Post on 02-Jun-2018
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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
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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 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
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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.
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UNIVERSITYOF THE WITWATERSRAND
BERNARD PRICE INSTITUTEOF GEOPHYSICRESEARCH
PRIVATE BAG 3
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JOHANNESBURG,SOUTHAFRICA
Manuscript received 18 November 1991