A Wavelet Analysis of Ground Motion Characteristics

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
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)
TCU031
USGS (C)
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.