Scaling relation between earthquake magnitude and the departure time from P wave similar growth

We introduce a new scaling relation between earthquake magnitude (M) and a characteristic of initial P wave displacement. By examining Japanese K-NET data averaged in bins partitioned by M_w and hypocentral distance, we demonstrate that the P wave displacement briefly displays similar growth at the onset of rupture and that the departure time (T_dp), which is defined as the time of departure from similarity of the absolute displacement after applying a band-pass filter, correlates with the final M in a range of 4.5 ≤ M_w ≤ 7. The scaling relation between M_w and T_dp implies that useful information on the final M can be derived while the event is still in progress because T_dp occurs before the completion of rupture. We conclude that the scaling relation is important not only for earthquake early warning but also for the source physics of earthquakes.