Testing the ElarmS Methodology on Japanese Earthquakes

Holly Brown and Richard Allen


Earthquake early warning systems are algorithms designed to detect the initial P-waves from an earthquake, rapidly estimate the magnitude of the event, and predict subsequent ground shaking in the surrounding regions. Earthquake Alarm Systems, or ElarmS, is one early warning algorithm that uses a network of seismic stations to hone in on the size and location of the earthquake. Averaging the magnitude estimates from multiple stations improves the accuracy of the estimate. ElarmS has been tested on multiple Northern and Southern California datasets, and now automatically processes streaming seismic data across California. In order to improve the robustness of the methodology, we test it on a dataset of large-magnitude events from Japan's Kyoshin Net (K-NET) strong-motion seismic network.


K-NET consists of 1,000 digital strong-motion seismometers spaced at approximately 25km intervals throughout Japan. Each station is capable of recording acceleration up to 2000 $cm/s^{2}$. Our K-NET dataset contains 84 earthquakes occurring within 100km of K-Net stations between September 1996 and June 2008 (Figure 2.61). The local magnitudes range from 4.0 to 8.0, the largest being the 26 September 2003 Tokachi-Oki event. Forty-three of the events are of magnitude 6.0 or greater.

Figure 2.61: Map of events and K-NET stations: Large circles are events used in this study. Small triangles are K-NET stations.
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ElarmS estimates magnitude from the frequency content and peak displacement of the first several seconds of the P-wave arrival at each station. Allen and Kanamori (2003) and Olson and Allen (2005) documented an empirical relationship between the magnitude and the maximum frequency parameter $\tau_{p}^{max}$ of the P-wave. Wurman et al (2007) further showed a relationship between magnitude and peak displacement, $P_{d}$, in the initial seconds of the P-wave arrival. ElarmS utilizes both relationships to calculate two magnitude estimates, which it then averages together to improve accuracy in the final event estimate. As more stations report P-wave arrivals, ElarmS incorporates their $\tau_{p}^{max}$ and $P_{d}$ measurements into the average for an overall estimate of event magnitude.

ElarmS in California assumes a fixed depth of 8km and estimates the epicentral distance with a two-dimensional grid search. In the Japanese subduction zone this is inappropriate. For the Japanese dataset we create a three-dimensional grid and calculate the IASP91 P-S travel time for seismic waves originating at each point of the grid. We then compare the calculated travel times to the observed P-S travel times at each station to find the best estimate of hypocentral location. Data is used only from stations within 100km of the hypocenter.


We use a least-squares fit to calculate a local relationship between magnitude and $\tau_{p}^{max}$ of log10( $\tau_{p}^{max}$) = -1.22 + 0.21*M, compared to log10( $\tau_{p}^{max}$) = -0.78 + 0.15*M for Northern California (Wurman et al, 2007) (Figure 2.62a). The observed $\tau_{p}^{max}$ values from Japan are similar to those of Northern California, with a slightly steeper slope for Japan.

We also use a least squares fit to calculate a local relationship between magnitude and peak displacement of log10($P_{d}$) = -4.02 + 0.66*M, corrected for epicentral distance, compared to log10($P_{d}$) = -3.77 + 0.73*M for California (Wurman et al, 2007) (Figure 2.62b). The $P_{d}$ relations have comparable slopes for Japan and Northern California, but Japan displays lower observed $P_{d}$ values, implying greater attenuation in the region.

Figure 2.62: Observations from first 4 seconds of P-wave arrival at each station. (a)Observed log( $\tau_{p}^{max}$) versus Catalog Magnitude. $\tau_{p}^{max}$ is peak frequency filtered at 3Hz. (b)Observed log($P_{d}$) versus Catalog Magnitude. $P_{d}$ is peak displacement corrected for epicentral distance.
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We further consider the effect of different quantities of data by limiting the number of stations used for magnitude estimates. Figure 2.63 shows the average error in the ElarmS estimated magnitude using only the single closest station to the epicenter, the two closest stations, three closest, etc. The dashed lines show the error in the magnitude estimate using only $\tau_{p}^{max}$ or $P_{d}$. The solid line is the error using both $\tau_{p}^{max}$ and $P_{d}$.

The combined $\tau_{p}^{max}$ and $P_{d}$ estimate has an average error of less than 0.6 magnitude units using only one station for each event, and that error drops lower with the addition of more stations. $P_{d}$ by itself produces an average error of less than 0.5 magnitude units for all numbers of stations. $\tau_{p}^{max}$ by itself produces an error that is higher than that of $P_{d}$, but still less than one magnitude unit when using more than one station. Previous studies have shown that the ElarmS magnitude estimates are more robust for large events when $\tau_{p}^{max}$ and $P_{d}$ estimates are combined (Wurman et al, 2007), although we have not yet verified this for the Japanese dataset.

Figure 2.63: Magnitude error by number of stations
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The scaling relations between $\tau_{p}^{max}$ and magnitude and between $P_{d}$ and magnitude are clearly evident for this Japanese dataset. This is a particularly valuable result given the large number of large (M$>$6) earthquakes, implying that the ElarmS methodology remains robust and useful for large magnitude events. The hypocentral depth algorithm we added for this study extends ElarmS' range of geologic settings to subduction zones, in addition to the strike-slip faults of California.


Support for this project is provided by the USGS NEHRP program (06HQAG0147).


Allen, R.M., and H. Kanamori, The potential for earthquake early warning in southern California, Science, 300, 786-789, 2003.

Olson, E.L., and R.M. Allen, The deterministic nature of earthquake rupture, Nature, 438, 212-215, 2005.

Wurman, G., R.M. Allen and P. Lombard, Toward earthquake early warning in northern California, J. Geophys. Res., 112 (B08311), 2007.

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