波形合成法による1979年インペリアルバレー地震の震央域における強震地動の推定

(1)

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s",ra,,figi}refix,th,N.ra;.:

SIMULATION

AND

PREDICTION

OF

STRONG

GROUND

'

MOTION

IN

EPICENTRAL

REGION

OF

THE

1979

IMPERIAL

VALLEY

EARTHQUAKE

BY

SEMI-EMPIRICAL

METHOD

by

KAZUO

DAN",

TEIJI

TANAKA*'

and

TAKAHIDE

WATANABE"",

Members

of

A.I.J.

1. Introduction

Estimation

of earthquake

_ground

motlons

in

the

near-field,

in

spite

of

the,

fact

that

there

have

behn

few

accelerograms recorded

there,

is

an

important

subject since

it

provides

better

_guidelines

in

earthquake resistant structural

design.

Especially,

a shallow close-by earthquake with a magnitude

of

about

6.'5,

similar

to

the

1979

'

Imperial

Valiey

earthquake,

is

a

typical

earthguake considered

in

structural

design

of

nuclear

poweT

plants

in

Japan.

Since

Hartzell's

work

(1978)",

a

semi-empirical

method

to

simulate

_ground

motions

during

a

large

earthquake

by

utilizing records

for

small

events

as

Green's

functions

has

been

applied

by

many'reseafchers

such

as

Kanamori

(197g)*Z,

Hadley

&

Helmberger

(1980)'3,

Imagawa

&

Mikumo

_(1982>'`,

Tanaka

et al.

(1982)'5,

Irikura

(1983)'G,

Iida

&

Hakuno

<1984>"

and so on,

First,

in

this

_paper,

Tanaka

et al, 's method

has

been

modified consistently with

the

a,-square

rnodel

proposed

by

Aki

_(1967)'S

and

the

acceleration

ground

motions

for

the

₁₉₇₉

Imperial

Valley

earthquake

have

been

simttlated

by

synthesizing

the

aftershock records.

The

purpose

of

this

study

is

to

$how

the

applicability

of

this

method

to

epicentral

regions.

Second,

this

modified method

has

been

applied

to

the

_probLem

in

which records

for

small

events

are

not

available.

Instead

of

the

aftershock records, an artificially-computed accelerogram with reliable

averaged

characteristics of

earthquake

motions

has

been

synthesized as

Green's

function

to

_predict

the

main-shock

_ground

motions.

The

prediction

has

been

performed

by

considering

the

amplification

factors

of surface

layering.

'

2. The

1979

lmperial

Valiey

Earthquake

On

October

15,

1979,

the

largest

earthquake

in

Califor'nia

in

the

past

decade

occurred oll

the

Imperial

fault

near

the

United

States-Mexican

berder.

Aceording

to

the

U.S.

GeoLogical

Survey,

the

locql-magnitude

6,6

event, whose

epicenter was

located

in

northern

Mexico,

damaged

structures

in

and around

the

town

of

El

Centro,

California,

and was accompanied

by

surface movement on

four

fault

zones.

The

earthquake caused an estimated

$21,1

million

in

damage

and

injured

73 _people,

but

no

deaths

were reported

in

the

United

States.

The

eafthquake

and

its

aftershocks occurred

in

a region

that

has

experienced several similar-size earthquakes

in

the

recent

historical

_past,

including

the

well-known

local-magnitude

6.

4

earthquake near

El

CentTo

on

May

18,

1940.

A

total

of

22 USGS

strong-motion accelerograph stations was

in

operation

in

the

epicentral

region

during

the

main

shock

of

October

15 (23

h

16m

54.

29 s

G.

M.

T.

,

M,=6.

6).

Peak

horizontal

accelerations

greater

than

O.

5 g

were measured at seven stations within

le

km

of

the

ruptured

Imperial

fault.

The

USGS

Imperial

Valley

accelerograph network also recorded many aftershocks,

i.

e.

, more

than

260

aftershook records were obtained at

21

stations within

30 km

of

the

main-shock ruptured

fault,

An

aftershock

that

occurred

right after

the

main shock near

the

ruptured

fault

*

_Ohsaki

_Research

_Institute,

_Shimizu

_{Constructioll}

Co.,

Ltd,

M.Eng.

"

Ohsaki

Reseaich

Institute,

Shimizu

Constructien

Co.,

Ltd.

Dr.

Sc.

iii

Ohsaki

Research

Institute,

Shirnizu

Construction

Co.,

Ltd,

Dr.

Eng.

Note

:

Some

_parts

of

this

_paper

were

presented

at the

23

[d

_general

assernbLy ef

IASPEI

(International

Assoc;ation

of

Seismology

and

Physics

of

the

Earth's

Interior)

in

1985.

{Manuscript

received

May

26, 1986)

(2)

-50-Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute of Japan

Fig.1

Location

of

the

faults

and

the

stTong-motion stations

The

stai

in

the

lower

right

hand

corner

is

theepicenter ef

the

main shock and

the

solid circle

in

the

middle

is

the

epicenteT of the aftershock.

The

lines

are

the

Imperial

fault

traces.

The

pluses

indicate

15

strong-motien

sta-tions

that

recorded

the

accelerograms

during

the

rnain sheck and

the

aftershock.

These

are

the

locations

where we

have

simulated the mainsheck accelerograms

in

this study,

Data

points

were

taken

by

Thatcher

&

Hanks

(1973).

8765432119

20.

21

22

23

24

25

26 (a)

ML

vs.

IogM,

[dyne-cm]

Data

points

were

taken

by

Geller

{1976].

3

2

1 o

24 ₂₅

₂₆

₂₇

₂₈

₂₉

₃₀

(b)

logL[km]

vs,

IQgM,

[dyne･crn]

Data

points

were

taken

by

Geller

(1976).

3

27

2 1o24

31 Fig.2

25

26

27

28

29

30

31 (c)

logW

[km]

vs.

Iogua

[dyne･cm]

Similarity

relations

tietween

ML,

L,

W

and

Mi

(23h

19m

29.98s,

ML=5.2}

trigggred

accelerographs

at

16 stations,

the

_great

number ever

triggered

by

a single

aftershock,

This

data

set

contains

the

most comprehensive collection

of

near-field accelerograms

ever

recorded

in

the

world.

3. Size

and

Location

ct

the

Fault

Model

Figure

1 shows

the

locations

of

the

fault

traces

and

the

strong-motion

stations'.

The

star

in

the

lower

right

hand

corneris

the

epicenter

of

the

main

shock

(

M,=6.

6,

long,

115"18.

53'W.

_,

lat,

_32038.

_61'N,

,

focal

depth

of

10 km)

and

the

solid circle

in

the

iniddle

is

the

epicenter

of

the

afteTshock

(M,=s.

2,

long,

115e25.

6'W,,

lat.

_32e46,s'N.,

focal

depth

of

_10.5km)

meqtioned above.

The

lines

'are

Imperial

fault

traces,

The

_plttses

indicate

15

strong-motion

stations

that

recorded

the

accelerograms

during

the

main

shock

and

the

aftershock.

These'are

the

locations

_where

_we

have

simulated

the

main-shock accelerograms

in

this

study.

.

First,

we

determined

the

sizes of

the

fault

models

for

the

main shock and

the

aftershock,

based

on similarity

relations of source

_parameters

initially

suggested

by

Kanamori

&

Anderson

(1975)'9.

Figure

2 (a)

shows

the

relation

between

the

seismic

moment

and

the

local

magnitude

taken

by

Thacher

&

tianks

(1973)'iO,

Figures2(b)

and

(c)

show

the

retations of

the

seismic mornent and

the

fault

rupture

length

and width, respectively,

taken

by

Gellei

{1976>']'.

According

to

Figure

2,

following

empirical equations obtained

by

Thatcher

&

Hanks

_(lg73)'iO

and

Muramatsu

&

Irikura

(1980'i2

could iepresent

the

relations of

local

magnitude

M.

and

fault

rupture

length

L

_{and width}

W

_in

_km

_to

_the

_seismic _moment

_Mh

_in

_dyne･cm

_{with sufficient}

_accuracy.

IogMo=1.5ML+16.0

'

(1)

logL=1131ogMo-7.3

(2)

IogW=

1131ogM6-7.6

(3)

'

(3)

-51-Fig.3

Su[face

projection

ef

the

fault

plane

Approximate

fault

rupture

length

and width are

2o

km

and

10km,

respectively, and

the

dip

angle

is

s2eE,

-Station

Fig.4

Fault

medel

for

synthesis

Since

the

local

magnitude of

the

main sheck

is

6. 6,

it

corresponds

to

a seismic moment of

7.9

×

102S

dyne･cm,

which

is

generaily

equaL

to

7

×

1025

dyne･cm

estimated

by

Kanamori

&

Regan

(1982}'i3

from

Rayleigh

waves at

200 to

2so

second observed at seven

IDA

(International

Deployment

of

Accelerometers)

stations.

Approximate

fault

rupture

length

of

20 km

and width of

10km

are obtained

based

on

thi$

seismic moment.

In

tbe

case of

the

aftersheck with

a

local

magnitude of

5,

2 the

corresponding seismic moment

is

6.

3

×

1023

dyne

･

cm,

and

the

fault

rupture

length

of

4km

and

width of

2km

are approxirnated

by

extending

the

solid

lines

in

FiguresZ(b)

and

<c),

respectively.

By

placing

the

hypocenter

of

the

main shock on

the

lower

end of

the

fault

plane,

a

dip

angle

of

82"E

is

ebtained.

The

rectangle

'in

Figure

3 is

the

assumed

fault

model

for

the

main shock

_projected

on

the

ground

surface.

On

the

other

hand,

the

dislocation

distribution

on

the

fault

_plane

of

the

main shock

has

been

well

investigated

by

several researchers.

The

followings

are some of

these

studies

in

which

the

researchers used

the

strong-motion

accelerograms.

Hartzell

&

Helmberger

(lg82)"'`

_preferred

a

fault

model which

had

slip concentrated at

depth

of about

4-10km

and

between

Okm

and

24 krn

north of

the

epicenter

from

12 integrated

strong-motion

displacement

records.

Olson

&

Apsel

(1982)"S

estimated a

_peak

offset at

depth

of

5-10km

and

between

15 km

and

2o

km

north of

the

epicenter

from

26

strong-motion acceleration records

band-passed

from

3 to

10

second,

Hartzell

&

Heaton

(19s3)'i`

estimated

dislocation

distTibution

concentrated

at

depth

of about

5-10km

and

b,etween

5km

and

28km

north of

the

epicenter

from

12 integrated

strong-motion velocity records

band-passed

from

1 to

10

second.

These

researchers used a

discrete

wavenumbeTlfinite element

technique

to

get

the

Green's

functions.,

Fujino

et

al,

(1984)'i'

found,

by

using

distinct

_phases

of

the

accelerograms recorded at

32

streng-motion

stations,

that

the

earthquake

had

been

a multiple event with

three

smaller eVents

in

the

period

of

Iess

than

1 to

Z

second and

that

the

main

energy

of

this

_period

"ange

had

been

released

from

a

localized

area about

O

to

24 km

north of

the

epicenter.

Although

it

is

very

important

to

establish a

detailed

fault

model

te

simulate

_ground

motions

in

epicentral regions,

we

have

adopted

a uniform

fault

model shown

in

Figure

3

as an averaged

one

which roughly corresponds

to

the

region of energy release of

high

frequencies

investigated

by

Fujino

et al.

4. Synthesis

Method

Irikura

_(1983)'S,

based

on

scaling

relations of

the

source

parameters,

simulated main-shock velocity _motions

by

utilizing aftershock records as

Green's

functions,

in

which superpositions were made on

three

_parameters

of

fault

rupture

length,

width and

dislocation

rise-time.

Tanaka

et

al.

(1982)'5,

considering only

the

difference

of

the

fault

(4)

-52-Architectural Institute of Japan

NII-Electronic Library Service

areas

between

the

main

shock

and

the

aftershock

to

avoid

the

ghost

peak,

simulated

main-shock

accelerations

by

'

equation

(4

),

which represents

the

weighted

and

_{phase-delayed}

summation

over

the

aftershock records,

'

u{t)-i;.i.z,(it)･uatt-t,n

(4)

l(i-O.5)L/ne'+l(j-O.5)Wlnl'

r"

t"=

+

v c

Here

u.(

t)

is

an aftershock acceleration record,

r.

is

the

aftershock

hypocentral

distance,

r.

is

the

distance

between

the

site and

the

(

i,

_J')

element of

the

fault

_plane

for

the

main shock.

L

and

W

are

the

fault

rupture

length

and width of

the

main shock,

v

is

the

rupture velocity, c

is

the

wave velocity and

n

is

the

square root of

fault

area ratio

between

the

main shock and

the

aftershock.

n

is

also

described

as

the

cubic root of seismic moment ratio

between

the

main

'

shock and

the

aftershock

in

Irikura's

method.

'

As

Irikttra

(1986}'i8

pointed

out,

equation

(

4 }

by

Tanaka

et al,

is

consistent

_･/

in'

high-frequencies

_･

with

the

w-square model

initially

_proposed

by

Aki

(1967)'S.

In

the

w-square model,

the

displacement

spectrum,

9(w),

is

described

by

9(O)

9(w)=

<5)

1+[wl

ai,]2

'

Here

9(O)=M,F14

rrrloe, tuo

is

the

corner circular

frequency,

ua

is

the

seismic

moment,

F

is

_the

double-couple

radiation

_pattern

for

SH

or

SV

waves,

r

is

the

distance

from

the

_point

source

to

the

site,

_"

is

the

shear

modulus

(rigidity)

of elastic mediurn, and

P

is

the

shear wave velocity of

the

medium,

Given

_the

shape

of

displacerpent

spectrum

by

the

to-square model,

the

shape of

the

acceleration

spectrum,

A(w),

is

obtained

by

9{O)･w:

A(tu)=

{6)

1+[a,,1to]''

,

A(to)

converges

into

9(O).a)S

when _to

is

large

enough,

9(O)

is

_proportional

to

the

seismic moment

an

defined

by

pt.D.S,

where

D

is

the

averaged

final

slip and

S

is

the

area of

the

fault

_plane.

a),

is

_proportional

to

BIA,

where

Ais

the

characteristic

length

which

describes

the

size ef

the

source

(Papageorgiou

&

Aki,l983)'i'.

Thus

9(O),a,:

is

proportional

to

A,

vXS' or

MafS

and we obtain

the

relationship

that

the

ratio of

the

acceleration spectrum

in

high

frequencies

between

the

main shock and

the

aftershock

is

equal

to

the

cubic' rootof

the

seismic moment Tatio

between

two

of

them.

This

relationship makes sense on

the

assumption

that

the

double-couple

radiation

_pattern,

F,

and

the

distance

･from

_the

_point

source

to

the

site,

r,

for

the

main shock are same as

those

for

_the

afteTshock.

On

the

other

hand,

accoiding

to

the

random vibration

theory,

when waves of

high-frequency

components

are

superposed

n2

times

randomly

in

time

dornain,

the

expected amplitudes of

the

waves

become

_n

times.

_Consequently

the

high-frequency

_ground

motionS

during

the

main shock can

be

simulated

by

superposing

the

record of

the

aftershock

n'

times,

where

n

is

the

cubic root of

the

seismic momept ratio

between

the

main

shock

and

the

aftershock.

Since

the

low-frequency

components simulated

by

equation

(

4 )

are underestimated

because

of

lack

of

the

seismic

moment,

Tanaka

et

al,

restricted

the

application of

their

method only

to

the

synthesis

of

the

accelerograms

with

high

frequencies.

Let

Tanaka

et

al.

's synthesized motion

be

u{t)

and assume a ramp source

time

function

to

preserve

the

seismic

moment,

then

the

motion with as much a seismic moment as

that

of

the

main

shock,

f(t},

is

written

as

"-1

f(t)=

£

u(t-hTb).

_.

(7)

k;O

'

Its

Fourier

transform

_pair,

F(w),

is

obtained

by

'

F(co):::.IC::a.lu(t-ktlt)exp[-iwt]dt

-u(a,}･

.Si."

l."'Ei!>2,]]

･exp[-

`O

(,:-Td}

],

(s)

'where

i--A,

U(tu)

is

the

Fourier

transform

_pair

to

u(t),

r

is

the

rise

time

of

the

main shock and Tz,

[

=Tln]

is

the

rise

time

of

the

aftershock.

(5)

We

find

out

the

difference

between

_U(to)

and

F(to)

to

be

.sln[[.a)E:li22]]･..p[-ia'ST-TO].

'

(g)

Fermula

₍

g

)

was also

described

by

Imagawa

&

Mikumo

(1982)'`.

Since

formula

(

9 )

is

unity without any

_phase

shift at aj!4 nl(T-

ta)

for

any

integer

n

larger

than

2,

we

choose

4

rr1(r-

T.)

as

the

boundary

_point

between

low

and

high

frequencies,

Actual

computation

was

_performed

in

the

following

manner.

Since

the

fault

_plane

for

the

main

shock

is

2okm

×

lokm

and

that

for

the

aftershock

is

4kmx2km,

we

divided

the

fault

plane

into

5

×

5

small elements, as shown

in

Figure

4,

and

the

aftershock was applied each element as, a

_point

source.

The

modification

of

the

aftershock

records

by

formula

(

₉

)

was carried out

for

frequencies

below

_2.

₅

Hz,

because

we assumed T of

1

second and

_T.

of

O,

2

second.

Subsequently,

the

modified aftershock records were summed up

by

equation

(

4 )

in

time

domain

considering only

the

difference

of

the

fault

area

as

Tanaka

et al.

did.

In

equation

(

4 )

,

the

difference

of

the

radiation

pattern

is

ignored

and

difference

of

the

distance

is

corrected

by

the

attenuation of

the

body

waves,

Since

the

main-shock accelerograms

had

been

band-passed

with ramp

functions

from

O.

03 to

O.

17 Hz

and

from

23 to

2sHz,

and

the

aftershock accelerograms

had

been

high-passed

with

a

Butterworth

filter

(n!!4,

fU==O.5Hz),

we

processed

the

main-shock accelerograms with

the

sarne

Butterworth

high-pass

filter,

and

the

aftershock accelbrograms with

the

same

band-pass

filter,

After

examining

the

results

by

changing

the

rupture

velocity v

from

2.

0 to

2.

7 kmls

with an

increment

of

O,

1 kmls,

we adopted

v

as

2.1kmls.

Here,

the

shear wave velocity

6

was assumed

to

be

3,3kmls.

5. Results

Using

Aftershock

Records

Three

of

the

results

for

the

15

strong-motion

stations

are

_presented

in

detail.

Figure

5 is

the

result of simulation at

El

Centro

Array

No.

3 (E

03 in

Figure

3)

with

(a)

as

the

modified aftershock

accelerogram

with

the

_peak

value of

127 Gal,

{b)

the

synthesized and

(c>

the

observed accelerograms.

Although

we could not simulate

the

two

wave-groups

found

in

the

observed accelerogram, we

ceuld

successfully

simulate

the

_peak

value

of

abeut

270Gal,

duration

time

and waves with

_predominant

frequency.

Figure

6 shows

the

velocity response spectra with a

damping

factor

h

of

O. 05,

They

represent

the

seismic wave

energy

which should

be

applied

to

astructure.

In

this

discu$sion,

we

focus

our

attentionon

a

range

of

natural

_periods

limited

between

o.

os

to

_1.

₀

second.

The

solid

line

is

a velocity response $pectrum

for

the

$ynthesized motion and

the

detted

line

for

the

observed.

The

velocity response spectrum

is

found

to

be

simulated

pretty

well.

,

Figure

7 is

the

simulated motion at

Bonds

Corner

(BCR

in

Figure

3)

which

is

located

close

to

the

modeled

fault

plane

and

to

the

epicenter

where

<a),

(b)

and

(c)

are again

the

modified aftershock,

the

synthesized and

the

observed accelerograms.

The

simulation of

the

intensity

and

the

envelope of

the

motion

is

_good,

and

the

error

of

the

peak

value

is

only

6%.

Figure8

is

the

corresponding result of velocity

response

spectra.

Figure9

shows

the

simulation

at

Calexico

{CXO

in

Figure

3).

As

shown,

the

synthesized motion simulates

the

actual motion

in

detail,

Figure

10 is

the

velocity response spectra

for

the

motions

in

Figure

9. They

correspond

quite

well with each other.

Results

fgr

30 horizontal

components

at

the

15

strong-motion stations are summarized

in

Figure

11 as

the

peak

accelerations,

and

in

Figure

12

as

the

spectral

intensity

in

the

natural

_periods

of

O. os-1.

o

second with a

damping

factor

of

O.

05. In

the

figures,

the

horizontal

axis

is

the

observed motions and

the

vertigal axis

is

the

synthesized motions, respectively,

The

band,

limited

by

two

straight

lines,

indicates'the

region within an error of

30%.

As

to

the

_peak

acceleiations, about

80 %

of

the

total

is

included

in

the

band.

As

to

the

spectraL

intensity,

about

7e

%

of

the

total

falls

the

bounded

area.

From

these

results, as awhole, we can conclude

that

the

present

synthesis

method

is

powerful

enough

to

simulate acceleration

_giound

motions

in

epicentral

regions.

However,

we notice

here

that

some of

the

values

for

the

synthesized

moEions

in

Figures11

and

12 differ

considerably

from

those

for

the

obseved ones, ancl

that,

to

improve

these

resillts,

it

shoulcl

be

necessary

to

establish

a

more

detailed

fault

model with

localized

energy release zenes as

Hartzell

&

Helmberger

(1982)

and other researchers

(6)

proposed.-54-Architectural Institute of Japan

NII-Electronic Library Service

Architectural Institute of Japan

3oo.Goat

(a)

o.o

-300.0

3oo

.Goat

TsoD･8,,

3DO.O

{c)

o,o

ModifiedafLershockaccelerograrn

Synthesizedaceeleregram

Observedaceelerogrnrn

'

ii

t

Peak

Aee.

121416

127Gal

268Gal

272Gal

(sec)L8

2D

'

Gal

800.0 (a)

o.D

-eoo.D

Gat

eDo.o

(b)

o,o-SOD.O

Set

BOO.D

(c)

o.e

-eao,o

Gal'

300.0 (a)

o.o

-aeo.o

Gal

300,0

(b)e,o

-soo.o

Gat

300.0 {c)

o,O

-100.D

Fig.5

Accelerograms

at

El

Centro

Modifiedafterghockaccelerogram

ArrayNo.3

(i4oO)

Peak

_"cc.

101Gal

Synthesizedaccelerogram

8e5Ga]

1

ram

i"

O 2' 4 6 8'le12t4

758Ga]

(sec]

16'

l8

20

Fig.7

Accelerograms

at

Bonds

Modifiedaftershockaceelerogram

Corner{23o")

Peak

Aec.

67Ga]

Synthesizedaccelerogram

op

Observedaccelerogram

2o

46 WMmp

34SGal

261Gal

e10

t

w

121416

(see)ZB

EO

Fig9

Accelerograms

at

Calexico(22sO>

soo,o

s

20e,o,E=v

100,OE6

so.Dath$

20.0:aan

10.0eb

s.o'8g>

2,O

1,O

O.5

O.05

O.1 O,2

O.5 l.O

Natura]period(sec)

Fig.6

Velocity

response spectra

for

El

Centro

Array

No.3

500.0 T

200.0rtYwri

100.0eG

so.o:aZ

20.og8

10.oLe"

s.o'5Rtu>'

2.0

1.0

O.5

O.05

O.1 O,2

O.S

!,O

Natural

period

(sec)

Fig.8

Velocity

response $pectra

foT

Bonds

Corner

50D.D

-

200.Btu.E.X

100.DLge

so.Dgezz

20.0gnm

to.o2b

s.o'sRo>

2.0

1.0

D.5

O.05

O.1 O,2

O.5

t,O

Natural

period

(sec)

Fi'g.10

Velocity

response spectra

fer

Calexico

'

NII-Electronic Mbrary l

_iig

h=O.05'

Obs.

SN--.T-F7-m

'

tt-tt

'

::-"t".'s'.ttt":Syn. 'r.t'"t

Obs.h=o.05----.-s:'s,:t-.t:"'t-t

fi･H...v':S

y-:t::t"':.:

Syn.

'ts'tt,

1

h=O.05

Syn."t--tL

tt:vt-tt-v"::

t-Is"

･t

t.:'.rr.Obs.

(7)

:';-:.-.':t-1000.0

loo,a

Syn.(Gal}

'+30%o

o0

oeO

.30%

o

Obs.(Gal}

loo,o

leoo.o

Fig.11

Syntbesized

vs. observed

Peak

accelerations

100,O

to.o

Syn.(kine･sec)

:

_o

-

'+30%

o

L-3e%

rObs.(kine･sec)'

10.0

100.0

Hg.12

Synthesized

vs. observed

Spectral

intenslty

6. Generation

of

an

Artificially-Computed

Accelerogram

In

practical

prediction

problems

in

the

field

of earthquake resistant structural

design,

appropriate observed

record$

to

be

used as

Green's

fun6tions

are

not

always

available.

Therefore,

we

have

tried

to

use an artificially-computed

accelerogram with reliable

averaged

characteristics of real earthquake motions as

Green's

function,

instead

of

the

observed afteTshock records.

For

the

_present

case,

the

observed

accelerograms

from

earthquakes

in

the

ImpeTial

Valley

district

would

be

'

preferred

to

obtain

the

reliable

averaged

characteristics

for

an artificially-computed accelerogram,

Since

our

accelerogram

data

base

is

limited,

however,

we substituted

the

recoTds observed

in

Japan

for

them,

and examined whether

it

is

_possible

or not

to

use

the

records

in

Japan

for

_prediction

of

strong

motions

in

the

Imperial

Valley

t/

district.

We

used

the

accelerograms recorded on

the

outcrop

to

aveid

the

effect of surface

layering

which might

'

contribute

to

amplify

high-frequency

components of earthquake

ground

motions, and considered

later

the

effect

of

'

surface

layering

at

each

observation

station.

The

actual computation was carried out

ln

the

following

manner,

First,

we

_prepared

adata

base

of

14 horizontal

'

components of accelerograms

from

7 earthquakes,

giv.en

in

Tabie1,

whose seismic rnagnitude

is

around

s,

with epicentral

distances

of

4 to

30 km.

Neglecting

the

depth

parameter,

we normalized

these

records

to

represent a

motion

at an epicentral

distance

of

15 km

using attenuation of

the

body

waves.

After

evaluating velocity response spectrum

for

each

normalized accelerogram, we averaged

them

with

the

result shown as

the

solid

line

in

Figure

13. We

finally

generated

an

artificial

acceleTogram

for

a

M=5.

2

event

in

Figure

14,

to

fit

the

aVeraged

velocity

response

spectrum

with an envelope

function

for

the

shallow shock motibn close

to

the

fault

with

aseismic

magnitude

of

4 or

5 proposed

by

Jennings

et

al.

0968)"20.

The

dotted

line

in

Figure

13

shows

the

for

the

generated

accelerogram.

7. 'Resuets

Using

an

Artificially-Computed

Accelerogram

Since

the

artificially-computed

accelerogram

in

Figure

14 is

defined

on

the

ointcrop.

the

effe,ct

of surface-iayering

should

be

considered

nexL

Porcella's

underground structural models

(1984}'!i

were

used

to

account

for

the

soil

amplifications

at each station,

Tables

2,

3

and

4

are

the

underground

structural models

for

El

Centro

Array

No.

3 (Eo3),

Bonds

Corner

(BCR)

and

Brawley

(BRA),

respectiyely.

Here

the

damping

factor

h[==ll2Q]

was

calculated

by

assuming

that

_Q

is

one

fifteenth

of

the

sheai wave yelo6ity

in

m!s.

Soil

amplification

factors

are

'

evaluated

by

the

one

dimensional

shear

wave

_propagation

theory

(Schnabel

et

al.,

1972)*2Z.

Figure

15 is

the

result of

_prediction

at

El

Centro

Array

No.

3

where

(a)

is

the

synthesized accelerogram,

(b)

and

(c)

are

the

observed

230"

and

14oO

components of

the

main-shock motion, respectively.

Peak

values,

duration

times

and waves with

_predominant

frequency

are simulated well.

(8)

-56-Architectural Institute of Japan

NII-Electronic Library Service

ArchitecturalInstitute ofJapan

Table1Data

of earthquakes ebtain

the

averagedand

accelerograms used to yelocity respense spectrum

Magr!itudeEpicentral

distance(krn)

Peakacceleration(Gal)

tsTS

EW

5.3

15

64.4

68.0 5,3

12

81.8

102.8

5.4

4 204.2402.5

4.7

6 220,5

87.8

4.5

6 286,8

89.6 '4.9

₅

_157.6218.4

4.8

30

25.2 27.e

50,O

6=

2D,O..-x

_'

N--Nts8 lo.ok$g

5,Dfifl

h･--uS

2.0

di>1,O

O,5

O.05 I

h=O.05

Generated

i

."1./---'

[I

""

't-s

".-"

:..N.

1 Averaged

'-t-t

1Jx

:I

Fig.13

Gtl70.0 o,o

-70.0

0.1 O,2

O.5 Natural

period

(sec)

Averaged

o

wti

12

w

3 LO

ltfiWtwVuaVwhStwVMpmtw.

4s67B

(sec)

9 10

11 Table2

Seilprofile

at

ElCentro

Array

No,3

Depth(rn)Thickness(m)

UnitweSght(Vm3)

Swavevelocity(Tn/s)

Dampingfactorh(%}

O.O-5.05.0

2,O

115

6.5 5,e-25.020.0

2.0

171

4.4 25,O-40.015.0

2.0

223

3.4 4o.e-67,s27.8

2.0

308

2.4

67.8.90.022.2 2,O.340

2.2 90.0-180.090.0

2.0

430

1.7 180.0-250.070.0

2.0

510

1.5 2so.e-3oe.o50.0

2.0

690 Ll

300.0-

-

2.l

850 e.g

Table3

Soil

profileat

Bonds

Coiner

Depth(rn}Thickness(m)

Unitweight(Vm3)Swavevelocity(mls)Dampingfactorh(tyo)

O.O-10.010.0

2,O

167

4.5 10.0-20.010.0

2.0

224

3.3 20.0-45.025.0

2.0

332

2.3

45.0.90.045.0 2.e

399 1,9

90.0.180.090,O

2.0

430

1.7 IBo,o-2se.o70.0

2,O

510

1.5 250.0-300,O50.0

2,O

69e

1,1

3oe,o-

-

_2.1

S50

O.9 Table4

Soilprofileat

Brawley

Fig.14Artificially-cornputedground

motion

Depth(m)Thickness(rn)

Unitweight(Vm3)Swayevelocity(mls)Dampingfacterh{%)

O.O-22,522.5

2.0

198

3.8 22.5-3S.415.9

2.0

248

3.0 38.4.90.05L6

2.D

340

2.2 go.o-lso.e90.0

2.0

430

1.7 ISO.O.250.070.0

2,O

510

1.5 2so,o-3oo.e50,O

2,O

690 Ll.

300.ot

-

2,1

₈₅₀

_O.9

Figure

16 is

the

comparison of velocity reFponse spectra with

the

soild

line

due

to

the

s.ynthesized accelerogram,

the

dotted

line

due

to

the

observed

2300

component of

the

main-shock accelerogram, and

the

chained

iine

for

the

observed

140e

component.

The

velocity Tespense spectrum

for

the

synthesized accelerdgrarn

is

in

the

same range

as

those

for

the

observed ones except

in

the

Tange

_gf

periods

longer

than

about

O.s

second.

The

reason

for

underestimation of

the

spectral amplitudes

in

this

range may attribute

to

the

char'acteristics of

the

data

base,

Figure

17

shows

the

_prediction

at

Bonds

Corner.

The

motion

has

a

longer

duration

than

that

of

Array

No.

3,

since

the

ruptu:e

_propagates

away

from

the

station.

The

synthesized accelerogram

has

the

same

level

as

those

of

the

observed ones.

Figure

18

shows

the

comparsion

between

velocity response spectra.

The

for

the

synthesized accelerogram corresponds with

those

for

the

obseiveO ones with _appropriate

degree

_{of accuracy,}

-･-

57

(9)

Gtt1

300.0 (a)

O.0 -3DO,D

6tt

300.0 (b)

o.o

-300,O

Gat

300.0 (c)

o.o

-300.0

o

Gal

soe.o

{a)

o,o

-eoo,a

Gal

800.0 (b)

o.o

..800.D

Gal

Boe.o

(c)

o,o

-800,O

o

lerogram

MMsPetwt

Observedaceelerograrn(140")

-

tw

246B

10 Peak

Acc.

218Gal

216Gal

272Ga]

121416

(sec}!8

20 Fig.15

Acceleregrams

at

El

Centro

Array

No.3

.

synthesizedaccelerograM

_peak

_Aee.

_883Gal

va

'

Observedaccelerogram(230")

758Gal

ebservedacceleregram(14o")

563Gal

2

4

6 B

IO

12

14

16 te

20 Gtt

200.0 (a)

o.o

-20D,D

Gat

200.0 (b)

o.o

-2DO.O

Gat 200.0

(e>

o.o

-200.0o

Fig.

17 AccelerogTams

at

Bonds

Corner

'

Synthesizedaccelerograrn

Peak

Acc.

172Gal

WitSiVdvivt""w

t

Observedaecelerograrn(225")

156Gal

Observedacce]eregram(315")

219Gal

hatwww1wtM"

(see)

2

4 S

B

10

12 t4

le

tB

20

58 Fig.19

Accelerograms

at

Brawley

500,0

-

200,0e.se

loo.oEti

so,oKut8

2o.og8

ID,OLh.t

5,O"e.z>

2,O

1,D

o,S

O.OS

O.1

O.2

O.5 l.O

Natural

period

{sec)

Fig.16

Velocity

response spectra

for

the

motions

in

Fig.15

'

500.0 .-.

200.0

o.EM

looLO'l;

L

S

50.0g

th

8 2o.o

=

i

to.oE

b

_s.o-g"v

>

2.0

1.0 o.s

o.as o,1 D.2 o.s r,o

Natura]period{see)

Fig.18

Velocity

response spectra

for

the

motions

in

Fig.17

500.0

200.DT =A

100.DtEIts

so.D

ves

8 20,og

th

s.o

'g

-8

::

Fig.

20 Velocity

response spectra

for

the

rnotionS

in

Fig.19

1li llh=O,05-=

Obs."4oe)

"

_'S'h'

-:,'

--.!-,.,.'ttttt:ttc'

Vs'tt""-`ntL

'lt.;･tlm..T･Th,--n

:tt"+,kObs.c23on

iSyn.

-'ttt-tttttJ;ttT!t.tHs le

Obs.(23oo)h=O.05

Syn.i'

r:---.+--lt'.!"'-'L.t-.

t:icF;:-:::h'ls-'r.`;.･.-.

s.'XObs.

-"4oo)r

s･"5i"..y'

'

(10)

Architectural Institute of Japan

NII-Electronic Library Service

'

Figure

19

shows

the

results at

Brawley

which

is

located

on

the

oppasite side of

the

epicenter.

We

can see

the

waves arrive

as

a

_group

with a short

duration

in

contrast

to

Bonds

Corner

and

find

the

_prediction

here

excellent.

In

Figure20,

the

response

spectra

for

the

synthesited and

the

observed are

all

in

the

same

range,

The

three

examples

suggest

that

it

should

be

_possible

to

use an artificially-computed

accelerogram

as

Green's

function

to

_predict

aceeleration

ground

motions

in

epicentral regions.

'

8. Conclusions

First,

Tanaka

et al. 's method was modified consistently with

the

a,-square

model

proposed

by

Aki

and

the

acceleration

_ground

motions

for

the

1979

Imperial

Valley

eafthquake were

simulated

to

show

the

applicability of

this

method

to

the

epicentral

region

of ashallow close-by earthquake with amagnitude of about

6.

5. In

this

method,

the

number

of

aftershock

records,

which were superposed as

Green's

functions,

was

taken

as

the

seismic moment ratio

between

the

main shock and

the

aftershock

in

lew

frequencies,

and as

213 power

of

the

seismic

moment ratio

in

high･

frequencies,

The

sizes

of

the

fault

models

for

the

main shock and

the

aftershock were

determined

based

on

the

similarity

relations

of source

_parameters,

'

Second,

this

method was applied

to

the

_problem

in

which no appropriate･observed records

for

smal･1 events

are

available,

Instead

of

the

actual

aftershock

records, an artificially-computed accelerogram with reliable averaged characteristics

of

earthquake motions was used

to

_predict

the

main-shock

_ground

motions.

The

_prediction

was

performed

by

considering

the

amplification

factors

of

the

surface

layering

at

each

strong-motion

station.

Based

on

the

obtained

results,

we

can

conclude

that

(

_i

)

the

modified synthesis method

presented

in

this

paper

is

powerful

enough

to

simttlate

acceleration

_greund

motions

in

epicentral regions, and

that

(

ii

)

it

should

be

possible

to

use an artificially-computed accelerogram as

Green's

function

when no

appropriate

observed records

for

small events are available,

We

are

now

further

studying

synthesis method considering aseurce mechanism of

the

aftershock

and

detailed

fault

models

for

the

main shock, and also

discussing

eharacteristics of

the

data

base

for

artificially-computed accelerograms

in

order

to

obtain

Green]s

functions

for

the

earthquake motions

of

other

sizes.

9. Acknowledgments

Authors

wish

to

express

their

appreciation

to

formeT

Prof,

H. Kobayashi

at

Tokyo

Institute

of

Technology

and

to

Prof.

Y. Ohsawa

at

University

of

Tokyo

for

their

_permission

of

the

usage of

the

aftershock and

the

main-shock

records of

the

1979

Imperial

Valley

earthquake.

The

acknowledgment

is

extended

to

Dr.

V. Avanessian

at

Ohsaki

Research

Institute,

Inc,

for

his

careful review of

the

manuscript.

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