Estimation of rupture speed for the 1995 M_L 4.1 Shacheng,Hebei,China,earthquake sequence based on the minimum radiation energy criterion

From variational principle,we have derived the minimum radiation energy criterion(MREC),and use it in the earthquake source dynamics study.For the 1995 ML 4.1 Shacheng Heibei earthquake sequence,we come to the conclusion that the dynamic rupture processes of main shock and aftershocks are totally different: the rupture speed of the ML 4.1 main shock is about 0.89 of shear wave speed,closing to the Rayleigh wave speed,while the rupture speeds of the remained 28 aftershocks range from 0.05 to 0.55 of shear wave speed,which is much smaller than shear wave speed.In addition,based on the circular crack extending model,we also calculate the seismic radiation efficiencies for this earthquake sequence,and the results indicate that,for most aftershocks,the radiation efficiencies are less than 10%,inferring a low seismic efficiency.In our study,we suggest that the dynamic rupture processes of these aftershocks could be related to the crack(sub-fault) extension inside the main fault,rather than the simple momentum of the moving block,which has been commonly assumed in the fault frictional motion if an overshoot occurs during earthquake rupture.The local stress concentrations inside the fault after main shock may play an important role in sustaining the crack extension.Therefore,the fracturing process associated with the crack extension for the aftershock becomes a main energy dissipation mechanism.Compared with the ML 4.1 main shock,we also find that there exists an essential difference in the earthquake energy partition for the aftershock source dynamics.In other words,the fracture energy dissipation could not be ignored in the source parameter estimation for the earthquake faulting,especially for small earthquakes.Otherwise,the radiated seismic energy could be overestimated or underestimated.