Scaling Law of Earthquake Source Time-Function

Further evidences support the scaling law of far-field seismic spectrum based upon the ω-square model (Aki) for earthquakes with Ms > 6 and for periods T > 10 s. Recent observations, however, unequivocally require the modification of the above law for periods T < 10 s. Unfortunately, the presently available data are not sufficient for a unique revision of the scaling law. We propose two alternatives and discuss their implications and consequences. In either case, we have to conclude that a large earthquake and a small one are substantially different. One interesting feature of the ω-square model appears to be unaffected by the required revision; that is, the spectral density of the fault-slip time-function for periods T < 5 s takes the same absolute value, independent of magnitude, for earthquakes greater than Ms = 6.5. This result has important consequences in earthquake engineering because the seismic motion in the vicinity of an earthquake fault will scale as the fault-slip motion.