PROTOTYPE DATABASE FOR TSUNAMI EARLYWARNING SYSTEM WITH DATA ASSIMILATIONIN MALAYSIACHAI Mui Fatt*
MEE07171

Supervisor :Yushiro Fujii**

ABSTRACT
In order to create a prototype of tsunami database for tsunami early warning system with data
assimilation in Malaysia, we located 16 source points in total around the Andaman Sea with 4
magnitudes (Mw6.5, 7.0, 7.5 and 8.0) and 4 depths (0, 10, 20 and 30 km). The coastal and forecast
points are located along the Malaysian coastal area at 1 m and 30, 40, 50 and 60 m of bathymetriccontour depth with random interval distance, respectively. In numerical simulation, TUNAMI-N2(Tohoku University’s Numerical Analysis Model for Investigation of Near-field tsunamis, No.2) isused to calculate the tsunami waveforms at the output points. Tsunami arrival times at the coastal
points are calculated using inverse tsunami travel time by TTT (Tsunami Travel Time). Tsunami
database was constructed by using MySQL database which contains of 256 scenario earthquakes thatcover historically most active subduction zone around the Andaman Sea. The nearest surrounding data
points of a determined hypocenter can be retrieved from database by interpolation, extrapolation andtwo maximum risk methods. In tsunami data assimilation, TUNAMI-F1 (Tohoku University’s
Numerical Analysis Model for Investigation of Far-field tsunamis, No.1) is used to calculate thetsunami waveforms at the buoy station of Malaysia. Green’s functions, which are calculated tsunami
waveforms from faults assigned 1.0 m of slip, are prepared for 16 model sources. In two inversion
tests, the initial conditions are precisely resolved by non-negative least squares method. For inversionsof two real cases, the slip is almost resolved at the nearest fault and has shown instability in slip
distributions for whose epicenter is located closer and slightly out from model sources, respectively.
Keywords: Numerical Simulation, Tsunami Database, Tsunami Data Assimilation.
INTRODUCTION
The Sumatran mega-thrust earthquake that occurred on 26 December 2004 in Indian Ocean has
triggered massive tsunami which devastated along the northwest coastal areas of Peninsula Malaysia.
In response to this event, Malaysian government has decided to set up the Malaysian National
Tsunami Early Warning System in 2005. The purpose of this study is to create a prototype of tsunami
database for tsunami early warning system with data assimilation in Malaysia.
THEORY AND METHODOLOGY
Bathymetry Data
In this study, we used GEBCO (The General Bathymetric Chart of the Oceans) with spatial grid sizeof one arc-minute (~1850 m) to calculate the tsunami travel times and waveforms. The map ofbathymetric data in the region of study area is shown in Figure 1.
________________________*Malaysian Meteorological Department (MMD), Malaysia**International Institute of Seismology and Earthquake Engineering (IISEE), Building ResearchInstitute (BRI), Tsukuba, Japan1

Tsunamigenic Earthquake Locations
The tsunamigenic earthquake events were searchedthrough Global Centriod Moment Tensor (CMT)
Project catalog search from the year 1976 until
2007 (http://www.globalcmt.org/CMTsearch.html).
The magnitude and depth range between 6.3 to 10
and 0 to 100 km, respectively. Epicenters chosen
lie within 30N to 120N and 900E to 1030E in
latitude and longitude, respectively. Comparison ismade with other searcher tsunami databases from
Integrated Tsunami Database for the World Ocean(WinITDB) and National Geophysical Data Center(NGDC)
TsunamiEvent
Database(http://www.ngdc.noaa.gov) which covers wider
data for a year -2000 to 2007. The comparison has
shown that the locations of the tsunamigenic
earthquake were located along the subduction zone
and Sumatra Fault line (Figure 1).

Global CMT,NGDC,WinITBD

Figure 1. Locations of the tsunamigenic
earthquakes with bathymetry data (GEBCO,
one arc-minute) in this study area.

Magnitude and Depth
We chosen 4 magnitudes (Mw6.5, 7.0, 7.5 and 8.0) and 4 depths (0, 10, 20 and 30 km), based on thehistorical earthquake events from WinITDB and Global CMT Project catalog search at study sourcearea. The minimum magnitude of Mw6.5 was chosen based on the tsunami warning criteria of
Malaysian Meteorological Department when distant tsunami more than 200 km from Malaysian
coastline exists (e.g. Saw, 2007).
Source Points
We located 16 source points in total at Andaman Sea
northern part of Sumatra which covers the region from6.830N to 9.500N and 91.920E to 94.580E in latitude andlongitude, respectively (red line in Figure 2). Eachsource point is located on the grid with distance intervalof 40 arc-minute (~74 km).
Forecast and Coastal Points

Figure 2. Locations of the 16 source
points at Andaman Sea (red circles).
The purple triangle shows the locationof Malaysian deep ocean buoy.

17 coastal points and 44 forecast points in total arelocated along the bathymetric contour depths of 1 m and30, 40, 50 and 60 m, respectively, with random interval
distance. Each bathymetric contour depth of the forecast
points is consists of 11 points (Figure 3). The location of
the coastal points are placed and searched through
Google Earth (2008) considering the most valuableareas for tsunami impacts, denser population areas andtourism attractions. The tsunami heights at the coastal
points are estimated by Green’s Law.

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Green’s Law
The Green’s Law, conservation of potential energy
along the rays (e.g. Satake, 2008), is applied toestimate reliable tsunami heights for coastal points
from the forecast points at different bathymetriccontour depths. This law is only applicable to direct
waves and is not taken account for the reflected
waves or edge waves. The tsunami wave front at aforecast point is assumed to be parallel with the one
at a coastal point. The tsunami height at a coastal
point is calculated by the following equation:1

 d 4h0 =  1  h1
 d0 
Here, h0 and h1 are tsunami height at the coastal andforecast point and d0 and d1 are water depth at thecoastal and forecast point, respectively.
Initial Condition

1

30

40

50

60

m

Figure 3. Bathymetry contour map ofcoastal points (blue dots) and forecast
points (green, red, yellow and purple dots).

An initial profile of tsunami source is assumed to be the same as a deformation of ocean bottom due toearthquake when the wavelength of the ocean bottom is much larger than the water depth (Kajiura,
1963). We used the elastic theory of Okada (1985) to calculate the crustal deformation at the ocean
bottom due to a fault motion. In this study, a single segment is applied to all 16 source points. For eachsource point, we assume that the fault model has the same angle of strike ( φ ) as 3400 (Fujii and Satake,2007) which is parallel to the trench axis, dip angle (δ) is 450 and rake angle (λ) is 900. Other
parameters such as slip amount (U) in cm, length (L) and width (W) in km which are controlled bymoment magnitude (Mw), are determined by Scaling Law (Tatehata, 1997). The equations of Scaling
Law are expressed as follows:

log L = 0.5M W − 1.9 , W =L, log U = 0.5M W − 1.4
2

Tsunami Travel Time (TTT)
TTT can calculate tsunami travel times on all of the grid points from a supplied bathymetric data using
Huygen’s principle (e.g. Fujii, 2008). In this study, tsunami travel times were inversely calculated
from the coastal points to the source points. The minimum value of tsunami travel time from a coastal
point to the grid points of a deformation source area which has absolute value more than 0.04 m isselected as the tsunami arrival time.
Numerical Simulation by Using TUNAMI-N2
TUNAMI-N2 is applied to shallow water theory in shallow and deep seas. The propagation of tsunami
which initiated at each fault is numerically solved by using the finite-difference method (Imamura,1995). The procedures to run the tsunami numerical simulation are described by Fujii (2008). The
dimension of calculation area is 781 and 541 grid points for longitude and latitude, respectively, which
covers the region from 900E to 1030E in longitude and from 30N to 120N in latitude. The temporalinterval (∆t) is 3 s to satisfy the CFL (Courant Friedrics Lewy) stability condition. The calculation
time was set to 12 hours. The total number of computations is 256 cases for the source points.

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Tsunami Database
Tsunami database was constructed by using MySQL database which consists of 258 tables, out of
which one table for “FP” and “HYP” each, and 256 tables for simulation results. FP table contains thenumber, longitude, latitude, depth, name and block of the coastal points. HYP table contains the casename, longitude, latitude, magnitude, depth, strike, dip, rake, length, width and slip of the source
points. Each table in simulation result contains the number of the coastal points, case name of source
point, arrival time of tsunami, maximum tsunami height and its time at coastal points.
Retrieving from Tsunami Database
Input data to retrieve results from the tsunami database are recently determined hypocenter parameterssuch as longitude, latitude, depth and magnitude. Four corners surrounding the input data point arecontained values of longitude, latitude, depths and magnitudes. The tsunami heights at each nearest
corner with a determined hypocenter are retrieved from the database. The tsunami heights according
the determined hypocenter are retrieved by using epicenter location, magnitude and depth interpolation
methods. Otherwise, the extrapolation method is performed when no surroundings data point isavailable. In maximum risk method 1 or 2, data point which gave the maximum tsunami height at eachcoastal point among the source points within the circle area with a half of fault length or therectangular fault area, respectively, is selected as the database output. We assumed that the recently
determined hypocenter is located at 93.2500E and 8.1670N in longitude and latitude with Mw8.5 and 12
km depth, respectively.
Tsunami Data Assimilation
Initial Condition
The deformation on the ocean bottom is computed for each fault with 1.0 m of slip by the equations of
Okada (1985). This displacement is used as an initial condition for the synthetic waveform or Green’s
function from each fault.
Numerical Simulation by using TUNAMI-F1
TUNAMI-F1 is applied to linear theory for tsunami propagation over the ocean in the sphericalcoordinates system and numerically solves the governing equations by using finite-difference method(e.g. Nagano, 1991). The area of the numerical calculations covers the region from 900E to 1030E in
longitude and from 10N to 140N in latitude. The dimension of calculation area is 781 and 781 grid
points for longitude and latitude, respectively. A temporal interval of 3 s was used to satisfy the CFL
stability condition. The computation time of numerical simulation was set to 12 hours.
Tsunami Waveform Inversion
The observed tsunami waveform at the buoy station is expressed as a linear superposition of thecomputed waveforms from all the faults. The slip amount on each fault can be estimated by using theinversion of non-negative least squares method (Lawson and Hanson, 1974). In numerical simulation,
16 single faults are selected with Mw7.5 and 20 km depth for each source point. The initial conditionsof the Green’s functions are tested by two cases in which the slips of 1.0 or 2.0 m of are assigned to afaults. For real case inversions, two cases with Mw7.5 and 20 km depth for each were selected astsunami generation. The locations of the epicenters are closer or slightly out from model sources.
RESULT AND DISCUSSION
Based on the numerical simulation and TTT results, the tsunami heights and arrival times depend on
the magnitude and depth of the source. The tsunami heights and arrival times at coastal points are
increased and become faster as the magnitude getting higher. As the source depth is getting deeper, thetsunami heights and arrival times at the coastal points are slightly higher and faster, respectively than ashallower source.

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0.9

0.8

The comparison of resultsshows that tsunami heights at coastal
points obtained directly fromnumerical simulations (CP) havelower values than the ones at forecast
points by the application of theGreen’s Law (GL) calculations formost cases (Figure 4). Therefore, thetsunami heights calculated with
Green’s Law are more appropriate
and applicable for tsunami warning.

Tsunami Height (m)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
CP1 CP2 CP3 CP4 CP5 CP6 CP7 CP8 CP9 CP10 CP11 CP12 CP13 CP14 CP15 CP16 CP17

Coastal Point
2.2
Risk 1
Risk 22.0

Figure 4. Tsunami heights at the coastal points
by different magnitudes and depths.
The database output of maximum risk
method 1 has shown that the maximum tsunami
height at each coastal point is a combination datafrom source points of S12 and S8 (red line in
Figure 5). For the maximum risk method 2, thesource point of S11 has shown the maximum
tsunami height at each coastal point and wasselected as the database output (green line in
Figure 5).
The initial conditions of Test Case 1 and2 were precisely resolved by the inversion
methods and each synthetic waveform iscompletely agreed with the observed one at thebuoy station (Figure 6A and 6B).

Tsunami Height (m)

1.8

1.6

1.4

1.2

1.0

0.8

CP1 CP2 CP3 CP4 CP5 CP6 CP7 CP8 CP9 CP10CP11 CP12CP13 CP14 CP15CP16 CP17

Coastal Point

Figure 5. Maximum tsunami heights at thecoastal points obtained by the maximum risk
method 1 (red line) and 2 (green line).

Observed

A

B

C

D

Synthetic

Figure 6. Comparison of observed tsunami
waveforms and synthetic ones at the buoy
station (right) and inversion results of slip
distribution at each fault (left). (A) Case 1, (B)Case 2, (C) Real Case 1 and (D) Real Case 2.
The red rectangle is the fault of each real case.

5For Real Case 1 (Figure 6C), the largest slip was resolved at fault S6 (1.711 m) which is thevicinity to the epicenter than other faults and the synthetic waveform generally agrees with theobserved waveform at the buoy station. However, for the Real Case 2 (Figure 6D) has shown an
instability in slip distribution as the largest slip was estimated at fault S2 (0.436 m) and the synthetic
waveform is not well reproduced.
CONCLUSIONS
A prototype of tsunami database for tsunami early warning system with data assimilation was
successfully constructed. In tsunami database, the nearest data points of a determined hypocenter are
retrieved from database by interpolation method. Otherwise, extrapolation method is performed whenno surrounding data is available. To optimize the most severe case of tsunami event at each coastal
point, two maximum risk methods can be applied.
According to the result of analysis, variation of tsunami heights and tsunami arrival times atcoastal points depend on magnitude and depth of the source. The tsunami heights and travel times atcoastal points are increased and faster, respectively, as the magnitude becomes larger. On the other
hand, the tsunami heights and travel times at the coastal points are slightly higher and faster as thesource depth is deeper.
For tsunami data assimilations, the slip amount distributions were determined by using theinversion of non-negative least squares method. The initial conditions of the Green’s functions were
tested by Case 1 and 2. They were precisely resolved and the synthetic waveform completely agreed
with the observed one at the buoy station. For the Real Case 1, the slip distributions are almost
resolved at the nearest fault and the synthetic waveform generally agreed with the observed one at thebuoy station. However, the Real Case 2 has shown the instability in slip distribution and the synthetic
waveform were not well reproduced to match with the observed one at the buoy station.
Combination of the tsunami database by pre-computed scenario earthquakes and the tsunami
data assimilation for source estimation will be the useful tool for tsunami forecasting.
AKNOWLEDGEMENT
I would like to express my gratitude to Dr. Bunichiro Shibazaki (IISEE, BRI) for their helpful
discussions, valuable comments and guidance during my study in IISEE.
REFERENCES
Fujii, Y., and Satake, K., 2007, Bulletin of the Seismological Society of America, 97, pp. S192-S207.
Fujii, Y., 2008, IISEE Lecture Note 2007-2008, IISEE, BRI.
Imamura, F., 1995, manuscript for TUNAMI code, School of Civil Engineering, Asian, 1-45.
Kajiura, K., 1963, Bulletin Earthquake Research Inst, 41, 535-571.
Lawson, C. L., and R. J. Hanson, 1974, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 340 pp.
Nagano, O., Imamura, F. and Shuto, N., 1991, Natural Hazards 4, 235-255.
Okada, 1985, Bulletin of the Seismological Society of America, 75, 1135-1154.
Satake, K., 2008, IISEE Lecture Note 2007-2008, IISEE, BRI.
Saw, B. L., 2007, IOC, Doc. No. IOC/PTWS-XXII/14.16.
Tatehata, H., 1997, Perspectives on Tsunami Hazard Reduction, 175-188.

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