Relation between Corner Frequency and Seismic Moment for Shallow Earthquakes in Japan

Strong motion records for three groups of shallow earthquakes in Japan (20 Kagoshima events with M_w=3.6 ∼ 6.1, 47 Tottori events with M_w=3.3 ∼ 6.6, and 16 Miyagi events with M_w=3.4 ∼ 6.1) are analyzed to investigate the similarity of earthquakes. A lot of high-quality close-in records at K-NET and KiK-net stations operated by the National Research Institute for Earthquake Science and Disaster Prevention, Japan (NIED) are available for these events. Spectral ratio of transverse component accelerograms observed at the same station is calculated between the largest event and each one of the other events in the same group to remove the station site response and the attenuation effect along the wave propagation path. Spectral ratios at stations around the epicenters of the events are averaged to remove the effect of small differences in the hypocenter location and the focal mechanism. The source spectrum is assumed to have omega-squared decay in the frequency range higher than the corner frequency, f₀. The seismic moment, M₀, determined by NIED is used in this study. Fitting the theoretical source spectral ratio to the observed spectral ratio, f₀ is estimated for each event. The relationship, M₀ ~ f_0^-3, is expected from the similarity of earthquakes. However, the present result shows M₀ ~ f_{0^{-(3+ɛ )}}, where ɛ is positive. Although the location and the focal mechanism of the three groups are different (Kagoshima and Tottori events are strike-slip and Miyagi events are reverse faulting.), the results for the three groups are very similar. The seismic energy is calculated from the estimated source spectra. The energy-to-moment ratio increases with the earthquake size. This scale-dependence is very similar to that found earlier for earthquakes in Southern California.