ASSESSING THE APPLICABILITY OF L-SHAPEARRAY FOR MICROTREMOR SURVEY
LI Jinggang∗
MEE08156

Supervisor: Toshiaki YOKOI∗∗

ABSTRACT
Site effects play a major role in destructive ground motion. The effects of local geology may modify
ground motion significantly on soft soils.To evaluate the site response, Microtremors methods haveadvantages: low cost and environment friendly for urban area and effective for low or moderate
seismicity area. But standard array shape is strict circular. In urbanized area, it is usually very difficult
to find an area for circular array observation due to existing buildings and other facilities. Therefore,
irregular array should be investigated and in the paper L-shape array was checked by comparing theperformances of circular array and L-shape array (both even and uneven interval) in the same site. The
SPAC coefficients fit well with theoretical Bessel function, so the results are reliable. The results showthat L-shape can have good performance in microtremors surveying. A shear wave profile wasobtained by L-shape array and had good agreement with existing borehole data. The theory of
Shiraishi et al.(2006) was attested by the observation data. Moreover, an effective and efficient method
for the key step of SPAC analysis, frequency range selecting, was proposed.
Keywords: SPAC, L-shape array, Vs structure, Microremors

1. INTRODUCTION
China is one of the most earthquake-prone countries. Long time historical documents record thesedestructive earthquakes and huge number casualties, for which site effects is one of most importantfactors. The effects of local geology may amplify in a very significant way ground motion on soft
soils.Most of Chinese people live in plain area with threat of potential earthquakes, and more and more
people live in urban area with the urbanization of the world. So it is very important to evaluate the riskof strong ground motion. Microtremors method is a useful tool, but circular array sometimes is a strict
constraint especially in urbanized area, where only L-shape array can be found. Shiraishi et al. (2006)
proposed a new formula to deal with irregular arrays. The purpose of this study is to understand theeffectiveness, limitations and advantages of L-shape array for the SPAC method using microtremors
array measurement as a tool for seismic microzonation and earthquake disaster mitigation by applying
them to a known old filled lake in Tsukuba City, comparing the results of them and then accessing theapplicability of L-shape array.

2. METHODOLOGY
2.1 SPAC method with triangular array
Aki (1957;1965) proposed spatial autocorrelation method (or SPAC method) which exploited ambient
vibration measurements to determine the underground shear wave velocity structure. Microtremors∗

Institute of Seismology, China Earthquake Administration, China.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Tsukuba,
Japan.

∗∗

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mainly are treated as stationary surface waves. Under this hypothesis, the azimuthal average of realpart of complex coherence function(CCF) (called the SPAC coefficient ρ (r , ω ) ) equates to certain
zero-order, first-kind Bessel function (Eq. (1)).

ρ (rAB , ω ) =

1 2π
2π ∫0

Re ( E[C A, B (ω )])E[C A, A (ω ) ⋅ CB , B (ω )]dθ = J 0 ( kr ) ,(1)

2.2 Formulation of Shiraishi et al. (2006) for arbitrary shape array
According to the theory of Shiraishi et al. (2006), the real part of CCF can be expressed by taking
finite terms as Eq. (1) due to drastic attenuation of higher order within range of interest.

{

}

∞
L
⎡
⎤
n
Re ( γ z )ij = J 0 ( krij ) + 2∑ ⎢( −1) J 2 n ( kri , j ) ⋅ ∑ λij ,l cos 2n (θl + φij ) ⎥n =1 ⎣
l =1
⎦
L
L
⎧
⎫
= J 0 ( krij ) − 2 J 2 ( krij ) ⎨cos 2φij ∑ λl cos 2θl − sin 2φij ∑ λl sin 2θl ⎬
l =1
l =1
⎩
⎭

(2)

L
L
⎧
⎫
+ 2 J 4 ( krij ) ⎨cos 4φij ∑ λl cos 4θl − sin 4φij ∑ λl sin 4θl ⎬
l =1
l =1
⎩
⎭
L
L
⎧
⎫
− 2 J 6 ( krij ) ⎨cos 6φij ∑ λl cos 6θl − sin 6φij ∑ λl sin 6θl ⎬ + O J 8 ( krij ) ,
l =1
l =1
⎩
⎭

(

)

For equi-lateral triangular array, the real part of CCF was obtained by substituting φ01 = 0°

, φ02 = 60°, φ03 = 120°; r01 = r02 = r03 into Eq. (2).
ρ L (ω , r01 ) =

{

}

{

}

{

Re ( γ z )0,1 + Re ( γ z )0,2 + Re ( γ z )0,3

} = J ( kr ) − 2 J ( kr ) ⎧ λ cos 6θ ⎫ + O ( J ( kr ))L⎨∑ l⎩ l =1= J 0 ( kr01 ) + O ( J 6 ( kr01 ) ) .
0

3

01

6

l

01

⎬
⎭

8

01

(3)

For L-shape array , we get the real part of CCF by substituting φ01 = 0°, φ02 = 90°,

r01 = r02 into Eq. (2) respectively and obtain Eq. (4).
ρ L (ω , r01 ) =

{

}

{

Re ( γ z )0,1 + Re ( γ z )0,22

} = J ( kr ) + J ( kr ) ⎧2 λ cos 4θ ⎫ + O ( J ( kr ) ) .
L

0

01

4

01

⎨ ∑ l
⎩ l =1

l

⎬
⎭

8

01

(4)

Naturally, the average of two pairs that form the short sides can reduce the influence ofJ2(kr) term drastically, where as the oblique side follow Eq.(2) and suffers this influence.
In this paper, we use Common Middle Point Cross-correlation (CMPCC) method (Hayashi
and Suzuki, 2004) to analyze MASW8 and MASW9. Combination of the Down Hill Simplex Method
and the Very Fast Simulated Annealing (VFSA) method is used to find optimal values of Vs structure
and layer depths, based on least misfit values between the observed and computed dispersion curves.
The combination of these two methods drastically shortens the time consumption in comparison withthe conventional VFSA(Yokoi,2005).
3. DATA
3.1 Observation site2

We conducted a field observation of microtremors in Tsukuba city, Ibaraki Prefecture, located on thenorthern outskirts of Tokyo. The subsurface soil profile is well documented using PS logging records(geological columns and SPT data) and geological documents (Unozawa et al., 1988).
3.2 Array deployment and data acquisition
Totally 21 seismic sensors(natural frequency 2Hz), portable recording systems “GEODE”
manufactured by Geometrics Corporation with the available frequency range from 1.75Hz to 20KHz,
are used for microtremors observation. 24 geophones (natural frequency 4.5Hz) are deployed for
multichannel analysis of surface waves (MASW).The map view of observation site is shown (Fig. 1).
Table 1. Array information
Array
symbol

MAM1Array type
Put together
on thehorizontal
groundTriangular
array

MAM3

Even
interval
L-shape

MAM4

MAM6

Profileremarks

6
Borehole 6

MAM2

MAM5

Duration

65 seconds
each time,
5 times

65 seconds
each time,
30 times

Uneveninterval
L-shapeHuddletest(21
verticalcomponent
sensors)
19 verticalcomponent
sensors

3,4

MASW9

MASW
Linear array

2 shots

Borehole 5

5
1

2

8

Figure 1. Observation site map view. Numberswith ellipse indicate different arrays andhereafter in the report and analysis thesenumbers with prefix “MAM” for microtremors
method and “MASW” for MASW method areused to represent these arrays and their results.
We put arrays with different methods (MAM2,
MAM3, MAM4 and MASW9; MAM5 and
MASW8) in the same site. The nearest
borehole locations are also showed with red
filled circles. Borehole data will be employed
to check the results from profile crossing arrays
MAM 6, MAM 7, MAM 5, and MAM 3
indicating by dashed line.

11 verticalcomponent
sensors

MAM7
MASW8

7

9

24
geophones

Table 2. Inter-station distance range for different arrays in experiment

Triangular array
Even interval
L-shape array
Uneven interval
L-shape array

With/without
oblique sides\
withwithout
withwithout

Min. of inter-station
distance(m)
2
6.0
6.0
2.0
2.0

Max. of inter-station
distance(m)
60.6
42.4
30.0
32.0
45.3

Table 2 shows parameters of triangular array(MAM2) and L-shape array(even and uneveninterval).Numbers of inter-station pairs of each inter-station distance of even and uneven interval
arrays are 19 and 25 with oblique sides and 5 and 10 without oblique sides respectively. Althoughsome of the inter-station distances have many inter-station pairs, azimuths of inter-station pairs aremainly within limited azimuth, which may import error of higher order Bessel function into SPAC

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coefficients from theory of Shiraishi et al.(2006). Without oblique sides, there is obviously influenceof 4-order Bessel function for both even and uneven L-shape arrays.

4. RESULTS AND DISCUSSION
We filtered the observation data with Chebyshev-I band-pass causal filter(parameters:
FL=0.1Hz,FH=20.0Hz, FS=25.0Hz, AP=0.1,AS=10.0), and then new sampling interval is 0.02 second.
Block size of analysis is 256, and the frequency range of analysis is [1.75-25Hz]. From the whole
length, 65 seconds, of the array seismograms, we extracted data segments of duration 5.12 s withoverlapping ratio 0.05. Then, for each of the blocks, the spectral densities were calculated by FFT.
Those spectral densities were then each smoothed with a Parzen window of bandwidth 0.7 Hz, andwere averaged over all data segments before they were used to estimate the inter-sensor correlations.

4.1 Determination of frequency range for analysis
It is very difficult to determine automatically and steadily by computer and time-consuming todetermine frequency range by hand. The start and end points of the frequency range carefully pickedby hand for each inter-station distance and then fitted with two exponential functions. The end points
of frequency range fitted very well with root mean square (rms) error less than 0.5 and the start pointsof the range frequency range were less precise but still have a rms error less than 1.5 Hz ,freq _ start =20,
dist 0.5

freq _ end =35,
dist 0.6

(5)

where
freq _ start , freq _ end

dist— start point and end point of frequency range(unit: Hz),— inter-pair distance(unit: m).

4.2 Comparison of different methods at the same site
Equi-lateral triangular, even and uneven L-shape array for microtremors method and linear array for
MASW method were conducted at the same site in the western part of Amakubo Park to check thevalidity of L-shape array. MASW is used to complement the performance of SPAC method.
According to Shiraishi et al.’s theory, equi-lateral triangular has highest accuracy in these arrays withsimilar size array, which is viewed as a standard. From Figure 2, we can see:(i)
The triangular array(MAM2) combined with MASW9 is standard for comparison overbroad frequency range [2-24Hz]( written as MAM29)(ii)
Even interval L-shape array(MAM3) have frequency range [3.5-11Hz] both with andwithout oblique sides;(iii)
Uneven interval L-shape array MAM4 has frequency range [3.5-21Hz] and [3-21Hz] forwith and without oblique sides. These frequency ranges are consistent with corresponding
inter-station distance ranges.
(iv)
Compared with MAM29, uneven interval array (MAM4) has higher accuracy then evenone (MAM3) both with and without oblique sides. Moreover, dispersion curves of
L-shape array without oblique side (MAM3ST and MAM4ST) are have less deviationfrom the standard one MAM29, which indicates that oblique sides import higher order
Bessel function error into SPAC coefficients.
(v)
Vs structures show similar results as dispersion curves, even interval array in theexperiment is better than uneven one. Uneven interval array shows good agreement with
MAM29, while even one has relatively large bias.

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Figure 2. Dispersion curves(Left panel) and inverted Vs structures (Right panel)of
MAM2, MAM3, MAM4 and MAM29 (combination of MAM2 and MASW9).
Suffix “LT” and “ST” for MAM3 and MAM4 mean data of L-shape with andwithout oblique sides, respectively.

4.3 Results from even and uneven interval L-shape array
The frequency range of both with and without oblique sides of even L-shape array MAM3 is [2-12Hz]
and that of uneven interval L-shape array MAM4 is [2-20Hz]. So with the same field effort, unevenarray is advantageous over even one.
Usually we want to increase the number of observation to cancel out or minimize therandom errors, so it is natural to use as many sensor pairs as possible to get the dispersion curves.
For L-shape, using sensor pairs of oblique sides may import influence of the 2nd order
Bessel function because of giving too much weight to some directions, at the same time averaging of
two short sides of L-shape array can remove the influence of 2nd order Bessel function. So it isnecessary to check whether it is appropriate to include the oblique sides or not.
Both dispersion curves and Vs structures show that L-shape with and without oblique sides
have similar performance. Furthermore, oblique sides have wider inter-distance range and hence wider
frequency range.

4.4 Vs profile by Microtremors methods
MAM6

0

MAM7

MAM5

MAM4
100
115

10

20

230

30

300

350
40
Depth
Unit:mVelocity
Unit:m/s

Figure 3 shows the Vs profile determined by MAM6,
MAM7, MAM5 and MAM4. This profile is in between
Borehole 5 and Borehole 6. Left side numbers show thedepth of each layer, and the right side ones indicate theshear wave velocity of each layer. Layers of the profile
have good conformability with those of Borehole 5 andBorehole 6. The results show that microtremors method
at frequency range [2-12Hz] can detect 20m with someaccuracy.

Figure 3. Vs profile through MAM6,
MAM7, MAM5 and MAM45

5. CONCLUSIONS
1.

Empirical formulas from fitting method can also provide reasonable frequency range.The
formulas for the inter-station distance less than 60m are as follow respectively.

freq _ end =
2.
3.

4.

5.

6.
7.

35
dist 0.6

and freq _ start =20
dist 0.5

As far as analysis method of simple averaging of different azimuth, triangular array has higher
accuracy than L-shape array, especially in the low frequency range.
Multichannel analysis of surface waves method has advantages in higher frequency, while
triangular arrays have good performance in relatively low frequency range. Combination of thesetwo can provide better constraint on Vs structure. Actual data of our experiment attest it.
For L-shape, uneven interval array has wider range of inter-station distance, then wide frequency
range. Also, uneven interval array has more inter-station distance, which provides smootherdispersion curves.
Including oblique side sensor pairs in analysis can diminish stochastic error, but at the same time,
it can import second order Bessel function J2(kr). Data of our experiments show that there seems
to be no higher modes imported. Another advantage is that with oblique side we can get wider
frequency range, because they have more and wider inter-station distances.
Microtremors method can provide shallow Vs profile for site effect evaluation up to about 20 m.
The theory of Shiraishi et al.(2006) is appropriate for identifying higher order Bessel function as adeviation to ideal circular array.
ACKNOWLEDGEMENT

I would like to express my sincere gratitude to Dr. Koichi Hayashi, OYO Corp. for his help during
field work.

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