Abstract
The purpose of this research is to make clear the phase spectrum characteristic of earthquake motion. After the introduction of past researches 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 with a constant correlation coefficient. Using several observed earthquake motion we demonstrate this fact and show the efficiency of newly founded result to simulate realistic earthquake motion phase and also compare simulated earthquake motions with those of observed ones. We also simulate design response spectrum compatible earthquake motions by simulating the earthquake motion phase using the identified Hurst index and variance of the given earthquake motion. We investigate the effect of hypocenter distance on the variance and Hurst index of earthquake motion phase, as well as on the mean gradient of earthquake motion phase with respect to the circular frequency.
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