Rupture Velocities of Small Earthquakes

Whether the rupture process of small earthquakes differs from those of large earthquakes has been a long- standing question in seismology. Recent proposals as to whether and how the physics of rupture may change with earthquake size have sparked interest in the energy budget, which depends strongly on the rupture velocity (Vr). Small earthquake rupture velocities have proved difficult to determine due to the strong attenuation of high-frequency waves. We analyze P and S waves of small earthquakes to detect rupture directivity and constrain Vr. We apply the projected Landweber deconvolution (PLD) method to a data set of 30 earthquakes 3.6<M<4.5 recorded by the HiNet seismic array. We use small aftershocks as empirical Green's functions (EGF) to deconvolve from the main shocks and obtain the relative source time functions (RSTF). The EGF approach removes the effects of complex structure between the earthquakes and the stations. Variation in RSTFs with azimuth yields estimates of Vr for 6 earthquakes from 0.4 to 0.9β. Our results are broadly consistent with those of Yamada and Mori (JGR, 2005) and McGuire (BSSA, 2004). We now explore the implications of the range in Vr for static stress drop (Δσ), and the ratio of radiated energy to seismic moment, which are interrelated. Kanamori and Rivera (BSSA, 2004) discuss how Vr and Δσ must change with earthquake moment, if the ratio of energy to moment ɛ increases with moment, as has been suggested by various studies. There is currently no consensus that such a change in this ratio truly occurs. The increase in the energy-to- moment ratio is controlled by the relation between moment and corner frequency, which has moment inversely proportional to corner frequency raised to the power (3 + ɛ). Data compiled in Kanamori and Rivera suggests ɛ of 0.5. Then Vr of 0.4 to 0.9β for M3 events require that Δσ of M3 events range from 1 to 0.1 respectively, of that of M7 events. More constraints on rupture velocities of small earthquakes will help to resolve possible changes in the energy budget, and thus earthquake physics, with earthquake size.