地震動の位相情報に関する基礎的研究

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書誌事項

タイトル別名
  • A FUNDAMENTAL STUDY ON EXTRACTION OF PHASE-INFORMATION IN EARTHQUAKE MOTIONS
  • 地震動の位相情報に関する基続的例究
  • ジシンドウ ノ イソウ ジョウホウ ニ カンスル キ ゾクテキレイ キュウ

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As it is well known, earthquake motions are nonstationary phenomena whose characteristics vary with the lapse of time, and this nonstationarity has significant influence on the response of structures, especially on their nonstationary behavior. The authors have noticed the close relation between the nonstationarity and phase-characteristics of earthquake motions. The accumulated studies are arranged and summarized in this paper, where two complex valued functions, f^^-(t)=|f^^-(t)|e^<iψ(t)> (complex enveloper) and F^^-(ω)=|F^^-(ω)|e^<-iψ(ω)> (the Fourier transform of f(t)), are used to describe the phase characteistics in earthquake accelerograms, and two corresponding functions, 2πf_<gr>(t)=dψ(t)/dt and t_<gr>(ω)=dφ(ω)/dω, are introduced to extract the phase information. As the results of both theoretical and numerical studies, the following conclusions are obtained : (1) Wasted phase in formation φ(ω) in Fourier analysis of earthquake motions can be well utilized when it is expressed in the differential form t_<gr>(ω). (2) f^^-(t), |f^^-(t)| and f_<gr>(t) in time domain are directly connected to F^^-(ω), |F^^-(ω)| and t_<gr>(ω) in frequency domain. For instance, contributions of |F^^-(ω)|^2 and t_<gr>(ω) on |f^^-(t)|^2 are very similar to those of |f^^-(t)|^2 and f_<gr>(t) on |F^^-(ω)|^2. Existence of |f^^-(t)|^2 and f_<gr>(t), which correspond to |F^^-(ω)|^2 and t_<gr>(ω), can not be found if only f(t) and F(ω) are analyzed. (3) The meanings of the phase functions t_<gr>(ω) and f_<gr(t)> have become clear when the moments of |f^^-(t)|^2 and |F^^-(ω)|^2 are considered as; [numerical formula] Accordingly, the mean value of t_<gr>(ω) weighted by |F^^-(ω)^2| indicates the center of gravity of |f^^-(t)|^2, and the mean value of f_<gr>(t) weighted by |f(t)|^2 indicates the center of gravity of |F^^-(ω)|^2. Moreover, the variance of t_<gr>(ω) weighted by |F^^-(ω)|^2 is related to the width of |f^^-(t)|^2, and the variance of f_<gr>(t) weighted by |F^^-(ω)|^2 is related to the width of |f^^-(t)|^2, and the variance of f_<gr>(t) weighted by |f^^-(t)|^2 is related to the width of |F^^-(ω)|^2. (4) If we divide each domain into several parts and consider the nature of the f_<gr>(t) and t_<gr>(ω) fluctuations for each part, we can obtain information on the spectral changes with time and nonstationary characteristies of waves in each frequency part. Thus, the nonstationarities in earthquake acceleration records can easily be examined with their phase inclinations t_<gr>(ω) and f_<gr>(t). Therefore, it is possible to say that t_<gr>(ω) and f_<gr>(t) are good mathematical tools to describe the nonstationarity of seismic accelerograms.

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