Synopses of Master Papers

Bulletin of IISEE, 47, 115-120, 2013

DETERMINATION OF SLIP DISTRIBUTION
OF THE 28 MARCH 2005 NIAS EARTHQUAKEUSING JOINT INVERSION OF
TSUNAMI WAVEFORM AND GPS DATA
Tatok Yatimantoro ∗MEE11621

Supervisor: Yuichiro TANIOKA∗∗

ABSTRACTThe large 28 March 2005 Nias earthquake (M w 8.6) occured on megathrust of the Sumatra subduction
zone and generated a small tsunami. We estimated the slip distribution of the 2005 Nias earthquake
using joint inversion of tsunami waveforms and GPS data. We used 5 tide gauge stations around
Indian Ocean and 9 GPS stations from Sumatran GPS array (SuGar) around Sumatra to perform thejoint inversion. We assumed that the fault length was 300 km and the width was 150 km. To
determined the slip distribution, we divided the ruptured area into 18 subfaults. The result shows thatthe maximum slip amount of 12.35 m was found below Nias Island. The large amount of the slip was
located at intermediate (21 – 27 km) and deeper (> 27 km) depths. The large slip area of the 2005 Nias
earthquake did not reach the Sumatra trench. The rupture area of the 2005 Nias earthquake was similar
to that of the 1861 earthquake. The total seismic moment was calculated to be 1.06 × 1022 Nm (M w =8.6) by the slip distribution.
Keywords: Nias earthquake, Joint inversion, Slip distribution

1. INTRODUCTION
On 28 March 2005 at 16:09:36 UTC a large earthquake occured in the northern part of Nias Island.
The Nias earthquake occured only three months after the Sumatra-Andaman earthquake, 26 December
2004 (M w = 9.1). According to United States Geological Survey (USGS), the epicenter of the Nias
earthquake was located at 2.074°N, 97.013°E and its depth was 30 km. The Harvard Centroid Moment
Tensor (Harvard CMT) solutions estimated fault parameters as strike = 329° , dip = 7°, rake = 109°and seismic moment Mo = 1.1 x 1022 Nm (M w = 8.6). Historical records of the last 300 years reveal an
additional great interplate earthquakes near Nias Island in 1861 with a moment magnitude M w 8.5(Newcomb and McCann, 1987). Subarya et al. (2006) and Prawirodirdjo et al. (2010) estimated thatthe 2005 Nias earthquake ruptured approximately the same region as that of the 1861 earthquake.
A tsunami by the 2005 Nias earthquake was recorded by some tide gauge stations around
Indian Ocean. Tsunami by the 2005 Nias earthquake hit on Nias Island and surrounding areas. The
maximum tsunami elevation in Nias Island, Banyak Island, Simeuleu Island were 3.6 m, 3.5 m, and
4.2 m, respectively (Borrero et al., 2010). The 2005 Nias earthquake ruptured the plate interface which
in some part is located beneath Nias Island. The vertical and horizontal displacements due to theearthquake on the Nias Island and surrounding area recorded by Sumatran GPS array (SuGar). We
used the GPS data and the tsunami waveforms in a joint inversion to estimate the slip distribution of
the 2005 Nias earthquake.

∗

Meteorological Climatological and Geophysical Agency of Indonesia (BMKG)
Professor, Institute of Seismology and Volcanology (ISV), Hokkaido University∗∗

2. OBSERVATION DATA
2.1 Tsunami Waveform and Bathymetry Data

Figure 1. Epicenter of the 2005 Nias
earthquake and location of available tidegauge stations.

In this study, we used 5 tide gauge stations in around
Indian Ocean (Figure 1). We obtained the tide data
for Sibolga station by digitizing a figure by Aydan etal.(2005) showing the record, and the tide data forMale, Gan, Colombo stations were obtained bydigitizing figures by Liu and Wang (2005) showing
the records, while the tide data for Cocos station we
get from Australian Bureau of Meteorology (BoM).
For bathymetry data, we used data from GEBCO(General Bathymetric Chart of the Oceans) provided
by the British Oceanographic Data Centre (2012)
with spatial grid interval 30’’ (~ 0.925 km).

2.2 GPS Data
The crustal deformation due to the 28 March 2005 Nias
earthquake was recorded by GPS stations of SuGar. We
used 9 SuGar GPS stations (Figure 2) which are: ABGS,
SAMP, and UMLH on Sumatra Island; LEWK and BSIM
on Simeuleu Island; LHWA on Nias Island; PSMK on
Simuk Island; PBAI on Bais Island; and PTLO on Telo
Island. The vertical and horizontal displacements at eachGPS station were obtained from Kreemer et al. (2006).

Figure 2. Location of GPS stations
used in this study
3. METHODS
3.1 Estimation of the Fault Plane
For the study of the Nias earthquake, we assumed a rupture
plane with a length of 300 km and a width of 150 km byreferring to the aftershock distributions. Then, for the
purpose of estimating the slip distribution, we divided thefault plane into 18 subfaults with the size of 50 km x 50 km
each (Figure 3). For the subfaults number 1 – 6 we used top
depth of 15 km, for the subfaults number 7 – 12 we used top
Figure 3. Location of 18 subfaults
depth of 21 km, and subfaults number 13 – 18 we used top
which are assumed for the 28
depth of 27 km. The focal mechanism of strike 329°, dip 7°,
March 2005 Nias earthquake study and rake 109°, obtained from Harvard CMT solution, wasassumed for all the subfaults. We applied the Okada (1985) formula to compute the deformation on theocean bottom for each subfault.

3.2. Numerical Tsunami Simulation
For the numerical calculation of tsunami simulation, we used the linear shallow-water theory inspherical coordinates. The computation area of this study is 15°S - 10°N and 70°E - 105°E (Figure 1).
We used a nested grid method for the calculation of tsunami simulation. In this study we resampled
GEBCO 30” to become 3 different spatial grid sizes: 135”, 45” and 15”. The linear shallow-water orthe linear long-wave theory is given by the following equations (Johnson, 1998) :

∂Qϕ 
∂h
1 ∂
+
 (Qθ sin θ ) +=0∂t R sin θ  ∂θ
∂ϕ 

∂Qϕ

gd ∂h
R sin θ ∂ϕ
∂t
∂Qθ
gd ∂h
= fQϕ −∂tR ∂θ= − fQθ −

(1)
(2)
(3)

where, φ is longitude, θ is colatitude (90° - latitude), f is the Coriolis coefficient, t is time, h is thewater level, Q φ and Q θ are the flow flux along latitude and longitude axes, respectively, g is thegravitational acceleration, and d is the water depth. The Coriolis coefficient is given by f = 2 Ω cos θ,
where Ω is angular frequency of the earth’s rotation. We applied the Courant-Friedrichs-Lewy (CFL)
condition to checking the stability.

∆x

∆t ≤

(4)

2 gd

where Δx is spatial grid size. We used time step of 1 second to satisfy the CFL stability condition for
finite difference computation.
3.3 Synthetic Vertical and Horizontal Displacements
In the slip distribution studies, GPS data can be used as a reference value for the surface deformation
caused by the all subfaults. For the 2005 Nias earthquake, the observed vertical and horizontal
displacements at each GPS SuGar station were obtained from Kreemer et al. (2006). Then, to obtainedsynthetic vertical and horizontal displacements at each GPS SuGar station from all subfaults we used
Okada (1985) formula.
3.4 Inversion
Slip amount is very important because it is related to the seismic moment of the earthquake. Observed
tsunami waveforms are expressed as a superposition of computed waveforms as follows (Satake,1987) :A ij (t) . x j = b i (t)(5)

where A ij is the computed waveform, or Green’s function at the i-th station from the j-th subfault, x j isthe amount of slip on the jth subfault and b i is the observed tsunami waveform at the i-th station. To
avoid a negative slip value, we applied non-negative least square method (Lawson and Hanson, 1974)
for determining slip amount. The formula of the non-negative least square method is as follows :[A (t ).x − b (t )] → minimum ; x ≥ 0
2

ij

j

i

j

(6)

Because we also involved the GPS data for joint inversion, we modified Eq. (5) as follows : STij  DTi SG .X j = DG i  ij 

(7)

where ST ij is the synthetic tsunami waveforms at station i-th from segment j-th, SG ij is the synthetic
vertical and horizontal displacements at station i-th from segment j-th, x j is the slip amount at segment
j-th, DT i is the observation of tsunami waveforms at station i-th and DG i is the observation of verticaland horizontal displacements at station i-th.
The spatial variation of fault slip must be smooth to some degree because of the finiteness inthe fracture strength of actual rocks (Yabuki and Matsu’ura, 1992). We used the following objectivefunction minimized in the inversion.

s (m ) = (d − Gm ) E −1 (d − Gm ) + α 2 m t Hm
t(8)

where d is the observed tsunami waveforms and GPS data in the joint inversion, G is the Green’s
function containing the synthetic tsunami waveforms and synthetic vertical and horizontal
displacements, m is the model parameter vector, α2 is the smoothing factor, H is the smoothing matrix
consisting of a Laplacian operator that spatially smooths the slip distribution and E is the measurement
errors, which are assumed to be the covariance matrix of the data.
To obtain the optimal value of smoothing factor (α2), the Akaike’s Bayesian Information
Criterion (ABIC) proposed by Akaike (1980) is used in this study.

( )ABIC α 2 = ( N + P − M ) log s (m ) − P log α 2 + log G t E −1G + α 2 H + C(9)where N is the total number of data points in the tsunami waveform and GPS data, P is number of thesubfault, M is the number of model parameter and C is a constant.
The modified “delete-half” Jackknife method (Tichelaar and Ruff, 1989) was applied toestimate error. In this method, the inversion is repeated many times by deleting half the number of data
randomly. The errors defined as the standard deviation are multiplied by a scale factor, K, where theformula of K is calculated as follows :K = [(n − j − p + 1) / j ] 2
1(10)

where n is the total number of data points, j is the number of dropped data points and p is the numberof the model parameters that can be assumed as the number of subfaults.

4. RESULTS AND DISCUSSION
The slip distribution (Figure 4a and Table 1) shows that the largest slip amount of 12.35 m was locatedat subfault 8 with depth between 21 km and 27 km. This subfault is located at below Nias Island.
Figure 5a shows that the northwest part of Nias Island had uplift of around 3 m, Simeuleu Island andBanyak Island had uplift of around 2.5 m, while subsidence around 1 – 1.5 m occured in Sumatra
Island. Graph of ABIC and smoothing factor are shown in Figure 5c.
The result of slip distribution calculation suggests that before the 2005 Nias earthquake
occured, there was a locked zone in and around Nias Island. We have an assumption that the 2005
Nias earthquake was the recurrence of the 1861 event. The result of our slip distribution calculation isconsistent with the result of Walker et al. (2005), Kreemer et al. (2006), and Konca et al. (2007), witha large amount of slip distributed in northern part of Nias Island, Simeuleu Island, and Banyak Island.
The large slip area of the 2005 Nias earthquake did not reach the Sumatra trench.
Table 1. Slip amount of each subfault
Subfault Slip Amount
Number(meter)
1
2.92
2
6.21
3
0.31
4
0.00
5
3.26
6
3.44
7
2.53
8
12.35
9
3.08
10
1.61
11
4.99
12
4.87
13
0.00
14
5.83
15
9.50
16
8.58
17
5.64
18
4.94

Error
(meter)± 0.05± 0.05± 0.26± 0.35± 0.60± 0.80± 0.19± 0.97± 1.31± 0.11± 2.28± 0.40± 0.02± 0.73± 0.43± 0.65± 1.80± 2.14

(a)

(b)

a

Figure 4. (a) Estimated slip distribution of the 2005 Nias
earthquake determined by joint inversion of tsunami
waveforms and GPS data. (b) Comparison of the observed(blue lines) and synthetic tsunami waveforms (green lines)
computed from the calculated slip distribution.

(b)

(c)

Figure 5. (a) Crustal deformation computed from the slip distribution. (b) Comparison of observed
displacements (vertical and horizontal) and displacements calculated from the slip distribution (c)Values of ABIC plotted as a function of α2, where the ABIC values are minimized at α2 = 0.03
In general, our comparison of observed and computed tsunami waveforms, as shown in
Figure 4b, are consistent except for that of Gan station which has a large error compared with the otherstations. We suppose this is because of resolution of the bathymetry data is low in the area of theMaldives Islands. Overall, for comparison of observed and computed displacements as shown in
Figure 5b, the computed displacements (vertical and horizontal) explain the observed ones.
The total seismic moment calculated from these slip distribution is 1.06 × 1022 Nm (M w =8.6), with the assumed rigidity (Fujii and Satake, 2008) 4.0 × 1010 N/m2 for subfaults number 1-12

(shallow and intermediate subfaults) and 7.0 × 1010 N/m2 for subfaults number 13-18 (deeper
subfaults). The result was slightly smaller than seismic moment of Harvard CMT solution and theseismic moment that was obtained using joint inversion of seismic wave and geodetic data by Konca
et al. (2007). The result of moment magnitude was similar to the result of the Harvard CMT solution
and Walker et al. (2005), but larger than moment magnitude that was obtained using GPS data byKreemer et al. (2006).

5. CONCLUSIONSThe 28 March 2005 Nias earthquake was a large earthquake that occured in the megathrust of theSumatra subduction zone. This earthquake generated a small tsunami with a maximum tsunami heightof around 1.3 m recorded at closest tide gauge station (Sibolga). We have estimated the slip
distribution of the 28 March 2005 Nias earthquake by using joint inversion of tsunami waveforms andGPS data. We assumed that the fault length was 300 km and the width was 150 km. The slip
distribution shows that the large amount of the slip was located in the intermediate (21 – 27 km) anddeeper (> 27 km) subfaults. The maximum slip amount was 12.35 m located at below Nias Island. The
large slip area of the 2005 Nias earthquake did not reach the Sumatra trench. The rupture area of the2005 Nias earthquake was similar with that of the 1861 earthquake. The slip distribution is consistent
to the source model that were obtained by teleseismic wave (Walker et al., 2005), GPS data (Kreemer
et al., 2006) and joint inversion of seismic wave and geodetic data (Konca et al., 2007). The total
seismic moment calculated by the slip distribution was 1.06 × 1022 Nm (M w = 8.6).

ACKNOWLEDGEMENTS
I would like to express my gratitude to Dr. Bunichiro Shibazaki (IISEE, BRI), Dr. Aditya R. Gusman(ISV, Hokkaido University) and Dr. Yushiro Fujii (IISEE, BRI) for their discussions and usefulknowledge.

REFERENCES
Akaike, H., 1980, pp. 143-166, Univ. Press, Valencia, Spain.
Aydan et al., 2005, Journal of The School of Marine Science and Technology, Vol.3 No.2 pp. 67-83.
Borrero et al., 2011, Pure Appl. Geophys., 168, 1075-1088.
Fujii, Y. and Satake, K., 2008, Earth Planets Space, 60, 993-998.
Johnson, J. M., 1998, Adv. Geophys., 39, 1-116.
Konca et al., 2007, Bull. Seis. Soc. Am., Vol. 97, No. 1A, pp. S307-S322.
Kreemer et al., 2006, Geophysical Research Letters, vol. 33, L07307.
Lawson, C. L., and Hanson, R. J., 1974, 340 pp., Prentice-Hall, Englewood Cliffs, N. J.
Liu, P. L. F., and Wang, X., 2005, Cornell University.
Newcomb, K. R. and McCann, W. R., 1987, JGR, vol. 92, no. B1, pages 421-439.
Okada, Y., 1985, Bull. Seismol. Soc. Am., 75-4, 1135-1154.
Prawirodirdjo et al., 2010, JGR, vol. 115.
Satake, K., 1987, J. Phys. Earth, 35, 241-254.
Subarya et al., 2006, Nature, vol. 440, doi:10.1083/nature04522.
Tichelaar, B. W., and Ruff, L. J., 1989, Eos Trans. AGU, 70, 593, 605-606.
Walker et al., 2005, Geophys. Res. Let., vol. 32, L24303.
Website : http://www.gebco.net
Website : http://www.globalcmt.org/CMTsearch.html
Website : http://earthquake.usgs.gov/earthquakes/ eqinthenews/
Yabuki, T., and Matsu’ura, M., 1992, Geophys. J. Int., 109, 363-375.