ElarmS uses the arrival times of Pwaves to locate earthquakes. When the first station triggers, an event is located at that station with a depth typical of events in the region. The earthquake is then located between the first two, and then the first three stations to trigger. Once four stations have triggered a grid search method is used to locate the event, minimizing the misfit between predicted and observed arrival times. The warning time is defined as the remaining time until the onset of peak ground shaking and can be estimated given the origin time and location of the earthquake using Swave arrival time curves. Offline testing of ElarmS using a dataset of 32 earthquakes in southern California shows that the first predictions of ground shaking are available before the Sarrival at the epicenter for 56% of earthquakes (Figure 13.20).
Figure 13.20:
The results of testing ElarmS offline using a set of 32 earthquakes in southern California and the current distribution of stations. All panels show errors as a function of time with respect to the Swave arrival at the epicenter which represents the earliest time of peak ground shaking during and earthquake. A) The error in the magnitude estimate. A magnitude estimate is available for 56% of earthquakes at the time of the Sarrival at the epicenter with an average magnitude error of 0.44 magnitude units. Within 5 sec magnitude estimates are available for 97% of events with an average error of 0.33. B) Average absolute error in PGA estimates at all stations. At the time of the Sarrival the average absolute error is 1.08. It drops to 1.00 within 5 sec, 0.98 within 10 sec, and reaches 0.95 at 15 sec. When the correct magnitude is used in the attenuation relations (i.e. removing the error in the ElarmS magnitude estimate), the error is 0.89, only slightly lower. C) Average error in PGA once available PGA observations are incorporated. The most important use of PGA observations is to remove outliers. The error in the PGA estimates is calculated in the usual way: the error is the natural logarithm of the predicted PGA minus the natural logarithm of the observed PGA for the event.

Figure 13.21:
Earthquake early warning time probability density function for the city of San Francisco. Warning times were calculated for the 35 rupture scenarios identified by the Working Group on California Earthquake Probabilities (2003) and the probability of each rupture assigned to the warning time. Epicenters were distributed at 1 km intervals along the complete length of each rupture and the cumulative probability of all events set equal to the probability of the rupture scenario. The warning time is defined at the time at which 4 sec of the Pwave is available at 2 stations and a 2 sec delay for telemetry has been added. This distribution of warning times is based on the current distribution of stations with a moderate improvement to telemetry. The warning times are color coded by the predicted intensity of ground shaking in the city using the scenario ShakeMaps. The inset shows the probability of 0, 5, 10, 20 and 30 sec warning along with the total probability of all 35 rupture scenarios (labeled QUAKE).

Warning time probability density functions have been calculated for northern California. These are based on the current distribution of broadband velocity and accelerometer stations across the region and the 35 earthquake rupture scenarios identified by the Working Group on California Earthquake Probabilities (2003). Figure 13.21 shows the probability that there will be an earthquake in the next 30 years for which there would be a given warning time for the city of San Francisco. These calculations show that it would be possible to provide warning for the vast majority of these damaging earthquakes. It also shows that for the most damaging events that cause ground shaking with MMI X in the city, it is more likely than not that there will be more than 20 sec warning.
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