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Keywords:

  • tsunami earthquake;
  • finite-fault modeling;
  • real-time warning;
  • tsunami modeling

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[1] The moment magnitude 7.8 earthquake that struck offshore the Mentawai islands in western Indonesia on 25 October 2010 created a locally large tsunami that caused more than 400 human causalities. We identify this earthquake as a rare slow-source tsunami earthquake based on: 1) disproportionately large tsunami waves; 2) excessive rupture duration near 125 s; 3) predominantly shallow, near-trench slip determined through finite-fault modeling; and 4) deficiencies in energy-to-moment and energy-to-duration-cubed ratios, the latter in near-real time. We detail the real-time solutions that identified the slow-nature of this event, and evaluate how regional reductions in crustal rigidity along the shallow trench as determined by reduced rupture velocity contributed to increased slip, causing the 5–9 m local tsunami runup and observed transoceanic wave heights observed 1600 km to the southeast.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[2] While any earthquake that creates a tsunami can be classified as “tsunamigenic”, the term “tsunami earthquake”, hereafter TsE, is reserved for a special class of events that generate tsunamis much larger than expected for their magnitude [Kanamori, 1972]. These earthquakes are relatively rare, the classification having been attributed to less than ten events in the past century or so. TsE are normally identified to have anomalously slow rupture velocities, and are thus inefficient at radiating seismic energy, often making such events only weakly felt by local populations. Growing evidence suggests that TsE rupture slowly because they occur in the shallowest segment of the subduction megathrust [Polet and Kanamori, 2000], which may have ∼1/10th the rigidity μ of the deeper thrust, causing a reduction in shear velocity VS and hence the rupture velocity VR, which is usually ∼0.8 VS [Bilek and Lay, 1999].

[3] On 25 October a moment magnitude MW 7.8 earthquake struck just west of the Mentawai Islands off the west coast of Sumatra (Figure 1), generating a surprisingly large local tsunami which caused more than 400 human causalities. The event ruptured immediately updip of and was possibly triggered by stress changes following the September 2007 MW 8.5 Sumatran earthquake [Stein, 1999]. This area may have last ruptured as part of the 1797 and 1833 MW 8.6–8.9 events, described by Natawidjaja et al. [2006] as having as much as 18 m of megathrust slip to explain the coseismic uplift of local microatolls by 3m. Further north, a segment that ruptured in 1861 was likely comparable in magnitude (MW ∼8.5) to the 2005 MW 8.6 Nias earthquake that ruptured the same approximate area [Newcomb and McCann, 1987; Briggs et al., 2006]. Available high-resolution bathymetry along the trench adjacent to the giant 2004 MW 9.15 Sumatran earthquake suggests that significant faulting in the region may be due to rupture through the prism toe during the 2004 and previous earthquakes [Henstock et al., 2006]. The large slip estimated in the shallow trench during the 1833 earthquake, and the considerable faulting near the trench toe further north support the hypothesis that the subduction zone off western Indonesia is capable of supporting shallow megathrust slip, the type seen in TsE events. This is supported by a recent study that suggests slow rupture of a magnitude 7.6 earthquake offshore Sumatra in 1907 (∼2°N) caused a large local tsunami [Kanamori et al., 2010].

image

Figure 1. Rupture area of the 2010 Mentawai, and previous historic and recent large earthquakes ([inset] study region highlighted by box). Events include the combined rupture of the 1797 and 1833 MW 8.6 to 8.9 earthquakes [Natawidjaja et al., 2006], the southern extent of the 1861 and 2005 MW ∼8.6 events [Newcomb and McCann, 1987; Briggs et al., 2006], and 2007 MW 8.5 earthquake [after Ji et al., 2002]. Also shown is the gCMT mechanism and location, and other earthquakes with magnitude >4 since 2000 colored by date and corresponding to histogram. The high-slip area shown in Figure 3 defines the approximate rupture area of the Mentawai event.

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2. Real-Time Detection

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[4] Using the set of programs called ‘RTerg’ (A. V. Newman and J. A. Convers, A rapid energy-duration discriminant for tsunami earthquakes, submitted to Geophysical Research Letters, 2010), we automatically determine earthquake energies and estimated rupture durations in near real-time at Georgia Tech for global earthquakes greater than magnitude 6.5, starting in January 2009 (Newman and Convers, submitted manuscript, 2010). This information is useful for rapidly characterizing strong shaking in large earthquakes and its tsunami potential, and is detailed in Text S1 of the auxiliary material.

[5] In the case of the Mentawai earthquake, because the first iterations used data from stations that did not yet record the termination of rupture, the event duration was underreported (Table 1). The first iteration found TR = 53 s and Me = 6.95, considerably smaller than the final reported MW = 7.8. By iteration two, 8.5 minutes after rupture initiation, TR increased to 96 s and Me to 7.17, a result that in retrospect could have identified the event as slow. By the fourth iteration, 16.5 minutes after the rupture began, RTerg stabilized to its near final solution with TR = 126 s and Me = 7.09. A final determination was made after an analyst reviewed the event, and corrected for the reported global Centroid Moment Tensor (gCMT) focal mechanism [Ekström et al., 2005], finding TR = 127 s and Me = 7.03 using 51 stations, comparable but smaller than the final result determined independently by the USGS (Me = 7.2) [Choy and Boatwright, 2007].

Table 1. Real-Time and Final Energy and Duration Determinations for 2010 Mentawai Eventa
IterationTR (s)Ehf (Me-hf) (×1014 J)E (Me) (×1014 J)Ehf/TR3 (×107 J/s3)NstatLatency (s)
  • a

    Shown are the high frequency Ehf and broadband estimated energies E, their ratio used as the tsunami earthquake discriminant, the number of stations used Nstat and the latency of the determination.

1531.3 (6.97)5.9 (6.95)8511393
2962.2 (7.12)13.0 (7.17)2418513
3941.0 (6.90)8.6 (7.06)1244693
41261.0 (6.91)9.6 (7.09)5.254993
51240.90 (6.87)7.6 (7.02)4.7511615
Final1270.91 (6.87)7.8 (7.03)4.551N/A

[6] While real-time assessments of TR, and E, are independently useful for assessing the size of a large earthquake, their combination yields a robust discriminant for TsE [Lomax et al., 2007, Newman and Convers, submitted manuscript, 2010]. Because TR3 scales with M0 for most earthquakes [Houston, 2001], the long duration of slow-source TsE stand out particularly well when compared to their deficient rupture energy. Newman and Convers (submitted manuscript, 2010) identified that real-time high-frequency solutions are optimal and implemented in RTerg a discriminant threshold for TsE to be Ehf/TR3 < 5 × 107 J/s3. Thus, after iteration 5, the event was automatically classified as a possible TsE, and notifications were sent to a distribution list including individuals from the USGS National Earthquake Information Center (NEIC) and Pacific Tsunami Warning Center (PTWC). The progression of the discriminant in real time is shown along with other post-processed and real time solutions in Figure 2c.

image

Figure 2. (a) Broadband seismic stations available for real time energy analysis (25°–80°; stations added in subsequent iterations are differentiated by shade). (b) The high-frequency energy growth identifies the approximate event duration TR while the total event energy E is determined using broadband energy at TR (iteration 4 shown). (c) The per-iteration (I-V) determination of E/TR3 are shown relative to other real-time solutions since 2009 (gray circles), solutions with known mechanisms (open circles), and other TsE events (dark circles). By iteration 4 (IV) the result stabilized and comparable to the final solution determined using the gCMT mechanism (5). (d) Like other TsE, E/M0 for this event is significantly reduced (Θ = −5.9).

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[7] Like other TsE, the 2010 Mentawai earthquake can be uniquely identified as a slow-rupturing TsE through a comparison of its energy to seismic moment M0 ratio. Newman and Okal [1998] initially identified that while most events have Θ = log10(E/M0) between −4.0 and −5.0, slow TsE have Θ ≤ −5.7. Using the final energy given the corrected gCMT mechanism, we find the Mentawai earthquake to have Θ = −5.9, clearly discriminating it as a slow-TsE (Figure 2d). Because RTerg does not determine focal mechanisms, this solution was not determined in real-time. However, Θ determinations are routine at the PTWC [Weinstein and Okal, 2005].

3. Finite-Fault Modeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[8] Using teleseismic waveforms recorded within the Global Seismic Network, we invert for the source rupture based on the finite fault algorithm of Ji et al. [2002], using a 1D velocity model regionally based on Crust2.0 [Bassin et al., 2000] and detailed in Text S1. However, the upper plate in the Mentawai region is reduced in P-wave velocity by 30% or more compared to crust landward of the trench and below the fault interface [Collings et al., 2010]. This velocity reduction may be interpreted in global subduction zone environments from teleseismically observed increased TR corresponding to reduced regional VR [Bilek and Lay, 1999]. Because tsunami excitation is controlled by the amplitude of upper plate slip and its translation into seafloor uplift, it is necessary to correct for the discrepancy between the teleseismically inverted slip and the true regional slip that may be subdued when traveling through the lower crust. To do so, we variably scale the slip using regional estimates of the shear velocity VS. To conserve energy that goes into work, M0 is considered constant, and hence the product of slip equation image and regional rigidity μ are constant assuming constant rupture area:

  • equation image

Hence, because VS2 is equated to μ divided by density, the scaled fault slip equation image is related to the original finite-fault determined slip equation image0 by the ratio of the squared reference shear velocity used in the inversion VS-ref and Vs. This can be estimated from VR, as:

  • equation image

assuming negligible density changes and VS ∼ 125% VR [e.g., Bilek and Lay, 1999]. The ratio of the squared velocities is the scale-factor χ. Because VR is spatially variable in the inversion, χ varies across the fault between 3.0 and 8.2 over the sub-fault patches, with a slip-weighted mean = 5.6 ± 1.0. The final scaled model (Figure 3) has a shape similar to the original (Figure S3), but with ∼5 times the slip, equating to a new maximum slip of 9.6 m, and yielding a large area of 2+ m uplift (Figure 3b), contributing significantly to the event's tsunami potential. Because many assumptions are necessary to scale slip in this manner, including the differential excitation of surface and body waves, such method should be considered a first-order approximation.

image

Figure 3. (a) The preferred interface slip model strikes N35°W, and extends from the seafloor to 33.9 km depth at a dip of 11.6°, has primarily thrust motion with large slip focused updip and primarily NE of the hypocenter (star). The spatially distributed slip form the scaled finite fault solution is used as input to predict (b) the surface uplift, and (c) the earthquake source-time function.

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4. Tsunami Modeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[9] To model the tsunami waves observed in the eastern Indian Ocean we used the Method of Splitting Tsunamis (MOST) model, which is a suite of integrated numerical codes capable of simulating tsunami generation, transoceanic propagation, and its subsequent inundation in the coastal area as described by Titov and González [1997]. Because detailed local bathymetry is unavailable, these models do not necessarily yield highly precise inundation scenarios, but are useful for evaluating the average runup, and the overall shape and timing of the open-ocean tsunami waves. Details of the tsunami model are included in Text S1.

[10] For each source model tested, the spatially distributed slip from the original or scaled finite fault solution is used to predict the surface uplift following the dislocation model of Okada [1992]. While the finite-fault method inherently solves for the timing of slip along individual patches, the MOST tsunami model requires the seafloor displacement as an instantaneous initial condition, and hence the roughly 125 s rupture duration causes <10% compression of predicted tsunami waves that have a dominant wave period >30 min (Figure 4d).

image

Figure 4. Comparison of tsunami data with model predictions using the seafloor displacement in Figure 3. (a, b) The distribution of predicted (black bars) runup is projected along the E and W sides of the islands (separated by dashed line). (c) An ocean-bottom pressure sensor ∼1600 km to the SE (d) observed open-ocean tsunami waves (black line), with timing and period well predicted by the model (red line).

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[11] The preferred scaled source model (Figure 3) leads to promising predicted tsunami results (Figure 4) when compared to preliminary post-tsunami survey results (K. Satake, personal communication, 2010), and deep-ocean observations. The ocean wave height time series recorded by an ocean-bottom pressure sensor ∼1,600 km southeast of the earthquake source agrees well with the observed arrival time, wave period, and approximate amplitude (Figures 4c and 4d). While the scaled model overestimates the first wave by about 40%, it more closely represents the observed tsunami than the original unscaled model that under-predicts the observed wave by nearly a factor of 5. While some of the inaccuracy may be due to oceanic bathymetry and detiding effects, it is more likely that the scaled model may still overpredict the maximum slip in the updip region. This likely occurs because the regionally derived variable rigidity along the fault was not used to compute synthetic seismograms, but was inferred from estimated rupture velocities and used to scale slip accordingly. Given the poorly known, three-dimensional velocity structure of the near-source region, the scaling used here is adequate within the framework of uncertainties arising from one-dimensional models commonly used in source inversions. The model predicts a runup distribution along the coastline of the islands, with maximum 3–12 m runup along the western coast and mostly meter-level runup on the eastern coasts (Figure 4a). The western side of the southern Island, Pulau Pagai-seletan, has the highest runup, with sustained values greater than 5–12 m (Figure 4a), comparing well to the range of 5–9 m runup found along the western shore by the Japanese survey team, but overestimates the maximum observed (K. Satake, personal communication, 2010). As previously mentioned, the lack of local high-resolution bathymetry makes more careful direct comparisons unwarranted. An alternative model developed from a lower-angle finite fault solution (dip = 8° rather than 11.6°) is shown in Figures S4 and S5. This model performs similarly in most aspects, but creates both more variable tsunami runup along the southern island that are not described in initial reports (K. Satake, personal communication, 2010), and more variable coastal subsidence patterns.

5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[12] Because TsE are observed in the shallow near-trench region of the subduction interface [Polet and Kanamori, 2000], the relatively large distance to the coast, and slowing effect of shallowing ocean on tsunami waves frequently allows for considerable time between the earthquake rupture and tsunami inundation. In the case of the 2006 Java event, the initial positive tsunami waves reached the shore ∼40 minutes after the earthquake, and a rapid TsE warning could have been valuable [Fritz et al., 2007]. While, this was not the case for the very proximal Mentawai islands that were likely inundated within 15 minutes of rupture (based on our preferred tsunami model), RTerg detected the Ehf/TR3 discriminant could be useful for most coastal environments. Care should be used in determining an appropriate cut-off value for this discriminant, since an upward shift from the current value of 5 to a more sensitive 25 (×107) J/s3 would have detected the event as a slow-source TsE as early as 9 minutes after rupture initiation, but with an increased expectation of false-positives (on ∼5–10% of events with M ≥ 6.5).

6. Evidence for a Slow-Source Tsunami Earthquake

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

6.1. Tsunami Size Versus Magnitude

[13] Large regional tsunamis are normally identified for earthquakes MW > 8, however the 2010 Mentawai MW 7.8 earthquake is reported to have up to 9 m of runup, and an observable cm-level open ocean tsunami 1600 km away. Kanamori's [1972] definition of TsE related the tsunami to higher-frequency body mb and surface wave MS magnitudes that are reduced due to slow rupture. This is comparable to the determination of Me = 7.03, and Me-hf = 6.87 found in this study, agreeing with mb = 6.5 and MS = 7.3 determined by the NEIC; values far too small to otherwise expect an earthquake generated tsunami.

6.2. Long Rupture Duration

[14] Two lines of evidence clearly denote this events' excessive TR. We identified TR = 127 s (124 in near-real time) using the termination of continued high-frequency energy growth (Figure 2b). Secondly, as a part of the finite-fault determination, the event source-time function was determined to be nearly identical (∼125 s). Such a long duration rupture would scale to an MW 8.5 earthquake following the relation found by Houston [2001].

6.3. Shallow, Near-Trench Rupture

[15] The locations of early aftershocks, the W-phase and gCMT mechanisms, and the area of dominant slip in the finite-fault models, all identify that the event ruptured updip of the point of nucleation (hypocenter) and very near the trench (Figures 1 and 3). Such near-trench rupture is noted as an endemic feature of TsE [Polet and Kanamori, 2000], which is likely to control its enhanced tsunami excitation due to increased slip near the free surface [Satake and Tanioka, 1999], regardless of the rupture speed (A. V. Newman et al., The energetic 2010 MW 7.1 Solomon Islands Tsunami earthquake, submitted to Geophysical Journal International, 2010).

6.4. Deficiency in Radiated Seismic Energy

[16] Using the established E/M0 [Newman and Okal, 1998], and newly tested Ehf/TR3 discriminants [Lomax et al., 2007, Newman and Convers, submitted manuscript, 2010], we identify this event as a slow rupturing TsE. This event is more deficient than 99.5% of all E/M0 recorded events since 2000 (J. A. Convers and A. V. Newman, Global evaluation of earthquake energy to moment ratio from 1997 through mid-2010: With improvement for real-time energy estimation, submitted to Journal of Geophysical Research, 2010), and more deficient in Ehf/TR3 than any other event with Me ≥ 6.5 tested since the beginning of 2008, and similar to the four other slow-source TsE occurred since 1992 (Figure 2d).

7. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[17] The MW 7.8 Mentawai earthquake is a classic example of a rare slow-source tsunami earthquake, exhibiting deficient radiated energy (Me 7.0) and extended rupture duration (125 s), identifying the characteristically reduced rupture velocity (∼1.25–1.5 km/s). Using the spatially determined rupture velocity, we scaled the finite fault derived displacement field to accurately predict the seafloor deformation and observed tsunami excitation. This correction well explains the magnitude and distribution of large 5–9 m local tsunami runup and the timing, wave period and approximate wave heights of the detected transoceanic wave observed 1600 km to the southeast.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

[18] This paper was made possible through the availability of real-time GSN seismic data managed by the USGS-NEIC. We value the constructive reviews by G. Choy, S. Hammond, E. Bernard, S. Weinstein and an anonymous reviewer. USGS-NEHRP grant 08HQGR0028 supported the development of real-time energy calculations.

[19] M. E. Wysession thanks the two anonymous reviewers.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Real-Time Detection
  5. 3. Finite-Fault Modeling
  6. 4. Tsunami Modeling
  7. 5. Discussion
  8. 6. Evidence for a Slow-Source Tsunami Earthquake
  9. 7. Conclusions
  10. Acknowledgments
  11. References
  12. Supporting Information

Auxiliary material for this article contains a text file and five figures.

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FilenameFormatSizeDescription
grl27847-sup-0001-readme.txtplain text document5Kreadme.txt
grl27847-sup-0002-txts01.pdfPDF document145KText S1. Additional details about the “RTerg” automatic algorithms, the Finite fault slip inversion method used here, and additional references described within.
grl27847-sup-0003-fs01.pdfPDF document498KFigure S1. Solutions for earthquake energies and duration are shown for each of the five real-time iterations and the post-processed result using the gCMT determined focal mechanism described in Table 1.
grl27847-sup-0004-fs02.pdfPDF document1706KFigure S2. Waveform fits for our preferred rupture model, for teleseismic P- and SH-body waves and long period Rayleigh and Love waves.
grl27847-sup-0005-fs03.pdfPDF document263KFigure S3. Cross-section of slip distribution for our alternate rupture model and rupture velocity of our alternate rupture model.
grl27847-sup-0006-fs04.pdfPDF document2108KFigure S4. Alternative fault model with dip = 8°.
grl27847-sup-0007-fs05.pdfPDF document560KFigure S5. Alternative tsunami model determined from the finite fault model shown in Figure S4.
grl27847-sup-0008-t01.txtplain text document1KTab-delimited Table 1.

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