Figure 1
From: The Limits of Earthquake Early Warning Accuracy and Best Alerting Strategy
Ground motion variability and alerting accuracy. Consider a user who wishes to receive alerts for ground motion exceeding 10%g. In the first example, (A) the EEW system expects the ground motion at the user’s location to be 20%g and issues that user an alert. In the second example, (B) the expected ground motion is only 5%g, and thus no alert is issued. However, the ground motion calculated from a GMPE represents the median expected ground motion. Observed ground motions are typically distributed about that median with factor of two uncertainty10, shown by bell curve probability density functions (PDFs). By construction, in both of these examples, the EEW system will be correct for most earthquakes: (A) mostly results in correct alerts (green region of PDF) and (B) mostly results in correct no alerts (black region). However, (A) will result in a false alert in the unlikely case that this earthquake produces much less ground motion than expected (red region of PDF), and (B) will result in a missed alert for damaging ground motion in the unlikely case that this earthquake produces much stronger shaking than expected (orange region of PDF). In (A) and (B) probability is plotted as a function of log10 PGA, shown on the x-axis. The top x-axis calls out the four PGA thresholds we will explore in detail: 2, 5, 10, and 20%g. (C) We can alternately visualize this as a binary classification. There is some ground motion threshold above which damage is expected to occur (blue line). (This threshold was 10%g in (A) and (B)). The user is alerted to take action if the expected PGA is greater than some triggering value (purple line). If the expected PGA is greater than the alerting threshold, an alert will be issued (as in (A)) and this alert will be either correct or a false alert depending on what the observed PGA turns out to be. Likewise, if the expected PGA is less than the alerting threshold, no alert is issued (as in (B)) and this results in either a missed alert or the “correct no alert” case depending on the observed PGA. Note that the alerting threshold can be lower or higher than the damage threshold depending on whether the user is tolerant or intolerant of false alerts, respectively.
