Expected Value Metrics for Earthquake Early Warning Seismic Station and Redundant Telemetry System Applications

The addition of individual stations and telemetry improve Earthquake Early Warning (EEW) by increasing the area covered and reducing the time to detection of the earthquake. Improvements can be expressed in physically meaningful units of km2-s (Biasi and Alvarez, SRL, 2018). The impact of station loss (say, to wildfire or equipment malfunction) is computed the same way except for the sign of the effect. For engineering evaluations, however, a further factor is required, that of expected utilization. In a related way, funding agencies are interested in ways to measure the expected benefits from investments in new and existing seismic stations. Stations where few earthquakes are expected contribute less often to EEW than stations near active faults. Similarly, the expected cost of telemetry loss in terms of station availability, or the corresponding value of telemetry redundancy to keep the stations contributing, depends on the likelihood that the stations will be needed in a detection. The seismic engineering metric of return time describes how often shaking of a given intensity is expected to return at a point. At a ground motion level of EEW significance (say, peak ground acceleration (PGA) = 5 cm/s/s), the responsible fault is likely to be nearby. In this case the return time can be used as a proxy for station participation in an earthquake detection. In California, the Uniform California Earthquake Rupture Forecast v.3 (Field et al., 2014) fault model and earthquake rupture rates can be used to directly estimate return times. Spectral acceleration at 1 Hz gives a related, though less precise, measure and is available throughout the western U.S. The expected value metric is the product of return frequency and the area-time measure, in km2/s. With this metric, relative values of stations or telemetry can be compared in physically meaningful units. The value of redundant telemetry can be calculated in a similar way. We illustrate with stations and telemetry projects in the Southern California Seismic Network. The expected value metric fits the intuition about station coverage. Stations filling modest holes in a network near a high slip rate fault can be as valuable in their expected contribution as stations filling much larger holes near low slip rate faults.