Testing ElarmS in Japan

Holly Brown and Richard Allen


Earthquake early warning systems detect the initial P-waves from an earthquake, rapidly estimate the magnitude of the event, and predict subsequent ground shaking in the region. Earthquake Alarm Systems, or ElarmS, is a network-based earthquake early warning algorithm that uses the amplitude and frequency content of P-waves from multiple stations to estimate the size and damage potential of an earthquake in realtime.

ElarmS has been tested on multiple California datasets (Allen and Kanamori, 2003; Olson and Allen, 2005; Tsang, et al., 2007; Wurman, et al., 2007). However there are limited numbers of recent, well-recorded, large earthquakes in California. We test ElarmS with a dataset of large earthquakes from Japan to improve the robustness of the system and to examine the adaptability of the algorithm to other seismic environments.

We then analyze the accuracy of the ElarmS magnitude estimates, location estimates, and ground shaking predictions, and produce error distributions for each of these three ElarmS outputs. The distributions depend on the quantity of available data, and can be accessed in realtime for uncertainty estimation during an event. We use the error distributions to create a model of the errors in the system. The model identifies the greatest source of error in the final ElarmS output.

Figure 2.31: Mean errors in magnitude estimates, location estimates, and peak ground shaking predictions. Location error is in km. PGA error is the ratio of the predicted PGA to the observed PGA; a factor-of-two error in the predicted PGA relative to the observed PGA corresponds to an error of 0.7.
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The dataset consists of 84 earthquakes, which occurred in Japan between September 1996 and June 2008 (Figure 2.31). The magnitudes range from 4.0 to 8.0, with 43 events of magnitude 6.0 or greater. The largest event is the 26 September 2003 Tokachi-Oki event, with magnitude 8.0.

The events were recorded by Japan's Kyoshin Net (K-NET) strong motion network. K-NET consists of 1,000 digital strong-motion seismometers spaced approximately 25km apart throughout Japan. Each station records ground motions as large as 2000 $cm{/s^2}$.


ElarmS estimates magnitude from the frequency content and peak displacement of the first few seconds of P-wave at each reporting station. Allen and Kanamori (2003) and Olson and Allen (2005) demonstrated an empirical relationship between magnitude and the observed maximum predominant period, $t_{pmax}$, of the P-wave. Wurman, et al., (2007) documented a relationship between magnitude and peak displacement, $P_{d}$, of the first few seconds of P-wave. ElarmS uses both relationships independently to calculate two magnitude estimates for a given event, and then averages the estimates together. As additional stations record P-wave arrivals, ElarmS incorporates their period and displacement measurements into the average to create a single magnitude estimate for the event.

ElarmS calculates event location by a three-dimensional grid search. Observed P-wave arrival times are compared to those predicted for a hypocenter at each node of the grid. For the Japanese events, grid layers occur in 10km depth increments, down to 80km.

When ElarmS has an estimated hypocenter and magnitude, it applies these to National Earthquake Information Center (NEIC) ShakeMap attenuation relations to predict ground shaking in the surrounding region. Initially, the prediction is based entirely on the estimated location and magnitude. As stations report peak ground shaking, the observations are incorporated into the predictions.

Error Distributions

We isolate the location, magnitude and ground shaking processing steps to determine independent error distributions for each of these steps. The error in each step depends on the number of stations triggering, the number of seconds of P-wave arrival, and the number of stations reporting peak ground shaking observations. Thus we have separate error distributions for each quantity of inputs. Figure 2.31 shows the mean error for each distribution curve.

Error Model

We use these error distributions to create an error model for ElarmS processing. The model calculates the total error in the system, after magnitude, location, and attenuation relation errors have propagated through to the final prediction of shaking. In total, we consider 1081 different combinations of data input quantities, and create a separate error distribution for each combination. These are collectively shown in Figure 2.32a. These 1081 distributions are contained in an ElarmS library, which can be accessed in realtime. Given any combination of number of stations reporting, number of seconds of P-wave arrival, and number of peak ground shaking observations, the appropriate error distribution can be consulted to produce a realtime estimate of uncertainty in the ElarmS prediction of ground shaking.

From the model we isolate the error contribution of each processing step, by ``turning off" each contribution in turn. For example, Figure 2.32c shows the error model when the location estimate exactly equals the catalog location (zero location error); all error in the system comes from magnitude estimation and the attenuation relations used to predict ground shaking. Figure 2.32d is the error model when the magnitude estimate exactly equals the catalog magnitude, and error is contributed only by location and attenuation relations. Figure 2.32b is the error model when the attenuation relations are perfect, and all error comes from the location and magnitude estimates. Note the sharper, higher peak in Figure 2.32b. This indicates less error in the system for this scenario. That is, if the attenuation relations were perfect, the error in ElarmS' output would be significantly reduced. We conclude from this that the prediction of ground motions, produced from NEIC ShakeMap attenuation relations, contributes far more error to the final ElarmS prediction of localized shaking than do the magnitude estimate or location estimate. This suggests that more work should be devoted to improving attenuation relations, and that regional relations should be used whenever possible.


ElarmS' successful tests on Japanese events confirm that the ElarmS algorithm is relevant in a subduction zone environment and for large-magnitude events. The error distribution curves and error model show that the attenuation relations contribute the largest source of error to the final ElarmS prediction of ground shaking.


We thank K-NET for the use of their data. This work was funded by USGS/NEHRP award 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.

Tsang, L., R.M. Allen, and G. Wurman, Magnitude scaling relations from P-waves in southern California, Geophys. Res. Lett. 34, L19304, 2007.

Wurman, G., R.M. Allen and P. Lombard, Toward Earthquake Early Warning in Northern California, J. Geophys. Res. 112, B08311, 2007.

Figure 2.32: Error Model, with 1081 individual error distributions, based on differing quantities of input data (number of stations, number of seconds, number of PGA observations). (a) Complete error model. Error is contributed by magnitude estimate, location estimate, and attenuation relations (used to predict ground shaking). (b) Error model when attenuation relations error is removed. (c) Error model when location error is removed. (d) Error model when magnitude error is removed.
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