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2064
Bulletin of the Seismological Society of America, Vol. 94, No. 6, pp. 2064–2078, December 2004
Near-Source Ground Motions from Simulations of Sustained Intersonic
and Supersonic Fault Ruptures
by Brad T. Aagaard and Thomas H. Heaton
Abstract
We examine the long-period near-source ground motions from simu-
lations of
M
7.4 events on a strike-slip fault using kinematic ruptures with rupture
speeds that range from subshear speeds through intersonic speeds to supersonic
speeds. The strong along-strike shear-wave directivity present in scenarios with sub-
shear rupture speeds disappears in the scenarios with ruptures propagating faster than
the shear-wave speed. Furthermore, the maximum horizontal displacements and ve-
locities rotate from generally fault-perpendicular orientations at subshear rupture
speeds to generally fault-parallel orientations at supersonic rupture speeds. For rup-
ture speeds just above the shear-wave speed, the orientations are spatially hetero-
geneous as a result of the random nature of our assumed slip model. At locations
within a few kilometers of the rupture, the time histories of the polarization of the
horizontal motion provide a better diagnostic with which to gauge the rupture speed
than the orientation of the peak motion. Subshear ruptures are associated with sig-
nificant fault-perpendicular motion
before
fault-parallel motion close to the fault;
supershear ruptures are associated with fault-perpendicular motion
after
significant
fault-parallel motion. Consistent with previous studies, we do not find evidence for
prolonged supershear rupture in the long-period (

2 sec) ground motions from the
1979 Imperial Valley earthquake. However, we are unable to resolve the issue of
whether a limited portion of the rupture (approximately 10 km in length) propagated
faster than the shear-wave speed. Additionally, a recording from the 2002 Denali
fault earthquake does appear to be qualitatively consistent with locally supershear
rupture. Stronger evidence for supershear rupture in earthquakes may require very
dense station coverage in order to capture these potentially distinguishing traits.
Introduction
Observations of crustal earthquakes indicate that fault
ruptures tend to propagate at around 80% of the shear-wave
speed (e.g., Heaton, 1990), which is a little below the the-
oretically limiting speed. On some occasions the ruptures
appear to propagate at a speed that exceeds the shear-wave
speed. Two well-studied cases of plausible supershear rup-
ture include the 1979 Imperial Valley, California, earthquake
(Olson and Apsel, 1982; Archuleta, 1984; Spudich and
Cranswick, 1984) and the 1999 Kocaeli (Izmit), Turkey,
earthquake (Anderson, 2000; Bouchon
et al.
, 2000, 2001;
Sekiguchi and Iwata, 2002; Thio
et al.
, 2004), although there
is still much debate about the robustness of the conclusions
that the rupture speeds were supershear for these cases (Hart-
zell and Heaton, 1983; Archuleta, 1984; Thio
et al.
, 2004).
Other possible cases of supershear rupture include the 2001
Kunlunshan, Tibet, earthquake (Bouchon and Vallee, 2003)
and the 2002 Denali fault, Alaska, earthquake (Dunham and
Archuleta, 2004; Ellsworth
et al.
, 2004).
Olson and Apsel (1982) inferred that the rupture in the
1979 Imperial Valley earthquake propagated faster the
shear-wave speed from their source inversion. However,
Hartzell and Heaton (1983) argued that the waveforms could
be simulated with a rupture speed that varied between 70%
and 90% of the shear-wave speed, and that the estimate of
supershear rupture by Olson and Apsel was the result of
excessive smoothing of the distribution of slip in the inver-
sion. Archuleta (1984) maintained that trial and error match-
ing of the waveforms with a zone of supershear rupture simi-
lar to the one proposed by Olson and Apsel created a better
fit than the one obtained by Hartzell and Heaton. Addition-
ally, Spudich and Cranswick (1984) examined the data from
the 213-m El Centro differential array and found evidence
in the high-frequency (

1.5 Hz) motion consistent with su-
pershear propagation of the leading edge of the rupture, al-
though the location of the supershear rupture lies slightly
north of the region suggested by Archuleta.
In the 1999 Kocaeli earthquake, Bouchon
et al.
(2001)
found that the shear-wave arrival for the Sakarya (
SKR
) re-
Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2065
cording is consistent with 50 km of supershear rupture. Dig-
ital records of fault-parallel (east–west) and vertical acceler-
ations were obtained at Sakarya about 1 km north of the fault
rupture and 40 km east of the epicenter. Unfortunately, this
station did not have a synchronized clock. Furthermore,
the fault-perpendicular (north–south) component malfunc-
tioned. Second time integrals of the
SKR
records show a
fault-parallel displacement that is dominated by a 5-sec lin-
ear ramp, which Bouchon
et al.
interpreted as the near-field
shear wave radiated from the fault adjacent to the station. A
key feature of the
SKR
displacement record is that the dis-
placements are very small prior to the onset of the ramp.
Bouchon
et al.
simulated the
SKR
displacements with a su-
pershear rupture speed that produces near-nodal dilatational
waves and very short
S
-
P
times. However, Bouchon
et al.
’s
simulated dilatational-wave displacements are much larger
than those in the
SKR
record. If their interpretation is correct,
then
SKR
experiences near-nodal dilatational waves even
smaller than those produced along the strike of vertical
strike-slip fault in a layered half-space model. Alternatively,
Thio
et al.
(2004) favor onset of rupture on the Sakarya seg-
ment from triggering by the arrival of the dilatational wave,
not supershear rupture on the Sapanca Lake segment. Nev-
ertheless, if the the
SKR
record is correct, then there is strong
support for at least a supershear
apparent
rupture speed.
Arguably stronger evidence for supershear rupture
comes from the 2002 Denali fault earthquake. In this event
all three components were successfully recorded within a
few kilometers of the fault at pump station 10 along the
Alyeska pipeline. As we will discuss in detail later, the po-
larization of the motion is consistent with supershear rupture.
Finally, through kinematic forward modeling of the 2001
Kunlunshan earthquake, Bouchon and Vallee (2003) con-
cluded that regional surface wave observations were best fit
with supershear rupture over several hundred kilometers.
Whereas these earthquake case histories generally pro-
vide only circumstantial evidence for the existence of super-
shear rupture in earthquakes, laboratory experiments with
propagating mode-II cracks and numerical models of earth-
quake ruptures actually corroborate the existence of ruptures
that propagate at supershear speeds. Experiments by Rosakis
et al.
(1999) and Xia
et al.
(2004) demonstrated that shear
cracks could propagate at intersonic speeds in homalite (a
brittle polyester resin) from either projectile impact loading
or shear loading with nucleation controlled by an exploding
wire. Analytical models of steady-state rupture demonstrate
that mode-II shear cracks can indeed propagate stably at this
speed (Freund, 1979; Broberg, 1994, 1995; Samudrala
et al.
,
2002). Numerical simulations of dynamic earthquake rup-
tures support extrapolation of these laboratory findings to
earthquake ruptures (Burridge, 1973; Andrews, 1976; Das
and Aki, 1977; Das, 1981, Day, 1982). For example, An-
drews (1976) demonstrated that mode-II shear cracks could
accelerate from subshear rupture speeds to the Eshelby
speed. More recently, Madariaga and Olsen (2000) estab-
lished that the ratio of the the energy release rate to the
fracture energy controls the speed of propagation in these
numerical models, with higher values allowing supershear
rupture speeds. Aagaard
et al.
(2001) found large slip rates
near the free surface combined with a high apparent rupture
speed along the surface enabled ruptures to propagate stably
near the Eshelby speed.
The four cases of suspected supershear rupture in real
earthquakes mentioned earlier occur on strike-slip faults.
While it is clear that a rupture propagating at slightly below
the shear-wave speed for this geometry creates strong direc-
tivity in the shear wave radiated along the strike of the fault,
what happens to the ground motions when the rupture ac-
celerates to faster speeds? Does the mechanism for directiv-
ity break down? How do the characteristics of the ground
motions change? We investigate these issues by computing
the long-period near-source ground motions using kinematic
ruptures by forcing the rupture to propagate at a given rup-
ture speed. We examine the characteristics of the ground
motions and look for features that undergo significant
changes as the scenarios vary over a wide range of rupture
speeds. We then use these features to examine records from
the Imperial Valley and Denali fault earthquakes to see if
the evidence supports supershear rupture.
Methodology
We employ the finite-element method to solve the three-
dimensional dynamic elasticity equation with a kinematic
source. We select a kinematic source because we want to
examine the effect of rupture speed on the near-source
ground motions for a continuous range of rupture speeds
from subshear speeds to supersonic speeds. While a dynamic
(spontaneous) rupture source can generate more physically
realistic ruptures (assuming the constitutive relations gov-
erning the fault rupture are chosen correctly), the rupture
speeds are restricted only to those allowed by the assumed
fault constitutive relations; the rupture speed depends on the
ratio of the strain energy release rate to the fracture energy
associated with the friction model (Day, 1982; Madariaga
and Olsen, 2000). On the other hand, these dynamic rupture
models do allow behavior not present in most kinematic
source models, such as bifurcation of the rupture into super-
shear and subshear slip pulses (see, e.g., Aagaard
et al.
, 2001
and Dunham and Archuleta, 2004). This means that by
choosing to use kinematic sources for ruptures propagating
at various speeds with only a single slip pulse, we are fo-
cusing on the seismic radiation from the leading edge of the
rupture.
These simulations follow the same methodology and
use the finite-element model from our previous work that
examined the effect of fault geometry on near-source ground
motions (Aagaard
et al.
, 2004). The length scale of the dis-
cretization allows accurate propagation of waves with pe-
riods of 2 sec and longer. The domain encompasses a region
160 km long, 80 km wide, and 40 km deep, as shown in
Figure 1. We focus on the results from a layered half-space
2066
B. T. Aagaard and T. H. Heaton
40km
Eas
t
North
160km
80k
m
20km
120km
90km
40km
6km
20km
Figure
1.
Geometry of the simulation do-
main. The center of the fault lies 10 km south
of the center of the domain. We examine shear-
wave polarization at the sites denoted by the
dots, which sit at distances of 0 km and 6 km
from the fault trace near the northern end of the
rupture.
Density (g/cm
3
), Velocity (km/s)
Depth (km)
v
p
v
s
ρ
0
1
2
3
4
5
6
7
8
40
30
20
10
0
Figure
2.
Dilatational-wave speed (
v
p
), shear-
wave speed (
v
s
), and mass density (
q
) as a function
of depth for the layered half-space.
with a spatially heterogeneous slip distribution, but we also
refer to results from a uniform half-space with spatially uni-
form slip to highlight the principal observations. Figure 2
and Table 1 display the variation in the material properties
as a function of depth for the layered half-space. For the
uniform half-space we use the material properties from a
depth of 90 km in the layered half-space.
The kinematic source uses the integral of Brune’s far-
field time function,
D
(
x,y,z,t
)

(
t

t
(
x,y,z
))
t

t
(
x,y,z
)
00

1

exp
1


s
(
x,y,z
)
s
(
x,y,z
)
D
(
x,y,z
)

(1)
D
(
x,y,z
)

s
(
x,y,z
)

,
̇
De
max
for the slip time history with the final slip (
D

(
x,y,z
)), peak
slip rate (
D
̇
max
), and slip starting time (
t
0
(
x,y,z
)) as param-
eters. For the layered half-space with spatially heteroge-
neous slip, as shown in Figure 3, we low-pass filter a uniform
random distribution using a first-order (single-pole, causal)
Butterworth filter. The average slip is 2.9 m with a maximum
value of 7.1 m, which results in events with a moment mag-
nitude of 7.4. For the uniform half-space the slip is 2.9 m
over the entire fault. In both sets of simulations, we use a
uniform peak slip rate of 2.0 m/sec. With spatially hetero-
geneous slip, this creates variations in the slip duration.
The hypocenter lies approximately middepth one-
quarter of the distance along the strike of the fault. Figure 4
displays the relative location of the hypocenter as well as
the propagation of the rupture using an anisotropic specifi-
cation of the rupture speed. By using kinematic ruptures, we
can force the ruptures to propagate at any given speed, in-
cluding those that would be unstable for dynamic shear
cracks. The relative rupture speed in the mode-II and mode-
III directions depends on the fracture energy, with the speed
in the mode-III (perpendicular to slip) direction more sen-
sitive to the level of fracture energy compared with the
mode-II (parallel to slip) direction (Andrews, 1976; Day,
1982; Freund, 1990; Madariaga
et al.
, 1998). This means
that faster rupture speeds in our kinematic ruptures corre-
spond to smaller fracture energies. With mode-III rupture
more sensitive to the fracture energy than mode-II rupture,
the ratio of the mode-II to mode-III rupture speed generally
increases with faster rupture speeds. The precise nature of
this relationship between the relative rupture speeds, how-
ever, has yet to be determined. For this reason, we choose a
mode-III rupture speed that is 20% slower than the mode-II
rupture speed, which is consistent with the relative speeds
generally observed in numerical models of subshear rupture.
Although this results in mode-III rupture speeds that exceed
the shear-wave speed (which is theoretically impossible) in
the cases where the mode-II rupture speeds exceeds 1.25
times the shear-wave speed, this is not a significant issue
because the earthquakes are dominated by mode-II rupture.
Table 2 gives the rupture speeds for each simulation. The
infinite rupture speed corresponds to simultaneous rupture
of the entire fault. Thus, the only variation in the kinematic
source in each suite of models (uniform half-space and lay-
ered half-space) is the change in rupture speed; the slip time
Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2067
Dist. Along Strike (km)
Dist. Down Dip (km)
0
10
20
30
40
50
60
70
80
90
100
110
120
20
10
0
Final Slip (m)
0.0
2.0
4.0
6.0
8.0
Figure
3.
Distribution of final slip created from low-pass filtering a random distri-
bution. The average slip is 2.9 m, with a maximum value of 7.1 m, yielding a moment
magnitude of 7.4.
Table 1
Control Points Describing Linear Variation of Material Properties
with Depth in the Layered Half-Space
Depth
(km)
Mass Density
(kg/m
3
)
Dilatational-Wave Speed
(km/sec)
Shear-Wave Speed
(km/sec)
0
1943
3.37
1.91
4.0
2400
4.41
2.62
9.0
2600
5.53
3.15
19.2
2600
6.44
3.72
33.4
3000
7.28
4.21
40.0
3000
7.28
4.21
histories are kept constant at each point on the fault except
for the time at which slip begins, corresponding to changes
in the rupture speed.
Results
We begin our analysis of how increasing the rupture
propagation speed from subshear speeds through intersonic
speeds to supersonic speeds affects near-source ground mo-
tions by examining the snapshots of the particle velocities
on the ground surface for six of the rupture speeds. Two
ruptures fall into each of the three regimes (subshear, inter-
sonic, and supersonic). The snapshots for both the uniform
half-space and layered half-space display very similar
trends, so we show only the ground velocities for the layered
half-space. Figure 5 displays the fault-perpendicular and
fault-parallel components of the velocity of the ground sur-
face after the rupture has propagated about 65 km down the
length of the fault for each of the six scenarios.
The two ruptures that propagate at or below the shear-
wave speed in the mode-II direction generate significant
shear-wave rupture directivity by reinforcing the far-field
shear wave radiated along the strike of the fault (see Som-
erville
et al.
[1997] for a thorough discussion). This far-field
shear wave, which has particle motion perpendicular to the
fault and was generated by slip at locations earlier in the
rupture, arrives before the near-field shear wave, which has
particle motion parallel to the fault and was generated by
slip at locations nearby. Thus, a site close to the surface
rupture undergoes large-amplitude fault-perpendicular mo-
tion
prior
to fault-parallel motion. With the horizontally lay-
ered medium, these shear waves with fault-perpendicular
particle motion develop into large-amplitude Love waves.
The anisotropic rupture speed and the depth-dependent
structure diminish the sharpness of the abrupt shear-wave
arrival for rupture at the shear wave speed, so the maximum
particle velocities do not approach extremely large values
(relative to the theoretical limit of infinite velocities in con-
tinuum models of ruptures propagating in the mode-II di-
rection precisely at the shear-wave speed).
As the rupture speed increases into the intersonic range,
the sharp arrival of this shear wave forms a Mach cone em-
anating from the leading edge of the rupture. The rupture
propagates faster than the shear-wave speed so that at lo-
cations near the fault trace, the shear wave radiated along
the strike of the fault (from locations earlier in the rupture)
arrives after the shear wave radiated perpendicular to the
fault (from locations nearby). Consequently, a site near the
surface trace of supershear rupture experiences its large-
amplitude fault-perpendicular motion
after
fault-parallel
motion. Additionally, the directivity-induced reinforcement
of the far-field shear wave propagating along the strike of
the fault decreases substantially. This leads to a decrease in
the amplitude of motion in the fault-perpendicular compo-
nent. Meanwhile, with nearby areas of the fault rupturing
within a shorter time window, the shear wave radiated per-
pendicular to the fault begins to grow in amplitude. This
process continues as the rupture speed moves into the su-
personic regime. For an infinite rupture speed (simultaneous
rupture of the entire fault), this shear wave radiated perpen-
dicular to the fault (as opposed to the shear wave radiated
along the strike of the fault) dominates the near-source mo-
tion. We examine the variation in the polarization of the
shear wave at several sites as a function of the shear-wave
speed in more detail later.
We now turn to the maximum horizontal displacements
and maximum peak-to-peak velocities displayed in Figure 6
to show how the spatial distribution of the shaking changes
with rupture speed. We determine the maximum peak-to-
peak velocity by finding the maximum amplitude between
consecutive peaks in the velocity time histories after resolv-
ing the horizontal velocity into all possible horizontal ori-
2068
B. T. Aagaard and T. H. Heaton
Dist. Down Dip (km)
Uniform Half–Space
2
4
4
6
6
8
8
10
10
12
14
16
1
8
20
22
24
26
28
30
32
20
0
Dist. Along Strike (km)
Dist. Down Dip (km)
Layered Half–Space
2
4
6
6
8
8
10
10
12
14
16
18
20
22
24
26
28
30
0
20
40
60
80
100
120
20
0
Figure
4.
Progression of the leading edge of rupture as shown by contours of slip
starting time (in seconds) for the uniform half-space (top) and the layered half-space
(bottom) for a rupture propagating at 85% of the local shear-wave speed in the mode-
II direction and 20% slower in the mode-III direction. In both cases, the rupture prop-
agates predominantly in the mode-II (horizontal) direction. In the layered half-space
the rupture propagates faster at depth and drives the rupture along the surface. The
hypocenters indicated by the stars sit 30.0 km and 27.2 km along strike at depths of
10.0 km and 11.2 km, respectively. Roughness in the contours for the layered half-
space arise from generating contours from an unstructured finite-element mesh with
significant variations in element size.
Table 2
Rupture Speeds in the Mode-II and Mode-III Directions
for Each Simulation
Rupture Speed (
v
s
)
Mode II
Mode III
0.850
0.680
0.925
0.740
1.000
0.800
1.10
0.883
1.21
0.966
1.41
(2)

1.13
1.57
1.26
1.73
(3)

1.39
2.60
2.08
3.46
(2 3)

2.77

entations with a 2

resolution. For the bandwidth of these
simulations (
T

2 sec), the maximum peak-to-peak ampli-
tude of a time history resolved into any given direction gen-
erally corresponds to the difference between the maximum
velocity and minimum velocity. The maximum velocity dis-
tributions for rupture propagation at or below the shear-wave
speed exhibit the tear-drop shape associated with rupture
directivity along the strike of the fault. The maximum peak-
to-peak velocities for mode-II rupture at the shear-wave
speed are particularly large (approaching 4 m/sec), as one
expects for this case of maximum along-strike directivity.
As mentioned earlier in the discussion of the snapshots of
velocity on the ground surface, the anisotropic rupture speed
in the layered medium, as well as the limited bandwidth of
the model, prevents the velocities from approaching the
theoretical limit of infinite amplitude.
For ruptures propagating between the shear-wave and
dilatational-wave speeds (intersonic speeds), the lack of rup-
ture directivity in the along-strike direction greatly dimin-
ishes the prominence of the tear-drop shape in the distribu-
tion of the maximum amplitudes; peak-to-peak velocities are
generally less than 2 m/sec, and they decay less rapidly with
distance perpendicular to the fault. As the rupture speed
moves into the supersonic range, the displacements and ve-
locities within one fault width (20 km) of the fault increase
from about 2 m and 2 m/sec to about 2.5 m and 3 m/sec,
respectively, due to the nearly simultaneous rupture. That is,
the motions are dominated by a planar shear wave propa-
gating perpendicular to the fault.
In addition to the changes in the spatial distribution of
the shaking, we also observe changes in the orientation of
the maximum motion, as briefly outlined in our discussion
of the snapshots of velocity. Figure 7 shows the orientation
of the maximum horizontal displacements and peak-to-peak
velocities in the layered half-space. The uniform half-space
simulations display the same general trends but exhibit less
spatial variation due to the uniform slip. For rupture speeds
at or below the shear-wave speed, the maximum peak-to-
peak velocities close to the fault exhibit a very strong pref-
erence toward a fault-perpendicular orientation (except near
Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2069
Distance East (km)
Fault
Perpendicular Component
v
r
=0.85 v
s
0
20
40
60
80
Fault
Parallel Component
v
r
=1.00 v
s
Distance East (km)
v
r
=1.41 v
s
0
20
40
60
80
v
r
=1.73 v
s
Velocity (m/s)
0.0
0.5
1.0
1.5
Distance East (km)
v
r
=3.46 v
s
0
20
40
60
80
Distance North (km)
v
r
=
0
20
40
60
80
100
120
140
160
Distance North (km)
0
20
40
60
80
100
120
140
160
Figure
5.
Snapshots of the fault-perpendicular and fault-parallel components of the
velocity on the ground surface. The solid line delineates the fault trace, and the asterisk
identifies the epicenter. The snapshots for each rupture speed correspond to the time
at which the rupture at the surface has propagated approximately 65 km down the fault,
except for the case of an infinite rupture speed for which the snapshot is taken at 6.0
sec after the initiation of rupture. As the rupture speed increases, the amplitude of the
shear wave radiated along the strike of the fault decreases, whereas the amplitude of
the shear wave radiated perpendicular to the fault increases.
2070
B. T. Aagaard and T. H. Heaton
Distance East (km)
Max. Horiz. Displacement
v
r
=0.85 v
s
0
20
40
60
80
Max. P
to
P Horiz. Velocity
v
r
=1.00 v
s
Distance East (km)
v
r
=1.41 v
s
0
20
40
60
80
v
r
=1.73 v
s
Displacement (m)
0.0
1.0
2.0
3.0
4.0
Velocity (m/s)
0.0
1.0
2.0
3.0
4.0
Distance East (km)
v
r
=3.46 v
s
0
20
40
60
80
Distance North (km)
v
r
=
0
20
40
60
80
100
120
140
160
Distance North (km)
0
20
40
60
80
100
120
140
160
Figure
6.
Maximum horizontal displacements and peak-to-peak velocities on the
ground surface for six rupture speeds. The solid line delineates the fault trace, and the
asterisk identifies the epicenter. Increasing the rupture propagation from subshear
speeds to supersonic speeds shifts the distribution of shaking from a tear-drop shape
associated with larger amplitudes along the strike of the fault away from the epicenter
to an elliptical shape associated with very large amplitudes along the entire strike of
the fault at distances out to one fault width from the fault trace.
the epicenter). Increasing the rupture speed into the inter-
sonic range rotates the orientation of the maximum ampli-
tudes toward the fault-parallel direction. For rupture at the
Eshelby speed (
times the shear-wave speed), even though
2

we can identify a gross shift away from a fault-perpendicular
orientation, the orientation of the maximum motion is spa-
tially very heterogeneous because of the random distribution
of slip. As the rupture speed increases further, the spatial
variability in the orientation of the peak motion disappears.
When the rupture speed approaches infinity, all locations
have similar motions parallel to the strike of the fault; only
areas near the ends of the fault have significant fault-
perpendicular components.
As discussed earlier, supershear rupture speeds pro-
duce large-amplitude fault-parallel motion
before
fault-
perpendicular motion at locations close to the fault; this is
Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2071
Distance East (km)
Orientation of Max. Displacement
0
20
40
60
80
Orientation of Max. P
to
P Velocity
v
r
=0.85 v
s
v
r
=1.00 v
s
Distance East (km)
0
20
40
60
80
v
r
=1.41 v
s
v
r
=1.73 v
s
Distance East (km)
0
20
40
60
80
v
r
=3.46 v
s
Distance North (km)
0
20
40
60
80
100
120
140
160
FP
FN
Distance North (km)
v
r
=
0
20
40
60
80
100
120
140
160
Figure
7.
Orientation of the maximum horizontal displacements and peak-to-peak
velocities for six rupture speeds. The solid line delineates the fault trace, and the asterisk
identifies the epicenter. The maximum motion rotates from predominantly fault-
perpendicular (
FN
) to fault-parallel (
FP
) orientations as the rupture propagation moves
from subshear speeds to supersonic speeds. Figure 8 shows the velocity time histories
for the sites designated by

.
the opposite of what happens at subshear rupture speeds. The
polarization of the horizontal motion for two sites located
near the northern end of the rupture (Figs. 8 and 9) illustrates
this trend. For subshear rupture in both the layered half-
space and the uniform half-space, the site along the fault
trace experiences large-amplitude fault-perpendicular mo-
tion before fault-parallel motion. Rupture at the shear-wave
speed accentuates this feature. At both sites, as the rupture
speed increases above the shear-wave speed, the fault-
parallel motion increases in amplitude and arrives earlier
2072
B. T. Aagaard and T. H. Heaton
Uniform half–space, Uniform slip
v
r
=0.85 v
s
0 km
E of Fault
v
r
=1.00 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
v
r
=
Vel (m/s)
1. 0
0.0
1.0
2.0
v
r
=0.85 v
s
6 km
E of Fault
v
r
=1.00 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
v
r
=
Time (s)
Vel (m/s)
0
10
20
30
40
50
1.0
0.0
1.0
2.0
Layered half–space, Random slip
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
v
r
=
1.0
0.0
1.0
2.0
FN
FP
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
v
r
=
Time (s)
0
10
20
30
40
50
1.0
0.0
1.0
2.0
Figure
8.
Fault-parallel (
FP
) and fault-perpendicular (
FN
) velocity time histories at
two sites (see Figs. 1 and 7) for seven different rupture speeds in the uniform half-
space with uniform slip (
left
) and the layered half-space with random slip (
right
). The
sites lie 0 km or 6 km east of the fault near the north end (100 km along strike). These
time histories illustrate that for sites near the rupture, at subshear propagation speeds
the energy arrives with strong fault-perpendicular motion. As the rupture speed in-
creases, the energy arrives with increasingly earlier and larger fault-parallel motion,
whereas the fault-perpendicular motion decreases.
relative to the fault-perpendicular motion. These features are
present at sites all along the fault (except very close to the
epicenter). However, this polarization becomes weaker with
increasing distance from the rupture because of the decreas-
ing influence of the far-field shear wave with fault-perpen-
dicular motion relative to the other phases. The striking sim-
ilarity of these trends in the layered half-space and the
uniform half-space indicates that they are tied to the effect
of the rupture speed on the radiation of the seismic waves
at the leading edge of the rupture; they are relatively inde-
pendent of the details of the geologic structure (layered ver-
sus uniform half-space) and spatial variations in slip (low-
pass-filtered random slip versus uniform slip).
Figure 10, which displays the overall maximum fault-
parallel and fault-perpendicular displacement and peak-to-
peak velocity on the ground surface, summarizes this change
in polarization of the motion as a function of rupture speed.
Because only the largest offsets along the fault trace control
the overall maximum fault-parallel displacements, we find
very little change in the overall maximum fault-parallel dis-
placements as the rupture speed increases to intersonic and
supersonic speeds. This explains why the uniform half-space
with uniform slip has a much smaller maximum fault-
parallel displacement than the layered half-space with ran-
dom slip. The fault-perpendicular displacements, on the
other hand, are sensitive to the amount of rupture directivity
induced reinforcement of the far-field shear wave radiated
along the strike of the fault, so that the overall maximum
displacement is largest for rupture speeds near the shear-
wave speed. The overall maximum fault-perpendicular peak-
to-peak velocity displays a similar trend; the overall maxi-
mum peak-to-peak fault parallel component increases with
rupture speed, following the rotation of maximum motion
from fault perpendicular to fault parallel directions.
While the distribution of slip and slip rate are identical
in all of the simulations, the profound differences in direc-
tivity mean that the radiated energy varies with rupture speed
(Haskell, 1964). Figure 11 shows how rupture speed affects
the energy dissipated at the absorbing boundaries on the
truncated edges of the domain (radiated energy). By contin-
uing the simulation until there is negligible kinetic energy
left in the domain, the boundaries absorb all of the energy
radiated into the far-field. In the layered half-space, the depth
variation of the rupture speed resulting from the depth-
dependent structure reduces the amount of directivity. As a
result, the local maximum in the radiated energy near the
shear-wave speed is smaller for the layered half-space than
for the uniform half-space.
The radiated energy reaches a local minimum at the
Eshelby speed (
times the shear-wave speed). This is con-
2

Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2073
0 km E of Fault
Uniform half
space, Uniform slip
o
x
Fault
Perpedicular Disp. (m)
1. 0
0. 5
0.0
0.5
1.0
1.5
2.0
6 km E of Fault
o
x
Fault
Parallel Disp. (m)
Fault
Perpedicular Disp. (m)
0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
Layered half
space, Random slip
o
x
1.0
0.5
0.0
0.5
1.0
1.5
2.0
o
x
Fault
Parallel Disp. (m)
0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.0
0.5
0.0
0.5
1.0
1.5
2.0
Figure
9.
Displacement trajectories at two sites (same sites as in Fig. 8) for four
different rupture speeds in the uniform half-space with uniform slip (left) and the
layered half-space with random slip (right). The trajectories begin at the origin (denoted
by circles) and end at the Xs. The trajectories demonstrate that sites very close to the
fault experience fault-parallel motion
after
fault-perpendicular motion for subshear rup-
ture, whereas for supershear rupture, the sites experience fault-parallel motion
before
significant fault-perpendicular motion. Beginning at distances of around 6 km from the
fault, the effects of the dilatational wave become significant, and this feature disappears.
sistent with stable propagation of dynamic shear cracks at
this rupture speed with “subsonic-like” behavior (Freund,
1979). The sharp arrival of the shear wave associated with
the Mach cone generates large velocities so that the energy
radiated by intersonic ruptures exceeds the energy radiated
by ruptures propagating below the shear-wave speed. As the
rupture speed increases to infinity, the radiated energy grad-
ually increases to its asymptotic limit; when the rupture
speed is infinite, most of the energy is in the far-field shear
wave, propagating as a plane wave perpendicular to the si-
multaneous rupture.
Discussion
This set of simulations illustrates that as the sustained
rupture speed increases from below the shear-wave speed to
near the dilatational-wave speed, three changes take place:
(1) at locations within a few kilometers of the surface rup-
ture, the shear wave with fault-parallel particle motion ar-
rives before, rather than after, the shear wave with fault-
perpendicular motion; (2) rupture directivity along the strike
of the fault is lost, so that the maximum horizontal peak-to-
peak velocities no longer increase along the strike of the fault
away from the epicenter, and they decay less rapidly with
distance from the fault; and (3) the orientations of the max-
imum peak-to-peak velocities rotate from being predomi-
nantly fault-perpendicular to being predominantly fault-
parallel.
As mentioned earlier, these simulations use a uniform
mode-II rupture speed, whereas the rupture speed in real
earthquakes fluctuates and may be supershear over only part
of the rupture. Can the three diagnostics for supershear rup-
2074
B. T. Aagaard and T. H. Heaton
Max. Disp. (m)
Uniform half
space, Uniform slip
//
//
//
//
0.0
0.5
1.0
1.5
2.0
2.5
3.0
FN
FP
Rupture Speed (v
s
)
Max. P
to
P Vel. (m/s)
//
//
//
//
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Inf
0.0
1.0
2.0
3.0
4.0
5.0
Layered half
space, Random slip
//
//
//
//
Rupture Speed (v
s
)
//
//
//
//
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Inf
Figure
10.
Overall maximum fault-parallel (
FP
) and fault-perpendicular (
FN
) dis-
placement and peak-to-peak velocity for any point on the ground surface as a function
of rupture speed. The left column shows the values for the uniform half-space with
uniform slip, and the right column shows the values for the layered half-space with
random slip. The maximum motions rotate from predominantly fault perpendicular to
fault parallel as the rupture speed increases to intersonic and supersonic speeds. The
two models display very similar behavior, although the random spatial variation in slip
in the layered half-space results in a much larger maximum fault-parallel displacement.
ture help to interpret records from suspected cases of super-
shear rupture in real earthquakes? It might be possible to
infer supershear rupture if the maximum ground velocities
are nearly fault-parallel for stations close to the fault. Of
course, this requires that the energy arriving at the site
(which is related to the velocity amplitude) from the super-
shear portion of the rupture exceeds that arriving from the
subshear portion of the rupture. If only a small portion of
the rupture jumps to supershear speeds (regardless of how
close this occurs to the recording site), this condition will
likely not be met. In such cases, the near-source ground mo-
tions may be relatively unaffected by supershear rupture.
Thus, the presence of slip heterogeneity means that it would
be difficult to argue for supershear rupture based on the ori-
entation of peak ground motions at only a few stations. On
the other hand, the ground-motion time histories recorded
close to the portion of the fault where the rupture may have
propagated faster than the shear wave could be affected and
may exhibit significant fault-parallel motion prior to fault-
perpendicular motion.
The 1999 Izmit, Turkey, earthquake has been simulated
with supershear rupture. Unfortunately, there was only one
near-source station (Sakarya,
SKR
) along the fault trace in
the direction of the suspected supershear rupture (east of the
epicenter), and it failed to accurately record the north–south
(fault-perpendicular) motion. Consequently, we cannot ex-
amine the orientation of the maximum velocity or the po-
larization of the shear-wave motion at this station in order
to look for evidence of supershear rupture. However, in two
other cases of strike-slip events with suspected supershear
rupture, the 1979 Imperial Valley, California, and the 2002
Denali fault, Alaska, earthquakes, ground motions were re-
corded within a few kilometers of the fault trace near the
areas with suspected supershear rupture.
In the Imperial Valley earthquake, five stations within
a few kilometers of the fault (Fig. 12) recorded the ground
motions. The portion of the fault between station
EMO
and
the strong-motion array contains the portion of the rupture
suspected of propagating faster than the shear-wave speed.
We apply
v
0
baseline corrections (Boore, 2001) to the un-
corrected acceleration time histories (Porcella
et al.
, 1982;
Porter, 1982) before integrating to obtain velocity time his-
tories. The records are then low-pass filtered using a fourth-
order (four poles, causal) Butterworth filter with the pass-
band extending to 0.5 Hz. Because the velocity records
contain numerous oscillations even after low-pass filtering,
the maximum peak-to-peak velocity measured using con-
secutive peaks is considerably smaller than the peak veloc-
ity, so to find the orientation of the maximum motion we
use the peak velocity as opposed to the peak-to-peak velocity
(which we used in the earlier discussion and has a similar
orientation for the simulations). The maximum velocities at
Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2075
Rupture Speed (v
s
)
Radiated Energy (J) x10
16
//
//
//
//
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Inf
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Layered half
space, Random slip
Uniform half
space, Uniform slip
Figure
11.
Far-field radiated energy as a function
of rupture speed for both the uniform half-space with
uniform slip and the layered half-space with random
slip. The maximum in the shear-wave radiation pat-
tern along the strike of the fault results in a significant
increase in the radiated energy for rupture speeds ap-
proaching the shear-wave speed. In the layered half-
space, the depth variation in the shear-wave speed
limits the amplitude of the peak in radiated energy for
a rupture propagating at the shear-wave speed. The
local minimum for intersonic rupture occurs at the
Eshelby speed. Approaching supersonic speeds, the
radiated energy increases because of effective rein-
forcement of the shear waves radiated perpendicular
to the fault.
all five stations are closely aligned to the fault-perpendicular
direction. This suggests that most of the energy arriving at
the stations corresponds to a rupture propagating near the
shear-wave speed.
The velocity waveforms support subshear rupture prop-
agation. Stations
EMO
, E06, and E07 all experience large-
amplitude fault-perpendicular motion that arrives prior to the
largest fault-parallel motion, consistent with subshear rup-
ture as illustrated by the close correspondence to seismo-
grams from similar locations in the simulations with ruptures
propagating at or below the shear-wave speed. Note that all
of the simulations use a uniform mode-II rupture speed. Sta-
tions E05 and E08 do not fit the subshear pattern as well,
but they are more distant from the fault; station E05 may
also be affected by the nearby branching of the rupture.
Thus, we find the orientation of the motion and the wave-
forms are consistent with most of the energy being generated
by subshear rupture. This generally agrees with the obser-
vations of predominantly subshear rupture in more detailed
studies (Olson and Apsel, 1982; Hartzell and Heaton, 1983;
Archuleta, 1984; Spudich and Cranswick, 1984). Unfortu-
nately, the results presented here do not help resolve the
issue of whether a limited portion of the rupture (approxi-
mately 10 km in length) propagated faster than the shear-
wave speed.
Archuleta (1984) argued that the region of supershear
rupture may be too far to the south for detection with ob-
servations of the polarization of the motion using the El
Centro strong-motion array. Spudich and Cranswick (1984)
investigated the apparent velocity of high-frequency dilata-
tional-wave phases recorded on the El Centro differential
array. They found that these apparent velocities were con-
sistent with a small patch of supershear rupture, although
that interpretation may not be unique. Unfortunately, the di-
agnostics we develop here are not appropriate for detecting
such localized patches of supershear rupture.
In the 2002 Denali fault earthquake the ground motion
was recorded within a few kilometers of the fault along the
Alyeska pipeline at pump station 10. This location sits about
65 km along the fault from where the strike-slip rupture be-
gan. We again low-pass filter the velocity record using a
fourth-order Butterworth filter to match the bandwidth of the
simulations (
T

2 sec). To compare the velocity record
from pump station 10 to our suite of strike-slip simulations
with uniform rupture speeds, we place the simulation epi-
center at the junction of the Susitna Glacier and Denali faults
(where the rupture transitioned from oblique slip on the Sus-
itna Glacier fault to predominantly lateral slip on the Denali
fault). An 8-sec delay applied to the pump station 10 time
histories accounts for the dilatational-wave travel time from
the hypocenter (

15 sec) (Ellsworth
et al.
, 2004), delayed
rupture on the the Denali fault (

9 sec) [Chen Ji, 2003],
and differences in the nominal shear-wave speed in Alaska
(Ellsworth
et al.
, 2004) compared to the simulations (

2
sec).
The timing of the shear-wave arrival would be consis-
tent with an average rupture speed from the Susitna Glacier
fault to pump station 10 at 80% of the shear-wave speed.
On the other hand, the velocity waveforms suggest that the
energy arriving at pump station 10 may have been generated
by locally supershear rupture. Figure 13 shows that the ori-
entation of the peak velocity lies closer to the fault-parallel
direction than the fault-perpendicular direction (consistent
with our simulations of supershear rupture). Furthermore,
the first large-velocity pulse on the fault-parallel component
has an amplitude at least as large as the fault-perpendicular
component (using either the average fault orientation or the
local fault orientation). Examining the velocity time histories
from the corresponding location in the simulations for the
various rupture speeds, we find a mode-II rupture speed be-
tween 10% and 20% above the shear-wave speed provides
the best overall qualitative fit. The relative amplitudes of the
fault-parallel and fault perpendicular components are more
closely fit by mode-II rupture speeds 20%–40% above the
shear-wave speed, but the nearly simultaneous arrival of the
two components is more closely fit by rupture speeds closer
to the shear-wave speed.
A kinematic source inversion (Chen Ji, 2003) indicates
that the average rupture speed remains subshear but allows
a short duration of supershear rupture near this location, with
shorter durations allowing faster rupture speeds. Detailed
modeling by Ellsworth
et al.
(2004) and Dunham and Ar-
2076
B. T. Aagaard and T. H. Heaton
EMO
Easting (km)
E05
E08
Northing (km)
630
640
650
660
3610
3620
3630
3640
data x1.3
EMO
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.10 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
1. 0
0.0
1.0
2.0
FN
FP
data x1.3
E07
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.10 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
Vel (m/s)
1.0
0.0
1.0
2.0
data x1.3
E06
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.10 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
1.0
0.0
1.0
2.0
data x1.3
E08
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.10 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
Time (s)
Vel (m/s)
0
5
10
15
20
1.0
0.0
1.0
2.0
data x1.3
E05
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.10 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
Time (s)
0
5
10
15
20
1.0
0.0
1.0
2.0
Figure
12.
Orientation of the peak velocity (upper left) and comparison of velocity
waveforms from the 1979 Imperial Valley earthquake for four stations in the El Centro
strong-motion array (stations E05 to E08) and station
EMO
. The triangles identify the
station locations, and the vectors show the amplitude and orientation of the maximum
velocity. The solid line indicates the fault trace, and the asterisk identifies the epicenter.
The dashed line and open circle show the comparable geometry for the simulations.
The maximum velocities are generally aligned with the fault-perpendicular direction,
and the stations generally experience significant fault-perpendicular (
FN
) motion prior
to fault-parallel (
FP
) motion, implying most of the energy was generated while the
rupture propagated slower than the shear-wave speed.
chuleta (2004) suggests the rupture speed may have ex-
ceeded the shear-wave speed by up to 50%–60% over a dis-
tance of about 15 km just west of pump station 10. Thus,
the orientation of the maximum velocity and the polarization
of motion appears consistent with supershear rupture im-
mediately to the west of pump station 10 in the Denali fault
earthquake and agrees with the much more in-depth analysis
by Ellsworth
et al.
(2004) and dynamic rupture modeling of
Dunham and Archuleta (2004). In this case, the supershear
rupture appears to have been of sufficient duration and to
have occurred close enough to the recording station for the
recorded motion to exhibit the characteristics of supershear
rupture found in our simulations.
Conclusions
We simulated kinematic ruptures of
M
7.4 events on a
strike-slip fault with different rupture speeds, including rup-
tures that propagate below the shear-wave speed (subsonic),
between the shear-wave speed and the dilatational wave-
speed (intersonic), or above the dilatational wave-speed (su-
personic). Increasing the rupture speed to values faster than
Near-Source Ground Motions from Simulations of Sustained Intersonic and Supersonic Fault Ruptures
2077
Easting (km)
Northing (km)
460
480
500
520
540
560
580
600
7000
7020
7040
data LO x1.5
PS10
data AO x1.5
v
r
=0.85 v
s
v
r
=1.00 v
s
v
r
=1.10 v
s
v
r
=1.21 v
s
v
r
=1.41 v
s
v
r
=1.73 v
s
v
r
=3.46 v
s
Time (s)
Vel (m/s)
0
5
10
15
20
25
30
35
40
45
1. 0
0.0
1.0
2.0
FN
FP
Figure
13.
Orientation of the peak velocity (top)
and comparison of velocity waveforms from the 2002
Denali fault earthquake for the pump station 10 rec-
ord. The triangles identify the station location, and
the vector shows the amplitude and orientation of the
maximum velocity. The thick solid line indicates the
fault trace, and the asterisk identifies the epicenter.
The dashed line and open circle show the comparable
geometry for the simulations. The data are shown
with fault-parallel (
FP
) and fault-perpendicular (
FN
)
components relative to the local fault orientation (
LO
)
and the average fault orientation (
AO
). An 8-sec time
delay applied to the data to allows a more direct com-
parison with the simulations. The orientation of the
peak velocity and the velocity waveforms fit the pat-
tern for rupture above the shear-wave speed.
the shear-wave speed reduces the rupture directivity induced
reinforcement of the far-field shear waves propagating down
the fault, resulting in smaller-amplitude directivity pulses.
As the rupture speed is increased through the intersonic
range, the rupture begins to more effectively reinforce shear
waves radiated perpendicular to the fault. As a result, the
maximum velocities remain relatively uniform along the
strike of the fault, but the displacements and velocities decay
less rapidly with distance perpendicular to the fault. Addi-
tionally, the orientation of the maximum horizontal displace-
ments and peak-to-peak velocities rotate from predomi-
nantly fault-perpendicular to predominantly fault-parallel
directions in regions close to the fault. However, these
changes may be difficult to observe if there are a limited
number of observations; heterogeneity in the distribution of
slip creates fluctuations in the orientation of the peak motion.
A more robust characteristic for supershear rupture is the
arrival of fault-parallel motion prior to fault-perpendicular
motion at sites very close to the rupture. This was evident
from its clear display in the simulations of both a layered
half-space with random slip and a uniform half-space with
uniform slip.
Based on these simulation results, we examined long-
period near-source recordings from the 1979 Imperial Valley
and 2002 Denali fault earthquakes, in which others have
found some evidence for supershear rupture. In the Imperial
Valley earthquake, the long-period ground motions contain
much more energy in the fault-perpendicular direction com-
pared with the fault-parallel direction, suggesting predomi-
nantly subshear rupture. This is consistent with previous
studies that found the rupture remained below the shear-
wave speed or only a limited portion of the rupture exceeded
the shear-wave speed. The polarization of the velocity wave-
forms are also consistent with subshear rupture, suggesting
supershear rupture, if it occurred, was limited to a small
portion of the fault away from the locations that recorded
the ground motion very close to the fault rupture. On the
other hand, in the 2002 Denali fault earthquake, the record-
ing closest to the fault exhibits characteristics found in the
simulations with rupture above the shear-wave speed: ori-
entation of the peak velocity away from fault-perpendicular
direction and nearly simultaneous arrival of large-amplitude
motion in the fault-perpendicular and fault-parallel direc-
tions. Thus, these simulations and recordings provide addi-
tional support for the existence of supershear ruptures in
earthquakes but illustrate the difficulty in obtaining defini-
tive evidence without a dense seismic network along the
surface trace of the fault.
Acknowledgments
We thank Ralph Archuleta, Paul Spudich, David Wald, and an anon-
ymous reviewer for their constructive comments, which improved the
manuscript. Access to the Hewlett-Packard V-Class computer was provided
by California Institute of Technology’s Center for Advanced Computing
Research through the National Partnership for Advanced Computational
Infrastructure—A Distributed Laboratory for Computational Science and
Engineering, supported by the NSF cooperative agreement ACI-9619020.
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U.S. Geological Survey, MS977
345 Middlefield Rd.
Menlo Park, California 94025
(B.T.A.)
Department of Geologic and Planetary Sciences
Mail Stop 252-21
California Institute of Technology
Pasadena, California 91125
(T.H.H.)
Manuscript received 22 December 2003.