An Automatic S-phase Picker

8/10/2019 An Automatic S-phase Picker

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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 e ty o f A m e r i c a V o l. 8 3 N o . 1 p p . 1 8 0 - 1 8 9 F e b r u a r y 1 99 3

A N A U T O M A T I C S - P H A S E P I C K E R

B Y A R T U R C I C H O W I C Z

B S T R C T

A n a l g o r i th m h a s b e e n d e v e l o p e d f o r t h e a u to m a t ic p i c k i n g o f t h e S p h a s e

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

l a te d in t h e p r o g r a m : d e f l e c t io n a n g l e d e g r e e o f p o l a r i z a t i o n a n d t h e r a ti o

b e t w e e n t r a n s v e r s e e n e r g y a n d t o ta l e n e r g y . T h e S p h a s e i s d e c l a r e d w h e n

t h e p r o d u c t o f t h e th r e e p a r a m e t e r s i n c r e a s e s a b o v e t h e r e f e r e n c e l e ve l . M o s t

p a r a m e t e r s a r e c o m p u t e d a u t o m a t i c a l ly a n d m o d i f ie d i f n e c e s s a r y . T h e S - p h a s e

p i c k e r is u s e d to a n a l y z e d a t a f ro m a lo c a l u n d e r g r o u n d m i n e s e i s m i c n e t w o r k .

I N T R O D U C T I O N

E v e n t d e t e c t i o n a l g o r it h m s ( P - w a v e d e t e c t o rs ) a r e n o w c o m m o n l y u s e d w i t h

d i g it a l se i s m i c n e t w o r k s . M o s t o f t h e s e n e t w o r k s u s e s h o r t - t e r m a n d l o n g - t e rm

a v e r a g e r a t i o a l g o r i t h m s ( A l le n , 1 9 7 8) . T o fu l l y i d e n t i f y c h a n g e s i n s i g n a l p h a s e

a n d a m p l i t u d e , a l g o r i t h m s b a s e d o n a l i n e a r p r e d i c t i o n f il t e r ( e.g ., C ic h o w i c z

a n d L e l i w a - K o p s t y n s k i , 1 9 75 ; G r a n e t , 1 9 8 3 ) w e r e p ro p o s e d . T h e l i n e a r p r e d i c -

t i o n f i lt e r i m p r o v e s t h e s i g n a l -t o - n o i s e r a t i o s i g n i fi c a n t ly .

T h r e e - c o m p o n e n t d a t a g i v e s t h e p o s s i b il i ty o f d e t e c t in g t h e S a r r iv a l o n t h e

b a s i s o f p h y s i c a l d i f fe r e n c e s b e t w e e n t h e P w a v e a n d S w a v e . T h e r e a r e a

r e l a t i v e l y la r g e n u m b e r o f p a p e r s d e a l i n g w i t h t h e p o l a r iz a t io n p r o p e r t i e s o f t h e

s e i s m i c s ig n a l , w i t h d e t a i l e d a n a l y s i s o f t h e S w a v e (e .g ., R o b e r t s et al . 1989) .

T h e o b j e c t iv e o f t h i s p a p e r i s t o p r e s e n t i n d e t a i l a n a l g o r i t h m f o r a u t o m a t i c

d e t e c t i o n o f t h e S p h a s e , e v e n in t h e p r e s e n c e o f a s t r o n g P - c o d a s ig n a l . T h e

a l g o r i th m e x p l o it s t h r e e - c o m p o n e n t d a t a . I t i s a s s u m e d t h a t t h e f i r s t P - w a v e

a r r iv a l c a n b e o b t a i n e d b y a n y o t h e r a l g o ri th m . W e p r e f e r th e v e r y r e li a b le

a l g o r i t h m o f B a e r a n d K r a d o l f e r ( 1 98 7 ).

BASIC PICKING ROU TINE

T h e p r o p o s e d S - p h a s e p i c k e r is b a s e d o n t h e c o m b i n a t io n o f t i m e - d o m a i n

p o l a r i z a t i o n a n d e n e r g y r a t io f i l t e rs c a l c u l a t e d o v e r a f i lt e r t i m e w i n d o w . T h e

c o m p u t e r m e t h o d i n v o lv e s fo u r s te p s : p r e l i m i n a r y c a lc u l a ti o n , g r o u n d - m o t i o n

r o t a t i o n i n t o t h e w a v e s y s t e m , P - c o d a s ig n a l p r o c e s s i n g , a n d d e c l a r a t i o n o f S

a r r i v a l .

Pre l im inary C a lc u la t ion

A l m o s t a ll fi l te r s t h a t a n a l y z e s e i s m i c s i g n a l c a l c u l a t e v a l u e s o v e r a s p e c i fi e d

t i m e w i n d o w . T h e w i n d o w ' s l e n g t h i s a f i lt e r p a r a m e t e r t h a t h a s t o b e c h o s e n

a r b i t r a r i l y a f t e r g a i n i n g s o m e e x p e r i e n c e f r o m r e a l d a t a . I n t h e c a s e o f a s m a l l

u n d e r g r o u n d s e is m i c n e t w o r k , t h i s a p p r o a c h is r a t h e r d i ff ic u l t b e c a u s e e v e n t s

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

c o m p u t e t h e t i m e w i n d o w o f t h e f il te r ,

N F I L T E R

o n t h e b a s i s o f t h e p r e d o m i -

n a n t f r e q u e n c y , f 0 :

N F I L T E R = 1 / ( f o A t ) , ( 1 )

1 8 0


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A N A U T O M A T I C S - P H A S E P I C K E R 181

where At is the sampling interval in time units and

N F I L T E R

is the averaging

window length in samples. Predominant frequency, fo, can be calculated in

terms of the integrals that are moments of the ground spectrum Boore, 1983;

Andrews, 1986):

1

f o = m o / / m 2 1 / 2 ,

where

m o = 2 f D 2 f ) d f ,

m 2 = 2 f V 2 f ) d f ,

D 2 f )

is the displacement power spectrum, and

V 2 f )

is the velocity power

spectrum. Numerical values of these integrals are affected by truncation of the

interva l of integration. The low limit is equal to l / T , and the upper limit is the

Nyquist frequency, 1//2 At, where T is the length of signal used to calculate the

integrals.

Ground Mot ion Ro ta t i on i n to t he Wave Sys t em

A three-component station monitors ground motion along the nor th X), east

Y), and vertical Z) directions. The first P-arriva l pulse is used to compute the

covariance matrix in order to obtain the polarization direction of the initial

compressional particle motion. Ground motion is rotated into the longitudinal

and two perpendicular components Kanasewich, 1981). The covariance matrix

for a set of

N F I L T E R

points taken over each of the three orthogonal compo-

nents of ground motion is computed as follows:

- C O V X , X ) C O V X , Y ) C O V X , Z ) I

C O Y Y , X ) C O V Y , Y ) C O V Y , Z ) .

C O Y Z , X ) C O Y Z , Y ) C O Y Z , Z )

3 )

The covariance between N F I L T E R observation of two variables X and Y is

given by

N F I L T R

C O Y X , Y ) = 1 / N F I L T E R ~ x~ - ~ ) Y i - Y ) , 4)

i

where x, y are the average values. The diagonalization of the covariance matr ix

gives the principle axis of this matrix. The direction of polarization may be

measured by considering the eigenvector of the largest principal axis.

The X, Y, Z components are rotated into L, Q, T components, where L coin-

cides with the principle direction of the P-wave particle motion

U l l U 1 2

U 2 1 U 2 2

U 3 1 U 3 2

u13 X

U 2 3 y

u 3 3

Z

5 )

where Ui,y j = 1, 2, 3 are the direction cosines of the ith principle direction.


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82 A . C I C H O W I C Z

P - C o d a S i g n a l P r o c e s s i n g

T h e p o l a r i z a t io n f i l te r o f K a n a s e w i c h 1 9 8 1 ) i s u s e d t o a n a l y z e t h e P - c o d a

s ig n a l. E i g e n v a l u e s a n d e i g e n v e c t o r s a re c o m p u t e d f o r e a c h t im e p o i n t t . T h e

w i n d o w t i m e A t . N F I L T E R i s m o v i n g b y o n e t i m e p o i n t t h r o u g h t h e e n t i r e

c o d a. I n t h e w i n d o w t i m e , t h e f o ll o w in g t h r e e p a r a m e t e r s o f t h e t h r e e - c o m p o -

n e n t s e i s m i c s i g n a l , F 1 , F 2 , F 3 a r e c a l c u l a t e d .

T h e d e f l e c t i o n a n g l e , F l t ) , i s d e f i n e d a s t h e a n g l e b e t w e e n t h e l o n g i t u d in a l

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

e i g e n v a l u e

C O S - I [ U l l [

F l t ) , 6 )

v / 2

w h e r e u l l i s t h e d i r e c ti o n c o s i n e s i n t h e L , Q , T c o o r d i n a t e n o t t h e s a m e a s

d e f i n e d i n e q u a t i o n 5 ) . F l t ) i s n o r m a l i z e d t o 1 .

T h e s e c o n d p a r a m e t e r i s t h e d e g r e e o f p o l a r i z a t io n , F 2 t ) S a m s o n , 1 9 77 ):

V l - v 2 ) 2 + V l - v 3 ) 2 + v 2 - v 3 ) 2

F 2 t ) = 7 )

2 - v l + v 2 + v 3 ) 2

w h e r e v l , v 2 , v 3 a r e e i g e n v a l u e s o f t h e c o v a r ia n c e m a t r i x a t t i m e t.

B o t h c o m p r e s s i o n a l a n d s h e a r w a v e s e x h i b i t a h i g h d e g r e e o f l i n e a r p o l a ri z a-

t io n . T h e P - w a v e c o d a m a n i f e s t s a g e n e r a l l y e l li p t ic a l p o l a r i z a t io n w i t h a

s i g n if i ca n t ly l o w e r v a l u e o f F 2 t ). M o r e i n f o r m a t i o n a b o u t t h e b e h a v i o r o f t h e

d e g r e e o f p o l a r i z a t i o n i n r e a l d a t a c a n b e f o u n d i n C i c h o w i c z

e t a l .

1 9 8 8 ) .

T h e t h i r d p a r a m e t e r ,

F 3 t ) ,

i s t h e r a t io b e t w e e n t r a n s v e r s a l a n d t o t a l e n e r g y ,

w h e r e t r a n s v e r s a l r e f e rs t o t r a n s v e r s a l t o t h e d i re c t io n o f P - w a v e p a r t i c le

m o t i o n

~ Q i 2 + T i 2 )

i

F 3 t ) = ~ _ , q i 2 + T ~2 + L i 2 ) . 8 )

i

T h i s p a r a m e t e r i s n o t v e r y s e n s i t i v e t o n o i s e i n a s i g n a l ; t h e r e f o r e i t c a n

s i g n if i ca n t ly i m p r o v e t h e p e r f o r m a n c e o f t h e S - p h a s e p i ck e r .

T a b l e 1 s u m m a r i z e s f e a t u r e s o f t h e c h o s e n p a r a m e t e r s b y d is p l ay i n g t h e

e x p e c t e d v a l u e s o f F 1, F 2 , F 3 fo r d i f f e r e n t p a r t s o f a s e i s m i c s i g n a l . I t i s d i f f i c u l t

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

n o i s e a s w e l l a s r e f le c t e d P a n d P - t o - S c o n v e r te d w a v e s a r e s u p e r i m p o s e d o n

t h e s i g n a l . T h e f i r s t S a r r i v a l f o r r e a l d a t a s h o u l d b e a s s o c i a t e d w i t h a f a r

T A B L E 1

T H E E X P E CT E D V A L U E S O F F 1 F 2 A N D F 3

F i r s t P a r r i v a l P C o d a F i r s t S A r r i v a l

F 1 = 0 0 < F 1 < 1 F 1 = 1

F 2 = 0 < F 2 < 1 F 2 ~ 1

F 3 = O 0 < F 3 < l F 3 = l


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A N A U T O M A T I C S - P H A S E P I C K E R 1 8 3

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

v a l u e o f 1.

T h e p r o d u c t o f t h e t h r e e s q u a r e d p a r a m e t e r s i s ca l le d t h e c h a r a c t e r i s ti c

f u n c t i o n o f th e s e i s m i c s ig n a l :

F t ) = F 1 2 t )

F 2 2 t ) F 3 2 t ) . 9 )

T h e c h a r a c t e r i s ti c f u n c t i o n is u s e d t o e n h a n c e t h e m o t i o n t h a t e x h i b i t s a l in e a r

p o l a r i z a t io n i n a d ir e c ti o n p e r p e n d i c u l a r t o th e L c o m p o n e n t s a n d w i t h a

m o t i o n t h a t is s t r o n g e r o n Q a n d T c o m p o n e n t s t h a n o n t h e L c o m p o n e n t

S - w a v e s i g n a l ) . T o a c h i e v e a m o r e d i s ti n c t s ig n a l , w e s q u a r e d e a c h e l e m e n t o f

t h e F t ) . T h e S a r r iv a l c a u s e s a n a b r u p t i n c r e a s e i n t h e v a l u e o f t h e c h a r a c te r -

i s ti c f u n c t i o n . I n r ea l r e c o rd s , a s u d d e n i n c r e a s e i n v a l u e s o f t h e p a r a m e t e r s i s

o b s e r v e d w h e n t h e S p h a s e a p p e a r s in t h e P c o d a.

L

. . .. . ~ ' ' ' ' I '' ' ' ' 'J ' ' ' ' ' I ~ ' ~ ' ~ ' ' ' ' ~ ' T ' ' ' ' '' ~ ' ' ~ ` ' ` ' ' ~ ' ' ' ' ' ` ' ' '~ ' ' ' ' ' ' I ' ' ~ ' ` ' ' ' T ' ` ' I ' ' ' . ` ~ ' ' ' ' '' ' i

T I H s e c

i - - 0 0 1 l l l l l l [ [ E I I I I I I I I f I J ~ I I I I i I I fl l l U l lI I ~ l ~ t l l [ I l l l l l , I l l l l l l ll . l l l , l l l I I I F I I I I r I I l l { ~ l l t , I f i . l l I l l r l O l l l l i l l l l l~ I I ~ . l

1 . 2

2 ~

5

1 . 2 .

o 2 4

o.

F ~

o

o

6 . .. .. .. . . . . . . . . . . . i r m m m i H m m rm l m m m m m j m H I m j d m

I I J I I

~ . i i . i. i ~. i

3

2

o i . . [ . j . i ] . . r ~ i . ~ r . l ~ r . j i . i i i j

o . o 1 2 2 . 4

g T I M s e

F IG . 1 . A n e x a m p l e o f p r o c e s s i n g t h r e e - c o m p o n e n t d a t a w i t h t h e S - p h a s e p i c k e r a ) R e c o r d e d

d a t a a f t e r r o t a t i o n to lo n g i t u d i n a l , L , a n d t w o t r a n s v e r s e d i r e c ti o n s , Q , T . L o n g i t u d i n a l a n d

t r a n s v e r s e m e a n s p a r a l l e l a n d p e r p e n d i c u l a r t o th e e s t i m a t e d d i r ec t io n o f P - w a v e p a r t ic l e m o t io n .

b ) T i m e v a r i a t i o n o f d e f l e c ti o n a n g l e , F l t ) ; d e g r e e o f p o l a r i z a t i o n , F 2 t ) ; r a ti o o f t r a n s v e r s a l e n e r g y

t o t o t a l e n e r g y , F 3 t ) ; a n d t h e c h a r a c t e r i s t i c fu n c t i o n ,

F t ) .

T h e a r r o w a n d v e r t i c a l l i n e i n d i c a t e t h e

h a n d p ic k . N o t e t h e i n c r e a s e o f th e

F l t )

a n d

F3 t )

p a r a m e t e r s a t t h e a r r i v a l of t h e S p h a s e . A

h o r i z o n t a l li n e o n t h e u p p e r d i a g r a m f r o m F i g u r e 1 A i n d i c a te s t h e l e n g t h o f t h e f i l t er N F I L T E R . A t .

O n t h e l o w e s t d i a g r a m o f F i g u r e 1 B th e S a r r i v a l t i m e s p i ck e d b y th e t w o t e c h n i q u e a r e s h o w n . T h e

a r r o w o n t h e r i g h t i n d i c a t e t h e S a r r i v a l d ec l a re d w h e n F t ) e x c e e d s t h e t h r e s h o l d le v e l A , a n d a

h o r i z o n t a l l i n e i n d i c a t e s t h e t i m e w i n d o w f o r c a l c u l a t i o n t h e A v a l u e . T h e S a r r i v a l d e f in e d b y t h e

t i m e o f t h e f i r s t m i n i m u m b e f or e tm ~ ~ i s m a r k e d w i t h a r r o w l a b e l ed

Smi n.

T h e p r e d o m i n a n t

f r e q u e n c y i s 7 . 2 H z .


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1 8 4 A . C I C H O W I C Z

D e c l a r a t i o n o f S - a r r i v a l

Two different techniques for picking the S-wave arrival are discussed: first

techniq ue based on the calculation of a threshol d level in the P coda and

second a techniqu e based on the calculation of the max im um value of a

characteristic function.

The most time-consuming calculations are associated with F ( t ) . Therefore in

order to speed up the S-picker the character istic function is calculated only in a

time window th at sta rts at t 1 and ends a t t2:

t I = t p a r r i v a l + t S m a x - - t p a r r i v a l ) / 2 ,

t 2 = t l + t s m a x - N F I L T E R At

10)

where t s m a x is the time related to the maximum amplitude in S-wave group

and

t p a r r i v a l

is the time relate d to the first P-wave arrival. It is unlikely that

the first S-wave arrival wilt fall outside this window. For a situation where a

low-frequency signal is recorded close to a seismic sta tio n and the

N F I L T E R . h t

can be larger t ha n the proposed window t 2 - tl th en the calculation of the

0

q

_ _ L

~ m

o

o,

o o

8 -

o o

..........llll[i.llllllll...i.i...IE~jI~IIII.. . . . r . . . j I H I. IW . . . . i i . . i ~ . .. [ l l r . ~ . Tl ~ . l l l

L u

1 I M E s ec ~

........ ' '`''''I' ''''T' '' 1 ' ''''~ ''''' ~'''' 'r' ~ ~'i '' ''?'' ''T '' ~'~ '''''T' ' ~'~ '''''''~

1 ~ 2 4

I,:,.I,, ,,I.,,,I...,, ,i...,.I.,..,,I ,,..,,L....l,...,,i. ,,, ~rir~r~,

~ . _ ~ 0 0 8

o ~`''~ '[ ''' ~ ' ' .~''' .~'~' ' ~T ~ ''~'' ~'~ ~'`~i'r~' '?' ''''~ ' [' '' ~ '''' ~'' ' L

o . o 1 2 2 4

g T I M E s ec

2

F IG . 2 . N o t e t h e s i g n i f i c a n t i n c r e a s e o f t h e d e g r e e o f p o l a r i z a t i o n

F 2 t )

a t t h e a r r i v a l o f t h e S

p h a s e . P o o r d e f i n i t i o n o f t h e f i r s t P - w a v e a r r i v a l c a u s e s t h e d e f l e ct i o n a n g l e , F l t ) a n d e n e r g y r a t i o ,

F s t )

t o i n c r e a s e b e f o r e t h e S - p h a s e a r r i v a l . T h e p r e d o m i n a n t f r e q u e n c y is 5 .2 H z . S e e c a p t i o n o f

F i g u r e 1 fo r f u r t h e r e x p l a n a t i o n s .


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A N A U T O M A T I C S - P H A S E P I C K E R 85

c h a r a c t e r i s t i c f u n c t i o n s t a r t s a f t e r t h e P - w a v e a r r i v a l t o t - S ~ a x s e e , fo r

e x a m p l e , F i g s . 3 a n d 4 ) .

I n t h e f i r s t t e c h n i q u e , f o r e a c h r e c o rd t h e i n i t i a l v a l u e o f t h e t h r e s h o l d i s

d e f i n e d a s A = F + 3 a , w h e r e F i s t h e a v e r a g e v a l u e o f t h e c h a r a c t e r i s t i c

f u n c t i o n ,

F t ) ,

for t 1 < t A f o r t h e c o n s e c u t i v e k A t t i m e p o i n t s ,

T H E N S a r r i v a l i s d e cl a r ed .

T h e S p h a s e i s d e c l a r e d w h e n t h e c h a r a c t e r i s t ic f u n c t i o n i n c r e a s e s a b o v e t h e

t h r e s h o l d f o r a t i m e p e r i o d e q u a l t o a f e w A t . I f t h i s v a l u e o f t h e t h r e s h o l d f a i l s

t o d e t e c t t h e S p h a s e , t h e n t h e P c o d a i s p r o c e s s e d o n c e a g a i n w i t h a n e w v a l u e

o f A t h a t i s la r g e r b y 3 a . T h i s a l g o r i t h m i s s l o w a n d t h e re f o r e se l d o m u s e d ,

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

O n t h e o t h e r h a n d , h o w e v e r , i t i s v e r y s a f e , b e c a u s e t h e n u m b e r o f f a l s e a l a r m s

i s l o w . E x a m p l e s o f t h e v a l u e s o f A a n d

F t )

a t t h e t i m e o f d e c la r a t i o n o f t h e S

a r r i v a l a r e p r e s e n t e d i n F i g u r e s 1 t o 6 .

I n t h e s e c o n d t e c h n i q u e , t h e t i m e ,

t m a x ,

a s so c ia t e d w i t h t h e m a x i m u m o f t h e

c h a r a c t e r i s t i c f u n c t i o n F t ) i s o b t a i n e d . T i m e a r o u n d t h e t m x i s a s s o c i a t e d

w i t h a p u l s e o f t h e d i r e c t S w a v e s e e T a b l e 1 ). T h e S a r r i v a l i s d e f i n e d a s t h e

m

d m

. . .. . .. . . I ' ' T ' ' I ' I ' I ' ' T ' ' I ' ' ' ' I ' ' ' ' ' ' ' ' ' I ' ' ' ' ' ' I ' ' ' ' ' ' ' ' ' I ' ' ' ' ' ' ' ' I ' ' ' ' ' ' ' ' T ' ' ' ' ' I

o o 1 2

2 1

T I M s ~ c

. . . . . . . ` ` ' ' ' ' ' ' T ' ' ' ' ` ' ' ' '' ' ` ' ' 1 ' ' ' ' '' ' ' ' ` ` ` ' ' ` 1 ' ' ' ' ' ` ' ' 'r ' ' ' ` ' ' T ' ' ' ' ' ' ' ` ' ' '' ' ' ' T ' ' ' ' ' T ' ' ` ' T ' ' ' ' ' ' ' T ' ' ' ` ' ' '

d

' - . . . .. . . .. I ' ' ' I ' ' I ' ' ' I ' ' I ' ' ' I ' ' ' r ' ' I I ' ' ' I ' ' I ' ' ' I ' ' T ' ' ' ' I

0 0 1.2 2 4

2

o F

d

o

o

~_

. .. . . i ' ' ? i ' l ' ' ' I ' T ' ' J ' i ' '' ''I'''' T'''' ''L'~ 'i

~ F A = 0 0 3 1

= 0 0 6 1

i ' : ' ' ' ' " ' r ' ' ' ' , ' ' ' ' '" ' ' l ' ' ' " ' ' ' ' l ' ' ' ' '" ' ' l ' ' ' ' ' ' '' l "" ' " : ,

T

I M E

eec

3

F IG . 3 . N o t e t h e c o n s i s t e n t i n c r e a s e o f a l l t h r e e p a r a m e t e r s o f t h e c h a r a c t e r i s t i c f u n c t i o n . T h e

p r e d o m i n a n t f r e q u e n c y i s 8 . 5 H z . S e e c a p t i o n o f F i g u r e 1 fo r fu r t h e r e x p l a n a t i o n s .


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1 8 6 A . C I C H O W I C Z

~

. . . . . . . . . .- I ' ' ' I ' ' T I ~ ' ' I ' ' ' I ' ' ' I' ' ' ' ' ' j ' ' '~ '~ ' ' ' l ' ' ' '' ' ' ' ' l ' '' ' ' ' ' ' ' } '4 ' ' ' ' ' ' ' l' ' ' ' ' ' ' ' l ' ' ' r ~

o . o ~ 2 2 t

T I H E s e c

, d - -

I l l l l l l l I l i l l l t l l I J I I

c~

c;

. . .. . . .. . ~ ' ' ~ ` ' ' ' ~ ' ' ` ' ' ' ' ~ ' ~ ' ' ' ' , ~ ' ' ' ' ' ' ' I ` ' ' ' ' ' ' ~ ' ' 1 ' ~ ` ' ' ' r ' ' ' ' ' ' ~ ` ' ' ' ' ' ' h ' ' ` ~ ' ' ' i ' ' ' ' ' ' ~ ' ' ' ' ~ ' ' ' ' ' ' L i ' ' 1 ' 1 ' ~ ]

0 0 1 . 2 2 . 4

6 -

5 - -

o

I / ~ L .

o.o 1 2 2

B T I H E

-:ec

4

F r o. 4. N o t e t h e i n t e r f e r e n c e o f t h e S - w a v e a r r i v a l w i t h t h e P - w a v e c o d a , t h u s c a u s i n g a d e c r e a s e

i n th e d e g r e e o f p o l a r i z a t io n a t th e a r r ic a l o f t h e S p h a s e , F 2 t ) . T h e t w o o t h e r p a r a m e t e r s w o r k

w e l l . T h e p r e d o m i n a n t f r e q u e n c y i s 5 .6 H z . S e e c a p t i o n o f F i g u r e 1 f o r f u r t h e r e x p l a n a t i o n s .

t i m e o f t h e f i r s t m i n i m u m b e f or e

tma x .

E x a m p l e s o f p i c k in g t h e S a r ri v al w i t h

t h i s a l g o r i t h m a r e p r e s e n t e d i n F i g u r e s 1 t o 6 s e e a r r o w w i t h d e s c r i p t io n o f

S t a i n .

ens i t iv i ty analys i s was performed by apply ing the fo l lowing smoothing

operator to the characterist ic function

F t )

:= 1 -

1 / 5 ) F t -

1) +

1 / 5 F t ) .

1 1 )

N o s i g n i f i c a n t c h a n g e s i n p i c k i n g t h e S - w a v e a r r i v al w e r e d e t e c te d .

R E S U L T S

S i x e x a m p l e s o f t h e a p p l i c a t i o n o f t h i s t e c h n i q u e t o r ea l r e co r d s a r e p r e s e n t e d

i n F i g u r e s 1 t o 6. T h e s e e x a m p l e s a r e r e c o r d s f r o m a l o c a l u n d e r g r o u n d m i n e

n e t w o r k , e q u i p p e d w i t h 4 . 5 - H z g e o p h o n e s a t a d e p t h o f a b o u t 2 5 0 0 m . T h e

S - p i c k e r p a r a m e t e r s a r e s e t t o p r o c e s s s e i s m i c e v e n t s i n a m a g n i t u d e r a n g e

v a r y i n g f r o m - 1 . 0 t o 3. 0 .

T h e s a m p l i n g p e r i od , A t , o f r e c o r d s i s 0 . 0 0 2 s e c , a n d t h e i n t e r v a l o f i n t e g r a -

t i o n s e e e q u a t i o n 2 ) v a r i e s f r o m 0 .9 7 t o 8 0 H z . T h i s m e a n s t h a t h i g h - f r e q u e n c y


8/10

A N A U T O M A T I C S - P H A S E P I C K E R 1 8 7

. . .. . . .. ' L ' I ' ' ' ' ' ' l ' ' ' l ' ' ' ' ' F r ~ l ' ' ' ' ' ' ' j ' ' ' ' ' l ' ' ' ' ' ' ' ' ' l ~ ' ' '' '' ~ ' 1 ' ~ ' ' ' ' ' ' l ' ' ' ' ' ' ' l ' ' ' ' ' ' ' l ' ' ' l

c:

~ F 1

o - - ~ 1 p ,

o

, ~ 1 , l i n T T , , ,T ~ j r x ~

T Z M s ~ s

-5

N

m S

o , 0 1 . 2 2 . 4 0 . c ,

s B

1 2 2 ~

T ]~ H E s ~ c

5

F IG . 5 . N o t e t h e c o n s i s t e n t i n c r e a s e o f a l l t h r e e p a r a m e t e r s o f t h e c h a r a c t e r i s t i c f u n c t io n . I n t h i s

c a s e t h e h a n d p i c k w a s p r o b a b l y t oo e ar l y . T h e p r e d o m i n a n t f r e q u e n c y is 1 0 . 8 H z . S e e c a p t i o n o f

F i g u r e 1 f o r f u r t h e r e x p l a n a t i o n s .

s i g n a l is e x c l u d e d fr o m t h e a n a l y s i s o f t h e d o m i n a n t f r e q u e n c y . T h i s i n t e rv a l

w a s c h o s e n e x p e r i m e n t a l l y . I t w a s f o u n d t h a t i n c l u d in g m o r e h i g h - f re q u e n c y

s i g n a l c a u s e s in s t a b i li ty . T o e s t im a t e t h e d o m i n a n t f r e q u e n c y , T m u s t b e e q u a l

t o a t l e a s t o n e f u l l c y c le o f t h e l o n g e s t p e r i o d e x p e c t e d b y t h e n e t w o r k . F o r t h i s

c a l cu l a ti o n , t h e f a c t t h a t t h e p r e d o m i n a n t f r e q u e n c y is a s s o c i a t e d w i t h t h e p u r e

P - w a v e c o r n e r f r e q u e n c y i s n o t o f c r u ci a l im p o r t a n c e . T h e d i ff e r en c e b e t w e e n

t h e P - w a v e a n d S - w a v e c o r n e r f r e q u e n c i e s is m u c h s m a l l e r t h a n t h e d i ff e re n c e

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

m o r e d a n g e r o u s s i t u a t i o n c a n o cc u r w h e n t h e i n t e g r a ls i n e q u a t i o n 2 ) a r e

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

P - w a v e p u l s e .

T h e e x a m p l e s a r e c h o s e n t o c o v e r a w i d e r a n g e o f p o s s i b le t y p e s o f p o s s i b le

s e i sm i c s i g n a ls w i t h t h e p r e d o m i n a n t f r e q u e n c y v a r y i n g f r o m 1 0 .8 to 5 .2 H z .

F i g u r e s 3 a n d 4 s h o w e x a m p l e s i n w h i c h t h e d i r e c t P - w a v e p u l s e p r o b a b l y

o v e r l a p s w i t h t h e S - w a v e f i r s t a r r iv a l . R e c o r d s p r e s e n t e d i n F i g u r e s 1 , 3 , 4 , a n d

5 h a v e w e l l - d e f i n e d f ir s t P - w a v e a r r i v a l s , w h i l e o n F i g u r e s 2 a n d 6 t h e f i r s t P

w a v e i s n o t a s c l e a r .

D u r i n g t h e p r o c e s s o f d e v e l o p i n g th e a l g o r i t h m t o c a lc u l a t e t h e c h a r a c t e r is t i c

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


9/10

188 A. CICHOWICZ

c~

_ ,,,,,,:?.,.,,,,1~,,,,,,i,,,,,,,,,[,,.,~,,,,i,,,,,,,,,i,,~,,,,,r,,,,,,,,i,.,,,,i,,,,,%,,,,,,,,I,,,,,,Hl,,,,~rm~

V

~ ......... ''~'~H'~''~''''~'''~''~''~' ''~'~''~''~' 'r~ ~ T'~ ~' ~ ~'~`~''''~' '~'~''''i ' ''~''''''1 ~ d r ~

o.o ~.2 2.~ ~ '~ i

~ o /

o s 1

......... '~'~'~ ~I~ '~`~' ~`'''''i~ '~'~'~' r~`'~` ~ '~'' ~ ~i'''''~i'''''''t

o a 1 2 2 4 0 0 1 2 2 4

6 6

F r o . 6 . N o t e t h e v e r y s t r o n g P - c o d a s i g n a l o n t h e L c o m p o n e n t , w h i c h c a u s e s b a d p e r f o r m a n c e o f

t h e e n e r g y r a ti o p a r a m e t e r ,

F3 t ) .

H o w e v e r , t h e f i r s t a r r i v a l o f t h e S - w a v e p h a s e i s s t i ll a s s o c i a t e d

w i t h t h e l a r g e s t i n c r e a s e i n t h e c h a r a c t e r i s t i c f u n c ti o n . T h e p r e d o m i n a n t f r e q u e n c y is 7 .8 H z . S e e

c a p t i o n o f F i g u r e 1 f o r f u r t h e r e x p l a n a t i o n s .

transverse components. No advantage was gained, and we dropped this parame-

ter to reduce computation time.

Figures i to 6 also show the p ara met ers of the chara cteristic function sepa-

rately, which do not always reliably declare the S phase. It can be seen that the

individual parameters of the characteristic function have a larger numb er of the

false alarms than does the characteristic function. The last graph on the figures

shows that the characteristic function, F(t), has better signal-to-noise behavior

than the separate parameters. A sudden increase in

F t )

is observed when the

S-phase appears in the P coda. Those graphs show the real st ren gth of the

product defined by equation (9).

C O N C L U S I O N S

Due to the nat ure of noise in a real seismic signal, an S-picker works well if

the algorit hm exploits a few par ame ter s of the seismic signal th at are disti nctly

different for the P wave and S wave. An algorithm tha t exploits only one

featu re of the seismic signal can fail. The a dvan tag e of the characteristic

function,

F t ) ,

is th at it includes several attr ibut es of the S phase. Therefore,


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AN AUTOMATIC S-PHASE PICKER

189

even small simul tane ous increases of each par ame ter cause a significant in-

crease of the characte ristic function.

This algor ithm can serve local seismic netwo rks as it provides flexibility for

different signal-and -noise conditions. A high degree of control of the software

parame ters obviates the time-consuming adju stmen t of constants at a new site.

For good performance of the S-phase picker, the pulse of the first-arrival

P-wave mu st be well defined. The algo rithm works well for 65 to 70 of dat a

with a range of magni tude from -1 to 3. For a FORTRAN impleme ntation of

the algorithm, send a request to author.

ACKNOWLEDGMENTS

I am grateful to the anonymous reviewer whose critical remarks improve considerably the text of

the paper.

REFERENCES

Allen R. V. 1978). Automatic earthquake recognition and timing from single trace, Bull. Seism.

Soc. Am. 68, 1521-1532.

Andrews, D. J. 1986). Objective determinatio n of source parameter s and simil arity of earthquakes

of different size, Maurice Ewing Symposium on Earthquake Source Mechanics, American

Geophysical Union; Washington, D.C., 20-23 May.

Baer, M. and U. Kradolfer 1987). An automatic phase picker for local and teleseismic events, Bull.

Seism. Soc. Am. 77, 1437-1445.

Boore, D. M. 1983). Stochastic simula tion of high- frequency ground motion, Bull. Seism. Soc. Am.

73, 1865-1894.

Cichowicz, A., R. W. E. Green, and A. van Zyl Brink 1988). Coda polarization properties of

high-frequency microseismic events, Bull. Seism. Soc. Am. 78, 1297-1318.

Cichowicz, A. and J . Leliwa-Kopystynski 1975). Algorithm for the determinatio n of the f irst

approach of P-wave, Publs. Inst. Geoph. Pol. Ac. Sci. 96, 121-130.

Granet, M. 1983). An automatic seismic signal detection based on linear prediction filter theory,

Ann. Geophys. 1, 109-114.

Kanasewich, E. R. 1981). Time Sequence Analysis in Geophysics The University of Alberta Press,

334-354.

Roberts, R. G., A. Christoffersson, and F. Cassidy 1989). Real-time event detection, phase identifi-

cation and source location estimation using single station three-component seismic data,

Geophys. J. 97, 471-480.

Samson, J. C. 1977). Matrix and Stokes vector representations of detectors for polarized waveforms:

theory, with some applications to teleseismic waves, Geophys. J. R. Astr. Soc. 51,583-603.

UNIVERSITYOF THE WITWATERSRAND

BERNARD PRICE INSTITUTEOF GEOPHYSICRESEARCH

PRIVATE BAG 3

WITS 2050

JOHANNESBURG,SOUTHAFRICA

Manuscript received 18 November 1991

An Automatic S-phase Picker

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