RECENT DEVELOPMENTS IN SYNTHESIS OF EARTHQUAKE MOTIONS USING LINEAR JOINT TIME FREQUENCY ANALYSIS TECHNIQUES

Abstract

Temporal distribution of the frequency contents of a multi-component signal like seismic motions are not captured and well-represented in Fourier Transform (FT) techniques. Linear Joint Time-Frequency Analysis (LJTFA) addresses this issue and can transform and represent a signal in not only time domain and frequency domain, but in time-frequency domain simultaneously. Considering the better resolution and less spectral spillage when compared to Short Time Fourier Transform (STFT) and less complexity when compared to Wavelet Transform (WT), Gabor Transform (GT) is adopted in the current study. Actual recorded time-histories from recording stations in Japan had been considered for a LJTFA based synthesis of earthquake motions in this study considering the high seismicity of the area and large number of data available. Recorded time-histories of 23 earthquakes throughout Japan has been collected from K-Net and Kik-Net Strong Motion Seismograph Network of Japan and is categorized according to various Magnitude and hypocentral distances. Events of magnitude ranging from 5 to 5.5 and hypocentral distances 0 to 100km is sorted and GT is applied to transform the signals to their time-frequency domain and estimate their Gabor amplitude coefficients. Mean Gabor amplitude coefficients are estimated for different Magnitude (M<inf>x</inf>) and Distance (D<inf>y</inf>) combinations like M<inf>5</inf>D<inf>0-25</inf>, M<inf>5</inf>D<inf>25-50</inf>, M<inf>5-5.5</inf>D<inf>0-</inf> 25, and M<inf>5-5.5</inf>D<inf>25-50</inf>. Using an inverse GT process; Gabor Expansion (GE), the mean transformed Gabor amplitude coefficients are used to reconstruct and synthesize a time-history which doesn’t compromise on the quality of their spectral and frequency contents, thus yielding reliable synthetic seismic motions. Response spectra is developed from the actual and synthesized time-histories and are compared. A statistically good fit in terms of the coefficient of determination factor, R2 is observed between the actual and synthetic response spectrum developed. © 2021, International Association for Earthquake Engineering. All rights reserved.