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A Wavelet Analysis of Ground Motion Characteristics

A Wavelet Analysis of Ground Motion Characteristics. R. Z. Sarica M. S. Rahman. Outline. Introduction Wavelet transform (WT) vs. Fourier transform (FT) Wavelet analysis of ground motion characteristics (Chi-Chi earthquake motions) Example analysis Effect of distance

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A Wavelet Analysis of Ground Motion Characteristics

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  1. A Wavelet Analysis of Ground Motion Characteristics R. Z. Sarica M. S. Rahman

  2. Outline • Introduction • Wavelet transform (WT) vs. Fourier transform (FT) • Wavelet analysis of ground motion characteristics (Chi-Chi earthquake motions) • Example analysis • Effect of distance • Effect of ‘softening’ • Closure

  3. Introduction • Ground Motion • Time History • Fourier Transform, Response Spectrum • Wavelet Transform • Applications to Geotechnical Earthquake Engineering • Study of Ground Motions • Simulation of Ground Motion • Wavelet domain analysis of site response (Including liquefaction)

  4. Fourier Transform a1, w1 a3, w2 a3, w3

  5. Fourier Transform

  6. Wavelet Transform

  7. Wavelet Analysis: Evaluation of Coefficients

  8. ao = a1 + d1 ao a1 = a2 + d2 a1 d1 a2 = a3 + d3 a2 d2 ao = a3 + d3 + d2 + d1 a3 d3 Discrete Wavelet Representation • a function aj(t) is resolved to several level(j) functions • a0(t) can be expressed in the following series of detail functions dj(t) • Thus, where, with ,

  9. Energy Calculation • Total energy : • Energy density : • Cumulative energy : • Total energy in terms of level cumulative energies : • Frequency range : with

  10. Frequency and period ranges

  11. Wavelet Analysis of Chi-Chi motion TCU129-N

  12. Wavelet Coefficients

  13. Approximations (aj) and Detatils (dj)

  14. Fourier Spectra of a0 and dj

  15. Wavelet Analysis : Energy contents Change this figure Cumulative energy profile normalized wrt the total energy Total energy profile Energy density dEj,k

  16. Effect of Site Distance Selected Motions Closest distance to Distance to fault rupture epicentre Site Classification (km) (km) Motion Location Site Condition Alluvial deposit composed of cemented or poorly cemented clay, silty sand and gravel distributed on valleys and alluvial plateau Geomatrix or CWB (1) USGS (C) TCU078 Nantou 7.5 7.1 Geomatrix or CWB (1) USGS (C) TCU031 Nantou 26.78 78.3

  17. Effect of Site Distance

  18. Effect of Site Distance

  19. Wavelet Analysis : Effect of softening Selected Motions

  20. Wavelet Analysis : Effect of softening

  21. Wavelet Analysis : Effect of softening

  22. Wavelet Analysis : Effect of softening

  23. Wavelet Analysis : Effect of softening

  24. Wavelet Analysis : Effect of softening Computed surface motion (TCU120-Go) Recorded surface motion (TCU110) Computed surface motion with reduced G,(TCU120-Gf) Liquefiable layer Base motion (TCU120)

  25. Wavelet Analysis : Effect of softening Computed Recorded

  26. Wavelet Analysis : Effect of softening Recorded Computed

  27. Closure • Wavelet analysis has been used to study the characteristics of several ground motions recorded during Chi-chi earthquake. • Effect of site distance and site softening has been investigated. Reduction in energy and redistribution of energy contents observed. • Wavelet analysis has potential of providing more insight into ground motion characteristics including the energy content in both frequency and time domain simultaneously.

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