Howard Hwang

Professor

Graduate Institute of Architecture and Sustainable Planning

National Ilan University

Attenuation of Arias Intensity Based on

the Chi-Chi Earthquake Data

Outlines of Presentation

Introduction

Objective of study

Strong-motion data from the Chi-Chi earthquake

Estimation of Arias intensity

Two-step regression analysis

Discussion of regression results

Conclusions

Introduction

Suitable parameter for describing ground shaking?

Peak ground acceleration

Spectral acceleration

Arias intensity

Objective of Study

Develop attenuation relations of Arias intensity for

various site conditions based on the strong-motion

data recorded in the Chi-Chi earthquake.

The Chi-Chi earthquake resulted

from a rupture of the Chelungpu

fault and produced an energetic

aftershock sequence.

ﾊﾚ

Chelungpu Fault

Epicenter of Chi-Chi Earhtquake

N

0 20 40 Kilometers

Date Universal

time

Latitude

(N)

Longitude

(E)

Local magnitude

ML

1999/09/20 14:49:40.07 23.977 120.830 6.07

1999/09/20 17:57:15.58 23.912 121.044 6.44

1999/09/20 18:03:40.83 23.797 120.861 6.60

1999/09/20 18:11:54.21 23.865 121.067 6.70

1999/09/20 18:16:17.95 23.862 121.041 6.66

1999/09/20 21:46:38.11 23.585 120.857 6.59

1999/09/22 00:14:40.77 23.826 121.047 6.80

1999/09/22 00:49:43.45 23.765 121.031 6.20

1999/09/22 12:17:20.96 23.739 120.981 6.00

1999/09/25 23:52:49.51 23.854 121.002 6.80

1999/10/22 02:18:56.90 23.517 120.423 6.40

1999/10/22 03:10:17.46 23.533 120.431 6.00

2000/06/10 18:23:29.45 23.901 121.109 6.70

Large Aftershocks of the Chi-Chi Earthquake

Strong-motion data used in this study are taken

from the mainshock and three large aftershocks of

the Chi-Chi earthquake.

Summary of Four Earthquake Events

Event Mainshock /

aftershock Date Universal time

Focal depth

(km) ML MW

1 Mainshock 1999/09/20 17:47:15.85 8.0 7.3 7.7

2 Aftershock 1999/09/20 18:03:40.83 3.5 6.6 6.2

3 Aftershock 1999/09/22 00:14:40.77 15.6 6.8 6.4

4 Aftershock 1999/09/25 23:52:49.51 9.9 6.8 6.5

With extensive strong-motion stations in Taiwan, strong-

motion data resulting from the mainshock and aftershocks

of the Chi-Chi earthquake are well recorded.

Site Classification of Strong-Motion Stations

Lee et al. (2001) classified strong-motion stations into four site

classes.

Site class B: rock sites

Site class C: sites with very dense soils

Site class D: sites with stiff soils

Site class E: sites with soft soils

The site classes of these strong-motion stations are utilized and

implemented as a GIS data file.

Site class D

(stiff soil sites)

Criteria for Selecting Strong-Motion Data

1. Most digital accelerometers used in Taiwan have a 16-bit or

better resolution. Only one type of digital accelerometer A800

has a 12-bit resolution. In addition, the stations with A800 are

collocated in the stations with A900. The strong-motion data

recorded at 37 stations with A800 accelerometer are excluded.

2. The high peak horizontal acceleration recorded at station

TCU129 is due to the effects of a concrete recording pier. The

strong-motion data recorded at TCU129 are excluded.

3. The site classes of 7 strong-motion stations are not

available. The strong-motion data recorded at these

stations are excluded.

4. The characteristics of strong motion in the hanging

wall area are quite different from those in the footwall

area. These are 13 hanging wall stations within 35 km

from the surface trace of Chelungpu fault. The strong-

motion data recorded at these stations are excluded.

In summary, strong-motion data selected for this study

are from stations located in the footwall area or in the

area away from the fault.

The strong-motion data are separated into four groups

according to site classes B, C, D, and E.

Numbers of Strong-Motion Data in Four Site Classes

Event Number of

selected data

Site class

B

Site class

C

Site class

D

Site class

E

1 387 48 62 177 100

2 316 24 50 151 91

3 367 45 53 170 99

4 356 38 56 166 96

Total 1426 155 221 664 386

Estimation of Arias Intensity (Arias, 1970)

0t

0

2EWEW dt(t)][a

g2

πI

NSEWh III

-300

-200

-100

0

100

200

300

0 15 30 45

Time (sec)

Acce

lera

tio

n (

cm

/se

c/s

ec)

TCU055 E-W Direction

MW = 7.7 R = 6.49 km

Site Class D

Mainshock of Chi-Chi Earthquake

55

-300

-200

-100

0

100

200

300

0 15 30 45

Time (sec)

Acce

lera

tio

n (

cm

/se

c/s

ec)

TCU055 N-S Direction

MW = 7.7 R = 6.49 km

Site Class D

Mainshock of Chi-Chi Earthquake

55

Horizontal Acceleration Time Histories at TCU055

IEW = 1.753 m/sec

INS = 1.524 m/sec

Ih = INS + INS = 3.277 m/sec

GIS Mapping of the Chelungpu Fault

The Chelungpu fault is an east-dipping thrust fault. After

the Chi-Chi earthquake, an approximately 100-km surface

trace of the Chelungpu fault was mapped in detail by the

Central Geological Survey (CGS) of Taiwan. The results

were published in a series of 1:25,000 scale maps.

On the basis of these maps, a digital coverage of the

Chelungpu fault is created using ArcView, a geographic

information system (GIS) software package.

Chelungpu Fault

0 5 10 Kilometers

N

Hanging wall areaFootwall area

Shortest Horizontal Distance

The shortest horizontal distances R of all strong-motion

stations to the surface trace of the Chelungpu fault are

determined using the spatial analysis tools built into

ArcView.

R = 6.49 km

Hanging wall areaFootwall area

Hanging wall area

Footwall area

2/122 )hR(r

h is the focal depth in km.

The source distance r is defined as

Example: TCU055

h = 8 km (Event 1, mainshock)

r = ( 6.492 + 82 )1/2 = 10.30 km

R

h

r

Factors Affecting Arias Intensity

• Seismic source Moment magnitude (MW)

• Path attenuation Source distance ( r )

• Local site condition Site classes B, C, D, and E

Regression Model

For each site class, the regression model for Arias intensity is

ln Ih = a MW + b ln r + c + ε (1)

ε is the random error (residual) and N( 0, σ2 ).

a, b, and c are unknown regression coefficients.

Two-Step Regression Analysis

The two-step regression analysis method proposed by

Joyner and Boore (1981, 1993) is used to derive the

attenuation relation.

Advantage: It decouples the determination of the

magnitude coefficient from the determination of the

distance coefficient.

Using strong-motion data, an attenuation relation of Arias

intensity for each site class is derived.

ln Ih = a MW + b ln r + c + ε

Regression coefficients Site class

a b c σ

B 2.071 -2.178 -8.492 1.29

C 2.290 -1.245 -13.539 1.23

D 2.155 -1.323 -11.920 1.25

E 1.746 -1.585 -7.409 0.82

Attenuation Curves of Arias Intensity for Site Class D

Comparison of Attenuation Curves with

Different Moment Magnitudes

Median Attenuation Curves of Arias Intensity with Four Moment Magnitudes

0.01

0.1

1

10

1 10 100 1000

Shortest Distance to Surface Projection of Fault (km)

Arias I

nte

nsity (

m/s

ec)

ln Ih = 2.155 MW - 1.323 ln r - 11.920 + ε

Site Class D

Focal Depth = 10 km

MW = 7.5

MW = 6.5

MW = 6.0

MW = 7.0

Comparison of Attenuation Curves

for Four Site Classes

Median Attenuation Curves of Arias Intensity for Four Site Classes

0.01

0.1

1

10

1 10 100 1000

Shortest Distance to Surface Projection of Fault (km)

Arias I

nte

nsity (

m/s

ec)

Site Class B

Site Class C

Site Class D

Site Class E

MW = 7

Focal Depth = 10 km

The attenuation curves of Arias intensity for soil sites (site

classes C, D, and E) have a similar shape. The attenuation

curve for sites with soft soils (site class E) has the largest

amplitude and the attenuation curve for sites with very

dense soils (site class C) has the smallest amplitude.

The attenuation curve of Arias intensity for rock sites (site

class B) decreases faster than the curves for soil sites (site

classes C, D, and E).

Conclusions

The attenuation relations of Arias intensity for four site

classes (B, C, D, and E) have been derived based on data

from the Chi-Chi earthquake.

The attenuation relations established in this study can be

used to estimate Arias intensity from a rupture of a thrust

fault for stations located in the footwall area or in the area

away from the fault.