Rapid estimation of earthquake magnitude from the arrival time of the peak high-frequency amplitude

We propose a simple approach to measure earthquake magnitude M using the time difference (T_op) between the body‐wave onset and the arrival time of the peak high‐frequency amplitude in an accelerogram. Measured in this manner, we find that M_w is proportional to 2logT_op for earthquakes 5≤M_w≤7, which is the theoretical proportionality if T_op is proportional to source dimension and stress drop is scale invariant. Using high‐frequency (>2  Hz) data, the root mean square (rms) residual between M_w and M_Top(M estimated from T_op) is approximately 0.5 magnitude units. The rms residuals of the high‐frequency data in passbands between 2 and 16 Hz are uniformly smaller than those obtained from the lower‐frequency data. Top depends weakly on epicentral distance, and this dependence can be ignored for distances <200  km. Retrospective application of this algorithm to the 2011 Tohoku earthquake produces a final magnitude estimate of M 9.0 at 120 s after the origin time. We conclude that T_op of high‐frequency (>2  Hz) accelerograms has value in the context of earthquake early warning for extremely large events.