GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L14306, doi:10.1029/2011GL047864, 2011

The 25 October 2010 : Slip in a slow patch Susan L. Bilek,1 E. Robert Engdahl,2 Heather R. DeShon,3 and Maya El Hariri1 Received 20 April 2011; revised 13 June 2011; accepted 15 June 2011; published 28 July 2011.

[1] Various models for the generation of tsunami and shallow afterslip [e.g., Hsu et al., 2006; earthquakes have been proposed, including shallow Konca et al., 2008] (Figure 1). Approximately 700 km north, earthquake slip through low strength materials. Because another may have occurred along these physical conditions would likely affect other Island in 1907 [Kanamori et al., 2010]. earthquakes in the same rupture zone, source properties of [3] Given that models link shallow slip in weak near‐trench other events may provide a guide to locations of tsunami materials to tsunami earthquake occurrence, an important earthquakes. The 25 October 2010 Mw = 7.8 Mentawai question is whether these fault conditions also impact the tsunami earthquake and surrounding events provide a test rupture of other events in the same area. Our efforts here of this hypothesis. We determine slip patterns for the address this question by first defining the rupture area and and relocate , with the majority source characteristics of the 2010 event as well as relocating occurring in the near trench region. The two largest aftershocks of the event. We then compare the rupture extent magnitude aftershocks occurred within the downdip end of to source parameters computed for other regional earthquakes the mainshock rupture area and have long moment‐ in order to assess the possibility of consistent slow behavior normalized rupture duration, likely related to fault zone along specific patches of the plate interface. conditions. Several older relocated earthquakes at the northern edge of the 2010 rupture area also have long 2. Dataset duration character, suggesting both spatial and temporal consistency in the conditions needed to produce slow [4] Our source analysis of the 2010 mainshock incorporates both broadband P and SH waves recorded at teleseismic seismic processes along this margin. Citation: Bilek, S. L., – E. R. Engdahl, H. R. DeShon, and M. El Hariri (2011), The 25 October distances (30 90°) and a large suite of long period vertical 2010 Sumatra tsunami earthquake: Slip in a slow patch, Geophys. component seismograms for the Rayleigh wave (R1) signal Res. Lett., 38, L14306, doi:10.1029/2011GL047864. used in the relative source time function deconvolution. We also determine source parameters for 74 moderate magni- tude events from 1990–2009 (Mw > 5.5, thrust mechanism 1. Introduction based on Global Centroid Moment Tensor (GCMT, www. [2] Tsunami earthquakes, events that produce larger tsu- globalcmt.org) solutions) using teleseismic P and SH waves. nami waves than expected given the earthquake size, have occurred in several zones around the world, 3. Methods including Nicaragua (1992), Java (1994 and 2006), and Peru 3.1. Source Parameters: Mainshock (1996) [e.g., Kanamori, 1972; Kanamori and Kikuchi, 1993; Newman and Okal, 1998; Polet and Kanamori, 2000; Bilek [5] Estimates of the rupture extent are initially developed ’ and Lay, 2002]. Other characteristics of these events include using a theoretical Green s function deconvolution [e.g., Lay deficiency in high frequency seismic radiation, very long et al., 2009] with 59 R1 surface wave records that are duration, and shallow slip along the plate azimuthally well distributed around the source. Point source interface. Models for these unusual events tend to require synthetic seismograms are created using normal mode slip through low strength materials at the shallow end of the summation for each distance and azimuth range represented seismogenic zone [e.g., Kanamori and Kikuchi, 1993; Bilek by the data collected using PREM [Dziewonski and Anderson, and Lay, 1999; Satake and Tanioka, 1999; Polet and 1981] for the velocity model. These synthetic seismograms are Kanamori, 2000]. A recent tsunami earthquake occurred deconvolved from the observed seismograms to remove along the Mentawai Islands offshore the island of Sumatra theoretical path effects, leaving a relative source time function (25 October 2010, 14:42:22 UTC) [Lay et al., 2011; (STF) to describe the source effects at each station [e.g., Lay Newman et al., 2011], in an area adjacent to recent great et al., 2009] (Figure 2a). We pick the onset and end of each STFs main source pulses (dt) and using the definition for the directivity parameter [G, G = cos(station_azimuth − rupture_ azimuth)/phase_velocity], solve for the best fit rupture dura- tion, azimuth, and duration length (Figure 2a). 1New Mexico Institute of Mining and Technology, Socorro, [6] We also use broadband body waves (P and SH) to invert New Mexico, USA. for fault finiteness, obtaining estimates of the overall rupture 2 Department of Physics, University of Colorado at Boulder, Boulder, duration and slip distribution on the fault plane (M. Kikuchi Colorado, USA. ‐ 3CERI, University of Memphis, Memphis, Tennessee, USA. and H. Kanamori, Note on teleseismic body wave inver- sion program, 2006, http://www.eri.u‐tokyo.ac.jp/ETAL/ Copyright 2011 by the American Geophysical Union. KIKUCHI). We use a grid of 25 km along strike by 40 km in 0094‐8276/11/2011GL047864

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3.2. Source Parameters: Moderate Magnitude Events [7] For moderate magnitude earthquakes that occurred prior to the 2010 mainshock as well as 3 aftershocks, we also determine source time functions and depth estimates for each event by deconvolving a point source Green’s function from the P and SH waves, solving for the source time function at a range of depths between 3–65 km [e.g., Ruff and Miller, 1994; Bilek and Lay, 1999]. Synthetic seismo- grams generated for each depth are compared with the observed seismograms, with the optimal time function and depth producing the lowest misfit. In all cases these depths are compared to the relocated depths (section 3.3). Duration is measured from the final event time function as the time from onset to the first zero crossing, capturing the majority of the moment release of the event. These durations are then scaled by the cube root of seismic moment (Mo) to remove the effect of increasing duration with increasing seismic moment, and normalized by the duration of an Mw = 6.0 event [e.g., Bilek and Lay, 1999].

3.3. Earthquake Relocations [8] Teleseismically recorded earthquakes along the Sunda system have been relocated using the Engdahl, van der Hilst, and Buland (EHB) method [Engdahl et al., 1998]. This method uses reported International Seismic Centre (ISC) and National Earthquake Information Center (NEIC) reported phases and increases location accuracy using itera- tive relocation with dynamic phase identification, variable Figure 1. Setting of the 2010 October Mw = 7.8 tsunami phase weighting, ellipticity and station patch corrections, and earthquake (red star, NEIC location, red square and focal the ak135 velocity model. Only a small percentage of depth mechanism from GCMT, www.globalcmt.org) along the phases (pP, pwP, sP) are reported to ISC/NEIC, but the subduction zone between the Australian and Sunda plates. inclusion of these phases can significantly improve depth Plate boundary from Bird [2003]. Aftershocks (defined in determination. time relative to mainshock) of the 2010 event (diamonds, [9] For earthquakes prior to 2010, we have integrated NEIC locations between 25 October and 06 December) additional depth phases derived using automated methods show significant activity to the north and updip of the main- to better constrain hypocentral depths. This frequency‐ shock location. Other significant earthquakes in the region based technique identifies depth phase onset times on both also shown, including the 1907 tsunami earthquake (purple velocity and displacement waveforms by searching for star [Kanamori et al., 2010]) and rupture areas for earth- abrupt changes in the gradient of the power spectral den- quakes Mw > 7.5 (dashed and solid colored lines [Hsu et al., sity function (see Pesicek et al. [2010] for further details). 2006; Konca et al., 2008]). For the 2010 mainshock and aftershocks, depth phases were derived using the automated method but also verified by analyst (Figure 3). Analyst verification was done because depth phases generally have low frequency con- dip direction to define moment subevents on a fault plane tent as they propagate through near surface layers where defined by the GCMT geometry. Subevent moment pulses, there is high attenuation and may be obscured in the P‐ defined with 5 overlapping triangles of 10 s duration, are wave coda or noise, making auto‐identification difficult. removed from the P and SH waveforms at various timing and Additionally, not all ISC phase picks for the 2010 sequence fault grid positions, allowing for synthetic seismograms to be have been reported due to the 2‐year lag in compiling such a constructed for each of the observations. Moment rate func- large database. For this study, it is imperative that reported tion and moment distribution at each grid point are computed, depth phases for potentially shallow and complex earth- and we choose the solution that minimizes misfit between the quakes be correct. observed and synthetic seismograms (Figure 2b). Slip is [10] We find a common depth that satisfies both arrival‐ computed from the moment distribution, using a value of based and waveform modeling depth constraints for all 20 GPa for fault rigidity, appropriate for the shallow region earthquakes along this margin (Figure 4) (see auxiliary of this fault zone based on global and regional estimates material).1 Earthquakes with multiple local minima in the from earthquake parameters [Bilek and Lay, 1999; Bilek, waveform modeling misfit function are flagged, and the 2007]. Peak slip is 4.7 m in the area near the , arrival residual associated with the corresponding earth- similar to the 4.5 m determined by Lay et al. [2011], but less quake location re‐analyzed. In many cases, the arrival data than the 9.6 m estimated by Newman et al. [2011]. Moment rate functions, duration, and spatial distribution of slip are 1Auxiliary materials are available in the HTML. doi:10.1029/ similar between each study. 2011GL047864.

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Figure 2. Earthquake source modeling results. (a) (left) Data used to estimate duration and rupture extent based on 59 R1 STFs, (right) dt is the measured duration of each STF (indicated on the STFs, sorted by G), G is the directivity parameter. Azimuth is varied in the calculation and the best azimuth (308°) results from highest correlation coefficient. These results sug- gest rupture towards the NW, rupture length of ∼140 km, and a duration of ∼130 s, consistent with the body wave results. (b) Finite fault modeling results using 20 P and 12 SH waves (http://www.eri.u‐tokyo.ac.jp/ETAL/KIKUCHI). (top left) Best fit focal mechanism, (top right) moment rate function and (bottom) slip distribution on the fault plane are shown. Rupture dura- tion estimate of ∼130–140 s, depth of 22 km, and maximum slip of 4.7 m near the epicenter and rupture towards the NW (positive along‐strike direction) provide the best fit to the body wave data. (c) (top) Example data processing for moderate magnitude events using P and SH waves to determine (bottom left) moment rate functions and (bottom right) depth. For this example of an Mw = 5.9 , the best fit synthetic seismograms are computed for a depth of 25 km and a moment rate function with a 5 s primary moment pulse. This duration is scaled by the cubed root of the seismic moment, producing a moment‐normalized source duration (NSD) of 5.45 s. can help identify the correct local minima to interpret for the is consistent with the extent of the relocated aftershocks waveform model, or vice versa. updip of the mainshock and to the NW. The northern edge of the rupture area extended into a portion of the megathrust zone where long duration events occurred in 2005 and 2007 4. Results with normalized durations of 5.9 s and 6.9 s, respectively [11] The source parameters determined for the mainshock (Figure 4). These past events were deeper (30 km and 28 km) suggest that the 2010 event was indeed a tsunami earth- than the majority of slip observed in the 2010 mainshock. quake, with rupture duration of ∼130 s. The mainshock [12] The two largest aftershocks of the 2010 mainshock ruptured NW from the epicenter, extending for approxi- had high signal to noise ratios and are suitable for the body mately 110–150 km in length (Figure 2). This rupture length wave deconvolution analysis. These events had longer than

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Figure 3. Example waveforms and phase onset identifica- tions from an Mw 5.4 aftershock on 26 October, 2010 at 10:51:23.56 UTC. The event was revised from a fixed depth at 15.0 km to freely constrained depth at 13.2 km depth fol- lowing relocation with new depth phases. Theoretical phase arrivals for the initial EHB location are marked by vertical dashed lines. Revised phases following autopicking and analyst review are marked with solid black lines. The gray windows indicate the associated phase name (P, pP, and sP). Waveforms have been high‐pass filtered at 0.8 Hz. average NSD (5.5 s and 8.7 s) relative to the mean value for the entire margin (4.7 s). These events are deeper than the mainshock and the majority of the rest of the aftershocks, but lie in the depth range with the majority of the other past events in our dataset (Figure 4). The other relocated after- shocks are located in the very shallow portion of the seis- mogenic zone, shallower than much of the previously observed seismicity in this region.

5. Discussion and Conclusions

[13] The observed shallow slip and long duration source characteristics of the mainshock suggest that this event was indeed a tsunami earthquake. Our relocated aftershocks Figure 4. (top) Source parameters for the 2010 mainshock provide further evidence of very shallow, near trench rup- (star shows relocated epicenter; solid ellipse shows rupture ture. We also show that the rupture extends NW into an area extent estimated from body and surface wave analysis), relo- of the fault that exhibited other slow processes, specifically cated earthquakes from 1990–2009 (circles, colored by the long normalized rupture durations of previous events. NSD), and relocated aftershocks (diamonds, grey, or colored [14] In addition, we show that two of the largest after- by NSD where available). Events 1 and 2 are long duration shocks also had longer than average durations. Only one of events in 2005 (1) and 2007 (2). Events 1a and 2a are the long the older earthquakes occurred in the aftershock region, and duration aftershocks. Aftershocks defined by time relative to this event had a shorter than average duration (2.6 s). This mainshock. NSD of the mainshock is ∼18 s, higher than difference may indicate that the mainshock slip could shown in the color bar. Dashed box outlines area of cross sec- modify fault zone conditions at the downdip edge to cause tion. (bottom) Cross section across the 2010 epicentral region these long duration events. However, because we have only showing relocated aftershocks (grey diamonds) primarily in one older event in this region, we cannot rule out the pos- the updip portion of the seismogenic zone. A small number sibility that the fault conditions responsible existed previ- of aftershocks also occurred within the 20–30 km depth ously and were not significantly modified during mainshock region, two of which (1a and 1b, diamonds colored by slip. Unfortunately, the smaller magnitude aftershocks at the NSD) had long normalized rupture durations, similar to the updip edge had poor signal to noise ratio records and we are mainshock and older events (circles colored by NSD) at the unable to assess their source durations with the methods northern extent of the rupture zone. Slab position (solid line) used here. based on Slab 1.0 model [Hayes and Wald, 2009]. [15] Even with the limited dataset, our results suggest a spatial link between slow seismic processes over a range of

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Lett., 38, L05302, doi:10.1029/2010GL046498. another long duration event in 1993 suggests that these fault Pesicek, J. D., C. H. Thurber, H. Zhang, H. R. DeShon, E. R. Engdahl, and conditions may persist for decades. Additional analysis of S. Widiyantoro (2010), Teleseismic double‐difference relocation of events in other tsunami earthquake regions can be used to earthquakes along the Sumatra‐Andaman subduction zone using a 3‐D model, J. Geophys. Res., 115, B10303, doi:10.1029/2010JB007443. examine these patches in other areas, but in some cases, the Polet, J., and H. Kanamori (2000), Shallow subduction zone earthquakes earthquake catalog might not be sufficient to see this effect. and their tsunamigenic potential, Geophys. J. Int., 142, 684–702, The Sumatra margin is an area that has experienced many doi:10.1046/j.1365-246x.2000.00205.x. earthquakes in the last decade, allowing us to define these Ruff, L. J., and A. D. Miller (1994), Rupture process of large earthquakes in the northern Mexico subduction zone, Pure Appl. Geophys., 142, patches of long duration events as areas that may also pro- 101–172, doi:10.1007/BF00875970. duce tsunami earthquakes. Satake, K., and Y. Tanioka (1999), Sources of tsunami and tsunamigenic earthquakes in subduction zones, Pure Appl. Geophys., 154,467–483, doi:10.1007/s000240050240. [19] Acknowledgments. We gratefully acknowledge NSF funding for this project, NSF‐OCE 0840908 (SLB) 0841040 (ERE) and 0841022 S. L. Bilek and M. El Hariri, New Mexico Institute of Mining and (HRD). All waveform data was obtained from the IRIS Data Management Technology, 801 Leroy Pl. Socorro, NM 87801, USA. ([email protected]) Center. H. R. DeShon, CERI, University of Memphis, 3890 Central Ave., [20] The Editor thanks Richard Briggs and an anonymous reviewer for Memphis, TN 38152, USA. their assistance in evaluating this paper. E. R. Engdahl, Department of Physics, University of Colorado at Boulder, Campus Box 390, Boulder, CO 80309, USA.

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