VALIDATION OF SPAC AND HVSR METHODS, AN
EXPERIMENTAL STUDY
Agha BABAR Ali Khan ∗MEE09184

Supervisor: Toshiaki Yokoi ∗∗ABSTRACTPakistan is an earthquake prone country. A wide area including major cities is covered by thicksediments and the amplification of seismic waves is likely to occur. Studies to estimate velocity
structure and amplification ratios in sedimentary layers in various parts of country are necessary. The
microtremor can be considered as a dominant tool for estimating the earthquake site response.
Therefore, the two methods, i.e., SPAC and HVSR, selected to carry out the present study are mainly
based on microtremor. This study was carried out to check the validity of these microtremor methods.
The focus was on the estimation of subsurface shear wave velocity structure and the calculation of theresonant frequency and/or the amplification of seismic waves in sedimentary layers. Velocity
structures estimated by SPAC method were reliable and fairly accurate. The HVSR curve
corresponded to the resonant frequency of the thick sediments but no clear relationship was foundbetween this ratio and the amplification of waves.
Keywords: Amplification of seismic waves, velocity structure, microtremor, SPAC, HVSR.

1. INTRODUCTION
It is earnestly needed first to carry out a detailed study to estimate the sedimentary thickness at various
areas in the country and secondly to determine the level of shaking while considering the amplificationof seismic wave in those areas and eventually to upgrade the building codes and by laws accordingly.
The methods used in this study are the SPatial AutoCorrelation (SPAC) and the Horizontal to Vertical
Spectral Ratio (HVSR). Both of these methods have characteristics of being cost effective,noninvasive and reliant on passive source(s). Also they do not have any bad impact on theenvironment. These features make these methods more practical for their implementation in urbanizedareas.

2. METHOD
For the evaluation of expected level of earthquake damage at a given site, Horizontal to Vertical
Spectral Ratio (HVSR) method is used. It was empirically found by Nakamura (1989) and based on
short period microtremor but have been extended to the longer period range up to 10 s. The HVSR
reflects the S-wave resonance on soft surface layer. However, this hypothesis has been contradicted byseveral other researchers who argue that there is a relationship between the ellipticity of the Rayleighwaves of fundamental mode and the HVSR curves, e.g., Bonnefoy-Claudet (2004) and Yamanaka et al.
(1994).
Aki (1957) proposed a theory based on the relationship between the temporal and spatial
spectra of seismic waves to obtain phase-velocity dispersion curve. Based on this theory, he developed∗

Pakistan Meteorological Department (PMD), Islamabad, Pakistan.

∗∗

Senior Research Scientist, International Institute of Seismology and Earthquake Engineering, Building
Research Institute, Japan.

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an array technique called SPatial AutoCorrelation (SPAC) microtremor method to determine theunderlying subsurface velocity structure of the S-waves and phase velocity of Rayleigh waves using
short period microtremor with frequency more than 1.0 Hz. The SPAC coefficient is a function of thefrequency and phase velocity based on the distances between various stations in the array is a quantity
to be calculated firstly during data analysis.

3. DATA ACQUISITION AND ANALYSIS
In this study two microtremor datasets were processed by SPAC and HVSR methods. One of them istermed as Dataset N101. This dataset consists of the synthetic microtremor waveform computed for
1D model. The simulation was done using the finite difference method (Cornou et al. 2006). The rangeof frequency for this dataset is from 0.1 Hz to 20 Hz. The array of receivers used to simulate Dataset
N101 comprised of fifteen stations in all and consisted of one equilateral triangle with side 150 m,within which there was a regular hexagon of side 24 m and a smaller regular hexagon of side 6 m,
The other dataset was obtained from two field surveys at the same site. First field survey was
performed from March 5 to 7, 2009 and the other was from June 15 to 17, 2010, and the site for thesefield surveys was located near the Toyota Community Baseball Ground, Jyoso City, Ibaraki Prefecture,
Japan. The suspension P- and S-wave (PS) velocity logs (SPSVL) method was earlier applied before
these two surveys at this site and the data so obtained then from SPSVL method was used as areference model in the present study. There are two main roads passing nearby the site for field survey,
which are regarded as the main source of microtremor for this field survey. The VSE12-CC (0.01 Hz
to 100 Hz) feed back type long period velocity seismometers were used in both field surveys. The
seismometers had sensitivity 5.0 V/cm/s and the manufacturers are Tokyo Soku-shin Ltd. The 24 bit
single channel digital recorders McSeis-MT were used on the field. Their frequency coverage is fromDC to 500 Hz (manufactured by OYO Co.). During the field surveys in March, 2009 and June, 2010
equilateral triangular arrays with a side length of 150 m and 600 m each were deployed, respectively.
Each array had seven stations.
3.1 Data Analysis for SPAC
The sampling rate at the data acquisition in the field was 100 Hz. A digital anti-alias low pass filtering
technique was applied on this dataset. This filtered data was re-sampled at a new sampling interval of
0.04 s. The length of time block used was 512 data and the consecutive time blocks were overlapped
50% upon each other. Then screening was done which had two steps. 1st step: Elimination of the time
blocks that contained impulsive noise due to traffic. The time blocks of which maximum absolutevalue exceeded "a" times of its root mean square amplitude within the same time block were excluded
from the analysis. 2nd step: Elimination of the time blocks of which root mean square amplitude was
deviated "b" times of the standard deviation from the average of root mean square amplitude over alltime blocks survived from the 1st step. The values of "a" and "b" were set as 4.0 and 2.0 respectively
for both datasets, i.e., Dataset N101 and data from field survey. It was necessary to give the value ofthe band width of the Parzen window. In the present analysis, its value was set equal to 0.04 for bothdatasets. From this procedure SPAC coefficient was yielded.
The next step was to estimate the dispersion curve from SPAC coefficients. For this purpose,the inversion of SPAC coefficient ρ(ω,r) was done within a frequency range corresponding from kr =0.0 to the first trough of J0(kr), the Bessel’s function of first kind and zero order. In the process offinding the dispersion curves from the SPAC coefficient, heuristic searches were also conducted using
the downhill simplex method (DHSM, e.g., Press et al. 2002) combined with the very fast simulated
annealing method (VFSA) proposed by Ingber (1989). The combined method is called the
DHSM-VFSA.
The inversion of underground velocity structure from the dispersion curve of Rayleigh waves
is done using the optimum, namely, the fastest schedule. According to Yokoi (2005) the parametersdescribing the cooling schedule of VFSA are t0, m, and n, having values equal to 1.0, 0.6 and 1.3,

2mrespectively. The cooling schedule itself can be given as, tk = t0 exp( -nk ), where tk denotes thetemperature at the k-th step iteration (Ingber 1989; Yamanaka 2004). The compressional wave velocity
Vp was calculated from shear wave velocity Vs using the formula Vp = 1.11 Vs + 1.20 (km/s) proposedby Kitsunezaki et al. (1990).
3.2 Data Analysis for HVSR
For data analysis, the data recorded in all was divided into several time windows. Then
aforementioned screening was applied. After that Fast Fourier Transform (FFT) was applied to obtain
power spectra of each time block for two horizontal and one vertical component. These power spectra
were averaged over the time blocks survived from the screening. In order to get a better correlation
between the amplification factor of shear waves and peak values in HVSR, Konno and Omachi (1998)
smoothing function was applied to the curves of averaged power spectra. Finally horizontal to vertical
spectral ratios were generated

4. RESULTS AND DISCUSSION
4.1 Dataset N101
The SPAC coefficients for each inter-station distance in an array were calculated and plotted against
the frequency, as seen in Figure 1. The curves for each inter station distance r shown with different
colors and patterns, look like the one for Bessel’s function of first kind and zero order.
1

6.0m
11.0m
18.0m
23.0m
24.0m
28.0m
40.0m

0.5

SPAC Coefficient

SPAC Coefficient

1

0

23.0m
40.0m
66.0m
77.0m
83.0m
100.0m105.0m
112.0m155.0m

0.5

0

-0.5

-0.5
0

2

4

6

8

0

10

2

4

6

8

10

Frequency (Hz)Frequency (Hz)Figure 1. SPAC coefficients obtained from
(Left: Small array, Right: Large array) Dataset N101.

3

0.6

Observed Velocity

Calculated Velocity

0.5
Velocity (km/s)

After performing the inversion process inorder to find the phase velocity c( f ), a dispersion
curve was achieved as shown in Figure 2. It can beseen clearly that the best fitting of the observed
dispersion curve with that of theoretical one isfound at lower frequency e.g., below 2.5 Hz. The
velocity model obtained after performing heuristic
search is shown in Figure 3. The dashed lines show
the velocity model obtained after applying the
SPAC microtremor method while the solid lines
show the one theoretically calculated and used as areference model. At shallow depths the differenceof Vs in both models is very small, but in deeper

0.4

0.3

0.2
1

2

3

4

5

6

7

Frequency (Hz)Figure 2. Dispersion curve from Dataset N101.

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Depth (m)Velocity (m/s)
parts this difference becomes significant. In contrast to
0
500
1000
1500
2000
2500
3000
the compressional wave velocity Vp, the shear wave
0
Vs-Refvelocity Vs, has values very close to each other in both
Vp-RefVs-Obsvelocity models. The estimated Vs values had a good
Vp-Obs50
agreement on the average with those provided in thereference model. The number of layers given in theestimated Vs profile was less than that in reference
100
model but the noticeable fact is that there was gradualincrease in the velocity with depth in the reference
model while clear contrasts were assumed at each150
interface of every layer in estimated model. That is
why it is asserted that the Vs values yielded from
200
Dataset N101 had a good agreement on the averagewith those in the reference model.
The HVSR curve obtained by processing
250
Dataset N101 had a maximum at a value slightly lower
than 4.0 on vertical axes. This value of HVSR did not
300
fulfill the criteria set by Horike et al. (2001) for peakvalue of HVSR to be pronounced as the resonant
Figure 3. Velocity model comparison
frequency of sedimentary layer. Hence, the limitationfrom Dataset N101.
of HVSR method was observed. By comparing the
HVSR from each receiver with their average, it was found that the curves so obtained had stability at
frequency band under consideration, which implied the reliability of calculated HVSR.

4.2 Data from Field Survey

10.0

1

Figure 4. HVSR curves
for Dataset N101.10
1

0.1

Frequency (Hz)115.4m200.0m305.5m346.4m400.0m461.9m529.1m600.0m0.75
SPAC Coefficient

SPAC Coefficient

0.5

1.0

1

43.3m
75.0m
86.6m
129.9m150.0m0.75

H/V

The curves for SPAC coefficient plotted against
frequency are shown in Figure 5. In case of both large
and small array, it can be seen that the curves are notas smooth as in an ideal case for plotted Bessel’sfunction. However, their characteristics are similar to
the Bessel’s function i.e., the first peak value is lying
close to 1.0 and then gradually decaying. The peaks of
SPAC coefficient curves do not lie at 0.0 Hz becauseof the limitations of frequency coverage of equipments
used.

S1032
S1046
S1113
Av All

0.25
0

0.5
0.25
0
-0.25

-0.25

-0.5

-0.5
0

2

4

6

8

0

10

2

4

6

Frequency (Hz)Frequency (Hz)Figure 5. SPAC coefficients, obtained from (Left: Small array with radius = 150
m. Right: Large array with radius = 600 m) field survey data.

4

8

10

Hz. Also due to the paucity of data at lower
frequency range, the HVSR from microtremor isalso considered at higher frequencies e.g., higherthat 4 or 5 Hz.

The observed dispersion curve is in good fittingwith the theoretical one at almost all thefrequencies, as can be seen in Figure 6. The
reason for this good fitting may be the size of thearray. The larger arrays are designed usually toinvestigate the deeper parts of the sedimentary
structures. The frequency range of the waves
recorded with the help of large arrays is mostly
very small e.g., in the case under consideration,
the frequency ranges from 0.4 Hz to 2.6 Hz.
The estimated velocity model has verysmall contrasts with the reference model. As it
can be seen from Figure 7 that right from thesurface of the ground to depths as shallow asaround 580 m, the velocities are in niceagreement with each other. However, parts
deeper than that have a clear contrast. The reason
for this big difference in velocities is the size ofthe array. The radius or lateral extent of thearrays used for field survey, were 150 m and 600
m. While applying a geophysical exploration
technique, especially using an array method, it isbelieved that the deepest possible depth exploredis of the order of the size of array. Therefore, it
can be seen clearly that the values of velocities
are very close to each other at a depth shallower
than 600 m which is also the lateral extent of thelarge array.
The values of Vs at all depths were inconcise agreement in case of microtremor datafrom field survey. The depth resolution ofinterfaces of some sedimentary layers withrespect to the reference model had differences. In
spite of this minute discrepancy, the overall goalof estimation of Vs was achieved successfully.
The microtremor data from single stationin the field survey were used to calculate H/Vspectral ratio and a curve for the same wasplotted against frequency, as shown in Figure 8.
In order to check the reliability of the HVSR,
these ratios were also calculated using the recordof aforementioned July 4th event. The horizontal
to vertical Fourier ratio, hereafter referred as
H(S)/V(S), for this event was calculated, for dataof ground motion from surface and also thehorizontal to horizontal Fourier ratio, hereafterreferred as H(S)/H(B), for data of ground motion
from bottom seismometer. These ratios have beenplotted against frequency and shown in Figure 8.
The earthquake records had not sufficient signal
to noise ratio in the frequency range lower thanaround 0.6 Hz; therefore, the frequency underconsideration in this case was set higher than 0.6

2

Observed Velocity

Calculated Velocity

Velocity (km/s)

1.5

1

0.5

0
0

0.5

1

1.5

2

2.5

3

Frequency (Hz)Figure 6. Dispersion curve from field survey data.
Velocity (m/s)
0

1000

2000

3000

0

4000

5000

6000

Vp-RefVs-Ref100

Vp-Obs
Vs-Obs200

300

Depth (m)

400

500

600

Figure 7. The comparison of velocity model forthe field survey data is illustrated.

H / V & Amplification

100

HVSR
H(S)/H(B)
H(S)/V(S)

10

1

0.1
0.1

1
Frequency (Hz)Figure 8. Curves showing HVSR (green) and
H/V Fourier spectral ratio (red) from surface
seismometer and the ratio between the vector
sums of horizontal components at surface tobottom seismometers at IBRH10 (blue).

510

In case of HVSR computed from field survey microtremor data and that from the earthquake
record from surface seismometer at IBRH10 station, a good agreement was observed between thedominant peaks of curves. Horike et al. (2001) showed that HVSR of microtremor is comparable withthose of earthquake records or relatively smaller. Figure 8 shows the same tendency. No clear
relationship was found between HVSR of microtremor and H(S)/H(B) of earthquake which is
generally regarded as amplification.

5. CONCLUSIONSThis study was based on experiment for the validation of SPAC and HVSR microtremor methods.
Two datasets were processed by SPAC method, one is the field survey while the other syntheticallysimulated. In addition, an earthquake record from surface and borehole seismometers was also taken
into account to check the reliability of results from field survey data processed by HVSR method.
For Dataset N101, the number of layers was different for estimated and reference model.
However, there was a significant match between the two velocity models. For the data from fieldsurvey, the estimated velocity structure of shear waves was in good comparison with its reference
model. The curve of H/V spectral ratio obtained from microtremor had similar characteristic ascompared with that of the earthquake data recorded by the seismometer at ground surface. The ideathat there exists a relationship between HVSR of microtremor and that of earthquake records was
supported by this study. The comparison between S-wave amplification from earthquake record and
HVSR from microtremor did not show any resemblance. Therefore, the idea that there exists a
relationship between H/V spectral ratio and amplification of waves in sedimentary layers was notsupported by this study.

AKNOWLEDGEMENT
The author would like to express his gratitude to Dr. Koichi Hayashi, OYO Corporation, Tsukuba,
Japan and Prof. M. Saito for the subroutine package of the digital filter (Saito 1978) and DISPER80(Saito 1988). It is worthwhile mentioning gratitude to Dr. Qamar-uz-Zaman Chaudry, Director
General, the Pakistan Meteorological Department for nominating the author for this JICA grouptraining.

REFERENCES
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Bonnefoy-Claudet, S., 2004. Ph.D. thesis, University Joseph Fourier, Grenoble, France.
Cornou, C., et al., 2006, Third International Symposium on the Effects of Surface Geology on Seismic
Motion, France. Paper Number: NBT
Horike, M., Zhao B., and Kawase H. (2001). Bull. Seism. Soc. Am. 91, 1526–1536.
Ingber, L., 1989, Mathematical and Computer Modeling, 12, 967–973.
Kitsunezaki, C., et al., 1990, Journal of Japan Society for Natural Disaster Science, 9, 1-17 (inJapanese with English Abstract).
Konno, K. and Omachi, T., 1998, Bull. Seism. Soc. Am., 88, 228-241.
Nakamura, Y, 1989, Q. Rep. Railway Tech. Res. Inst., 30, 25-30
Press, W.H., et al., 2002. Numerical Recipes, Cambridge University Press.
Yamanaka, H., Takemura, M., Ishida, H., and Niwa, M., 1994. Bull. Seism. Soc. of Am. 84 (6),1831–1841.
Yamanaka, H., 2004, Proc. of the 13th World Conf. on Earthquake Engineering, Paper 1161.
Yokoi, T., 2005. Seismological Society of Japan Fall Meeting, Program and Abstract B049.

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