13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 1736

EFFECTS OF SEDIMENTARY LAYERS
ON DIRECTIVITY PULSE AND FLING STEP
Yoshiaki HISADA1 and Jacobo BIELAK2

SUMMARY
Effects of sedimentary layers on the long-period directivity pulse and the fling step are investigatedusing the theoretical method developed by Hisada and Bielak [1]. First, basic physics of the directivity
pulses and the fling step are investigated using a simple strike-slip fault model in a homogeneous halfspace. Next, the method is applied to the strong motion recorded at the Lucerne valley during the 1992
Landers earthquake, using the fault model and the local layered structure model by Wald and Heaton [2].
It was confirmed that the maximum amplitude of the velocity and displacement was inclined to the fault
plane at 30 – 50 degree due to the combined effect of the long-period pulse and the fling. The inclusion of
sedimentary layers increases greatly both amplitudes and durations of the directivity pulses, whereas it
does not affect those of the slip pulses. This is because the directivity pulses are the body and surface
waves excited in the sedimentary layers from wide range of faults (the nearest fault to the furthest fault),
whereas the fling steps are generated by the slip of the nearest surface fault.

INTRODUCTION
The long-period directivity pulse and the fling step areprobably the most important near-source strong groundmotions in earthquake engineering (e.g., Somerville et.
al. [3]; Abrahamson [4]). The directivity pulses, as seenin the 1994 Northridge and 1995 Kobe earthquake, havedestructive effects on short- to medium-period structures,
whereas the fling steps, as seen in the 1992 Landers and1999 Chi-Chi earthquakes, may have destructive effects
on long-period structures, such as high-rise and baseisolated structures. As an example showing the fling
step, Fig. 1 shows velocity response spectra (h=5%) for
the 1992 Landers and 1999 Chi-Chi earthquakes. Theiramplitudes exceed constant level of the velocities of1
2

Fig. 1 Examples of the velocity response
spectra showing the fling steps

Department of Architecture, Kogakuin University
Department of Civil & Environmental Engineering, Carnegie Mellon University

building codes (80 to 100 cm/s) at longer periods.
Recently, we developed an efficient method for simulating near-fault strong ground motions in layered
media (Hisada and Bielak, [1]); the method rigorously evaluates the dynamic and static terms of Green’s
functions of layered half-spaces for efficiently computing near-fault strong motions. We first introduce theformulation of the method, and show basic physics of the directivity pulses and the fling step using asimple strike-slip fault model in a homogeneous space. Then, we apply the method to the near-fault strong
motion recorded at the Lucerne valley for the 1992 Landers earthquake to investigate the effects of thesedimentary layers on the directivity pulses and the fling steps.

THEORETICAL METHOD FOR SIMULATING NEAR-FAULT STRONG MOTIONS,AND PHYSICAL INTEPRETATION OF DIRECTIVITY PULSE AND FLING STEP
Theoretical Method for Efficiently Simulating Near-Fault Strong Motions
In order to simulate theoretical strong ground motions for near-faults, Hisada and Bielak [1] introduced
an efficient method using the following new representation theorem, which evaluates the fault integrationof the dynamic and static terms, separately,{}

U k (Y ;ω ) = ∫ TikD ( X , Y ;ω ) − TikS ( X , Y ) Di ( X ;ω )dS + ∫ TikS ( X , Y ) Di ( X ;ω )dS . ………. (1)SS

where, Uk is the kth component of displacement in the
Cartesian coordinate system, X and Y are an observation
and a source point on the fault plane, respectively, S is
the fault plane, Di is the ith component of the fault slip,
and TikD and Tikk are the dynamic and static traction
Green's functions of layered half-spaces.
Equation (1) simulates near-fault ground motions
much more efficiently than the original representation
theorem, which is represented by the total traction
Green’s function alone. The original theorem requires a
lot of CPU time to evaluate the near-singularities of the
dynamic Green’s function numerically, which show
extremely sharp peaks centered at the source point, asshown in Fig.2.By contrast, the first integral of equation Fig. 2 An example of the near-singularity of(1), in which the static Green’s function is subtracted
an integrand of fault integration.
from the dynamic function, can eliminate the nearsingularities completely, because the static function includes all the sources of the singularities of the
dynamic function. The near singularities appear only in the second integral of equation (1). The evaluationof this integral necessitates that a dense set of integration points be distributed in the neighborhood of theobservation point (Fig. 2); this uses up some CPU time. However, since the values of the static functions
remain invariant for all frequencies, this integration needs to be done only once.
When we model surface faulting, we need to compute a lot of Green’s functions with the source points
on and near free surface. For these cases, the wavenumber integrations of Green’s functions require a lotof CPU time, because the integrands do not converge to zero with increasing wavenumbers (e.g., Hisada[5][6]). To cope with this problem, we use the following wavenumber integrations for the integral of thefirst integrand of equation (11),TikD ( X , Y ; ω ) − TikS ( X , Y ) = ∫∞0{ t ( X , Y ;ω , k ) − t ( X , Y ; k )}dk ……….. (2)
D
ik

S
ik

where t ikD ( X , Y ;ω ) and t ikS ( X , Y ; ω ) are the dynamic and static terms of the integrands of the traction
Green's functions, respectively. Since the dynamic integrand converges to the static integrand with

increasing wavenumber, the integrand of equation (2) attenuates rapidly, even for source points on freesurface. On the other hand, we employ the contour deformation method (Greenfield [7]) to evaluate thewavenumber integration of the static Green's functions in the second integration of equation (1). For moredetails, please see Hisada and Bielak [1].
Physical Interpretation of Fling Step and Directivity Pulse
Strike Slip Fault Model
Before investigating effects of sedimentarylayers on near-fault strong motions, we
briefly explain physics of the fling step andthe directivity pulse using simple models
embedded in a homogeneous half-space(Hisada and Bileak [1]). In particular, we
pay special attention to the contribution of
the static and dynamic terms of equation (1)to strong ground motions.
Fig. 3 shows a surface fault and a buried
fault. They are the same left-lateral strike
slip fault with 10 km x 5 km sizes. The
maximum slip is 1 m including the top edgesof the faults, and tapers at both side edges Fig.3 The surface fault model (left), and the buried
fault model (right).
and at the bottom of the fault. The depths ofthe top of the faults are 0 km and 2 km, forthe surface and buried faults, respectively. The slip velocity function is an isosceles triangle with a 1second duration. The location of the hypocenter is shown in the figure, half way down the fault, and therupture velocity is 2.5 km/s. The physical properties of the homogeneous half-space are Vs = 2.5 g/cm3,
Vp = 5 km/s, Vs = 3 km/s, Qp = 200, and Qs = 100.

Results
Fig. 4 shows the vectors of the maximum velocities on the free surface using (a) the surface fault and (b)the buried fault. Both figures include three sets of waves on the line; the left and middle waveforms
correspond to the dynamic and static terms, which stem from the first and second integrals in equation (1),respectively, and the rightmost panels represent the sums of the two terms. The amplitude scale for theburied fault is about half of that for the surface fault. The dynamic terms excite the directivity pulses in thefault normal components for both fault models, especially in the forward rupture direction (the lower halfof the figures). By contrast, the static terms of the surface fault model generate large fling steps, i.e., thelarge amplitudes in the fault parallel components in the vicinity of the fault. As the observation points get
further from the fault, the static terms are quickly attenuated, whereas the dynamic terms are not. This isbecause the static terms consist of the static traction Green’s function (i.e., the order of attenuation is 1/r2),
as seen equation (1), whereas the dynamic terms consist of the body and surface waves (i.e., the order ofattenuation is 1/r to 1/ r ). Therefore, the directions of the maximum velocities of the total waves are
inclined with respect to the fault plane in the vicinity of the surface fault, because of the combined effectsof the directivity pulses and fling steps. On the contrary, as for the buried fault model, the fling steps
disappear and the directivity pulses are dominant. This is because in addition to the large attenuation of
the fling steps, when an observation point is located above a buried fault, the slip dislocation of the fault
cannot fling the ground, because of the presence of the continuous medium above the fault.

Dynamic Term
hypocenter

Static Term
hypocenter

Total
hypocenter(a) Surface Fault
Dynamic Term
hypocenter

Static Term
hypocenter

Total
hypocenter(b) Buried Fault
Fig.4 Vectors of maximum velocities on free surface for (a) the surface fault, and (b) the buried fault

EFFECTS OF SEDIMENTARY LAYERS ON DIRECTIVITY PULSE AND FLING STEP
Application to the 1992 Landers Earthquake
In order to investigate the effects of sedimentary layers on the directivity pulse and the fling step, weapply the above-mentioned method to a near-fault strong motion recorded during the 1992 Landers
earthquake. Fig. 5 shows the fault model of the Landers earthquake by Wald and Heaton [2], and theobservation station at the Lucerne valley. The fault model consists of the three left-lateral strike slip faults:
the Camp Rock/Emerson fault (CEF), the Homestead valley fault (HVF), and the Johnson valley fault(JVF) from north to south. The right panel in Fig. 5 shows the sizes of the faults and their slip distribution.
The station is about 2 km away from CEF, and is close to a large slip area of the fault (up to about 6 m).
Table 1 shows the layered structure model used by Wald and Heaton [2].

N40W

N130W

Fig.5 1992 The Landers earthquake model by Wald and Heaton [2], with the Lucerne valley
station. The fault model consists of the three left-lateral strike slip faults: the Camp Rock/Emerson
fault (CEF), the Homestead valley fault (HVF), and the Johnson valley fault (JVF). The right figure
shows the slip distribution on the three faults (after Wald and Heaton [2])Table 1 Layered Structure Model for the 1992 Landers Earthquake (Wald and Heaton [2])
Num.
1
2
3
4
5

Density (g/cm3)
2.3
2.6
2.7
2.87
3.5

Vp (km/s)
3.8
5.5
6.2
6.8
8.0

Qp
100
600
600
600
600

Vs (km/s)
1.98
3.15
3.52
3.83
4.64

Qs
30
300
300
300
300

Thickness (km)
1.5
2.5
22.0
6.0
0.0

}

1-layer model
4-layers modelFault Normal

Fault Parallel(a) Velocity

Fault Normal

Fault Parallel(b) Displacement
Fig.6 Comparisons between simulations (solid lines) and observations (dashed lines) at the Lucerne
Valley station. The observed displacement records are corrected by Iwan [8].
Fig. 6 shows comparisons between simulations (solid lines) and observations (dashed lines) at theLucerne Valley station, using a single layer on a halfspace; the observed displacement records arecorrected by Iwan [8]. The fault normal and parallel components are N40W and N130W degrees,
respectively (see Fig.5). The agreement between the simulated results and the observations is excellent,
not only for the directivity pulses seen in the fault normal component, but also for the fling steps in thefault parallel component.
Fig. 7 shows the maximum velocities and displacements in the fault normal and parallel components,
and the directions of the maximum values. In the figure, the first and second percentages in theparenthesis show the fractions of the dynamic and static terms, respectively. More than 90% of the fault
normal velocity is composed of the dynamic term, whereas about 90% of the fault parallel displacement
consists of the static term. As we have explained earlier, the combined effect of the directivity pulse andthe fling step makes the directions of the maximum amplitudes inclined to the fault plane, about 41 and 36
degrees from the fault plane for the simulated velocity and displacement, respectively. Those values are
fairly close to the observations, 48 and 38 degrees, respectively.

81
120
89
FN

48°

FP

68 (50%+50%)
9041°

59 (92%+8%)

Observation
Simulation(a) Maximum Velocity (unit: cm/s)

209
264 38°

162

FN

FP

179 (13%+87%)
221 36°129 (60%+40%)

Observation
Simulation(b) Maximum Displacement (unit: cm)

Fig.7 The maximum (a) velocities and (b) displacements in the fault normal and parallel
components at the Lucerne valley station, and the directions of the maximums and those values.
The first and second percentages in parenthesis show the fractions of the dynamic and static
terms, respectively.
Effects of Sedimentary Layer on Directivity Pulse and Fling Step
We will check the effects of the sedimentary layer on the strong motion at the Lucerne valley station. In
the following calculations, we use three layered structure models shown in Table 1. The first model is theoriginal five-layered model, and the second is a homogeneous half-space model, whose material properties
are those of Num. 3 in Table 1. The last is a 4-layered model, whose structure is the same as that of Table
1 except that the top sedimentary layer has been removed. In addition, we will also check the contributionof the three faults: CEF, the nearest fault (about 2 to 20 km), HVF, the middle fault (about 8 to 35 km),and JVF, the furthest fault (about 30 to 55 km) to the station (see Fig.5).
Figs 8(a) and (b) show the velocities and displacements simulated using CEF, the closest fault. Bothfigures include three sets of waves; the middle and right waves correspond to the dynamic and static
terms, which stem from the first and second integrals in equation (1), respectively. The leftmost waves
represent the sums of the two terms. As in the previous simple model, the dynamic term excites directivity
pulses in the fault normal component, whereas the static term generates a very large fling step (up to about
1.8 m) in the fault parallel component. The static term dominates over the dynamic term in the fault
parallel displacement. As for the effects of the sedimentary layer, the larger waves with longer duration
can be seen in the 5-layered model in the directivity pulses than those of the 1- and 4-layered models.
Clearly, these waves are the body and surface waves excited in the sedimentary layer. On the contrary, we
cannot see big differences in the fling step (i.e., the static term) among the three layered structure models.
This is because the fling step is dominated by the slip of the nearest fault, about 2 km in this case.
Similarly, Figs 9(a) and (b) show the velocities and displacements, respectively, simulated using HVF,
the middle distance fault. The amplitudes of the directivity pulses are still comparable with those of CEF,
about 70 cm/s of velocities, as seen in the fault normal components in Figs. 8(a) and 9(a).However, thefling steps become much smaller than those of CEF, as seen in the static displacements of the fault
parallel components of Figs. 9(b) and 8(b) (i.e., 30 cm for HVF and 170 cm for CEF). Again, much larger
waves with longer duration are seen in the 5-layered model in the dynamic terms than those of the 1- and4-layered models. By contrast with CEF, some differences can been seen in the amplitudes of the static
terms among the three layered models, especially in the displacements. This is probably due to the long
distance in the highly attenuated (i.e., the low-Q value) sedimentary layer. Honda [9] reported similar
results by comparing a homogenous model and a layered model.

20

velocity (cm /s)

10

Static

10

-10
30
40 10
tim e (sec)
-30

20

-10
30
40 10
tim e (sec)-30

70

1 layer (F P 70)
4 layers (FP )5 layers (FP50)

1 layer (FP )70
4 layers (FP )5 layers (FP50)

10-10 10

30

Total
20

-30

velocity (cm /s)(a) Fault Normal -50

velocity (cm /s)

-50

30

Static

10

-10
30
40 10
tim e (sec)
-30

20

-10
30
40 10
tim e (sec)-30(b) Fault Parallel-50

70

70

70

Total

10
-10 10
-30
-50

20

30

10
40 10
-10

tim e (sec)20

1 layer (FP )4 layers (FP)
5 layers (FP)Dynamic
20

30
40
tim e (sec)

1 layer (U D )4 layers (U D )5 layers (U D )StaticDynamic

10

-10
30
40 10
tim e (sec)2030(c) Up-Down

40

tim e (sec)

-30

-30
-50

30
40
tim e (sec)

1 layer (U D )4 layers (U D ) 50
5 layers (U D )30velocity (cm /s)

30

20

10

-50

50

Dynamic30-50

1 layer (U D)
4 layers (U D) 50
5 layers (U D)30

1 layer (FN )4 layers (F N )5 layers (F N )

10

-50

50
velocity (cm /s)

30

Total

-30

velocity (cm /s)velocity (cm /s)

30

velocity (cm /s)velocity (cm /s)

50-10 1070
1 layer (FN )4 layers (FN50)
5 layers (FN )30

70
1 layer (F N )4 layers (FN50)
5 layers (FN )

70

-50

Fig.8(a) Velocities simulated at the Lucerne Valley site using the Camp Rock/Emerson fault model (CEF)Total
0
10

20

-50

0
30
40 10
tim e (sec)
-50

20

100
1 layer (FN )4 layers (F N )5 layers (F N )50

1 layer (FN )4 layers (F N )5 layers (F N )StaticDynamic

displacem ent (cm )displacem ent (cm )50displacem ent (cm )100
1 layer (FN)
4 layers (F N )5 layers (F N )
50

100

0
30
40 10
tim e (sec)
-50

20

30

40

tim e (sec)(a) Fault Normal

20

20
10

40 10
-30

20
30
tim e (sec)

150

150

100

50

1 layer (U D100)
4 layers (U D )5 layers (U D )
50

0

0

-50

20

30
40 10
tim e (sec)-50

Dynamic

1 layer (FP )4 layers (F P )5 layers (F P )1 layer (F P )70)
4 layers (FP5 layers (FP )
20
40 10
-30

20
30
tim e (sec)2030
tim e (sec)

40

150

(b) Fault Parallel

1 layer (U 100
D)
4 layers (U D )5 layers (U D )50

1 layer (U D )4 layers (U D )5 layers (U D )Dynamic

Static

Total
10

120

displacem ent (cm )70

1 layer (FP )4 layers (FP70)
5 layers (FP )Staticdisplacem ent (cm )displacem ent (cm )

120

Total

displacem ent (cm )displacem ent (cm )

120

-30

displacem ent (cm )

-100
170

-100
170

-100
170

20

0
30
40 10
tim e (sec)
-50

20

30
40
tim e (sec)(c) Up-Down
Fig.8(b) Displacements at the Lucerne Valley site using the Camp Rock/Emerson fault model (CEF)60

1 layer (FN60)
4 layers (F N )40
5 layers (F N )20

1 layer (F N60)
4 layers (FN40)
5 layers (FN )
20

40
20

Total

0
-20

10

20

-40

40 10
-20
tim e (sec)
-40

30

-80
80

-80
80

40

-80
80
1 layer (FP )60
4 layers (F P )5 layers (F40P)

20

Total 20

1 layer (F P60)
4 layers (FP40)
5 layers (FP )
20

0

0
30
40 10
-20
tim e (sec)
-40

0
30
40 10
-20
tim e (sec)
-40

10

20

-40

velocity (cm /s)(a) Fault Normal-60

velocity (cm /s)

20

-60

-80
80

-80
80

60

1 layer (U D ) 60
4 layers (U D) 40
5 layers (U D)20

1 layer (U D )60
4 layers (U D 40)
5 layers (U D )
20

Total

Static

20
0
-20

10

20

30

0

40 10

-20

tim e (sec)

20

30
40
tim e (sec)

1 layer (F P )4 layers (F P )5 layers (F P )Dynamic
20

30

40

tim e (sec)

-60

-60

40

Dynamic

Static(b) Fault Parallel

-80
80

20

30

velocity (cm /s)velocity (cm /s)

20

-60

-20

1 layer (F N )4 layers (FN )5 layers (FN )Static 0-6060velocity (cm /s)

0
30
40 10
-20
tim e (sec)-40

velocity (cm /s)

80

velocity (cm /s)

80

velocity (cm /s)velocity (cm /s)

80

0

40 10

-20

tim e (sec)

-40

-40

-40

-60

-60

-60

-80

-80

(c) Up-Down

1 layer (U D )4 layers (UD )5 layers (UD )Dynamic
20

30

40

tim e (sec)-80

Fig 9(a). Velocities simulated at the Lucerne Valley site using the Homestead Valley fault model (HVF)

90

50

1 layer (FN)70
4 layers (FN )50 )5 layers (FN

1 layer (FN)70
4 layers (FN )50 )5 layers (FN

1 layer (FN )4 layers (FN)
5 layers (FN)30

Total 30

Static 30

Dynamic

10

10

10

20
30
tim e (sec)2030
tim e (sec)

-10
40 10

20

-30

tim e (sec)-50(a) Fault Normal-50

90

90

90

50

1 layer (FP)70
4 layers (FP )5 layers (FP50 )

1 layer (FP70)
4 layers (FP)50
5 layers (FP)

30

30

30

70

10
-10 10

Total
20

30
tim e (sec)

10
-10
40 10

20

displacem ent (cm )-50

Static

10

30

-10
40 10

-30

tim e (sec)

-50

-50

-50
(b) Fault Parallel

90

90

90

70

1 layer (UD)70
4 layers (U D)50
5 layers (U D)

1 layer (U D)70
4 layers (UD )5 layers (UD50
)

50
30

Total

10
-10 10
-30
-50

20

30
tim e (sec)30

Static

10
-10
40 10
-30
-50

20

30
tim e (sec)(c) Up-Down

30

40

1 layer (FP )4 layers (FP)
5 layers (FP)Dynamic
20-30

displacem ent (cm )-30displacem ent (cm )

-10
40 10
-30

displacem ent (cm )displacem ent (cm )-30displacem ent (cm )-10 10displacem ent (cm )displacem ent (cm )70displacem ent (cm )

90

90

30
tim e (sec)40

1 layer (UD)
4 layers (U D)
5 layers (U D)

30

Dynamic

10
-10
40 10
-30

20

30
tim e (sec)-50

Fig.9(b) Displacements at the Lucerne Valley site using the Homestead Valley fault model (HVF)40

Total 10

5

5

-5

0

10

20

-10

-10

-15
20

-15

20

0
30
40 0
-5
tim e (sec)

5

20

-10

-10

-15
20

10

-15
1 layer (U D )20
4 layers (U D15)
5 layers (U D )
10

5

5

15

0
-5

Total

0

10

20

0

30
40 0
tim e (sec)-5

Static

10

20

0
30
40 0
-5
tim e (sec)

1 layer (FP )4 layers (F P )5 layers (F P )Dynamic

10

20

30
40
tim e (sec)-10(b) Fault Parallel-15

20
1 layer (U D )4 layers (U D )15
5 layers (U D )10velocity (cm /s)

10velocity (cm /s)

5

0

30
40
tim e (sec)

-15

5

-5

20

(a) Fault Normal

Total

0
30
40 0
-5
tim e (sec)

10

-10

10

velocity (cm /s)velocity (cm /s)

10

5

20
1 layer (F P)
4 layers (FP15)
5 layers (FP )10

0

Dynamic

Static20
1 layer (F P)
4 layers (FP15)
5 layers (FP )1015velocity (cm /s)

0
30
40 0
-5
tim e (sec)velocity (cm /s)velocity (cm /s)

0

1 layer (FN )4 layers (F N)
5 layers (F N)

20
1 layer (F N )4 layers (FN15)
5 layers (FN )10velocity (cm /s)

10velocity (cm /s)

15

1 layer (F N20)
4 layers (FN )15)
5 layers (FN

20

Static10

20

1 layer (U D )4 layers (U D )5 layers (U D )Dynamic

5
0

30
40 0
tim e (sec)-5

-10

-10

-10

-15

-15

(c) Up-Down -15

10

20

30
40
tim e (sec)Fig.10(a) Velocities simulated at the Lucerne Valley site using the Johnson Valley fault model (JVF)

0

10

20

-10

-15
20

-15
1 layer (FP20)
4 layers (F P )5 layers (F P15)

5

Total

0
-5

0

10

20

10

20

10
5

5

10

20

0
30
40 0
-5
tim e (sec)
-10

-15
20

(b) Fault Parallel-15

15-15
1 layer (U D )20
4 layers (U D )5 layers (U D15
)

10

10

0
-5

0

10

20

-10

-10

-15

-15

1 layer (FP )4 layers (F P )5 layers (F P )Dynamic

10

20
1 layer (U D )4 layers (U D15)
5 layers (U D )10Static

5

0
30
40 0
tim e (sec)-530
40
tim e (sec)

Static

0

-10

5

20

(a) Fault Normal -15

-10

Total

10

-10
20
1 layer (FP )4 layers (FP15)
5 layers (FP )
10

30
40 0
-5
tim e (sec)Dynamic

5

0
30
40 0
-5
tim e (sec)1020displacem ent (cm )displacem ent (cm )displacem ent (cm )10displacem ent (cm )

-10

15

Static

5

0
30
40 0
-5
tim e (sec)displacem ent (cm )010displacem ent (cm )

Total

5

-5

displacem ent (cm )10displacem ent (cm )displacem ent (cm )15

1 layer (FN )4 layers (FN )5 layers (FN )20
1 layer (FN )4 layers (F15N)
5 layers (F N )101 layer (FN20)
4 layers (FN )15)
5 layers (FN

20

20

30
40
tim e (sec)

1 layer (U D )4 layers (UD )5 layers (UD )Dynamic

5

0
30
40 0
tim e (sec)-5

10

20

30
40
tim e (sec)-10(c) Up-Down-15

Fig.10(b) Displacements simulated at the Lucerne Valley site using the Johnson Valley fault model (JVF)

Finally, Figs. 10(a) and (b) show the velocities and displacements, respectively, simulated using JVF,
the furthest fault. Even though we still see the fling step in the fault parallel displacements, the directivity
pulses are dominant over the fling steps, especially in the fault normal velocities. The amplitudes of thepulses are largely attenuated as compared with those CEF and HVF (about one fourth). Again, larger
waves with longer duration are seen in the 5-layered model in the dynamic terms than those of the 1- and4-layered models. The differences of the static terms among the three models are more clearly seen thanthose of CEF and HVF, as seen in the displacements of Fig. 10(b). This is again due to the longer distancein the low-Q sedimentary layer.

CONCLUSIONS
We investigated the effects of sedimentary layers on the long-period directivity pulse and the fling stepusing the theoretical method (Hisada and Bielak [1]). After checking the basic physics of those waves, weapplied the method to the strong motion recorded at the Lucerne valley during the 1992 Landers
earthquake. We confirmed that the combined effect of the long-period pulse and the fling step made themaximum amplitude of the velocity and displacement inclined to the fault plane at 30 – 50 degree. We
found that the inclusion of sedimentary layers increased greatly the amplitudes and durations of thedirectivity pulses, whereas it did not affect significantly the directivity pulse. This is because thedirectivity pulses are excited from the wide range of the faults including the nearest to the furthest fault,
whereas the fling steps are mostly generated by the slip of the nearest fault.

ACKNOWLEDGMENT
This research was partly supported by a special project of US-Japan Cooperative Research for Urban
Earthquake Disaster Mitigation (No.11209201), Grant-in-Aid for Scientific Research on Priority Area
(Category B), Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), andEarthquake and Environmental Research Center of Kogakuin University funded by the Frontier Research
Promotion Program of MEXT (Y.H.). This work was also supported by the National Science Foundation
KDI program, under grant CMS-9980063 (J.B.); the cognizant program director is Clifford Astill. We are
grateful for this support. We obtained the strong motion records used in this study from COSMOS Virtual
Data Center.

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