Supporting Online Materials The Potential for Earthquake Early Warning in Southern California By Richard M Allen and Hiroo Kanamori,

Materials and Methods The recursive relation (equations 1-3) provides an estimate of the frequency content of a waveform. The approach is based on the fact that for a harmonic signal x(t) with angular frequency ω,

22

2 xdtdx

=ω (6)

where the bar indicates an average. When a timeseries is the sum of a number of harmonic signals with different angular frequencies then ω in equation (6) becomes an estimate of the predominant angular frequency from which the predominant period,

pT , is simply determined, ωπ2=pT . pT is a weighted average of the frequency content, the weights being the amplitudes of each frequency component. ElarmS uses a realtime implementation of predominant period estimation. The averages in equation (6) are replaced by smoothed averages and calculated for each time step i as shown in equations (2) and (3). When the smoothing time window is much greater than the period of the timeseries, the recursive equation (1) provides an accurate, stable estimate of the predominant period of the signal. If the smoothing time window approaches the period of the signal, the predominant period estimate oscillates about the true estimate. ElarmS uses a 1 s smoothing constant (for 100 sps data α=0.99, for 20 sps data α=0.95).

iX iD

#:L1:

530.70

530.56

510.48

460.45

410.45

380.41

370.42

360.41

340.39

300.35

290.30

280.30

280.30

280.30

280.29

280.29

280.28

280.28

260.27

3

4

5

6

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8

Even

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0 5 10 15 20Number of stations triggered

A

B

280.29

Fig. S1. Plot of the ElarmS event-magnitude estimate available as a function of the number of stations providing a station-magnitude estimate. The order of station inclusion is determined by epicentral distance, closest to furthest. Events with a TriNet magnitude of 5 or greater are shown as solid lines, smaller magnitude events are shown with a dashed line. (A) Plot of absolute magnitude estimate, the TriNet magnitudes for events greater than magnitude 5 are indicated as a blue dot connected to the last ElarmS estimate. (B) Plot of the error in the ElarmS magnitude estimate with respect to the TriNet magnitude estimate. Blue histograms are frequency distributions of the magnitude error, the reduction in the width of the histograms illustrates the improvement in the magnitude estimate as the number of reporting stations increases. The average absolute error (L1 norm), given at the bottom of the figure and labeled "L1", decreases from 0.70 to 0.27 magnitude units as the number of stations increases from 1 to 19. The number of events available for calculation of the L1 norm is also given at the bottom of the figure and labeled "#".

#:L1:

20.61

120.52

190.56

230.41

260.36

270.29

270.26

280.26

280.26

280.26

280.25

280.24

280.22

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0.20

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0 5 10 15Time after the S-wave arrival at the epicenter

280.20

Fig. S2. Plot of the error in the ElarmS event-magnitude estimate as a function of time for the purpose of earthquake early warning. The zero time for each earthquake represents the earliest possible time of damaging ground motion at the surface which is the estimated S-wave arrival time at the epicenter determined using the event depth and a 1D velocity model for southern California (1). Events with a TriNet magnitude of 5 or greater are shown as solid lines, smaller magnitude events are shown with a dashed line. The blue histograms show the frequency distribution of the magnitude estimate errors at each time. Their decreasing width indicates the improvement in the magnitude estimate as time increases. The number of events for which a magnitude estimate is available (labeled "#"), and the average absolute error (labeled "L1"), are given at the bottom of the figure. The error drops to 0.24 and 0.19 magnitude units after 10 and 15 seconds respectively. A subset of 28 events (Fig. 2) was chosen to best represent how ElarmS would operate today given the density of TriNet stations in the more densely populated regions of southern California. Earthquakes at the southern end of the Sierra Nevada and in the Mojave Desert (the Hector Mine sequence of events), where the station density is much lower than south of the San Andreas, where population is highest, are rejected. The Landers and Northridge mainshocks for which there are only two broadband recordings within 100 km are also rejected.

Table S1. Table of earthquake source parameters for the 53 events used in this study. A “yes” in the Subset column indicates the event was included in the test of ElarmS performance as a function of time (Fig. 4B).

Date Time Magnitude Latitude Longitude Depth

Number of broadband

waveforms recorded within 100 km Subset SCEC event ID

06/28/92 11:57:34.12 7.3 34.200 -116.440 0.0 2 01/17/94 12:30:55.40 6.7 34.213 -118.537 18.4 2 09/20/95 23:27:36.27 5.8 35.761 -117.638 5.4 3 3231786 01/07/96 14:32:53.02 5.2 35.761 -117.646 4.0 3 3248846 11/27/96 20:17:24.11 5.3 36.075 -117.650 1.2 4 7050470 03/18/97 15:24:47.72 5.3 34.971 -116.819 1.6 4 7062511 04/26/97 10:37:30.67 5.1 34.369 -118.670 16.5 5 yes 9008753 03/06/98 05:47:40.33 5.2 36.067 -117.638 1.8 3 9044494 03/07/98 00:36:46.84 5.0 36.076 -117.618 1.7 4 9045109 10/16/99 09:46:44.13 7.1 34.600 -116.272 5.0 9 9108652 10/16/99 09:59:35.21 5.8 34.678 -116.292 10.8 6 3320848 10/16/99 10:20:52.60 4.8 34.362 -116.148 0.1 6 9108709 10/16/99 11:26:04.70 4.7 34.813 -116.341 0.0 5 9108775 10/16/99 12:57:20.99 5.6 34.442 -116.248 1.9 3 3320736 10/16/99 20:13:37.60 4.6 34.689 -116.280 1.3 8 9109442 10/16/99 22:53:41.20 4.5 34.710 -116.353 7.5 10 9109636 10/21/99 01:54:34.17 5.1 34.874 -116.391 1.0 5 3321590 10/22/99 16:08:48.06 5.0 34.865 -116.409 0.9 4 9114812 02/21/00 13:49:43.10 4.3 34.047 -117.255 15.0 34 yes 9140050 03/11/00 21:46:07.80 3.1 33.839 -117.744 3.5 20 yes 9142593 06/26/00 15:43:07.50 4.6 34.783 -116.294 4.3 8 9155518 09/16/00 13:24:41.30 3.2 33.976 -118.424 12.2 24 yes 9163314 01/14/01 02:26:14.00 4.3 34.284 -118.404 8.8 48 yes 9613229 02/10/01 21:05:05.70 5.1 34.289 -116.946 9.1 32 yes 9627721 02/13/01 03:04:35.60 3.5 34.289 -116.942 6.2 26 yes 9628901 02/18/01 06:09:32.10 3.3 33.675 -116.809 16.7 28 yes 9630113 03/25/01 00:41:25.20 3.4 34.048 -117.570 7.5 49 yes 9639729 04/13/01 11:50:12.40 3.6 33.878 -117.688 3.6 54 yes 9644101 04/20/01 09:52:12.20 3.4 33.705 -116.776 16.9 27 yes 9645945 05/14/01 17:13:30.20 3.8 34.226 -117.440 8.7 57 yes 9652545 05/17/01 22:56:45.80 4.1 35.796 -118.046 8.4 11 9653493 07/03/01 11:40:48.10 3.9 34.264 -116.764 3.3 30 yes 9666905 07/17/01 12:07:26.30 4.8 36.014 -117.861 7.0 7 9674049 07/17/01 12:59:59.10 4.7 36.017 -117.882 0.4 7 9674213 07/20/01 12:53:07.50 4.4 35.995 -117.877 3.4 10 10992159 07/23/01 21:02:47.20 3.7 35.990 -117.879 4.0 9 yes 9683913 07/30/01 23:34:17.90 3.7 36.049 -117.883 2.8 9 9688025 08/20/01 07:34:23.10 3.0 34.044 -117.250 15.7 30 yes 9696461 09/09/01 23:59:18.00 4.2 34.059 -118.388 7.9 57 yes 9703873 09/17/01 01:14:49.00 3.1 33.922 -117.774 11.8 41 yes 9706897 10/28/01 16:27:45.50 4.0 33.922 -118.270 21.1 56 yes 9716853 10/28/01 16:29:54.60 3.0 33.929 -118.296 23.6 31 yes 9716861 10/31/01 07:56:16.60 5.1 33.508 -116.514 15.2 33 yes 9718013 11/13/01 20:43:14.90 4.1 33.317 -115.700 5.5 19 yes 9722633 12/14/01 12:01:35.50 4.0 33.955 -117.746 13.8 57 yes 9735129 01/29/02 05:53:28.90 4.2 34.361 -118.657 14.2 47 yes 9753485 01/29/02 06:00:39.80 3.9 34.370 -118.668 14.2 46 yes 9753489 01/29/02 06:08:01.80 3.8 34.365 -118.664 14.4 44 yes 9753497 01/29/02 20:23:07.00 3.6 34.363 -118.667 12.6 44 yes 9753949 01/30/02 18:47:57.30 3.5 34.366 -118.661 12.8 45 yes 9755013 03/17/02 05:50:43.10 3.2 33.873 -117.856 9.5 35 yes 12663484 04/05/02 08:02:56.00 4.4 34.524 -116.295 5.6 18 9775765 07/01/02 22:03:59.60 3.3 34.103 -116.651 10.0 24 yes 9796589

References and Notes

1. E. Hauksson, Journal of Geophysical Research-Solid Earth 105, 13875-13903 (2000).

Supporting Online Material www.sciencemag.org Materials and Methods Figs. S1, S2 Table S1