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

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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

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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)

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Fourier Transform a 1, w 1 a 3, w 2 a 3, w 3

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Fourier Transform

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Wavelet Transform

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Wavelet Analysis: Evaluation of Coefficients

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Discrete Wavelet Representation a function a j (t) is resolved to several level(j) functions a 0 (t) can be expressed in the following series of detail functions d j (t) Thus, ao a1d1 a2d2 a3d3 ao = a1 + d1 a1 = a2 + d2 a2 = a3 + d3 ao = a3 + d3 + d2 + d1 where, with,

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

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Frequency and period ranges

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Wavelet Analysis of Chi-Chi motion TCU129-N

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Wavelet Coefficients

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Approximations (a j ) and Detatils (d j )

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Fourier Spectra of a 0 and d j

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

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Effect of Site Distance MotionLocation Site Classification Site Condition Closest distance to fault rupture (km) Distance to epicentre (km) TCU078 Nantou Geomatrix or CWB (1) USGS (C) 7.57.1 TCU031 Nantou Geomatrix or CWB (1) USGS (C) 26.7878.3 Alluvial deposit composed of cemented or poorly cemented clay, silty sand and gravel distributed on valleys and alluvial plateau Selected Motions

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Effect of Site Distance

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Selected Motions Wavelet Analysis : Effect of softening

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

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Recorded Computed

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Wavelet Analysis : Effect of softening RecordedComputed

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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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