Synopses of Master Papers

Bulletin of IISEE, 47, 109-114, 2013

TSUNAMI SIMULATIONS OFF THE WEST COAST OF
SUMATRA USING DISPERSIVE AND
NON-DISPERSIVE WAVES
Dwi Hartanto ∗MEE11620

Supervisor:

Tatsuhiko SAITO ∗∗Yushiro FUJII ∗∗∗ABSTRACT
To reduce future tsunami hazards, tsunami simulations for possible future events in the
Mentawai region, especially the Padang area, based on dispersive wave equations (DSP) andnon-dispersive wave equations, namely liner long-wave (LLW) and non-linear long-wave (NLLW),
were conducted in this research. Through these simulations we attempted to estimate maximum
tsunami height and tsunami arrival time for the Padang area assuming probable scenarios for future
events. An additional objective was to understand which dispersive and non-linear terms affect thetsunami simulation results.
The simulation results were categorized into two parts. For deep water we compared DSP
with LLW, and for shallow water, NLLW with LLW. From these comparisons we found that in deep
water DSP almost similar with LLW; dispersive waves appear when a station is located perpendicular
to the fault strike. Comparison of difference depth of 5, 10, and 20 km in the DSP simulations for
scenario earthquake of Mw 8.5 shows that dispersive wave appears more clear at shallow depth. This
indicates that dispersive wave may be useful for judging whether earthquake rupture reaches very
shallow part near the trench or the rupture occurs only in deep part. In shallow water, advection andbottom friction terms should be considered when the depth is less than 50 m. Our simulations
produced a maximum tsunami height in the Padang area of 0.91, 2.02 and 5.65 m for scenario
earthquake of Mw 8.1, 8.5 and 8.9. The tsunami arrival times was 24, 20 and 17 min, for the scenariosof Mw 8.1, 8.5 and 8.9, respectively. In the Padang area tsunami countermeasures should be increased
for the future earthquakes.
Keywords: Tsunami simulation, dispersive wave, maximum tsunami height, tsunami arrival time,
Mentawai, Padang area.

1. INTRODUCTION
After the megathrust earthquakes in Aceh on December 26, 2004 and Nias on March 28, 2005 the next
megathrust earthquake is predicted to occur in the Mentawai region (Natawidjaja, 2007). The lastmegathrust earthquake in the Mentawai region were in 1797 (Mw 8.4) and 1833 (Mw 8.9)
(Natawidjaja et al., 2006).
The Bengkulu earthquake (Mw 8.4) on September 12, 2007 and the Mentawai earthquake(Mw 7.7) on October 25, 2010 both occurred in the area of the Mentawai megathrust (Figure 1). This∗

Meteorology Climatology and Geophysics Agency (BMKG), Jakarta, Indonesia.
National Research Institute for Earth Science and Disaster Prevention (NIED), Tsukuba, Japan.
∗∗∗International Institute of Seismology and Earthquake Engineering (IISEE), Building Research Institute (BRI)
Tsukuba, Japan.
∗∗two earthquakes reduced the energy that is stored in the Mentawai region, however, much energy is
still stored and will be released in the future. The rupture area of the 2010 Mentawai earthquake and2007 Bengkulu earthquake is only 1/3 of the 1797 and 1833 earthquakes.
If we plot the data from USGS and Global CMT (1973 - May 2012), it shows that to the westof Padang there is a seismic gap (Figure 1). The purpose of this study is to estimate the maximum
tsunami height and tsunami arrival time in Padang area using probable scenarios for future events.
Also we attempted to find how influential dispersive wave (DSP) and non-linear effects would be tothe simulations, by comparing DSP with linear long-wave (LLW) for deep water, and non-linear
long-wave (NLLW) with LLW for shallow water.
Figure 1. The rupture areas of the 1833
earthquake (orange rectangle) modified
from the figure by Newman et al.,(2011). Red (uplift) and blue(subsidence) contours are seafloor
deformation from the 2010 Mentawai
earthquake (Satake et al., 2012), with acontour interval of 0.1 m. Green (uplift)
and yellow (subsidence) contours areseafloor deformation from 10-subfault
model of the 2007 Bengkulu earthquake(Fujii and Satake, 2008), with a contour
interval of 0.2 m. Purple circle indicatesa seismic gap near Padang. The figure
also includes assumed single fault withlength of 250 km and width of 100 km(black rectangle).
2. THEORY AND METHODOLOGY
2.1 Linear dispersive equations: tsunami in deep water
In Cartesian coordinates the 2-D DSP equations can be written as (Saito et al., 2010)𝜕𝜂𝜕𝑀 𝜕𝑁= −�+�𝜕𝑡
𝜕𝑥 𝜕𝑦𝜕𝜂 1 2 𝜕 2 𝜕𝑀 𝜕𝑁
𝜕𝑀+ 𝑔ℎ= ℎ�+�𝜕𝑥 3 𝜕𝑥𝜕𝑡 𝜕𝑥 𝜕𝑦𝜕𝑡𝜕𝜂 1 2 𝜕 2 𝜕𝑀 𝜕𝑁
𝜕𝑁+ 𝑔ℎ= ℎ�+�𝜕𝑦 3 𝜕𝑦𝜕𝑡 𝜕𝑥 𝜕𝑦𝜕𝑡

(1)

(2)

(3)

,where M and N are the velocity components(𝑢, 𝑣) in x and y direction integrated along thevertical direction from the sea bottom to the sea
surface, 𝜂 is sea surface fluctuation, h is water
depth, and g is acceleration due to gravity. The
right hand sides of Eq. (2) and Eq. (3) indicatedispersion terms

2.2 Nonlinear long-wave equations: tsunami near shore
For very shallow water or near coast, we need tokeep the advection terms and to consider thecontribution of bottom friction. The NLLWequations including these effects can be written
as(Intergovernmental
Oceanographic
Commission (IOC), 1997),
𝜕𝜂 𝜕𝑀 𝜕𝑁++=0𝜕𝑡 𝜕𝑥 𝜕𝑦(4)𝜕 𝑀𝑁
𝜕𝜂𝜕𝑀 𝜕 𝑀2+ � �+�
� + 𝑔𝐷𝜕𝑦𝐷𝜕𝑥
𝜕𝑡 𝜕𝑥 𝐷
𝑔𝑛2+ 7/3 𝑀�𝑀2 + 𝑁 2 = 0𝐷(5)𝜕𝜂𝜕 𝑁2𝜕𝑁 𝜕 𝑀𝑁+ ��+� � + 𝑔𝐷𝜕𝑦𝜕𝑦 𝐷𝜕𝑡 𝜕𝑥 𝐷
𝑔𝑛2+ 7/3 𝑁�𝑀2 + 𝑁 2 = 0𝐷,where(6)𝐷 =ℎ+𝜂𝑔𝑛2
𝑀√𝑀2 + 𝑁 2
𝐷 7/3

istotalwater𝑔𝑛2and 𝐷7/3 𝑁√𝑀2 + 𝑁 2depth.

are thebottom friction terms. 𝑛 is called Manning’s
roughness coefficient.

2.3 Linear long-wave equations as conventional equations
The LLW is an approximation of the DSPequations or NLLW equations. If we neglect theright side Eqs. (2) and (3) of the DSP equations
or if we neglect the advection and the bottomfriction terms, we will obtain the LLWequations.
2.4 Procedure for tsunami simulations

𝜕𝑀 𝜕𝑁
𝜕𝜂
= −�+�𝜕𝑥 𝜕𝑦𝜕𝑡𝜕𝑀𝜕𝜂+ 𝑔ℎ=0𝜕𝑡𝜕𝑥𝜕𝜂𝜕𝑁+ 𝑔ℎ=0𝜕𝑦𝜕𝑡

(7)

(8)

(9)

To perform tsunami simulations, the bathymetry data, output points (tide gauge and Ocean Bottom
Pressure Gauge (OBPG)) and initial seafloor deformation as tsunami source must be prepared.
The computation area for our simulation is from 95°E-104°E and 6°S-2°N (1620 × 1440).
For DSP simulation, we prepared the bathymetry data with a grid size of 999 km × 888 km from the
20 arc-second (dx = 616.6667 m and dy = 616.6667 m) bathymetry data (Satake et al., 2012), which
was used for estimating the tsunami source of the 2010 Mentawai earthquake. Time step of 1 s werechosen for all simulations considering the Courant-Friedrichs-Lewy (CFL) to avoid numericalinstabilities.
3. RESULT AND DISCUSSION
3.1 A future event of Mw 8.5 as a probable scenario
For the future event we assume an earthquake
characterized by a single fault with a length of 250 kmand width of 100 km around the seismic gap in the thewest part of Padang area (Figure 1). Also, we assume
that the maximum slip is 9.0 m which is the same as thatof the 2007 Bengkulu earthquake (Fujii and Satake,2008) and the shear modulus (µ) is 2.66 × 1010 N/m2
from the Preliminary Reference Earth Model (PREM)(Dziewonski and Anderson, 1981). These fault
parameters would produce an earthquake of magnitude
8.5. Initial seafloor deformation calculated from theearthquake fault model produces maximum uplift of 3.39
m and maximum subsidence of 1.82 m (Figure 2).

Figure 2. Initial seafloor deformation for a future eventof Mw 8.5.
3.1.1 Tsunami propagation in deep water
We can see that dominant dispersive waves appear in a
direction perpendicular to the fault strike (Figure 3a). In deep water, the results of the DSP are almost
similar with LLW, but for the OBPG TA7 (Figure 3b) the waveform calculated by the DSP simulationis very different from the LLW.

(a)

(b)

Figure 3. (a) Snapshot of the tsunami wave propagation (t = 33 min) obtained from the DSP simulation.
(b) DSP (red line) and LLW (green line) calculated at TA7, a OBPG station assumed in this study,
which located at water depth of 4654.1 m.
Dispersive waves dependent on fault depth
DSP simulations for a future event of Mw 8.5 using different fault depths are also conducted. The fault
depth becomes deeper to the east, following the subduction zone. Simulated all waveforms for fault
depths of 5, 10, and 20 km shows that when the fault depth is shallow, the uplift becomes steep anddispersive wave becomes more dominant at TA7. If the fault depth is deeper the uplift becomes a moregentle slope, and there are no dispersive waves predicted at TA7. This implies that the dispersive wave
may be a good measure for judging whether earthquake rupture reaches very shallow part near thetrench or the rupture occurs only in deep part.
3.1.2 Tsunami propagation in shallow water
To investigate the contributions of non-linear effects in shallow water, NLLW was compared withLLW. Figure 4 shows the calculated waveform at the Padang tide gauge, together with the simulation
results of the LLW equations, which indicates that there is a significant difference between thewaveforms of the NLLW and LLW equations. This difference is caused by the advection and bottomfriction terms included in the NLLW equations.
Figure 4. Comparison of tsunami
waveforms among LLW, NLLW
with no bottom friction andNLLW including advection andbottom friction terms.

Effect of bottom friction in shallow water
In order to examine the effect of bottom friction in shallow water, the results of an NLLW simulation(Mw 8.5) without bottom friction (Manning’s roughness coefficient n is set to 0) and those of an
NLLW simulation with n = 0.025 are compared (Figure 4). The results of our simulation show thatNLLW without bottom friction almost similar with NLLW (e.g. Satake, 1995). In very shallow water
areas (h < 10 m) bottom friction becomes important to reduce the tsunami amplitude. But generally if
we compare LLW, NLLW without bottom friction, and NLLW (Figure 4), the effect of advection
terms are more dominant than the effect of bottom friction.

To find the relationship between linear effects, non-linear effects and sea depth a Normalized Mean
Square Residual (NMSR) was calculated. NMSR equations can be written as
𝑁𝑀𝑆𝑅 =∑𝑛𝑖=1|𝑦𝐿 (𝑡𝑖 ) − 𝑦𝑁 (𝑡𝑖 )|2(10)∑𝑛𝑖=1|𝑦𝑁 (𝑡𝑖 )|2

where 𝑦𝐿 and 𝑦𝑁 are amplitudes of LLW and of NLLW at time i, respectively.
The calculated NMSR (Figure 5) shows thatwhen the sea depth is greater than 50 m, the NMSR
value is low, except blue triangle (Tua pejat station), thisindicates that for deep water we can use both LLW andNLLW. At the Tua pejat station, which is located at thesource, it is difficult to distinguish propagation waves if
the station suddenly records a tsunami. For shallow
water less than 50 m, NMSR gives scattered results andhigher values indicating that we should consider non
linear effects in this case.

Figure 5. NMSR from the calculated waveforms of LLW
and NLLW for the future event of Mw 8.5.

Maximum tsunami height and tsunami arrival time in coastal area
The simulation for a future event of Mw 8.5 resulted maximum heights at Padang station (PAD)(Figure 6a) of 2.02 m using NLLW and 3.40 m using LLW. This tsunami height would be dangerous
as Padang is very close to the sea, and also does not have a sea wall to reduce the energy of a tsunami.
Tsunami arrival time at PAD is around 20 min (Figure 6b). Our institution (BMKG) gives a tsunami
warning 5 min after origin time of earthquake, in this case the people of the Padang area have 15 minto escape to an evacuation area.
(a)(b)

Figure 6. (a) Distribution of maximum tsunami heights at tide gauge stations with comparison ofNLLW (blue bars) versus LLW (green bars). (b) Tsunami arrival times at tide gauge stations for afuture event of Mw 8.5.

3.2 Future events: large scenario of Mw 8.9 and lower scenario of Mw 8.1
Assuming Mw 8.9 for larger case and Mw 8.1 for smaller case, we evaluate how maximum tsunami
height in the Padang area changes. For both scenarios, we assume that the fault length and width are
the same as the Mw 8.5 scenario, only the slip amounts are different.
Maximum tsunami height and tsunami arrival time in coastal area
Future events of Mw 8.9 and 8.1 produce the maximum tsunami height at At Padang area is 5.65 m(13.6 m using LLW) and 0.91 m (1.05 m using LLW). Tsunami arrival times in the Padang area are 17and 24 min for Mw 8.9 and 8.1, respectively. Tsunami arrival times in the Padang area, where firsttsunamis are negative waves, shows that tsunami arrival times in all cases are very short. For thepreparedness we should make good evacuation maps for communities near the coastal sea.

4. CONCLUSIONS
1.

2.

3.

In deep water, DSP equations well agree with LLW. Dispersive waves appear at TA7 which islocated perpendicular to the fault strike. We found that dispersive waves depend on fault depth.
If the fault depth is shallow, more dispersive waves will appear. Dispersive waves play asignificant role to judge the rupture of the earthquake reached to the very shallow part neartrench or occured only in deep part.
When water depth is shallower than 50 m, the effects of advection terms and bottom frictions
should be considered. In shallow water the effect of advection terms are more dominant than thebottom frictions.
Simulation results for a future event in the Padang area indicate the maximum heights of 0.9 m,
2.0 m and 5.7 m for the scenarios of Mw of 8.1, 8.5 and 8.9, respectively. The arrival time of thefirst negative tsunami wave in the Padang area are 24, 20 and 17 min for Mw 8.1, 8.5 and 8.9,
respectively.

REFERENCES
Dziewonski, A. M., and D. L. Anderson., 1981, Phys. Earth Planet. Inter., 25, 297–356,
doi:10.1016/0031- 9201(81)90046-7.
Fujii, Y., and Satake, K., 2008, Earth Planets Space, Vol. 60, pp. 993-998.
Intergovermental Oceanographic Commission, 1997, IUGG/IOC Time Project, IOC Manuals andGuides No 35, UNESCO.
Natawidjaja, D. H., Sieh, K., Chlieh, M., Galetzka, J., Suwargadi, B. W., Cheng, H., Edwards, R. L.,
Avouac, J. P., and Ward, S. N., 2006, J. Geophys. Res., Vol. 111, B06403,
doi:10.1029/2005JB004025.
Natawidjaja, D. H., 2007, pelatihan pemodelan run-up tsunami, RISTEK.
Newman, A. V., Hayes, G., Wei, Y., and Convers, J., 2011, Geophys. Res. Lett, Vol. 38, L05302,
doi:10.1029/2010GL046498.
Saito, T., Satake, K., and Furumura, T., 2010, J. Geophys. Res, Vol. 115, B06303,
doi:10.1029/2009JB006884.
Satake, K., 1995, PAGEOPH, Vol. 144, pp. 455-470.
Satake, K., Nishimura, Y., Putra, P. S., Gusman, A. R., Sunendar, H., Fujii, Y., Tanioka, Y., Latief, H.,
and Yulianto, E., 2012, PAGEOPH, doi 10.1007/s00024-012-0536-y.