Acceleration Velocity Displacement of Strong Motion accelerograph

8/11/2019 Acceleration Velocity Displacement of Strong Motion accelerograph

1/15

B u l le t in o f t h e S e i s m o l o g ic a l S o c ie t y o f A m e r i c a . V o l . 5 1 N o . 2 p p . 1 7 5 - 1 8 9 . A p r i l 1 9 6 1

I N T E G R A T E D V E L O C I T Y A N D D I S P L A C E M E N T O F

S T R O N G E A R T H Q U A K E G R O U N D M O T I O N

B Y G V B E R G AN D G W

HOTJSNEI~

A B S T R A C T

Th e ear th qua ke ground accelera t ions recorded a t E1 Cen tro , 30 Dece mb er 1934; E1 Cen tro , 18

M ay 1940; Olympia, W ashington, 13 April 1949; and Ta ft, Ca lifornia, 21 Ju ly 1952, hav e been

in tegra ted w i th a d ig i ta l com pute r to ob ta in a t each loca t ion the th ree componen ts o f g round

velo ci ty and ground displacem ent . Maximum horizon ta l d isplacem ents of 10 and 20 inches are

indicate d, and maximum ver t ic a l d isplacements of 5 inches are indicated .

S t r o n g g r o u n d m o t i o n s a r e u s u a l l y r e c o r d e d b y a c c e l e r o m e t e r s si nc e t h e g r o u n d

a c c e l e r a t i o n i s t h e q u a n t i t y m o s t p e r t i n e n t t o e n g i n e e r i n g s t u d i e s ; h o w e v e r , f o r

s o m e e n g i n e e r in g p u r p o s e s a k n o w l e d g e o f g r o u n d d i s p l a c e m e n t s d u r i n g s t r o n g

e a r t h q u a k e s i s i m p o r t a n t . I n a d d i t i o n t o a c c e l e r o m e t e r s ( p e ri o d 0 . 06 se e) t h e U n i t e d

S t a t e s C o a s t a n d G e o d e t i c S u r v e y m a i n t a in s a n u m b e r o f C a r d e r d i s p l a c e m e n t

m e t e r s ( p e r io d 2 .5 se c) a n d a f e w d i s p l a c e m e n t m e t e r s h a v i n g a n a t u r a l p e r i o d o f

1 0 s e c o n d s. T h e n a t u r a l p e r i o d o f t h e C a r d e r d i s p l a c e m e n t m e t e r i s m u c h t o o s h o r t

t o g i v e a n a c c u r a t e m e a s u r e o f t h e g r o u n d d i s p l a c e m e n t d u r i n g s t r o n g g r o u n d m o -

t i o n , 1 a n d e v e n t h e 1 0 -s e co n d p e r i o d i n s t r u m e n t p r o b a b l y d o e s n o t g i v e a c c u r a t e

m e a s u r e m e n t s o f s t r o n g g r o u n d m o t i o n . T h e d i f fi cu l ti es i n v o l v e d i n i n st a ll in g a n d

m a i n t a i n i n g a n e t w o r k o f d i s p l a c e m e n t m e t e r s h a v i n g p e r i o d s su f f ic i e n tl y l o n g to

r e c o r d a c c u r a t e l y s t r o n g g r o u n d m o t i o n s a r e t r u l y f o r m i d a b l e . T h e l a t e H a r r y

W o o d , o f t h e S e i s m o l o g ic a l L a b o r a t o r y a t t h e C a l i f o r n ia I n s t i t u t e o f T e c h n o l o g y ,

d e s i g n e d a n d h a d c o n s t r u c t e d a p a i r o f h o r i z o n t a l p e n d u l u m s t h a t p r e s u m a b l y

w o u l d h a v e a c c o m p l i s h e d s a t i s f a c t o r y m e a s u r e m e n t s b u t t h e i r si ze a n d w e i g h t

p r e c l u d e d t h e i r i n s t a l l a t io n i n t h e b a s e m e n t s o f o r d i n a r y c o m m e r c i a l b u i ld i n g s

w h e r e t h e a e c e l e r o m e t e r s a r e i n s ta l le d .

A l t h o u g h g r o u n d v e l o c it ie s a n d d i s p l a c e m e n t s a r e n o t o f a s m u c h i n t e r e s t t o e n -

g i n e e r s a s g r o u n d a c c e l e r a t i o n s t h e r e i s s t i l l i n t e r e s t i n k n o w i n g t h e m a g n i t u d e s

i n v o l v e d a n d , t h e r e f o r e , i n t h e p a s t t h e r e h a v e b e e n a t t e m p t s a t i n t e g r a t i n g t h e

a c c e l e r a t io n s t o o b t a i n t h e s e q u a n t i t i e s . ~,3 W h e n d o n e g r a p h i c a l l y o r n u m e r i c a l l y

t h e s a t i s f a c t o r y i n t e g r a t i o n o f t h e a c c e l e r o g r a m s is v e r y d i f fi c u lt . T h e c h i e f d i f f i c u l t y

a r i se s f r o m t h e f a c t t h a t t h e t r u e a x i s ( z e r o a c c e l e r a t i o n ) o f t h e a c c e l e r o g r a m i s n o t

k n o w n a n d h e n c e i t m u s t b e a p p r o x i m a t e l y l o c a t e d b y t r i a l a n d e r r o r . R e c e n t l y

w h e n t h e t h r e e c o m p o n e n t s o f g r o u n d a c c e l e r a t i o n f o r t h e f o u r s t r o n g e s t r e c o r d e d

g r o u n d m o t i o n s w e r e p u t o n p u n c h c a rd s , i t w a s a r e l a ti v e l y s i m p l e m a t t e r t o d o

t h e i n t e g r a t i o n s f o r t h e v e l o c it i es a n d d i s p l a c em e n t s .

T h e a c c e l e r o g r a m s w e r e p u t o n p u n c h c a r d s a s f o l l o w s . F i r s t t h e t r a c e w a s a p -

p r o x i m a t e d a s f a i th f u l l y a s c o u l d r e a s o n a b l y b e a c c o m p l i s h e d w i t h a s e r ie s o f s t r a i g h t

M anu scrip t rec eived for publica tion A ugust 27, 1960, and, as revised, O ctobe r 13, 1960.

1 Housner , G . W. and D. E . Hudson , Th e Por t H ueneme Ear thq uake o f March 18, 1957 ,

Bull. Seism. Soc. Am. 48:163-168 (1958).

2 Neum ann , F . , United States Earthquakes 1940 (Serial No. 647) , U. S . De par tm ent of C om-

m erce, 1942.

3 I -Iousner, G . W. , Gro und D isp lacement Co mputed From S t rong-Mot ion Acce le rograms ,

Bull. Seism. Soc. Am. 37:299-305 (1947).

175


2/15

76

BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

line segments. A temporary straight base line was drawn on the accelerograms and

the coordinates of the intersection points of successive line segments, measured

from the base line using some convenient scale of measurement, were recorded on

punch cards.

It was assumed tha t the recorded initial ground velocity and ground displacement

were zero. It was further assumed that in the true time-acceleration coordinates

the equation of the temporary base line would take the form Co -~ clt ~ - c2t2 where

the constants Co, cl, and c2 would have the values that would make the mean

square computed ground velocity a minimum. The punch cards were processed by

computer to introduce appropriate scale factors for time and acceleration, to find

the equation of the base line meeting the above conditions, and to adjust the ac-

celeration readings accordingly. The computer produced a deck of scaled and cor-

rected punch cards as its output.

The integrations were performed in the following manner. Let h be an interval

of time such that the ground acceleration is a linear function of time in the interval

t, t -t- h), let ao, v0, and x0 be the values of ground acceleration, velocity, and

displacement at time t, and let a~ be the ground acceleration at time t -t- h. The

ground velocity and displacement at time t -t- h are then

vl = v0 + h a0 -4-

al)

h 2

x l = xo A- vo -t- ~

2a0 A- al).

By repeated use of these formulas one can advance step by step through the solu-

tion. No t runcat ion error occurs, and roundoff error is negligible.

All computation was performed on the IBM 704 computer at The University

of Michigan Computing Center.

The question of accuracy of the computed velocities and displacements is asso-

ciated with the accuracy of the accelerometer as well as the accuracy of the dig-

itized data in representing the smooth accelerogram. Comparative measurements

made with a USCGS accelerometer and an instrument of much more extended

frequency range indicate that the USCGS instrument gives a quite accurate repre-

sentation of earthquake ground acceleration.4 There would appear to be no reason

why the integrated velocities and displacements should be grossly in error, but it

is not possible to make an assessment of the accuracy of the results. The three com-

ponents of acceleration were integrated to obtain the velocities and displacements

shown in the accompanying diagrams for the following records:

E1 Centro, California, 18 Ma y 1940 figs. 1, 2, and 3)

E1 Centro, California, 30 December 1934 figs. 4, 5, and 6)

Olympia, Washington, 13 April 1949 figs. 7, 8, and 9)

Taf t, California, 21 Ju ly 1952 figs. 10, 11, and 12)

Pasadena, California, 21 July 1952 fig. 13)

Specific comments on the integrated curves are as follows:

4 Hudson, D. E., J. L. Alford, and G. W. Housner, Measured Response of a Structu re to an

Explosive-Generated Ground Shock, Bull. Seism. Soc. Am. 44:513-527 (1954).


3/15

S T R O N G E A R T H Q U A K E G R O U N D M O T IO N

77

E1 Centro 18 May 1940. This shock has been given a Richter Magnitude of 7.0

formerly 6.7). The instrument was somewhat less than 10 miles southwesterly of

the trace of the fault which showed relative surface displacement over a length of

approximately forty or fifty miles, with a maximum relative displacement of ap-

2

U

I

.N

j

>

O

15

I0

5

5

1 0

15

WEST

I

TIME Seconds

Z

W

:E

bJ

_J

1.

u)

r~

Z

1 5

I

5

WEST

|

o

0

EAST

t

TIME Seconds

F IG . 1 . E 1 C e n t r o 1 94 0 E - W c o m p o n e n t .

3O


4/15

78

B U L L E T I N O F T H E S E I S M O L O G I C L S O C I E T Y O F M E R I C

p r o x i m a t e l y t w e l v e fe e t T h e c e n t e r o f t h e s l ip p e d l e n g th o f f a u l t w a s e s t im a t e d t o

b e a p p r o x i m a t e l y 2 5 t o 3 0 m i l e s s o u t h e a s t e r l y o f t h e i n s t r u m e n t T h e i n t e g r a t e d

d i s p l a c e m e n t s i n d i c a te p e r m a n e n t d i s p l a c e m e n t s o f a p p r o x i m a t e l y 9 i n ch e s to t h e

w e s t a n d 7 i n ch e s t o t h e n o r t h T h i s is c o n s i s t e n t i n d i r e ct i o n w i t h t h e o b s e r v e d

15

IO

o , 5 .

I 0

20.

5 ,

t /

4

0

..Re O.

Z

b J

_.1

a .

u

c~

z

t o ,

~

.9

NORT H

3 0

T IME, Seco n d s

SO~TH

I

5 0 ~ , b ;5 ~

T I M E , S e c o n d s

F I G . 2 . E1 C e n t r o 1 94 0 N - S c o m p o n e n t .

5 0


5/15

STRONG E RTHQU KE GROUND MOTION 79

f a u l t s l i p p i n g . T h e r e s u l t a n t p e r m a n e n t d i s p l a c e m e n t o f 1 1 t o 1 2 i n c h e s i s n o t u n -

r e a s o n a b l e i n v i e w o f t h e 6 f e e t e x p e r i e n c e d a t t h e c e n t e r o f t h e s u r f a c e t r a c e . A

p e r m a n e n t d o w n w a r d d i s p l a c e m e n t o f a p p r o x i m a t e l y 2 i n c h e s is a ls o in d i c a t e d .

15

0

> 5

a

z

0 I0

15

D OW N

~ _ ~ ~ ~ _ _ J 11 ~ V V ~ - V V - Y ~ v , , , '~

VV, l lV - - i j ,w

- U P -


N

G

t .

u 5 '

c:

I1.

m_

r~

Z

D 5

0

n*

D

I0

D O W N

U P

15 20 25 30

T I M E ,

S e c o n d s

:FzG. 3. E1 Cen tro 1940 ver t ica l com ponent .


6/15

1 8 0 B U L L E T I N O F T H E S E I S M O L O G I C A L S O C I ]~ T Y O F A M E R I C A

E l Centro 30 December 1934.

This shock of Magnitude 6.5 had a center approxi-

mate ly 35 miles south of the i nstrument. The slipping along the fault did not extend

to the surface. The east-west component of the integrated motion does not indicate

W

>

Q

Z

0

n,

(.0

15

IO

O ~

5

I0

15 0

SOUTH

I

I

N O R T H

T I M E ,

Seconds

IS

n

4 )

e

~

z

w

N

J

Q.

Q

Q

z

0

S

0

S O ~ T H

I

N O R T H

T I M E S e c o n d s

FIG. 4. E1 Centro 1934 N-S component.


7/15

STRONG E RTHQU KE GROUND MOTION

8

a n y p e r m a n e n t d i s pl a ce m e n t . T h e n o r t h - s o u t h c o m p o n e n t w o u l d ~ p p e a r t o in d i-

c a t e a p e r m a n e n t d i s p l a c e m e n t o f 3 o r 4 in c he s , b u t t h e s t e p- l ik e a p p e a r a n c e o f t h e

v e l o c i t y c u r v e in d i c a te s t h a t p e r h a p s t h e i n s t r u m e n t w a s n o t b e h a v i n g p r o p e r l y .

5

i

I0 15 2O

T I N E , S e c o n d s

Z 5

I 0 -

o

Z

w

. J

o .

n

,m

z:::)

5

0

n~

.9

A

EAST


FIO. 5 . E1 Centro , 1934, E-W com ponen t .


8/15

182 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

I n t h e e a r l y d a y s o f t h e a c c e l e r o m e t e r c e r t a in d i ff ic u lt ie s w e r e e n c o u n t e r e d w i t h

the suspens ion sys t em and sh i f t i ng base l i nes

5

~ D

o l

D

J

. I

c 5

]

Ld

> 5

Z

: 3

0 I0

n~

.9

15

D O W N

U P

: - : : : ;

5 I 0 1 5 2 0 2 5

T IME Seconds

t / /

Q . )

~

5

W 0

Q

Z 5

O~

I0

D O W N

U P

T IME Seconds

FzG. 6. E1 Cent ro 1934 vertical co mpon ent.


9/15

S T R O N G E A R T H Q U A K E G R O U N D M O T I O N 1 8 3

Olympia 13 Ap ril 1949. T h i s s h o c k o f M a g n i t u d e 7 .1 c e n t e r e d a p p r o x i m a t e l y

4 5 m i l e s n o r t h - n o r t h e a s t o f t h e i n s t ru m e n t a n d t h e h y p o c e n t e r w a s l o c a te d a p p r o x i-

15

.)

c

I - -

w

>

z

I0

5

0

5

I 0 .

, ~ ~ o

TIME Seconds

3 0

5

~ ' O .

(J

lad

IaJ

.3

< I

. - I

CL

(D

Q I 0 '

Z

::~

0

5

0

A

N - 8O e - E

I

i

S - 8Oo -W

, b , ~ 2 o

TIME Seconds

F z G . 7 . O l y m p i a 1 94 9 N - 8 0 - E c o m p o n e n t .

N-8OO-E

S - 8Oe -W

3 0


10/15

184 U L L E T I N OF THE SEISMOLOGICAL SOCIETY OF AMERICA

mately 45 miles beneath the surface of the ground. The north south component of

computed ground displacement indicates no permanent displacement but the other

1 5

4

~ ,o .

e

0 o

> 5

Q

z

~ I0

0

15

0

I

S - l O e - E

t

30

TIME Seconds

W

5

N - I O - W

0

I 0 -

I

S - I O e - E

t


30

FIG. 8. Olympia 1949 N-10-W comp onen t.


11/15

S T R O N G E A R T H Q U A K E G R O U ND M O T I O N 1 8 5

horizontal component indicates perhaps 5 inches of permanent displacement The

vertical component also indicates some upward displacement

15-

I 0

n

0

.9

1 5

- D O W N -

- k i P -

TIME Seconds

5 '

~)

o - D O W N -

c

I--

z

w

r ~

Z

:D

0

o~

I 0

O

U P

TIME Seconds

F IG . 9 . O l y m p i a 1 94 9 v e r t i c a l c o m p o n e n t .


12/15

86 B U L L E T I N O F T H E S E I S M O L O G I C L S O C I E T Y O F M E R I C

Ta f t 21 Ju l y 1952 . T h i s s h o c k o f M a g n i t u d e 7 .7 c e n t e r e d a p p r o x i m a t e l y 4 0 m i le s

e a s t - s o u t h e a s t o f t h e i n s t r u m e n t . T h e W h i t e W o l f f a u l t o n wh i c h th e s h o c k o ri g -

i n a t e d is p e r p e n d i c u l a r t o t h e S a n An d r e a s f a u l t a n d t h e s l ip p in g wa s p r e d o m i n a n t l y

15

Q )

m

W~ 5

0

Z

:~ I0

0

S -6 9e -E

50 ~ ,~ ,~ ~

TIME Seconds

K

ttJ

.A

G.

Z::)

O

fig

.9

N-69e -W

5

0

5

'

s ~ ,~ ~ ~


FIG. 10. Taft , 1952, N-69-W co mpo ne nt .


13/15

S T R O N G E A R T H Q U A K E G R OU N D M O T IO N 187

v e r t i c a l r a t h e r t h a n t h e h o r i z o n t a l s l i p p i n g u s u a l l y a s s o c i a t e d w i t h d e s t r u c t i v e

C a l i fo r n i a e a r t h q u a k e s No p e r m a n e n t h o r i z o n t a l g r o u n d d i sp l a c e m e n t is i n d i c a t e d

b u t a s m a l l p e r m a n e n t d o w n w a r d d i sp l a c e m e n t i s i n d ic a te d T h e n a t u r e o f t h e

15

5

41)

U )

G )

c 5

>

o -

~

Ld

O

S-21o-W

I

N - 2 1 * - E

t

TIME Seconds

3 0

5 S - 21 - W

4 ) I

o

N

I 0 N ' 2 1 - E

t

o ~ i b , ~ z o

TIME Seconds

F I G . 1 1. T a f t 1 95 2 N - 2 1 - E c o m p o n e n t .

~ o


14/15

88 BULLET IN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

f a u l t s l ip i s r e f l e c t e d i n t h e t r a n s i e n t v e r t i c a l g r o u n d d i s p l a c e m e n t w h i c h i s r e l a -

t i v e l y l a rg e r t h a n f o r th e o t h e r t h r e e e a r th q u a k e s . A p e r m a n e n t d o w n w a r d d is -

p l a c e m e n t w o u l d b e c o n s i s t e n t w i t h t h e n a t u r e o f t h e f a u l t in g .

15

U

I0~

~ 5

0

.~

I 0

150

- D O W N -

, . A ~ q ~ / I .,A ,., , . ~ , _ , t , ~ J ~ ^ . ~ . A ~ ~ ^ ^

U P

I , , , , ~

T I M E S econds

I0

I n

l i d

r -

u 5

c

z

hi

W

~

J

m_

a

Q

o

I 0

- U P -


FzG. 12. Taf t 1952 ver t ica l com ponent .


15/15

S T R O N G E A R T H Q U A K E G R O U N D M O T I O N 189

SOUTH

w

q

.1=

o

Z

bJ

:E

bJ

0

Acceleration Velocity Displacement of Strong Motion accelerograph

Documents