STOCHASTIC CHARACTERISTICS OF FOURIER AMPLITUDE IN OBSERVED EARTHQUAKE MOTIONS

Abstract

 We investigated the stochastic characteristics of Fourier amplitude of observed earthquake motion which is assumed to be a stochastic process in the circular frequency domain. First we extracted the nonstationary characteristic of Fourier amplitude by calculating a smoothed Fourier amplitude using Parzen window filter. Dividing the Fourier amplitude by this smoothed one we could standardize the Fourier amplitude. The main theme of this paper was to discuss the stochastic characteristic of this standardized Fourier amplitude. We investigated the variance of the incremental difference of this standardized Fourier amplitude with different circular frequency interval and obtained that the variance was expressed as a power function of circular frequency interval. Based on this result we defined the normalized standard Fourier amplitude inclement by dividing the standard Fourier amplitude increment with respect to the circular frequency interval. We found that the probability distribution characteristic of this increment could be modeled by the truncated Levy distribution. Because this distribution possesses the stable nature we discussed a possibility developing an algorithm to generate a Fourier amplitude process as a stochastic process.