Simulation of Earthquake Motion Phase considering Its Fractal and Auto-covariance Features

The earthquake motion phase (EMP) is decomposed into linear delay and fluctuation parts. In this paper, the peculiar stochastic characteristics of the fluctuation part of the phase (FPP) are discussed. First, we show that the FPP has self-afSne similarity and should be expressed as a fractal stochastic process by using several observed earthquake motion time histories, as well as the FPP has a long term memory in the frequency domain. Moreover, the possibility of simulating FPP using the simple fractional Brownian motion (fBm) is discussed and conclude that this is not possible. To overcome this problem, we develop a new stochastic process, the modified fBm that is able to simulate a stochastically rigorous sample FPP. This newly developed algorithm represents the phase characteristics of the observed EMP well.