Bulletin of the Seismological Society of America, Vol. 83, No. 3, pp. 830-850, June 1993
IMPACT OF BROADBAND SEISMOLOGY ON THE
U N D E R S T A N D I N G OF STRONG MOTIONS
DON HELMBERGER, DOUGLAS DREGER, RICHARD STEAD,
AND HIROO KANAMORI
ABSTRACT
Most analyses of strong motion attenuation assume simple whole-space
type geometrical spreading, namely ( 1 / R ) or its modified form e kR/R.HOWever, broadband data presently becoming available suggests a more complex
behavior with substantial crustal effects. Events such as the Sierra Madre
event, M = 5.8, triggered the strong motion channels at all of the TERRAscope
stations allowing for 0.01-sec sampling of the wavefield. We find that most of
the well-defined crustal bodywave arrivals defined and modeled in the 1 to
0.1-hz bandpass also contain high-frequency energy. By comparing the triggered channels with the continuous channels we see that several of the more
distant stations triggered on the depth phase SPmP.These phases as well as
the depth phase sSmS are obvious in velocity and quite apparent in accelerations. Our best models for Southern California contain a relatively thick
low-velocity layer at the surface, roughly 5 km thick with shear velocities
below 3 km/sec. This layer or zone, because it appears to vary considerably,
controls the wavefield at nearly all frequencies out to about 60 km and yields
attenuation decay faster than (1 / R). At larger ranges the lower crustal triplications dominate and the attenuation curve flattens. Adding random scatters to
these layered models adds additional complexity but does not alter the basic
flat-layer predictions.
INTRODUCTION
Amplitude decay or attenuation as defined by the strong-motion community
has received a great deal of attention in recent years. Earlier strong-motion
datasets were truncated at relatively small distances, typically around 70 km.
This seemed to be caused by the prevalent processing method, in which one
truncates the range of interest at the' first strong-motion station that failed to
trigger. However, more complete datasets such as those produced from the
Loma Prieta earthquake, show strong evidence for a flattening and a possible
increase in amplitude near a distance of 100 k m Campbell, 1991 and Somerville
and Yoshimura 1990. The latter study suggested that reflections from the Moho
discontinuity was responsible for this effect. Weak-motion observations from
aftershocks seem to confirm the "Moho-reflected hypothesis" as reported by
McGarr et al. (1991). The relatively thin crustal thickness and relatively large
source depth in this region are apparently the reasons for the shift in Moho
phases to nearer distances. I-Iowever, given the scattered nature of the amplitudes produced by the relatively narrowband conventional strong-motion instruments, it proves difficult to resolve these issues. Fortunately, the recently
installed TERRAscope array is providing the ideal data to address the role of
the crust in strong-motion generation. In particular, we can now examine the
broadband wavefield for relatively strong earthquakes and their aftershocks
along similar paths. Thus, the Sierra Madre earthquake, M = 5.8, has been
recorded well enough to examine displacements, velocities, and accelerations
830
BROADBAND
SEISMOLOGY
ON UNDERSTANDING
STRONG
MOTIONS
831
with little concern about instrumental distortions. Moreover, we find that the
displacement field can be relatively well explained with standard Southern
California travel time models, at least at long periods. Such models indicate a
cross-over in distance at about 130 km, where ray paths bottoming in the lower
crust become the first arrivals. By comparing the observed broadband records
with the strong motions, we find that the critical angles identified for l-sec
signals correspond with the timing of strong high-frequency arrivals. This paper
is primarily concerned with characterizing the seismic paths at these ranges, 20
to 160 km, and their associations with the complete field of motion.
The data analyzed in this report were produced by the well-studied Sierra
Madre earthquake of 28 June 1991 (Dreger and Helmberger, 1991a; Wald;
1992). The latter study indicates that this event was relatively high-stress drop,
and thus an appropriate source for studying the attenuation of the strong-motion
field. Figure 1 displays the locations of the existing TERRAscope array stations
in which the event proves to be equidistant to four of the stations (Table 1). A
comparison of the displacements produced by these stations with corresponding
synthetics is given in Figure 2. The waveform data are plotted in absolute time,
whereas the synthetics appropriate for a SoCal velocity model A (Table 2) have
been delayed by 0.35 sec for alignment with the first arrivals. Arrival times of
Pn (mantle headwave), PmP and S mS (reflection from the Moho), and the depth
phase SPmP appropriate for model SoCal are indicated. The phase marked Pn is
near the critical angle, so the Moho reflection, PmP, dominates the associated
Sierra Madre Event: 28 June 1991
36
35
0
34
33
-120
-116
-116
West Longitude
FIG. 1. M a p of Southern California showing the locations of the TERRAscope stations and the
Sierra Madre event indicated by the star. Note that four of the stations are essentiallyat the same
range of 160 kin: GSC, ISA, PFO, and SBC.
832
D.
ETAL.
HELMBERGER
TABLE 1
TERRAsCOPE STATIONLOCATIONS
Station
Latitude
(n)
Longitude
(w)
Distance
(km)
GSC
ISA
PAS
PFO
SBC
35.300
35.643
34.148
33.609
34.442
116.810
118.480
118.172
116.455
119.713
Azimuth*
158.2
159.6
20.6
159.6
159.4
44
344
232
117
277
* A z i m u t h to t h e station in degrees.
Comparison
of B r o a d b a n d
Tangential
GSC
Radial
~ ~
1.03e-01
--~,,
S~nth
crn
i,
I
iii~
- ... •
ISA
Vertical
t
,
~ '
~
~
8.38e-02
cm
02 cm
~-01 crn
i
i
i
i
i
i
Data and Synthetics
i
i
f~
7.75e-02
I
I
I
i
I
t
I
i
i
I
ic
i'
,
G.36e-02
cm
'l
m
'M
I
i
i, i,
~.lle-02
i
i
,
i
l
i,
J . . . . . . . . . . . . . .
r
i
i
i
i
i
i
I
i
J. . . . . . . . . . . . . . .
J.j . . . . .
i
i
i
i
i
i
t
p
.J_t- ....
i i
i
02 crn
I
i ,
i
crn
~,
J ..............
i ~
i L
1.29e-01
crn
i
i
i
i
i
i
i
,
i
t- . . . . . . . . . . . .
6.08e-02 cm
~,.11o-02~m
~-02cm
I:
i
i
l
l
i
i
i
i
i
i
i
i
i
.k . . . . . . . . . . . . . .
I
.LJ ..................
l i
.J_L. . . . .
f t
01 c m
l
i
3.86e-02cm
1
,,
i
02 cm
,1
~'6eiO~
i
02 cm
i
--L-£
....
l I
cm
,,
~.
__i
i
I
Synth
Synth
i
I
i
~
4.32e-02cm
I
i
,
i
A
i
I
i
i
,
i
I
i
i
i
i
i
,
i
r
- . L - .U . . . .
SBC
,
I
i
i
i
r
i
l
7.29e-02
I
i
i
02 crn
;
~
i
Synt
PFO
r
i
,
i
i
i
, ,
i
r
I
i
i
~
i
i
l
|
1.1~'e-01 cm
i
~ 4i
i
l
i
i
J
i
i
i
i
i
t
i
i
i
i
i
i
i
i
i
i
F
i
sPmP
srns
sPmP
sins
/~ 3 . 6 3 e - 0 2
cm
i
,
.
1 ,09.ecO1 c m
02 cm
J
,
L
r
Pn
r
i
sPmP
S~S
I
30.00
see
Pn
Pn
FIG. 2. Comparison of t h e b r o a d b a n d d i s p l a c e m e n t d a t a w i t h corresponding synthetics. P e a k
a m p l i t u d e s are expressed in cm. Pn indicates the m a n t l e arrival. T h e reflections from the crustm a n t l e interface are labeled sPmP a n d SINS, respectively.
BROADBAND
SEISMOLOGY
ON UNDERSTANDING
STRONG
MOTIONS
833
TABLE 2
CRUSTAL MODELS
Station
Vp
(km/sec)
Vs
(km/sec)
p
(g/cc)
Th
(kin)
A
5.5
6.3
6.7
7.8
5.5
6.3
6.7
7.8
7.85
3.8
5.5
6.2
6.8
8.3
5.4
6.2
6.6
7.5
7.8
3.18
3.64
3.87
4.5
3.0
3.6
3.8
4.3
4.4
1.98
3.15
3.52
3.83
4.6
3.2
3.6
3.75
4.1
4.25
2.4
2.67
2.8
3.0
2.4
2.6
2.8
3.0
3.4
2.3
2.6
2.7
2.87
3.36
2.7
2.85
3.2
3.42
3.45
5.5
10.5
19.0
-5.5
9.5
19.0
5.0
B
C
D
1.5
2.5
22.0
6.0
4.0
16.0
8.0
3.0
p u l s e a t l e a s t a t s h o r t periods. R e m a r k a b l y , t h e o b s e r v e d v a r i a t i o n s in t h e
t r a v e l t i m e s of t h e s e m o h o reflection p h a s e s a r e less t h a n 3%. H o w e v e r , t h e
s u r f a c e w a v e s s h o w c o n s i d e r a b l y m o r e s c a t t e r ; t h i s is e s p e c i a l l y t r u e for t h e
SBC s t a t i o n w h e r e t h e o b s e r v e d Love w a v e a p p e a r s to be a t l e a s t 10 sec late.
T h e R a y l e i g h w a v e fit is q u i t e good a t s t a t i o n GSC, b u t s o m e w h a t m i s a l i g n e d in
t i m i n g a t s t a t i o n s I S A a n d P F O . I t a p p e a r s t h a t s o m e m o d e l a d j u s t m e n t s of
s h a l l o w s t r u c t u r e for t h e s e t h r e e p a t h s could b r i n g t h e s e s y n t h e t i c s u r f a c e
w a v e f o r m s into b e t t e r a g r e e m e n t w i t h t h e d a t a , b u t t h e r e a r e s o m e obvious
a d v a n t a g e s in w o r k i n g w i t h a 1D model. B e c a u s e t h e b o d y w a v e s a p p e a r m o r e
s t a b l e in t i m i n g , we c a n t r u n c a t e t h e w a v e f o r m s j u s t before t h e s u r f a c e w a v e s
a n d u s e t h e r e l a t i v e s t r e n g t h s of t h e v a r i o u s pulses, SInS to sSmS etc., to
d e t e r m i n e source c h a r a c t e r i s t i c s . I f we f u r t h e r s m o o t h t h e s e o b s e r v a t i o n s b y
convolving w i t h a l o n g period filter, we find t h a t t h e s m a l l differences in t i m i n g
c a n be n e g l e c t e d a n d a direct w a v e f o r m i n v e r s i o n t e c h n i q u e c a n b e applied. A
m o m e n t of 2.5 × 1024 d y n e - c m a n d t h e f a u l t o r i e n t a t i o n p a r a m e t e r s , s t r i k e =
235 ° , r a k e - 7 4 ° , a n d dip = 50 ° , u s e d in c o m p u t i n g t h e s e s y n t h e t i c s , w e r e
o b t a i n e d f r o m a l o n g - p e r i o d source i n v e r s i o n s u c h as is d i s c u s s e d b y D r e g e r a n d
H e l m b e r g e r (1991a). T h e a b o v e o r i e n t a t i o n a n d m o m e n t a r e in e x c e l l e n t agreem e n t w i t h s t r o n g - m o t i o n w a v e f o r m a n d t e l e s e i s m i c d a t a as i n v e r t e d b y W a l d
(1992). T h e l a t t e r s t u d y p r o d u c e d a d i s t r i b u t e d f a u l t m o d e l in w h i c h t h e r u p t u r e
p r o p a g a t e d u p a n d to t h e s o u t h w e s t . A s i m i l a r p i c t u r e is o b t a i n e d b y c o m p a r i n g
t h e a f t e r s h o c k s w i t h t h e m a i n s h o c k on t h e T E R R A s c o p e a r r a y ( D r e g e r a n d
H e l m b e r g e r , 1992).
A l t h o u g h d i r e c t i v i t y h a s a s t r o n g effect on t h e a n a l y s i s of t h e motion, as
d i s c u s s e d in t h e a b o v e p a p e r , we will a s s u m e a s i m p l e p o i n t source in t h i s s t u d y
a n d c o n c e n t r a t e on p a t h effects. T h u s , we a s s u m e a t r i a n g u l a r t i m e h i s t o r y , 0.5
sec u p a n d 0.5 sec down, for t h e far-field d i s p l a c e m e n t p u l s e as d e d u c e d b y
834
D. H E L M B E R G E R E T A L .
Dreger and Helmberger (1991a). This was the time history used in generating
the synthetics displayed in Figure 2.
In the next section, we introduce the broadband velocities and accelerations.
This is followed by a discussion of forward-modeling attempts involving flatlayered models and the properties of the crustal waveguides. Following this, we
introduce random scatterers into the various layers and investigate their contributions to the wavefield and their impact on amplitude attenuation.
Velocity and Acceleration Data
The TERRAscope system operates in two modes: one samples every 0.05 sec
continuously, while the other is triggered and samples every 0.01 sec. This is
accomplished by employing two types of sensors, Streckeisen STS-1 for the very
broadband (vbb) channel, and Kinemetrics FBA-23 for the low-grain (lg) channel. For the P a s a d e n a station, the displacement response of the vbb ~channel
with a Quanterra 24-bit digitizer is given as a function of frequency f by
I ( f ) = 2 ~ i f 3 G / [ f 2 - 2ihfo f -
f02],
(1)
where fo = 0.00278 Hz, h = 0.707, and G = 1.04 × 107 counts//(cm/sec). At
frequencies higher than 7 Hz, and anti-alias filter with an f-2 roll-off is
applied. This response is approximately flat for ground-motion velocity over a
frequency range of 7 Hz to 0.0033 Hz (300 sec). This channel is digitized at 20
samples/sec.
The displacement response of the lg system with a Quanterra 16-bit digitizer
is given by
I ( f ) = 4 ~ 2 f o 2 f 2 G / [ f 2 - 2ihfo f -
fo2],
(2)
where f0 = 50 Hz, h = 0.7, and G = 37.38 counts/(cm/sec2). This response is
approximately flat for a ground-motion acceleration at frequencies lower than
20 Hz. This channel is digitized at 100 samples/sec.
The deconvolution of the instrument response for the vbb channel is usually
performed on the frequency domain using (1). For the lg channel, deconvolution
is performed either on the frequency domain using (2) or in the time domain by
doubly integrating the acceleration trace. The gain factors at stations other
than P a s a d e n a are within 10% of that for Pasadena; detailed constants are
published in Wald et al. (1991).
The calibration of the entire system has been performed whenever a large
amplitude motion was recorded with both STS-1 and FAB-23. We do not
calibrate the shape of the response curve, b u t calibrate the gain factor by
comparing the amplitudes recorded with STS-1 and FBA-23. The response is
very stable, and we believe that the overall gain is accurate within 5%.
On the top three rows of Figures 3, 4, 5, and 6 are the vbb responses
(continuous sample) and on the bottom three rows are the lg responses (triggered). The velocities are essentially identical, which demonstrates the calibration stability. The accelerations are somewhat different as a result of the
sampling differences, b u t the depth phases are still apparent on the velocity
times histories, as indicated by the dotted lines. It appears that most of lg
channels triggered on the phase sPm P. Unfortunately, some of the beginning
835
B R O A D B A N D S E I S M O L O G Y ON U N D E R S T A N D I N G S T R O N G M O T I O N S
PFO Velocities
0.2 -
II
'
'
'
PFO Accelerations
'
U
-
0.1
0.0
-0.1
I
-
0.1(]
'
'
i
'
'
II
1
'
'
'
I
_
t
I
II
'
'
i
I
,i
_--
0.05
,
,
,
,
,
,
t
~
0.00
-0.05 -0.I0
Rod vbb
r
iJ
'
r
q
i
-
'
II
'
'
'
~
'
'1'
d
'
'
'
~
0.1
0.0
~
-0.I -Ver vbb
-
I
.-
f
-
I
0.2
0.1
0.0
-
~lon Ig
-OJ
0.10
i
iI
,
~
_
'
I I
'
'
'
I
'
iI
'
0.05
0.00
-0.05
O.l
" Rod Ig 1
~
L
0.0
-0.1 -Ver Iglll
-(
Ver Ig
,
I
,
I1
J
-'
30
40
50
60
30
40
50
60
FIG. 3. Comparison of the observed velocities and accelerations at PFO, generated by taking the
derivative of (vbb) and by integrating (lg).
portions of the wavetrain were lost due to bugs in a new system (see Figures 4
and 6).
Crustal Structure a n d P a t h Contributions
We begin by convolving the observed broadband data through a series of
instrumental responses, as shown in Figures 7 and 8. These three instruments
have recorded data in P a s a d e n a for m a n y years, and comparing TERRAscope
data with the existing dataset provides highly useful, as reported by
Helmberger et al. (1992). Note that although the surface waves are quite
prominent on the long period P r e s s - E w i n g (3090) in Figure 7, they are not
apparent on the conventional Wood-Anderson (WASP). The intermediate channel, or WALP (long period Wood-Anderson), contains some arrivals associated
with surface waves and body waves. Included in these figures are the motions
produced by a magnitude 4.2 aftershock (28 June, 1700UT). The aftershock has
a slightly different mechanism which enhances the phase P~ P in Figure 7 as is
particularly apparent in the WALP bandpass (see Zhao and Helmberger, 1993).
The similarity between the mainshock and aftershock observed in these figures
is, also, apparent at the other stations indicating the deterministic nature of the
wavefield. The 3090 response is relatively easy to match with synthetics from
standard models, whereas the WASP data is more difficult. However, it appears
that all three responses can be explained to some degree with some small
836
ET AL.
D. HELMBERGER
GSC Velocities
II
0.1
i
I
,
GSC Acceleration
iI
_
I I
'
'
I
II
'
'
I
i
0.[
-0.1
0.1
"
il
'
I
I
,
i
,
,
'
'
.
0.[
-
I
-0.1 - Rod vb5
'~1
i
0.1
1.0L-
0.0
0.51-0
-0.5
-0.1
il
0.1
i
'
I
.
'
iI
,
. J
0
~
II
-
I
I
I
0.10 •
025
0.00 •
I
-0.05 I
-0.10 Rod Ig r
-0.15 tP
0.10
I
0.05 I
020
-0.05 I
-0.I0 _-Vet Ig I
-0.15
II
3O
I
I .
I
Ton Ig
'
I
I
0.0
-0.1
I
F-'L
Tan
•
,glI
I 1
'
'
'
I
'
'
'
I
,
,
,
'
'
'
'
I
~
l
'
"
-
-Vet
40
FIG. 4. C o m p a r i s o n
50
60
'
II
Ig I
30
I
'
,
,
,
40
' -
II
II
50
=
,
,
60
of the observed velocities and accelerations at GSC.
adjustments in the crustal model, see the middle columns of synthetics. An
overlay of these synthetics with the mainshock observations shows remarkable
waveform agreement in all three passbands. Note t h a t in the synthetics the
phase sPmP is obvious on the vertical component, whereas the phase sSmS is
strong on the tangential component as predicted by the radiation pattern. The
same features are clear in the data as well. Note t h a t the phase sSm S is slightly
delayed in the data compared with the synthetic. A slight reduction in the upper
crustal shear velocity would correct this feature, but model B presented in Table
2 does quite well in fitting the other three stations as discussed later.
The amplitudes of the synthetics displayed in Figure 8 are about 50% larger
t h a n the mainshock observations. There are two reasons for this discrepancy.
First, the amplitudes observed at PFO are smaller t h a n those at the other
stations relative to the synthetics used in the source inversion by about 25%
(Fig. 2). This suggests t h a t the receiver structure at PFO is basically harder and
faster t h a n at the other stations. The other reasons is t h a t the shear velocities
displayed in model B (Table 2) are lower t h a n in model A which tends to amplify
the surface motions by about 25%. Thus, by slowing down the shear velocity we
can model the observations with less moment, in this case M 0 = 1.7 × 10 24
dyne cm. Presumably, the enlargement of the TERRAscope array, now in
progress, will help resolve this issue when the crust and receiver structures
become better known. Note t h a t the radial component is particularly sensitive
to the receiver structure, as displayed in Figure 9, in which a soft surface layer
B R O A D B A N D S E I S M O L O G Y ON U N D E R S T A N D I N G
ISA VelociUes
0.10 - '
•
0.05
0.00
-0.05
-0.10
837
ISA Accelerations
i
I
STRONG MOTIONS
I I
'
'
'
I
'
'
'
I
i
0.05
0.00
"
-0.05
O.lO
0.05
0.00
-0.05
-0.10
0.10 -
I
I
,
,i
II
11
-
'
--
0.05
O.OG
-0.05 -Ton Ig I
-'- Ton Ig
iI
0.06
0.04
0.02
O.OC
-0.02
-0.04 Rod Ig
-8R
iI
"
It'
I--
]
I
0,0~
O.OC
-0.0~ -Ver
-0.IC
Ver !g
'
30
40
50
50
30
40
59
60
FIG. 5. Comparison of t h e observed velocities a n d accelerations at ISC.
has been included (see model C in Table 2). Such a layer increases the ratio of
WASP to 3090 by about a factor of 2.
Comparing the long period synthetic waveforms from the latter two models
indicates the relative insensitivity of the long period synthetics to structure.
Furthermore, by breaking down the contributions from the various layers, we
can see that the shallow crustal structure dominates the longer period behavior
with distance whereas the deeper structure controls the high-frequency arrivals. The evolution of this behavior with distance will be addressed later. We
derived model B by making some adjustments in the shear velocities of model A
based on examining particular generalized ray paths (Helmberger et al. 1992).
Note that the previous synthetics have been generated by reflectivity, which
produces complete solutions. Figures 10 and 11 display the evolution of the
P-SV field as a function of distance and path. These synthetics are expressed in
velocity so that they can be compared directly with data.
The first column of these figures displays the arrivals associated with the top
layer. Two groups of arrivals develop, the first is dominated by P and multiple
P - S V waves in which the main source of energy is the up-going SV ray, as
displayed at the top of the figure. The longer period contributions of this control
the first 15 sec of the 3090 responses discussed earlier, and is derived essentially from energy traveling as P-head waves or refractions along the bottom of
this waveguide. Similar types of motions are associated with the lower crustal
838
E T AL.
D. H E L M B E R G E R
SBC Velocities
SBC Accelerotions
0.4
0.2
0.0
-0.2
-0.4
0.4
0.2
0.0
-0.2
-0.4
0.2
2
3.
t
I
-
I
"
-
I
0.0
-0.2 - Ver vbbl
--]-q[-~1-'----'~[--i"--
0.4
--
r
I
-
'
0.2
I
O.C ~_
Ton
Ig
J
-0.;~
-
I
I
i
Ton Ig I
~
-
I
-
Rod Ig I
--
I
I
I
:
-
I
50
40
50
60
tO
t0
50
60
FIG. 6. C o m p a r i s o n of t h e o b s e r v e d v e l o c i t i e s a n d a c c e l e r a t i o n s a t S B C .
waveguide (crust-mantle) where t h e y are are referred to as PL waves,
(Helmberger and Engen, 1980). They appear to be quite insensitive to structure.
Note t h a t adding a shallow layer does not change the long period substantially,
compare Figures 8 and 9 and see Dreger and Helmberger (1990).
The second group of arrivals in the lower traces of column one are produced
by multiple SV waves. They decay with distance rapidly because the upward
transmission is coefficient is weak. Shallow PL waves arrive as P-waves along
the surface and tend to be the strongest on the radial, whereas the second group
tends to be strongest on the vertical. This feature is well-defined in the
broadband seismograms discussed earlier.
The second column of these figures contains the summation of column one
plus arrivals t h a t r e t u r n from the lower crust as displayed. The latter have
little effect at the closer distances. They contribute when critical angles are
reached at 60 km for the Conrad and at 120 km for the Moho. Adding in the
surface reflections (pP, sP, pS, sS), third column, produces little effect on the
vertical component except at the largest distance, at which sSmS becomes
apparent. The phase sPinP is very apparent on the radial component.
A comparison of the observations in the velocity domain with the corresponding synthetics is given in Figure 12. These synthetics were generated with a
reduced moment, 35% of the long period level, which reduces the amplitudes
accordingly. Thus, the peak amplitude of the vertical component at PFO is 0.18
BROADBAND SEISMOLOGY ON UNDERSTANDING STRONG MOTIONS
839
VERTICAL
Aftershock
I'1
'trlrr
~
. . . .
f~
3oo0
Synthetic
Mainshock
2 cm
~
~
2.07e-04cm
/
C
e-
m
Cm
J
I
W A L P ~
1.70e+O0c r n
02 cm
1.24e+o2cm
l e 0 cm
3.57c+0[cm
I
PrnP SPmP I SrnS
E
30.00secI
FIG. 7. Display of the vertical motions for the mainshock, aftershock, and synthetic (model B in
Table 2) after the simulation of the various instrumental responses at station PFO. The
Wood-Anderson responses, WALP (6 sec torsion) and WASP (0.8 sec torsion) gain factors were
included in the amplitudes.
TANGENTIAL
Aftershock
Synthetic
1,2e-O1cm
1.20e-03cm
D
I
S
P
~
~
~
1.20e÷OOcm
SmS
II
sSmS
Mainshock
2 cm
cm
~
crn
02 cm
01 cm
I
~
~
t cm
30.00secI
FIG. 8. Display of the tangential motions for the mainshock, aftershock, and synthetic (model B
in Table 2) after the simulation of the various instrumental responses at station PFO. The
Wood Anderson responses, WALP (6 sec torsion) and WASP (0.8 sec torsion) gain factors were
included in the amplitudes.
840
D. H E L M B E R G E R
ET AL.
PFO LP3090 synthetics
Tangential
~.
~
c
Radial
Vertical
m
UP
13
UP and
Conrad
13
Total
F
30 s e c o n d s
P F O WA.SP s y n t h e t i c s
Tangential
Radial
Vertical
13 cm
7.4 cm
6.9 cm
UP
UP and
Conrad
7
Total
--I
30 s e c o n d s
FIG. 9. Display of synthetics (model C in Table 2) indicating contributions from the upper
waveguide relative to the entire model. The traces marked U P are appropriate for no layering below
the source.
cm/sec instead of 0.5 as in the earlier Figure 6. This reduced moment produces
about the right level of motion at most stations except SBC, which is in the
direction of rupture and is enhanced by directivity, (Dreger and Helmberger,
1992). Station ISA is both near a tangential node and spread out by directivity,
a feature also apparent in waveshape, where it appears to have longer periods
than the others. Still another difficulty at ISA is the lack of clean separation
B R O A D B A N D S E I S M O L O G Y ON U N D E R S T A N D I N G
STRONG MOTIONS
841
VELOCITYFIELD(VERTICAL)
A~
_• 1.1
~
1.1
~
1.I
~.44
+
1.1
~
1.1
80 ~ . 2 8
~
.81
~
100~ . 1 8
~
.47
~
SmS
.71
~
km
40
60
120
~.15
.81
.48
-~-w#- 4~t .78
140
~
160
.10
~
..~.50
I
I
20 sees
I
sPmP
Fro. 10. Vertical component s y n t h e t i c s (GRT) as a function of distance a n d ray s u m m a t i o n . The
n u m b e r s indicate the p e a k a m p l i t u d e s in c m / s e c where t h e M o w a s set at 2.4 × 10 24 ergs for
i n s t a n c e s in which model B was u s e d in c o m p u t i n g the synthetics.
into the P-SV and SH systems of motions. Note that most of the stations rotate
quite well, especially PFO, which also produces the best fit to the synthetics.
The drop in moment required to model the higher frequency waveforms, as in
this case, has been noted in m a n y studies. In particular, it has been discussed in
Bent and Helmberger (1991) in which five events along the extension of the
Transverse Ranges have been studied as a group. They find that the 1973 Point
Mugu event, M = 6, has the strongest teleseismic short period to long period
ratio, roughly 90% of the long period moment also required to model the short
842
D. H E L M B E R G E R
ETAL.
VELOCITY FIELD(RADIAL)
40
60
80
100
120
~
~
~
~
~
~
2.0
.85
.28
2.0
~
.84
~
2.0
.83
3o
.16
~
.09
t .10
140 # ~ ~ j . 0 8
~
160 ~ . 0 8
~t~~~.08
t
20secs
~.
21
.07
t
FIG. 11. Radial c o m p o n e n t s y n t h e t i c s (GRT) as a function of distance a n d r a y s u m m a t i o n for t h e
s a m e model. The n u m b e r s indicate t h e p e a k a m p l i t u d e s in c m / s e c where the M 0 w a s set at
2.4 x 10 24 ergs.
period. The smallest ratio occurred for the Santa Barbara 1978 event, in which
only 15% was required. Generally, this ratio has not been considered too
meaningful, because the Earth's attenuation is not known to the precision
necessary to uniquely determine the short period moment. However, in this case
m a n y of the paths are nearly identical, the relative differences between events
are probably real.
A simple interpretation of these results can be given in terms of slip distribution, as recently concluded in a broadband study of the Upland event, M = 5.2,
BROADBAND SEISMOLOGY ON UNDERSTANDING STRONG MOTIONS
PFO
GSC
~l~li¢' .28
T
•••..17
syn
1~"~.25obs
~
V
843
~
.21 obs
.18 syn
.20
.15
.13
ISA
.06
T
syn
.11obs
~ - ~ ~
.55
[-'
.,5
obs
V
t .22 syn
10 s e c s
I
I
FIG. 12. Comparison of observed velocities for which peak amplitudes are given in cm/sec.
Dotted lines indicate the timing of sPmP and sSmS.
(Dreger and Helmberger, 1991b). They find t h a t modeling the whole broadband
waveforms of this event requires a faulting area of about 8 km 2 with a high
stress drop patch, 1 km 2, which contains about 30% of the moment. Similar
results were obtained for the Sierra Madre event from modeling the strong
motion and teleseismic data (Wald, 1992). Wald concludes t h a t a 12-km 2 area
was required with a 3-km 2 patch at the center. His results seem quite compatible with our 35% value required in simulating the velocities. A detailed study of
TERRAscope data from the Sierra Madre earthquake sequence, indeed, produces a distributed fault offset compatible with these results (Dreger and
Helmberger, 1992).
Despite the m a n y inconsistencies in modeling the detailed observed waveforms in Figure 12, it appears t h a t the phase sPmP and sSmS are clearly
844
D. HELMBERGER ET AL.
observed in velocity, and consequently the lower crustal structure becomes the
dominant path at these distances for short periods. Also, the close association in
timing of these phases, between the observed velocities and accelerations,
indicates that this path is the controlling strong motion at these distances.
Thus, there must be a cross-over in distance at which diving energy paths begin
to dominate the direct arrivals. Figure 10, discussed earlier, suggests that this
occurs at about 50 kin, b u t this is influenced by m a n y factors including the
component, the radiation pattern, source depth, and the detailed nature of the
crust. The latter problem will be addressed in the next section in which we
introduce some complexities into the crustal waveguide.
Numerical Scattering Experiments a n d Attenuation
The introduction of laterally varying structure causes considerable interference between the three ray-groups discussed earlier. This is especially true at
mid ranges, 50 to 90 kin, in which the summation has about the same amplitude as each individual group (see Figures 10 and 11). In this section, we
discuss the theoretical results from models containing random scatterers embedded in the various layers. We are particularly concerned with the development of high-frequency arrivals and their amplitude decay with distance.
The model setup is displayed in Figure 13. We investigated four cases with
variation allowed in particular layers: RMOHO (thin, 3 km, layer at the top of
the mantle), R S U R F (surface layer only, 4 kin), RBOTH (both layers at the
surface and at the top of the mantle), and RALL (variation throughout all
layers, total 31 km). The scattering model follows the scheme discussed by
Frankel and Clayton (1984), in which a Gaussian correlation function is imposed on a random medium. We have modified this scheme to permit the
correlation distance to differ between the x and z directions. We note here that
total coda m a y be underestimated, as Frankel and Clayton (1986) have shown
that a self-similar correlation function is preferred to generate sufficient coda.
However, this affects primarily higher frequencies (up to 30 Hz), whereas we
consider nothing above 4 Hz in these finite difference results. Note that the
difference in the nature of the SH and P-SV systems requires different time
A, 50 km
100
150
200
V
V
V
V
l Source
250
V
3.2
2.7
fl=3.6
p= 2.8
3.75
4.1
4.25
I
2.S
2.9
3.3
3.4
SURF
MOHO
FIG. 13. Diagram displaying crustal heterogeneity with layers containing up to 20% velocity
anomalies.
B R O A D B A N D S E I S M O L O G Y ON U N D E R S T A N D I N G
STRONG MOTIONS
845
steps and grid spacings. We used 0.2 km for P-SV and 0.25 for SH, with steps of
0.015625 sec and 0.025 sec, respectively. The variance is set for the P-wave
velocity and is proportional for the S-wave velocity, whereas the density variance is 30% of the proportional variance. The variances and correlation distances used are as follows. For the surface layer, the RMS variance is 0.4
km//sec and the correlation distances are 5 km in x and 15. km in z. For the
mantle layer, variance is 0.3 k m / s e c and the correlation distances are 5 km in
x and 1.5 km in z. For the body of the crust in RALL, the variance is 0.5
k m / s e c , and the correlation distances are 12.5 km in x and 5 km in z. The
RMS variance is up to 10%, and the peak variation8 produced are up to 20% of
average velocities. The position and form of the ~¢ariations are indicated in
Figure 13. Variations of this size have been suggested by Frankel and Clayton
(1984), and others and are probably on the high side based on the stability of
observed crustal arrivals.
The complete wave field for these models was generated with the finitedifference method for ranges from 50 to 275 km with frequencies up to about 2
hz. The technique used in this calculation is discussed in Helmberger and
Vidale (1988), Vidale and Helmberger (1987). It is based on the expansion of the
complete 3D solution of a dislocation source in asymptotic form, which provides
for the separation of the motions into SH and P-SV systems of motion. Closeformed expressions appropriate for finite-difference source excitations are derived for the three f u n d a m e n t a l fault types, requiring separate finite-difference
runs. Only the strike-slip case will be discussed, which conveys the principal
effects of including scatterers on the waveforms.
Results for the P-SV system are displayed in Figures 14 and 15. Two cases
are compared: the case of uniform layered crust (RMOHO) and shallow scatterers (RSURF). These results are displayed broadband, and through a WoodAnderson instrument.
The synthetics appropriate for model RMOHO display m a n y of the characteristics of those models discussed earlier. Note t h a t the shallow structure dominates the motions until about 100 km, at which time the Moho reflection
becomes prominent. This feature is particularly prevalent at WASP, in which
the amplitude increases substantially near 100 km. Note t h a t sSmS is easily
identified starting at about 140 km. The generation of these Moho arrivals
develops sooner in distance in this particular model t h a n in other models
because the crust is slightly thinner. The synthetics for the RSURF model are
more interesting but show the same basic behavior. When WALP responses are
constructed from these two models, we obtain nearly identical results. However,
WASP synthetics for model RSURF show considerably more complexity associated with up-going SV energy t h a n do those for model RMOHO, and makes the
presence of the Moho arrivals less dramatic except for the phase sPmP. The
extended S-wavetrain at high frequency looks like m a n y observed records in
which they are conventionally called Lg.
A sample of the SH synthetics for all the models is displayed in Figure 16. It
becomes difficult to interpret these complex waveforms because we can no
longer decompose the waveform into subgroups, although we can still identify
some of the more important phases such as SmS and sSmS. A brief review of
Figure 16 indicates t h a t sSmS becomes strong near 200 km, and SInS and
SS,nS are particularly obvious at ranges of 170 and 185 in the first three
columns. Direct SmS becomes weaker in the most severe case (right column).
846
D. H E L M B E R G E R E T A L .
RSURF
RMOHO
8.7
~
s.7 50
11.0 u ~
,.,
~0.0
4.1
~
......
i
9,5
8.7
~
6.1
7.2
,o
6.3
6.2
4.6
y~
4,7
~
~
BB
WASP
~
20 sec~ k(-
5.o
,~,~
4.2
@1~
4.7
BB
WASP
FIG. t4. Profiles of synthetics from 50 to 120 km comparing a plane-layered crust (RMOHO) with
a model with scatterers in the upper layer (RSURF). The motions are simulated broadband (BB)
and with respect to a Wood-Anderson instrument. Peak amplitudes are indicated above each
trace in cm.
Apparently, as the ray paths flatten they become more sensitive to lateral
variation, as one would expect, and the multiples t h a t travel more vertically
become increasingly important.
The broadband SH responses of Figure 16 show considerable modulation in
amplitude (see Figure 17). Included in this figure is a ( l / R ) reference which is
commonly assumed in simulation techniques, (Chin and Aki, 1991). This would
correspond to a direct arrival in halfspace, or would be expected for a model
with a smooth velocity increase with depth. The direct arrival attenuates much
faster in the models presented in this paper as compared with models in other
papers because of the effects caused by the thick low-velocity layer near the
surface. The small flattening t h a t occurs near 60 km is caused by the strength
of the first multiple or higher mode Love waves. The increased amplitude near
100 km is caused by the lower crustal transition zone and the sharpness of the
Moho. The strong arrival at the range of 105 km in the full-scattering model,
RALL, is caused by constructive interference between the Moho reflection and
first multiple in the top layer (Love wave). In general, the strong scattering
introduced in this exercise was sufficient to obscure the moho reflection, but the
possibility of large motions near the cross-over distance appears difficult to
avoid.
There are obviously m a n y other reasons for amplitude fluctuations other t h a n
those displayed in Figure 17, such as source radiation patterns, source duration
BROADBAND S E I S M O L O G Y ON U N D E R S T A N D I N G STRONG M O T I O N S
847
RSURF
RMOHO
5.0
1 3 0 ~
,.o
4.,
~_~
4.5
,.2
1,o
,.o
__.
.....
18o
3.6
BB
2.0
WASP
zo sees~
BB
WASP
FIG. 15. Continuation of Figure 14 from 125 to 195 kin.
and complexity, mini-basin structures, nonlinear behaviors, and site-conditions.
Many of these features are discussed in the special Loma Prieta issue (Hanks
and Kruwinkler, 1991) and cannot be neglected in assessing strong motion
hazards.
CONCLUSIONS
We have reviewed the broadband observations of the recent Sierra Madre
earthquake in terms of displacement, velocity, and acceleration on the TERRAscope array. We found that the depth phases sP m P and sS,n S are apparent in
velocity and acceleration at four stations near 160 km. These phases are less
apparent at longer periods, in which the upper crustal waveguide still dominates their behavior. These features can be modeled in displacement and
velocity, as demonstrated, and require relatively slow shear velocities in the top
5 km of the crust. This shallow zone has a dramatic effect on the rapid decay of
direct S with distance and probably contributes to its rather unstable observed
behavior in that numerical results from models containing shallow scatterers
predict irregular behavior. Beyond the cross-over distance, the lower crust
dominates and appears to return relatively clear phases, even after adding
scatterers to the crustal models. Essentially, pulses following ray paths travelling more vertically remain less scattered than those travelling more horizontally. Thus, our numerical results, in conjunction with the broadband observations, indicate that directivity m a y be more apparent in S , , S and s S m S than in
direct arrivals.
848
D. HELMBERGER
FD w i t h R a n d o m
E T AL.
Media Reducing ¥=3.90
-~Okm._P~IOHO
_~
RSURF
ICBOTH
RALL
3.62e-05C m _ ~ _ _
4.41e-05cm ~
4.41e-05c m _ ~
80krn A~
2.12e-05crn_~
f
1.97e-05c r n ~ e - 0 5
llOkm_j~ 1.56e-05c m ~ e - 0 5
155kl"n / ~
1.74e-05cm ~
cm~e-05
1.60e-05cra ~ e - 0 5
4.38e-05cm
crn~e-05
cm
3.02e-05cm
cm
1.38e-05crc
i
245km
crn
crJE
1.13e-05cm
1.08e-05c r ~ ~ e ~ ' O 5
I
c m ~ e - 0 6
cm
l
16.00 sec
FIG. 16. Comparison of SH broadband synthetics for the various models along a profile from 50 to
260 kms. Peak amplitudes are given in cm.
BROADBAND SEISMOLOGY ON UNDERSTANDING STRONG MOTIONS
M a x i m u m A m p l i t u d e s f r o m R a n d o m Media F i n i t e D i f f e r e n c e
5e-05
J
4e-05
'
i rmo
-vf_--ho
'
,
I-7
~
•,•
849
,,,,
....
ivf_rsurf 1
ivf_rboth~
ivf_rall |
IlR
3e-05
0
0
".
°
.~ 2e-05
DZX z ~
le-05
0
I
I
50
100
E
150
D i s t a n c e (kin)
I
I
200
250
FIG. 17. Attenuation of amplitude decay with distance showing the effects of the various models.
A ( l / R ) curve is included for comparison. The symbols indicate the peak amplitudes obtained from
Figure 16 after convolution with the Wood-Anderson instrument.
In short, we have demonstrated the role of crustal structure in influencing
strong motions and suggest that modern broadband data m a y contribute to the
resolution of the many issues associated with their generation.
ACKNOWLEDGMENTS
This research was supported by U.S.G.S. contract 14-08-001-G1872 and contribution No. 5143,
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California, 91125.
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850
D. HELMBERGER E T A L .
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SEISMOLOGICALLABORATORY
CALIFORNIAINSTITUTEOF TECHNOLOGY
PASADENA,CALIFORNIA91125
Manuscript received 18 August 1992