ESTIMATION OF SHEAR WAVE VELOCITYSTRUCTURE USING ARRAY OBSERVATION OF
SHORT PERIOD MICROTREMOR
IN KOSHIGAYA CITY, JAPANDayra Yessenia BLANDON SANDINO*
MEE07161

Supervisor: Toshiaki Yokoi**
Koichi Hayashi***

ABSTRACTIn this study, Spatial Autocorrelation Method (SPAC Method) was carried out in Koshigaya City,
Saitama Prefecture, Japan. Additionally, we applied H/V spectral ratio or Nakamura method to thesame area.
We obtained that in the western part of the study area the engineering bedrock(Vs>400m/sec) is as shallow as 10-15 m, where as in the eastern part it is much deeper and reaches to50-60m. The former is categorized in Class D or Stiff Soil of NEHRP (2001) Ground Classification,and the latter in Class E or Soft Soil. We could obtain the same soil classification by implementing themethod proposed by Kon’no et al. (2007), which allow us to skip the inversion of the dispersion curve.
Finally, H/V spectral ratio could not show any correlation of its predominant period withthe underground velocity structure determined by SPAC method. Furthermore, with the provided
information from Nakamura method it is difficult to obtain the ground classification at a site.
Keywords: Microtremor, SPAC method, H/V spectral ratio, S-wave structure.

1 INTRODUCTION
The interaction of the Caribbean and Cocos plates in the subduction area of Nicaragua provokes agreat number of earthquakes per year. Many important cities are located in this zone, where mitigationof Seismic Risk is essential. This is the case of Managua, the capital of Nicaragua that has been
impacted for two destructive earthquakes in current times (1931 and 1972). This situation led to theelaboration of the seismic microzonation map, by using H/V spectral ratio (Nakamura method). Thismethod, however, is under criticism for its validity and it is suggested that a better result can beobtained by using new techniques of microtremor observation.
Thus, the purpose of this study is to understand the effectiveness, limitations andadvantages of the SPAC method using microtremor array measurement as a tool for seismic
microzonation and earthquake disaster mitigation by applying them to the study area in Koshigaya
City where a complicated underground structure is expected. Nakamura method is conducted
additionally.

*

Geoscientific Research Center, National Autonomous University of Nicaragua (CIGEO/UNANManagua).
**
International Institute of Seismology and Earthquake Engineering (IISEE), BRI, Japan.
***
OYO Technology and Engineering Center, OYO Corporation.

12 DATAThe microtremor field measurements were performed in the urban area of Koshigaya city,
approximately in the coordinates: lat. 35o 52’ 12’’N, lon. 139o 48’ 36’’E, at the southeast of Saitama
Prefecture, approximately 25km from central Tokyo (Figure 1).
The measurements were conducted at 12 sites, on June 12 and 13, 2008 in day time. The
arrays were deployed in the shape of the letter “L” for SPAC method, which consists of elevengeophones (Natural frequency 2Hz) and simultaneously, we used the three-component seismometer
GEO-SPACE LP of Geometrics (Natural frequency 1Hz) for H/V spectral ratio at each site.

Figure 1 Map showing array configuration adopted in microtremor measurements.
The test field is located in Koshigaya City, Saitama Prefecture, Japan. The box in
the right-down side indicates the L-shape array with the distance among sensors.
3 METHOD
3.1 SPAC Method
The SPAC Method is based on the theory developed by Aki (1957) to comprehend the relationshipbetween the temporal and spatial correlation of seismic waves and microtremors, which it became thekey to successful extraction of dispersion characteristics of Rayleigh waves. (Okada, 2003).
The SPAC coefficients denoted by equation (1) can be directly calculated in a frequency
domain using the Fourier Transform of the observed microseism, that is,ρ (ω; r ) =2πreal [S CX (ω; r ,θ )]1∫
2π 0 S cc (ω ;0,0 ) ⋅ S xx (ω ; r ,θ )(1)

where real []⋅ stands for the real part of a complex value, and S cc (ω ;0,0) and S xx (ω ; r , θ ) are the power
spectra of the microseism at two sites, C (0,0 ) and X (r , θ ) , respectively. S cx (ω ; r , θ ) is the crossspectrum between u (t; ω ,0,0) and u (t; ω ,0, θ ) . The two autocorrelations in the denominator make thelocal amplification effect canceled out (Okada, 2003).

2

Then, the velocity that makes the misfit function minimum is searched for each available frequency
using all considered inter-station distance. The obtained value of c is considered as the phase velocity
at the corresponding frequency. After that, we obtained the optimum underground structure for the
given dispersion curve of Rayleigh wave based on the Down Hill Simplex Method (DHSM) combinedwith the Very Fast Simulated Anealing (VFSA) approach (Yokoi, 2005).
The initial model used has fives surface layers and a half space that represents the
bedrock of which Vs is about 400 m/sec (Table 2). For making this initial model, the information
obtained from a borehole GS-SK-1A was considered (Ishihara, 2004; Hayashi et al., 2006).
Table 2 Initial Model for all the sites
hmax (km)Vsmin (km/sec)
Vsmax (Km/sec)
0.03
0.08
0.15
0.03
0.1
0.15
0.03
0.08
0.15
0.03
0.15
0.25
0.03
0.25
0.35
999
0.35
0.45

hmin (Km)
0
0.001
0.001
0.001
0.001
998

The Vp and the density ρ are calculated using the following empirical formulas for eachstep of iteration (Ludwig et al.,1970; Kitzunezaki et al., 1990, respectively).
Vp=1.11 Vs+1.29(Km/sec)

ρ=1.2475+0.399 Vp-0.026 Vp2(2)(g/cm3)(3)

3.2 Nakamura method
Nakamura (1989) proposed a method of inferring site amplification factors from incident seismic
shear waves using microtremor H/V spectral ratios at a single site. This method is easily applied anddirectly estimates the site amplification factors without reference site, and many researchers have done
to investigate the validity by observation and in theory. (e. g., Horike et al., 2001; Lermo and ChavezGarcia, 1994).
The calculation is done by the following formula

H / Vspectralratio =∑ P (ω ) + ∑ P (ω )∑ P (ω )
NS

EW

(4)

V

where PNS(ω), PEW(ω) and PV(ω) are the power spectra of NS, EW and the vertical component
respectively, summation is taken over data blocks.

4 RESULTS AND DISCUSSION
4.1 SPAC method
We obtained the dispersions curves or phase velocity for each observation site. The result indicatesphase velocities lower than 0.5 (Km/sec) at all the sites and suggests that the region is covered by soft
sediments up to the depth that can be explored in this research (Figure 2).
Figure 2 shows the result of dispersion curve for all the sites except the site G where
unusual phenomena occurred in SPAC coefficients. Namely, the usual order, in which those of longer
inter station distance, has smaller value in the range from kr=0 to the first zero cross, is not observed.

3

This may be interpreted as the failure of theassumption: horizontal stratified layers or
0.5
unrecognized human made noise. Therefore,
C
0.4
D
the site G is excluded from the analysis.
E
0.3
The sites can be separated into fourF
0.2groupsby
the similarity of the shape andH
0.1
valuesofthedispersion curves. Namely,
I
J
0Group 1 corresponds to the sites B, C and D.
0
1
2
3
4
5
6
7
K
Group 2 corresponds to the sites A, E and H.
Frequency (Hz)L
Group 3 corresponds to sites F, I, and J.
Group 4 corresponds to the sites K and L.
Figure 2 Dispersion curves for all sites except theAfter obtaining dispersion curve,site G.
the result was inverted to Vs structure.
Figure 3 shows Vs structure for all the sites
except the site G. It is evident that even though we conduct array measurements in a small area, a clear
variation exists in Vs structures among the observation sites.
For Group 1, we found the engineering bedrock (Vs about 0.400 (Km/sec)) at depth of
0.055 (Km), except at the site D where it appears at about 0.040 (Km); the layer with Vs
approximately 0.200 (Km/sec) appears at depth about 0.030 (Km). For Group 2, the depth of theengineering bedrock varies from 0.030, 0.024 and 0.053 (Km), at the site A, E, and H, respectively;
the layer with Vs approximately 0.200 (Km/sec) appears at depth of about 0.15 (Km/sec), but at thesite A appears at 0.022 (Km). For Group 3, the engineering bedrock was found at depth from 0.015 to
0.018 (Km); the layer with Vs approximately 0.200 (Km/sec) appears at depth of about 0.008 (Km).
Finally Group 4, the engineering bedrock was found at depth from 0.010 to 0.015 (Km); the layer with
Vs approximately 0.200 (Km/sec) appears at depth less than about 0.008 (Km).
We can judge clearly that Group 1 located at north-east part of the study area corresponds
to the thickest sediment, while Group 4 located at the south-west part corresponds to the thinnest andthat the thickness of the soft sediment is decreasing from north-east to south-west.
Comparison Dispersion Curve

A

Velocity (Km/sec)

B

Vs (Km/sec)

Depth (Km)

0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08

Group 3
0

0.2

0.3

0

0.5

B
C
D

Vs (Km/sec)
0.1

0.2

0.3

0.4

0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08

0
0

0.01

0.01

0.02
0.03

0.05

0.1

F
J
I

0.2

0.03
0.04
K
L

0.06

Figure 3 S-wave structures of four groups.

4

0.3

0.4

0.5

0.4

0.5

Vs (Km/sec)
0.1

0.02

0.05

0.06

0.2

H
E
A

Group 4

0.5

0

0.04

Vs (Km/sec)

Group 2
0.4

Depth (Km)

Depth (Km)0.1

Depth (Km)Group 10.3

4.1.1 Soil profile
By using the result about Vs structure, we drew two soil profiles. The profile one connects the sites
KFDB with direction south-west to north-east, and the profile two, connects the sites KLJIH from west
to east in a straight line. (Figure 4)
The profile one shows that, the depth change considerably with difference around 23 m ina distance of 246 m between site F and D. After this point, the depth increases up to about 55 m at thesite B. Here, the sub-area at west side of the site F including the site K may correspond to the buried
terrace, while at north – east of the site F may correspond to the slope between buried terrace and theburied channel.
For the profile two, the depth change considerably between site I and H (136.33 m of
distances between these sites) which is significant for the layers four and five. The maximum depth
reached is about 53 m for layer 5.
Profile one
100

200

Profile two
Distances (m)

600

700

800

0

0

0

10

10

20

20
Depth (m)Depth (m)0Distance (m)
300
400
500

30

40

50

50

K

200

300

400

500

L

J

600

700

800

30

40

60

100

60

F

D

Layer 1

Layer 2K

B

Layer 3Layer 4I

H

Layer 5Figure 4 Soil profile along the sites K-F-D-B (left) and K-L-J-I-H (right).
4.1.2 Ground classification
By using the result from SPAC method, the ground classification is conducted based on AVS30, basedon the following equation:n∑d
AVS 30 =Soft soil: class E

i =1
n

i

di
Vs
i
i =1

∑

Stiff soil: class D
Stiff soil except at this site

Figure 5 Map showing the site classification forobservation sites, indicating soft soil at the northeastand stiff soil at the southwest of the study area (except
at the site J that is soft soil).

5

,

(5)

where Vs i is the shear wave velocity inm/sec, d i the thickness of i-th layer
between 0 and 30 m. (NEHRP, 2001).
The result was Soft soil (Class
E: AVS30< 180 m/sec) at the north-east
parts (the sites A, B, C, D, E, H, and J)
and Stiff soil (Class D: 180 m/s ≤AVS30≤ 360 m/s) at the south-west (thesites F, I, K and L). Even though it is not
visible on the topography, there is alateral variation of the bedrock depth. As

250

Vs30mt

200
150
100
50
0
0

50

100

150

200

250

Vs30SPAC

Figure 6 Comparison of Vs30mt with
Vs30SPAC

the calculated values for the sites I and J are close to thethreshold, it is better to consider that these two sites are intransition between Class D and Class E (Figure 5).
Also, we use the method proposed by Kon’no etal. (2007) as an approximate way to estimate AVS30
without performing the inversion of the dispersion curve.
They have proposed the use of the phase velocity provide
by SPAC method for the wavelength 40m as an
approximation of AVS30 (Vs30mt).
The result was the same as that of the previous
method. Only for the case of the site J of which value was
not found due to limitation of the available frequency.
However, Vs30mt can be guessed less than 213 (m/sec) for
this site at least. In Figure 6 the comparison between these
two methods is shown, of which deviation is acceptable.

4.2 H/V spectral ratio (Nakamura Method)
The sites in Group 1 show a clear peak of predominant period less than 1sec. For the rest of Groups,
the predominant period is longer than 1 sec, except at the site A where was around 0.9 sec.
Taking into account the soil classification provide by SPAC method, we can say that thelonger period corresponds to Stiff soil class, and shorter one is found at Soft soil class. This is oppositeof the relation of the predominant period of amplification of up-coming S-wave. The result is anevidence of the failure of Nakamura method in the study area, which predominant period of
amplification is supposed to be shorter at Stiff soil and longer at Soft soil.

5 CONCLUSIONSPAC method could give a quantitative estimate of shear wave velocity structure that is consistent
with previous information about the depth of bedrock and geology of the area. Namely, in the westernpart of the study area the engineering bedrock (Vs>400 (m/sec)) is as shallow as 10-15 m, where as in
the eastern part it is much deeper and reaches to 50-60 m. The former is categorized in Class D or Stiff
Soil of NEHRP (2001) Ground Classification, and the latter in Class E or Soft Soil.
We could obtain the same soil classification by implementing the method proposed by
Kon’no et al. (2007), which use phase velocity for the wavelength 40m as an approximation of AVS30(Vs30mt), without performing the inversion of the dispersion curve.

REFERENCES
Aki, K., 1957, Bull. Earthq. Res. Inst. Univ. Tokyo, 35, 415-457.
Hayashi, K., et al., 2006, Bull. Geol. Surv. Japan, 57, 309 – 325.
Horike, M. , B. Zhao and H. Kawase , 2001, Bull. Seism. Soc. Am., 91, 1526-1536.
Ishihara, Y.et al., 2004, Bull. Geol. Surv. Japan, 55, 183-200.
Kitzunezaki, C., et al., 1990, Jour. of Japan Soc. for Natural Disaster Science, 9-3, 1-17
Kon’no, K., et al., 2007, Jour. of Japan Society of Civil Engineering, 63, 639-654.
Lermo, J and Chavez-Garcia F. J, 1994, Bull. Seism. Soc. Am. 84, 5, 1350-1364.
Ludwig, W. J., et al., 1970, Seismic refraction, The Sea 4-1, 53-84.
Nakamura, Y, 1989, QR of RTRI 30, no 1, Februrary, 25-33.
NEHRP, 2001, Part 1. Provisions (FEMA 368), Washington DC. Building Seismic Safety Council.
Okada, H., 2003, Geophysical Monograph Series No. 12, Society of Exploration Geophyscists, Tulsa.
Yokoi, T., 2005, Programme and abstracts, The Seismological Society of Japan, Fall meeting.

6