Using τc to estimate magnitude for earthquake early warning and effects of near-field terms

This paper analyzes strong motion records of 24 large earthquakes to investigate the relationship between tau(c) (the period parameter of the first motion) and moment magnitude. The records of some of the large-magnitude events very close to the source include large near-field terms. Therefore, if we include the data with large near-field terms, we may overestimate the final size of the magnitude. We identified records with large near-field terms and did not include these data in processing the records to compute tau(c) for each event. Our analysis shows that the value of tau(c) is between the earthquake corner period and the period determined by the record duration tau(0). If the magnitude is less than 6, tau(c) closely approximates the corner period, whereas tau(c) for larger earthquakes depends on the rupture process and location of asperity. tau(c) for large earthquakes provides a lower bound on the event magnitude and approaches the corner period if a longer record is used. We also propose a method to classify the records with and without large near-field terms. If the peak displacement amplitude for the first 3 s (Pd3) exceeds 1 cm and tau(c) exceeds 2 s, the record is more likely to include large near-field terms. For the purpose of quick onsite warnings, stations observing large near-field terms provide valuable information. Large near-field terms can be observed only if the magnitude is large and the epicentral distance is small. Therefore, if the displacement exceeds a threshold (e.g., Pd = 0.5 cm), the ground motion at the site would likely become very large. This criterion will help to issue warnings to the blind zone, which is the region where there is insufficient time to issue a warning before the strong shaking arrives.