PRELIMINARY ANALYSIS FOR EVALUATION OF
LOCAL SITE EFFECTS IN LIMA CITY, PERU FROMSTRONG GROUND MOTION DATA BY THE
SPECTRAL INVERSION METHOD
Mileyvi Selene Quispe Gamero
MEE09185

Supervisor:

Hiroaki YAMANAKAABSTRACTThe present study applies the spectral inversion method, proposed by Iwata and Irikura (1986, 1988),
to separate the source, propagation path, and local site effects from observed strong motion records inthe frequency range from 0.5 to 10 Hz for the analyses of the relationship between the local subsurface
conditions and the local site amplifications in some areas of Lima city, Peru. The analyzed data are
S-wave portions of accelerograms in horizontal components observed at 5 stations for 11 events
recorded along the Pacific coast of Lima city. These events are superficial and intermediate
earthquakes with local magnitudes (ML) from 4.0 to 5.7 and with hypocentral distances from 40 to
180 km. From the spectral inversion, solutions for source spectra, inelasticity factor of propagation
path for S-wave (QS-value), and site amplification factor at each site are obtained. The factors of siteamplification Gj(f) obtained in the present study are compared with the results obtained by Cabrejos(2009) for stations CSM, CAL, MOL and CDLCIP employing the standard spectral ratio (SSR)
method, which support our results especially at frequencies below 5 Hz. QS-value obtained shows
frequency dependency of the form QS(f)=80.4f0.63. In addition, the influence of non-linearity on the site
response is evaluated during the Pisco earthquake which it is concluded that nonlinear response of thesoils was not detected at acceleration levels below 115.2 gal (the maximum peak ground acceleration
recorded in Lima city). The study also proposed relationships between the amplifications with average
S-wave velocity in top 30 meters of the S-wave profiles for some stations at each frequency.
Keywords: Spectral Inversion Method, Lima city, Site Amplification, QS-value, Pisco earthquake.

1. INTRODUCTION
Lima city, Peru has been continuously affected by several earthquakes that have caused slight,
considerable and severe damages. This city is prone to this kind of natural disaster due to thesubduction of the Nazca plate underbeneath the South American plate. In the last 60 years, according
to the earthquake catalog compiled by the Geophysical Institute of Peru (IGP), the city of Lima has
been subjected to earthquakes with the biggest Mw of 8.1. It is during the earthquake of October 3,1974 (Mw=8.1) that a few areas outside of Lima center were severely damaged, such as La Molina
and Callao – La Punta (Repetto et al. 1980). Works described by Husid et al. (1977), Espinoza et al.
(1977) and Repetto et al. (1980) refer that these areas were affected by the influence of local
subsurface conditions.
The spectral inversion proposed by Iwata and Irikura (1986) is applied in this study forestimating local site effects in some areas of Lima city. This approach utilizes the direct S-waves.

Japan Peru Center for Earthquake Engineering and Disaster Mitigation (CISMID), Lima city, Peru
Professor, Tokyo Institute of Technology, Tokyo, Japan1

2. DATA & DATA PROCESSING
The analyzed data are the S-wave portions of 30 accelerograms from 11 events observed at 5 strong
ground motion recording stations (CSM, CAL, MOL, CDLCIP and LMO stations). The seismic events
are superficial and intermediate earthquakes (depth < 140 km) from 40 to 180 km in hypocentral
distance. The observed peak ground accelerations (PGA) range from 5.5 to 109.0 gal. Besides, the ML
is ranging from 4.0 to 5.7. Table 1 exhibits the geological period at each station and the average
shear-wave velocity to 30 meters (Vs30) for some stations.
Table 1. Surface geology of the stations and Vs30.
Code Station
CSM
CAL
MOL
CDLCIP
LMO

Geological period
Quaternary
Quaternary
Quaternary
Quaternary
CretaceousGeology
Alluvial
AlluvialAlluvial
Alluvial
Santa Rosa Granodiorite

Vs30 (m/s)
533.23104.79--565.82---The S-wave portions of two horizontal components (NS and EW) of seismic groundmotions are analyzed. To recognize the onset time of S-wave, particle motion plots and Husid plots
are realized. After the onset time of S-wave has been determined, the S-wave portion ofaccelerograms (to) is extracted. A cosine-type tapered data-window has been applied to S-wave
portion to improve the problem of finite record length using the same criterion took by Takemura et al.
(1990). Fourier acceleration amplitude spectra of two horizontal components are computed andsummed vectorially. Before using the inversion scheme, the Fourier acceleration amplitude spectra
were smoothed with seventeen-point moving average method.

3. METHOD OF ANALYSIS
3.1. Spectral Inversion
One of the big advantages of the spectral inversion is separated source, propagation path, and local site
effects from observed seismic waves to examine the relation between local site effects and surface
geology (Takemura et al. 1991). In the present study, we adopt the inversion method proposed by
Iwata and Irikura (1986, 1988). They assume the quality factor of the wave propagation is independent
from the path and only depends on frequency (i.e., Q=Q(f)). Then the observed S-wave Fourier
amplitude spectrum is expressed by  Rij f

Oij ( f )  S i ( f )G j ( f ) Rij1 expQs ( f )Vs (1)where, Oij(f), observed S-wave Fourier amplitude spectrum of i-th event at j-th station; Si(f), source
amplitude spectrum of i-th event; Gj(f), factor of site amplification at j-th station; Rij, hypocentral
distance between i-th event and j-th station; QS(f), average QS-value along the wave propagation path;
VS, average S-wave velocity along the wave propagation path (=3.7 km/s) (Kato et al. 1992).
To separate source, path, and site effects simultaneously from spectra of observed seismic
waves as described hereafter, the first step is to take the logarithm of Eq. (1) to obtain simultaneous
logarithmic equations in the form.

log Oij ( f )  log S i ( f )  log G j ( f )  (f QS ( f )VS ) Rij2(2)These equations have unknown parameters of I (source terms) + J (site amplification terms)+ 1 (QS – value), which can be determined by the least squares method from IxJ data for Oij(f) at eachfrequency. However, there is still one unconstrained degree of freedom. Therefore, a constraint
condition is needed to determine the unknown parameters.
As a result of this need, Iwata and Irikura (1988) set up a constraint conditions that the site
amplification factor must be 2 or over considering the free surface amplification. The constraint
condition taking account is explained in the following subchapter.
3.2. Choice of Reference Site
The CDLCIP accelerometer station is used as a constraint condition for the inversion analysis, and thestation is located on a shallow, dense to very dense coarse gravel. So, for inversion the factor of site
amplification at a reference station CDLCIP is assumed to be the same as that of theoreticalamplification of S-wave. This constraint condition represents the free surface amplification effect.

4. RESULTS AND DISCUSSION
4.1. Site Amplification Factor and Standard Spectral Ratio
Figure 1 shows the site amplification factor obtained by the spectral inversion method Gj(f)represented by the solid blue line. The Gj(f) is compared with the standard spectral ratio (SSR)
obtained by Cabrejos (2009) represented by the solid green line in Figure 1. Cabrejos (2009) estimatedthe amplifications of ground motions for the same stations evaluated in this study. Since the spectral
ratio is not necessary to know the S-wave velocity structure of the reference site, he used the LMOstation, a station located on intrusive rock as reference site.
Figure 1 explains that there is a good agreement between both results, especially in lowfrequencies, which support our results although different techniques for estimating site response havebeen applied and different reference sites have been used, as previously mentioned.
It is noted from Figure 1, that Gj(f) has large values at frequencies above 5 Hz comparedwith the SSR values, because the amplification at the reference site (CDLCIP station) becomes large
in this frequency range.
CSM station

CAL station

10.0

10.0

1.0

1.0

Gj (f)
SSRGj (f)
SSR
0.1

0.1
0.1

1.0

10.0

0.1

Frequency (Hz)

1.0

10.0

Frequency (Hz)Figure 1. Comparison of site response with different techniques. The Gj(f) and the SSR arerepresented by the blue and green lines, respectively (Continue).

3

MOL station

CDLCIP station

10.0

10.0

1.0

1.0

Gj (f)SSR

Gj (f)
SSR

0.1

0.1
0.1

1.0

10.0

0.1

Frequency (Hz)

1.0

10.0

Frequency (Hz)Figure 1. Comparison of site response with different techniques. The Gj(f) and the SSR arerepresented by the blue and green lines, respectively.
4.2 Surface Geology and Local Surface Conditions

Site amplification factor

According Table 1, CSM, CAL, MOL and CDLCIPstations are located on Quaternary alluvial deposits. Figure
10.0
2 shows the comparison of site amplification factors Gj(f)for these four stations. It is noted that Gj(f) for CSM, MOL
and CDLCIP stations have larger amplifications at
frequencies above 4 Hz (represented by solids lines), butnevertheless a considerable variation is observed in CAL
1.0station (represented by a broken line), located also in
Quaternary deposits, in which the amplification values are
CSM station
CAL stationmuch higher at frequencies below 4 Hz.
MOL station
According to the soil type map of Lima city
CDLCIP station
0.1
developed by CISMID in 2003 with the support of the0.1
1.0
10.0
recognized Peruvian geologist Alberto Martinez Vargas
Frequency (Hz)(Aguilar 2005), CSM, CDLCIP and MOL stations are
Figure 2. Comparison of Gj(f) for CSM,
located on alluvial gravel overlying the denser Lima
CAL, MOL and CDLCIP stations.
Conglomerate. Alluvial gravel covers a large portion ofLima city, and presents a good geomechanic behavior (Aguilar 2005). On the other hand, CAL station
is located on soft soil, which is conformed by a 5 to 15 m thick layer of soft saturated clay and organicsoil (Aguilar 2005).
4.3 Source Spectra and QS-values
The source acceleration amplitude spectra are obtained from the inversion technique. It is divided overω2 to obtain the source displacement spectra and to replace in the equation proposed by Kanamori(1972) to get the seismic moment density M(f). The shear-wave velocity of 4.0 km/s, density of 3.0
g/cm3, and the average point-source radiation coefficient of 0.6 are assumed. Figure 3 (a) shows
examples of the source spectra for events with ML from 4.0 to 5.7. Figure 3 (b) shows the QS-values
obtained by the inversion and a model of QS(f)=80.4f0.63 which fits the results.
In Figure 3 (a), there is a conspicuous trough in the frequency range between 5 and 6 Hz.
As known, higher frequency values provide close surface depth data whereas lower frequency values
shed light on deep sections of the ground. In the analyzed data, there is not enough data in the shallow
part that can provide information in higher frequencies. In Figure 3 (b), a conspicuous peak in thesame frequency range is also observed, and this occurs because the QS-value along the wave
propagation path influences the form of the source spectrum.

41.E+03

1.E+22
Seismic momet density f unction Mi(f )Qs-value (This study)Qs(f) = 80.4f 0.63

Qs value

R² = 0.7974

1.E+02

1.E+01
0.1

1.0

10.0

20050725 (ML=4.0)
20060525 (ML=4.5)

1.E+21

20080607 (ML=5.0)
20050302 (ML=5.7)

1.E+201.E+191.E+181.E+17
1.E+160.1

Frequency (Hz)

1.0

10.0

Frequency (Hz)(a)(b)
Figure 3 (a) Examples of seismic moment density functions. (b) QS-values.
4.4 Analysis of Non-linearity of the Soil
On August 15, 2007, a strong offshore earthquake hit the coast of Central Peru. This earthquake, also
known
asthePisco
earthquake,hadamagnitudeof8.0
Mw(USGShttp://earthquake.usgs.gov/eqcenter/eqinthenews/2007/us2007gbcv/). The maximum peak groundacceleration recorded in Lima city was of 115.2 gal in La Molina district (Bernal and Tavera 2007). In
the present study, the influence of non-linearity on the site response is evaluated during the Pisco
earthquake.
From the spectral inversion method, QS-value and Gj(f) at reference site are already known.
To analyze the influence of the soil’s non-linearity on the Gj(f) at CSM, CAL, MOL and LMO stations,first the source amplitude spectrum Si(f) of the Pisco earthquake is calculated applying Eq. (1). Afterthat, Eq. (3) is applied to get the site amplification factor during this strong ground motion whereanother amplification factor Gij(f) is newly defined for avoiding confusion

Gij  f  Oij  f Rij

S i  f  exp Rij f QS  f VS (3)where, Oij(f) is obtained by the vectorial of two observed horizontal components, Si(f) is the source
spectrum and QS(f) is the QS-value (Takemura et al. 1991).
No systematic change is found for the difference between Gj(f) obtained by the inversion
analysis and Gij(f) for this strong ground motion, namely there is not found explicit evidence ofstrong-motion deamplifications, accompanied by changes in resonant frequencies (Beresnev and Wen
1996). Thus, it is concluded that nonlinear response of the soils was not detected at acceleration levels
below 115.2 gal during the Pisco earthquake.
4.5 Average S-wave Velocity and Site Amplification
The site amplifications are compared with average S-wave velocity in top 30 meters of the S-wave
profiles (Vs30) for CSM, CAL and CDLCIP stations, and proposed linear relations between them ateach frequency (0.5 Hz, 1.0 Hz, 2.0 Hz, 5.0 Hz, 10.0 Hz and 20.0 Hz). We know that Vs30 is only
available for a few stations so far, but we want to know the possible relationships between Vs30 andSAF, and to improve our results for the future researches in the same area of interest.
These relationships illustrate that Vs30 can be considered as a good indicator to estimate
site amplification for frequencies less than 10.0 Hz; however for frequencies above 10.0 Hz isobserved the trendline can not fit the calculated data well because the data are dispersive.

55. CONCLUSIONS
From the spectral inversion method, the site amplification factors for some areas of Lima city were
evaluated from strong motion records at 5 accelerometers. Out of the five stations used in this study,
four stations (CSM, CAL, MOL and CDLCIP stations) are located on alluvial soil deposits belonging
to the Quaternary Holocene. It is noted that Gj(f) for CSM, MOL and CDLCIP stations have largeramplifications at frequencies above 4 Hz compared with CAL station, in which the amplification
values are much higher at frequencies below 4 Hz. These differences between CAL station and otherstations are due to the local subsurface conditions. CSM, CDLCIP and MOL stations are located on
alluvial gravel overlying the denser Lima Conglomerate and CAL station is located on soft soil.
The obtained results were confirmed with the results obtained by Cabrejos (2009)
employing the Standard Spectral Ratio (SSR) in his study. There is a good agreement between bothresults, especially at frequencies below 5 Hz, although different techniques for estimating site response
have been applied and different reference sites have been used.
About the QS-value obtained in this study, there is a conspicuous trough in the frequency
range between 5 and 6 Hz because there is not enough data in the shallow part that can provide
information in higher frequencies. So it is recommendable that we should reanalyze these results withnew data so that we should be able to get and improve our results.
The influence of non-linearity on the site response is evaluated during the Pisco earthquake,and it is concluded that nonlinear response of the soil was not detected at acceleration levels below
115.2 gal during this strong ground motion.
Relationship between site amplifications obtained from spectral inversion and Vs30 are
proposed for frequencies 0.5 Hz, 1.0 Hz, 2.0 Hz, 5.0 Hz, 10.0 Hz and 20.0 Hz using the few data that it
is currently available. So it is strongly recommendable to get information of another accelerometerstations located in Lima city to estimate better relationships for evaluating the local site effect.
AKNOWLEDGEMENT
I am really indebted to Dr. Toshiaki YOKOI – Building Research Institute – who sincerely advised
and guided me during this work. I thank Ms. Elsie Benedit Jaimin, Mr. Roberto Armando Torres
Corredor and Mr. Hussam Eldein Zaineh Adel Wasfieh whose comments improved the paper, and Mr.
Jonathan Cabrejos Hurtado for providing information personally collected.

REFERENCES
Aguilar, Z., 2005, Seismic Microzonation of Lima City, Japan-Peru WS on Eq. Disaster Mitigation,CISMID, Fac. of Civ. Eng., Nat. Univ. of Eng., Lima, Peru.
Beresnev, I. and Wen, K., 1996, Bull. Seism. Soc. Am. 86, 1964–1978.
Bernal, I. and Tavera, H., 2007, Volumen Especial-IGP (Informe Preliminar) (in Spanish).
Cabrejos, J., 2009, Fac. de Ing. Civil, Univ. Nac. de Ing., Lima, Peru (in spanish).
Espinoza, A. F. et al., 1977, Bull. Seism. Soc. Am. 67(5), 1429-1439.
Husid, L. R., Espinoza A. F. and De Las Casas, J., 1977, Bull. Seism. Soc. Am. 67(5), 1441-1472.
Iwata, T. and Irikura, K., 1986, Zisin, Ser. II, 39, 579-593 (in Japanese with English Abstract).
Iwata, T. and Irikura, K., 1988, J. Phys. Earth. 36, 155-184.
Kanamori, H., 1972, Phys. Earth Planet. Inter., 6, 346-359.
Kato, K. et al., 1992, J. Pyhs. Earth, 40, 175-191.
Repetto, P., Arango, I., and Seed, H. B., 1980, EERC Report, College of Engineering, University ofCalifornia, Berkeley, California, NTIS, 80–41.
Takemura, M., Ikeura, T., and Sato, R., 1990, Tohoku Geophys. J. 32, 77-89.
Takemura, M., Kato, K., Ikeura, T., and Shima, E., 1991, J. Phys. Earth, 39, 537-552.

6