GENERATION OF SPECTRUM COMPATIBLE TIMEHISTORIES FOR BUILDING DESIGN BY AN
EMPIRICAL METHOD USING MEGATHRUST
EARTHQUAKE SCENARIOS
Armando Sifuentes
MEE12607

Supervisor:Izuru OKAWAABSTRACTAn empirical method is used to simulate spectrum compatible time histories for a megathrustearthquake scenario in Peru. The Pisco earthquake (Mw 8.0) is the earthquake scenario. An empiricalattenuation formula for acceleration response spectra provides the target spectrum. Moreover,empirical formulas to evaluate the meanand the varianceof group delay time are used.
The empirical formulas use site coefficients to represent local characteristics of ground motions due tounderlying soil structure. Deep shear-wave velocity profiles in Lima, Peru and soil profile informationfrom the KiK-net seismic network in Japan are used to calculate transfer functions and evaluate thesite effect. Although there is good agreement with response spectra in a certain range of periods andpeak acceleration values in time domain for observed and simulated ground motions, it is notadvisable the direct use of empirical formulas. However, the procedure to construct waveforms, basedon the phase content, used has proven to be a good technique to simulate ground motions.
Keywords: Lima city, Pisco earthquake, spectrum compatible time history, group delay time, transferfunction.
1. INTRODUCTION
1.1. Background
Peru and Japan are both located in the “Ring of Fire”, an area where about 90% of the total number ofearthquakes in the world occurs (USGS, 2012). As a part of actions taken to aim for disaster risk
reduction, the design and construction of safety infrastructure must be taken into consideration and aperformance evaluation must be conducted if required. Thus, it is necessary to use a design groundmotion expressed as a time history when performing nonlinear dynamic analysis, usually applied tohigh-rise and base-isolated buildings. In this study, to achieve the time history generation for building
design using Peru earthquake scenarios, the empirical method proposed by Satoh et al. (2010) is used.
1.2. Objectives
The objective of this study is the use of an empirical method to simulate earthquake ground motions tobe used in building design for a megathrust earthquake scenario in Peru and to compare the resultswith observed recorded ground motions. The method uses empirical formulas developed with recordedground motions in Japan. Therefore, the possibility of the use of these empirical formulas tocharacterize earthquake ground motions in Peru, to overcome the lack of these formulas, will beevaluated.
Japan-Peru Center for Earthquake Engineering Research and Disaster Mitigation (CISMID), Lima, Peru
BRI Chief Fellow, Building Research Institute (BRI), Tsukuba, Japan.

12. DATA
2.1. Empirical Formulas
Empirical formulas used in this study were proposed by Satoh et al. (2012). These formulas wereproposed as a method for evaluating the long-period ground motion time history with periods from 0.1
to 10 s using earthquake magnitude, shortest distance to the source area and location of the hypocenter.

3. METHOD
3.1. Spectrum Compatible Time History
Spectrum compatibles time histories are time histories with their response spectrum consistent with atarget spectrum. This target spectrum could be referred to as a design spectrum, uniform hazard
spectrum or any other that represents buildings responses including the characteristics of the sitewhere the analysis is being carried out.
3.2. Target Spectrum
An empirical formula for the Pacific plate events is used to define the target spectrum. This formula
relates the 5% damping acceleration response spectrawith the moment magnitude and theshortest distance from recording station to the assigned source area of each recorded event.
Acceleration values of response spectra are expressed bywhere,
is period in seconds.
is moment magnitude andis shortest distance from therecording site to the coseismic rupture in kilometer, and,,,,,,are coefficients determined with the least squares analysis.
andare thecoefficients representing the source properties.
represents the property for propagation fromthe Pacific plate. The coefficientis assumed to be the site amplification factor for the KiK-net
FKSH19 station which is regarded as the benchmark station on the seismic bedrock and,is thesite coefficients for the j-th recording station
3.3. Mean and Variance of Narrow-band Group Delay TimeThe mean valueof group delay time corresponds to an average arriving time of wave group in anarrowband and the standard deviationof group delay time corresponds to the scatter of thearriving time that is the duration time of the wave group in a narrowband (Satoh et al., 2010).
The meanand the varianceof group delay are expressed by the following
empirical formulas

where,is seismic moment in dyne-cm (10-7 N-m),is hypocentral distance in kilometer,isfrequency.
,,,,andare coefficients determined by the least squares
analysis. The inverse ofindicates the propagation velocity of seismic waves radiated from theseismic sources from the Pacific plate.
andare called site coefficients.

23.4. Generation of Waveform
Satoh et al. (1996) explained fundamental formulation of group delay time based on the relation
between group delay time
and the phase angle shown in Eq. (4) (Papoulis, 1962) , written as

where,

is circular frequency andis Fourier phase angle.
Therefore, since group delay time is the first derivative of the Fourier phase angles withfrequency, once the initial phase angle is fixed and random numbers are given, the other phase angles
are recursively calculated using a normal distribution with the meanand standard deviation(Satoh et al., 2010). Finally, it is possible to construct a Fourier phase spectrum that combinedwith an assumed Fourier amplitude spectrum generates a waveform applying the Inverse Fourier
Transform. The Fourier amplitude spectrum must be iteratively changed to match the target spectrum.

4. PERU CASE
4.1. Earthquake Scenario

Figure 1. Surface projection of slip distribution andsource division (dashed line). Epicenters for eachsegment are indicated by yellow stars.

where, for each subfault ,for each segment.

is rigidity,

is slip and3

The August 15, 2007 Pisco earthquake isused as the earthquake scenario. Thisearthquake had a moment magnitude Mwof 8.0 (USGS, Harvard CMT). The
hypocenter was located at 13.354S and76.509W, at a depth of 39 km (USGS) incentral Peru, offshore of the city of Pisco.
Source models for this earthquake favor theexistence of two subevents (Ji and Zeng,report, 2007; Sladen, 2010) about 60 s apart,i.e., slip on the second event started 60 s
after slip initiated on the first event.
To simulate adequately twoevents, it is indispensable to divide thesource area into two, each one
characterized by values of seismic momentand moment magnitude. For this purpose,
slip distribution information for eachsubevent of the source model proposed byJi and Zeng (2007) and rigidity values
calculated using information from theglobal crustal model CRUST 2.0 (Bassin etal. 2000) are used. The following equation
describes how to calculate seismic moment
for each segment:

is area; andis the number of subfaults

Figure 1 shows the surface projection of slip distribution, epicenter and geometry of thetwo segments into which the source area was divided. Moment magnitude
is obtained using
seismic moment
and the following equation (adapted from Hanks and Kanamori, 1979)

where the seismic moment
is in N-m.
The seismic moment in N-m for the first and second segment is 0.6104E+21 and1.2718E+21, respectively. The moment magnitude Mw for the first and second segment is 7.8 and 8.0,respectively. The epicenter for the first segment is the same as the epicenter given for USGS. The
epicenter for the second segment is obtained based on the time between ruptures and the source model
proposed by Ji and Zeng (2007).
4.2. Choice of Site Amplification Factors
To use empirical equations correctly it is important to define appropriate values of site coefficients thatrepresent local characteristics of ground motions due to soil structure for soils in Japan and used themto represent soil behavior in Lima, Peru.
CAL, CSM, PQR and VSV profiles in Lima, Peru from Calderon (2012) are used. CAL,
CSM and VSV profiles correspond to CISMID accelerometer network (www.cismid-uni.org/redacis/)
stations with the same name. PQR profile and the CDL-CIP station differ in their locations eventhough they are located in an area with the same type of soil (CISMID, 2005). Quispe (2010)
presented a shear-wave velocity profile for shallow soil structure of the CDL-CIP station; however,PQR profile is used since it provides information for deeper soil structure. The VSV station had notbeen deployed during the Pisco earthquake and VSV profile is used to evaluate how the groundmotion had been in this location. In Japan, the KiK-net seismic network(http://www.kyoshin.bosai.go.jp/) provides the soil structure information of locations where its stations
are deployed.
Thus, site effect is evaluated using transfer functions to compare soils in Lima, Peru andJapan. It is found that the CAL station in Lima exhibited similar behavior to the FKSH11 andMYGH02 stations in Japan as shown in Figure 2(a) and (b). In addition, the CSM station showedsimilar behavior to the FKSH17 and IWTH21 stations (see Figure 2(d) and (e)), the CDL-CIP station
to the FKSH02 and FKSH16 stations, and the VSV station to the IWTH24 station.

5. RESULTS
Figure 2(c) and (f) show response spectra for observed ground motion and simulated ground motions
for the Pisco earthquake using selected site coefficients ( ,andin Eq. (1), (2) and (3),respectively) at stations CAL and CSM, respectively. Response spectra of simulated ground motions
are the arithmetic average of ground motions generated using six sets of random numbers.
The response spectra of simulated ground motions exhibited in most of the cases
coincidences of the interval of period where maximum acceleration values were observed for observed
ground motion. However, values of acceleration differ due to different levels of amplification between
selected station in Lima and Japan. The response spectra of simulated ground motion at the VSV
station showed acceleration values greater than 300.0 cm/s2 for periods less than 0.6 s.
Figures 3 shows simulated ground motions for stations CAL and CSM using different setsof random numbers. Simulated ground motions are compared with observed recorded ground motions
for stations CAL and CSM.
There is a good agreement between amplitudes of observed and simulated groundmotions for the two subevents. The duration of simulated ground motions in most of the cases is lessthan the duration of observed ground motions at each station. Simulated ground motions at the VSV

4station present peak acceleration values near 120.0 cm/s2 with evident long period content. Amplitudes
for the two subevents do not differ significantly. However, as the observed ground motions in different
stations the peak acceleration values of the simulated ground motions for the first subevent are lessthan for the second subevent for most of the sets of random numbers.

CAL

FKSH11MYGH02

CSM

FKSH17

IWTH21Figure 2. CAL, FKSH11 and MYGH02 (a) shear-wave velocity profiles and (b) transfer functions. (c)Response spectra of observed ground motion and generated ground motions at the CAL stations.
CSM, FKSH17 and IWTH21 (d) shear-wave velocity profiles and (e) transfer functions. (f) Response
spectra of observed ground motion and generated ground motions at the CAL stations.

Figure 3. Observed and generated ground motions at stations CAL and CSM.

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6. CONCLUSIONS
Although there is good agreement with response spectra in a certain range of periods and peakacceleration values in time domain for observed and simulated ground motions, it is not advisable thedirect use of empirical formulas to characterize ground motions in Peru. Site coefficients in empiricalformulas were used to estimate a similar behavior of soils in Lima, Peru and may not represent overallsite conditions. However, the procedure to construct waveforms used in this study, based on phaseangle characteristics and their relation with the mean and standard deviation of group delay time inearthquake ground motions, has proven to be a good technique to simulate ground motions. Therefore,
efforts must be made to developed empirical formulas to characterize earthquake ground motions inPeru. This involves tasks as the enhancement of strong ground motion observation to obtain thenecessary data.

ACKNOWLEDGEMENTS
I would like to express my gratitude to Dr. Toshiaki YOKOI -International Institute of Seismology andEarthquake Engineering- for his valuable advice, guidance and support during the time this study wascarried out.
In this study, strong motion records and soil profile information from KiK-net seismic
network of the National Research Institute for Earth Science and Disaster Prevention (NIED) wereused. In addition, The Generic Mapping Tools (GMT) was used for making maps.

REFERENCES
Bassin, C., Laske, G. and Masters, G., 2000, EOS Trans AGU, 81, F897.
Calderon, D., 2012, Graduate School of Engineering, Chiba University, Japan.
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Ji, C. and Zeng Y., 2007, Retrieved July 2013 from http://earthquake.usgs.gov/earthquakes/eqinthenews/2007/us2007gbcv/finite_fault.php
Papoulis, A., 1962, McGRAW-Hill.
Quispe, G., 2010, Master Thesis, National Graduate Institute for Policy Studies, Building ResearchInstitute, Japan, 32p.
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