STRONG GROUND MOTION SIMULATION OF THE
JANUARY 13, 2001 EL SALVADOR EARTHQUAKEUSING EMPIRICAL GREEN’S FUNCTION METHOD
Nelson Eduardo Ayala Leiva∗
MEE08157

Supervisor: Toshiaki YOKOI∗∗

ABSTRACTIn January and February 2001, a very intense seismic activity occurred in El Salvador, it caused many
damages in the country. The biggest two earthquakes with magnitude Mw= 7.7 and Mw= 6.5 occurred
exactly one month separation, the first one occurred on January 13 and the second one on February 13.
Using the empirical Green’s function method we simulated the January 13, 2001 earthquake
using strong ground motion data (accelerograms) and an aftershock with magnitude Mw= 5.7. We usedsource spectral fitting method in order to find an estimation of parameters to be used in EGF method.
Two fault plane models determined by previous studies were considered for the simulation inthis study. One has strike/ dip/ rake angles 306.°/ 48.°/ -107.° and another 297.°/ 58.°/ -93.°,
respectively. For the former we tested two possibilities with the same asperity area (30 km x 30 km)
but different number of subfaults.
We performed the ground motion simulation for three stations with large PGA and PGVvalues and a clear directivity pulse. From the result we determined that the former fault model
provided us with the best results obtained in this study. This fault model is composed by a grid of 36
subfaults with individual area of 5 km x 5 km.
Keywords: 2001 El Salvador earthquakes, Empirical Green’s Function method, Strong Motion
Records.

1. INTRODUCTIONEl Salvador is a small country with 21,040 km2 area and it is located in the Central America isthmus.
The population is about 6 millions and is highly concentrated in the capital city, San Salvador, where
about 1.8 millions are living now. The recent earthquakes on January 13 and February 13, 2001
showed the vulnerability of El Salvador. These earthquakes have affected not only the poorest people
but also the middle-upper class. Many people were buried in landslides areas, other lost their houses
and their relatives and many cities were not communicated because landslides obstructed the ways.
The seismicity of El Salvador is produced by three sources, the tectonics, the active fault
system and the volcanic chain. The tectonics of Central America and Caribbean is composed of theinteraction of five plates, The North American, Cocos, Caribbean, Nazca and South America plate. El
Salvador is strongly affected by earthquakes generated in the zone where Cocos plate is subducting
beneath the North American and Caribbean plates. The last strong and destructive event generated bythis source occurred in January 13, 2001. The active fault system produces earthquakes withmagnitude lower than 6.5, but they are too destructive due to the shallow focal depth. On February 13,
2001 occurred the last large event produced by this source.

∗

Universidad Centroamericana José Simeón Cañas.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

∗∗

12. METHODOLOGY.
In this study, a useful approach was applied to estimate strong ground motion for a large earthquake
using the record of small earthquakes, considered as Empirical Green’s Function, EGF, (Hartzell,1978; Irikura, 1986; Irikura and Kamae, 1994) , being the main idea of the EGF method that small
event has already included the properties of the propagation path and local site effects, so it isnecessary to know the details of the velocity structure (Poiata, 2005). EGF takes in consideration two
similarity relations between large and small events which are scaling relation of source parameters andscaling of source spectra.
In the first scaling relation, the parameters studied by Kanamori and Anderson (1975) and by
Yokoi and Irikura (1991) are expressed by the following equation:
L/l = W/w = (Mo / mo)1/3= (C N 3)1/3,

D/d = (C N 3)1/3,

C = ∆σL / ∆σs(1)where L, l , W , w, M o , mo , D and d are fault lengths, fault widths, seismic moments and slip
duration times for large and small event respectively. C is the stress drop correction factor and isdefined as the ratio of stress drop for large event ( ∆ σ L ) and small event ( ∆ σ S ).
The second relation is represented by ω −2 source spectra scaling model (Aki, 1967) and(Brune, 1970). The shape of the source model is given by Eq. (2). In Eq. (2) f c , f and U o arespectral corner frequency, the low frequency, and flat level of displacement spectrum respectively,
also f c is proportional to the inverse of square root of the fault dimension ( LW ) −1 2 and U o is
proportional to the seismic moment M o .
U(f) = Uo / {1+(f / fc )2}.

(2)

The second relation was studied by Aki (1967) and Brune (1970), and then it was modified
by Irikura and Kamae (1994) by adding the stress drop correction factor. This relation is expressed by
Eq. (3) and Eq. (4)
Uo Mo
(3)
=
= C N3,uomo
1

Ao  M o  3
 =CN,=a o  m o 

(4)

where

Fig. 1. a) Displacement source spectra. b) Acceleration
source spectra (Poiata, 2005)

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U o , u o , Ao and a o areflat level of displacement spectrum
and flat level of acceleration
spectrum for large and small
events (Figure 1). To perform thesimulation of strong groundmotion it is necessary to find thevalues of N and C, then divide thefault plane in N x N sub faults as
Fig. 2 shows.

The waveform of the target
event
can
be
U (t )
expressed in terms of thesmall event through Eq. (5)and F (t )where t i jhave to be determined byequations (6) (Irikura et al,1997).
Figure 2. a) Schematic of fault parameters used for EGF.
b) Filtering function (Poiata, 2005)
NNr
F (t − ti j ) * u ( t ) ,i =1 j =1 ri j

ti j =

ri j − ro

β

+

ξi j
VR

,

U (t ) = C ∑∑

(5)





( N − 1) n'1(k −1)T  1
F (t ) = δ (t ) +∑  (k −1) δ t − ti j (N −1)n'  1
n' 1 −  k = 1  (k −1) 


e


 e ( N −1) n'(6)Here: r , ri j , ro are the respective distances from site to the hypocenter of small event, to(i , j ) subfault and to starting point of rupture on the fault plane of large event; ξ i j , distance between

starting point and (i , j ) subfault; β , shear wave velocity; VR , rupture velocity; F(t), filteringfunction; T , rise time of target event and n' , appropriate integer to eliminate spurious periodicity

3. DATA.
To perform this study we have used strong ground motion records from “Universidad
Centroamericana José Simeón Cañas” (UCA University) network for events required in empiricalGreen’s function method (Figure 3). The UCA network by the time of the earthquake was constitutedby 10 digital accelerographs type SSA-2 (Kinemetrics) located in the central area of the country as
shown in Figure 3. A wider description of this strong motion network is presented by Boomer et al.
(1997). UCA strong groundmotion network recorded theJanuary 13, 2001 earthquake
and 78 aftershocks. The main
event was recorded at 9
stations. In the selection of theaftershock to be used as a small
event in EGF method weselected the event recorded in
the majority of the stations andwith epicenter location nearthat of the main shock. To
achieve this purpose we foundthe available information in
USGS web site.
Figure 3. Distribution of stations of UCA strong ground motion
network (triangles)3In order to achieve the purpose of this study we have taken into account two studies relatedwith source characterization, we have considered their results as input in this study. The studies are:• “The 13 January 2001 El Salvador earthquake: A multidata analysis”, (Vallée et al., 2003).
• “The January 13, 2001 Off the coast of El Salvador Earthquake, chapter 1, Source Characteristics
and Strong Ground Motion”. (Pulido, 2001).
4. ANALYSIS.
Using the records of the main event and the selected aftershock we made a spectral analysis in order todetermine the corner frequencies for both events. Figure 4 a) shows the acceleration spectra for 9
stations and it is possible to notice that the main event does not follow properly the ω2 model, becauseof the decay rate at the lower frequency side. These spectra are smoothed using a Parzen window of
the band width 0.30. The spectral ratios of the main shock events to the selected aftershock arecalculated in order to cancel out the site and the path effect. The average of spectral ratio was
calculated in order to correct the effect of radiation pattern, but also with the aim of preventing the
involvement of possible non-linear effects in the spectral ratio’s average, we did not use the stations
which recorded PGA’s values higher than 500 gals during the mainshock, Figure 4 b). We have used
the available frequency range from 0.4 Hz to 4 Hz, the minimum is set in order to avoid the deviation
due to noise included in the aftershock records for frequencies lower than 0.4 Hz, while the maximum
is set at 4 Hz because of the decay of spectra in high frequency range due to the difference of fmax. We
used the theoretical source spectral ratio fitting method proposed by Miyake et al. (1999) in order tofind the corner frequency for the main event and the selected aftershock, namely fcm and fca and theseismic moment ratio. Then it was necessary to fit the curve define by source spectral ratio function(SSRF). We set the frequency range for theoretical curve at the same values of the available frequency
range explained above. The fitted curve and spectral ratio’s average are shown in Figure 4 c).
1.0E+01

1.E+03

1.E+03CSBR
UPAN

Spectral ratio average

HSRF

Theoretical SSRF

UTON
1.0E+00ESJO
UARM mHSTR

CSBR mSpectral ratio average

USPN m

1.E+02

1.E+02

1.0E-01

HSRF mUTON mESJO mHSTR mUARM a1.0E-02

Spectral ratio

UPAN mS pectral Ratio

Acceleratio n sp ectra (G al*s)

ULLB m

1.E+01

1.E+01

CSBR aULLB aUSPN aUPAN aHSRF a1.0E-03

UTON aESJO aHSTR a1.0E-04
1.0E-02a)

1.0E-01

1.0E+00

1.0E+01

1.E+00
1.E-02

1.E-01

1.E+00

1.E+01

1.E+00
1.E-02

1.E-01

1.E+00b)c)
Figure 4. Spectral analysis. a) acceleration spectra, b) spectral ratio for stations with
PGA’s lower than 500 gal. c) spectral ratio average and theoretical SSRF curve.
Frequency (Hz)Frequency (Hz)Frequency (Hz)

1.E+01

T able 1. V alues ob ta ine d from sp ectral ratio
It is possible to find many values ofCase M mz) f c(Hz)CN
f c (HmaooMo/mo, fcm and fca in the fitting of the theoretical
A
55
0
0.2
1.6
1.07
8
curve, we found two sets that are showed in Table
B
35
0
0.25
1.6
1.33
6
1, that is deviated from the average seismic
moment – corner frequency relation. Namely it is higher than the general trend according to its
magnitude. It is, however, possible considering that intraslab earthquakes can have a high stress drop.
We performed the simulation for three stations with high PGA values and with a clear directivity
pulse. Using Case A values from Table 1 and the characteristics of faults and main asperity found bystudies considered we started finding for good spectra and waveforms fitting using empirical Green’s
function program. First we started using the fault plane model obtained by Pulido (2001). In the fittingof Vallée et al. (2003) fault model we conserved the subfault size but we modified N and C values.

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From the results obtained for cases
mentioned before we determinedthat Pulido (2001) fault model
gives a better approximation ofsynthetic waveforms and spectrathan Vallée et al. (2003) fault
model. Taking these results into
account we performed the case Bof spectral ratio fitting for Pulido(2001) fault model. A resume ofall parameters for different cases
is shows in Table 2. The results
obtained for Pulido (2001) fault
model using values for case B are
shown in Figures 5 to 7.

Table 2. Parameters used for simulation in both fault models.

Pulido et al (2001)
Vallée et al
Case A
Case B
2003
Parameters
Strike, Dip and Rake of main event (°)
306, 48, -107 306, 48, -107 297, 58, -93
Strike, Dip and Rake of aftershock (°)
303, 80, 147 303, 80, 147 303, 80, 147
Moment magnitude of main event/aftershock
7.6/5.7
7.6/5.7
7.7/5.7
Depth main/aftershock (km)39.0/59.3
39.0/59.3
54.0/59.3
Rupture area (km^2)
70 x 70
70 x 70
70 x 70
Asperity area (along strike x along dip) (km)30 x 3030 x 3050 x 25
Rupture/S-wave velocities (km/s)
2.9 / 3.99
2.9 / 3.99
3.5 / 4.4
Subfault area (dx and dw) (km)3.75 x 3.75
5x53.75 x 3.75
dx0 and dw0 (km)0, -2.50
0,0
8.50, 7.50
nx, nw, nsx, nsw, c factor
8, 8, 1, 3, 2.5 6, 6, 1, 2, 3.2 13, 7, 4, 7, 2.0
Number of subfaults
64
36
91

Figure 5. Waveform simulation for ULLB station using Pulido (2001) case B fault model, for N-S( two figures at left) and E-W (two figures at right) components.

Figure 6. Waveform simulation for UARM station using Pulido (2001) case B fault model, for N-S( two figures at left) and E-W (two figures at right) components.

Figure 6. Waveform simulation for HSRF station using Pulido (2001) case B fault model, for N-S (twofigures at left) and E-W (two figures at right) components.

55. CONCLUSIONS
Determination of the parameters for waveform synthesis is conducted using source spectral
ration function (SSRF). All existing strong motion records are used to average out the radiation
coefficient except those which have PGA bigger than 500 gals in order to prevent the non-linear effect.
Fitting the theoretical curve defined by SSRF we found two possible sets for moment ratio - cornerfrequency pairs. For both of them the small event’s corner frequency value is determined 1.6 Hz.
Two fault plane models determined by Pulido (2001) and Vallée et al. (2003) have been
considered for the simulation in this study. Looking at the results obtained, Pulido (2001) fault model
gives a better approximation between synthetic and observed spectra and waveforms of the selected
three stations where a clear directivity pulse are observed. Considering two cases for Pulido (2001)
fault model, the difference was not significant between case A and B in similarity between synthetic
and observed waveforms and spectra related, but if we consider seismic moment values as 4.57 x 1027
dyne-cm and 3.81 x 1024 dyne-cm (Harvard-CMT) for main and small event respectively and Eq. (3)we find that synthetic events produce asperity seismic moments equivalent to 107% of total seismic
moment of main event for case A. For case B it is only 57%. Taking into account both aspects
mentioned above we select the Pulido (2001) case B fault model which provided the best results
obtained in this study.
We determined that signal/noise ratio is not enough to reproduce well fitted synthetic
displacement waveform and the low frequency part of acceleration, velocity and displacement
synthetic spectra. This problem could be generated by ambient noise due the conditions in stations.

6. RECOMMENDATION
It is necessary to continue improving the study of fault characterization of the complexity of
subducting zone and its earthquakes generated. It is essential to start studying the fault characterizationof earthquakes produced by intraplate fault system and the volcanic chain. The study of the complex
relationship between subduction source and intraplate fault system become necessary.
ACKNOWLEDGEMENT
I am very grateful with Dr. H. Miyake because this study was conducted using the program that she
opens to public in internet. I thanks to UCA for provide me the strong motion data.
REFERENCES
Aki, K., 1967, J. Geophys. Res., 72, 1217-1231.
Boomer, J. et al., 1997, Seismological Research Letters, vol. 68, N. 3, 426 – 437.
Brune, J. N., 1970, J. Geophys. Res. 75, 4997-5009.
ERI (Earthquake Research Institute), Hiroe Miyake. http://www.eri.u-tokyo.ac.jp/hiroe/egfm/
Hartzell, S. H., 1978, Geophysical Research letters, 5, 1-4.
Irikura, K., 1986, Proc. 7th Japan Earthq. Eng. Symp., 151-156.
Irikura, K. and Kamae, K., 1994, Annali di Geofisica, XXXVII, 25-47.
Irikura. K., Kagawa, T. and Sekigushi, H., 1997, Seism. Soc. Japan, 2, B25. (in Japanese).
Kanamori, H. and Anderson, D. L., 1975, Bull, Seismol. Soc. Am., 65, 1073-1095.
Miyake, H., Iwata, T. and Irikura, K., 1999, Zisin, Ser. 2, 51, 431-442 (in Japanese).
Poiata, N., 2005, Individual studies by participant at the IISEE, 41, 131-144.
Pulido, N. E. (2001), Japan Society of Civil Engineering.
Universidad Centroamericana (UCA), 2001, Strong motion data of January earthquakes in El Salvador
Vallée, M. and Bouchon M., 2003, Journal of Geophysical Res., vol. 108, N° B4, 2203, 7-1 to 7-19.
Yokoi, T and Irikura, K., 1991, Zisin, Ser. 2, 44, 109-122 (in Japanese).

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