Abstract
We decomposed the earthquake motion phase (EMP) into two parts such as a linear delay part and a fluctuation part. Based on the assumption of the identically independent distribution characteristic of phase difference on the fluctuation part of EMP we derived that the EMP should be defined at least as a Brownian motion process. More generally we found that the EMP could be defined as a fractional Brownian motion (fBM) process. A simulated sample earthquake motion phase using the fBM process can represent well several observed earthquake motion characteristics and can simulate a very realistic earthquake time history. The effect of uncertainty of EMP on the earthquake motion amplitude was studied by taking expectation calculus on the uncertainty part of EMP using the probability density distribution function which was derived by considering the fractal characteristics of observed EMP. Based on these analyses the physical meaning to model the EMP by using the fBM process was clearly defined.
