Geophysical Journal International

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1 Geophysical Journal International Geophys. J. Int. (2010) 182, doi: /j X x Delineating the rupture planes of an earthquake doublet using Source-Scanning Algorithm: application to the 2005 March 3 Ilan Doublet, northeast Taiwan Chih-Wen Kan, 1,2 Honn Kao, 3,4 Gwo-Bin Ou, 2 Rong-Yuh Chen 1 and Chien-Hsin Chang 1 1 Seismological Center, Central Weather Bureau, Taipei, Taiwan. kkevin@scman.cwb.gov.tw 2 Institute of Seismology, National Chung Cheng University, Chia-Yi, Taiwan 3 Geological Survey of Canada, Pacific Geoscience Centre, Sidney, BC, Canada 4 School of Earth and Ocean Sciences, University of Victoria, BC, Canada GJI Seismology Accepted 2010 May 14. Received 2010 May 3; in original form 2009 July 31 SUMMARY Correct identification of the fault plane(s) associated with an earthquake doublet is a very challenging problem because the pair of events often occurs in close space and time with almost the same magnitude. Most long-period waveforms of an earthquake doublet are severely tangled and thus unsuitable for conventional waveform inversion methods. In this study, we try to resolve this issue by utilizing the recently developed Source-Scanning Algorithm (SSA). The SSA systematically searches the model space for seismic sources whose times and locations are most compatible with the observed arrivals of large amplitudes on seismograms. The identification of a seismic source is based on the brightness function, which is defined as the summation of the normalized waveform amplitudes at the predicted arrival times at all stations. By illuminating the spatiotemporal distribution of asperities during an earthquake s source process, we are able to constrain the orientation of the rupture propagation that, in turn, leads to the identification of the fault plane. A series of synthetic experiments are performed to test SSA s resolution under various scenarios including different directions of rupture propagation, imperfect station coverage and short origin time difference between the two events of a doublet. Because only short-period records are needed in the analysis, the proposed method is best suited for an earthquake doublet with a short time gap between the two events. Using the 2005 Ilan doublet (the origin time difference is only 70 s) that occurred in northeast Taiwan as an example, we show that the trace of the brightest spots moves towards the west and infer the E W-striking plane to be the actual fault plane. Keywords: Earthquake source observations; Computational seismology; Asia. 1 INTRODUCTION An earthquake doublet is often defined as a pair of earthquakes, with almost the same magnitudes, that are separated by small gaps in both time and space (e.g. Astiz & Kanamori 1984; Xu & Schwartz 1993; Kagan & Jackson 1999). Earthquake doublets are unique because they are manifestations of complex interactions of tectonic stress regimes that might be associated with different structures and/or rheological conditions (Kagan & Jackson 1999; Ammon et al. 2008). From a seismic hazard s point of view, an earthquake doublet could potentially cause much more damage than a single event due to the increased duration of ground shaking. The source study of earthquake doublets is a challenging subject. The proximity between the two events inevitably results in tangles of the waveforms generated by each source, thus severely limits the application of conventional waveform inversion techniques (Dziewonski et al. 1981; Sipkin 1982; Nabelek 1984; Mori & Hartzell 1990; Dreger & Helmberger 1993; Ritsema & Lay 1993; Dreger & Kaverina 2000; Kuge 2003). One of the fundamental questions regarding the source characteristics of an earthquake doublet is to confidently identify the rupture plane of each event. This is especially important in a tectonically complex region because a different choice of the rupture planes often leads to a totally different interpretation. Unfortunately, since most waveform-based methods identify the rupture plane by minimizing the misfit between the long-period portion of synthetic and observed waveforms (e.g. Mori & Hartzell 1990; Dreger & Kaverina 2000; Kuge 2003), those methods might be inappropriate for the source study of an earthquake doublet, particularly if the two events are only minutes apart. 956 C 2010 The Authors

2 Delineating fault planes of earthquake doublet 957 Figure 1. Maps showing the regional tectonic framework of Taiwan (upper-left insert), station distributions of the Central Weather Bureau Seismic Network (CWBSN, circles), the Broadband Array in Taiwan for Seismology (BATS, squares) and the Taiwan Strong-Motion Instrumentation Program (TSMIP, triangles). Solid blue symbols mark stations whose waveforms are used in the analysis. Red stars mark the epicentres of the 2005 March 3, Ilan earthquake doublet. The best double-couple fault plane solutions are derived from the centroid-moment-solutions reported by the Data Management Center of BATS, and plotted in low-hemisphere projection. Green crosses in the source region mark the location of aftershocks that occurred within 24 h of the Ilan doublet. The size of each symbol is proportional to the reported M L. In fact, determining the rupture plane of an earthquake is never a straightforward task, especially from seismic records alone. Assuming that an earthquake source can be reasonably represented by a double-couple model, the traditional way of distinguishing the fault plane from the auxiliary plane is to perform a slip distribution inversion for each plane, and the one with an overall better waveform fit is chosen (e.g. Mori & Hartzell 1990; Dreger & Kaverina 2000; Kuge 2003; Dreger et al. 2005). Because such an approach depends on the accurate construction of synthetic seismograms, its success could be greatly compromised if detailed knowledge of the velocity model is unavailable and/or the cost of calculating synthetics becomes too heavy. Kao & Shan (2007) develop an innovative approach to identify the fault plane of an earthquake from short-period waveforms at local/regional distances. The method, named as the Source-Scanning Algorithm (SSA), was originally designed to locate seismic tremor sources with emergent arrivals (Kao & Shan 2004). The advantage of SSA is three-folded. First, the source analysis is performed without any phase readings from seismograms. Secondly, it does not require any aprioriknowledge on the fault plane s corresponding dimension and geometry. And thirdly, the results are directly constrained from the observed waveforms without the need of constructing synthetic seismograms. The SSA approach has been successfully tested using the 2003 San Simeon and 2004 Parkfield (central California) earthquakes (Kao & Shan 2007). A more recent study applying SSA analysis to the 2002 Nisqually, Washington, earthquake further demonstrates its success when other methods failed to unambiguously resolve the corresponding rupture plane (Kao et al. 2008). In this study, we expand the application of SSA to the study of earthquake doublets, using the 2005 March 3, Ilan, northeast Taiwan, earthquake doublet as an example (Fig. 1). This doublet represents one of the most difficult scenarios in the identification of earthquake rupture planes. The source region, near the junction of the southernmost terminus of the Ryukyu subduction zone and the Taiwan collision zone (Fig. 1), is tectonically very complicated (Hsu et al. 1996; Kao et al. 1998; Lallemand & Liu 1998) and gives no obvious choice for either planes. The size of this doublet is moderate (M L 5.9 for both events), thus produces very limited directivity effect in long-period waveforms to be used for the rupture analysis (Douglas et al. 1988). Furthermore, the extremely short time difference between the two shocks (only about 70 s) makes the proper separation of long-period waveforms associated with each event nearly impossible. The main purpose of this study is to demonstrate that SSA is a powerful tool capable of identifying earthquake rupture planes even under the extreme conditions of a doublet. We also discuss the necessary data selection and processing procedures to ensure the robustness of the SSA analysis. Finally, we outline the

3 958 C.-W. Khan et al. most effective way to identify earthquake fault planes from SSA images and address the likely scenarios when the identification might become ambiguous. 2 METHOD AND DATA PROCESSING The essence of SSA is to illuminate the spatiotemporal distribution of seismic sources via the so-called brightness function (Kao & Shan, 2004). In this section, we briefly explain the theory of SSA and how it was modified for the purpose of identifying earthquake rupture planes. Readers are referred to the original SSA papers (Kao & Shan 2004; Kao & Shan 2007) for more technical details. The brightness function for a given source location in space (η) and time (τ) isdefinedas br(η, τ) = 1 N u n (τ + t ηn ), (1) N n=1 where u n is the normalized seismogram recorded at station n,andt ηn is the traveltime from point η to station n. When a significant seismic source exists at the given location and time, large amplitudes are expected at the predicted arrival times (i.e. τ + t ηn ), thus resulting a large brightness value (a bright spot). A complete picture of the source distribution can be obtained by systematically scanning the entire model space (η, τ) for bright spots. There are many practical concerns when SSA is applied to real data for earthquake rupture analysis. First of all, our imperfect knowledge of the velocity model used in the traveltime calculation could misalign the predicted arrival times of large amplitudes from the observed ones, creating a defocusing effect. Secondly, because the strength of the rupture is a function of time, there is an ambiguity whether a spot with less brightness represents a smaller/weaker source or a less likelihood of having a stronger source. Thirdly, the SSA formula does not discriminate the direct, source-related phases from any structure-related ones (e.g. coda waves, diffracted phases and reflection/refraction from velocity discontinuities). Therefore, coherent arrivals due to a particular structure will be mapped to a false source image, unless they are either avoided or removed from the input. Finally, for each phase, most travel time algorithms calculate the time of the initial arrival rather than the time corresponding to the largest amplitude. Although such time differences are always small for short-period records, they must be adjusted properly to enhance the resolution of SSA source images. In addition to the modifications made by Kao & Shan (2007), we further improve the definition of a brightness function by allowing variable time segments before and after the predicted arrival times to better align the largest amplitudes as br(η, τ) = 1 N N n=1 M 2 [ ( Wm U n τ + tηn + mδ t + tn corr m= M 1 M W m m= M )], where U n is the normalized waveform envelope of the P wave train recorded at station n; tn corr is the corresponding station correction; M 1 and M 2 are the numbers of samples before and after the predicted arrival time (i.e. τ + t ηn ), respectively (Fig. 2); δt is the sampling interval and Wm is a weighting factor. The inclusion of neighbouring samples around the predicted arrival times in the brightness calculation serves two purposes. The first is to increase the SSA s tolerance against possible traveltime errors due to our imperfect knowledge about the velocity model (Kao & Shan 2007). The second is to maximize the SSA s image resolution by adjusting the parameters M 1 and M 2 in eq. (2) such that the number of included samples is comparable to the duration of the energy bursts emitted by source asperities (Fig. 2). It turns out that an appropriate set of M 1 and M 2 is particularly important to the (2) Figure 2. A schematic diagram showing how a station correction (t n corr ) and the numbers of neighbouring samples (M 1 and M 2 ) around the predicted arrival time are determined in the calculation of the brightness function. Black and red lines correspond to the observed waveform and its envelope, respectively. The purpose of a station correction is to align the predicted arrival time with the arrival of the largest amplitude. Samples immediately around the largest amplitude (within M 1 δt and M 2 δt) are included to maximize their brightness contribution. The signal-to-noise ratio (S/N) is empirically defined as the ratio between the two 5-s windows 0.5 s before (noise segment) and after (signal segment) the predicted arrival time.

4 delineation of the rupture plane for a moderate-sized event, which is often characterized by smaller asperities. Synthetic experiments indicate that the SSA image can no longer resolve individual asperities if the total length of the time window used in the brightness calculation (i.e. M 1 δt+m 2 δt) significantly exceeds the duration of the largest burst as measured from observed seismograms. In general, the ratio of M 1 /M 2 is between 1/3 and 1 depending on the overall size of the seismic source. The effectiveness of including a station correction term and utilizing waveform envelopes has been explained previously (Kao & Shan 2007). Here we elaborate more on how station corrections should be obtained to maximize SSA s resolution. Because SSA relies on the alignment of large waveform amplitudes at multiple stations to image the spatiotemporal distribution of sources, it requires a time table for the arrival of the largest amplitude as a function of epicentral distance and source depth, not the onset of the seismic phase as predicted by most ray-tracing programs (e.g. Hole & Zelt 1995). Consequently, we define the station correction term in eq. (2) as the difference between the observed and predicted arrival times (of the onset of the phase) plus the difference between the onset and the largest amplitude of the phase. The later is measured from synthetic waveforms assuming a simple triangular source time function of the same time length as that used in the brightness calculation (Fig. 2). A set of general rules can be established for the selection of input waveforms. The most fundamental one is the overall signalto-noise ratio (S/N) of each trace. We empirically define the S/N of a waveform as the ratio between the average absolute amplitudes of two 5-s segments, 0.5 s from the observed first arrival on each side (Fig. 2). Generally speaking, a minimum S/N of 2 is required to obtain a good source image. More details on the S/N issue are presented in the next section. To minimize the uneven effect of geometric attenuation with distance, waveform data that are recorded too close to the epicentre are avoided. Depending on the size of the target earthquake, the minimum epicentral distance appropriate for SSA analysis should be at least several times the source dimension. Because the traveltime of body waves is more sensitive to the change in origin time than in source depth as the epicentral distance increases, it is important to have data from a wide distance range to prevent any significant trade-off between the two parameters (Kao & Shan 2004; Kao & Shan 2007). However, stations beyond 170 km are generally not used to reduce any unknown wave propagation effect (e.g. scattering phases from structures not included in the assumed velocity model). The length of each input waveform is directly linked to the duration of the source, which can be roughly estimated from the corresponding magnitude. For the case of long source duration (e.g. >5 s), we can subdivide each input trace into several segments with some overlap, and demand that the contribution from each station to the brightness function is within the same segment. Although this step may not always be necessary because the chance of having a time location combination that satisfies the arrivals of large amplitudes both in the early part of the wave train at some stations and in the late part at others is usually small, it is effective in eliminating any artefacts at extreme times and locations as a result of the wrong mapping. To incorporate waveform records from different seismic networks and instrumentations, we resample all waveforms to a constant interval of 0.02 s (50 Hz), followed by unifying the instrument response to an S-13 short-period seismometer. Individual waveforms are normalized between 1 and 1 such that the brightness function will not be dominated by the nearest stations. Finally, the amount Delineating fault planes of earthquake doublet 959 of time correction for each station is determined by subtracting the calculated arrival time (corresponding to the reported source parameters in the earthquake catalogue) from that of the largest amplitude (Fig. 2). Because our purpose is to delineate the rupture plane from the relative positions of bright spots (i.e. the scanned sources), the absolute location of the assumed reference point is irrelevant. 3 RESOLUTION TESTS USING SYNTHETIC DATA The effectiveness of SSA in delineating the rupture plane of an earthquake has been thoroughly tested using both synthetic data and real seismic observations in previous studies (Kao & Shan 2004; Kao & Shan 2007; Kao et al. 2008). In this section, we conduct more experiments to further explore SSA s robustness when the azimuthal coverage of seismic stations is imperfect and to investigate the relationship between SSA s resolution and the origin time difference between the two events of an earthquake doublet. Fig. 3 shows the configuration of our synthetic tests. We adapt the seismic network configuration in northern Taiwan such that our synthetic test results can be compared directly to that from real observations shown in the next section. A point source is placed in the epicentral area of the 2005 Ilan earthquake doublet at a depth of 6 km. The horizontal location of the point source is displaced successively to mimic the failure of asperities as the rupture propagates. Four different source propagation scenarios are simulated (from east to west, from west to east, from north to south and from south to north) with a rupture speed of 2.5 km s 1. The strength of the source is assumed to vary with time, reaching the peak at the middle with 20 per cent fall-off towards the two ends. Synthetic seismograms are calculated from the assumed sources to each station using the Thompson-Haskell propagator matrix method (Zhu & Rivera 2002) and the same 1-D velocity model routinely used by the Central Weather Bureau, Taiwan, for locating regional earthquakes (Shin & Chang, 1993). All waveform data are processed according to the procedures described in the previous section. The grid size and time step used in the scanning process are set to 1 km and 0.1 s, respectively. These two values are intrinsically linked to the length of the time window used in the calculation of the brightness function. For a rupture speed of 2.5 km s 1,two asperities separated by 1 km will generate a waveform with two peaks separated by 0.4 s. This implies that the time window in eq. (2) should be 0.5 s or less to achieve the best resolution. In the first part of our experiment, we add random noise to all synthetic traces to explore the limit of SSA s tolerance against background noise. The level of background noise is increased incrementally with respect to the largest amplitude of the inputted signal until the source image can no longer be discerned. Our final result suggests that SSA can successfully delineate all three asperities even when the level of noise is as high as 30 per cent. Because the amplitudes of the three inputted sources are 0.8, 1.0 and 0.8, respectively, a 30 per cent noise is roughly equivalent to a S/N of 1.5 according to the definition described earlier (Fig. 2). A quick check on the S/N of the 2005 Ilan doublet waveforms indicates a very wide range from 1.9 to >100 depending on the epicentral distance. Consequently, we set the S/N threshold to 2.0 to ensure the quality of our SSA analysis. Next, we add eight imaginary stations offshore east of the epicentral area to establish a reference case in which the azimuthal coverage is nearly perfect (Fig. 3). The composite SSA image over a 5-s time window (i.e. from 1 s before the origin time to 4 s after) for a point source propagating westward is shown in Fig. 4(a). The

5 960 C.-W. Khan et al. Figure 3. Configuration of our synthetic experiments. (a) Solid triangles mark the locations of seismic stations, as adopted from Fig. 1. Eight imaginary stations east offshore of the epicentre (inverted triangles) are created to test the effect of imperfect azimuthal coverage. The centroid epicentre of the 2005 Ilan earthquake doublet is marked by an open star. (b) Three asperities are placed 3 km apart at a depth of 6 km in the epicentral area to mimic an E W-propagating source. The propagation speed is assumed to be 2.5 km s 1. The direction of propagation is determined by the relative timing of the asperities. For example, a westward rupture (solid arrow) corresponds to asperity No. 1 at 0 s, No. 2 at 1.2 s, and No. 3 at 2.4 s; whereas the relative timing is reversed for an eastward rupture (grey arrow). (c) Similar to (b) but for a source propagating on a N S-striking plane. locations of the brightest spots effectively trace the asperities within 1 km from their respective true places, and the direction of rupture propagation is consistent with the input. Notice that the maximum values of the brightness actually varies with time (the largest for the second asperity, Fig. 4a), which also agrees well with the assumed source configuration. The input waveform envelopes have three large phases corresponding to the three asperities in the source model (Fig. 4b). The relative timing clearly changes from one station to another depending on the station s epicentral distance and azimuth. For example, the arrival time difference between the first and the third phases at station DPDB is 2 s, but increases to 3.4 s at IM20. Because the general trend is that all inland stations have relatively shorter time differences than offshore stations, the directivity pattern clearly suggests a rupture from east to west. In a more realistic scenario, the offshore stations do not exist and the widest azimuthal coverage is about 175 (i.e. the western side; Fig. 3a). The third part of our synthetic experiment is to scan the source using only inland stations. The results are presented in Fig. 4(c f). For the case of a rupture propagating westward, the locations of the asperities, as marked by the brightest spots at the respective snapshots, remain unchanged from the previous results (Fig. 4a vs. c). However, the image of individual asperities becomes blurry with a tail dipping to the east. This blurry tail is caused by a combined contribution from the rising and/or falling parts of the same phase at various stations. We have conducted the same experiments for different directions of rupture propagation, and all have similar outcomes (Fig. 4d f). These results indicate that the apparent shapes of individual asperities may not truly represent the actual orientation of the fault plane when the azimuthal coverage of recording stations is less than 180. Instead, the rupture propagation should be delineated from the locations of the brightest spots at consecutive times. In the last part of our tests, we try to determine the minimum origin time difference between the two events of an earthquake doublet below which individual rupture images cannot be adequately resolved. We repeat the source configuration shown in Fig. 4(a) twice with a time delay varying from 1 to 60 s. Because each event lasts 2.6 s and the directivity effect is expected to change the apparent duration of the source wave train by as much as 0.8 s depending on each station s azimuth and distance, our tests indicate that the minimum origin time difference is about 3 s. Below this threshold, the first phase of event 2 will interfere with the third phase of event 1, thus the individual asperities of the two events cannot be successfully resolved (Fig. 4g). In other words, the condition for a successful delineation of individual events is that the phase of the last asperity of the first event must arrive no later than the phase of the first asperity of the second event. A more conservative approach is to ensure that the wave trains between the two events are separated by one source duration or more. 4 APPLICATION TO THE 2005 ILAN EARTHQUAKE DOUBLET Although the density of seismograph stations in Taiwan is among the highest of the world, data selection for the 2005 Ilan earthquake doublet is still challenging due to the lack of coverage offshore to the east (Fig. 1). There are three major seismic networks currently in operation in the Taiwan region. The Central Weather Bureau Seismic Network (CWBSN) is equipped with short-period seismometers that are distributed uniformly throughout the region. The Broadband Array in Taiwan for Seismology (BATS) has a larger average inter-station distance, but consists of broadband sensors and high-resolution data loggers. The Taiwan Strong-Motion Instrumentation Program (TSMIP) has the highest station density in major metropolitan areas, yet the distribution in the central mountainous region is sparse. We could not use any CWBSN waveforms for the SSA analysis of 2005 Ilan earthquake doublet because most of them are clipped. Waveform data from BATS and TSMIP are examined and selected according to criteria described in previous

6 Delineating fault planes of earthquake doublet 961 Figure 4. Results of our synthetic experiments. (a) When the station coverage is perfect (i.e. including the imaginary stations (IM) offshore east of the epicentre, Fig. 3), the locations of the brightest spots (stars) effectively trace the asperities of a westward rupture to within 1 km from their respective true places. (b) The predicted arrivals from the three asperities identified from (a) at selected stations along six different azimuths. Black and red lines correspond to synthetic waveforms and waveform envelopes, respectively. Phases originated from the same source are plotted in the same colour. The directivity effect of rupture propagation from east to west is apparent by the wider and narrower waveform trains for stations to the east and west, respectively. (c) Same as (a) but only inland stations are used in the analysis. Although the locations of the brightest spots can still trace the true locations of the inputted asperities reasonably well, the image of individual asperities becomes blurry with a tail dipping to the east. (d,f) Same as (c) but for eastward, southward, northward ruptures, respectively. (g) The predicted arrivals from an earthquake doublet consisting of two events shown in (b). The minimum difference in the origin times between the two events is 3 s, as constrained by the latest phase of the first event and the earliest phase of the second event. The corresponding location of each image is shown in Fig. 3.

7 962 C.-W. Khan et al. sections. In total, 20 and 17 stations surrounding the western half of the focal sphere are chosen for the first and second events of the doublet, respectively, with epicentral distances ranging from 42 to 164 km. Fig. 5 shows waveform examples of the Ilan earthquake doublet. The source duration is estimated to be 5sbasedonP-wave trains at stations closer to the epicentre. The S-wave trains arrive approximately 6 18 s after the P, depending on the epicentral distance. Because the origin time difference between the two events is only 70 s, the wave train of the second event is clearly contaminated by the coda wave of the first (top panel, Fig. 5). This is especially obvious after bandpass filtering the waveforms between 0.02 and 0.1 Hz (i.e s; mid panel, Fig. 5), as the S/N ratio of the second event s P phase is only slightly higher than 1. Consequently, we would not expect traditional finite-fault inversion methods to work properly due to the interference of long-period waveforms between the two events. Short-period waveforms filtered at >1 Hz, on the other hand, show clear separation of the two events (bottom panel, Fig. 5), which is essential for a successful SSA analysis according to our synthetic test results (Fig. 4). These waveforms are used in our SSA analysis and the results are presented in Figs 6 and 7 for the first and second events, respectively. As expected from the results of our synthetic tests (Fig. 4c), the SSA images of both events exhibit elongated tails dipping to the east that are simply artefacts contributed from the rising and falling parts of a source phase at different stations (Fig. 6a). Therefore, the source propagation is best illuminated not by the shape of the tails, but by tracing the brightest spot as a function of time. For the first event, the brightest spot stays more or less at the reported epicentre for the first two seconds (stars 1 and 2, Fig. 6b), during which the corresponding brightness increases monotonically. The brightest spot corresponding to the next time window is found 4 kmtothe west (star 3, Fig. 6b). Such a pattern suggests that the rupture starts to propagate westward once the rupture strength is fully established (Fig. 6b). In Fig. 6(c), we arrange the input waveforms according to their azimuths and highlight the predicted arrival times of the asperities in different time windows with different colours. The time difference between the predicted arrivals of the first and the second asperities is almost identical at stations along all azimuths, implying a difference in the origin times of the two sources but not in space. On the other hand, the arrivals of the phase corresponding to the third asperity are systematically earlier at stations due west (e.g. stations U045 and U147; Fig. 6c) with respect to stations to the north and south (e.g. stations T077 and H056). The line connecting the illuminated asperities imposes a geometric constraint on the possible orientation of the fault plane, that is, the fault plane must include this line. Given the two nodal planes shown in Fig. 1, we therefore infer that the E W-striking plane is most likely the rupture plane. The spatial distribution of asperities for the second event of the Ilan doublet cannot be well resolved with the same length of time window used in the brightness calculation of the first event (i.e. M 1 δt+m 2 δt, which is 0.5 s). After carefully examining the P-wave trains of the second event, we find that the time window needs to be shorter to match the narrower envelope peaks. We have tried a range of different time windows from 0.15 to 0.5 s and found that 0.3 s gives the biggest brightness value. Fig. 7 shows our best result for the second event of the Ilan doublet. There are many similar features between the two events. For example, the total duration of the source process also lasts 5 s. The SSA image has tails dipping to the east as a result of the imperfect azimuthal coverage (Fig. 7a). The location of the brightest spot remains almost unchanged during the first two seconds of the source process, during which the brightness continues to grow (Fig. 7b). And the third asperity is located to the west of the first two by 3 km. Unlike the first event, however, the depth of the third asperity is shallower at 5 km (Fig. 7b). Our results suggest that the rupture process of the second event is basically the same as the first one, that is propagating westward once the full strength is reached (Fig. 7b). The directivity effect of the westward rupture propagation can be visually confirmed by the relative timing of the phases associated with individual asperities. Specifically, stations to the west of the epicentres have shorter time differences between the phases of the second and third asperities than stations along other azimuths. For examples, the predicted arrival of the third asperity is 2 s behind that of the second asperity at station T077 (located directly north of the epicentres) for event 1 and 2.4 s for event 2 (Figs 6c and 7c). In contrast, the time difference decreases to 1.3 s at station U147 for event 1 and 1.8 s at station U021 for event 2 (both stations are located to the west). The effect of directivity is reduced by about half to 0.3 s for stations located to the northwest (e.g. T109/T066) or southwest (e.g. H056). 5 DISCUSSION AND CONCLUSION The principal objective of SSA is to seek the optimal combinations of times and locations in the specified model space that can satisfy the arrival times of large phases on observed seismograms. The locations of asperities can be well imaged when the rupture has grown to its full strength (i.e. producing the maximum amplitudes). However, determining the locations of the asperities during the initial and ending stages of the source process may be more complicated because the corresponding amplitudes are often much smaller. A practical approach is to subdivide the observed waveforms into several segments, then limit the source-scanning process such that only the same segment is allowed to contribute to the brightness function. The advantage of such an additional condition is to effectively prevent mapping the large phases (mostly in the middle part of observed waveforms) into the source images of other time steps. Although there is no unique way to define segments, the rule of thumb is to ensure that the length of each segment is long enough to accommodate the corresponding directivity effect. In our case, because the expected arrival time difference caused by the rupture directivity is 0.8 s (Fig. 4), a generous 2-s segment is used in the SSA analysis to map the source image during the initial and ending stages of each event. When we combine the SSA results of individual segments to restore the overall rupture process, it is important to scale the brightness functions according to the original amplitude differences. This is because the brightness functions are calculated from normalized waveforms (eq. 2) and does not preserve the absolute size of the source. After the amplitude adjustment, the brightest spots identified in the initial or ending segments would have much smaller values (0.6 in Figs 6 and 7) due to their smaller waveform amplitudes. This practice should not be confused by the procedures described in an earlier study in which SSA was used to determine the hypocentre of seismic tremor bursts (Kao et al. 2005). The high brightness threshold of 0.85 used in the tremor study refers to results from one waveform segment with no rupture effect. Even with the additional step of subdividing each waveform into segments, it is still possible to have a few stations where no

8 Delineating fault planes of earthquake doublet 963 Figure 5. Observed waveforms for the 2005 March 3, Ilan earthquake doublet at three representative Broadband Array of Taiwan for Seismology (BATS) stations. The origin time difference between the two events is only 70 s, with the first arrivals marked as T1 and T2, respectively. The original waveforms are displayed in the top panel, and the middle and lower panels show bandpass ( Hz) and high-pass (>1 Hz) filtered seismograms. It is clear that the long-period portion of the observed waveforms of the second event is significantly contaminated by the code wave of the first event, making it unsuitable for most finite-fault inversion methods. In contrast, the short-period seismograms show clear separation of the two events, resulting in good S/N ratios for SSA analysis. Time 0 corresponds to the origin time of the first event (2005 March 3, 19:06:51.7 UT).

9 964 C.-W. Khan et al. Figure 6. SSA analysis result for the first event of the 2005 March 3, Ilan earthquake doublet. (a) The epicentre and locations of stations used in the analysis are marked by an open star and solid triangles, respectively. (b) The brightness function (after normalization) as a function of time is shown to the left. To the right, snapshots at three different instances representing the beginning, peak and ending stages of the source process are shown. The centre of each image corresponds to the reported epicentre shown in Fig. 1. The brightest spot at each time instance is marked by a star. A composite image showing the relative locations of the brightest spots at the three time instances are shown to the right. The brightest spots basically stay at the same place during the first 2 s (stars 1 and 2). Once the rupture reaches its full strength, it starts propagating westward by at least 4 km (star 3). Given the two nodal planes shown in Fig. 1, the inferred westward rupture constrains the E W-striking plane to be the actual fault plane. (c) The predicted arrival times from the brightest spots at the three time instances. Notice that the arrivals of the third asperity are systematically earlier at stations due west, consistent with the inference of a westward rupture propagation. Solid and red lines are observed short-period waveforms and waveform envelopes, respectively, after normalization between 1 and 1. Azi: azimuth from the source to station as measured clockwise from the north.

10 Delineating fault planes of earthquake doublet 965 Figure 7. SSA analysis result for the second event of the 2005 March 3, Ilan earthquake doublet. Similar to the result of the first event, the brightest spots stay more or less unchanged during the beginning stage of the source process (stars 1 and 2). However, the rupture starts propagating westward once it reaches its full strength, as shown by the location of the brightest spot at a later time (star 3). The relative timing between the phases associated with asperities at different time instances (marked by different colours in c) shows a pattern similar to Fig. 6c, implying the same rupture propagation. Layout is the same as that offig.6. The centre of each image corresponds to the reported epicentre shown in Fig. 1. significant waveform peaks can be found at the arrival times predicted by the brightest spots during the initial and ending stages (e.g. Figs 6c and 7c). One possible explanation is the destructive interference between the source phase and local scattering waves in the vicinity of the recording sensor. Alternatively, the interference may be caused by non-stationary random noise related to local natural and/or cultural activities. Because SSA is a systematic forward-searching process that examines every possible combination of time-location pairs, its design is tuned to find a solution to satisfy as many stations as possible. One necessary condition to uniquely determine the orientation of a fault plane is to illuminate at least three asperities that do

11 966 C.-W. Khan et al. not form a straight line. For relatively large events that may have several asperities ruptured at the same time, this condition can be met if the spatial distribution of these asperities is resolvable from the observed waveforms. For smaller events, however, it is often possible to resolve only one asperity at any given time. Therefore, the trace of the brightest spot across the source volume becomes the most important constraint in recognizing the fault plane. If unfortunately all the brightest spots fall more or less on the same line, additional information about the source characteristics must be obtained to uniquely determine the fault plane s orientation. Under such a scenario, the easiest and most common practice is to compare the resolved trace of asperities to the two nodal planes of the earthquake s focal mechanism, and choose the most compatible one. The choice is unambiguous unless the trace coincides with the null axis. To conclude, we have demonstrated that SSA can be an effective tool in identifying the fault plane(s) of an earthquake doublet. Unlike conventional methods that determine the orientation of the fault plane by minimizing the misfit between synthetic and observed waveforms, SSA systematically searches the model space to illuminate the time and location of each asperity during the source process that generates a large phase on short-period seismograms. For a given time location pair, the brightness function, which is defined as the summation of the normalized amplitudes observed at each station at the predicted arrival times, is calculated to determine if a seismic source is likely to exist. A series of synthetic experiments have been performed and the results suggest that the brightest spots indeed corresponds to the location of the input asperities, but the exact shape of the SSA image may be distorted when the azumuthal coverage of stations is insufficient. We apply the proposed method to the 2005 Ilan earthquake doublet that occurred in northeast Taiwan with the two events being only 70 s apart. Available moment tensor solutions show strike-slip faulting with two nodal planes striking E W and N S, respectively. The trace of asperities for both events shows a similar pattern of rupture that propagates upward during the initial 2 s then westward for about 3 km. Such an image constrains the E W-striking plane to be the fault plane, which is also consistent with the distribution of aftershocks that occurred within 24 h of the Ilan doublet. ACKNOWLEDGMENTS Constructive comments by Ralph Currie (internal), the Associate Editor and two anonymous reviewers (external) are greatly appreciated. This paper is finished during a 6-month visit to the Pacific Geoscience Centre, Geological Survey of Canada (GSC) by one of the authors (C.-W. Kan). The logistic support given by GSC staff during his visit is greatly appreciated. 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