Earthquake Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki , Japan 3 Meteorological and Geophysical Agency, Jakarta Pusat 10720, Indonesia Accepted 2010 January 7. Received 2010 January 5; in original form 2009 January 6 SUMMARY On 2007 March 6, an earthquake doublet occurred along the Sumatran fault, Indonesia. The epicentres were located near Padang Panjang, central Sumatra, Indonesia. The first earthquake, with a moment magnitude (M w ) of 6.4, occurred at 03:49 UTC and was followed two hours later (05:49 UTC) by an earthquake of similar size (M w = 6.3). We studied the earthquake doublet by a waveform inversion analysis using data from a broadband seismograph network in Indonesia (JISNET). The focal mechanisms of the two earthquakes indicate almost identical rightlateral strike-slip faults, consistent with the geometry of the Sumatran fault. Both earthquakes nucleated below the northern end of Lake Singkarak, which is in a pull-apart basin between the Sumani and Sianok segments of the Sumatran fault system, but the earthquakes ruptured different fault segments. The first earthquake occurred along the southern Sumani segment and its rupture propagated southeastward, whereas the second one ruptured the northern Sianok segment northwestward. Along these fault segments, earthquake doublets, in which the two adjacent fault segments rupture one after the other, have occurred repeatedly. We investigated the state of stress at a segment boundary of a fault system based on the Coulomb stress changes. The stress on faults increases during interseismic periods and is released by faulting. At a segment boundary, on the other hand, the stress increases both interseismically and coseismically, and may not be released unless new fractures are created. Accordingly, ruptures may tend to initiate at a pull-apart basin. When an earthquake occurs on one of the fault segments, the stress increases coseismically around the basin. The stress changes caused by that earthquake may trigger a rupture on the other segment after a short time interval. We also examined the mechanism of the delayed rupture based on a theory of a fluidsaturated poroelastic medium and dynamic rupture simulations incorporating a rheological velocity hardening effect. These models of the delayed rupture can qualitatively explain the observations, but further studies, especially based on the rheological effect, are required for quantitative studies. Key words: Earthquake source observations; Earthquake interaction, forecasting, and prediction; Continental tectonics: strike-slip and transform; Dynamics and mechanics of faulting; Dynamics: seismotectonics; Rheology and friction of fault zones. GJI Geodynamics and tectonics 1 INTRODUCTION The Sumatran fault is a trench-parallel strike-slip fault system that accommodates the oblique convergence of the Indo-Australian Plate subducting beneath Sumatra, Indonesia (Fig. 1). Over its entire length of 1900 km, the fault is divided into 19 major fault segments, ranging in length from 35 to 200 km (Sieh & Natawidjaja 2000). Now at: Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto , Japan The convergence rate between the Indo-Australian Plate and the Eurasian Plate at Sumatra ranges from 60 mm yr 1 in the south to 52 mm yr 1 in the north (Prawirodirdjo et al. 2000). The slip rate on the Sumatran fault also varies from north to south. Recent Global Positioning System (GPS) observations show that the rightlateral slip rate is about 20 mm yr 1 in central Sumatra (Genrich et al. 2000). More than 20 destructive earthquakes with magnitudes larger than six have occurred along this fault system in the past 100 yr (e.g. Pacheco & Sykes 1992; Bellier et al. 1997). On 2007 March 6, an earthquake doublet occurred along the Sumatran fault near Padang Panjang, central Sumatra (Fig. 2). C 2010 The Authors 141

2 142 M. Nakano et al. Figure 1. Map of Sumatra showing tectonic features. Open triangles with station codes indicate locations of the JISNET broad-band seismic stations. The Sumatran fault trace, represented by the solid black lines on Sumatra, is based on data collected by Sieh & Natawidjaja (2000). The trace of the Sunda trench is based on data collected by Muller et al. (1997). The rectangle outlined by dotted lines is the area shown in Fig. 2(a). The first earthquake of the doublet, with a moment magnitude (M w ) of 6.4, occurred at 03:49 (UTC). Two hours later (05:49 UTC), the second earthquake of similar size (M w = 6.3) occurred close to the source location of the first earthquake. The rapid hypocentre determinations by the National Earthquake Information Center (NEIC) of the U.S. Geological Survey (USGS, Sipkin 1994) and the GEOFON global seismic monitor system of the GeoForschungsZentrum Potsdam, Germany (GFZ, indicated that the hypocentres of the two earthquakes were north of Lake Singkarak at a depth of about 10 km and within a horizontal distance of 10 km (Fig. 2b). The centroid moment tensor (CMT) solutions estimated by the Global CMT (GCMT) Project ( on the other hand, placed the source centroid locations of these earthquakes about 20 km apart. The source centroid of the first earthquake was below the southwestern shore of Lake Singkarak, whereas that of the second earthquake was below a point north of the lake (Fig. 2b). The centroid depths of both earthquakes were estimated as about 20 km. A week after the earthquakes, Natawidjaja et al. (2007) conducted field investigations of the surface fault ruptures caused by the earthquakes. They also interviewed local people affected by the earthquakes, and found that people who lived south of Lake Singkarak felt a stronger shock during the first earthquake and those who lived north of the lake experienced the second earthquake as stronger. Natawidjaja et al. (2007) found two separated fault rupture zones, one southeast and one northwest of the lake (red dots in Fig. 2a), which may correspond to the first and second earthquakes, respectively. Surface fault ruptures of the first earthquake were observed along the Sumani segment of the Sumatran fault, southeast of Lake Singkarak. The surface ruptures run from the middle of the southwestern shore of the lake to southeast of the lake, for a total distance of about 15 km. The fault ruptures represent a right-lateral movement with the strike oriented NW SE. The maximum offset Figure 2. (a) Tectonic features around Lake Singkarak, central Sumatra. Three segments of the Sumatran fault are labeled. Years of major historical earthquake doublets are also shown. The labels A and B attached to the years denote the first and second earthquakes, respectively, for each earthquake doublet. Red solid circles show the locations of the surface rupture traces of the 2007 earthquake doublet observed by Natawidjaja et al. (2007). Open squares show populated areas. (b) Enlarged map of the area around Lake Singkarak. Circles and squares indicate the epicentres of the 2007 earthquake doublet estimated by NEIC and GFZ, respectively. Diamonds indicate the horizontal source centroid locations estimated by the GCMT Project. The source models of the 2007 earthquakes estimated by this study are also shown. The thick lines denote the source faults, the stars indicate the rupture initiation points, and the focal mechanisms are plotted at the most probable horizontal source centroid locations. Red and blue colours denote the first and second earthquakes, respectively. The Sumatran fault trace is based on data collected by Sieh & Natawidjaja (2000). Journal compilation C 2010RAS

3 Source model of an earthquake doublet 143 of the surface ruptures is about 20 cm. The ruptures also show clear vertical movement with the western side moving down. Natawidjaja et al. (2007) found fault traces of the second earthquake north of the lake along the southern half of the Sianok segment, which extend 22 km from the northern tip of Lake Singkarak towards the northwest. The surface fault ruptures show a right-lateral movement with a maximum offset of about 10 cm. These observations indicate that the first and second earthquakes ruptured the southern Sumani segment and the northern Sianok segment, respectively. Lake Singkarak is in the middle of the Sumatran fault system in a pull-apart basin (Burchfiel & Stewart 1966) formed at the boundary between the Sumani and Sianok fault segments (Sieh & Natawidjaja 2000). The discontinuity between these faults consists of a 4.5-kmwide right step and is a dilatational step over. The basin may have formed by repeated earthquakes with right-lateral strike-slip motion along the fault segments, resulting in opening of the crust between the fault segments at the jog (Sieh & Natawidjaja 2000). At Lake Singkarak, the total estimated geomorphic offset of the misaligned fault segments is 23 km. The dextral rate of slip estimated from offsets of stream channels is 11 mm yr 1, while the rate obtained from recent GPS measurements is 23 mm yr 1 (Prawirodirdjo et al. 2000). The slip rate estimated from GPS observations represent recent crustal motions, while the one estimated from geomorphological observations may represent the motion of long-term average. Therefore, these estimations do not always give the same value if tectonic features have changed after the geomorphological features were created. Geological features indicate that the lake is no more than a few million years old, which is consistent with the offset and slip rate. Around Lake Singkarak, earthquake doublets have occurred repeatedly (Fig. 2a) (Untung et al. 1985; Pacheco & Sykes 1992). In 1926, the first earthquake of a doublet occurred along the Sumani segment and, a few hours later, the second earthquake of similar size ruptured the northern Sianok segment. The magnitudes of both earthquakes have been estimated as M w 7 by data inversion of historical triangulation data and recent GPS survey measurements (Prawirodirdjo et al. 2000). The estimated surface displacement associated with these earthquakes is 1.7 ± 1.0 m. In 1943, another earthquake doublet occurred: The first earthquake ruptured the Suliti segment, and the second earthquake ruptured the Sumani segment several hours later. Their estimated magnitudes (M s ) were 7.1 and 7.4 for the first and second earthquakes, respectively (Pacheco & Sykes 1992). The observed surface offsets associated with these earthquakes were 1 2 m (Untung et al. 1985; Sieh & Natawidjaja 2000). The tectonic settings of the source regions of the 1926 and 1943 doublets are very similar. The discontinuity of the Suliti and Sumani segments at the jog is a 4.5-km-wide right step and represents a dilatational step over. Lakes Diatas and Dibawah are at the segment boundary, suggesting that a pull-apart basin is also evolving there. Therefore, the occurrence of earthquake doublets may be controlled by the tectonic settings at the segment boundary. The fault models of the doublets constructed by Prawirodirdjo et al. (2000) show that the two fault segments associated with the individual doublets adjoin each other at the segment boundary. In this paper, we extensively studied the earthquake doublet of 2007 using various approaches to better understand the source processes. We used data obtained from a broadband seismograph network in Indonesia (JISNET) to estimate the source locations, focal mechanisms, and rupture propagations of the earthquake doublet. Our analysis indicates that the two earthquakes initiated at the segment boundary and ruptured the Sumani and Sianok segments individually and in opposite directions. We proposed a source model to explain the observed feature of the earthquake doublet based on interseismic and coseismic Coulomb stress changes. We further investigated the mechanism of the delayed rupture in the doublet based on a theory of a fluid-saturated poroelastic medium and dynamic rupture simulations incorporating a rheological velocity hardening effect. 2 DATA AND WAVEFORM INVERSION METHOD We used waveform data obtained from a broad-band seismograph network in Indonesia (JISNET) to analyse the earthquake doublet that occurred on 2007 March 6. JISNET is operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) and the Meteorological and Geophysical Agency of Indonesia (BMKG) (Nakano et al. 2006). The distribution of JISNET stations around Sumatra is shown in Fig. 1. Each JISNET station is equipped with a CMG-3T EBB three-component broad-band seismograph ( s). Data from the seismographs are sampled at 20 Hz for each channel and transmitted to BMKG and NIED in nearly real time. We used the waveform inversion method of Nakano et al. (2008) to estimate the source centroid locations and focal mechanisms of the two earthquakes. In this method, the inverse problem is solved in the frequency domain for efficient computation, as follows. The displacement field excited by a point seismic source may be written in the frequency domain as (e.g. Stump & Johnson 1977) N m ũ n (ω k ) = G ni (ω k ) m i (ω k ), k = 1,...,N f, (1) i=1 where ω k is the angular frequency; ũ n (ω k ), m i (ω k )and G ni (ω k )are the Fourier transforms of the nth trace of a displacement seismogram, the ith base of the moment function tensor, and the spatial derivative of Green s function, respectively; N m is the number of independent bases of moment tensor components; and N f is the number of frequency components used for the waveform inversion. Eq. (1) is written as N f sets of matrix equations d(ω k ) = G(ω k ) m(ω k ), k = 1,...,N f, (2) where d(ω k ) is the data vector consisting of ũ n (ω k ), G(ω k ) is the data kernel matrix with its elements G ni (ω k ), and m(ω k ) is the model parameter vector consisting of m i (ω k ). In this approach, the matrix equations for all frequencies are independent of each other and can be solved separately (Stump & Johnson 1977), and the computation is much more efficient than that for solving the inverse problem in the time domain. A double-couple focal mechanism is assumed in our inversion in order to stabilize the solution by using data from a small number of seismic stations. The source centroid location is estimated by a spatial grid search, in which we minimize the normalized residual R defined by R = N f k=1 d(ω k ) G(ω k ) m est (ω k ) 2 N f k=1 d(ω, (3) k ) 2 where m est (ω k ) is the estimated model parameter vector m(ω k ) and represents the length of a vector. The moment function obtained by the inverse Fourier transform of m est (ω k ) corresponds to a bandpassed form, as we need to apply a bandpass filter to the observed waveforms before the inversion. The seismic moment and rupture duration are estimated from the deconvolved form of the moment function (see Nakano et al. 2008, for details).

4 144 M. Nakano et al. Three-component seismograms obtained from stations BSI, KSI, TPI and LEM were used for the inversion of both earthquakes. Data from station PPI, which is closest to the sources, were not used, since the waveforms were clipped during the two earthquakes. The observed velocity seismograms were corrected for instrument response and then integrated in time to obtain the displacement seismograms. These waveforms were bandpass filtered between 50 and 100 s and decimated to a sampling frequency of 0.5 Hz. We used the total data length of 512 s (256 data points in each channel) for the inversion. Green s functions were synthesized by using the discrete wavenumber method (e.g. Bouchon 1979). We assumed the standard earth model ak135 (Kennet et al. 1995) for calculation of Green s functions. We used the hypocentre locations estimated by the automatic GEOFON global seismic monitor system as the initial locations. For the spatial grid search, we used adaptive grid spacings, starting from a horizontal grid spacing of 0.5 and a vertical grid spacing of 10 km. In the next step, the grid spacing was reduced to horizontally and 5 km vertically. Finally, the horizontal grid spacing was reduced to 0.1. At each source location of the spatial grid search, the fault parameters (the dip, slip, and rake angles) were searched in 5 steps. For each combination of source location and fault and slip orientation angles, the waveform inversion was carried out to estimate the best-fitting source parameters. 3 RESULTS We first estimated the source centroid location and focal mechanism of the first earthquake. Figs 3(a) and (b) show the horizontal and vertical residual distributions, respectively, around the best-fitting source location obtained from our waveform inversion. The bestfitting source is about 10 km southwest of Lake Singkarak at a depth of 15 km. The focal mechanism obtained at the best-fitting source location shows strike-slip motion on a vertical fault: Two nodal planes correspond to the fault parameters (strike, dip, rake) = (147, 80, 165)/(240, 75, 10). The strike of one nodal plane (147 )is similar to that of the Sumatran fault (Fig. 2). The seismic moment of this earthquake was estimated as M 0 = N m, and the corresponding moment magnitude was M w = 6.4. The estimated moment function shows a step-like function with a rupture duration of 4 s. Waveform fits between observed and synthetic seismograms calculated for the best-fitting source parameters are shown in Fig. 4. We obtained good fits with a normalized residual of Although the fits were good at the best-fitting location, the contour plot of the horizontal residual distribution shows elongation in the NE SW direction (Fig. 3a). This indicates a weak resolution for the estimated source location in this direction. The weak resolution may be because the stations used for our inversion and the earthquake source are aligned almost linearly in the NW SE direction (Fig. 1). The field investigations of Natawidjaja et al. (2007) show that the first earthquake ruptured the Sumani segment. The focal mechanism estimated from the waveform inversion is also consistent with the rupture of this segment. The slight deviation of the estimated source centroid location from the Sumani segment may be caused by the weak resolution in the NW SE direction. The actual source should be on this segment, and is most probably under the middle of Lake Singkarak (Fig. 3c), where the residual of the waveform inversion is the minimum along the segment (Fig. 3a). This location is close to the one estimated by the GCMT Project (Fig. 2b). The rupture initiation point of this earthquake was investigated from the particle motion at the event onset in the original (a) 1 S (b) (c) 0 Depth (km) 5 S 0.5 S 0.75 S E A E A km 101 E E A A 105 E 105 E Distance (km) km E PPI E E Lake Singkarak E 0 1 S 5 S 0.5 S 0.75 S Figure 3. (a) Contour plot of the horizontal residual distribution around the best-fitting source of the first earthquake. The open star indicates the best-fitting source centroid location obtained by the waveform inversion. The grey star indicates the source centroid location under the assumption that this earthquake ruptured the Sumani segment of the Sumatran fault as discussed in the text. Crosses denote the node points for the spatial grid search. (b) Vertical cross-section of the residual distribution along the profile A A shown in Fig. 3(a). (c) Source model of the first earthquake of the doublet. The solid black line indicates the horizontal particle motion of the event onset at station PPI. The black dashed line indicates an extrapolation of the particle motion to the direction of the P-wave arrival. The black and grey stars indicate the estimated rupture initiation point and source centroid location, respectively. The thick grey line denotes the source fault, and the open arrow indicates the direction of the rupture propagation. See text for details. Journal compilation C 2010RAS

5 Source model of an earthquake doublet 145 BSI EW BSI NS BSI UD KSI EW KSI NS KSI UD TPI EW TPI NS TPI UD LEM EW LEM NS LEM UD Time/s 0.5 mm Obs. Syn. Residual = 0.10 Figure 4. Waveform matches obtained from the waveform inversion of the first earthquake. Black and grey traces represent the observed and synthesized seismograms, respectively. The station code and component of motion are indicated at the upper left-hand side of each seismogram. seismograms observed at station PPI (Fig. 3c), which is about 20 km northwest of Lake Singkarak. Although the seismograms at this station were clipped during the arrival of the S wave, the onset portion of the P wave was clearly recorded in the three-component seismograms. The initial horizontal motion was towards the northwest. Since the initial vertical motion was upward, the P wave arrived from the southeast. The extrapolation of the horizontal particle motion towards the southeast intersects the surface trace of the Sumani segment at the northern end of Lake Singkarak (see Fig. 2b). Therefore, we concluded that the first earthquake initiated at the northern end of the Sumani segment and ruptured this segment towards the southeast. We also analysed the second earthquake using the same methodology. The horizontal and vertical residual distributions obtained from the waveform inversion around the best-fitting source location are shown in Figs 5(a) and (b), respectively. The estimated focal mechanism shows a strike-slip of a vertical fault: Two nodal planes correspond to (strike, dip and rake) = (145, 80, 165)/(238, 75, 10), which are almost identical to those obtained for the first earthquake. The strike of one nodal plane (145 ) is also similar to that of the Sumatran fault (see Fig. 2). The seismic moment of this earthquake was estimated as M 0 = Nm corresponding to a moment magnitude of M w = 6.3, which is slightly smaller than that of the first earthquake. The estimated moment function shows a step-like function with a rupture duration of 4 s. The fits between observed and synthesized seismograms are shown in Fig. 6. We obtained good waveform fits for this earthquake with a normalized residual of The best-fitting source of the second earthquake is located off the Sumatran fault, about 20 km west of Lake Singkarak. The horizontal residual distribution shows elongation in the NE SW direction, and therefore the resolution is weak in this direction (Fig. 5a). It is also evident from the field investigations of Natawidjaja et al. (2007) that the second earthquake ruptured the Sianok segment, and thus the source centroid is most probably northwest of Lake Singkarak (Fig. 5c), where the residual of the waveform inversion is the minimum along the Sianok segment (Fig. 5a). We note that the estimated centroid depth of 20 km may be too deep because the locking depth of the Sumatran fault in this region is about 20 km (Genrich et al. 2000). This discrepancy may also originate from the weak resolution of the source depth (Fig. 5b). We also investigated the rupture initiation point of the second earthquake. Fig. 5(c) shows the horizontal particle motion at the event onset, which was towards the northwest. Since the vertical initial motion was upward, the P wave arrived from the southeast. The direction is slightly different from that of the first earthquake (see Fig. 3c). The extrapolation of the particle motion to the southeast intersects with the surface trace of the Sianok segment at the northern end of Lake Singkarak. We therefore concluded that the second earthquake initiated at the northern end of Lake Singkarak and ruptured the Sianok segment towards the northwest. We estimated the relative hypocentre location between the two earthquakes using the differences in the arrival times at stations KSI and BSI. The distance L between the hypocentres of the two earthquakes along the fault can be approximated by L = v 2 {(t K 2 t B2 ) (t K 1 t B1 )}, (4) where t K1 and t K2 are the P-wave onset times of the first and second earthquakes, respectively, measured at station KSI; t B1 and t B2 are the onset times of the two earthquakes measured at station BSI; and v is the P-wave velocity. A positive L means that the hypocentre of the first earthquake was closer to station KSI. We picked the onset times at stations KSI and BSI from the original seismograms, and obtained t K1 t B1 = s for the first event and t K2 t B2 = s for the second event. Assuming the P-wave velocity of the shallow crust to be v = 5.8 km s 1, which we adopted from the velocity structure shallower than 20 km in the ak135 earth model, we obtained L = 1.3 km. Therefore, the hypocentres of these earthquakes were very close to each other, supporting the results of our particle motion analysis. We also found the effect of the rupture directivity in the original seismograms of the two earthquakes. We plotted the vertical components of the original velocity seismograms of the first and second earthquakes (Fig. 7). Since the earthquakes share similar focal mechanisms, we may use the observed amplitudes to evaluate

6 146 M. Nakano et al. (a) 1 S (b) (c) 0 Depth (km) 5 S 0.5 S 0.75 S B E 100 E B km 101 E E B B 105 E 105 E Distance (km) PPI km E E E Lake Singkarak E 0 1 S 5 S 0.5 S 0.75 S Figure 5. (a) Contour plot of the horizontal residual distribution around the best-fitting source of the second earthquake of the doublet. (b) Vertical cross-section of the residual distribution along the profile B B shown in Fig. 5(a). (c) Source model of the second earthquake. Symbols here are the same as those in Fig. 3. the effect of the rupture directivity. Because the difference in the hypocentres of the two earthquakes is very small compared with the distances to the sources from the stations, the effect of the difference in the hypocentre locations is negligible except at station PPI. At the stations located southeast of the source (KSI, TPI and LEM), the maximum amplitudes of the first earthquake at the individual stations were larger than those of the second one. At the station to the northwest (BSI), on the other hand, the maximum amplitude of the second earthquake was larger, even though its magnitude was smaller than that of the first one. This may be attributed to the rupture directivity. The rupture of the first earthquake propagated southeastward and short-period waves were amplified in the direction of rupture propagation, whereas the rupture of the second one propagated northwestward and short-period waves were amplified in that direction. Similar features were also observed in the horizontal components, although they are not shown here. The effect of the rupture directivity becomes smaller as the periods of waves get longer than the rupture duration. In our inversion we used the seismograms filtered between 50 and 100 s, which are much longer than the rupture duration (4 s); thus, the effect of the rupture directivity is negligible in the inversion results. We summarize the results of our waveform analyses of the doublet earthquakes as follows: The first earthquake initiated below the northern end of Lake Singkarak and ruptured the Sumani segment southeastward (Fig. 3c). Two hours later, the second earthquake initiated at a location close to the hypocentre of the first one, and the rupture propagated along the Sianok segment northwestward, in the opposite direction to that of the first earthquake (Fig. 5c). 4 SOURCE MODEL OF THE EARTHQUAKE DOUBLET 4.1 Coseismic stress changes The proximity of the two earthquakes in time and space suggests that the second earthquake was triggered by the stress changes caused by the first one. Triggering of seismic activity by large earthquakes is generally evaluated by the Coulomb failure criterion (e.g. King et al. 1994). The change in the static Coulomb failure function CFF caused by an earthquake is given by CFF = σ s + μ ( p σ n ), (5) where σ s is the shear stress change on a given fault plane (positive in the direction of fault slip), σ n is the fault-normal stress change (positive when the fault is clamped), p is the pore pressure change, and μ is the effective coefficient of friction. When CFF is positive, a failure on the given fault plane tends to occur, whereas a negative value of CFF indicates that failure is suppressed. It has now been widely recognized that static stress transfer plays a governing role in interactions of earthquakes, including aftershock activity (Harris 1998; Stein 1999). We calculated CFF around Lake Singkarak associated with the first earthquake using the Coulomb 3.1 program (Lin & Stein 2004; Toda et al. 2005). For simplicity, we assumed a rectangular vertical fault as the geometry of the input fault. The length of the fault along strike was assumed to be 26 km, which we estimated from the distance between the epicentre location of our waveform analysis and the southern end of the surface fault ruptures (Natawidjaja et al. 2007). The fault extended vertically from the surface to 20 km depth. The seismic moment was set at N m, from the result of our waveform inversion. A linear taper with width of 10 km in the horizontal direction was applied to the slip distribution on the fault, in which the seismic moment was kept as the input value. Poisson s ratio, Young s modulus, and the effective coefficient of friction were assumed to be 5, 80 GPa, and 0.6, respectively. The fault and slip orientation angles of the receiver fault were set at those of the second earthquake. We did not consider pore pressure change here. The calculated spatial Coulomb stress changes at a depth of 15 km caused by the first earthquake (Fig. 8a) and the stress profile along the fault plane of the second earthquake (Fig. 8b; thick solid line) indicate that Coulomb stress increased along the Sianok segment at the time of rupture on the Sumani segment. This modelling of the Coulomb stress field was relatively consistent for different combinations of effective coefficient of friction, dip angle, Journal compilation C 2010RAS

7 Source model of an earthquake doublet 147 BSI EW BSI NS BSI UD KSI EW KSI NS KSI UD TPI EW TPI NS TPI UD LEM EW LEM NS LEM UD Time/s 5 mm Obs. Syn. Residual = 0.08 Figure 6. Waveform matches obtained from the waveform inversion of the second earthquake. Black and grey traces represent the observed and synthesized seismograms, respectively. The station code and component of motion are indicated at the upper left-hand side of each seismogram. BSI V PPI V KSI V TPI V LEM V 1st event (03:49) 2nd event (05:49) mm/s 14 mm/s 4 mm/s 0.5 mm/s 0.5 mm/s Time/s Time/s Figure 7. Comparison of the original vertical velocity seismograms of the first earthquake (left-hand column) with those of the second one (right-hand column). The rows are ordered from top to bottom according to the alignment of the stations from northwest to southeast. The station code is indicated at the left-hand side of each row. The vertical scale of the seismograms is the same for both events. Note that the waveforms at station PPI were clipped during the two earthquakes.

8 148 M. Nakano et al. (a) y x -l/2 l/2 (b) Figure 8. (a) The Coulomb stress changes ( CFF) at 15 km depth on the fault of the second earthquake caused by the first earthquake. The yellow and white stars indicate the epicentres of the first and second earthquakes, respectively. The white solid and black dotted lines indicate the fault models of the first and second earthquakes, respectively. The green lines indicate the surface fault traces of the Sumatran fault, after Sieh & Natawidjaja (2000). (b) CFF along the source fault of the second earthquake. Thick grey, thick black, and thin grey solid lines indicate CFF assuming effective coefficients of friction of 0.4, 0.6 and 0.8, respectively, with the fault dipping at 90. Black and grey dotted lines indicate CFF assuming the fault dips of 80 and 70, respectively, with an effective coefficient of friction of 0.6. The dash dotted line indicates CFF assuming an effective coefficient of friction of 0.6 and a fault dip of 90 obtained at a depth of 10 km. and the depth at which Coulomb stress was estimated (Fig. 8b). These results suggest that the second earthquake was triggered by the stress changes caused by the first one. We also estimated the effect of the Coulomb stress changes on the faults of the earthquake doublet due to the 2005 Nias-Simeulue earthquake (M w = 8.6). For this estimation we used the source centroid location and fault parameters obtained for the Nias-Simeulue earthquake by the GCMT project and its fault dimension of km 2 (Konca et al. 2007). We obtained that the Coulomb stress changes on the faults of the doublet were decreases of less than 5 KPa. These changes are one order of magnitude smaller than that of the first event of the doublet, and thus may be negligible. Stress change / Δσ ΔCFF Pore pressure Nondimensional time (t/t r ) Figure 9. (a) Schematic representation of the fault system used in our calculation of stress changes in a poroelastic medium. The thick solid line indicates the source fault. The filled star indicates the location where the pore pressure and the Coulomb stress changes are calculated. (b) Black and grey lines indicate the pore pressure and CFF. The values of pore pressure and CFF are normalized by the stress drop σ of the main rupture. The time is normalized by the characteristic relaxation time t r. See text for details. 4.2 Delayed rupture The deformation of a fluid-infiltrated poroelastic medium is a mechanism that may explain the delayed triggering of an earthquake (e.g. Nur & Booker 1972). Because the pore fluid in a poroelastic medium diffuses down the pressure gradient, the pore pressure, and accordingly the Coulomb stress, changes with time after an earthquake (e.g. Piombo et al. 2005). Hudnut et al. (1989) and Horikawa (2001) explained delayed triggering of earthquakes based on a linear, quasi-static, elasticity theory of a 2-D fluid-saturated porous medium developed by Rice & Cleary (1976). We calculated changes in the pore pressure and CFF due to the first earthquake of the 2007 doublet by following the method of Rice & Cleary (1976) and Li et al. (1987). Fig. 9(a) shows schematically the fault system we used in our calculation. We assumed ν = 5, ν u = 0.34 and B = 0.85 for the poroelastic medium, where ν and ν u are Poisson s ratios when the medium is deformed under drained and undrained conditions, respectively, and B is Skempton s coefficient, which is defined as the ratio of the induced pore pressure to the change in applied stress for the undrained condition (Wang 2000). These values were obtained from Westerly granite samples (table 1 of Rice & Cleary (1976). We also assumed μ = 0.6 for the effective coefficient of friction. Fig. 9(b) shows the temporal changes of pore pressure and CFF at the source location of the second earthquake, which is located 4 km away from the fault of the first one. In this figure the stress changes are shown in non-dimensional units normalized by the stress drop σ of the main rupture of the first earthquake. The time is also normalized by the characteristic relaxation time t r = l 2 /16c, where l is the fault length and c is the fluid diffusivity of the medium. Since the hypocentre of the second earthquake is within the region of dilatation, the pore pressure initially decreases from its static value. Journal compilation C 2010RAS

9 It then gradually recovers to its static value because of diffusion of pore fluids from the surrounding region. Because of the decrease in the pore pressure, CFF is initially less than zero. As the pore pressure recovers, CFF increases, which may cause the delayed triggering of a second earthquake. The relaxation becomes evident after t/t r 0.01 and CFF becomes positive after t/t r 0.06 (Fig. 9b). Assuming c = m 2 s 1 estimated for Westerly granite samples (Rice & Cleary 1976) and a fault length l = 26 km, we obtain t r s and the time when CFF becomes positive t d = t r s, which are much longer than the observed delay of 2 hr. As the hypocentre region may be heavily fractured because of repeated earthquakes, the fluid diffusivity may be much higher there. If we assume c = 5m 2 s 1, which is comparable to that of sandstone (Hudnut et al. 1989), we have t r 10 7 sandt d 141 hr, which are still longer than the observed delay. We investigated the effect of dynamic stress changes on the delayed triggering by solving the temporal evolution of dynamic fault ruptures. We employed an elastodynamic boundary integral equation method (BIEM) for the simulation of dynamic mode II fault rupture in a 2-D infinite, homogeneous, and isotropic elastic medium. We used the method developed by Tada & Madariaga (2001) and Ando et al. (2004). Two strike-slip faults were aligned with an offset representing a dilatational step over (Fig. 10a). The initial rupture is nucleated on Fault 1, at the step over, and the rup- (a) (b) (c) Slip velocity (m/s) Slip velocity (m/s) Distance (km) Fault 2 -l 0 l 20 x=-11.4 km p=0.5 η=0 y Fault 1 w η=0.5 η=1.0 x Fault 2 Fault 1 Time (s) η=1.13 η= Time (s) Figure 10. (a) Schematic diagram showing the fault system used in our calculation of dynamic fault ruptures. Thick lines indicate the alignment of the faults of the first ( Fault 1 ) and second ( Fault 2 ) earthquakes, respectively. (b) Spatio-temporal distribution of slip velocity on the fault planes, in which T p = 1.1 and η = 0 were assumed. (c) The slip velocity functions on Fault 2 for the effective viscosities η = 0, 0.5, 1.0, 1.12 and The functions were obtained at x = 11.4 assuming p = 0.5 and T p = 1.1. Source model of an earthquake doublet 149 ture propagates along Fault 1. When the dynamic stress change on Fault 2 caused by the rupture on Fault 1 is large enough, rupture on Fault 2 may be triggered. The fault length, strike, and slip direction were fixed during our calculations. In previous studies of dynamic fault rupture propagations (e.g. Harris et al. 1991; Harris & Day 1993, 1999; Duan & Oglesby 2006) the rupture of the second event is triggered immediately after the passage of seismic waves of the first event. These studies assume the linear slip weakening friction law (e.g. Ida 1972; Ando & Yamashita 2007). In addition to the slip weakening friction, we introduced a rheological velocity hardening effect commonly observed in rock frictions (e.g. Dieterich 1979), using the power-law form of creep behaviour in frictional properties. The shear traction τ on the fault surface is given by τ = f (d)σ n + ηv p, (6) where d and v are the slip and slip velocity, respectively; f (d) is the coefficient for the slip weakening friction; σ n is the effective normal stress; η is the pre-exponent factor and p is the exponent. We first assumed only the slip weakening friction (i.e. ignoring rheological effect) in our simulations. The friction coefficients at the static and dynamic states were assumed to be 0.6 and, respectively. The length of critical slip displacement D c was assumed to be 0.5 m. The shear strength of the faults relative to the level of initial shear stress applied to the faults is specified by a parameter T p, which is defined as T p = τ p τ r, (7) τ 0 τ r where τ p, τ r and τ 0 are, respectively, the shear strength of the static state, the shear strength when fault slip is larger than D c, and the initial shear stress. See Ando & Yamashita (2007) for the definitions of τ p, τ r and τ 0. Note that the stress drop due to fault slip is given by τ 0 τ r. Ando & Yamashita (2007) used T p = 2 for the simulations of rupture propagation along a branched fault. Using this value in our study, the rupture on Fault 2 was not triggered by the dynamic stress changes caused by the rupture on Fault 1. Smaller values of T p, namely a higher level of the initial stress, may be required. Therefore, we searched the range of T p within which the rupture on Fault 2 was triggered by the rupture on Fault 1. We assumed P-wave velocity, rigidity, and Poisson s ratio of 6 km s 1, 30 GPa and 5, respectively. The stress drop was assumed to be constant at 10 MPa along the two faults. The fault length l and step-over width w were assumed to be 26 and 4 km, respectively. The rupture initiation point on Fault 1 was set at the jog (x = 0 in Fig. 10a). We simulated the ruptures on the faults using a time window of 40 s. Fig. 10(b) shows the slip velocity on the fault planes as a function of the location and time and assumes T p = 1.1. When we assumed T p = 1.1 and 1.2, the rupture on Fault 2 was triggered immediately after the arrival of rupture-stopping phase from Fault 1. If we assumed T p larger than 1.2, namely a higher peak strength compared to the initial stress, the rupture on Fault 2 was not triggered. Next, we added the rheological effect to our simulations. In the following calculations, we assumed T p = 1.1. Accordingly, the behaviour of fault ruptures depends on the parameters η and p. We investigated the fault-slip behaviour assuming p = 0.3, 0.5, 0.8 and 1. The slip-velocity functions for various values of η at the centre of Fault 2 assuming p = 0.5 are shown in Fig. 10(c). As the value of η increases, the rupture initiation delays on Fault 2. A delay longer than 20 s was observed for η = Assuming η = 1.13, the rupture on Fault 2 was not observed within the calculated time window. The delayed rupture was clearly observed in the calculations assuming

10 150 M. Nakano et al. p = 0.3 and 0.5. The delay became shorter for p = 0.8, and was hardly observed for p = 1. Our calculations indicated that the delay in the rupture on the second event occurred when we used both the slip-weakening friction and the power-law creep. Therefore, the rheological velocity hardening effect may also be a mechanism of the delayed rupture of the second earthquake. However, we obtained a delay of up to 20 s, which is much shorter than the observed delay of 2 hr. A longer delay may occur if we set the parameters properly. However, we were not able to carry out such calculations, which require a longer time window and thus extensive computer memory and time. 4.3 Model of an earthquake doublet at a segment boundary As described above, earthquake doublets have occurred repeatedly around Lake Singkarak, which suggests that there is a common mechanism that generates the doublets during sequential earthquake cycles. We modelled the interseismic and coseismic static Coulomb stress changes at a segment boundary of a fault system as follows. Two vertical fault segments representing a right-lateral strike-slip motion are aligned in a half-space, as shown in Fig. 11. The discontinuity of the faults at the segment boundary is a right step and thus represents a dilatational step over. During an interseismic period, the crust is loaded by the motion of the oceanic plate. In this period, the faults are locked, that is, the slip shallower than the locking depth is zero. At extensions of the faults below the locking depth, slip may occur aseismically at a steady rate (Savage & Burford 1973; Scholz 2002). Genrich et al. (2000) showed that the interseismic crustal movement around the Sumatran fault, as estimated from GPS measurements, was well explained by the model of Savage & Burford (1973). This indicates that the Sumatran fault is locked above a depth of about 20 km and aseismic slip occurs below that level during interseismic periods. We therefore estimated the interseismic Coulomb stress changes by assigning secular slip during an interseismic period on the deep extensions of the faults below the locking depth. The coseismic stress changes due to faulting were computed by assigning slip on the faults above the locking depth, while zero slip was assumed on the deeper extensions. The Coulomb stress changes were evaluated for right-lateral strike-slip faulting with the same strike as the fault segments depicted in Fig. 11. Figs 11(a) and (b) show schematic views of the interseismic and coseismic Coulomb stress changes. During an interseismic period, the Coulomb stress increases both along the faults and at the segment boundary as a result of crustal loading (Fig. 11a). After earthquakes occur along the faults, the Coulomb stress decreases on and around the faults because the causative stress is released by the faulting (Fig. 11b). At the segment boundary, on the other hand, the Coulomb stress increases again. This occurs because the lobes of the increase of Coulomb stress due to faulting are distributed asymmetrically with respect to the fault plane (see Fig. 8a). Because the faults are aligned with only a small offset, the areas of stress increase due to the slip of the two faults interfere positively with each other, resulting in a coseismic stress increase at the segment boundary. Thus, the stress there increases both interseismically and coseismically, and remains at a high level unless new fractures are created. Accordingly, ruptures may tend to initiate at a segment boundary representing a dilatational step over. When an earthquake occurs along one fault segment, a rupture of the other segment may be triggered after a short time interval by stress changes caused by the first event. The earthquakes may constitute a doublet, in which the ruptures propagate in opposite directions. Figure 11. Schematic diagrams of the Coulomb stress changes around a segment boundary of a fault system representing a dilatational step over. (a) Continuous Coulomb stress accumulations during an interseismic period. (b) Coseismic Coulomb stress changes associated with faulting on the fault segments. The lefthand panels show spatial distributions of the Coulomb stress changes. The black lines indicate strike-slip fault segments. The right-hand figures display the Coulomb stress changes as a function of time. The purple and green lines indicate the Coulomb stress on the fault (annotated as 1 in the left-hand panel) and at the segment boundary between the faults (annotated as 2 in the left-hand panel), respectively. Journal compilation C 2010RAS

11 5 DISCUSSION Our waveform analyses of the earthquake doublet along the Sumatran fault indicate that the earthquakes nucleated below the segment boundary and ruptured the two adjacent fault segments. We presented a model to explain this feature based on the interseismic and coseismic Coulomb stress changes. We can find a similar example of an earthquake rupture that initiated at a fault segment boundary of a dilatational step over. The İzmit earthquake (M w = 7.4) on 1999 August 17 in Turkey. This earthquake occurred along the North Anatolian Fault Zone (NAFZ). The tectonic setting of the fault system is similar to that of the Sumatran fault. The NAFZ is a 1500-km-long fault system with right-lateral, strike-slip motion (Barka & Kadinsky-Cade 1988). GPS observations show that the slip rate on the fault is mm yr 1 (e.g. McClusky et al. 2000). This fault system can be separated into a number of fault segments, and pull-apart basins are found at the segment boundaries. The rupture of the İzmit earthquake initiated at the boundary between the Sapanca and Gölcük segments of the NAFZ. It then propagated bilaterally along both fault segments and along other segments beyond the eastern Sapanca segment, resulting in a single large event (e.g. Yagi & Kikuchi 2000; Delouis et al. 2002; Sekiguchi & Iwata 2002). Barka & Kadinsky-Cade (1988) thoroughly investigated the historical activity of each fault segment along the NAFZ. Sixteen earthquakes of M > 6 occurred along the NAFZ between 1939 and After 1967, there was little seismic activity along the NAFZ until the İzmit earthquake of Dewey (1976) recalculated the epicentres of earthquakes that occurred in northern Anatolia between 1930 and Poor seismic data quality during this period limited the accuracy of these epicentre locations to a few tens of kilometres at best. Accordingly, if a recalculated epicentre was at a segment boundary, within that range of the accuracy, we considered it to be an earthquake that initiated at a segment boundary. We found five such earthquakes at segment boundaries of dilatational step overs along the NAFZ. In particular, earthquakes on 1943 November 26 and 1944 February 1 initiated at a segment boundary representing a dilatational step over near Bayramuren, and these earthquakes ruptured the segments east and west of the boundary, respectively. These observations support our proposal that ruptures tend to initiate at segment boundaries. Initiation of earthquake ruptures at segment boundaries is also supported by numerical simulations. Duan & Oglesby (2006) simulated dynamic ruptures on two parallel, strike-slip faults representing a dilatational step over. In their computations, the rupture initiation point is not fixed: its location depends on the state of stress immediately before an earthquake, which is determined by the stress changes due to previous earthquakes and interseismic loading. Their simulations showed that the coseismic stress changes, which are non-uniform along the two faults, accumulate after repeated ruptures and the ruptures of the two fault segments initiate at the jog after the system approaches a steady state. Segall & Pollard (1980) also showed that ruptures tend to initiate at jogs representing dilatational step overs because the normal stress decreases around such jogs. The conditions that govern rupture propagation along adjacent fault segments were investigated by Lettis et al. (2002) and Wesnousky (2006). They showed from field observations that ruptures can propagate beyond segment boundaries where step overs are less than 1 2 km, whereas step overs wider than 4 5 km arrest ruptures. Numerical studies (e.g. Harris et al. 1991; Harris & Day 1993, 1999) agree with these observations. During the Source model of an earthquake doublet İzmit earthquake on the NAFZ, the rupture propagated beyond the segment boundaries because step-over widths were small (1 2 km), as shown by Lettis et al. (2002). The step-over widths between the Sumani and Sianok segments and between the Suliti and Sumani segments of the Sumatran fault are about 4.5 km (Sieh & Natawidjaja 2000), which may be large enough to arrest ruptures. We examined the mechanism of delayed ruptures based on pore pressure changes in a poroelastic medium and the dynamic stress changes. Assuming a porous medium corresponding to sandstone, the time scale of the pore pressure change is two orders of magnitude larger than the observed delay. Our dynamic rupture simulations showed that a delayed rupture occurred if we employed the rheological velocity hardening effect using the power-law form of creep behaviour in frictional properties. A similar rheological effect, in the form of the logarithm of the slip velocity, is used in the rate and state friction law (e.g. Dieterich 1994). Belardinelli et al. (1999) pointed out that the rate and state friction law can explain a delayed rupture of a subevent (nearly 20 s after the first rupture) during the 1980 Irpinia earthquake in Italy. We believe that our study is the first that has simulated a delayed rupture by using a fully dynamic rupture model. However, we obtained a delay of up to 20 s, which is two orders of magnitude smaller than the observed delay. Limitations of available computer power prevented us from performing extensive dynamic simulations using time windows long enough to reproduce the observed delay. Clearly, further studies are required to investigate the mechanism that governs delayed triggering of earthquakes. 6 CONCLUSIONS On 2007 March 6, an earthquake doublet occurred near Lake Singkarak, which is in a pull-apart basin between the Sumani and Sianok segments of the Sumatran fault system, in Indonesia. Our study showed that the first earthquake initiated at the northern end of the Sumani segment, and the rupture propagated along this fault southeastward. The second earthquake initiated at a location close to that of the first one, and its rupture propagated along the Sianok segment northwestward. Earthquake doublets for which two adjacent fault segments have ruptured sequentially have occurred repeatedly near Lake Singkarak. Our study of the Coulomb stress changes in the region of the fault segment boundary showed that stress increases both interseismically and coseismically at the segment boundary. Accordingly, the stress below a pull-apart basin that has formed at a segment boundary remains high until new fractures form, and earthquakes tend to initiate there. When an earthquake occurs along one such fault segment, after a short time interval the stress changes caused by that earthquake trigger rupture on the other segment. This pair of earthquakes may constitute a doublet in which the first and second ruptures propagate in opposite directions. We also investigated the mechanism of the delayed rupture based on pore pressure changes in a poroelastic medium and the dynamic stress changes. Although these models can qualitatively explain the delayed rupture, we were not able to reproduce the observed delay, and further studies especially based on the dynamic stress changes are required. Our detailed waveform analysis of the earthquake doublet, the model of interseismic and coseismic Coulomb stress changes, and the examination of the delayed rupture provide new clues to understand source processes of earthquake doublets at segment boundaries.