Abstract
A scaling relation of source spectra is discussed, which is a basis of semi-empirical methods for synthesizing the strong ground motion of a large earthquake from the observed records of small earthquakes. Inhomogeneous displacements on a fault plane may be represented as the distribution of a displacement of a small sub-event multiplied by random variables with a standard deviation of SD. The source spectrum of a large event in very high frequency range is determined by the two key parameters of the source spectrum of a small event and the standard deviation SD, while in the low frequency range it is determined by the seismic moment ratio of the large to the small event. We also obtained the result that the power spectral density of the synthesized waves for the large event is proportional to SD2ΔσE4/3Δσ2/3 in the high frequency range, where ΔσE is the stress drop of the small event and Δσ is the average stress drop in the fault plane of the large event. Another characteristic of strong ground motion is determined by an effect of fault heterogeneity, in which the seismic directivity effect is not shown for the amplitude of the Fourier spectrum of the synthesized waves in the high frequency range. This is consistent with the results obtained by using other stochastic fault models. It is found that the parameter SDΔσE2/3Δσ1/3 corresponds to the local stress drop and/or the rms stress drop of the stochastic fault models. This indicates that the stress drop ΔσE of the small event is an important parameter which determines the heterogeneity of faulting quantitatively, when the strong ground motion due to large earthquake is synthesized by the semi-empirical method.
