ESTIMATION OF FOURIER PHASE BASED ON FOURIER AMPLITUDE OF DIGITIZED EARTHQUAKE GROUND MOTION BY WIENER-LEE TRANSFORM
Kazuo DAN, Takahide Watanabe, Jun Kanda
Abstract
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Kazuo DAN, Takahide Watanabe, Jun Kanda
Abstract
Open-access reader
An approximate representation of Wiener-Lee transform which describes the relation between Fourier amplitudes and phases of the minimum-phase-shift function is introduced in this paper. It is applied to the Fourier amplitudes of the earthquake ground motions to estimate the Fourier phases. The minimum-phase-shift functions are generated by the inverse Fourier transform of the amplitudes and the estimated phases. The results indicate that the complicated acceleration and velocity motions, such as those recorded in the epicentral regions of the 1979 Imperial Valley earthquake (M_L=6.6) or the 1983 Coalinga earthquake (M_L=6. 7), are quite different from the minimum-phase-shift functions. But their aftershock motions, with local magnitude of about 5. are similar to the minimum-chase-shift functions.
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An approximate representation of Wiener-Lee transform which describes the relation between Fourier amplitudes and phases of the minimum-phase-shift function is introduced in this paper. It is applied to the Fourier amplitudes of the earthquake ground motions to estimate the Fourier phases. The minimum-phase-shift functions are generated by the inverse Fourier transform of the amplitudes and the estimated phases. The results indicate that the complicated acceleration and velocity motions, such as those recorded in the epicentral regions of the 1979 Imperial Valley earthquake (M_L=6.6) or the 1983 Coalinga earthquake (M_L=6. 7), are quite different from the minimum-phase-shift functions. But their aftershock motions, with local magnitude of about 5. are similar to the minimum-chase-shift functions.
Key concepts: Fourier transform, Amplitude, Short-time Fourier transform, Phase (matter), Phase correlation, Fourier analysis, Mathematical analysis, Acceleration