Citation: Chavarria, N., T. Yokoi (2020), Strong motion estimation in Costa Rica at specific sites using
spectral inversion method, Synopsis of IISEE-GRIPS master report.

STRONG MOTION ESTIMATION IN COSTA RICA
AT SPECIFIC SITES USING SPECTRAL INVERSIONMETHOD
Nathalie Yoliana CHAVARRÍA ESQUIVEL1,2

Supervisor:

Toshiaki YOKOI3

ABSTRACTThe complex tectonic setting of Costa Rica implies the necessity of a real seismic hazard scenario
characterization for lifeline facilities and the country. In this paper, one of the conventional spectral
inversion technique is applied to strong ground motion records to separate the site effect, the source
spectra and the path effect. To assure the quality of the results, the broadband station JTS000 of
IRIS/IDA is also incorporated. Two newly developed consistency checks were established to assure theappropriateness of the input data using the individual site effects and Fourier synthetic spectra. The
frequency dependent quality factor 𝑄 = 179𝑓 0.5598 was obtained for the northern and central part of
Costa Rica. Also, synthetic amplification spectra for the 2012 Sámara earthquake of Mw 7.6 at specificstations were calculated, showing consistency with the intensity anomaly observed for this earthquake.
This new method allows the estimation of acceleration spectra of important seismic events.
Keywords: Synthetic acceleration spectra, Q value, Consistency check method
1. INTRODUCTION
The subduction of the Cocos plate and the Nazca
plate under the Caribbean plate defines thetectonic frame of Costa Rica (Figure 1). The
stress generated this convergence, among
different bathymetry features at Cocos plate,caused crustal deformation resulting in theformation of important fault systems. Also, one of
the notable important geological features in Costa
Rica are the volcanic deposits, that cover the
major part of the country. The soft deposits due tothis volcanism and sedimentary basins can causea significant amplification during a major
earthquake. This influence was observed during
the 2012 Sámara earthquake (Mw 7.6 (R.S.N.,
2012)), where an anomalous intensity distribution
in central Costa Rica was observed (Figure 2).
Therefore, such tectonic frame requires a special Figure 1. Tectonic setting of Costa Rica.
hazard assessment to estimate the site effect at Modified from Montero (2001).
sites of interest. For this purpose, in this study I
separate the source, the path and the site effect1

Costa Rican Electricity Institute, Costa Rica.
IISEE-GRIPS master course student.
3International Institute of Seismology and Earthquake Engineering, Building Research Institute.
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using the spectral inversion method at different
strong motion stations. In parallel I establish a
way to check the input data of the inversion.
Based on this separation, a comparison ofsynthetic spectra with the observed ones isperformed to assure the quality of the results.
Once the good condition of the separation isassured, a synthetic reproduction of the 2012
Samara earthquake at stations that were notavailable at the moment of the event is perform.
2International Institute of Seismology and
Earthquake Engineering, Building ResearchInstituteThis information is used to estimate the
Figure 2. Anomalous intensity at the 2012 Sámara
site effect, i.e., amplification at those stations
earthquake (R.S.N., 2012).
during a major earthquake. The target frequency
range is from 1 Hz to 10 Hz, but the dataprocessing is done in the working frequency
range from 0.5 Hz to 10 Hz to expect the good results in a wider range.
2. METHODOLOGY
Spectral Inversion Method
The Spectral Inversion Method (Moya and Irikura, 2003) is applied to separate the source effect 𝑆𝑖 (𝑓),the propagation path effect, and the site amplification 𝐺𝑗 (𝑓), from acceleration spectra 𝑂𝑖𝑗 (𝑓) observedat the j-th site during the i-th event using some reference events as the constraints based on the 𝜔−2source spectral model (Aki, 1967). The requirements to implement this method suggested by Moya andIrikura (2003) are that the seismic moment and the corner frequency of the reference events should be
accurate. The empirical frequency-dependent radiation-pattern proposed by Satoh (2002) is used tocorrect the horizontal components of strong motions based on the 𝜔−2 model by studying the ratio of
SV/SH.
Synthetic Spectra
Once the inversion results are obtained, it is possible to estimate the acceleration spectra of the target
record 𝑂𝐼𝐽 (𝑓) , i.e., the record at the J-th station during the I-th event, even though not recorded in reality.
However, two element records are required together with the results of the spectral inversion: one
observed record of the i-th event at the J-th station 𝑂𝑖𝐽 (𝑓) that shares the station with the target record,
the other record of the I-th event at the j-th station 𝑂𝐼𝑗 (𝑓) that shares the event.
3. SEISMIC NETWORKThe present study is performed using strong motion records from the National Seismological Networkof Costa Rica (R.S.N.), which is a collaboration program between the Costa Rican Electricity Institute(I.C.E) and the University of Costa Rica (U.C.R). To constrain the determination of the corner frequencyof the reference event, the broadband station JTS000 from IRIS/IDA was also included (Figure 3).
Nineteen earthquakes with a magnitude between 5.0 and 7.6 catalog were selected from 2009 to 2019
(Figure 4). All the records were converted into the KNET (NIED, 2020) format using the program
developed by Dr. Yokoi at Building Research Institute (B.R.I.). An orientation correction was also
performed to the stations that were not aligned in the conventional NS/EW. In general, the I.C.E. stations
obtained better signal to noise ratio (SNR). For this reason, the I.C.E stations along with the IRIS station
JTS000 were selected to perform the inversion, while the Sixaola stations (U.C.R) were used for thesynthetic spectra calculation.

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Figure 3. Distribution of selected stations.

Figure 4. Distribution of the selected events.

4. ANALISIS AND RESULTS
The determination of acceleration source
spectra for the reference events is performed to
set the input acceleration as a base for the
spectral inversion. For this purpose, direct
fitting method was chosen to constrain thesource spectra. This method was applied
through the direct fitting of the synthetic
acceleration spectra to the observed ones of thebroadband station JTS000. The four events infigure 5 shown by broken curves don’t follow
Figure 5. Observed acceleration Spectra obtainedthe 𝜔−2 source spectral model and may haveat JTS000.
intermediate segment of source spectra
between the corner frequency of displacement
spectra and that of acceleration spectra. Therefore, I did not use these four events to prevent unnecessary
complication. Other six events have their corner frequency 𝑓0 sufficiently lower for that the flat level ofacceleration may cover the target frequency range. In this condition, it doesn’t matter if the events follow
the 𝜔−2 source spectral modelor not.
Consistency check
Due to an abrupt instability of the output from the spectral inversion, a suspicion arose on the correctnessof the input data themselves and the following way of the consistency check was conducted for all 20
stations. In the spectral inversion, it is assumed that each site must have its unique site effect althoughvarious earthquakes were observed there. For each of the six reference events, it is possible to calculate
the ratio of the observed spectra to the basement input, which is the product of the given source effectand the path effect. Here it is called “individual site effect”. These for a site should be similar to eachother. Therefore, the first consistency check method consists in obtaining the individual site effect of
the used stations for the reference events to detect the outlier curves (Figure 6). As the correct values
are not known, I cannot conduct anything except to eliminate the records that correspond to the outlier
curves from the input data of the spectral inversion.

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Figure 6. Example of an outlier curve (orangeline) detected using the Individual Site Effectconsistency check for LPSV00.

Figure 7. Consistency Check using Synthetic
Spectra.
“#06JTS0_#06LPPG_#10JTS”
and“#06JTS0_#06PPA8_#10JTS” consist of the target
record and two elements: one shares the event, theother shares the station with the target record.
“ObsRdpCor” denotes the observed record.

The second consistency check consist in comparing the synthetic records obtained using
the results of the inversion with the real observed one. I compare the synthetic spectra using various
combination of two element records and check outlier curves, and also the standard deviation among
estimated curves. For example, the event #6 (EQ1612010025) recorded at JTS000 was reproduced by
two sets of element records: one for #06 at PPA800 and #10 (EQ1711130228) at JTS000, the other for#06 at LPPG00 and #10 at JTS000 (Figure 7). The synthetic one by the former pair shows an acceptablesimilarity with the observed one, however the latter pair shows a drastic discrepancy. This seems to becaused by the record of #6 at LPPG00 because the other element record was shared. Thus, this record
was eliminated from the inversion. This second consistency check was conducted for all possible target
records where observed records exist.
Results of the Spectral Inversion
By the final spectral inversion, the value of 𝑄 = 179𝑓 0.5598 was calculated. The site effects are shownin their normalized version (Figure 8), along with the source spectra for the six reference events andevent #1 (2012 Sámara earthquake).

Figure 8. Source spectra and Site Effects normalized ones by PPA800
results from the spectral inversion.
Reproduction of Fourier Amplitude Spectra of the 2012 Sámara earthquake.
The capacity to reproduce the synthetic spectra can be checked by comparing the average synthetic
spectra with the observed ones and the standard deviation. The synthetic spectra can be calculated using
all the stations available and compare then with the real observed spectra, to confirm the quality of the
final result. Taking this into account, the synthetic acceleration spectra during the 2012 Sámara
earthquake were calculated at the stations where observed records do not exist. The Sixaola station
NICO00 located at the colonial city of Nicoya is the closest one to the epicenter of the 2012 Sámara
earthquake. Of the synthetic reproduction, this station had more stable behavior, without high frequency
decay and with some peaks at 1.3, 1.9 and 6.6 Hz (Figure 9). The Sixaola station PAQE00, located in
Paquera at southeast of the Nicoya peninsula, showed clearly bigger amplification around 2Hz in
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Figure 9. Examples of reproduction of Fourier Acceleration Spectra of the 2012 Sámara
earthquake at stations where the strong motion record was not obtained: JTS000 (top - left),
Sixaola stations POAS00 (top - right), RAMO00 (middle left), NICO00 (middle right), MEXI00
located in the national capital with the observed spectra at SGBA00 (dotted curve, bottom- left),and PAQE00 (bottom right). Gray shadow shows the standard deviation.
comparison with NICO00. To analyze the anomalous amplification for the Sámara earthquake at
Naranjo town, the synthetic acceleration spectra of the Sixaola stations RAMO00 and POAS00 werealso obtained. RAMO00, located in San Ramón at 9 km of Naranjo town, showed amplifications around
1 Hz and 2.5 Hz (Figure 9). Its amplitude is comparable with the NICO00 but smaller than PAQE00.
On the other hand, POAS00 located in San Pedro de Poás at 14 km east of Naranjo town, showed
amplification comparable with PAQE00 with the peaks around 1.3 and 2 Hz. Finally, the Sixaola station
MEXI00 is located at the center of the capital city San José. This station showed peaks at 1.2 Hz with astrong decay at high frequencies. Its acceleration spectra show a similarity with those of SGBA (Black
broken curve) suggesting the MMI VI in MEXI. Thus the reproduced acceleration spectra show aconsistency with an anomalous intensity distribution in Figure 9.
5. DISCUSION AND CONCLUSION
Costa Rica requires the implementation of suitable seismic hazard assessment. the understanding of thesite effect at specific sites can be vital for a proper design. Moya and Irikura (2003) proposed a method
to quantify the site effect through the separation of the source and the path. For this, it is necessary thatthe reference event follows the 𝜔−2 source spectral model. However, this requirement was not always
satisfied. The separation of the corner frequencies into an intermediate segment and the exceptionallyhigh frequencies in some cases reflect the necessity for further source process studies in the region. The
events that did not follow the 𝜔−2 model were excluded from the analysis.
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The direct fitting method was applied to constrain the source spectra for the inversion. Thismethod was applied using the JTS00 broadband station of IRIS/IDA. The synthetic amplification spectra
method proved to be suitable as a checking method to assure the quality of the inversion results, andalso as a method to reproduce the Fourier amplitude spectra. The exclusion of outliers records wasnecessary due to the low SNR and strange behavior of some of the records. The resulting value of 𝑄 =170𝑓 0.5598 is considered representative for the north and central part of Costa Rica. This value has agood agreement with the study of Moya (2009), in which the author estimated a value of 𝑄 = 131.6𝑓 1.1
for the central part of the country. The attenuation values can be associated to the volcanic deposits andthe crustal deformation of this region.
Using the inversion results, the synthetic amplification spectra method was implemented
to calculate the 2012 Sámara earthquake (Mw 7.6) amplification at Sixaola stations. The Sixaola stations(R.S.N.- U.C.R.) NICO00 and PAQE00, located at Nicoya peninsula and the closest to the epicenter,show very different amplification behaviors related to the difference of the surface geology. The
synthetic results of Sixaola stations RAMO00 and POAS00 reflected important peak accelerations
around 1.3 and 1.8 Hz. The acceleration estimated for POAS00 station goes up to 300 gal. These results
have a good agreement with the intensity anomaly reported during the 2012 Sámara earthquake, with
MMI modified Mercalli Intensity up to VII were reported in the area R.S.N. (2012).
The acceleration spectra obtained at MEXI00 station, located at the central part of thecapital, showed amplifications similar to the observed ones at SGBA00 during this event. The estimationof an MMI intensity of VI for the capital has a good agreement with the eyesight reports (R.S.N., 2012).
The results obtained at the present work need to be extended with a bigger database for theSouth part of Costa Rica and North Panama. The synthetic spectra method applied in this study can beused in the future for further estimations at areas of interest.
ACKNOWLEDGEMENTS
This research was conducted during the individual study period of the training course “Seismology,
Earthquake Engineering and Tsunami Disaster Mitigation” by the Building Research Institute, JICA,
and GRIPS. I would like to thank Dr. Toshiaki Yokoi for developing the software tools necessary forthe analysis made in this project and for his guidance. My appreciation extends to all the teachers andstaff members of BRI. I would like to thank Mr. Luis Fernando Barrantes and Ms. Rosey Piedra, fromthe Instituto Costarricense de Electricidad (I.C.E.) and to Ms. Ivonne Arroyo and Mr. Lepolt Linkimer
from the U.C.R. (RSN-UCR) for providing all the data and the catalog necessary for this paper.
REFERENCES
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Moya, A. & Irikura, K., 2003, Estimation of Site Effect and Q value Using a Reference event, Bulletinof the Seismological Society of America 94, 1730-1745.
Moya, A., 2009, Inversion of site effects and Q value using spectral ratios, Estudios Geologicos 65, 67– 77, DOI:10.3989/egeol.39591.047
National Research Institute for Earth Science and Disaster Resilience (NIED), 2020, Kyoshin Network
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Montero, W., 2001, Neotectónica de la Región Central de Costa Rica: Frontera Oeste de la Microplaca
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