A search for seismic radiation from late slip for the December 26, 2004 Sumatra-Andaman (M w = 9.15) earthquake

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1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L18305, doi: /2006gl027286, 2006 A search for seismic radiation from late slip for the December 26, 2004 Sumatra-Andaman (M w = 9.15) earthquake Aaron A. Velasco, 1 Charles J. Ammon, 2 and Thorne Lay 3 Received 19 June 2006; revised 27 July 2006; accepted 11 August 2006; published 20 September [1] The great 2004 Sumatra-Andaman (M w = 9.15) earthquake ruptured a 1300-km-long segment of the Sumatra-Andaman Islands subduction zone in about nine minutes. The possibility of continued fault slip after the primary rupture has been raised by tsunami excitation models and by discrepancies between seismic slip models and geodetic observations. We examine the global seismic wavefield to identify any late seismic radiation that occurred during the first hour after the main rupture using stacking of deconvolutions and cross correlations of complete ground motion observations and point-source responses (Green s functions). We find no evidence for delayed seismic radiation larger than M w = 7.5. Any major slip within an hour after the main sliding with mechanism similar to the main shock involved deformation so slow that it radiated no detectable seismic waves in the body wave or surface wave passband for periods less than 500 s. Citation: Velasco, A. A., C. J. Ammon, and T. Lay (2006), A search for seismic radiation from late slip for the December 26, 2004 Sumatra-Andaman (M w = 9.15) earthquake, Geophys. Res. Lett., 33, L18305, doi: /2006gl Introduction [2] The 26 December 2004 Sumatra-Andaman earthquake (M w = 9.15), the largest earthquake to occur in the last four decades, ruptured an approximately 1300-km-long segment of the interplate thrust fault along northwestern Sumatra, the Nicobar Islands, and the Andaman Islands [e.g., Lay et al., 2005]. The rupture duration estimated from seismic radiation is about 8 to 9 minutes [e.g., Ni et al., 2005; Ammon et al., 2005; Park et al., 2005a; Tsai et al., 2005] with an average rupture velocity of about 2.4 km/s. All slip models for the event inferred from seismic body and surface waves exhibit a significant decrease in coseismic slip northward along the rupture area, with the largest slip concentrated in the south, offshore of Banda Aceh, Sumatra. Hydroacoustic observations indicate that the rupture velocity was somewhat lower in the north (1.5 to 2.1 km/s) than in the south (2.4 to 2.8 km/s) [e.g., de Groot-Hedlin, 2005; Guilbert et al., 2005]. Slip variation during the unilateral rupture can account for directivity of seismic waves [Ammon et al., 2005], but the decrease in slip as the rupture 1 Department of Geological Sciences, University of Texas, El Paso, Texas, USA. 2 Department of Geosciences, Pennsylvania State University, State College, Pennsylvania, USA. 3 Earth Sciences Department, University of California, Santa Cruz, California, USA. progressed complicates determination of the slip characteristics in the northern region. [3] Several lines of evidence suggest that significant deformation occurred within the first hour after the primary rupture. Modeling of tsunami signals from satellite altimetry recordings suggests a 3500 s long component of slip in the northern half of the rupture area [Lay et al., 2005] or the occurrence of a large aftershock (M w = 8.4) 37 minutes after the mainshock [Song et al., 2005]. Geodetic and field data initially suggested more slip in the northern segment of the rupture than indicated by the seismic models [e.g., Bilham, 2005; Banerjee et al., 2005], although the aseismic component now appears to be less than initially thought [Vigny et al., 2005; Subarya et al., 2006]. While much of the afterslip required to account for the total geodetic slip appears to have accrued in the 1.5 months following the rupture [Subarya et al., 2006], the coseismic slip modeling has sufficient uncertainty that significant slip within an hour of the mainshock could have occurred. The timing of tidegauge records in the Andaman Islands suggests that about 7 m of slow slip occurred commencing 30 minutes after the initial rupture passed by [Bilham et al., 2005]. Given the various suggestions of significant slip within an hour of the mainshock, we analyze global long-period recordings using an event detector to assess whether any unaccounted for seismic radiation is present within the complex signals generated by the main slip event. 2. Long Period Seismograms [4] A search for seismic radiation from any late slip event for the Sumatra-Andaman earthquake must be performed in the presence of ground motions generated by the primary rupture. The huge earthquake excited hours of substantial continuous global ground motions (see auxiliary material 1 Figure S1). Very little, if any, quiet interval exists in most long-period recordings in which to directly isolate coherent signals excited by any late slow slip event. To detect any late seismic excitation of long-period signals, the dispersive effects of surface wave motions from the main event must be minimized, concentrating the corresponding energy into an effective source time-function for the main radiation, thereby isolating any late signals. [5] If any late radiation occurred it must involve predominantly low frequency excitation, less than about 0.01 Hz, given that there is no report of a large aftershock detected by standard high frequency radiation (0.2 1 Hz) prior to a magnitude 7.5 aftershock about 3.3 hours after the mainshock. We have confirmed this by inspecting high-pass Copyright 2006 by the American Geophysical Union /06/2006GL027286$ Auxiliary materials are available in the HTML. doi: / 2006GL L of5

2 event. We rely on the predictable coherence of any true long-period signals expected for an actual source excitation to discriminate noise from signal. [7] Long-period ground displacements for 50 BDSN and TriNet stations spanning a distance range of and back azimuth range of are shown in Figure 1 for several passbands. The unfiltered signals (Figure 1a) are coherent. After applying a 500 s acausal lowpass filter (Figure 1b), some scatter in trace amplitudes and timing becomes noticeable. For a 1000 s acausal lowpass filter (Figure 1c), 14 stations have significant amplitude and phase instabilities, but the overall inter-station stability is impressive, as proves true for many GSN stations [see Park et al., 2005a]. Figure 1 illustrates the nearly continuous long-period motions within which any oscillations generated by late slip are intermingled. Figure 1. Overlain ground displacement seismograms for 50 TriNet (CI) stations with distance range of and back azimuth range of with (a) no filter, (b) low pass at 500 s, and (c) low pass at 1000 s. The coherency for the unfiltered seismograms is striking. There is minor degradation of coherency at longer periods. filtered seismograms from numerous stations. We also detect no visible coherent energy in the broadband signals for frequencies between 0.01 and 0.2 Hz. We assume that any large slow slip event of interest will have occurred on the interplate thrust plane, with a focal mechanism similar to that for the main radiation. Effectively, we seek an echo of the mainshock signals, systematically delayed at all stations, but having weak high-frequency signals that allow it to have gone undetected as a normal aftershock. [6] We collected about 180 vertical-component broadband seismograms spanning several hours after the mainshock origin time from the Federation of Digital Seismographic Networks (FDSN) as well as regional networks such as the Berkeley Digital Seismic Network (BDSN) and TriNet. We analyzed both the original seismograms and instrument-corrected ground displacements. We stabilized the instrument deconvolution using a frequency domain cosine taper with long-period corners corresponding to periods of 1500 s and 2000 s. The reliability of the very long-period instrument response for global digital stations is important to assess. The amplitude response for all broadband instruments falls off rapidly for periods longer than 300 s, and we noted numerous signals with spurious longperiod transients that are not accounted for by standard source and propagation models for the Sumatra-Andaman 3. Long Period Source Time Functions [8] To detect any echoes of the source radiation contained in the long-period seismic signals from the Sumatra- Andaman event, we employed deconvolution and crosscorrelation approaches. Both methods incorporate predictions of the response to a step dislocation for a shallow dipping underthrusting fault geometry. Our deconvolution approach isolates the source processes by deconvolving a point-source theoretical Green s function (TGF) from the observed seismograms. This provides, for each station, an effective source time function corresponding to the signals in the time window included in the deconvolution. Since our signals are dominated by long-period Rayleigh wave arrivals that arrive on both the short- and long-arcs (R1, R2, R3, and R4), our apparent source time functions are azimuthally averaged effective source time functions embedded within R1, R2, R3, and R4 waveforms. [9] To compute the TGFs, we sum normal modes computed for PREM [Dziewonski and Anderson, 1981] at periods longer than 30 s for a point source double-couple. We considered several point source locations and geometries, including a fault geometry with strike: 329, dip: 11 and rake: 110 (similar to the CMT major double-couple, with a 3 steeper dip), located at the USGS hypocentral location with a depth of 15 km. If late slip occurred in the northern region of the rupture, we might expect that using TGFs based on mainshock subevents in the north might be more appropriate for any late radiation. So we also considered point sources with the locations and faulting geometries of the 5 subevents in the multiple-source Centroid-Moment Tensor solution of Tsai et al. [2005]. For very long period (>100 s) signals, the precise source location is of secondary importance. Using Green s functions computed for a one-dimensional Earth model is a limitation. Errors in the computed propagation effects will contaminate the source time function estimates, particularly for periods shorter than 100 s or so, however, this has been shown not to be a major problem for deconvolution analysis of the primary radiation [e.g., Ammon et al., 2005]. We focus on the lower frequency components in our deconvolutions, increasing our confidence that the first-order propagation corrections are sufficient. [10] Rather than attempting to window individual Rayleigh wave arrivals, we took an s long window 2of5

3 as for raw observations with instrument responses convolved with the Green s functions. [11] Figure 2 shows deconvolutions for KIP, a station at an azimuth perpendicular to the fault, revealing the source radiation time series estimated for the point-source model and the five subevent mechanisms of Tsai et al. [2005]. We find that the source radiation estimates are similar for most of the subevent mechanisms, but the most northerly mechanism, with the most oblique slip, produces a variable signal, while the somewhat steeper dip of the average pointsource solution gives a somewhat lower peak amplitude (and lower seismic moment) than for the subevent geometries. The spectral division deconvolutions have a trough on which the 500 s pulse of the main rupture radiation rides. The finite bandwidth of the data are responsible for this effect, which is most pronounced for the deconvolutions of displacements, as the bandwidth was already delimited by the filter applied in deconvolving the instrument response. The iterative deconvolution approach with a positivity constraint provides one-sided source radiation time series that are stabilized with respect to the long-period trough, but which can have artifacts due to the positivity constraint. We prefer the results for deconvolution of the raw data by synthetics with instruments applied, as only one deconvolution is involved, and there is less amplification of very long-period noise. We will use our average point-source Green s functions, as there is no indication that small changes in the geometry will be resolvable. Figure 2. Deconvolutions for station KIP, located at an azimuth perpendicular to the fault, yielding source time function (STF) estimates for our slight modification of the Harvard point-source focal mechanism (S average), and the five subevent focal mechanisms of Tsai et al. [2005] (S1, S2, S3, S4, S5). Water-level deconvolutions of the instrument-removed ground displacement are shown in the top panel. Spectral division (zero water-level) and iterative deconvolution of the raw seismograms by Green s functions with instrument responses are shown in the middle and lower panels, respectively. The differences in deconvolutions are only significant for the fifth source subevent mechanism, which rotates in strike and rake significantly, and clearly does not give a good representation of the overall faulting geometry. starting 1000 s before the origin time. Using a long time window improves stability of the long period components, but averages the directivity effects that have been previously analyzed for individual isolated Rayleigh wave arrivals [Ammon et al., 2005]. We utilized two deconvolution methods: direct spectral division with or without a waterlevel and a time-domain iterative approach [see Ligorria and Ammon, 1999]. The TGFs have negligible long-period noise, a critical attribute essential to stable deconvolutions (especially for the spectral division). In both cases, the results are convolved with a low-pass Gaussian filter to reduce short-periods (<50 s), for which the TGF is inappropriate. One advantage of the iterative deconvolution is that we can impose a positivity constraint. We perform deconvolutions for data that have been deconvolved by their instrument response to obtain ground displacements as well 4. Source Time Function Stacking [12] Individual station deconvolutions are difficult to interpret because they are subject to Green s functions and bandwidth limitations, and possible instrument response errors. A robust detector of later radiation requires stacking of many deconvolutions to allow coherent features to emerge from the noise. Our stacking approach is similar to the slow-earthquake detector applied globally by Ekström et al. [2003], but we have tuned our detector for late slip with a specific faulting geometry. [13] After removing a number of stations that have spurious long-period recordings (either clipped or appearing non-linear after the passage of R1), we gathered approximately 180 stable mainshock Rayleigh wave trains with a good azimuthal distribution around the source. For the iterative deconvolutions, we then use percent fit of the seismogram (90% or higher) as a criterion for inclusion in the stacking, while for the water-level deconvolutions, we use visual inspection of the source time function stability. For the average focal mechanism solution we are left with 60 stackable traces for the iterative deconvolutions and 74 for the water-level deconvolution using a Gaussian filter of width factor of 0.02 Hz. The Gaussian filter, G(!) =e!2 /(4a 2), where! is frequency and a is the width, serves as a simple, zero phase, low-pass filter. We also stack more-heavily low-pass filtered time functions using a Gaussian filter width (a) of Hz. For this filter width, we have 16 stackable traces for the iterative deconvolutions and 24 for the spectral division. [14] Figure 3 displays the stacks; all sets of deconvolutions show a relatively simple pulse that corresponds to the primary s long rupture. For the stacks with 3of5

4 characterization of the time function. Auxiliary material Figure S2 shows stacked cross and auto correlation results using displacement seismograms, with low pass filters at 100 s and 500 s prior to stacking. These stacks are noisier than the deconvolution stacks, and also do not show any evidence of long period energy release in the first hour after the mainshock. Figure 3. Stacked source time functions (heavy lines) and standard deviations (light lines) for iterative and spectral division deconvolutions of raw seismograms by synthetics with instrument response included. (top plot) Stack of iterative deconvolution using stations (n = 60) having 90% or better fit to the seismogram, with Gaussian width filter parameter (a), a = 0.02 Hz. (second plot) Stack of 74 spectral divisions with a = 0.02 Hz. (third plot) Stack of iterative deconvolution using n = 16 stations having 90% or better fit to the seismograms with a = Hz. (fourth plot) Stack of 24 spectral divisions with a = Hz. 5. Discussion and Conclusion [16] To confirm our lack of detection of radiation from any late slip for this event, we compare observed and modesum (>30 s) predicted seismograms for station DGAR (D = 24.5 ), which is one of the closest non-clipped stations (Figure 4). We have correlated each trace with the corresponding windowed R1 seismogram to suppress dispersion effects. Little energy is seen between the R1 and R2 arrivals, other than the predictable major-arc overtones (O2), confirming our global stacking results. The small feature associated with the 7.5 aftershock indicates that no event that large occurred in the first hour after the main shock. Furthermore, tests with a M w = 7.5 secondary source with 500 s duration added to synthetic seismograms and similarly deconvolved shows that we should be able to detect corresponding long-period radiation if it were present, and we do not. Of course, this is a conservative upper bound on seismic moment for a smaller event with duration similar to the mainshock; if the duration is much longer, the excitation of waves in our passband will decrease and the slip could go undetected. There is no indication of any anomalous excitation in the lowest frequency normal modes [e.g., Park et al., 2005b], so durations greater than 1 hour might need to be invoked to avoid exciting detectable waves. [17] If there was large afterslip on the main thrust fault in the first hour after the 2004 event, it did not radiate in the body wave and surface wave seismic frequency range (<500 s), and must have a substantially longer source time a = 0.02 Hz, the iterative deconvolution and the somewhat noisier spectral division deconvolution show no sign of late radiation with periods around 250 s. Results for a = Hz show a possible small pulse after 2000 s in the iterative deconvolution, but the water-level stack, although noisier, shows no evidence of an arrival at this time. Careful analysis suggests that the positivity constraint causes signals with fluctuating polarity to appear in the iterative deconvolution at 2000 s. Overall, we find no substantial evidence for any seismic signals generated by afterslip in the first hour after the main radiation. [15] Another approach to characterizing long period source time functions is to perform cross correlations between the data and the synthetics, or auto correlations of the data. Since the synthetics contain the propagation and focal mechanism information, cross correlation provides a Figure 4. Data and synthetic seismograms from station DGAR (D = 24.5 ), cross-correlated with their corresponding R1 arrivals. The great-circle Rayleigh waves are prominent. O2 corresponds to Rayleigh wave overtone energy that has traveled along the major arc. A small arrival on the data is observed at the time of the R1 arrival from the M w 7.5 aftershock 3.3 hours after the mainshock. Note the quiet interval from 15 to 75 minutes after the origin in both the data and synthetics. 4of5

5 function. Secondary sources could have occurred that our processing might not resolve due to differences in the Green s function. For example, slumping in the sedimentary wedge could be a tsunamigenic process, but may not be well-represented by a double-couple source. But any such excitation will still produce dispersed surface waves, and deconvolution mainly collapses the signals back to the effective source pulse. Thus, the DGAR record provides rather tight upper bounds on such radiation. While some energy at very long periods (>500 s) appears between 2000 and 3000 s after the mainshock, it does not appear to have involved radiation consistent with underthrusting. [18] Acknowledgments. We thank the developers of SAC, and the many seismic network operators who have provide open-data-access for seismic research and monitoring. We thank the two reviewers for helpful comments. The facilities of the IRIS Data Management System were used to access the data required in this study. Supported by NSF grant EAR (T. L.) and USGS Award Number 05HQGR0174 (C. J. A.). References Ammon, C. J., et al. (2005), Rupture process of the 2004 Sumatra- Andaman earthquake, Science, 308, Banerjee, F., F. Pollitz, and R. Burgmann (2005), The size and duration of the Sumatra-Andaman earthquake from far-field static offsets, Science, 308, Bilham, R. (2005), A flying start, then a slow slip, Science, 308, Bilham, R., R. Engdahl, N. Feldl, and S. P. Satyabala (2005), Partial and complete rupture of the Indo-Andaman plate boundary , Seismol. Res. Lett., 76, de Groot-Hedlin, C. D. (2005), Estimation of the rupture length and velocity of the Great Sumatra earthquake of Dec. 26, 2004 using hydroacoustic signals, Geophys. Res. Lett., 32, L11303, doi: / 2005GL Dziewonski, A. M., and D. L. Anderson (1981), Preliminary reference Earth model, Phys. Earth Planet. Inter., 25, Ekström, G., M. Nettles, and G. A. Abers (2003), Glacial earthquakes, Science, 302, Guilbert, J., J. Vergoz, E. Schisselé, A. Roueff, and Y. Cansi (2005), Use of hydroacoustic and seismic arrays to observe rupture propagation and source extent of the M w = 9.0 Sumatra earthquake, Geophys. Res. Lett., 32, L15310, doi: /2005gl Lay, T., et al. (2005), The great Sumatra-Andaman earthquake of 26 December 2004, Science, 308, Ligorria, J. P., and C. J. Ammon (1999), Iterative deconvolution and receiver function estimation, Bull. Seismol. Soc. Am., 89, Ni, S., H. Kanamori, and D. Helmberger (2005), Energy radiation from the Sumatra earthquake, Nature, 434, 582. Park, J., et al. (2005a), Performance review of the Global Seismographic Network for the Sumatra-Andaman megathrust earthquake, Seismol. Res. Lett., 76, Park, J., et al. (2005b), Earth s free oscillations excited by the 26 December 2004 Sumatra-Andaman earthquake, Science, 308, Song, Y. T., et al. (2005), The 26 December 2004 tsunami source estimated from satellite radar altimetry and seismic waves, Geophys. Res. Lett., 32, L20601, doi: /2005gl Subarya, C., et al. (2006), Plate-boundary deformation associated with the great Sumatra-Andaman earthquake, Nature, 440, Tsai, V. C., M. Nettles, G. Ekström, and A. M. Dziewonski (2005), Multiple CMT source analysis of the 2004 Sumatra earthquake, Geophys. Res. Lett., 32, L17304, doi: /2005gl Vigny, C., et al. (2005), Insight into the 2004 Sumatra-Andaman earthquake from GPS measurements in southeast Asia, Nature, 436, C. J. Ammon, Department of Geosciences, Pennsylvania State University, 440 Deike Building, State College, PA 16870, USA. T. Lay, Earth Sciences Department, University of California, Santa Cruz, CA 95064, USA. A. A. Velasco, Department of Geological Sciences, University of Texas, El Paso, TX , USA. (velasco@geo.utep.edu) 5of5