Citation:
Olivar, M., T. Yokoi, T. Hayashida (2021), Site effects estimation from strong ground motion
and microtremor records around the city of Tsukuba, Synopsis of IISEE-GRIPS Master’s Thesis.

SITE EFFECTS ESTIMATION FROM STRONGGROUND MOTION AND MICROTREMOR RECORDSAROUND THE CITY OF TSUKUBA
Mónica Beatriz Olivar Amaya1,2Supervisor: Toshiaki YOKOI3, Takumi HAYASHIDA3
ABSTRACTWe obtained the site effects from two strong motion observation sites around the City of Tsukuba, withstrong ground motion and microtremor records. We estimated the Horizontal-to-Horizontal Spectral
Ratio (HHSR), which is a direct estimation of the site amplification, and the Horizontal-to-Vertical
Spectral Ratio (HVSR) from 13 earthquakes recorded at a KiK-NET station. We also calculated the
HVSR for microtremor records from measurements of a broadband seismometer and a strong motion
accelerometer, and the dispersion curves of Rayleigh waves from array measurements performed withbroadband seismometers, and short period sensors. With these products we performed the joint inversion
analysis and obtained the S-wave velocity structure for three groups of data: the reference group, when
we perform a single point measurement and array measurements with broadband sensors; the groupcalled Case-1, when we perform a single point measurement with a broadband sensor, but do not haveenough broadband seismometers to perform an array, so we use short period seismometers; and thegroup called Case-2, when we do not have any broadband sensor to perform single point and arraymeasurements. This way we highlighted the necessity of a broadband sensor to perform this type ofanalysis. Additionally, we estimated the theoretical site amplification factor, with the velocity structure
obtained from the joint inversion of the reference data. We concluded that we can obtain a reliable
inverted velocity structure with at least, one broadband sensor. The theoretical amplification factor basedon the reference inverted velocity structure can give a good and reliable estimation of the amplification
factor of the site. The HVSR of earthquakes and microtremor records cannot be regarded as site
amplification factor, however, they are useful to determine the resonant frequencies.
Keywords: Site Effects, Joint Inversion, Broadband Sensor, Microtremor.
1. INTRODUCTION
This study is aimed to perform a case study of site effect estimate in a well-controlled condition withborehole records, and an application of the latest methods for microtremor records, including theapplication of the seismic interferometry. The target area is the central part of Tsukuba City, where the
Building Research Institute (BRI) and the National Research Institute for Earth Science and Disaster
Resilience (NIED) keep strong motion observation stations, among them Tsukuba City Hall (TKC) andIBRH10, respectively. Additionally, it is intended to emphasize the necessity of a broadband sensor toperform the analysis of the site characterization, estimating the S-wave velocity structure and the site
1

GENSAI Project II, El Salvador.
IISEE-GRIPS Master’s course student.
3International Institute of Seismology and Earthquake Engineering, Building Research Institute.
2

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amplification, and to check the feasibility of using the HVSR of Strong Motion records in place of the
Broadband sensor. The results of this study will be very useful to apply the technology and methods forthe seismic hazard assessment in the Metropolitan Area of San Salvador, El Salvador.
2. DATAThe target area of this study is the City of Tsukuba, located at the rim of the tectonic Kanto basin, about
60 km North-East of Tokyo. The strong-motion observation sites used in this study are located aroundthe central part of Tsukuba City. The analyzed sites are IBRH10, a KiK-NET Strong Motion
Observation Station deployed by the NIED; and TKC in Tsukuba City Office deployed by the BRI to
observe seismic response of this base-isolated building of 7 stories, of which a sensor is installed at thebasement floor. IBRH10 is located on fluvial sediment of the Holocene age, and TKC is located on
middle terrace of Late Pleistocene epoch. In this study we selected thirteen earthquakes with magnitudes
from 4 to 6, of which epicenters are near the target sites. We also use the information of the velocity
structure measured at the borehole of IBRH10 for comparison.
For the microtremor analysis we use the records for IBRH10 and TKC stations shown in
Table 1.
Table 1: Microtremor single point and array measurements
IBRH10 Measurements
TKC Measurements
3 channel single point measurement (CMG40T, [0.033-50] Hz)
3 channel single point measurement (JEP6A3, Accelerometer 2[V/G])
7 points array (VSE12-CC [0.05-100] Hz side 3 points triangular array (CMG40T, side length:
lenght: 600 m, 40 m, radius: 2 m)
35 m)
7 points array (L22D, 2 Hz, radius: 2 m)
7 points array (L22D 2 Hz, side length: 4 m, 8 m)
3. METHODOLOGY
3.1.

.Direct Estimation of Site Amplification Factor and HVSR of Strong Motion andMicrotremor Records

The soil-to-rock spectral ratio HHSR(EQ) for strong motion directly provides the amplification factorof the S wave and it can be determined utilizing the strong ground motion records obtained from thesurface and from the borehole drilled into bedrock. On the other hand, the HVSR is used to assess theresonance frequencies of the surface soil layers. In this study, we apply the Fast Fourier Transform toobtain the Fourier Spectra and then, we estimate the HHSR(EQ), HVSR(EQ) and HVSR(MT) with thequadratic mean formula (Arai and Tokimatsu, 2004).
For the strong motion records, we calculate the HHSR for the S-wave windows, withwidths of 10.24 seconds measured from the S-wave onset; we calculate the HVSR(EQ) for the S-coda
windows with widths of 81.92 seconds taken from 20 seconds after the S-wave onset. For the
microtremor records, to calculate the HVSR(MT) we use different time windows depending on the howoften traffic noises appear in the records.
3.2.

Spatial AutoCorrelation (SPAC) Method

The SPAC method was proposed by Aki (1957; 1965). This method allows to determine the phasevelocity of surface waves that comes from different directions recorded by a bi-dimensional array ofseismographs, where the vertical component of the microtremor records is dominated by Rayleigh waves.
According to Okada (2003), the coherence function (SPAC coefficient) is obtained by the azimuthal
average of coherency between microtremor records observed by two sensors, and it is written as:

2𝜌 𝑟 ,𝜔

12𝜋

𝐸 ∅ 𝜔, 𝑟, 𝜃𝑑𝜃𝐸 ∅ 𝜔, 0,01
2𝜋

𝑅𝑒 𝐸 𝐶 , 𝜔, 𝑟
𝐸𝐶, 𝜔

𝑑𝜃

𝐽

𝑟𝜔
𝑐 𝜔

,

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where 𝜌 𝑟 , 𝜔 is the SPAC coefficient; 𝐴 0,0 and 𝐵 𝑟, 0 represent the location of the sensors;
𝐸 is the ensemble average over time blocks; 𝑅𝑒 denotes the real part of a complex number; 𝐶 , 𝜔
is the cross-spectrum between sensors 𝐴 and 𝐵 ; 𝐶 , 𝜔 is the power spectrum of sensor 𝐴 ;𝐽
3.3.

is the zero order Bessel Function of the first kind; and 𝑐 𝜔 is the phase velocity.
Joint Inversion of HVSR(MT) and Dispersion Curves of Rayleigh Waves

In this study, we perform the joint inversion of the HVSR(MT) and the Dispersion Curves of Rayleighwaves using the diffuse field theory (HV-Inv, García-Jerez et al., 2016). This method shows thepossibility of recovering the Green’s functions under the diffuse wavefield conditions (Salinas et al.,2014), it is derived from the energy equipartition principle (Sánchez-Sesma et al., 2011). It has been
established that if we assume that the seismic noise is diffuse, it is possible to express the HVSR(MT)in terms of the imaginary part of the Green’s function. The imaginary part of the frequency domain
Green’s function for a receiver and source that are coincident at the location 𝑥, measures the injected
power into the system by the unit harmonic load 𝑢 , considering waves emitted and returned to thesource; this allows us to express the directional energy density at a point 𝑥 as:
𝐸

𝑥, 𝜔

𝜌𝜔 〈𝑢

𝑥, 𝜔 𝑢∗ 𝑥, 𝜔 〉2𝜋𝜇𝐸 𝑘Im 𝐺𝑥, 𝑥, 𝜔,2where 𝜌 is the mass density; 𝜔 is the angular frequency; 𝜇 is the elastic shear modulus; 𝑘 is the𝑥, 𝑥, 𝜔 is the imaginary
shear wave number; 𝐸 is the average density of shear waves; and Im 𝐺
part of the Green’s function of the displacement 𝑥 in the direction 𝑚 , produced by a unit loadcoincident with the same direction and point.
HVSR(MT) can be expressed as:
𝐻/𝑉 𝑥, 𝜔𝐸 𝑥, 𝜔
𝐸 𝑥, 𝜔
𝐸 𝑥, 𝜔

Im 𝐺

𝑥, 𝑥, 𝜔Im 𝐺

Im 𝐺𝑥, 𝑥, 𝜔𝑥, 𝑥, 𝜔,3

where 𝐸 , 𝐸 , and 𝐸 are the directional energy density at a point 𝑥, allow us to obtain the theoretical
HVSR(MT) for the specific geometry and material properties of a site: 𝛼 , 𝛽 , 𝜌 , and ℎ . The
parameters correspond to the P-wave and S-wave velocities, mass density, and thickness of the i-th layer,
respectively, of a ground structure made of isotropic elastic layers.
4. RESULTS AND DISCUSSION
The result of the HVSR and SPAC analysis are shown in Figure 1, where Figure 1a and Figure 1b show
the HVSR of the broadband seismometer HV_ref (blue curve) and strong motion accelerometer HV_AC(orange curve) for IBRH10 and TKC respectively. In the case of IBRH10, we can see a clear peak ataround 1 Hz for both sensors, but at 0.3 Hz, HV_AC is almost four time smaller than the HV_ref. Thiscan be explained analyzing the Power Spectral Density (PSD) of the sensors, which showed that with
the HV_AC we lose information in the low frequency range, where the components of the PSD arealmost flat, this might be due to electric noise in the measuring instruments. The case of TKC is similar,
we can see in Figure 1b that in the low frequency range, the HV_AC does not show any peak at 0.3 Hz.
Without a broadband sensor we cannot obtain reliable information in the low frequency range. Figure
1c and Figure 1d show the dispersion curves of Rayleigh wave for the broadband sensors array DC_ref(blue curves) and short period sensors array (orange curves), in both cases we can see than thefrequencies bellow 3 Hz cannot be covered with a short period array.

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The results of thejoint inversion for IBRH10 isshown in Figure 2. The
computed
andobservedmodels of HV and DC showed
a good correlation in shapeand amplitude, this gives as
result the reference inverted
P-wave and S-wave velocities,(a)(b)
and density structure, which
are shown in Figure 2a. We
can observe a discontinuity at
570 m of depth, whichindicates the presence of hardrock. This result of theinversion is acceptable by its
similarity to the structure
based on the PS-Logging.
(c)(d)
Figure 2b shows the
Figure 1. HVSR and dispersion curves of IBRH10 and TKC. (a) andinverted velocity structure for(b) show HVSR of broadbad sensor (blue curves) and accelerometer
the Case-1, using the HV_ref,(red curves). (c) and (d) show dispersion curve of the broadband
and DC_SP. The observed
sensor array (blue curves) and short period seismometers (orange
curves and the computed ones
curves)show good correlation, andthe results agree well with the reference model. Although the DC_SP cannot cover the frequency range
below 3 Hz, the results indicate that this shortcoming is covered by the HV_ref. It can be pointed out
that, even without a broadband array, we can obtain reliable results. For the Case-2 there was not a goodcorrelation between the computed and observed models, therefore, we could not obtain any acceptable
and reliable velocity structure.
The reference
velocity - density
structure for TKC,
inverted from the
HV_refand
DC_ref, is shownin Figure 3a. The
computed HVSR
and DC curves
agree well with theobserved HV_ref
and
DC_ref,(a)(b)
showing a good
Figure 2. Results of the joint inversion for IBRH10. (a) shows the inverted
correlation. In thevelocities – density structure using HV_ref and DC_ref. Red lines indicate thevelocity structure
best model among computed ones for Vp, Vs, and Density. The color scale
there is a clear
indicates the misfit of the computed models with the observed data. (b) shows
discontinuity,
a comparison of the inverted velocity structures for IBRH10 between thea jump of Vs to avelocity structure of Case-1 and the reference velocity structure. Broken lines
bigger than 1,000
indicate the reference velocity structure. Green lines indicate the S-wave
m/sec, at around
velocity structure, whereas red ones the P-wave velocity structure.
510 m depth, whichindicates the presence of hard rock. The structure below this clear discontinuity might be not reliable.

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In this site, any information obtained by drilling is not available. Neither shallow structure, nor deep
one. We use this structure obtained from the HV_ref, and DC_ref as reference structure for TKC.
Figure 3b
shows the inverted
structure for the
Case-1, using the
HV_ref,and
DC_SP for TKC.
The
observed
curves and thecomputed
ones
using the inverted
structure agree well,and the results are(a)(b)
similar with the
Figure 3. Results of the joint inversion for TKC. (a) shows the inverted
reference model. It
velocities – density structure using HV_ref and DC_ref. Black lines indicate
can be pointed out
the mean model for Vp, Vs, and Density among computed ones. (b) shows athat, even without acomparison of the inverted velocity structures for TKC between the velocity
broadband array,
structure of Case-1 and the reference velocity structure.
we can obtainreliable results.
Regarding Case-2, we could not obtain any
reliable velocity structure. Using strong motion
accelerometer for a single point measurement,
and an array measurement composed of shortperiod seismometers, it is very hard to obtainacceptable results because we do not havereliable information for the low frequency range.
Figure 4 shows the comparison of thetheoretical amplification factor obtained fromthe reference velocity structure of IBRH10, with
the HHSR(EQ), HVSR(EQ), and HVSR(MT).
We can point out that the theoreticalamplification factor is similar in shape to the
HHSR(EQ), but it underestimates the amplitudeof the peaks for frequencies larger than 0.7 Hz.
All the spectral ratios show peaks at 0.3 Hz, andat around 1 Hz. Additionally, we can mention
Figure 4. Comparison of the Theoretical Sitethat HVSR(EQ) differs from HVSR(MT) on its
Amplification Factor (from Vs_ref), HHSR(EQ),
amplitude, however, both show information of
HVSR(EQ), and HVSR(MT).
the bedrock in the low frequency range.
Therefore, we cannot use the HVSR(EQ) as a proxy of HVSR(MT) to estimate the inverted velocity
structure in case of the absence of a broadband sensor to perform single point microtremor measurement.
Finally, we can see that above 1 Hz the amplitude of the HHSR(EQ) is the greatest, followed by thetheoretical amplification factor, the HVSR(EQ), and the HVSR(MT) respectively. We can mention thatthe theoretical amplification factor, based on the estimated velocity structure using the joint inversionof the HV_ref and DC_ref, can give a good and reliable estimation of the amplification factor, but it still
underestimates it. This might be due to the influence of the attenuation factor.
5. CONCLUSIONS
We determined the site characteristics with strong ground motion and microtremor records at two strong
motion observation sites, IBRH10 and TKC. The data used in this study are strong motion records of 13

5earthquakes for the KiK-NET station IBRH10, and microtremor single point measurements and arraymeasurements in IBRH10 and TKC. For the strong motion records, we calculated the HVSR for the Scoda windows, and the HHSR for the S-wave windows using the bottom of the borehole as a reference
site. We also calculated the HVSR for all the single point microtremor measurements, and divided theminto two groups: HV_ref, which were calculated with the records obtained by a broadband seismometer;and HV_AC, with the records obtained by a strong motion accelerometer. Additionally, we estimatedthe dispersion curves of Rayleigh waves from the microtremor array measurements, we called DC_ref
to the ones obtained with broadband seismometer array measurement, and DC_SP to the ones with shortperiod seismometer array measurement. With the HVSR and DC, we performed the joint inversion forthree different groups of analysis and obtained the S-wave velocity structure for each group. With thisinformation, we calculated the theoretical site amplification factor for the IBRH10 station, and compared
it to the HHSR, and HVSR of strong motion and microtremor records. The results are summarized asfollows:
1. Using strong motion accelerometer to perform single point microtremor measurement we lose
information in the low frequency range of the HVSR (HV_AC), where the peaks are very small
or nonexistent due to its low sensitivity, while using a broadband sensor we obtain large peaksin the low frequency range.
2. For the dispersion curves of Rayleigh waves, we cannot cover the frequency range below 3 Hz
using microtremor array measurements obtained by short period seismometers. Although the
DC_SP cannot cover the frequency range below 3 Hz, the results of the joint inversion indicatethat this shortcoming is covered by the HV_ref. Even without a broadband array, we can obtaina reliable velocity structure.
3. Without a broadband sensor, we cannot obtain a reliable velocity structure. For this analysis weneed at least one broadband sensor of three components.
4. The theoretical amplification factor based on the estimated velocity structure using the joint
inversion of the HV_ref and DC_ref, can give a good and reliable estimation of the amplification
factor, but it still underestimates the amplification factor due to the influence of the attenuation
factor.
5. The HVSR(MT) and HVSR(EQ) cannot be regarded as site amplification factor, but they allow
us to obtain the frequency of the resonance peaks.
6. HVSR(EQ) cannot be considered as a proxy of HVSR(MT) for the joint inversion process, incase of the absence of a broadband sensor.
ACKNOWLEDGEMENTS
This research was conducted as the individual study of the training course “Seismology, Earthquake
Engineering and Tsunami Disaster Mitigation” by IISEE/BRI, JICA, and GRIPS. I would like to express
my sincere gratitude to my supervisor Dr. Toshiaki Yokoi, for his for this continuous support, guidance,and valuable comments during my individual study. I am also thankful with my co-supervisor Dr.
Takumi Hayashida, for his suggestions and guidance.
REFERENCES
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Aki, K., 1965. Geophysics, 30(4), 493-667.
Arai, H., and Tokimatsu, K. (2004). Bulletin of the Seismological Society of America, 94(1), 53-63.
García-Jerez, A., Piña-Flores, J., Sánchez-Sesma, F. J., Luzón, F., & Perton, M. (2016). Computers &geosciences, 97, 67-78.
Okada, H., 2003. Geophysical Monograph Series Number 12.
Salinas, V., Luzón, F., García‐Jerez, A., Sánchez‐Sesma, F., Kawase, H., Matsushima, S., Campillo, M.,
2014. Bulletin of the Seismological Society of America, 104(2), 995-1001.
Sánchez-Sesma, F. J., Rodríguez, M., Iturrarán-Viveros, U., Luzón, F., Campillo, M., Margerin, L.,
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