Rapid magnitude determination from peak amplitudes at local stations
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2013
Received: 9 August 2012
Accepted: 12 March 2013
Published: 17 September 2013
The rapid determination of its magnitude soon after a great earthquake is necessary for the issuing of effective tsunami warnings, as demonstrated in the great earthquake off Tohoku district in Japan on March 11, 2011. The earthquake magnitude for the first tsunami warning was underestimated due to magnitude saturation. This paper proposes a method to determine magnitude rapidly from peak velocity and displacement of long-period seismic waves up to 100 seconds at local stations. When waveform data at local stations are available, the magnitude from S-wave peaks is expected to be determined faster than that from only P-wave peaks. It takes about 140 seconds to estimate a magnitude of about 9 for the March 11, 2011, earthquake, which would enable us to issue the first tsunami warning within three minutes after the same type of earthquake.
The displacement magnitude determined by the Japan Meteorological Agency (JMA) (Katsumata, 2004) indicated saturation during the 2011 off the Pacific coast of Tohoku Earthquake on March 11 of Mw 9.0 (Hirose et al., 2011). Magnitude determination is a key to issuing an effective tsunami warning. The JMA displacement magnitude is determined from the logarithm of the maximum displacement amplitude recorded with seismographs of natural period 6 s and damping coefficient of 0.55. Displacement records are currently obtained from acceleration records by numerical integration and digital filtering. Using longer-period seismic waves for magnitude determination should overcome the problem of magnitude saturation (Aki, 1967). Here, we use the peak velocity and displacement of a longer period than that used for the JMA magnitude to rapidly determine the magnitude.
Several magnitude determination methods have been proposed for a tsunami warning based on P-wave before the S-wave arrival (Tsuboi et al., 1995; Yoshida, 1995; Hara, 2007; Kanamori and Rivera, 2008; Lomax and Michelini, 2009). When the fault rupture lasts a long time, the epicen-tral distance of data should be great enough to get a T S −T P exceeding the rupture duration, where T p and T S are the travel times of P and S waves.
Quick magnitude determination methods have been proposed also for early earthquake warning (Wu et al., 1998; Kamigaichi, 2004; Wu and Zhao, 2006; Zollo et al., 2006). However, those methods are based on the amplitude measured on waveforms of intermediate period, or the amplitude of the initial parts after the onsets, and do not fit magnitude determination for great and long source duration earthquakes.
For the P-wave magnitude determination, it is necessary to restrict the amplitude search range within P- and S-arrivals to avoid S-wave contamination. When any phase type indicating the peak amplitude can be used, time windows for the amplitude search are not needed. This makes the process flow simple and robust. Here, we examine the magnitude determined from the peak amplitude of any phases including long-period S-waves and surface waves.
2. Method and Data
Velocity and displacement records are obtained from strong-motion acceleration records with numerical integration and low-cut filters. Second- (for velocity) and Third-(for displacement) order low-cut Bessel filters (Katsumata, 1993) are used in this study. The filters are recursive, and can be applied in real-time processing.
Parameter a is first estimated with data of earthquakes Mw > 7, then b and c are estimated with data including those of smaller events. When the constants a, b, and c are estimated simultaneously, M of great earthquakes (Mw > 8) diverges further from Mw. We adopt the value of a for a T c which indicates the least dispersion for earthquakes including small ones, since such a value would be applicable to great earthquakes as well as to moderate ones.
Velocity magnitude determination coefficients in Eq. (1).
T c (s)
Displacement magnitude determination coefficients in Eq. (1).
T c (s)
4.1 Velocity magnitude and displacement magnitude
In this section, we will briefly discuss the suitability for tsunami warning of velocity and displacement magnitudes. Dispersion of data (Figs. 5 and 6) and differences from Mw (Figs. 7 and 8) do not clearly differ between velocity and displacement magnitudes. Data from accelerometers are used here with numerical integration, and data availability is limited by a r /ω for velocity and a r /ω2 for displacement, where a r is the sensor resolution of the accelerometer and ω is the angular frequency. Velocity magnitude is available for more events due to the limitation on the amplitude range.
For tsunami earthquakes such as the 1992 Nicaragua earthquake (Kanamori and Kikuchi, 1993), the low-frequency component is more dominant than in normal earthquakes. The displacement magnitude is more sensitive to the low-frequency component than is the velocity magnitude. The displacement magnitude is thus preferable for tsunami warnings. The displacement magnitude is mainly examined in the following sections.
The integral of displacement is proportional to the seismic moment, and this might be better for tsunami warning than the displacement amplitude. However, accelerometers do not have enough resolution for more integration. When data of strong motion velocity meters are used for the same purpose, a longer-period component could be used. Since accelerometer networks are more dense than strong motion velocity meter networks, we use accelerometer data in this study.
4.2 Application to rapid magnitude determination
The proposed magnitude is considered to be used to observe the growth of magnitude value in real-time processing. Since recursive filters are used to obtain the velocity/displacement records and the transmission and processing delay could be no more than several seconds, it is possible to see the magnitude value change soon after the hypocenter determination. Because they are not used, inversion analysis and phase identification do not introduce additional delay.
For the 2011 off the Pacific coast of Tohoku earthquake, the magnitude reached the final value within 140 seconds. The target time of the first tsunami warning in JMA is three minutes, so 140 seconds is a satisfactory time for the first tsunami warning. The final magnitude was 8.8 in the figure, which is less than Mw 9.1.
The time to reach the final magnitude of other earthquakes is less than three minutes. The times are delayed for events with epicenters far from the closest stations such as earthquakes off the Kuril Islands. However, tsunami arrivals at the nearest coasts would also be delayed for those earthquakes.
As expected, magnitude saturation is observed in Fig. 9. Magnitudes of shorter cutoff periods are generally smaller than those of longer cutoff periods. Differences among M20, M50 and M100 are not so large, but the difference between M10 and M20 is relatively large (the subscript denotes the cutoff period). Two large pulsed peaks with widths of about twenty seconds are seen in the seismic records in Fig. 2. The asperity size and its slip process would have defined the pulse width which is related to the characteristics of the magnitude saturation. The similarity of M20, M50 and M100 might be related to fault-rupture characteristics of the regions.
For the 2010 Chile event, short-period magnitudes are greater than long-period magnitudes. This reversed magnitude relationship would be related to the concentrated distribution of the used stations in the northern region of the source area, the relatively southern location of the epicenter, and a large slip in the northern area (Lay et al., 2010). Since the amplitude decay is steeper in short-period magnitudes than in long-period magnitudes (Fig. 6), the uneven station distribution and the improper assumption of the distance to the source affect the short-period magnitudes more. Even in such a case, the long-period magnitude is considered to be more reliable than the short-period magnitude.
4.3 Effect of fault type
Velocity structure model used to calculate synthetic records for Fig. 12.
Depth (Top) km
Velocity (P) km/s
Velocity (S) km/s
The amplitude reduces considerably when the station is located in the direction of the nodal planes. Since the compression/tension axis is usually oriented normal to the trench axis for events around a convergent plate boundary and the stations are installed in inland areas, it is considered that the observed amplitude would not become so small for local events. When seismic waves from events near Kuril Islands are observed on the Japan Islands, the stations are distributed around the direction of the null axis of the events and the magnitude would be underestimated. For the strikeslip event, the averaged amplitude is a little smaller (×0.8) than that for the dip-slip event in Fig. 12.
4.4 Dependence on the epicenter location
The difference is greater for magnitudes of shorter periods due to high amplitude decay rates of short-period magnitudes (Fig. 5).
A rapid magnitude determination method for tsunami warning based on the peak velocity and displacement of long-period seismic waves is presented. Cutoff periods up to 100 seconds were used to obtain the seismic wave data from acceleration records. The magnitude did not saturate up to magnitude 9 and could be determined within three minutes for the great earthquake on March 11, 2011, off the Tohoku District, Japan.
We used data obtained by the Japan Meteorological Agency, University of Chile, and National Research Institute for Earth Science and Disaster Prevention. We used programs developed by Dr. Takeo to calculate synthetic records. We greatly appreciate kind and thoughtful comments from two anonymous reviewers. This study was partly supported by the SATREPS project of “Enhancement of technology to develop tsunami-resilient community”.
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