response spectr

8/8/2019 response spectr

1/19

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2010; 39:827845Published online 27 October 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.967

Ground-motion attenuation relationship for the Sumatranmegathrust earthquakes

Kusnowidjaja Megawati1,2,, and Tso-Chien Pan1

1School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue,

Singapore 639798, Singapore2 Earth Observatory of Singapore, Nanyang Technological University, 50 Nanyang Avenue,

Singapore 639798, Singapore

SUMMARY

A representative attenuation relationship is one of the key components required in seismic hazard assess-ment of a region of interest. Attenuation relationships for peak ground acceleration, peak ground velocityand response spectral accelerations for Sumatran megathrust earthquakes, covering Mw up to 9.0, arederived based on synthetic seismograms obtained from a finite-fault kinematic model. The relationshipsderived are for very hard rock site condition and for a long-distance range between 200 and 1500 km. Theyare then validated with recorded data from giant earthquakes on the Sumatran megathrust occurring sinceyear 2000. A close examination of the recorded data also shows that spectral shapes predicted by mostof the existing attenuation relationships and that specified in the IBC code are not particularly suitablefor sites where potential seismic hazard is dominated by large-magnitude, distant, earthquakes. Groundmotions at a remote site are typically signified by the dominance of long-period components with periodslonger than 1 s, whereas the predominant periods from most of the existing attenuation relationships and

the IBC code are shorter than 0.6 s. The shifting of response spectrum towards longer period range fordistant earthquakes should be carefully taken into account in the formulation of future seismic codes forSoutheast Asia, where many metropolises are located far from active seismic sources. The attenuationrelationship derived in the present study can properly reproduce the spectral shape from distant subductionearthquakes, and could hopefully give insights into the formulation of future seismic codes. Copyright q2009 John Wiley & Sons, Ltd.

Received 22 August 2008; Revised 17 August 2009; Accepted 21 August 2009

KEY WORDS: Singapore; Sumatra; Mentawai; subduction; giant earthquakes; attenuation; seismic hazard

Correspondence to: Kusnowidjaja Megawati, School of Civil and Environmental Engineering, Nanyang TechnologicalUniversity, 50 Nanyang Avenue, Singapore 639798, Singapore.

E-mail: [email protected]

Copyright q 2009 John Wiley & Sons, Ltd.


2/19

828 K. MEGAWATI AND T.-C. PAN

1. INTRODUCTION

Seismicity and attenuation relationship are the two key components in seismic hazard analysis for

a region of interest. The regional seismicity is represented by a series of recurrence relationships,

where each relationship describes the average rate at which an earthquake of a certain magnitudewill be exceeded in a particular source zone. The attenuation relationship expresses ground-motion

parameters, such as peak ground acceleration (PGA), peak ground velocity (PGV) and response

spectral acceleration (RSA), as functions of earthquake magnitude, distance and other variables.

In high-seismicity regions, representative attenuation relationships are usually derived empiri-

cally from actual ground motions records. The available records should cover earthquake magni-

tudes, distance range and site characteristics of interest. However, in moderate- and low-seismicity

regions, where the available ground-motion records are often not sufficient to cover earthquake

magnitudes and distance range of interest, derivation of attenuation relationships has to be based

on synthetic seismograms [1 4]. These attenuation relationships derived should then be validated

using the limited available records.

Singapore and peninsular Malaysia face a unique problem in seismic hazard analysis. The local

seismicity itself is very low as evidenced by the fact that all ground tremors felt in the last 50 years

originated from distant Sumatran earthquakes [5, 6]. Intuitively, it could be postulated that the

seismic sources that may potentially affect Singapore and peninsular Malaysia are large-magnitude

earthquakes on the Sumatran fault and the adjacent subduction zone. The closest distances from

Singapore to the fault and megathrust are 400 and 600 km, respectively. The highly segmented,

right-lateral, Sumatran fault could produce earthquakes with Mw up to 7.8 [7], and its attenuation

relationships have been derived [8]. On the other hand, the megathrust has known to repeatedly

produce giant earthquakes with Mw>8.0 [911].

The motivation of the present work originated from the fact that the existing attenuation relation-

ships derived for subduction zones in Japan, Taiwan, Cascadia, Alaska, Chile, Mexico, Peru and

other parts of the world [1217] could not reproduce response spectra from actual data recorded

in Singapore from the Sumatran subduction earthquakes. This will be elaborated further in alater section. Megawati et al. [18] have derived a set of spectral attenuation relationships for the

Sumatran subduction earthquakes. The study was based on synthetic seismograms produced using

a point-source dislocation model. Although the derived attenuation relationships could estimate

actual recorded data for earthquakes with Mw7.2, they were not tested for giant earthquakes

because actual recorded data were not available at that time [18].

The objective of the present study is to extend the work by Megawati et al. [18] to cover

larger-magnitude earthquakes. In the present work, synthetic seismograms will be generated using

a finite-fault kinematic model, which have been tested for simulating giant subduction earthquakes

[11]. The validation of the attenuation relationships derived is made possible by the availability

of good quality data recorded in Singapore from giant Sumatran earthquakes in December 2004,

March 2005 and September 2007. Some preliminary results have previously been presented in a

workshop held in Singapore in 2007 [19].

2. SUMATRAN MEGATHRUST

The Sunda arc, extending over 5600 km from the Andaman islands in the northwest to the Banda

arc in the east, was formed by the convergence between the subducting IndianAustralian plate

Copyright q 2009 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2010; 39:827845

DOI: 10.1002/eqe


3/19

SUMATRAN MEGATHRUST EARTHQUAKES 829

Figure 1. Tectonic setting of Sumatra, together with the epicentres of 12 significant earthquakes occurringon the Sumatran megathrust, from January 2000 to December 2007. The islands off the western coastof Sumatra are (from North to South): Sm, Simeulue island; Ni, Nias island; Sb, Siberut island; Sp,Sipora island; NP, North Pagai island; SP, South Pagai island; En, Enggano island. The Mentawai islands

comprise the four islands of Siberut, Sipora, North Pagai and South Pagai.

and the overriding south-eastern Eurasian plate. The Sumatran megathrust of the Sunda arc lies

250 km off the western coast of Sumatra island (Figure 1), with both Sumatra and Java islands

lying on the Eurasian plate. The convergence is nearly orthogonal to the trench axis south of Java,

but it is highly oblique southwest of Sumatra. Based on velocity vectors derived from the regional

Global Positioning System (GPS) data, the pole of rotation for the relative motion between the

two plates is in East Africa, about 50 west of Sumatra [20, 21]. Northern Sumatra is closer to

this pole than southern Sumatra; thus, the orientation and magnitude of the relative-motion vector

vary significantly along the Sumatran portion of the plate boundary, as shown in Figure 1.

Slip vectors of moderate earthquakes along this subduction zone were found to be nearly

perpendicular to the strike of the plate boundary [22, 23]. Most of the strike-slip component of

the oblique convergence between the IndianAustralian plate and the Eurasian plate southwestof Sumatra is accommodated by right-lateral slip along the trench-parallel Sumatran fault, lying

roughly 250 km northeast of the trench [7, 2224]. Therefore, the slip along the subduction zone

itself has relatively small strike-parallel components.

Six giant earthquakes (Mw8.0) have occurred along the Sumatran megathrust in the last 250

years, releasing the strain accumulated by the convergence between the two tectonic plates. The

rupture zones of these earthquakes are depicted in Figure 1. The earliest of these historical events


DOI: 10.1002/eqe


4/19


was that of February 1797 [9, 25]. The earthquake had an Mw of 8.7 and ruptured the 370-km

segment from 1S to about 4S [25]. This was followed by the giant earthquake of 1833 (Mw9.0),

which ruptured a 500-km-long segment south of Siberut island, and another one in 1861 (Mw8.5)

rupturing a 270-km-long segment beneath the Nias island [9, 25, 26].

Since 1861, no giant earthquake with Mw8.0 had occurred along the Sumatran megathrustuntil 26 December 2004, when the Mw9.15 Aceh-Andaman earthquake happened [10, 2729].

This was shortly followed by the Mw8.6 Nias-Simeulue earthquake on 28 March 2005 [30, 31],

which had a rupture zone coincident with that of the 1861 event. The latest giant earthquake of

Mw8.4 occurred on 12 September 2007, at 11:10:26 GMT, denoted as Event 10 in Figure 1.

3. SUMATRAN-SUBDUCTION EVENTS RECORDED IN SINGAPORE

The Meteorological Services Division of the National Environment Agency established a network

of digital seismic stations in Singapore, in September 1996. The network comprises one broadband

Global Seismographic Network (GSN) station, four teleseismic stations and two borehole arrays.

The GSN station, situated on a very hard rock site, at the centre of Singapore island, is equipped

with a comprehensive set of sensors to record ground tremors continuously, whereas the other

stations operate based on a triggering system.

Between January 2000 and December 2007, 12 Sumatran subduction earthquakes had generated

substantial ground tremors capable of causing perceptible levels of vibration in Singapore. They

include five earthquakes of Mw7.9. These significant earthquakes are listed in Table I and their

epicentres are plotted in Figure 1. The ground motions from these significant earthquakes are

recorded at the GSN station in Singapore. Although these12 sets of groundmotions are not sufficient

for deriving a representative attenuation relationship empirically, they are useful for the validation

of the spectral attenuation relationship that will be derived hereafter using synthetic seismograms.

Table I. Twelve significant Sumatran subduction earthquakes that caused perceivable tremors inSingapore, in the last 8 years.

Epicentre

No. Date Time (GMT) Latitude Longitude Depth (km) Mw R (km)

1 04 Jun 2000 16:28:47 4.730S 101.940E 43.9 7.9 7042 07 Jun 2000 23:45:35 4.630S 101.820E 16.6 6.7 6973 11 May 2004 08:28:48 0.415N 97.825E 21.0 6.1 6704 26 Dec 2004 00:58:50 3.090N 94.260E 28.6 9.1 16005 28 Mar 2005 16:09:37 1.670N 97.070E 25.8 8.6 7476 10 Apr 2005 10:29:11 1.680S 99.540E 12.0 6.7 5797 10 Apr 2005 11:14:20 1.770S 99.640E 15.0 6.5 5768 17 Apr 2005 21:23:51 1.660S 99.540E 23.0 5.4 578

9 14 May 2005 05:05:19 0.420N 98.240E 39.0 6.7 62510 12 Sep 2007 11:10:27 4.438S 101.367E 34.0 8.4 61911 12 Sep 2007 23:49:04 2.625S 100.841E 35.0 7.9 54912 13 Sep 2007 03:35:29 2.130S 99.627E 22.0 7.0 602

Note: The information for Events 19 is compiled from the Bulletin of the International Seismological Centre(ISC), and that for Events 1012 is from USGS National Earthquake Information Center (NEIC). R indicatesdistance from Singapore to the centre of the respective fault plane.


DOI: 10.1002/eqe


5/19


4. SYNTHETIC SEISMOGRAMS

A representative response-spectral attenuation relationship, which is a key ingredient in any seismic

hazard studies, will be derived based on the synthetic seismograms computed for large-magnitude

subduction earthquakes along the Sumatran megathrust. Six cities in the region, namely Singapore,Kuala Lumpur, Penang, Medan, Pekanbaru and Palembang, are selected as stations where ground

motions are to be synthesized. The locations of the cities are shown in Figure 1. Kuala Lumpur and

Penang are on the western coast of peninsular Malaysia, while Medan, Pekanbaru and Palembang

are on eastern coast of Sumatra island. The selection of these representative stations is made to

have a wide coverage of distance and azimuth from source to station.

4.1. Ground-motion simulation method

The ground-motion simulation method used in the present study follows a kinematic method, in

which the source rupture is represented using a finite-fault model [4, 11, 32, 33]. The fault plane

is subdivided into several subfaults and each subfault is treated as a point source. The rupture

starts at the hypocentre and propagates radially outward with a certain rupture velocity, triggeringeach subfault as the rupture front passes its centre. The ground motions at an observation point

produced by the ruptures of individual subfaults are summed with time lags to account for rupture

propagation on the fault plane.

The crustal structure representing the whole region of Sumatra and peninsular Malaysia is

extracted from the global crustal model CRUST 2.0 [34], which is a 22 global model for the

Earths crust based on seismic refraction data published in the period of 19481995. The one-

dimensional structure is summarized in Table II, where the properties of the structure are obtained

by taking the averages of the properties of all 22 grids covering the region.

Greens functions are based on synthetics derived from elastic wave-propagation model, which

provides proper phasing of body and surface waves.

4.2. Source parameters

Earthquakes with magnitudes ranging from Mw 5 to 9, with an interval of 0.5, are simulated.

The strike of the Sumatran megathrust is taken to be N320E, and the dip is 12 [10, 11]. The

length and width of the fault plane corresponding to each magnitude level are calculated based on

the empirical relationship proposed by Wells and Coppersmith [35], and they are summarized in

Table III. For each magnitude 12 rupture planes are considered, and they are randomly positioned

between latitudes 6N and 6S. The upper side of the fault planes is assumed to be exposed on the

surface of the uppermost crustal layer. The 12 fault planes for each magnitude level have random

Table II. Crustal structure of the region covering Sumatra and peninsular Malaysia.

Layer H (km) vP

(km/s) vS

(km/s) (t/m3) QP

QS

Upper crust 9.6 6.0 3.4 2.7 350 175Middle crust 9.5 6.6 3.7 2.9 500 250Lower crust 9.1 7.2 4.0 3.1 650 325Mantle 8.2 4.7 3.4 800 400

H= layer thickness; vP = P-wave velocity; vS= S-wave velocity; =mass density; Q P =quality factorof P-wave, Q S=quality factor of S-wave.


DOI: 10.1002/eqe


6/19


TableIII.RuptureparametersofsimulatedSumatransubdu

ctionearthquakes.

Mw5.0

Mw5.5

Mw6.0

Mw6.5

Mw7.0

Mw7.5

Mw8.0

Mw8.5

Mw9.0

Faultplane

Strike

N320E

N320E

N320E

N320E

N320E

N320E

N320E

N320E

N320E

Dip

12

12

12

12

12

12

12

12

12

Faultdimensions

alongthe

3

3

7.0

3.5

12

6

22

11

42

18

80

30

150

45

320

100

600

180

strikeanddownd

ip(km

km)

Subfaultsize(km

km)

3

3

3.5

3.5

6

6

5.5

5.5

6

6

10

10

15

15

20

20

20

20

Slipdistribution

Amplitude

Normallydistributed

withacoefficientofvariance(COV)of0.2

Rakeangle

Randomvaluebetween60

and120

Slipvelocityvd

Randomvaluebetween0.2and0.4m/s

No.ofasperities

0

0

0

2

2

2

2

2

2

Arearatioofasp

erities

0.25

0.24

0.21

0.23

0.23

0.22

Slipcontrastofasperities

2.0

2.0

2.0

2.0

2.0

2.0

D

(m)

0.11

0.23

0.44

0.73

1.31

2.32

4.64

6.04

7.61

D asp(m)

1.46

2.62

4.64

9.28

12.0

8

15.2

2

D 0(m)

0.49

0.90

1.70

3.25

4.24

5.46

Rupturepropagation

Rupturevelocity

Randomvaluebetween2.4and3.0km/s

Hypocentre

Randomlylocatedalongthefaultplane,butnotwithinthe

asperities

Arearatioofasperitiesistheareaoftheoverallasperitiesasafractionoftheoverallrupturearea.

Slipcontrastof

asperitiesisdefinedastheratiooftheaverageslipintheasperitiestothea

verageslipintheoverallrupturearea.

Distheaverageslipoftheentireruptureplane.

Daspistheaverageslipoftheasperities,whichisequaltotheproductoftheslipcontrastandD.

D0istheaverageslipoftheremainingruptureareae

xcludingtheasperities.


DOI: 10.1002/eqe


7/19


rupture patterns, which are constrained by the parameters described below. Each fault plane is

subdivided into numerous subfaults, where each subfault is modelled using a point dislocation

source. The size of the subfaults for each magnitude is summarized in Table III.

Some rupture parameters, such as rupture directivity, slip distribution, the presence of asperities,

rupture velocity and slip velocity, cannot be determined accurately for a future earthquake. Theseparameters have to be treated as random variables and constrained within a range of seismologically

possible values. To be realistic, each fault rupture is assumed to have two asperities, except for

earthquakes with Mw6.0, for which no asperity is considered. The total area of the asperities

is confined to be about 22% of the total rupture area. The slip contrast, which is defined as the

ratio of the average slip in the asperity area to the average slip in total rupture area, is fixed at

2.0. These parameters have been based on the analyses of fault asperities of 15 shallow crustal

earthquakes with Mw ranging from 5.7 to 7.2 [36]. The individual asperities are randomly located

along the fault plane without overlap.

The slips of the subfaults are lognormally distributed with a coefficient of variance (COV) of

0.2. The average slip of the whole fault plane and that in the asperity are summarized in Table III.

The rupture initiation may take place at any arbitrary location along the fault plane, but not within

the asperities [36]. The rupture propagates radially from the hypocentre with a velocity vr, which

may range from 2.4 to 3.0 km/s.

The source time function of the slip on each subfault is approximated by a ramp function with a

source duration of tr=Ls/vr+td, where Ls is the length of the subfault, vr is the rupture velocity

and td is the rise time of the local dislocation. The rise time td is equal to Ds/vd, in which Dsis the slip amplitude and vd is the slip velocity. The source duration tr is to reflect the effects of

rupture propagation within the subfault and the dislocation rise time.

4.3. Simulation results

Figure 2 presents the velocity time histories simulated at Singapore for earthquakes with threedifferent Mw values of 5, 7 and 9. The horizontal ground velocities are aligned in the NorthSouth

and EastWest directions. The epicentres of the earthquakes are located at about latitude 2S,

and the epicentral distances to Singapore are approximately 650 km. Note that the ground motion

shown for each magnitude level represents only one of the 12 random models simulated for that

particular magnitude level. The upper cut-off frequency of the simulations is 2 Hz. It can be seen in

the figure that the duration of ground motion increases with magnitude, with notable increase from

Mw 7 to 9. This is understandable because the length of the fault plane of the Mw 9 earthquake is

14 times that of the Mw 7 (Table III). With a length of 600 km and a rupture velocity of 2.7 km/s,

it takes 222 s for the rupture of the Mw 9 earthquake to complete if it is unilateral. For the Mw 7

earthquake, it is 16 s.

Figures 3 and 4 summarize the horizontal PGA and RSA with 5% damping ratio at a natural

period of 2 s, respectively, simulated for earthquakes with Mw of 6, 7, 8 and 9. The horizontalcomponent is represented by the geometric mean value of the NS and EW components. For each

magnitude level, there are 72 data points, resulting from the 12 random rupture models simulated

at the six representative cities. RSA values at different natural periods ranging from 0.5 to 50 s

have also been computed.

Note that the ground motions are simulated for a shear-wave velocity of 3.4 km/s at the ground

surface. This means that the results are for very hard rock sites. For typical rock and soil sites,


DOI: 10.1002/eqe


8/19


Figure 2. Velocity time histories from three Sumatran subduction earthquakes with Mw valuesof 5, 7 and 9, simulated for Singapore.

such as NEHRP site classes AE, corresponding site response factors, such as those proposed by

Boore and Joyner [37], should be applied.

5. DERIVATION OF ATTENUATION RELATIONSHIP

The idea of developing an attenuation relationship is to have a relatively simple equation in terms

of earthquake magnitude and source-station distance, which is able to represent the complicated

and time-consuming ground-motion simulations. The functional form adopted for the estimation

of the horizontal ground-motion parameters follows the basic principles of wave propagation in

elastic media as described below:

ln(Y)=a0+a1(Mw6)+a2(Mw6)2+a3 ln(R)+(a4+a5Mw)R+ln(Y) (1)

where Y is the geometric mean of the horizontal PGA, PGV or RSA values (5% damping ratio)

at various natural periods. The unit for the acceleration values is cm/s2

and that for velocity iscm/s. Mw is the moment magnitude and R is the distance from the station to the centre of the

corresponding fault plane, in km. The quadratic term of a2(Mw6)2 is adopted to account for the

fact that the corner period of earthquake source spectrum increases with the earthquake magnitude

and the source area, and the rate of increase in ground-motion amplitude Y becomes slower for

larger value of Mw [38]. Therefore, the regression coefficient a2 is expected to have negative

values.


DOI: 10.1002/eqe


9/19


Figure 3. Attenuation relationship of peak ground acceleration for different Mw values of 6, 7, 8 and 9.

Coefficient a3 in Equation (1) represents the geometrical attenuation rate, whereas a4 and a5account for the anelastic attenuation. The term ln(Y) accounts for the variations in the PGA, PGV

and RSA due to the randomness in source parameters considered in the simulations. The term

ln(Y) has a mean value of 0.0 and a standard deviation value ln(Y), representing the standard

deviation of the model due to the randomness in the source process.

The regression coefficients of a0 to a5 are determined to best fit the simulated data using a

least-squares procedure. The procedure minimizes the sum of squared residuals, where the residual

is defined as the difference between the ln(Y) simulated and that predicted using Equation (1).

The regression coefficients for PGV, PGA and RSA values at various natural periods of engi-

neering interest are summarized in Table IV, together with the standard deviation values. It should

be noted that the values ofln(Y), mostly ranging between 0.2 and 0.5, are relatively smaller than

the standard deviation values of other attenuation models for subduction earthquakes. For example,Youngs et al. [12] propose standard deviation values of 0.61.0, Gregor et al. [14] give values of

0.70.9, Atkinson and Boore [15] and Lin and Lee [17] suggest 0.50.8. It should be understood

that the ln(Y) in the present study only accounts for the randomness in the source parameters only,

and does not include the randomness in the propagation path. For future uses in regional seismic

hazard analyses, the ln(Y) values in Table IV need to be increased by about 0.2 to account for the

path effects.


DOI: 10.1002/eqe


10/19


Figure 4. Attenuation relationship of response spectral acceleration (5% damping ratio) at a natural periodof 2 s for different Mw values of 6, 7, 8 and 9.

The resulting attenuation relationships for PGA and RSA at a natural period of 2 s are plotted

in Figures 3 and 4, respectively, together with the simulated data. These figures show that thederived attenuation relationships match closely with the simulated data, indicating the adequacy

of the functional form given in Equation (1).

6. DISCUSSION

6.1. Validation of the attenuation relationships derived

The ground-motion attenuation relationships above were derived based solely on synthetic seismo-

grams. It is therefore necessary to validate these attenuation models. The ground motions recorded

in Singapore from the 12 significant earthquakes listed in Table I are used to validate the attenu-

ation relationships. Geometric-mean of pseudo-acceleration response spectra (5% damping ratio)of these events is plotted in Figure 5 with thick solid lines. The acceleration response spectra esti-

mated using the derived attenuation relationship are shown by three lines denoted as estimated in

each panel of Figure 5. The solid line in the middle indicates the mean spectrum, whereas the two

enclosing dashed lines reflect the mean one standard deviation spectra. Note that the standard

deviation values used are the ones that include both the uncertainty in source and path parameters,

namely the values in Table IV plus 0.2. The recorded spectra generally fall within the mean one


DOI: 10.1002/eqe


11/19


Table IV. Regression coefficients of attenuation relationships for PGV (cm/s), PGA (cm/s2) and RSA

(cm/s2) with 5% damping ratio for Sumatran subduction earthquakes.

Period (s) a0 a1 a2 a3 a4 a5 ln(Y)

PGV 2.369 2.0852 0.23564 0.87906 0.001363 0.0001189 0.3478PGA 3.882 1.8988 0.11736 1.00000 0.001741 0.0000776 0.23790.50 4.068 1.9257 0.12435 0.99864 0.001790 0.0000564 0.24100.60 4.439 1.9094 0.13693 0.99474 0.002462 0.0001051 0.24960.70 4.836 1.8308 0.13510 0.99950 0.003323 0.0001945 0.25650.80 4.978 1.8570 0.12887 1.00000 0.003054 0.0001475 0.26260.90 5.108 1.9314 0.13954 0.98621 0.002986 0.0001075 0.24241.00 4.973 1.9547 0.13913 0.97603 0.002851 0.0001106 0.23431.20 2.729 2.0316 0.13658 0.60751 0.002570 0.0000409 0.24361.50 2.421 1.8960 0.07075 0.59262 0.002453 0.0000668 0.26142.00 2.670 1.8182 0.07657 0.62089 0.002190 0.0000674 0.27803.00 1.716 1.7922 0.01895 0.61167 0.001177 0.0000121 0.29445.00 0.060 1.8694 0.09103 0.32688 0.001765 0.0000529 0.39637.00 0.518 2.1948 0.24519 0.47529 0.001064 0.0000189 0.4206

10.00 0.044 2.3081 0.29060 0.50356 0.000848 0.0000125 0.518315.00 0.525 2.5297 0.41930 0.52777 0.001454 0.0001435 0.449520.00 1.695 2.5197 0.42807 0.42096 0.001575 0.0001498 0.454330.00 2.805 2.6640 0.42674 0.43304 0.001576 0.0001568 0.368650.00 4.340 2.2968 0.27844 0.38291 0.002564 0.0002540 0.3946

standard deviation spectra for most of the events, indicating that the derived spectral attenuation

relationship can predict actual recorded spectra within an acceptable level of uncertainty.

Table V summarizes six existing attenuation relationships that have been derived from inter-plate

subduction earthquakes in Cascadia, Taiwan, Japan and other parts of the world. These attenuation

relationships are well established and have been validated extensively. The spectra resulting from

these six attenuation relationships are to be plotted in Figure 5 to study whether they can beextrapolated to predict spectra recorded in Singapore from the Sumatran subduction earthquakes.

However, before comparing the spectra predicted by the six attenuation relationships with the

recorded spectra, some adjustments have to be made with regard to difference in source-site

distance definition and site effect.

The two different definitions of source-site distance used by these attenuation relationships,

namely the closest distance to the rupture plane and the hypocentral distance, are different from

the distance definition used in Equation (1), which is the distance to the centre of the rupture plane.

As the present study deals with long-distance earthquakes, this difference in distance definition

would have marginal effects, except for earthquakes with very large rupture area such as the

26 December 2004 earthquake. Nevertheless, this difference in distance definition is considered

when computing response spectra from different attenuation relationships.

Site effect is the second factor that has to be corrected. The six existing attenuation relationshipsselected are derived for typical rock sites (NEHRP site class B with shear-wave velocity values

ranging from 760 to 1500 m/s). On the other hand, the ground motions were recorded at the GSN

station, which is located on a very hard rock site with a shear-wave velocity value exceeding

3000 m/s. Boore and Joyner [37] proposed the site responses, which are the combined effects

of amplification and attenuation, for NEHRP site classes B, C and D. The factor for NEHRP

site class B ranging between unity and 1.6 within a frequency band of 0.0110 Hz (Figure 11 of


DOI: 10.1002/eqe


12/19


Figure 5. Recorded and estimated acceleration response spectra (5% damping ratio) of the 12 significantearthquakes listed in Table I.


DOI: 10.1002/eqe


13/19


Table V. Six existing attenuation relationships for subduction earthquakes in other regions.

Mw range Distance definition and rangeReference Model description considered considered

Youngs et al. [12] Regression of recorded groundmotions from inter-plate earth-quakes occurring in subduc-tion regions of Alaska, Chile,Cascadia, Japan, Mexico, Peruand the Solomon islands

5.08.2 Rrup=The closest distance to therupture plane=10500km

Petersen et al. [13] Using the attenuation relation-ship derived by Youngs et al.[12] and scaling the resultingspectrum down by a factor of

e0.0038(R200)


Gregor et al. [14] Regression of synthetic groundmotions from the Cascadiasubduction zone earthquakes

simulated based on a stochasticfinite-fault model


Atkinson and Boore [15] Regression of recorded groundmotions from inter-plate earth-quakes occurring in subduc-tion regions of Alaska, Chile,Cascadia, Japan, Mexico, Peruand the Solomon islands


Kanno et al. [16] Regression of strong groundmotions recorded in Japan from1963 to 2003, supplemented bydata from 10 earthquakes inU.S.A. and Turkey


Lin and Lee [17] Regression of recorded ground

motions from inter-plate subduc-tion earthquakes in Taiwan andother regions

5.58.1 Rhypo=The hypocentral

distance=10400km

Reference [37]) is used to reduce the response spectra predicted by the six attenuation relationships

in Table V before comparing them with the recorded spectra.

In Figure 5, it can be seen that the spectra calculated based on the attenuation relationships

of Youngs et al. [12], Gregor et al. [14], Kanno et al. [16] and Lin and Lee [17] overestimate

the recorded spectra in all the 12 events by one-order of magnitude. The resulting spectra from

Gregor et al. [14] for earthquakes with Mw7 have a jagged shape, indicating that the attenuation

relationship was derived only for large-magnitude subduction earthquakes (Table V) and should

not be extrapolated to lower magnitude range. Petersen et al. [13] used a scaled-down attenuationrelationship from Youngs et al. [12] in a probabilistic seismic hazard analysis for Sumatra and

peninsular Malaysia. The distance-dependent scaling factor of exp[0.0038(R200)] was obtained

by fitting the predicted spectral values at a natural period of 1 s from Youngs et al. [12] to the actual

data recorded in Singapore from Sumatran subduction earthquakes [13]. Therefore, the resulting

spectra have identical shape with those from Youngs et al. [12], and fit well with the recorded

spectral values at the natural period of 1 s.


DOI: 10.1002/eqe


14/19


Among the six existing attenuation relationships, only the relationships derived by Atkinson

and Boore [15] and Kanno et al. [16] produce spectra with consistent shape to that of the recorded

ones. It predicts spectra with a long predominant natural period of 2 s, which agrees well with that

shown in the recorded spectra and are consistent with the values expected for distant earthquakes

[8, 11, 18, 32, 33]. The other four attenuation relationships produce spectra with short predominantnatural periods, below 0.6 s, which seem too short for distant earthquakes. It shows that these

attenuation relationships were not well constrained at long distance and they are only meant for

near-field earthquakes although the data used covered up to a distance of 500 km.

6.2. Estimation of hazard from future earthquakes on the Sumatran megathrust

Several lines of evidence have indicated that the Sumatran megathrust between 0.5 and 4S

(Figure 1) is very likely to rupture within the next few decades. Large sections of the Sumatran

megathrust have failed progressively over the past 9 years, involving three giant earthquakes

(Mw8) of Mw 9.15 in December 2004, Mw 8.6 in March 2005 and Mw 8.4 in September 2007

[10, 30, 31, 39, 40]. This sequence of big earthquakes left a portion of the megathrust beneath the

Mentawai islands, between 0.5 and 4S, unruptured in the current episode of strain release. This so-

called Mentawai segment last ruptured in 1797 and 1833, and the interseismic strain accumulated

has approached or exceeded the levels relieved in 1797, indicating that its rupture is very likely

within the next few decades [25, 39].

The expected earthquake magnitude if this segment ruptures depends on the size of the area

that ruptures and the amplitude of the slip involved. The length and width of the segment are 400

and 240 km, respectively. The potential slip on the Mentawai segment is not uniform, but varies

according to the degree of coupling between the subducting and overriding plates [41], the rate of

convergence orthogonal to the trench and the amount of slip released by the series of earthquakes

in September 2007. The potential slip on the segment, as computed by Sieh et al. [39] and shown in

Figures 4 and S44 of Reference [39], varies between 4 and 8 m. This is equivalent to an earthquake

with Mw 8.8.Figure 6 shows the acceleration response spectrum (5% damping ratio) in Singapore resulting

from the Mw 8.8 earthquake in Singapore. The distance R is taken as 600 km. The acceleration

response spectra estimated using the derived attenuation relationship are shown by the set of three

lines, where the solid line in the middle indicates the mean spectrum and the two enclosing dashed

lines reflect the meanone standard deviation spectra.

Current building design code for structures in Singapore has been developed largely based on

the BS 8110 [42], which does not have any provision for seismic loading. It does, however, require

that all buildings to be capable of resisting a notional ultimate lateral design load applied at each

floor level simultaneously for structural robustness. These static lateral loads are equal to 1.5% of

the characteristic dead weight of the structure. The minimum capacity of buildings can therefore

be taken as constant at 1.5%g (15cm/s2) across the entire natural period range, as shown by the

horizontal line in Figure 6.From Figure 6, it is understood that the risk for typical buildings with natural periods ranging

from 0.5 to 5.0 s on rock sites is very low as the demand spectrum is lower than the capacity. For

example, at T=2s, corresponding to buildings with 20 storeys widely found in Singapore, the

probability that the demand response spectral value exceeds 1.5%g is only 15.9%. However, the risk

to buildings founded on soft soil sites will be much higher because the demand spectrum would

increase due to soil amplification but the capacity would remain the same. It is therefore important


DOI: 10.1002/eqe


15/19


Figure 6. Pseudo-acceleration response spectrum (5% damping ratio) in Singapore resulting from the Mw8.8 earthquake in the Mentawai segment.

to quantify the site response in Singapore because the ground motion from future earthquake in the

Mentawai segment is likely to affect structures located in soft soil sites and not structures founded

on rock.

6.3. Spectral shape

The shape of a response spectrum depends on two key factors, namely the magnitude of the

earthquake and the distance from the site to the source of the earthquake. It is well accepted thatearthquakes with larger magnitude produce ground motions with richer long-period components

than do smaller magnitude earthquakes. Ground motions also attenuate with distance, where

the high-frequency components attenuate faster compared with the low-frequency counterparts.

Combining these two factors, it is expected that ground motion from a large-magnitude subduction

earthquake at a remote site would have a long predominant period. The recorded response spectra

in Figure 5, all showing predominant periods longer than 1 s, support this argument.

Standard seismic design codes, such as the IBC 2000 [42] and the Indonesian Seismic Code

(SNI-1726-2002), specify the design base shear for buildings as

Vb=I C

RW (2)

where W is the total dead weight of the structure, R is the strength reduction factor to account

for ductility capacity and inelastic performance of structures and I is the importance factor, which

is taken to be 1.0 for ordinary structures. The period-dependent seismic coefficient C depends on

the location of the structure, which is characterized by the seismic hazard at the site and the local

site condition. The spectral shape of seismic coefficient C is governed by the ordinates of the

pseudo-acceleration at a short natural period of 0.2 s, A(Tn =0.2 s), and that at 1.0 s, A(Tn =1.0 s).


DOI: 10.1002/eqe


16/19


Figure 7. Normalized acceleration response spectra from the IBC 2000 and three giantSumatran subduction earthquakes.

The normalized design spectrum from the IBC 2000 is shown in Figure 7, where the corner period

Tc indicates the intersection between the constant-acceleration and constant-velocity branches of

the spectrum. As the constant-acceleration branch is defined by A(Tn =0.2 s) and the constant-

velocity branch is determined by A(Tn =1.0 s), the corner period Tc always lies between 0.2

and 1.0 s. The Tc values for rock sites typically range between 0.4 and 0.6 s. Note that this

spectral shape was derived from statistical analyses of numerous ground motions recorded near the

epicentres, and thus it is suitable for sites where the seismic hazards are controlled by near-field

earthquakes.

The normalized response spectra of three giant earthquakes (Mw8.0) in Table I are plotted in

Figure 7. Comparing these spectra with the normalized IBC spectrum indicates that the latter is not

particularly suitable for sites where the potential seismic hazard is dominated by large-magnitude,

distant, earthquakes because it may under-predict the hazard at long-period range. Unfortunately,

this spectral shape with Tc=0.5s is currently used for the whole territory of Indonesia, regardless

of the local seismicity. For example, eastern coast of Sumatra (Figure 1), where the seismic hazard

is controlled by distant earthquakes on the Sumatran fault running along the western coast and the

subduction zone off the coast, is assigned the same design spectral shape as the high-seismicity

western coast.

Building authorities in Singapore and Malaysia are currently considering incorporation of

earthquake-resistant design to existing building codes. It should be understood that characteristics

of ground motions in Singapore and the Malay Peninsula are unique and do not resemble those in

high-seismicity regions. The shifting of response spectrum towards longer period range should be

carefully taken into account in the formulation of future seismic codes.

7. CONCLUSION

One of the key components required in seismic hazard assessment of a region is a set of repre-

sentative attenuation relationships. A new set of attenuation relationships for Sumatran subduction

earthquakes, covering magnitudes up to 9, have been derived based on synthetic seismograms.


DOI: 10.1002/eqe


17/19


It is necessary to develop the attenuation relationships because the existing relationships derived

for other regions were not well constrained for large earthquake magnitudes and/or long-distance

range. They systematically over-predicted the recorded data from the distant Sumatran subduction

earthquakes.

The attenuation relationships derived are for very hard rock site condition and for a long-distancerange between 200 and 1500 km. The derived attenuation relationships should not be extrapolated

to distances shorter than 200 km, for which the relationships derived by Atkinson and Boore [15]

and Kanno et al. [16] may be more appropriate.

The newly derived attenuation relationships have been validated with recorded data from giant

earthquakes on the Sumatran megathrust occurring in the last 9 years. The attenuation relationships

are also used to estimate ground-motion intensity in Singapore due to a highly expected earthquake

scenario on the Sumatran megathrust, and the result shows that the risk level to structures founded

on rock is rather insignificant. The earthquake may, however, pose some problems to structures

founded on soft soil deposits because of significant site amplification.

These recorded data also show that the IBC spectral shape may not be suitable for sites where

the potential seismic hazard is dominated by large-magnitude, distant, earthquakes. The IBC design

spectra, which have been adopted by many countries, were derived for near-field earthquakes

and may under-predict spectral values from large-magnitude, distant, earthquakes, in long natural-

period range. The shifting of response spectrum towards longer period range for distant earthquakes

should be carefully taken into account in the formulation of future seismic codes in Singapore and

Malaysia, where seismic hazard is determined by distant Sumatran earthquakes. The attenuation

relationship derived in the present study can properly reproduce the spectral shape from distant

subduction earthquakes, and could hopefully give insights into the formulation of future seismic

codes.

Although the attenuation relationships derived here are intended for the Sumatran subduction

earthquakes, they may be used as a reference for other regions facing similar threats from distant

earthquakes.

ACKNOWLEDGEMENTS

The authors thank the Building and Construction Authority of Singapore and Dr Jack Pappin of Arup forthe continuous discussions and collaboration. The ground motions recorded at the GSN station in Singaporewere provided by the Meteorological Services Division, National Environment Agency, Singapore.

REFERENCES

1. Atkinson GM, Boore DM. Ground-motion relations for Eastern North America. Bulletin of the Seismological

Society of America 1995; 85:1730.2. Toro GR, Abrahamson NA, Schneider JF. Model of strong ground motions from earthquakes in Central and

Eastern North America: best estimates and uncertainties. Seismological Research Letters 1997; 68:4157.3. Campbell KW. Prediction of strong ground motion using the hybrid empirical method and its use in the

development of ground-motion (attenuation) relations in Eastern North America. Bulletin of the SeismologicalSociety of America 2003; 93:10121033.

4. Megawati K. Hybrid simulations of ground motions from local earthquakes affecting Hong Kong. Bulletin of the

Seismological Society of America 2007; 97:12931307.5. Pan TC, Sun JC. Historical earthquakes felt in Singapore. Bulletin of the Seismological Society of America 1996;

86:11731178.6. Pan TC, Megawati K, Brownjohn JMW, Lee CL. The Bengkulu, southern Sumatra, earthquake of 4 June 2000

(Mw=7.7): another warning to remote metropolitan areas. Seismological Research Letters 2001; 72:171185.


DOI: 10.1002/eqe


18/19


7. Sieh K, Natawidjaja D. Neotectonics of the Sumatran fault, Indonesia. Journal of Geophysical Research 2000;

105:2829528326.

8. Megawati K, Pan TC, Koketsu K. Response spectral attenuation relationships for Singapore and the Malay

Peninsula due to distant Sumatran-fault earthquakes. Earthquake Engineering and Structural Dynamics 2003;

32

:22412265.9. Newcomb KR, McCann WR. Seismic history and seismotectonics of the Sunda Arc. Journal of Geophysical

Research 1987; 92:421439.

10. Chlieh M, Avouac JP, Hjorleifsdottir V, Song TRA, Ji C, Sieh K, Sladen A, Hebert H, Prawirodirdjo L, Bock Y,

Galetzka J. Coseismic slip and afterslip of the great Mw 9.15 SumatraAndaman earthquake of 2004. Bulletin

of the Seismological Society of America 2007; 97:S152S173.

11. Megawati K, Pan TC. Regional seismic hazard posed by the Mentawai segment of the Sumatran megathrust.

Bulletin of the Seismological Society of America 2009; 99:566584.

12. Youngs RR, Chiou SJ, Silva WJ, Humphrey JR. Strong ground motion attenuation relationships for subduction

zone earthquakes. Seismological Research Letters 1997; 68:5873.

13. Petersen MD, Dewey J, Hartzell S, Mueller C, Harmsen S, Frankel AD, Rukstales K. Probabilistic seismic hazard

analysis for Sumatra, Indonesia and across the southern Malaysian peninsula. Tectonophysics 2004; 390:141158.

14. Gregor NJ, Silva WJ, Wong IG, Youngs RR. Ground-motion attenuation relationships for Cascadia subduction

zone megathrust earthquakes based on a stochastic finite-fault model. Bulletin of the Seismological Society of

America 2002; 92:19231932.

15. Atkinson GM, Boore DM. Empirical ground-motion relations for subduction-zone earthquakes and their application

to Cascadia and other regions. Bulletin of the Seismological Society of America 2003; 93:17031729.

16. Kanno T, Narita A, Morikawa N, Fujiwara H, Fukushima Y. A new attenuation relation for strong ground motion

in Japan based on recorded data. Bulletin of the Seismological Society of America 2006; 96:879897.

17. Lin PS, Lee CT. Ground-motion attenuation relationships for subduction-zone earthquakes in Northeastern Taiwan.

Bulletin of the Seismological Society of America 2008; 98:220240.

18. Megawati K, Pan TC, Koketsu K. Response spectral attenuation relationships for Sumatran-subduction earthquakes

and the seismic hazard implications to Singapore and Kuala Lumpur. Soil Dynamics and Earthquake Engineering

2005; 25:1125.

19. Pan TC, Megawati K, Lim CL. Seismic shaking in Singapore due to past earthquakes. Proceedings of 2007

Workshop on Earthquakes and Tsunamis: From Source to Hazard Singapore, Singapore, 79 March 2007. Paper

No. 5.

20. Larson KM, Freymueller JT, Philipson S. Global plate velocities from the global positioning system. Journal of

Geophysical Research 1997; 102:99619981.

21. Prawirodirdjo L, Bock Y, Genrich JF, Puntodewo SSO, Rais J, Subarya C, Sutisna S. One century of tectonicdeformation along the Sumatran fault from triangulation and global positioning system surveys. Journal of

Geophysical Research 2000; 105:2834328361.

22. McCaffrey R. Slip vectors and stretching of the Sumatran fore arc. Geology 1991; 19:881884.

23. McCaffrey R. Oblique plate convergence, slip vectors, and forearc deformation. Journal of Geophysical Research

1992; 97:89058915.

24. Fitch TJ. Plate convergence, transcurrent faults, and internal deformation adjacent to Southeast Asia and the

western Pacific. Journal of Geophysical Research 1972; 77:44324460.

25. Natawidjaja DH, Sieh K, Chlieh M, Galetzka J, Suwargadi BW, Cheng H, Edwards RL, Avouac JP,

Ward SN. Source parameters of the great Sumatran megathrust earthquakes of 1797 and 1833 inferred from

coral microatolls. Journal of Geophysical Research 2006; 111(Art. No. B06403).

26. Zachariasen J, Sieh K, Taylor FW, Edwards RL, Hantoro WS. Submergence and uplift associated with the giant

1833 Sumatran subduction earthquake: evidence from coral microatolls. Journal of Geophysical Research 1999;

104:895919.

27. Ammon CJ, Ji C, Thio HK, Robinson D, Ni SD, Hjorleifsdottir V, Kanamori H, Lay T, Das S, Helmberger D,Ichinose G, Polet J, Wald D. Rupture process of the 2004 SumatraAndaman earthquake. Science 2005;

308:11331139.

28. Lay T, Kanamori H, Ammon CJ, Nettles M, Ward SN, Aster RC, Beck SL, Bilek SL, Brudzinski MR, Butler R,

DeShon HR, Ekstrom G, Satake K, Sipkin S. The great SumatraAndaman earthquake of 26 December 2004.

Science 2005; 308:11271133.

29. Subarya C, Chlieh M, Prawirodirdjo L, Avouac JP, Bock Y, Sieh K, Meltzner AJ, Natawidjaja DH, McCaffrey R.

Plate-boundary deformation associated with the great SumatraAndaman earthquake. Nature 2006; 440:4651.


DOI: 10.1002/eqe


19/19


30. Briggs RW, Sieh K, Meltzner AJ, Natawidjaja D, Galetzka J, Suwargadi B, Hsu YJ, Simons M, Hananto N,

Suprihanto I, Prayudi D, Avouac JP, Prawirodirdjo L, Bock Y. Deformation and slip along the Sunda Megathrust

in the great 2005 Nias-Simeulue earthquake. Science 2006; 311:18971901.

31. Konca AO, Hjorleifsdottir V, Song TRA, Avouac JP, Helmberger DV, Ji C, Sieh K, Briggs R, Meltzner A. Rupture

kinematics of the 2005M

w 8.6 Nias-Simeulue earthquake from the joint inversion of seismic and geodetic data.Bulletin of the Seismological Society of America 2007; 97:S307S322.

32. Megawati K, Chandler AM. Distant-earthquake simulations considering source rupture propagation: refining the

seismic hazard of Hong Kong. Earthquake Engineering and Structural Dynamics 2006; 35:613635.

33. Megawati K, Pan TC. Prediction of the maximum credible ground motion in Singapore due to a great Sumatran

subduction earthquake: the worst-case scenario. Earthquake Engineering and Structural Dynamics 2002; 31:

15011523.

34. Laske G, Masters G, Reif C. CRUST 2.0: a new global crustal model at 2 2 degrees. Institute of

Geophysics and Planetary Physics, The University of California, San Diego. Available from: http://mahi.ucsd.edu/

Gabi/rem.dir/crust/crust2.html [19 January 2008].

35. Wells DL, Coppersmith KJ. New empirical relationships among magnitude, rupture length, rupture width, rupture

area, and surface displacement. Bulletin of the Seismological Society of America 1994; 84:9741002.

36. Somerville P, Irikura K, Graves R, Sawada S, Wald D, Abrahamson N, Iwasaki Y, Kagawa T, Smith N, Kowada A.

Characterizing crustal earthquake slip models for the prediction of strong ground motion. Seismological Research

Letters 1999; 70:5980.

37. Boore DM, Joyner WB. Site amplifications for generic rock sites. Bulletin of the Seismological Society of America

1997; 87:327341.

38. Fukushima Y. Scaling relations for strong ground motion prediction models with M2 terms. Bulletin of the

Seismological Society of America 1996; 86:329336.

39. Sieh K, Natawidjaja DH, Meltzner AJ, Shen CC, Cheng H, Li KS, Suwargadi BW, Galetzka J, Philibosian B,

Edwards RL. Earthquake supercycles inferred from sea-level changes recorded in the corals of west Sumatra.

Science 2008; 322:16741678.

40. Konca AO, Avouac JP, Sladen A, Meltzner AJ, Sieh K, Fang P, Li Z, Galetzka J, Genrich J, Chlieh M,

Natawidjaja DH, Bock Y, Fielding EJ, Ji C, Helmberger DV. Partial rupture of a locked patch of the Sumatra

megathrust during the 2007 earthquake sequence. Nature 2008; 456:631635.

41. Chlieh M, Avouac JP, Sieh K, Natawidjaja DH, Galetzka J. Heterogeneous coupling on the Sumatra megathrust

constrained from geodetic and paleogeodetic measurements. Journal of Geophysical Research 2008; 113:B05305.

42. International Code Council. International Building Code, 2000.


DOI: 10.1002/eqe

Documents

response spectr