Analytical representation of phase characteristics for source time function modeled by stochastic impulse train

Abstract

In order to discuss the relationship between the lower and higher frequency components of earthquake source spectra, we deal with impulse train model as source time function of earthquake, because spectral characteristics of source time function depend on occurrence times of impulse function which corresponds to small extent on the fault. Then, the spectral characteristics of source time function are obtained analytically and numerically from the stochastic viewpoints: namely, on one hand, the trend of impulse train dominates the frequency characteristics in low frequency range, and on the other hand, the fluctuation from the trend settles high frequency range. Furthermore, it is shown that the spectral properties of source time function can be determined using only two parameters which are number of impulses n and the probability density function of occurrence time of impulses f T ( t).