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GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L14314, doi:10.1029/2006GL026303, 2006
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Rapid estimation of first-order rupture characteristics for large
earthquakes using surface waves: 2004 Sumatra-Andaman earthquake
Charles J. Ammon,1 Aaron A. Velasco,2 and Thorne Lay3
Received 14 March 2006; revised 1 June 2006; accepted 15 June 2006; published 29 July 2006.
[1] Broadband surface waves from large earthquakes can
be rapidly processed to estimate seismic moment, faulting
duration, and general slip distribution, supplying important
information for hazard response efforts, including tsunami
warnings. Deconvolution of surface-wave Green’s functions
removes propagation effects, yielding azimuthally varying
effective source time functions. Even a single faultperpendicular time function can provide robust first-order
estimates of the temporal history of seismic radiation and
associated slip distribution. Simplified two-dimensional
finite-fault modeling using a few surface-wave time
functions can reliably characterize the smooth component
of the overall rupture process. These procedures are
demonstrated using 13 Rayleigh wave observations for the
26 December 2004 Sumatra-Andaman earthquake, yielding
satisfactory agreement with models based on more complete
seismic data sets. Depending on source and station
locations, stable slip estimates can be obtained within 15 –
60 minutes of the onset of a large earthquake.
Citation: Ammon, C. J., A. A. Velasco, and T. Lay (2006),
Rapid estimation of first-order rupture characteristics for large
earthquakes using surface waves: 2004 Sumatra-Andaman
earthquake, Geophys. Res. Lett., 33, L14314, doi:10.1029/
2006GL026303.
1. Introduction
[2] The 26 December 2004 Sumatra-Andaman earthquake (Figure 1) was the largest event in four decades
and produced the longest known fault rupture (at least 1300
km) [e.g., Lay et al., 2005]. The associated tsunami cataclysm was one of the worst disasters in human history,
killing approximately 223,000 people and devastating many
coastal regions around the Bay of Bengal and Indian Ocean
(http://www.tsunamispecialenvoy.org/country/humantoll.
asp). No regional tsunami warning system was in operation,
and no regional public warnings were issued. For the local
vicinity of the source, only immediate warning, with prior
public awareness and response planning, could have facilitated life-saving efforts. However, ample time was available to analyze seismograms from many stations to quantify
the nature of the faulting and the associated tsunamigenesis
and to have initiated societal response efforts within the two
hours before the tsunami struck Sri Lanka and Thailand. We
1
Department of Geosciences, Pennsylvania State University, University
Park, Pennsylvania, USA.
2
Department of Geological Sciences, University of Texas, El Paso,
Texas, USA.
3
Earth Sciences Department, University of California, Santa Cruz,
California, USA.
Copyright 2006 by the American Geophysical Union.
0094-8276/06/2006GL026303$05.00
describe a robust procedure for rapidly estimating attributes
of future large earthquakes that can contribute to the prompt
assessment of the need for emergency response and/or
tsunami warnings.
2. Rapid Analysis of Seismic Signals
[3] Real-time telemetry of global seismic recordings creates opportunities for the rapid characterization of large
earthquake ruptures. The National Earthquake Information
Center (NEIC), the Pacific Tsunami Warning Center
(PTWC), and programs such as the Harvard CentroidMoment Tensor (CMT) project routinely utilize telemetered
seismograms to rapidly estimate earthquake locations, magnitudes, and point-source representations. In some cases,
these procedures are sufficient for appraising tsunami potential and societal impact, but for the largest, most devastating
earthquakes, a more complete characterization is desirable.
For the 2004 Sumatra-Andaman earthquake the extent of
faulting played a major role in the tsunami excitation that
impacted Sri Lanka and Thailand; standard point-source
characterizations proved inadequate for estimating the
event’s size and tsunami potential. Finite-source information,
indicating the total seismic moment, total rupture duration
and fault length, and variation of slip on the fault, is now
routinely derived for large events by analysis of teleseismic
waveforms. Several procedures can be applied very quickly
once seismic data are retrieved. For a rapid analysis system,
application of a hierarchy of seismic tools is logical, including
P-wave analyses [e.g., Ni et al., 2005; Ishii et al., 2005;
Kruger and Ohrnberger, 2005] and the approach that we
describe below, followed by more detailed finite-fault inversions [e.g., Ammon et al., 2005].
[4] Long-period surface waves exhibit larger rupture
directivity effects than teleseismic body waves and are
intrinsically sensitive to rupture duration and seismic
moment, but have the drawback of propagation time delay.
Close observations are the only solution to propagation
delay limitations; fortunately, the high dynamic range of
broadband Global Seismic Network (GSN) [Park et al.,
2005] and Federation of Digital Seismic Network (FDSN)
[Romanowicz and Giardini, 2001] instruments allow
retrieval of on-scale surface waves recorded relatively close
to large earthquakes. Although some of the closest instruments to the Sumatra-Andaman earthquake were contaminated by non-linearities, this problem is easily recognized.
3. Surface-Wave Source Time-Function
Estimation
[5] The 2004 Sumatran-Andaman earthquake provided
several hundred global broadband Rayleigh wave record-
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AMMON ET AL.: FIRST-ORDER RUPTURE CHARACTERISTICS
Figure 1. Map showing seismicity between the 26
December 2004 and 28 March 2005 earthquakes. Symbol
size increases with the cube root of magnitude. Observed
source time functions (shaded) obtained from Rayleigh
waves are shown distributed around the source region, with
predictions for the 2D model in Figure 4 shown by dotted
lines. The star indicates the main shock epicenter. The focal
mechanism identifies the assumed point-source fault
geometry used to compute Green’s functions. Map tick
marks are located every 2 of latitude and longitude.
ings. Surface-wave phase velocities are close to typical
earthquake rupture speeds, resulting in large directivity
effects. Deconvolution of propagation operators isolates
the azimuthally dependent effective source time functions
(STFs) (Figure 1). The STFs can be used to rapidly and
robustly resolve the rupture length, characterize the propagation, and image the smooth components of the seismic
moment distribution. Analysis of about 200 FDSN Rayleigh
wave STFs using an inverse Radon Transform (IRT) [e.g.,
Ruff, 1984] method is described in Ammon et al. [2005].
Our focus here is on using small subsets of the data to
construct simple images of the fault slip distribution with
procedures that can be applied routinely, building upon
initial body-wave analysis of large earthquakes.
[6] For previous analyses of large events we used small
earthquakes with similar location and fault orientation to the
mainshock to provide empirical Green functions (EGFs)
[e.g., Ammon et al., 1993; Velasco et al., 2000]. Many M >
6.0 events near the Sumatra-Andaman source region were
tried as EGFs, but it was difficult to resolve very long
period (>250 s) components of the mainshock due to the
weak long-period excitation of the smaller events. A 2002
Mw = 7.5 earthquake that occurred in the mainshock
epicentral region proved an exception, but records from
such an event will not always be available for rapid
analysis. So we use point-source synthetic seismograms
(theoretical Green’s functions: TGFs) computed using normal-mode summation (down to 30 s period) for the PREM
model [Dziewonski and Anderson, 1981]. For the Sumatra
recordings we assume a point-source location at the NEIC
epicenter with a depth of 15 km, and a faulting geometry
(strike: 329; dip: 11; rake: 110; see Figure 1). The dip is
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3 steeper than the Harvard CMT solution, consistent with
background seismicity.
[7] In an operational environment, one could use precomputed Green’s functions for interplate thrust events of
suitable geometry for a given region. Whether one computes these for 1D or 3D earth models, TGF errors will
mainly affect shorter period components of the signal, so
STF estimation will be most accurate for long periods. For a
great event, the advantage of having noise-free long-period
energy in the denominator of the deconvolution (the TGFs)
is decisive relative to our experience with EGFs. The key
issue is adequate isolation of long-period source information, and even PREM works well for this, as shown here.
Mode-sum TGFs can be quickly computed if a specific
focal mechanism is determined that differs from the standard interplate thrust geometry for a given event.
[8] Figure 2 shows an example of surface wave STF
estimation. The vertical component observed at station KIP
is compared with a PREM TGF (top panel). The lower
panel shows the deconvolution results. We isolated longperiod minor-arc Rayleigh waves (R1) using a groupvelocity range of 8 km/s to either 3.5 km/s or the start of
the major-arc Rayleigh waves (R2) as defined by 6 km/s
velocity. This long time window captures some body waves
in both traces, but this causes little trouble for extracting
first-order rupture characteristics when the long periods are
emphasized. We removed the mean and tapered the signals,
then deconvolved the TGF using both water-level deconvolution and an iterative time-domain procedure [Kikuchi and
Kanamori, 1982]. A low-pass Gaussian filter is convolved
with the result to reduce the influence of short-period
signals that are more sensitive to the assumed source depth
and focal mechanism as well as propagation errors in the
TGF.
[9] The finite bandwidth, finite time window deconvolution produces about an 800 s wide trough in the water-level
STF; the iterative time-domain approach includes positivity
Figure 2. (top) Observed vertical component seismogram
for station KIP, Kipapa, Hawaii and a point-source TGF.
(bottom) The STF estimates were estimated by deconvolving the TGF from the observation. We show results
obtained using a frequency-domain water-level method
(thin line) and an iterative time-domain approach (thick
line) that includes causality and positivity constraints.
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Figure 3. One-dimensional slip map estimated from the
iterative deconvolution STF from station KIP. The slip
distribution depends on the rupture direction and propagation speed (2.4 km/s); slip magnitudes depend on the shear
modulus (40GPa), rupture speed, and fault width (150 km).
and causality constraints that stabilize the baseline. The
recovered period range extends from about 100 to 500 s.
Both STFs show four pulses of seismic energy release. The
small pulse just after the onset time corresponds to an
interval of relatively weak seismic radiation lasting about
60 s. The ensuing major pulse continues for about 200 s.
Two smaller pulses follow with temporal centroids near 335
and 430 s after the onset, respectively. The total STF
duration is about 450 – 500 s.
[10] The KIP STF is special because the path azimuth is
roughly perpendicular to the rupture propagation direction
(about 10 difference). This geometry yields minimal bias in
total rupture duration caused by directivity; effectively, the
time history of energy release is faithfully extracted. Also,
the distance from different positions along the curving
rupture to the station varies little, which means that the
TGF computed for the hypocenter is valid for the whole
signal. Rayleigh-wave radiation in this direction is strong as
well, resulting in high signal quality. Thus, the 450– 500 s
STF duration immediately reveals the total rupture duration
along the subduction zone (for periods from 100 s to 500
s). Almost any circum-Pacific great event will have at least
one station with comparable geometry within 30– 60 minute
propagation time.
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is likely due to noise, errors in the long-period instrument
response at KIP and relatively short (2500 s) analysis
window which degrade the deconvolution at periods longer
than 500 s. Even so, the size of slip and the fault area over
which it occurred are large enough to guide an assessment
of tsunamigenesis and damage extent that is much more
accurate than a point-source characterization. Although we
have assumed a unilateral rupture, one may not know this
during a routine application – here both unilateral and
bilateral hypotheses could be applied – in either case, the
seismic moment will be the same.
[12] Information available from a single station perpendicular to the rupture is impressive, but incorporating just a
few more STFs into the analysis allows the construction of a
simple constant-speed 2D finite-fault rupture model. For
large ruptures, such a simple model can encapsulate the
first-order rupture characteristics well. An important advantage of a 2D model is that it can account for the initial
growth of rupture area with time that produces a large
moment-rate pulse and distorts ribbon fault models such as
those produced by 1D IRT analysis [Ammon et al., 2005].
[13] Thirteen azimuthally distributed time functions were
inverted using a uniformly expanding rupture with 2.4 km/s
rupture speed starting from the NEIC epicenter, 95.567E,
3.277N (Figure 4). We used a search-based algorithm
[Velasco et al., 2000] to estimate a smooth moment distribution that matches the observed STFs in a least-squares
sense. A rupture model is successively perturbed in a search
for better fitting models. We use a zero-slip initial model
and include several thousand perturbations, which takes
several minutes to complete. The mechanism and depth of
each point source in the model are assumed to be identical
to those specified for the Green’s Functions used in the STF
estimation. Thus, the inversion is parameterized in terms of
point-source strength, which we convert to slip by assuming
each point source represents a subevent with dimensions
equal to the distance between sources (5 km) and m = 40
GPa. Numerical experiments suggest that the main limita-
4. Fault Rupture Imaging
[11] The special geometry for the KIP STF also allows us
to estimate the fault slip since the slip function for a
unilateral rupture can be related to an STF observed
perpendicular to rupture using
sðvr tÞ ¼
f? ðt Þ
vr mW
where vr is the rupture velocity, f?(t) is the STF, m is the
shear modulus, and W is the fault width [Velasco et al.,
1994]. We can use this equation to stretch and scale the KIP
STF into a simplified slip function. A smaller fault width or
slower rupture would increase the slip magnitudes; a faster
rupture would increase the rupture length. If we assume that
m = 40 GPa, W = 150 km, vr = 2.4 km/s, the resulting slip
function for the iterative deconvolution STF has a peak slip
of about 8 m and the rupture length is about 1200 km
(Figure 3). The moment estimated from this single
observation is about 2.7 1022 N-m, a factor of 2.5 lower
than our preferred value of 6.5 1022 N-m [Ammon et al.,
2005]; the slip values are comparably underestimated. This
Figure 4. Contours of fault slip estimated from 13
Rayleigh wave STFs azimuthally distributed around the
source region (Figure 1). The geographic region over which
slip is permitted is shown with the dotted line. The star
indicates the event epicenter.
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AMMON ET AL.: FIRST-ORDER RUPTURE CHARACTERISTICS
tions from ignoring depth variations in the rupture model
are relatively small amplitude, low frequency artifacts in the
STF estimates (most pronounced near nodal stations, which
are inherently unstable anyway). The spurious features are
unlikely to be coherent as a function of azimuth and so are
not of major concern in a rapid analysis for first-order
rupture characteristics. We also constrained the inversion
by only allowing slip on a prescribed area, which is shown
in Figure 4. Allowing a larger region for rupture to the
southeast spreads some of the initial slip one or two hundred
kilometers in that direction, but as azimuthal coverage of the
data improves, the smearing is progressively reduced. The
spatial slip distribution varies with rupture speed intuitively;
higher speed results in a larger spatial spread of slip, and
lower speed produces more spatially concentrated slip
distributions. The variation is not dramatic for a typical
range of earthquake rupture speeds.
[14] The predicted STFs for this model (Figure 1) match
the main features of the observations, but the initial peak is
poorly fit to the southwest, and the initial rise time is not
always well matched. A lower rupture speed can improve
these features but the overall rupture velocity cannot be low
because it misfits the data. The complicated geographic
pattern of the first pulse amplitude may be related to rupture
complexity within the large asperity off northern Sumatra.
[15] This rupture model contains the primary features
found in analyses that include many body and surface
waves [Ammon et al., 2005]. Slip is relatively small near
the hypocenter, and extensive regions of large slip are
observed off the coast of northern Sumatra, and near the
Nicobar and Andaman Islands. The predicted moment rate
function for this model is in excellent agreement with those
found from IRT analysis, and finite fault models that include
long-period surface-waves [Ammon et al., 2005]. The seismic moment of 4.6 1022 N-m (Mw = 9.05) is about 70%
of the preferred moment. As described earlier, we expected
to underestimate the moment because it is difficult to
reliably extract periods much longer than 500 s with
relatively short time-window deconvolutions. Large
changes in mechanism could be a problem (as is true for
all rapid analyses), but even the roughly 30 strike rotation
and increase of the dip along the Sumatra-Andaman rupture
did not have a large influence on the surface waves for this
event.
5. Discussion and Conclusions
[16] The primary goal of rapid assessment of earthquake
signals is to quantify aspects of the rupture that may
influence seismic hazard. No single approach is perfectly
sufficient for the task and implementing any procedure in
near real-time is a challenge. An operational approach
involving a suite of tools sequentially implemented by a
seismic analyst during the first hour after alarms based on
P waves offers a sound approach for reliable event characterization. For most events, the more slowly propagating
surface waves will supplement first-order information already extracted from P-waveforms. However, for ‘‘tsunami’’ earthquakes, which are weak in short-period energy but
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produce large tsunamis [Kanamori, 1972], surface wave and
continuous geodetic analysis may be the primary bases for
correct assessment of hazard.
[17] The model in Figure 4 is a simplified reconstruction
of the earthquake slip, but the main rupture characteristics
needed to assess tsunami potential; total moment, total
rupture duration, and first-order slip distribution along the
plate boundary, are well recovered. With telemetered broadband surface-wave ground motions it is straightforward to
rapidly estimate these important characteristics of large
ruptures. This information can be obtained within minutes
of passage of surface waves, and rapid processing can
complement analyses of earlier arriving body waves to help
assess earthquake impact and tsunami excitation within 15 –
60 minutes after a large event.
[18] Acknowledgments. We thank two anonymous reviewers whose
comments helped improve this manuscript and the developers of GMT and
SAC, and the seismic network operators who have constructed a superb
open-data-access network for seismic research and monitoring. The facilities of the IRIS Data Management System were used to access the data
used in this study. Supported by NSF grant EAR01235595 (TL) and USGS
Award 05HQGR0174 (CJA).
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C. J. Ammon, Department of Geosciences, Pennsylvania State
University, 503 Deike Building, University Park, PA 16802, USA.
([email protected])
T. Lay, Earth Sciences Department, University of California, 1156 High
St., Santa Cruz, CA 95064, USA.
A. A. Velasco, Department of Geological Sciences, University of Texas,
500 West University Avenue, El Paso, TX 79968, USA.
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