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Initial 30 seconds of the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0)—amplitude and τ c for magnitude estimation for Earthquake Early Warning—
Earth, Planets and Space volume 63, Article number: 8 (2011)
We analyzed the waveforms of the mainshock (Mw 9.0) and three foreshocks of the 2011 off the Pacific coast of Tohoku Earthquake during the initial 30 s after P-wave onset to determine the maximum amplitudes of acceleration, velocity, and displacement, and τc (the period parameter of the waveform). The amplitudes for the Mw 9.0 event were quite small for the first several seconds, as small as those of the Mw 6 foreshocks, and the τc value was also as small as those of the foreshocks. For the first 30 s, the amplitude of the Mw 9.0 event was larger than that of the Mw 7.3 foreshock whereas τc was smaller. These results suggest that it is difficult to determine the eventual magnitude for very large earthquakes from the initial several seconds, that an updating procedure is important for Earthquake Early Warning using ongoing waveforms, and that τc might not be reliable for magnitude estimation at least for the main shock.
Earthquake Early Warning (EEW) systems have been researched and developed in Japan, Mexico, the United States, Taiwan, Italy, Turkey, and other countries (e.g., Hoshiba et al., 2008; Alcik et al., 2009; Allen et al., 2009; Espinosa Aranda et al., 2009; Hsiao et al., 2009; Kamigaichi et al., 2009; Nakamura et al., 2009; Zollo et al., 2009). One of the important aspects of EEW is the rapid and reliable estimation of magnitude using the early portion of ongoing waveforms. Maximum amplitudes have commonly been used for magnitude estimates, and these are adopted in some EEW systems (e.g., Yamamoto et al., 2008; Kamigaichi et al., 2009), in which the estimate of magnitude is updated repeatedly using ongoing waveforms.
New algorithms, such as τc and , have been proposed for making estimates of the eventual magnitude by using the frequency contents of the very early portion of the waveforms; these algorithms have been investigated by many researchers (e.g., Nakamura, 1988; Wu and Kanamori, 2005; Wu et al., 2007; Allen and Kanamori, 2003; Yamada and Mori, 2009; Brown et al., 2009; Zollo et al., 2010). Most of these researches have concluded that the frequency contents are more sensitive to the magnitude than the ground-motion amplitude during the initial several seconds of the P wave. They have also claimed that the sensitivity is appropriate for EEW and that it is possible to determine the eventual size of the events from the initial several seconds. However, Rydelek and Horiuchi (2006) and Rydelek et al. (2007) using the data from accelerometers networks and high-sensitivity velocity-meter networks concluded that the size of larger earthquakes are difficult to estimate from only the early part of the records. Yamada and Ide (2008) came to a similar conclusion after considering a complex-source model. The validity of the new algorithms such as τc and for estimates of magnitude is not yet fully accepted.
The 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0) occurred on March 11, 2011, following foreshock activity. We have used the waveform data of the mainshock and three foreshocks to estimate the maximum acceleration, maximum velocity, maximum displacement and τc from the initial tN seconds of the waveform from the onset of the P wave using tN values from 3 to 30 s. We then consider whether the amplitudes or τc could discriminate the main-shock from the smaller foreshocks during the initial portion of their waveforms.
The 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0) followed several large foreshocks. We used the waveform data of acceleration of the main shock and three foreshocks recorded at MYG002, MYG008, MYG011 and MYGH12 (surface) of the K-NET and KiK-net seismic networks of the National Research Institute for Earth Science and Disaster Prevention (NIED), which are the closest four stations to the epicenters of the events (Fig. 1). We chose to study foreshocks because of their relatively low noise level in comparison to the aftershocks of this enormous event. We used waveforms whose P-wave onsets were not contaminated by noise or by codas of preceding events, choosing three foreshocks of Mw 5.9, 6.0 and 7.3. The waveform at MYG011 from the Mw 5.9 event was noisy, so it was excluded. Focal depths of the events were 8 to 24 km, and the epicentral distances ranged from 121 to 164 km.
Some previous studies of τc used waveform data from many earthquake events and many recording stations, with differences in the distance between source and recording stations: many of them were from less than 100 km, and some were from larger than 100 km for larger events. The many different source-site geometries and site amplification factors may have affected the results of those studies. Variations due to differences in path factor were small in our analysis because we used only a few events that were close together, and a few observation sites that were also close together.
The offset of the vertical-component accelerogram was corrected by subtracting the mean of the early portion of the data to obtain ua(t). It was integrated, passed through a second-order one-way high-pass Butterworth filter of 0.075 Hz, and integrated and filtered again to obtain the displacement waveforms, ud(t). The displacement was then differentiated to obtain the velocity, uv(t). The peak amplitudes Pa, Pv and Pd are the maximum absolute amplitudes of ua(t), uv(t) and ud(t), respectively, for the range between tP and tP +tN, where tP is the P-wave onset time. For tN, we used values of 3, 4, 5, 10, 20 and 30 s. The parameter τc is obtained from
where f and Ud(f) are the frequency and the frequency spectrum of ud(t), respectively, and (f2) is the average of f2 weighted by ǀUd(f)ǀ2 (Kanamori, 2005). Thus, τc corresponds to the average period of ud(t), and is expected to increase with increasing earthquake magnitude.
4. Results and Discussion
Figure 2 shows the waveforms ua(t) and ud(t) of the Mw 9.0 earthquake recorded at MYGH12. Both ua(t) and ud(t) are small for the initial 5 s; ua(t) is as small as 1 cm/s2, and ud(t) is comparable to the noise level. This indicates that the initial phases do not suggest a large magnitude event.
Figure 3 summarizes Pa, Pv and Pd and τc for various values of tN for the four events. For tN = 3–5 s, the peak amplitudes of the Mw 9.0 event are comparable to, or even smaller than, those of not only the Mw 7.3 event but also the two smaller foreshocks, and τc does not show a clear tendency because of the large variation among the different sites. For tN = 20 s, Pa of the Mw 9.0 event is larger than that of the Mw 7.3 event beyond the variation among sites, which indicates that Pa discriminates the Mw 9.0 from the Mw 7.3 event. For tN = 30 s, Pv and Pd also effectively discriminate. However, although τc of the Mw 9.0 event is larger than that of the two smallest events, it is a little smaller than that of the Mw 7.3 event, which suggests that it is difficult to recognize the event to be larger than the Mw 7.3 from only τc at tN = 30 s when accelerations exceeding 100 cm/s2 are recorded at all four stations.
When the analysis was performed using a different high-pass filter of 0.166 Hz, and when the second filtering pass was omitted when obtaining ud(t), the results were similar.
The parameter also has been investigated for rapid estimates of earthquake magnitude (e.g., Allen et al., 2009), based on the expectation that increases with increasing magnitude. is the maximum value of the initial several seconds (4 s is used in many previous studies) of τP(t) which is defined as 2π(X i /D i )1/2 (Allen and Kanamori, 2003). Here and , where x i is the time series of the ground velocity, and α is a smoothing constant (for example, α = 0.99 is used for 100 samples/s data). Though both τc and τP are based on the frequency contents, the main difference is that τc is estimated from displacement and its differential using a time window from the P -wave onset, while τP is computed recursively from velocity and its differential. Thus τc represents the average period of displacement over the time window as shown in Eq. (1), while τP is the average period of velocity weighted by the lapse time, in which the weight is controlled by α (the contribution of a given waveform segment decreases with time). Because τP is estimated recursively, τP is expected to be more sensitive to the lapse time than τc. We estimated τP(t) using waveforms of the Mw 9.0 events and the three foreshocks recorded at MYGH12 (Fig. 4). Here, we use uv(t) directly as x i , or after passing through a second-order one-way low-pass Butterworth filter of 3 Hz in this analysis. The 3-Hz low-pass filter has been commonly used in many previous studies. In Fig. 4 (top: with a 3 Hz filter), τP(t) does not show a clear magnitude dependence at the early part of the waveforms, and while τP(t) of Mw 7.3 is larger than those of M 6 class earthquakes, that of Mw 9.0 is relatively small at the later part. This suggests that it is difficult to recognize the Mw 9.0 event to be larger than the Mw 7.3 event from . When the analysis was performed using a different low-pass filter of 1 Hz or a different order (6th order), the results are similar. In Fig. 4 (bottom: without a 3 Hz filter), τP(t) of Mw 9.0 is especially small for the 4 events after 15 s in comparison to the case with a 3 Hz filter, which suggests that a higher frequency greater than 3 Hz became relatively rich in the waveform of the M 9.0 event after 15 s.
Figure 5 shows the frequency spectra of waveforms of the Mw 9.0 and Mw 7.3 events at MYGH12. The spectrum of the Mw 9.0 is flat to the frequency of the anti-alias filter around 30 Hz for the time window of tp to tp + 30 s. The spectral ratio shows that high frequencies are richer for the Mw 9.0 event than for the Mw 7.3 event as compared with low frequencies. This high-frequency content is not apparent for the time window of tp to tp + 10 s, so it is thought that the high-frequency waves arrived after tp + 10 s, as is suggested in Fig. 4 (bottom). The high-frequency content is the reason that a smaller τc and τp(t) were obtained for the Mw 9.0 event even for a large value of tN. The waveforms of rich high frequency from the Mw 9.0 event are contrary to the expectation that τc increases with increasing magnitude.
Our results suggest that it would be difficult to estimate the eventual magnitude of the Mw 9.0 earthquake from the initial several seconds, even if the parameters based on frequency contents, such as τc and , were used, and indicates that an updating procedure is necessary, using ongoing waveforms, for EEW purposes. It would also be difficult to recognize that the Mw 9.0 event would be larger than the Mw 7.3 event using only τc based on the initial 30 s of the record, a time during which the ground-motion amplitude is clearly larger than that of the Mw 7.3 event. This is contrary to the claim that the frequency contents are more sensitive to earthquake magnitude than ground-motion amplitude.
As shown in Fig. 5, the frequency contents of the Mw 9.0 earthquake may be quite different from that expected for earthquakes of this size. The source process of the Mw 9.0 earthquake might be extraordinary for an Mw 9 class earthquake, and this analysis is only one case of an Mw 9 class earthquake. It is impossible to conclude from this case that τc and are ineffective for magnitude estimation for all larger events. But even so, our analysis shows that the extraordinary is not necessarily improbable. We believe that the EEW system should be robust even for extraordinary cases, especially for larger events.
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The authors thank the anonymous reviewer who encouraged them to analyze and τp(t) in addition to τc, and Dr. M. Böse and Professor K. Yomogida (editor), who gave useful comments for improving the manuscript. The waveform data are from K-NET and KiK-net of NIED. The hypocenter locations of the events are based on the unified hypocenter catalog of the Japan Meteorological Agency (JMA). Moment magnitudes are taken from the JMA CMT catalog and the F-net catalog of NIED. We thank all of these entities for their efforts in maintaining these observations and providing the data, despite the exigencies resulting from the disaster. The figures were made using Generic Mapping Tools (Wessel and Smith, 1995).
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Hoshiba, M., Iwakiri, K. Initial 30 seconds of the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0)—amplitude and τ c for magnitude estimation for Earthquake Early Warning—. Earth Planet Sp 63, 8 (2011). https://doi.org/10.5047/eps.2011.06.015
- Earthquake Early Warning
- τ c
- the 2011 off the Pacific coast of Tohoku Earthquake