The 26 December 2004 Sumatra earthquake (Mw 9.2

1
Rapid Determination of Earthquake Magnitude using
GPS for Tsunami Warning Systems Geoffrey
Blewitt, Corné Kreemer, William Hammond, and
Hans-Peter Plag Nevada Bureau of Mines and
Geology, and Seismological Laboratory, University
of Nevada, Reno, NV 89557, USA, email
gblewitt_at_unr.edu Seth Stein, and Emile Okal
Department of Geological Sciences,
Northwestern University, Evanston, IL 60208, USA
INTRODUCTION The 26 December 2004 Sumatra
earthquake (Mw 9.29.3) generated the most deadly
tsunami in history (Fig. 1). Yet within the
first hour, the true danger of a major oceanwide
tsunami was not indicated by seismic magnitude
estimates, which were far too low (Mw 8.08.5).
This problem relates to the inherent saturation
of early seismic-wave methods (Fig. 2). Here we
show that the earthquake's true size and tsunami
potential can be determined using Global
Positioning System (GPS) data up to only 15 min
after earthquake initiation, by tracking the mean
displacement of the Earth's surface associated
with the arrival of seismic waves (Fig. 3).
Within minutes, displacements of gt10 mm are
detectable as far away as India, consistent with
results using weeks of data after the event
refs 13. These displacements imply Mw 9.0
0.1, indicating a high tsunami potential (Fig.
4). This suggests existing GPS infrastructure
could be developed into an effective component of
tsunami warning systems.
RESULTS The resulting time series of station
positions (Fig. 3) clearly shows that most of the
permanent, static displacement occurs within a
few minutes of the first detectable arrival of
seismic waves, accompanied by strong shaking that
initially overshoots the final static position.
At 15 minutes after the origin time, rapidly
estimated displacements of 10 stations agree to
7-mm RMS with longer-term published estimates
refs 13. By applying F-tests to the misfit of
earthquake models (Fig. 4) of various magnitude
and rupture length, we can only accept
mega-thrust models in the range Mw 8.79.3, with
the most-probable magnitudes Mw 8.99.1, and
rupture length 1000 km (propagating
northward). To assess the accuracy of our rapid,
best-fitting model, we compared its predictions
with three published sets of displacements refs
13. The RMS differences in displacement range
from 2.54.1 mm, which is at the same level of
agreement as between the published displacements
themselves, indicating that our rapidly estimated
model is accurate at this level. Thus a rapid
analysis of the existing GPS network can estimate
Mw accurately and provide information on the
direction and length of rupture propagation, all
of which are important for assessing the
potential for an open ocean tsunami.
Figure 4. Reduced chi-square ??2 summarizing the
misfit of displacements from each model to
displacements rapidly determined with GPS, as a
function of Mw. Three cases are shown all
stations (blue), all except SAMP (green), and all
except SAMP and NTUS (red). The dashed lines
indicate 95 confidence intervals for each of the
three cases. The smallest misfit using all
stations (??27.0) has L1000 km and Mw 9.0.
Figure 1. Left The cycle of strain accumulation
and release that causes great thrust fault
earthquakes at a subduction zone. Right Travel
times for the December 2004 Indian Ocean tsunami.
V. Titov http//www.pmel.noaa.gov/tsunami/ind
o_1204.html
CONCLUSIONS We have shown that the magnitude,
mechanism, and spatial extent of rupturing of the
26 December 2004 Sumatra earthquake can be
accurately determined using only 15 min of GPS
data following earthquake initiation, using
publicly available data from existing GPS
networks. Most importantly, the GPS method would
have clearly ruled out the earliest misleading
indications from seismology that there was little
danger of a major oceanwide tsunami. By
implementing the GPS displacement method as an
operational real-time system, GPS could be
incorporated into tsunami warning systems.
Sensor networks for tsunami warning systems
currently include seismometers and deep ocean
pressure recorders that provide real-time data on
earthquakes and resulting tsunamis to warning
centers, which assess the possible threat and
alert emergency managers who advise the public.
The seismic data are important for the rapid
detection and location of potentially significant
events. GPS data could then be used to rapidly
model the earthquake and thus initialize
parameters for real-time modeling of tsunami
generation. The tsunami models could then be
validated and further constrained using ocean
sensor data. Thus seismic, geodetic, and oceanic
data could be truly integrated in tsunami warning
systems. Our results show greatly enhanced
sensitivity to the magnitude of great earthquakes
where the global IGS network is augmented by GPS
stations in the near field, indicating the
advantage of having real-time GPS networks near
oceanic subduction zones. Fortunately many such
networks exist, or are being planned, and so
could be upgraded with real-time communications
and incorporated into tsunami warning systems.
Figure 2. Left Illustration of earthquake
spectra showing corner frequencies (dashed
vertical lines) and different magnitude
determinations. The earthquake whose spectrum is
shown in red has larger Mw than the one with
spectrum shown in blue, even though they have the
same surface and body wave magnitudes, as shown
by the black part of the spectra that are the
same for both earthquakes. GPS samples the lowest
frequency part of the spectrum including static
offsets. Right Due to surface wave magnitude
saturation, earthquakes of the same Ms can have
very different moments and thus risk of
generating a far-field tsunami.
GPS DATA PROCESSING STRATEGY We simultaneously
reduced data from GPS stations ranging up to
7,500 km from the epicenter, including 37
operated by the International GNSS Service (IGS),
plus station SAMP in the near field (300 km).
Using GIPSY-OASIS II software, data at 30-second
epochs were reduced to a time series of station
longitude, latitude and height, using a
customized procedure that simulates a real-time
analysis situation. The analysis only used 24
hours of data until 20.4 minutes after the origin
time, applying a forward-filtering estimation
strategy designed to eliminate sensitivity to
information that would not have been available in
real time. Simultaneously estimated parameters
include the Earth's instantaneous pole position
and rate of drift, the Earth's rate of rotation,
state vectors of the satellite orbits
(initialized using the Broadcast Ephemeris),
stochastic solar radiation pressure on the
satellites, biases in the satellite and station
clocks at every 30-second epoch, random-walk
variation in zenith tropospheric delay allowing
for stochastic spatial gradients over each
station, constant biases plus random steps for
each station-satellite arc of carrier phase
observables, and coordinates of GPS station
positions. Station positions were estimated in
two categories the 28 far-field station
positions were estimated as constants over the 24
hour period, and the 10 near- to mid-field
station positions were estimated independently at
every 30-second epoch. Parameters were estimated
using a square-root information filter, a
sequential algorithm adaptable to real-time
applications. In addition, we applied a
position-based sidereal filter using the stacked
results of the previous 4 days of position
residuals, applying a 4-minute shift each day.
The actual processing time for a 38-station
network is 15 of real time on a common 1-cpu PC
running Linux, and so should pose no fundamental
time limitation for a real-time operational
system.
Figure 3. Time series of positions (blue)
estimated every 30 s for stations ranked (bottom
to top) by distance from the epicenter. Two
types of fit to the data are shown before and
after earthquake initiation. The black lines
indicate mean positions estimated empirically
from the time series, and the red lines are from
the best-fitting earthquake model.
ACKNOWLEDGMENTS This work was supported in part
by NASA Interdisciplinary Research and NASA Solid
Earth and Natural Hazards. We thank the
International GNSS Service (IGS) for making data
freely available. REFERENCES 1 Banerjee, P.,
F. F. Pollitz, and R. Burgmann (2005), The size
and duration of the Sumatra-Andaman earthquake
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R. Bamphenyu, C. Satirapod, N. Choosakul, C.
Subarya, A. Socquet, K. Omar, H. Z. Abidin, and
B. A. C. Ambrosius (2005), Insight into the 2004
Sumatra-Andaman earthquake from GPS measurements
in Southeast Asia, Nature, 436, 201-206. 3
Kreemer, C., G. Blewitt, W. C. Hammond, and H.-P.
Plag (2006), Global deformation from the great
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