Abstract
The purpose of this research is to make clear the physical characteristics of earthquake motion phase. Using stochastic characteristic of group delay time calculated from observed earthquake motions we developed stochastic simulation models of earthquake motion phase spectrum. Taking into account the fact that the phase characteristic is controlled by fault rupture process and the randomness of wave propagation medium we introduce the Hurst index to evaluate these characteristics based on the fractal theory. Using not only observed earthquake motions but also the simulation results of shear phenomena of particle assembled mediums as well as experimental results of ultrasonic wave propagation in grass bead embedded mortar specimens we confirm the efficiency of proposed method to grasp the fractal characteristic of earthquake motion phase. To simulate earthquake motion phase we introduce the concept of fractional Brownian process (FBP). A simple method is proposed to determine the Hurst index and the variance of a given process characterized by the FBP. We find that the phase characteristic of earthquake motion can be expressed by this process which is a non-stationery function of the circular frequency. Using several observed earthquake motion we demonstrate this fact and show the efficiency of newly founded result to simulate realistic earthquake motion phase.
