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 Effective tsunami early warning for coastlines near a tsunamigenic earthquake requires notification within 5–15 minutes. We have shown recently that tsunamigenic earthquakes have an apparent rupture duration, T0, greater than about 50 s. Here we show that T0 gives more information on tsunami importance than moment magnitude, Mw, and we introduce a procedure using seismograms recorded near an earthquake to rapidly determine if T0 is likely to exceed T = 50 or 100 s. We show that this “duration-exceedance” procedure can be completed within 3–10 min after the earthquake occurs, depending on station density, and that it correctly identifies most recent earthquakes which produced large or devastating tsunamis. This identification forms a complement to initial estimates of the location, depth and magnitude of an earthquake to improve the reliability of tsunami early warning, and, in some cases, may make possible such warning.
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 Effective tsunami early warning for coastlines near a tsunamigenic earthquake requires notification within 5–15 minutes after the earthquake origin time (OT). Organizations such as the Japan Meteorological Agency (JMA), the German-Indonesian tsunami early warning system (GITEWS) and the West Coast and Alaska (WCATWC), and Pacific (PTWC) Tsunami Warning Centers first identify potentially tsunamigenic earthquakes based on rapidly determined earthquake parameters such as location, depth and magnitude. JMA issues warnings for Japan about 3 min after OT for events expected to produce a tsunami with height exceeding 0.5 m. GITEWS issues warnings for Indonesia within 5 min after OT based on the earthquake parameters and corresponding, pre-calculated tsunami scenarios. WCATWC and PTWC issue regional warning notifications within about 5–10 min after OT for shallow, underwater events around North America and in the Pacific basin with moment magnitude Mw ≥ 7.5 [e.g., Hirshorn and Weinstein, 2009].
 Recently, through analysis of teleseismic, P-wave seismograms (30°–90° great-circle distance; GCD), we have shown that an apparent rupture duration, T0, greater than about 50 s forms a reliable indicator for tsunamigenic earthquakes [Lomax and Michelini, 2009] (LM2009). Here we exploit this result and introduce a “duration-exceedance” procedure to rapidly determine if T0 for an earthquake is likely to exceed 50 or 100 s and thus to be a potentially tsunamigenic earthquake. This procedure does not require accurate knowledge of the earthquake location or magnitude and can be completed within 5–10 min after OT for most regions in the world.
2. Tsunami Importance, Moment Magnitude, and Rupture Duration
 We consider a reference set of 76 underwater earthquakes since 1992 with Mw ≥ 6.6 (Table S1). Since there is currently no uniform, physical measure of size available for most tsunamis, following LM2009, we define an approximate measure of tsunami importance, It, based on 0–4 descriptive indices, i, of tsunami effects (deaths, injuries, damage, houses destroyed), and maximum water height h in meters from the NOAA/WDC Historical Tsunami Database (http://www.ngdc.noaa.gov/hazard/tsu_db.shtml): It = iheight + ideaths + iinjuries + idamage + ihouses-destroyed, where iheight = 4,3,2,1,0 for h ≥ 10, 3, 0.5 m, h > 0 m, h = 0 m respectively. We set It = 0 for events not in the database, and note that It is approximate and unstable since it depends strongly on the available instrumentation, coastal bathymetry and population density in the event region. It ≥ 2 corresponds approximately to the JMA threshold for issuing a “Tsunami Warning”; the largest or most devastating tsunamis typically have It ≥ 10.
Figure 1 shows a comparison of It with the Global Centroid-Moment Tensor (CMT) moment-magnitude, MwCMT [Dziewonski et al., 1981; Ekström et al., 2005], and with T0 durations calculated from high-frequency, P-wave seismograms at teleseismic distance following the procedure of LM2009. The thresholds MwCMT ≥ 7.5 and T0 ≥ 50 s both identify most of the events with It ≥ 2 (see also Tables 1 and S1). MwCMT, however, shows no clear relationship to It or to event type; in contrast, T0 tends to increase for larger It, especially for tsunami earthquakes (type T; characterized by unusually large tsunamis and a deficiency in moment release at high frequencies) [e.g., Satake, 2002]. We do not consider here the energy-to-moment parameter, Θ, which is useful for identification of tsunami earthquakes [Newman and Okal, 1998], because it is not a good indicator for tsunamigenic events in general (e.g., LM2009).
Table 1. Results for L50 Classification of tsunamigenic Earthquakesa
Percentage of all events with It ≥2 that are correctly identified.
 Since CMT-based Mw magnitudes are only available 30 min or later after OT, rapid magnitude estimates such as Mwp [Tsuboi et al., 1995, 1999] are used for tsunami warning. But Mwp performs poorly relative to MwCMT or T0 for identifying events with It ≥ 2 (Table 1). Other rapid magnitude estimates for large earthquakes (e.g., Hara , LM2009, Mwpd; and Bormann and Saul , mBc) may perform nearly as well as MwCMT or T0 (e.g., Mwpd in Tables 1 and S1), but are not available until about 15 min or later after OT. Thus very rapid determination of a large T0, e.g. T0 ≥ 50 s, would provide important complementary information to initial location, depth and magnitude estimates for early assessment of earthquake tsunamigenic potential.
3. Methodology for Rapid Rupture Duration Determination
 We determine if T0 for an earthquake is likely to exceed pre-determined thresholds T = 50, 100 s through high-frequency (HF) analysis of vertical-component, broadband seismograms [e.g., Lomax, 2005; Lomax and Michelini, 2005; Lomax et al., 2007; LM2009]. We proceed as follows for each seismogram (Figure 2): 1) apply a 4-pole, 1–5 Hz Butterworth band-pass filter to form a HF trace; 2) auto-pick the P arrival time on the HF trace; 3) measure Aref, the rms amplitude for the first 25 s after the P time on the HF trace; 4) calculate the ratio of the rms HF amplitude from 50–60 s after the P time with Aref to obtain a station duration-exceedance level for 50 s, l50, and a similar ratio for 100–120 s after P with Aref to obtain l100.
 We define event duration-exceedance levels, LT, T = 50, 100 s, as the median (50 percentile) of the station l50, l100 values after removing the upper 10 percentile of values to avoid noisy or anomalously long HF signals. If an event exceedance level LT is greater (less) than 1.0, then T0 is likely (unlikely) to exceed T seconds. This procedure does not require an event location or magnitude, and all processing can be performed in the time domain; indeed, individual station l50 and l100 values can be calculated autonomously at each station.
4. Application to Reference Earthquakes
 We apply the duration-exceedance procedure to the reference earthquakes using data up to 10 min after OT from stations at 0–30° GCD from each event to simulate the information available in the first minutes after an earthquake occurs. The L50 exceedance level results are tabulated in Table 1 and all event parameters and exceedance level results are tabulated in Table S1; plots of the time evolution of the L50 calculation for two events are shown in Figure 3 and for L50 and L100 for selected events are shown in Figure S1.
 A comparison of LT, T = 50, 100 s, with the T0 durations calculated from teleseismic observations (Figure 4 (top) and Table S1) shows that, in general, the duration-exceedance level LT increases with increasing T0 and is greater than 1 for events with T0 > T. There is much scatter in these results, due primarily to the difficulty in determining cutoff points on the HF seismograms (e.g., Figure 2 and LM2009), but they confirm that the rapidly available LT measures form reliable proxies for the teleseismic, T0 durations.
 A comparison of the L50 exceedance level with tsunami importance, It, (Figure 4 (bottom) and Tables 1 and S1) shows correct identification (L50 ≥ 1) of most events with It ≥ 2. The miss-identified events are a shallow, offshore thrust event, It = 8, 2003.05.21, Mw6.8, N Algeria, and two shallow, oceanic, strike-slip events, It = 13, 1994.11.14, Mw7.1, Philippines and It = 9, 2006.03.14, Mw6.7, Seram Indonesia. All of these events are also missed using the magnitude discriminant, Mw ≥ 7.5, and thus produced larger than expected tsunamis. There are 13 events with It < 2 that are falsely identified by L50 ≥ 1 values as likely tsunamigenic (It ≥ 2); 7 of these events have It = 1 and thus produced small tsunamis, while some may have involved under land or strike-slip rupture, or produced unobserved tsunamis. The remaining events with It < 2 are correctly identified as unlikely tsunamigenic by L50 < 1 values. For most events, the L50 values have stabilized within 4–6 min after OT (Figures 3 and S1).
 The L50 discriminant correctly identifies 90% of tsunamigenic events with It ≥ 2. The overall performance of the L50 discriminant is similar to that of MwCMT, Mwpd, and teleseismic T0 (Table 1), though these latter three measures are not available until at least 30, 15 and 15 min, respectively, after OT (LM2009). In contrast, the rapidly available Mwp discriminant correctly identifies only 52% of tsunamigenic events with It ≥ 2, primarily because Mwp underestimates the size of events with MwCMT > 7.0–7.5, particularly tsunami earthquakes and other events with long rupture duration (e.g., LM2009).
 The results for L100 (Figure 4 and Table S1) show that L100 ≥ 1 identifies well events with longer duration, T0, events with It ≥ 10, and most tsunami earthquakes (type T). In contrast, 1994.11.14 Philippines, 1998.07.17 Papua New Guinea, and two intraplate events (type P) with only moderately long T0 but large It have L100 < 1 values. For events in regions with denser station coverage, the L100 values have stabilized by 6–8 min after OT (Figure S1).
 Since the station lT exceedance values can be calculated autonomously at each station, they could aid in providing very early, local tsunami warning. For example, the first station l50 values for the 2006 Indonesian event in Figure 3 are available only 2–4 min after OT. Single lT exceedance values must be used with care, however, as they can be biased at small epicentral distances by HF radiation effects and secondary phases, especially S.
 We have shown that apparent rupture duration, T0, provides more information on tsunami importance, It, than does moment magnitude and that earthquakes with a high tsunamigenic potential (e.g., possible tsunami importance It ≥ 2 or It ≥ 10) can be rapidly and reliably identified through a procedure that determines if T0 is likely to exceed 50 or 100 s. This identification can be performed within 5–10 min after OT for most regions using currently available seismographic stations and probably in less than 3–5 min for regions with higher station density, such as Japan, Taiwan, Indonesia, the Mediterranean and Western North America. This identification forms a complement to initial estimates of the location, depth and magnitude of an earthquake to improve the reliability of tsunami early warning, and, in some cases, may make possible such warning.
 We thank Alessio Piatanesi and two reviewers for helpful comments. This work is supported by the 2008–2010 Dipartimento della Protezione Civile S3 project. We use SeisGram2K (http://www.alomax.net/software) for seismogram analysis and figures and GMT (http://gmt.soest.hawaii.edu/) and OpenOffice.org Calc for graphs. The IRIS DMC (http://www.iris.edu) provided access to waveforms used in this study.