On the estimation of seismic intensity in earthquake early warning systems



[1] The infamous Tokai Earthquake, which by some accounts is overdue, is expected to be a magnitude ≥ 8 event that will cause unprecedented damage in regions of Japan. To mitigate hazards from large earthquakes in Japan, an earthquake early warning (EEW) system was developed that is able to determine hypocentral locations from P-arrival data within a few seconds and then transmit this information before the onset of large ground motions from the later arrival of S-waves. We introduced a new source parameter for seismic intensity magnitude that can be estimated from the real-time P-wave data during the early stages of fault rupture for most earthquakes M ≥ 6.5. The use of this parameter results in a significant improvement in the uncertainty in the estimated seismic intensity compared to estimates derived from earthquake magnitude. A pre-established relation between the P- and S-wave seismic intensity therefore enables an EEW system to issue a rapid and reasonably reliable prediction of the amount of ground shaking that may be expected from the damaging S-waves.

1. Introduction

[2] It has been pointed out that great earthquakes of magnitude ≥ 8, called the Tokai, Tonankai and Nankai earthquakes, are expected to occur in areas that are relatively close to the most industrially developed regions in Japan. A widespread short-period seismic array (Hi-net) in Japan is currently used in an EEW system that makes it possible for these regions to have a few to several 10's of seconds of warning before the onset of a strong ground shaking. There are other dense arrays in Japan that use strong-motion (KiK-net; K-NET) and broadband sensors (F-net), which were installed and upgraded after the 1995 Kobe earthquake [Okada et al., 2004]. The development of an EEW was started over 20 years ago by Nakamura [1988] for Japanese railways and the recent Nowcast system was developed mainly from the analysis of single station data [Odaka et al., 2003], but the Hi-net array makes it possible to have an EEW system covering a wide area in Japan [Horiuchi et al., 2005]. Warning systems are also found in other countries such as Mexico [Espinosa-Aranda et al., 1995], Taiwan [Wu and Teng, 2002; Wu and Kanamori, 2005], Romania [Wenzel et al., 1999] and Turkey [Erdik et al., 2003].

[3] In 2003, a major project was started in Japan to develop an EEW that includes the National Research Institute for Earth Science and Disaster Prevention (NIED), the Japan Meteorological Agency (JMA), the Consortium of Real-time Earthquake Information (REIC), and the Japan Weather Association [Hoshiba et al., 2008]. Project objectives are: (1) an automatic system to determine hypocenters and source parameters within a few seconds; (2) a database for site amplification effects so that users can take these into account; (3) making the software available for long-term operation and maintenance of the EEW; (4) broadcasting a public warning that can be used to halt equipment in high vulnerability situations.

[4] An important concern of an EEW is the seismic intensity where key facilities are located and this has traditionally been estimated using earthquake parameters in empirical equations [Midorikawa, 1993; Somerville et al., 1997]. Seismic intensity is an essential parameter in Japan since strong shaking may cause abrupt stoppage of facilities, which would result in massive economic loss that could be largely mitigated by a controlled shutdown. Obviously, large uncertainties in the estimated intensity may result in false shutdowns; therefore an EEW should be able to determine seismic intensity not only quickly but also at some acceptable level of accuracy.

2. Magnitude Estimation

[5] There are fundamental difficulties in the rapid determination of the magnitude of a large earthquake. In general, earthquakes of magnitude 6, 7 and 8 have faults of about 10 km, 30 km, and 100 km, respectively, and with a rupture velocity in the neighborhood of 3 km/s, it would take about 3, 10 and 30 s to completely rupture these faults. Therefore, an observation time of approximately these times is needed to reliably estimate earthquake magnitude, which is why it is difficult to determine the magnitude of large events with limited amounts of real-time seismic data.

[6] There are claims that the magnitude of an earthquake can be predicted from analysis of only a couple of seconds of the initial P-wave data [Olson and Allen, 2005; Zollo et al., 2006]. Those methods may be useful to estimate the lower bound of magnitude [Kanamori, 2005]. However, rupture propagation depends on fault geometry, the strength of rocks and the distribution of stress over the fault; thus it is not evident how the final rupture size can be determined from analysis of a very limited amount of the initial waveform data. Indeed, we found it difficult to predict the final magnitude from our analysis of Hi-net [Rydelek and Horiuchi, 2006] and K/KiK-net data [Rydelek et al., 2007], especially given the large scatter in results for earthquakes M > 6.

3. Seismic Shaking Intensity

[7] The fundamental reason for an EEW system is to warn of strong ground shaking from large earthquakes. We introduce a new seismic parameter that is able to provide a reliable estimate of seismic intensity, and most importantly, it can be estimated from the real-time P-wave data. Earthquake magnitude is commonly determined from source models that make use of the displacement seismogram, e.g., MJMA is determined from maximum amplitude of displacement. But fault fracture is a complicated function of the distribution of stress and strength around the fault resulting in earthquakes with different source spectra [Sato and Mori, 2006]. This may produce large estimation errors of seismic intensity when estimates are based on displacement seismograms. Since seismic intensity is derived from ground acceleration in a limited frequency band, any estimate of the expected shaking should be a function of the observed acceleration data and not the displacement data. Therefore, we introduce a new parameter MI to characterize earthquake strength that is obtained directly from the observed seismic intensity I as follows,

equation image

where Va is a value that is obtained from a time-series V that is the vector amplitude of the three components of acceleration, which have been band-pass filtered (see Figure 1a) as described by Japan Meteorological Agency (JMA) [1996]. As shown in Figure 1b, Va is defined as the level at which the absolute value of VVa for a time duration of at least 0.3 s. This definition was chosen in order to maintain reasonable agreement and continuity between the instrumentally observed seismic intensity and a historic JMA intensity scale used from 1949 to 1996. Time window is chosen from onset of P-wave to the latest time before S-wave arrival predicted from real-time determination of hypocenter.

Figure 1.

(a) Amplitude response of JMA intensity filter. (b) Illustration that shows how the value of Va is obtained, which is used to determine the seismic shaking intensity in equation (1). Given a time window of the P-wave seismogram shown in this figure, Va is defined as the level at which the absolute value of the acceleration is above this level for 0.3 seconds; therefore the total time duration of the shaded peaks is 0.3 seconds. As the window lengthens, the value of Va may increase for larger earthquakes if the seismic shaking intensity increases. A value for S-waves is computed in a similar manner.

[8] We assume a standard source model in which Va is:

equation image

where, r, f, T and Q are the hypocentral distance, frequency, travel-time, and attenuation Q value. A station dependent correction Cj is used to account for the site effect. Therefore, Ao can be considered as a scale of the amplitude of Va at the earthquake source.

[9] We now introduce a new scaling parameter MI called the intensity magnitude, which is derived from A0. Here we assume that Va is exponentially related to MI:

equation image

Combining equations (1) through (3) results in:

equation image

[10] The parameter MI can be used to estimate the seismic intensity in a real-time EEW system. Since acceleration is the second time derivative of displacement, MI is found to be largely controlled by the amplitude of short-period seismic waves, which may suggest that it is a better estimator of seismic intensity in an EEW system than estimates derived from peak ground displacement.

[11] The importance of MI arises from the fact that it can be rapidly determined from real-time P-wave data. Therefore, the S-waves seismic intensity at any site can be estimated by using an a priori observed relation for the shaking intensity between P- and S-waves, which also takes into account the S-wave travel times and Qs structure.

[12] As discussed below, MI is unlike conventional magnitude; whereas the moment magnitude Mw is dependent on the final slip over the entire fault surface, MI is controlled by high-frequency seismic energy radiated at the rupture front. Cleary, fault failure in which the rupture front has in effect saturated because of geometrical constraints and/or a lack of significant stress inhomogeneities, will allow a corresponding rapid estimate of seismic intensity as compared to an estimate that relies on total slip.

4. Observations and Analysis

[13] We analyze waveform data from the F-net seismic array in Japan, which is comprised of 72 stations equipped with broadband (STS-1; STS-2) and strong-motion (VSE-355) sensors that are installed in 30 to 50 m long tunnels and sampled at 100 Hz with a 24 bit A-to-D converter. F-net data is used in order to investigate ground displacement versus acceleration and also to check the applicability of our method with a network that is independent of Hi-net [Yamamoto et al., 2007]. The data analyzed here is from 2002 to 2007 and consists of nearly 8000 seismic records from approximately 1600 events M3.5 to M7.9.

[14] For each earthquake, the raw seismic records from the F-net stations are first numerically filtered according to JMA intensity calculation [JMA, 1996] and then processed to find the value of Va, which is then used in equation (1) to determine the seismic intensity. Figure 2a displays the observed seismic intensity of the P-waves versus the S-waves and the straight-line fit indicates that the S-wave estimate is on average about one unit larger than the P-wave estimate. Estimates of seismic intensity for the S-waves are then used in equation (4) to obtain MI, which include a correction for attenuation and also taking into account the hypocentral distance and observed travel time. We note that the attenuation term (f/Qs = 0.0088) in equation (4) is in good agreement with the results of Kinoshita [1994] obtained from deep borehole observations. We included the station corrections and then used a least-squares regression to obtain the constant term b so that the average of MI becomes the same as MJMA. Figure 2b shows a plot of the MI versus the MW as defined by NIED. Of special interest is the result that MI appears to saturate for larger earthquakes Mw ≥ 6.5, which suggests that the determination of MI from the early stages of rupture may be sufficient to estimate the seismic intensity. The results in Figure 2 signify that if MI can be quickly determined from the P-waves in real-time, then the S-wave shaking intensity can also be estimated.

Figure 2.

(a) Plot of the seismic S-wave shaking intensity versus the P-wave intensity from a 6 second window. The straight line fit suggests that the intensity for S-waves is approximately one unit larger than the P-waves, on average. Station corrections have not been included in this plot but are used when the intensity magnitude MI is computed from the observed seismic shaking intensity I. (b) Estimates of the intensity magnitude from the P-waves versus the moment magnitude of earthquakes. The results in this figure suggest that for larger earthquakes (M ≥ 6), which are the main concern of an EEW system, a rapid determination of MI from the P-waves could be used to estimate the expected seismic shaking intensity from the damaging S-waves.

[15] We form the difference between the observed seismic intensity and the calculated intensity from both MI and a JMA algorithm that uses earthquake magnitude MJMA. In Figure 3, a comparison of the errors between these different methods shows a significant improvement from the use of MI since the average errors from MI for larger earthquakes (Mw ≥ 6) show about a 43% reduction compared to those derived from magnitude.

Figure 3.

Errors plotted here are the differences between the observed and calculated estimates of seismic shaking intensity. Upper plot is from a method that uses JMA magnitude MJMA; lower plot uses the seismic intensity magnitude MI. Crosses are the rms values of the uncertainties in the errors at any given magnitude. A comparison suggests that estimation errors can be decreased by using MI; for Mw ≥ 6 earthquakes, the overall reduction in uncertainly is about 43%.

[16] As new waveform data is continually available from the real-time seismic networks, the earthquake's hypocenter and magnitude is recalculated every second. Of crucial importance to an EEW system, however, we find that for a given seismic record the estimate of MI, which is proportional to I, becomes larger more rapidly than MJMA, which is a function of the logarithm of peak ground displacement, log(PGD). This is demonstrated in Figure 4 for a characteristic M 6.6 earthquake where estimates of intensity and log(PGD) are determined from increasing time windows after the initial P-wave arrival; the shaking intensity is found to increase, and then saturate, more rapidly than the peak ground displacement. This example shows that by using MI we are able to rapidly estimate the magnitude of the seismic intensity and broadcast this information in near real time.

Figure 4.

Starting with the P-arrival from a M6.6 earthquake, the abscissa shows the time window that was used to determine the seismic shaking intensity (left axis) and peak ground displacement (right axis). MI and MJMA are dependent on the shaking intensity and the logarithm of peak ground displacement, respectively; therefore this example shows that MI can be estimated more rapidly than MJMA.

5. Discussion

[17] A simple pedagogic example with homogeneous rupture can help explain why MI tends to saturate before rupture has ended. Consider two faults with identical physical properties that have the same area but are geometrically dissimilar; the first fault-plane is square but the second is long and narrow. Earthquakes on these faults with similar slip will have the same moment magnitude. When an earthquake occurs, however, the rupture front on the square fault will expand in a two-dimensional circular manner until the edges of the fault are reached. Rupture on the second fault will also expand outward but the edge of the narrow fault will be quickly reached and further rupture will progress in linear manner across the remainder of the long fault. Since seismic intensity is related to the maximum amplitude of short-period waves generated at the rupture front, the first fault will cause ever increasing shaking as the rupture front grows compared to the long fault in which the rupture front saturates relatively quickly. This simple model is amended to include fault asperities that will cause increased shaking intensity when they rupture.

[18] Earthquakes in Japan occur in three main regions: (1) shallow, inland areas, (2) on the boundary between the continental and oceanic plates, (3) and within the subducting plate. Most of the inland earthquakes in Japan are distributed in the seismogenic zone ranging from depths of a few km to about 15 km and if we assume a dip angle of 45°, then the maximum length of the fault plane along dip is about 21 km. The most intense short-period seismic waves are generated by asperity rupture, and if the area of this region is roughly 22% [Somerville et al., 1999] of the fault area, then the length of the asperity along dip for inland events may be about 10 km on average. Therefore a magnitude 7 intraplate earthquake may have a horizontal fault length of about 35 km but the length of the asperity would only be 10 km. With a subducting plate thickness of about 30 km, the average size of the asperity within the plate may be about 14 km across or less. Plate boundary earthquakes (M∼8) are larger than intraplate earthquakes and a rough estimate of the area generating the strongest intensity of shaking for an interplate earthquake may be ∼50 km, which is consistent with a source model for the Off Tokachi (MJMA = 8) earthquake obtained by Koketsu et al. [2003].

[19] For the largest subduction zone earthquakes, rupture propagates two dimensionally until it reaches the edge of the boundary at which point it then propagates one dimensionally along the direction of the long axis, which resembles rupture along a line source; this effect limits the size of MI during the latter stages of rupture propagation. However, it takes a few seconds to tens of seconds until the rupture front reaches the characteristic size of asperities in the dip direction. Prior results for the Off Tokachi earthquake shows that MI reaches a value of 7.0 within 10 seconds, remains mostly constant at this level, and then jumps to 7.4 at 25 seconds, thus suggesting the late rupture of a large area of asperity [Yamamoto et al., 2007]; this interpretation is consistent with a detailed modeling of the waveform data [Koketsu et al., 2003]. We note that the results given above from the analyses of F-net data support the previous results of Yamamoto et al. [2007] using Hi-net data.

6. Conclusion

[20] We continue to investigate the applications in which the earthquake early warning system in Japan would help to lessen the damage from large earthquakes. In this study, we have introduced a new parameter MI, called the intensity magnitude, that allows for the rapid and accurate estimation of seismic intensity in an EEW, which is the primary function of such a system. The seismic intensity estimated from MI is found to reach its final value before rupture termination and the resulting uncertainties in these estimates are significantly lower than intensity estimates derived from conventional magnitude. The continued development of a reliably and accurate EEW system will play a central role in helping to mitigate seismic hazard, especially from great Tokai and Tonankai earthquakes.


[21] We thank two anonymous reviewers for helpful comments.