Scaling relation between earthquake magnitude and the departure time from P-wave similar growth: Application to Earthquake Early Warning

The magnitude of an earthquake (M) for earthquake early warning (EEW), is typically estimated from the P-wave displacement using a relation between M and displacement amplitude (that is, a ground motion prediction equation). In the conventional approach the final M cannot be estimated until the peak amplitude is observed. To overcome this technical limitation, we introduce a new scaling relation between M and a characteristic of initial P-wave displacement. We use Japanese K-NET data from 150 events with 4.5 ≤ Mw ≤ 9.0 and hypocentral distance (R) less than 200 km. The data are binned by 0.1 magnitude units and by 25 km in hypocentral distance. We retain bins with at least 5 observations and measure the average of absolute displacement (AAD) in each bin as a function of time. We find that there is no statistical difference in AAD between smaller and larger earthquakes for early times (< 0.2 s), suggesting that the observed P wave begins in a similar way. However, AAD for smaller events departs from the similarity sooner than large events. Consequntly, we define the departure time (Tdp) as the first decrease in absolute displacement after the P onset. For the K-NET data the relation between Mw and Tdp is Mw = 2.29 × logTdp + 5.95 in the magnitude range of 4.5 ≤ Mw ≤ 7. Note that Tdp is much shorter than the typical source duration. This suggests that it is unnecessary to wait for the arrival of the peak amplitude to estimate the final M because the displacement scales with the final M after Tdp. Based on this observation, we derive a new estimator for M based on AAD measurements made up to time Tdp(M). Retrospective application of this equation provides faster determination of M than the conventional approach without loss of accuracy. We conclude that the proposed approach is useful to reduce the blind zone for EEW.