TSUNAMI SOURCE STUDY OF THE 2010 MENTAWAIEARTHQUAKE FROM TSUNAMI WAVEFORM
INVERSION AND INSAR ANALYSIS
Gian Ginanjar
MEE10517

Supervisor:

Yuichiro TANIOKA ABSTRACTThe source process of the 2010 Mentawai Tsunami is estimated by using tsunami waveforms at aDART station and tide gauge stations around the Indian Ocean. The inversion results show that themajor slip region for the October 25 2010 Mentawai earthquake is located near epicenter. The slip
amount near the epicenter is about 1.3 to 2.5 m, and the slip amount around the trench is about 1.8 m.
The seismic moment calculated from the slip distribution is 1.07 x 10 21 Nm (moment magnitude Mw=8.0), larger than that obtained from seismic inversion. However, comparison of the measured tsunami
heights at Mentawai islands region with the calculated maximum coastal tsunami heights from slip
distribution shows that the simulated tsunami heights is underestimated the measured tsunami heights
at Mentawai islands region.
The distribution of aftershocks and the area of dominant slip in the slip distribution modelfrom tsunami inversion suggest that the event ruptured up-dip from the point of nucleation(hypocenter) and very near the trench. Such near-trench rupture supports that this earthquake was a"tsunami earthquake".
The fringes calculated from InSAR data show one cycle of color corresponding to 2 pi
radians phase change. The one color cycle of 2 pi radians phase change would correspond to 2.8 cm ofdisplacement along the radar line of sight (LOS) for South Pagai island of Mentawai islands region.
The amount of displacement in the direction of the line of sight calculated from tsunami inversion isalso estimated to be one color cycle of 2 pi radians phase change.
Keywords: 2010 Mentawai earthquake, Tsunami source, Tsunami waveform inversion, Tsunami
earthquake, Slip distribution, InSAR.

1. INTRODUCTION
An earthquake with moment magnitude (Mw) of 7.7 according to United States Geological Survey(USGS) or 7.2 (MwmB) according to BMKG, occurred at Mentawai region off west of Sumatera
Island on October 25th 2010, at origin time of 14:42:22 UTC, in about 30 km west of Pagai Selatan,Mentawai - Sumatera Barat, Indonesia as shown in Figure 1. The epicenter is located at 3.61º S and99.93º E with focal depth of 10 km according to BMKG, or 3.484º S and 100.114º E with focal depthof 20.6 km according to USGS.
The earthquake occurred near the trench on subduction zone where the Indo-Australianplate is subducting beneath the Sunda plate at oblique angle. The focal mechanism from the USGS's
Wphase moment tensor solution shows that the earthquake has a thrust fault type mechanism systemwith strike of 326º, dip of 12º and slip of 101º. The earthquake occurred along the plate boundary
between the Indo-Austalian plate and the Sunda plate. Large earthquakes that occurred near the trenchIndonesian Agency for Meteorology, Climatology and Geophysics - BMKG (Badan Meteorologi, Klimatologi
dan Geofisika) Indonesia.
Institute of Seismology and Volcanology, Hokkaido University, Japan.

1with thrust fault mechanisms which have low angle of dip and produced large tsunami but not so bigof ground shaking are called tsunami earthquakes (Satake and Tanioka, 1999). The 2010 Mentawai
earthquake is possibly this type of a tsunami earthquake
While any earthquakesthat generate tsunamis can beclassified
as“tsunamigenicearthquake”, the term “tsunamiearthquake”, hereafter TsE, is used
for a special class of events thatgenerate much larger tsunamis than
expected from its seismic waves(Kanamori,1972).
For
thisMentawai earthquake, the tsunami
magnitude was Mt = 8.1, estimatedby Abe formula using the tsunami
wave heights from different tidegauge stations (Abe, 1989).
Other characteristic of
TsE is “slow and long rupture
Figure 1. The Location of 2010 Mentawai earthquake
processesofearthquakes”(Kanamori, 1972). For this Mentawai Earthquake, “the estimated duration is 109.7 s, andconsidering the low amplitude and long duration, which are the characteristics of TsE, the event islikely to be a tsunami earthquake” (Hara, 2010).

2. OBSERVATION DATA
2.1 Tsunami Waveform Data
The tsunami was recorded by many tide gauge stations around the Indian Ocean and by a DART
(Deep-ocean Assessment and Reporting of Tsunamis) buoy deployed in the deep sea ocean between
Indonesia and Australia (Table 1).
Table 1. Tide Gauge Stations and a Dart
These tide gauge and DART buoy records
Buoy station
include ocean tides, therefore the ocean tides need tobe removed to get the tsunami waveforms. First,Station Name
Latitude ()Longitude ()ocean tides approximation should be made by fitting aCocos-12.1167
96.8919polynomial function, then removed from the original
Colombo
6.95
79.85
records at all tide gauge and DART stations.
Denis_Island-3.8
55.6667
Hanimadhoo
Padang
Pt_LouisReunion
Rodrigues
SeblatTelukdalam
TanahbalaTrinconmalee
D56001Enggano

2.2 Tsunami Runup Data

6.7667-0.95-20.15716-20.92-19.68024-3.224167
0.554
-0.53
8.5637-13.985-5.3461

73.1667
100.3667
57.5043
55.28
63.42119101.5994
97.822
98.5
81.1996110.005
102.2781

From november 5 to 10, the “JICA (Japan International
Cooperation Agency) – JST (Japan Science andTechnology Agency) Indonesia Multi-disciplinary
Hazard Reduction from Earthquakes and Volcanoes inIndonesia” organized several teams to conduct a post
tsunami survey with several different focuses of survey.
Thirty-eight measurements of tsunami height range
from 2.5 to 9.3 m, but mostly 4 to 7 m. The tsunami
inundation was more than 300 m at three locations. The tsunami deposits, mostly coarse to medium
sand and 5 to 26 cm in thickness, were sampled along transects at three locations (Satake et al., 2011).

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2.3 InSAR Data
To detect the ground displacement on the Pagai Islandof Mentawai Islands region near the source area, thisstudy conduct an InSAR analysis by using the satellite
data of the ALOS/PALSAR, launched in 2006 andoperated by the Japan Aerospace Exploration Agency(JAXA), which has an L-band sensor with wavelengthof 23.6 cm.
For processing of the level-1.0 SAR data
to bobtain Interferogram SAR (InSAR), we used afree software package called GMTSAR: An InSAR
Processing System Based on Generic Mapping Tools(Sandwell et al., 2011). An InSAR data of the South
Figure 2. InSAR data of Mentawai
Pagai Island-Mentawai Islands region is obtained as Islands with 6 months of time spansshown in Figure 2.
shown displacement in line of sight
The PALSAR data pair used in the InSAR (LOS) direction.
analysis are from Desember 30 2010 as master image
and from June 29 2010 as slave image, with ascending flight direction and perpendicularbaseline (Bperp) is -323.09.

3. METHOD
3.1 Source Area from Tsunami Arrival Times
This study first estimate the tsunami source area from the observed tsunami travel time, by making an
inverse refraction diagram. This technique calculates the initial wavefronts through back projectionof tsunamis from tide gauge stations towards the source (e.g.,Fujii and Satake, 2006). The tsunami source is well constrainedby the travel time after we made a little adjustment for Cocos’stravel time because we believe that poor bathymetry data inshallow coastal area around Cocos Island is responsible for poor
constraints that need to be adjusted. Figure 3 shows the green
circle indicates the constraint area for the source, black lines
indicate estimatedinitial wavefronts
from the observed
tsunamiarrivaltimes, while yellow
line shows theadjusted travel timefor the Cocos.
Figure 3. Inverse refraction
For thisdiagrams for the 2010
study 15 subfaults
Mentawai tsunami.
located within theaftershock area are assumed (Figure 4). The length andwidth are 50 km × 50 km for each subfault. The focal
mechanisms of all the subfaults are strike of 326º, dip of
12º and slip of 101º from the USGS's Wphase moment
tensor solution. The top depths of the subfaults were
Figure 4. Fifteen assumed subfaults
assumedto be 5, 15.4 and 25.8 km for shallow, middle
located within the aftershock area.
and deep subfaults, respectively.

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3.2 Numerical Tsunami Simulation
The computational area ranges from 52E to 113E and from 25S to 10N. We used a bathymetry
grid data from General Bathymetric Chart of the Oceans (GEBCO) 30 arc-second grid data andresampled it to 1 arc-minute grid size for far field data, and for near field the GEBCO 30 arc-second
merged with nautical charts of Padang-Bengkulu-Nias-Mentawai and resampled the merged grid with15 arc-second grid size.
The linear shallow water or linear long wave theory is given by the following equations(Johnson, 1999):, whereis longitude,  is colatitudes (90ºlatitude), f is the Coriolis coefficient, t is time, h is thewater level,
andare the flow flux along longitude and latitude axes, respectively, g is thegravitational acceleration, and d is the water depth. The Coriolis coefficient is given by f = 2cos,
where  is the angular frequency of the Earth’s rotation. Computational time step of 3 s for far field
and 1 s for near field are chosen to satisfy Courant-Friedrichs-Lewy (CFL) stability condition that isexpressed by the following equation:, whereandare temporal and spatial grid lengths, d is the maximum still water depth
in a computation region. The physical meaning of the stability condition is that the time stepmust be equal or smaller than the time required for the wave to propagate in the spatial grid size.

3.3 Inversion
The fault plane is divided into 15 small subfaults and the deformation on the ocean bottom iscomputed for each subfault with a unit amount of slip. Using this displacement field as the initialcondition, tsunami waveforms are computed by a finite-difference method using actual bathymetry.
The observed tsunami waveforms are expressed as superposition of the computed
waveforms as follows:(5)
where Aij is the computed waveforms, or Green’s functions, at the i-th station from the j-th subfault, xj
is the amount of slip on the j-th subfault, and bi is the observed tsunami waveform at the i-th station(Sateke and Kanamori, 1991).
The Akaike’s Bayesian information criterion (ABIC) proposed by Akaike (1980) is used todetermine the optimal value of the smoothing factor (2).
3.4 Displacement in Line of Sight (DLOS)
The relationship between LOS displacement and displacement components on the ground is expressed
as follows (Hanssen, 2001):4(6)whereis a LOS displacement,is the horizontal displacement,is the verticaldisplacement,is the azimuth of the perpendicular to the satellite track,is the azimuth of thedisplacement, andis the off-nadir angle.

4. RESULTS AND DISCUSSION
4.1 Slip Distribution Determined by the Tsunami Waveform Inversion
The slip distribution inverted from the tsunami waveform data is shown in Figure 5(a). The optimalvalue of smoothing factor (2) that minimizes the value of ABIC is 0.5 (Figure 5(d)). According to theinversion result the major slip region is located near the epicenter with maximum slip amount of 2.5 m.
The seismic moment calculated from this slip distribution is 1.0705 x 10 21 Nm that corresponds tomoment magnitude of 7.9531 (Mw= 8.0) by assuming a rigidity of 4 x 1010 Nm-2. The comparison oftsunami waveforms are shown in Figure 5(c) and the comparison with the tsunami height from fieldsurvey in Mentawai island region is shown in Figure 5(b).
(a)

(c)

(b)

(d)

Figure 5. (a) Slip distribution of the 2010 Mentawai earthquake estimated from tsunami
waveform data. (b) Observed tsunami data and synthetic tsunami from the inversion, whereobserved tsunami records are shown in red (dashed line is original records and solid line iscut-data for inversion) and synthetic tsunami waveforms are shown in blue. (c) Simulated
coastal tsunami heights and comparison between simulated tsunami height and tsunami
height data from field surveys (Satake et al., 2011). (d) Values of ABIC plotted as a fucntionof 2, in which the minimized ABIC is at 2 = 0.5.

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4.2 DLOS Model Predicted from the Tsunami Inversion Result
The fringes for calculated DLOS model
generally shows the same pattern with thefringes by InSAR data that also show one
cycle of color corresponding to 2 pi radians
phase change (Figure 6). The one color cycleof 2 pi radians phase change, if interpreted as
ground displacement, would correspond to 2.8
cm of displacement along the radar line ofsight.
Figure 6. DLOS model (left) and InSAR data (right)
5. CONCLUSIONSThe 2011 Mentawai earthquake is an example of a rare slow-source tsunami earthquake, withMw=7.7, tsunami magnitude of Mt=8.1, and slow rupture duration of 109.7 s. The slip amount near
the epicenter is about 1.3 to 2.5 m, and the slip amount around the trench is about 1.8 m.
The seismic moment calculated from the slip distribution is 1.0705 x 10 21 Nmcorresponding the moment magnitude of 7.9531 (Mw 8.0), larger than that obtained using seismic
inversion. However, the simulated tsunami heights are underestimated at Mentawai islands region.
The distribution of aftershocks and the area of dominant slip in the slip distribution modelfrom tsunami inversion suggest that the event ruptured up-dip from the point of nucleation(hypocenter) and very near the trench. Such near-trench rupture supports that this earthquake was a"tsunami earthquake".
The displacement LOS model determined from tsunami inversion generally shows thesame pattern with the fringes by InSAR data that also show one cycle of color corresponding to 2 pi
radians phase change. The one color cycle of 2 pi radians phase change would correspond to 2.8 cm
of displacement along the radar line of sight (LOS) for South Pagai island of Mentawai islands region.
AKNOWLEDGEMENT
We would like to thank Dr. Yushiro Fujii of IISEE-BRI and Dr. Aditya Riyadi Gusman of Hokkaido
University for all the support. The ALOS/PALSAR data are copyright of METI (Ministry of Economy,Trade and Industry) and JAXA. Most of the figures were generated by using GMT-Generic Mapping
Tools (Wessel and Smith, 1998), and by MATLAB® R2011a Student Version.
REFERENCES
Abe, K., 1989, Tectonophysics 166, 27-34.
Akaike, H., 1980, pp. 143-166, Univ. Press, Valencia, Spain.
Fujii, Y., and Satake, K., 2006, Geophys Ress Lett, vol. 33, L24317, doi:10.1029/2006GL028049.
Hanssen, R. F., 2001, Kluwer Academic, Dordrecht, 2001. 328 pp. ISBN: 0-7923-6945-9.
Hara, T., 2010, http://iisee.kenken.go.jp/special/20101025sumatra/magnitude.htm
Johnson, J. M., 1999, Adv. Geophys., 39, 1-116.
Kanamori, H., 1972, Phys. Earth Planet. Inter. 6, 246-259.
Sandwell, D., et al., 2011, http://escholarship.org/uc/item/8zq2c02m
Satake, K., and Kanamori, H., 1991, Natural Hazards 4:193-208.
Satake, K., and Tanioka, Y., 1999, Pure appl. geophys. 154 (1999) 467-483, 0033-4553/99/040467-17.
Satake, K., et al., 2011, to be submitted to PAGEOPH.
Wessel, P., and W. H. F. Smith, 1998, EOS Trans. AGU, 79, 579.

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