Imaging an asperity of the 2003 Tokachi-oki earthquake using a dense strong-motion seismograph network

Transcription

1 Geophys. J. Int. (2008) 172, doi: /j X x Imaging an asperity of the 2003 Tokachi-oki earthquake using a dense strong-motion seismograph network R. Honda 1,S.Aoi 2, H. Sekiguchi 3 and H. Fujiwara 2 1 Hot Springs Research Institute of Kanagawa Prefecture, Iriuda 586, Odawara, Kanagawa , Japan. ryou@onken.odawara.kanagawa.jp 2 National Research Institute for Earth Science and Disaster Prevention, Japan 3 National Institute of Advanced Industrial Science and Technology, Japan Accepted 2007 November 27. Received 2007 November 27; in original form 2006 August 30 GJI Seismology SUMMARY The 2003 Tokachi-oki earthquake ruptured a large area of approximately 100 km 2. The location of the largest asperity was estimated to be several dozen kilometres offshore of Hokkaido, Japan. The magnitude measured 8.0 on the Japan Meteorological Agency scale, and several studies used waveform inversion analysis to estimate the moment-magnitude as M w Several studies reported that there was a minor asperity at the northeastern edge of the fault plane, and that the rupture velocity towards the minor asperity was less than that towards the main asperity. One of them illustrated that the location and timing of the minor asperity were poorly constrained. In this paper, we introduce a procedure based on semblance analysis to image the location of the minor northeastern asperity with improved resolution. We group 15 strong-motion seismographs into three arrays, and we perform semblance analysis on impulsive waves that were possibly generated from the minor asperity and were conspicuously observed at stations in eastern Hokkaido. By projecting the semblance values onto the fault plane, we estimate the location of the minor asperity. We find it to be shallower and farther from the coast than the previous results indicated. The average rupture velocity towards the asperity is estimated to be 2.5 km s 1, which is slower than the 3.6 km s 1 obtained by waveform inversion analysis. Key words: Time series analysis; Earthquake source observations; Wave propagation. 1 INTRODUCTION The 2003 Tokachi-oki earthquake was the largest interplate earthquake since the construction of the nationwide strong-motion networks, K-NET (Kinoshita et al. 1998) and KiK-net (Aoi et al. 2000). Using the K-NET and KiK-net records, Honda et al. (2004) obtained the spatiotemporal slip distribution of the earthquake by multitime-window linear waveform inversion (e.g. Olson & Apsel 1982; Hartzell & Heaton 1983), and concluded that there were three asperities (areas with relatively large slip) on the fault as shown in Fig. 1: (A) around the hypocentre, (B) at the northwestern region of the fault with a maximum slip of 5.9 m and (C) at the northeastern edge of the fault plane. Among the three asperities, the largest asperity (B) commonly appeared in several source models analysed with teleseismic data and/or near-field strong ground motion data (e.g. Yamanaka & Kikuchi 2003; Koketsu et al. 2004; Yagi 2004), and most of the stations in Hokkaido observed the dominant seismic waves radiating from the largest asperity. In eastern Hokkaido, impulsive waves following the signals from the largest asperity were observed at many stations. Honda et al. (2004) reported that these impulsive waves radiated from the northeastern edge of the fault plane, namely, from asperity (C) in Fig. 1. Fig. 2 compares the observed and synthesized seismograms obtained by Honda et al. (2004). We recognize that asperity (C) is essential in recovering the waveforms observed in eastern Hokkaido (HKD076 and HKD077). Unfortunately, most of the data obtained from other stations in eastern Hokkaido cannot be used for the inversion analysis due to contamination by dominant surface waves. This limitation of data in eastern Hokkaido could result in spatial and/or temporal uncertainty in the inversion results, particularly for asperity C. In addition, other studies have also reported the existence of a minor asperity northeast of the major asperity, although an exact comparison of these reports was difficult owing to the use of different station sets, parametrizations, and inversion procedures. Koketsu et al. (2004) reported that a minor asperity appeared northeast of the main asperity 216 s after rupture initiation. Miyazaki et al. (2004b), who examined the rupture process using 1 Hz GPS data also concluded that secondary slip occurred in the northeast segment of the fault plane. Compared with the post-seismic deformation determined by Miyazaki et al. (2004a), the region of the minor asperity identified by Honda et al. (2004) was located near the deeper edge of the significant post-seismic slip. Historically, several large earthquakes have occurred around the source region of this earthquake (e.g. Yamanaka & Kikuchi 2003; Miyazaki et al. 2004a). Therefore, 1104 C 2008 The Authors

2 Imaging an asperity with array data 1105 Figure 1. Results of waveform inversion obtained by Honda et al. (2004). The figure on the left-hand side shows the total slip distribution on the fault plane and the station distribution. The star in the figure on the left-hand side shows the epicentre (JMA 2003). Triangles denote the stations used in the waveform inversion analysis. Waveforms at the black triangles are shown in Fig. 2. Circles denote the stations used in this study. Dotted ellipsoids labelled (A), (B) and (C) in the figure on the left-hand side represent the asperities (A), (B) and (C), respectively. Moment rate functions of characteristic form in each asperity are shown in the top right-hand side figure. These moment rate functions are reduced by the rupture velocity (3.6 km s 1 ) obtained by the inversion analysis. determining the co-seismic slip distribution of the 2003 Tokachi-oki earthquake is important for understanding the recurrence of large earthquakes along the Kurile-Japan Trench. In this paper, we extract impulsive waves from the recordings to avoid contamination by surface waves and attempt to image the asperity the origin of the waves using strong-motion networks as arrays. Our approach is based on the semblance analysis technique using seismograms arranged in arrays. Such an array analysis technique has been developed to estimate the distribution of small-scale heterogeneities from coherent arrivals in coda waves (e.g. Capon 1969; Asano et al. 1999; Taira & Yomogida 2003). Several authors have applied array analysis to observe rupture propagation on a fault plane using short-baseline seismograph arrays, which are on the order of several hundred metres in length (e.g. Spudich & Cranswick 1984; Spudich & Oppenheimer 1986). Spudich & Cranswick (1984) attempted to analyse the rupture process of the 1979 Imperial Valley earthquake by using a set of strong-motion records observed at a short-baseline accelerometer array. The records were filtered by a 25-Hz low-pass filter, and a moving-window cross-correlation analysis was also applied. After calculating the apparent slowness at the array, they finally obtained the source region of the P and S waves on the assumed fault plane. Spudich & Oppenheimer (1986) calculated synthetic ground motions from an irregularly expanding rupture on the San Andreas Fault and performed frequency wavenumber (f k) analysis on sequential time windows of array data. They stacked the seismograms in the slowness domain and projected the power onto the fault plane based on the isochrones. They concluded that observations at such dense arrays are useful in deducing the rupture process. Although we do not have such short-baseline arrays around the source region of the 2003 Tokachi-oki earthquake, the nationwide strong ground motion seismograph networks, K-NET and KiK-net, and a high-sensitivity seismograph network (Hi-net; Obara 2002) cover Japan with an average station-to-station distance of about 20 km. These seismograph networks have been used in array analysis to study the source of earthquakes (Ishii et al. 2005) or the epicentre distribution of very low-frequency earthquakes at plate boundaries (Obara & Ito 2005; Ito et al. 2007). These analyses are useful in cases where the target area is sufficiently greater than the array size. Turning to the 2003 Tokachi-oki earthquake, the estimated rupture area is about km 2, and it is expected that the asperity distribution can be retrieved from the differing slowness of the seismic waves radiating from the causative fault. Since the major rupture process of the 2003 Tokachi-oki earthquake was obtained by waveform inversion analysis, we concentrate on determining the location of the minor asperity at the northeast edge of the fault plane and attempting to deduce the rupture process that is less well constrained in the inversion analysis. 2 DETERMINATION OF TARGET WAVE In this analysis, we integrate the acceleration recordings to obtain the velocity after bandpass filtering between 2 and 0.25 Hz. The bandpass-filtered seismograms, which were observed at 16 K-Net and KiK-net stations, are shown in Fig. 3. They are sorted by distance from the epicentre, which was determined by the Japan Meteorological Agency (JMA) (2003). The impulsive waves, which constitute the main part of the waveforms observed in eastern Hokkaido, are marked by rectangles. In contrast, signals assumed to be coming from the largest asperity (marked by arrows in Fig. 3) are not prominent in eastern Hokkaido, except at a few stations (e.g. HKD093 and TKCH03). Hereafter, we describe the impulsive wave, which

3 1106 R. Honda et al. Total Asperity B Asperity C HKD076 HKD077 HDKD07 TKCD08 EW NS UD 85 s Obs. Syn. Figure 2. Comparison between observed (solid lines) and synthetic (dotted lines) seismograms obtained by Honda et al. (2004). Synthetic seismograms of the upper trace for each observer are calculated from the total slip distribution shown in Fig. 1. The middle and lower traces show contributions from asperity (B) and asperity (C), respectively. The maximum values of each component are provided to the right-hand side of each trace in metres per second. Each trace is normalized by the maximum amplitude recorded at each station. All seismograms are bandpass filtered between 2 and 0.2 Hz and are resampled at 4 Hz for the inversion analysis. Contribution of array (C) is critical to recover waveforms at HKD076 and HKD077. is dominant in eastern Hokkaido, as the target wave and attempt to retrieve the location of an asperity as the origin of the target wave. In the next section, we introduce an approach based on semblance analysis. Before starting the analysis, we classify the stations in eastern Hokkaido into three arrays (A, B and C, as shown in Fig. 4) at which the observed waveforms are similar to each other, and we select a reference station for each array. Although we can use all the stations as a single array, we created three arrays in order to obtain a good semblance value in the following analyses. Since the focus is the target wave, we attempt to determine the arrival time of the target wave using simple polarization analysis for the velocity waveforms obtained at each reference site. Assuming that the dominant phase observed at each station is composed of S waves from the fault plane, the particle motion changes according to the directions of the source during the event. In this case, we expect that the particle motion of the target wave differs from that of the signals from the other asperity arriving earlier. Therefore, we assume that the target wave arrives when the particle motion changes. We draw the particle motions on the horizontal plane at 10 s time windows with intervals of 2.5 s and search for a time window that includes the target wave at least one cycle after the particle motion has changed. The velocity waveforms and the horizontal particle motion in each time window are plotted at the reference sites HKD089, HKD084 and HKD078 for array A, B and C, respectively (Fig. 5). The dots in the particle motions indicate the arrival of the target wave, and the delay time of the time windows are determined as 59.5, 49.5 and 52.0 s from the origin time determined by JMA (2003) for HKD089, HKD084 and HKD078, respectively. These time windows are almost identical to the box shown in Fig. 3. By performing semblance analysis on the waveforms within the time window chosen above, the influence of obstructive signals such as surface waves can be restricted and the source of the target wave can be estimated. First, we consider the features of the target wave. We estimate the apparent velocity of the target wave by semblance analysis and compare it with that of the surface waves. The semblance value, S, for a time window is calculated as follows: [ ] 2 M N A j (t i + dt j ) S = i=1 j=1 [ ], (1) M N A 2 j (t i + dt j ) i=1 j=1 where N is the number of stations in an array, and M is the number of time samples in a time window. A j (t) is the amplitude observed at the jth site at time t. Assuming a plane-wave incidence, dt j is the time difference expected from the incident azimuth and the slowness between the reference site and jth site. In order to reduce the noise due to the arrangement of stations, we average the obtained semblance values after calculating each of the three components. Hereafter, we refer to the averaged semblance values as the semblance value. In the array analysis, the site interval restricts the wavelengths that can be analysed. If the wavelength is shorter than half the site interval, slowness cannot be estimated precisely because of the aliasing effect (Matsumoto 2001). Since the strong-motion seismographs of K-NET and KiK-net have 205 km intervals and the dominant period of the target wave is 4 5 s, the valid slowness for the analysis is less than s km 1. Fig. 6 shows the semblance values in the slowness domain for the time windows determined above. Although we can recognize a coherent wave in Fig. 2, no remarkable peaks appear in the array A result. This implies that the target wave in the time window is superimposed on signals that come from other parts of the fault plane (e.g. the major asperity) and/or on surface waves. It may also be possible that the assumption of plane-wave incidence might not be appropriate because of the complex velocity structures. Slowness

4 Imaging an asperity with array data 1107 NS EW UD 180 KSRH03 HKD093 HKD079 TKCH03 HKD094 HKD089 KSRH04 KSRH05 HKD Distance (km) HKD078 TKCH05 KSRH07 HKD HKD077 KSRH09 HKD Time (s) Time (s) Time (s) Figure 3. Bandpass-filtered ( Hz) velocity waveforms observed at stations in eastern Hokkaido. Each trace is normalized by the maximum amplitude. Arrows show signals radiating from the main asperity, asperity (B). Rectangles marked as the target wave show characteristic pulses assumed to radiate from asperity (C). The distance origin is the epicentre (just above the rupture starting point). The time axis shows the elapsed time after the origin time (JMA 2003). Dominant surface waves appeared in many of the records. 1 Array A HKD093 TKCH Array C KSRH HKD089 KSRH04 HKD084 HKD094 HKD078 TKCH05 KSRH07 KSRH09 HKD077 HKD085 HKD083 Array B 7 KSRH03 HKD Figure 4. Station distribution for the array analysis. Solid lines show part of the fault plane of Honda et al. (2004). The reference sites in the array analysis are marked by circles. The star indicates the aftershock used to modify the velocity structure. Comparison between the observed and synthetic waveforms is shown in Fig. 7.

5 1108 R. Honda et al. Figure 5. Observed waveforms at the reference sites, integrated with respect to velocity and bandpass filtered between 2 and 0.25 Hz. The shadowed zone represents the time window used to calculate horizontal particle motion illustrated at the right-hand side of the waveforms. The time window is 10 s long with a slide interval of 2.5 s. Dotted rectangles represent the time window that includes the target wave. The time axis is the same as that in Fig. 3. Dots in the horizontal particle motion indicate arrival of the target wave. The arrival time is used to improve the resolution of the semblance distributions on the fault plane in Section 3.4. Array A Array B Array C NS : Slowness (s/km) EW : Slowness (s/km) Figure 6. value in the slowness domain for the three arrays. values are averaged after calculation for each component. Numbers on the top right-hand side of each figure show the time window represented by dotted rectangles in Fig. 5. No remarkable peaks appear in the figure on the left-hand side (array A), whereas we can recognize a coherent wave in Fig. 3. The result implies that the plane-wave incidence assumption does not work well in this case. with the peak semblance value is 0.17 and 0.23 s km 1, and the incident direction is N188E and N204E for arrays B and C, respectively. Maeda et al. (2004) reported that the apparent surface wave velocity in eastern Hokkaido is between 3.0 and 3.5 km s 1, which corresponds to s km 1 in the slowness domain. Compared with these results, the slowness values of the target wave are much smaller than those of the surface waves. While some uncertainty might arise regarding whether or not the target waves are reflections of the direct waves from the largest asperity [asperity (B) in Fig. 1], it is important to note that their amplitude is larger than those of the signals from the largest asperity, and also that such strong reflected waves did not appear in the aftershock recordings. It is thus reasonable to assume that they are not reflected waves and that the target wave is an S wave radiating from the fault. 3 I M A G I N G A S P E R I T Y O N FAU L T PLANE 3.1 Mapping semblance values of target wave on fault plane In this section, we attempt to deduce the location of the asperity responsible for the target wave by mapping the semblance values onto the fault plane using a method modified from Spudich & C 2008 The Authors, GJI, 172, C 2008 RAS Journal compilation

6 Imaging an asperity with array data 1109 Table 1. The velocity structure used in this study. Depth (m) Vp (m s 1 ) Vs (m s 1 ) Density (g cm ) Qp Qs Oppenheimer (1986). According to Spudich & Oppenheimer (1986), by assuming a velocity structure, semblance values can be projected onto the fault plane using seismic ray tracing. They calculated the semblance values by assuming plane-wave incidence. In our analysis, the distance from the fault plane to the arrays is km, which is three or four times the array size. Although the interval of the array sites is within the range where the analysis can be performed, it is preferable to use the traveltime difference for each station calculated by assuming a velocity structure rather than using the assumption of plane-wave incidence. In this case, we are able to use all of the stations as a single array. However, we use three arrays classified by the waveforms because the influence of the signals from other asperities and/or surface waves varies with each waveform. Simultaneous analysis using all waveforms results in an unfocused projection of the semblance values. The difference in the calculation of the semblance value from that in the previous section (eq. 1) is in the calculation of dt j. dt j = Tr j Tr, (2) where Tr j and Tr are the traveltimes calculated with an assumed velocity structure from the source to the jth site and from the source to the reference site of the array, respectively. In this procedure, it is not necessary to assume plane-wave incidence, but a good velocity structure model is necessary. Therefore, we modify the velocity structure given by Iwasaki et al. (1991) using the observed waveforms of several aftershocks. The obtained velocity structure model shown in Table 1 can recover the velocity waveforms in eastern Hokkaido over a frequency range of Hz. For example, Fig. 7 compares the synthetic and observed waveforms of the aftershock (2003 September 29, M w = 6.4). The fault model of the 2003 Tokachi-oki earthquake by Honda et al. (2004) has a dip angle of 18 and a strike angle of 246.We divide the fault plane into 244 subfaults and calculate the traveltime difference between the reference site and the other sites in the array for each subfault. The reference sites of each array and the time window of the reference site for calculating the semblance value are the same as those in the previous section. Once the traveltime difference dt j for a subfault is obtained, we can calculate the semblance value for the three components using eq. (1). We average the semblance values for the three components to reduce noise in the same way as Section 2 and project the average onto the corresponding subfault. By repeating this procedure for all subfaults, the distribution of the semblance values on the fault plane can be obtained, and a peak representing the origin of the target wave could be found. Since the semblance value is an index of the intensity of signal coherency and is not comparable with the signal amplitude, we employ the semblance value without regard to the amount or time history of the slip, but to determine the location of the asperity. Fig. 8 shows the semblance-value distribution obtained by arrays A, B and C. The semblance-value distribution obtained by array B, which is the nearest to the fault plane, has a peak that is close to that of asperity (C) of Honda et al. (2004). This result implies that the origin of the target wave deviates from the point estimated by Honda et al. (2004) in the direction of the shallower portion. Compared with the results of array B, the distributions obtained by arrays A and C occupy a wide belt of the high-semblance value zone. This is because these arrays are farther away from the fault plane than array B, and the difference in dt j for the subfaults is not large enough compared with the frequency range of the analysis. We will discuss this problem in detail later. The maximum semblance value obtained by array A is the lowest among the three arrays. Since array A is close to the direction of the main rupture propagation, the observed waveforms must be contaminated by the large-amplitude waves radiating from the main rupture, as shown in Fig. 2. In the next section, we perform numerical tests with synthetic seismograms to check the resolution of the source estimated from the semblance-value distribution. 3.2 Resolution analysis by numerical tests Considering the waveforms shown in Fig. 2, the asperity the origin of the target wave has a simple rupture process in the frequency range used in this analysis. Therefore, to model the target wave, we synthesize seismograms from a point source assuming a simple ramp function as the source time function. Since the results of array B show the most conspicuous peak in the semblance-value distribution, we place one point source (P1) near the peak of the semblancevalue distribution obtained by array B. Another point source (P2) is placed near the epicentre at the end of the high-semblance value zone obtained by arrays A and C. Both these point sources are placed at the centre of the subfaults. We calculate the semblance value in the same manner as described above using synthesized seismograms. The top and bottom rows in Fig. 9 show the results for P1 and P2, respectively. For all three arrays, the semblance-value distribution does not have a peak at the true source location, but the high-semblance value zone is distributed widely in both cases. We can see that the results are well constrained in the direction from the array to the source, but the distance constraint is not satisfactory. Focusing on the traveltime difference dt j between HKD084 and HKD077, dt j is 2.1 s for P1 and 2.8 s for P2. The difference in these two cases, 0.7 s, is an extremely short period of time compared to the frequency range that we have used. Although the actual semblance-value distribution is calculated not solely with these two sites, this difficulty causes a low distance resolution and cannot be avoided under the conditions of the fault geometry and site distribution for this earthquake as long as we use the 1-D velocity structure. Comparing the results of the numerical test with observations, the semblance-value distributions for P1 obtained by arrays B and C are similar to those of the observation shown in Fig. 8. On the other hand, the distribution pattern for P1 and P2 obtained by array A

7 1110 R. Honda et al. m/s 0.7 TKCH05 NS EW UD KSRH HKD HKD s Obs. Syn. Figure 7. Comparison between observed and synthesized velocity waveforms of an aftershock (2004 September 29, 11:37 JST, M = 6.5) shown in Fig. 4. Dotted and solid lines show observed and synthesized waveforms, respectively. Each trace is bandpass filtered in the range of Hz and normalized by the maximum amplitude recorded at each station. Arrows indicate S-wave arrival in synthesized seismograms. The velocity structure used for the calculation is shown in Table 1. Observed waveforms are well recovered, except for the latter phases Array A Array B Array C Figure 8. -value distribution obtained by arrays A, B and C. The semblance values were calculated for the time window determined in Section 2. Black solid lines on the fault plane represent the slip distribution obtained by Honda et al. (2004). Triangles represent observers, and the star is the epicentre. is quite different from the observation. This suggests that the target wave observed by array A is contaminated by the signal from the main asperity or surface wave, as mentioned before. Consequently, the resolution for the source location by an individual array is not sufficient to retrieve the exact location of a point source. However, the distribution pattern implies that P1 is the likely origin of the target wave. In the following section, we attempt to determine the location of the source more precisely. 3.3 Improvement of semblance-value distributions by site-correction functions We showed that the semblance distributions have wide peaks because the traveltime differences between the reference site and the other sites are significantly short compared with the frequency range used. Our velocity structure model was modified to explain the waveforms observed at stations in eastern Hokkaido using several aftershocks, and it is an average model for a wide area. However, there are deep sedimentary basins around the arrays, and they must be the cause of the velocity structure heterogeneity (Sasatani et al. 2006; Aoi et al. 2007). The velocity structure heterogeneity delays or advances the S-wave arrival at each site. Consequently, backward ray tracing using the average velocity structure would mislocate the sources. Hence, we introduced site corrections in order to improve the semblance distribution. Fletcher et al. (2006) observed an earthquake using the USGS Parkfield Dense Seismograph Array. They calculated the semblance value by assuming plane-wave incidence and plotted the peaks as

8 Imaging an asperity with array data 1111 Figure 9. Results of numerical tests using synthetic seismograms. Figures in the top row show the semblance value calculated for point source P1, while those in the bottom row show the results for point source P2. Circles show the point sources. Black solid lines are the same as in Fig. 8. sources of high-frequency arrival on to the fault plane using the apparent velocity and backazimuth. They introduced site corrections by calculating interpolating functions using the least-squares method for the backazimuth and apparent velocity as a function of the distance along the strike of the fault, using aftershock records. Since we used traveltime differences between the reference site and the other sites in the array to obtain the semblance distributions, we estimated site corrections for traveltime differences instead of backazimuth and apparent velocity. We picked S-wave arrivals for large aftershocks (M > 4) that occurred near the fault plane and found that the traveltime differences varied not only with backazimuth but also with the depth of the sources. Therefore, we partitioned the traveltime difference measurements into two groups at a depth of 45 km. In order to secure azimuthal coverage, the aftershocks between the depths of 45 and 50 km are included in both groups. The crosses in Fig. 10 are the O-C (observed-calculated) residuals of the traveltime differences. We applied a linear interpolation to the data and resampled by 0.5. Finally, we obtained the site-correction functions by adopting a 20th order Hanning window after the linear interpolation. We assumed that the site-correction functions are periodic functions with a periodicity of 360. Black lines indicate the estimated site corrections as a function of the backazimuth. The figures on the left-hand side show the site-correction functions for the shallow events, and the figures on the right-hand side show those for the deep events. Note that there is no physical basis on which the interpolation is performed, and the smoothing process and correction functions are purely empirical. We can see that the residuals of the traveltime differences show a large variation in the figures on the left-hand side. This implies that the S-wave velocity varies in the C 2008 The Authors, GJI, 172, C 2008 RAS Journal compilation shallow crust. For example, the observed traveltime difference at a backazimuth of 150 in HKD094 is 4 s shorter than that expected from the synthetic data. This agrees with the fact that the upper boundary of the basement rock, whose S-wave velocity is greater than 3.2 km s 1, beneath array A is deeper towards the sea and there are sedimentary basins on the basement rocks (Sasatani et al. 2006). Ray propagation in the basins to the reference site (HKD089) is delayed, and this results in the large O-C residual in the traveltime difference. When we calculate dt j from eq. (1), the S-wave delay or advance is calculated with the site-correction functions corresponding to the backazimuth and the depth of the subfault. Fig. 11 shows the semblance value modified by the site-correction functions. Comparing this result with that obtained without the corrections (Fig. 8), the high-semblance value zones have converged for all three arrays. The converged peaks obtained by the arrays are close to each other. They are clearly at the shallower edge of asperity (C) in Honda et al. (2004). We interpret the peaks as the source of a coherent wave, that is, the target wave. The correction functions, which are obtained by an empirical method, include some uncertainty that results from interpolating insufficient data and from the smoothing process. This uncertainty is one of the causes of the decrease in the peak semblance value. The semblance values are also decreased by (1) contamination by surface waves or signals that come from another part of the fault plane and (2) misestimation of the fault geometry and the velocity structure. However, it is important that the peak is well resolved, even if it has a lower value ( 0.4). From such a viewpoint, we try to improve the focusing of the peak by combining all the three arrays in the next section.

9 1112 R. Honda et al. Figure 10. Obtained site-correction functions of traveltime difference. Crosses denote the residuals of traveltime difference between the reference site and each site for the aftershock whose magnitude is greater than 4. If the observed traveltime difference is greater than that expected from the velocity structure shown in Table 1, the residual becomes positive. The left- and right-hand side of the figures correspond to the west and the east, respectively. The figures to the left- and right-hand side show the site-correction functions for the shallow and deep events, respectively. Aftershocks at depths between 45 and 50 km are included in both the figures. The site-correction functions are periodic functions with a periodicity of Estimation of source of target wave using data of three arrays In this section, we combine the semblance distribution by multiplying the semblance values obtained from the three arrays. The combined semblance value on each subfault is obtained by S = x S x, (3) where S x is the semblance value obtained from array x. In addition, we introduce a weight to improve the resolution and multiply it by the unified semblance value as follows. Since the target wave at each station is supposed to be generated from the same origin point at a common rupture time, we chose as a weight the degree of agreement of the inferred rupture time at the triggering point of asperity (C); this degree is estimated from the three arrays and acts as a weight for each subfault. The arrival times of the target wave at each reference site are indicated by the dots in Fig. 5 and the traveltimes from all subfaults to the reference stations are calculated using the assumed velocity structure. Site-correction functions for the traveltimes are obtained by interpolation and smoothing of the O-C residuals as done for the traveltime differences. The calculated traveltime is modified by the site-correction functions shown in Fig. 12. The site-correction

10 Imaging an asperity with array data Array A Array B Array C Figure 11. Same as Fig. 8, but for the site correction. Peaks appeared in the results of all the three arrays. O - C residuals (s) 2 3 HKD HKD HKD KSRH03 For shallow events For deep events Back azimuth (degree) Back azimuth (degree) 80 West South East West South East Figure 12. Obtained site-correction functions of traveltime for the reference sites. The classifying rule of the aftershocks is the same as that in Fig. 10. Existence of low velocity structures, such as basins between HKD089 and HKD084, is inferred from the site-correction functions. functions obtained from the aftershock records are classified into two groups, the same as those for the traveltime differences. The delay in the traveltime that appeared in the site-correction functions for HKD089 and HKD084 agrees with the existence of a deep basin between HKD089 and HKD084 (Sasatani et al. 2006). After the correction, the rupture time at each subfault can be uniquely estimated by backward ray tracing from the reference stations to each subfault. In addition to the reference sites, we use KSRH03, which provides a good rupture-time constraint. The onset of the target wave at KSRH03 is assumed in the same manner as that for the other reference sites; it is determined to occur with a delay time of 61.0 s after the origin time. The weight for the sth subfault, W s,is calculated as follows: W s = {[ N k=1 (T sk T s ) 2 ] / N} 1, (4) where T sk is the rupture time at the sth subfault as estimated from the traveltime to the kth station, and T s is the average value of T sk obtained by ( N k=1 T sk)/n. Four stations, three reference stations and KSRH03 are used (i.e. N = 4). Eq. (4) represents the variance of the estimated rupture time from the traveltime to each station. By repeating this procedure for all subfaults, we obtain the distribution of W s on the fault plane. By multiplying W s by S of the corresponding subfault, we obtain the distribution of an indicator showing the certainty of the presence of the target wave source. We regard the high-value point of SW s as the source of the target wave. Before applying this procedure to the target wave, we confirm that the location of an aftershock can be estimated. In order to check the procedure, the aftershock should be (1) large (M > 6), (2) near the fault plane and (3) recorded at all the stations in arrays A, B and C. Fig. 13 shows the distribution of SW s and the epicentre of the aftershock. The combined semblance value is normalized by the maximum value. The semblance peak extends along the fault edge. This is because the location of the source is at the edge of the fault plane, where the edge of the coverage by the correction functions also lies. The correction functions for the source include some uncertainty. In spite of this uncertainty, the semblance peak almost corresponds to the source location. Although there are no other aftershocks that are appropriate for checking the correction functions on the fault plane, we can expect that the source position of the target wave is obtained correctly by adopting the procedure.

11 1114 R. Honda et al. 100 km ~ SWs Figure 13. Comparison of source location with the combined semblance distribution. Since the aftershock is located at the edge of the correctionfunction coverage area, the semblance peak extends along the fault edge. However, the aftershock is included in the upper 10 per cent region of the semblance-value distribution, and the source location almost corresponds to the peak. Figure 14. Combined semblance-value distribution on the fault plane obtained from the data of the three arrays. The combined semblance-value distribution is normalized by the maximum value. The triangles, star and black solid lines are the same as those in Fig. 12. The location of the peak, which is the source of the target wave, is 65 km off HKD077 and at a depth of 52 km. Fig. 14 shows the final result for the target wave. Note that the combined semblance-value distribution is normalized by the maximum value. A peak is obtained 80 km off HKD077, at a depth of 47 km. The location is farther from HKD077 in the direction of the shallower part of the fault plane as compared with those of asperity (C) estimated by Honda et al. (2004). The rupture time at the point, inferred from the traveltime from the point to each station and the onset time of the target wave, is between 27 and 31 s after the origin time. In other words, the relocated asperity ruptures about 29 s after the origin time (JMA 2003). We can estimate the average rupture velocity from the rupture time and the distance from the hypocentre. The average rupture velocity from the hypocentre to the relocated asperity is 2.5 km s 1, which is considerably slower than 3.6 km s 1, the total rupture velocity obtained from the waveform inversion analysis. These results imply that the rupture propagated with different average velocities towards each asperity. 4 DISCUSSION AND CONCLUSIONS We imaged an asperity on the fault plane of the 2003 Tokachi-oki earthquake through a procedure that differs from waveform inversion analysis. In the inversion analysis, a minor asperity that generates impulsive waves is estimated to be located at the northeast edge of the fault plane, but the constraints for the existence or location of the asperity remain limited. We introduced semblance analysis to retrieve the location of the minor asperity as the source of the impulsive waves. In order to image the location of the asperity, we extracted impulsive waves from the recordings to avoid contamination by surface waves and performed semblance analysis on them. We applied a bandpass filter between 2 and 0.25 Hz to the observed waveforms and integrated them to obtain the velocity waveforms. Because the station interval of our array of K-NET and KiK-net stations is approximately 100 km, we could not analyse frequencies higher than 0.25 Hz. This limitation caused low distance resolution, because the variation in traveltime difference between stations responsible for the particularly distant source location was small compared with the frequency range. On the other hand, the resolution in direction was better than that in distance. To improve the resolution, we introduced site-correction functions of traveltimes and a weight based on the rupture time on the fault plane. As a result, we obtained the source of the impulsive wave as the peak of the weighted semblance-value distribution, which is more tightly constrained than the results of the waveform inversion analysis. Although we cannot determine the amount of slip and rupture processes in detail from the results, the rupture triggering point of asperity (C) in Honda et al. (2004) is relocated to a shallower point farther away from HKD077 (closer to the epicentre). The relocated asperity is close to the minor asperity that was obtained in Miyazaki et al. (2004b) by using 1 Hz sampling GPS data, and its location is complementary to the distribution of aftershocks greater than magnitude 4 (Ito et al. 2004) and with significant post-seismic deformation (Miyazaki et al. 2004a). Our result does not contradict the hypothesis that almost all of the accumulated stress was released by high-speed ruptures in asperities and post-seismic deformations, and some aftershocks were concentrated in the surrounding regions due to stress transfer (Miyazaki et al. 2004b). We estimate the rupture time at the relocated asperity to have occurred 271 s after the rupture initiation at the epicentre. In other words, the average rupture velocity towards the relocated asperity was km s 1. Such slip delay at the minor asperity agrees with the results of Miyazaki et al. (2004b). Koketsu et al. (2004) also obtained a similar minor asperity with a delayed rupture time, although it was shallower than our relocated asperity (C). On the other hand, they found that the rupture propagated towards the main asperity with supershear speed. These results imply that the rupture velocity varies over the fault plane.

12 Imaging an asperity with array data 1115 Here, we reconsider the results of Honda et al. (2004). Since they employed a linear waveform inversion with the multitime-window method, the source time function at each subfault is represented by a combination of multismoothed ramp functions. Although we assumed a constant rupture velocity for the triggering of the first time window, a variable rupture velocity is allowed depending on the number of time windows and their duration. In Honda et al. (2004), the slip function on each subfault is represented by six smoothed ramp functions whose rise time is 5 s. It allows a slip on each subfault for 17.5 s after the arrival of the rupture front with a velocity of 3.6 km s 1. If the rupture velocity varies according to the propagating direction, the inversion result is affected by the data constraints. In this case, the rupture velocity is affected by the main asperity, because seismic waves from the main asperity were observed at almost all stations and the main asperity is well constrained by the data, while lesser data including the target wave were used in their analysis. Source time functions of asperity (B) the main asperity have a large amplitude in their first or second time windows, while source time functions around asperity (C) have peaks at their heads and tails (Fig. 1). Considering the results of the semblance analysis, the peak at the tail rather than the head is the appropriate solution. One of the advantages of our approach is that we can obtain stable solutions even in the case of such a complex source process. In order to improve the distance resolution, denser arrays with a station interval of several hundred metres are necessary. This would make it possible to accurately estimate, not only the asperity distribution, but also the rupture process of the earthquake (e.g. Spudich & Oppenheimer 1986). Using a dense array with the station-interval of 500 m, Nakahara et al. (2004) suggested that the rupture process of the Miyagi-oki earthquake could be obtained. This method could be extended to obtain the whole rupture process. It is a challenging issue to estimate physical values (e.g. amount of slip) directly, because semblance values only evaluate coherency of waveforms. However, we would be able to estimate the relative strength of radiated energy from each portion of the fault plane by stacking the amplitudes of waveforms, and we can obtain entire images of the rupture initiation and propagation over a wide frequency range without any assumptions of the fault geometry and rupture velocity. The obtained results would be useful for constraining parameters for inversion analysis to estimate physical values. Consequently, array analysis using dense seismographs will be a powerful tool to help shed light on the broad-band analysis of source process. ACKNOWLEDGMENTS We are very grateful to Drs Youichi Asano and Kazushige Obara for their valuable advice and discussions. We thank Dr Ken Xian-Sheng Hao for his advice on our manuscript. This study was conducted under the auspices of the National Strong-Motion Mapping Project of the National Research Institute for Earth Science and Disaster Prevention, Japan. GMT (Wessel & Smith 1995) was used for the figures. The article was improved through constructive reviews by Drs. Martin Mai and Paul Spudich. REFERENCES Aoi, S., Obara, K., Hori, S., Kasahara, K. & Okada, Y., New strongmotion observation network: KiK-net, EOS. Trans. Am. Geophys. Union, 81(48), Fall Meet. Suppl. Abstract S Aoi, S., Honda, R., Morikawa, N., Sekiguchi, H., Suzuki, H., Hayakawa, Y., Kunigi, T. & Fujiwara, H., D finite-difference simulation of long-period ground motions for the 2003 Tokachi-oki, Japan, earthquake, J. geophys. Res., submitted. Asano, Y. et al., Spatial distribution of seismic scatterers beneath the Ou Backbone Range, north-eastern Japan, estimated by seismic array observations, ZISIN, 52, Capon, J., Signal processing and frequency-wavenumber spectrum analysis, Proc. IEEE, 57, Fletcher, J., Spudich, P. & Baker, L., Rupture propagation of the 2004 Parkfield, California, earthquake from observation at the UPSAR, Bull. seism. Soc. Am., 96, S129 S142. Hartzell, S.H. & Heaton, T., Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake, Bull. seism. Soc. Am., 73, Honda, R., Aoi, S., Morikawa, N., Sekiguchi, H., Kunugi, T. & Fujiwara, H., Ground motion and rupture process of the 2003 Tokachi-oki earthquake obtained by strong-motion data of K-NET and KiK-net, Earth Planets Space, 56, Ishii, M., Shearer, P.M., Houston, H. & Vedale, J.E., Extent, duration and speed of the 2004 Sumatra-Andaman earthquake imaged by the Hi- Net array, Nature, doi: /nature Ito, Y., Obara, K., Shiomi, K., Sekine, S. & Hirose, H., Slow earthquakes coincident with episodic tremors and slow slip events, Science, 315, Iwasaki, T., Hirata, N., Kanazawa, T., Urabe, T., Motoya, Y. & Shimamura, H., Earthquake distribution in the subduction zone off eastern Hokkaido, Japan, deduced from ocean-bottom seismographic and land observations, Geophys. J. Int., 105, Japan Meteorological Agency, The Seismological and Volcanological Bulletin of Japan, Japan Meteorological Agency, Tokyo. Kinoshita, S., Kyoshin Net (K-NET), Seism. Res. Lett., 69, Koketsu, K., Hikima, K., Miyazaki, S. & Ide, S., Joint inversion of strong motion and geodetic data for the source process of the 2003 Tokachi-oki, Hokkaido, earthquake, Earth Planets Space, 56, Maeda, T., Sasatani, T., Miura, T., Takai, N. & Shimizu, G., Characteristics of long-period seismic waves from the 2003 Toakchi-oki earthquake, Seismological Society of Japan Fall Meeting, Fukuoka, Japan. Matsumoto, S., Imaging of inhomogeneous structure based on seismic array observations, ZISIN, 54, 19301, in Japanese with English abstract. Miyazaki, S., Segall, P., Fukuda, J. & Kato, T., 2004a. Space time distribution of afterslip following the 2003 Tokachi-oki earthquake: implications for variations in fault zone frictional properties, Geophys. Res. Lett., 31, L06623, doi: /2003GL Miyazaki, S. et al., 2004b. Modelling the rupture process of the 2003 September 25 Tokachi-Oki (Hokkaido) earthquake using 1-Hz GPS data, Geophys. Res. Lett., 31, L21603, doi: /2004GL Nakahara, H., Takagi, N., Nishimura, T., Sato, H. & Fujiwara, H., Array observation by strong-motion seismometers in the vicinity of the source region of the expected Miyagi -Oki earthquake, Programme and Abstracts, Seismological Society of Japan Fall Meeting, B-11, Fukuoka, Japan, in Japanese. Obara, K., Hi-net: high-sensitivity seismograph network, Japan, Lecture Note in Earth Sciences, 98, Obara, K. & Ito, Y., Very low frequency earthquake excited by the 2004 off-the-kii-peninsula earthquakes: a dynamic deformation process in the large accretionary prism, Earth Planets Space, 57, Olson, A.H. & Apsel, R.J., Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake, Bull. seism. Soc. Am., 82, Sasatani, T., Maeda, T. & Takai, N., Long-period ground motion and deep subsurface structure in Hokkaido: a review, BUTSURI-TANSA, 59, 31526, in Japanese with English abstract. Spudich, P. & Cranswick, E., Direct observation of rupture propagation during the 1979 Imperial Valley earthquake using a short baseline accelerometer array, Bull. seism. Soc. Am., 74, Spudich, P. & Oppenheimer, D., Dense seismograph array observations of earthquake rupture dynamics, in Earthquake Source Mechanics, pp , eds Das, S., Boatwright, J. & Sholz, C.H., Maurice Ewing Series 6, AGU, Washington, DC.