# Improvement of back-azimuth estimation in real-time by using a single station record

- Shunta Noda
^{1}Email author, - Shunroku Yamamoto
^{1}, - Shinji Sato
^{1}, - Naoyasu Iwata
^{1}, - Masahiro Korenaga
^{1}and - Kimitoshi Ashiya
^{1}

**64**:640030305

https://doi.org/10.5047/eps.2011.10.005

© 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. 2012

**Received: **4 August 2011

**Accepted: **18 October 2011

**Published: **12 March 2012

## Abstract

We propose a new approach to improve the accuracy of the back-azimuth estimation in real-time by using a single station record. Compared with the conventional approach in which the length of the time window for the analysis is fixed for all data, the accuracy and speed of the estimation are drastically improved by introducing a variable-length time window which is determined by the first half cycle of the wavelength of the initial *P* -wave, because this window tends to reduce the influences of trailing scattered waves. The analysis, using the K-NET dataset, shows that the estimation, using this new approach, is improved by 28% and 0.25 s in accuracy and speed, respectively.

### Key words

Earthquake early warning back-azimuth principal component analysis single station method on-site method## 1. Introduction

The Earthquake Early Warning (EEW) system is a very effective approach to reducing earthquake hazards. In general, the EEW system can provide earthquake information, e.g. the magnitude and hypocenter, or epicenter, location, within several seconds after a *P*-wave is detected at the first station. In Japan, practical EEW systems have been developed for approximately 20 years. Nakamura (1988) developed the Urgent Earthquake Detection and Alarm System (UrEDAS) in order to halt the Shinkansen (bullet train) safely during earthquakes. In the UrEDAS, the magnitude is estimated from the predominant frequency of the *P*-wave for the initial 3 seconds, and then the epicentral distance is estimated from the magnitude and amplitude by using a predefined attenuation relation. This idea is adopted by Allen and Kanamori (2003) and Wu and Kanamori (2005). It is called the *τ*_{c} method.

*et al.*, 2005; Hoshiba

*et al.*, 2008; Nakamura

*et al.*, 2009). In this system, hypocenter locations are determined by a combination of several techniques. In the case that an earthquake is detected at only a single station, epicenter locations are determined by a combination of the following two kinds of methods (known as the single station method, or the on-site method). One is the Principal Component Analysis (PCA) (Meteorological Research Institute, 1985) (Fig. 1) by which the back-azimuth is estimated from the 1st principal component of the particle motion of the initial

*P*-wave. The 1st principal component is the direction with the minimum variance for the points of observed displacement. The other method is the

*B*-Δ method (Odaka

*et al.*, 2003) by which the epicentral distance is estimated from a coefficient

*B*of a fitting function

*Bt** exp(−

*At).*The characteristic of this method is to determine the epicentral distance at first, and then the magnitude is estimated from the epicentral distance and amplitude by using a predefined attenuation relation. Although the estimation order is the reverse, compared with the method in the UrEDAS, we consider that the method, by which the epicentral distance is estimated at first, would be more reliable for a large earthquake, because it can continue determining the magnitude during the spreading of the seismic rupture.

In the JMA system, when the number of stations which detect the earthquake is increased, the so-called Territory method, the Grid search method and the *T*_{now} method (Horiuchi *et al.*, 2005), are used to determine hypocenter locations (this is called the multi-station method or network method). The magnitude is calculated from the hypocenter location and amplitude by using a pre-defined attenuation relation.

RTRI developed a new EEW system for Shinkansen and replaced the UrEDAS with the new one in 2004–2005 (Ashiya, 2002; Iwahashi *et al.*, 2004; Yamamoto *et al.*, 2011). In this system, the PCA and the *B-*Δ method are also used to determine epicenter locations.

In general, earthquake information estimated from the single station method is obtained more quickly, and, yet, with a lower accuracy compared with that estimated from the multi-station method. Therefore, an improvement in accuracy using the single station method is essential in order to make the present EEW systems more stable. The speed should also be improved so as to make the present systems more effective.

In this study, we propose a new approach to improve the accuracy of the PCA, which estimates the back-azimuth by introducing a variable-length time window instead of the conventional fixed-length time window.

## 2. Conventional Approach

In this section, we present the conventional approach to estimate the back-azimuth by using the single station method, and we evaluate its accuracy by analyzing the K-NET data.

- (1)
The arrival time of the

*P*-wave is calculated using the STA/LTA (Short Time Average to Long Time Average) method (e.g. Horiuchi*et al.*, 2005). - (2)
The displacement data is calculated from the observed acceleration records by using the IIR (Infinite-duration Impulse Response)-filter.

- (3)
The displacement data is band-passed for 1–2Hzby using the IIR-filter.

- (4)
The back-azimuth is determined from the 1st principal component of the particle motion of the initial

*P*-wave by using the PCA (Fig. 1). The length of the time window for the analysis is set to be 1.1 s (start time is the*P*-wave arrival). The important point is that the length of the time window is fixed for all data.

1.1 s was selected as the length of the time window in the conventional approach by using the limited amount of the dataset, when the conventional approach was developed. However, we consider that a more detailed analysis was necessary for a more reliable approach with an updated dataset.

Next, we evaluate the accuracy of the back-azimuth estimated from the conventional approach. Waveform data observed at K-NET stations operated by NIED are used for the evaluation. The number of the waveform data is 1,991, which were selected with the following requirements; the period ranges from 1995 to 2010, the magnitudes exceed 5.5, the epicentral distances range within 300 km, the JMA seismic intensities exceed 3.5.

## 3. Relationship between the Fixed Time Window and Errors

In this section, we evaluate the accuracies of the errors in the case where the length of the fixed time windows are varied from 0.1 to 2.0 s by 0.1 s. The dataset used is the same as the one used in Section 2.

*P*-wave.

*P*-waves are often made when the conventional time window is used.

## 4. Variable Time Window

*P*-wave. In this case, the variable time window means the length of the first half cycle of the wavelength of the initial

*P*-wave in the band-pass displacement data (Fig. 5). In detail, its length equals the time from the

*P*-wave arrival to the first zero-cross point. The important point of this new approach is that the lengths of the time window vary according to the characteristics of each datum.

## 5. Discussion

As mentioned above, lengths in the range 0.4–0.6 s are the most frequently occurring in the appraisal of the length of the variable time window (Fig. 6). In addition, in the cases that fixed time windows of various lengths are used, rms of the errors is almost a minimum when the length of the fixed time window is in the range 0.4–0.6 s (Fig. 3). We consider that this coincidence shows the appropriateness of the above analyses.

The effect of the new approach not only improves the accuracy of the back-azimuth, but also reduces the time for the estimation compared with the conventional approach, because the average of the length of the variable time window is shorter than that of the conventional time window, as described above.

Furthermore, the new approach has two practical advantages for the present EEW systems. The first is that the new approach is so simple that the CPU requirement will hardly be increased even in a real-time process. The second is that the new approach needs only the addition of several code lines to calculate the length for the first half cycle of wavelength of an initial *P*-wave to the source code of the present systems.

## 6. Conclusion

We have proposed a new approach for improving the accuracy and speed of back-azimuth estimation from the PCA by introducing a variable time window to reduce the influences of trailing scattered waves, instead of a conventional fixed time window. By using the new approach, it is found that the accuracy and speed of the estimation is improved by 28% and 0.25 s, respectively, compared with the conventional approach. The effect of the new approach is so robust that the accuracy is statistically improved independent of magnitude, epicentral distance and JMA seismic intensity.

## Declarations

### Acknowledgements

We would like to thank the National Research Institute for Earth Science and Disaster Prevention for enabling us to use the waveform data observed at K-NET. We also wish to thank Dr. Mitsuyuki Hoshiba and an anonymous reviewer for their helpful comments.

## Authors’ Affiliations

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