A modified estimation method for amplification factor ofground and structures using the H/V spectral ratio
Yutaka Nakamura1

Abstract
There is a consensus that the predominant frequency of surface
ground can be estimated from the H/V spectral ratio of microtremor orstrong motion. However, on amplification factor estimated by the H/Vspectral ratio, there are still various discussions without any agreements. The author has claimed that the H/V spectral ratio method
stands on phenomenon of multi-refraction of SH wave in surface
ground. This paper explains a new technique on amplification factor
estimation of surface ground based on the H/V spectral ratio. Then
this proposed technique is confirmed by the verification with actual
measured microtremor and earthquake motion at Mexico City and actual measured microtremor and the damage situation caused by the2011 Off the Pacific Coast of Tohoku Earthquake at Urayasu.

1. Introduction
The H/V spectral ratio is called QTS, Quasi Transfer Function, according to its function. QTS is useful tool for characteristics investigation of surface ground and buildings. In general the predominant frequency derived from QTS gives extremely good result, but there is anobjection against that the peak of QTS is corresponding to the amplification factor. In this paper, a new modification technique for theamplification factor investigation of QTS will be described.
At first the characteristics of QTS are summarized as below;i) The first peak near F0 consists of S-wave mainly.
ii) The first trough near 2F0 caused by Rayleigh wave.
_______________________________
1 System and Data Research Co., Ltd., Japan.
273

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Yutaka Nakamura

Around F0 there is almost no energy of Rayleighwaves, so the dispersion curves are unstable
near F0. Rayleigh wave are growing from F0, 1.0
and reaches the first peak near the 2F0. QTS of
F 2F
both microtremor and strong motion are usefulfor estimation of at least fundamental frequency Tipical Shape of QTS
F0 and its amplification factor.
Figure 1 shows the result of comparing QTS of both strong motion
and microtremor. These strong motion records were observed at somestations in Mexico City. QTS is supposed to approximate the dynamic
characteristics of surface ground. The shape of the ratio as the peakvalue or predominant frequency can be well in agreement both strong
motion and microtremor. It shows that it is possible to estimate thedynamic characteristics from microtremor. However, QTS of microtremor is sometimes shifted to downward. This shift may be caused by
spike noise from walkers or Rayleigh waves related to deeper structure.
ooFigure1. Comparison between Microtremor and Strong Motion on Spectral Ratio
H/V, QTS, in Mexico City

So this paper describes a new technique to estimate the amplification
factor of ground and structures using QTS.
2. Fundamental idea
Because vibration at hard and uniform ground has no reason tocause particular bias, it is considered that the vibration is specially andtemporally uniform. A boundary of layers or ground surface with highA modified estimation method for amplification factor of ground…

275

impedance ratio leads a phenomena as reflect or refraction and thencauses uneven distribution of wave motion energy. Soft surface layer
tends to trap and accumulate the wave motion energy, so the amplitude of the wave motion becomes large. This is the amplification phenomenon of soft surface layer, and at this time the amplified frequency of vertical component V is higher than that of horizontal component H. So it is concerned that the vertical motion is not amplified at
the frequency range that the horizontal motion amplified. In case of
hard ground, because the vibration characteristics is similar to eachother between horizontal motion and vertical motion, it is consideredthat the vertical motion holds the vibration characteristics of the horizontal motion of the hard base ground at lower frequency range thanthat horizontal motion amplified at the surface ground. Thus in case of
focusing the horizontal motion, it is possible to estimate the amplification characteristics of the surface layer from QTS. This is the basic
idea of QTS.
This idea is applicable to not only ground but also buildings. At thistime there are two peaks which are corresponding to each, ground andbuildings, respectively.
While if pulse noise is mixed in the vertical motion, the spectrum
must be superposed uniform spectrum for wide frequency range. In
such case, the shape of the spectrum is similar but shifted lowly in all
frequency range. This phenomenon is caused by pulsed vibration excited by passing walker or vehicles close to the measurement point. As
a result, it is sometimes impossible to estimate the amplification factor
correctly by QTS. However even in such case, it is often possible toestimate the predominant frequency.
If it is possible to assume that the surface layer consists of one layer,
the vibration at the base ground boundary B can be estimated from thevibration at ground surface S following the equation below.
B(t )  S (t  h / Vs )  S (t  h / Vs )/ 2

Here, h and Vs are depth and velocity of shear wave propagation forsurface ground. And F is predominant frequency of QTS. Then, h/Vs
can be derived from next equation.

Yutaka Nakamura276

h / Vs  1 / 4F

Transfer spectrum can be calculated as a spectrum ratio between
ground surface and basement as follows, and then it becomes to bepossible to estimate the amplification factor at predominant frequency.
T ( f )  F S (t )( f ) / F B(t )( f )Here, F[*] is Fourier transform.

Figure 2. Illustration of Proposed Method for Amplification Factor Estimation

Discussion with strong motion records [1] says that the shape of QTS
is similar to that of standardized spectrum based on the hard groundeven in case of under estimation of QTS amplification. So, here a correction technique for amplification factor of QTS is proposed using
estimated peak amplitude of spectrum ratio to estimated base groundabove mentioned.
Below are validation and application of this technique.
3. Validation

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277

3.1. Measurement at Mexico City
The analysis of microtremor and strong motion observation in
Mexico City gave results below;i) QTS derived from strong motion at surface ground is almost similar
to amplification characteristics corresponding to a reference site withhard surface layer.
ii) QTS of earthquake motion is almost similar to that of microtremor.
Then it is confirmed that QTS of microtremor can appropriate the amplification characteristics of earthquake motion. However there weresome cases that QTS of microtremor shifted below even the shape issimilar. This is caused by enlargement of vertical component of microtremor in wide frequency range. The factor is seems to be influenced by a spike noise as caused by walkers passing by the sensor unit
or other vibration source to excite soft surface ground largely up-todown. Here is the examples of the correction applied the proposed
technique for these sites.
Strong motion observatories in Mexico City CI05 and CJ03 are chosen as examples of sites with lower shifted QTS of microtremor

EW

10

1

0.1
100

1

Frequency in Hz

10

1

EW

0.1
0.1

1

Frequency in Hz

100

10

10

CI05E
CI05M
H/H of EM
05/78B
05/78CＣＴＦ of ＭＴ

CI05MR
CI05MM1

Frequency in Hz

10

CJ03A
CJ03B
CJ03C
CJ03D
CJ03E
1 CJ03M
03/78A
03/78B
03/78CCJ03MR
CJ03MM

0.1

100

100
H/V of EM

CJ03A
CJ03B
CJ03C
CJ03D
CJ03E
H/V of ＭＴ
CJ03M
H/H of EM
03/78A
03/78B
03/78CＣＴＦ of ＭＴ
CJ03MR
CJ03MM

NS

0.1

CI05B
CI05C

H/V of ＭＴ

CI05MR
Original QTS of MT
CI05MM
0.1

10

Calculated Transfer
Function

H/V of EM

NS

CI05B
CI05C

CI05E
CI05M
1
05/78B
05/78C

0.1

0.1

Amplification Factor

10

Amplification Factor

Amplification Factor

Modified QTS

Amplification Factor

100

1Frequency in Hz

10

Figure 3. Verification of Proposed Method for sites in Mexico City

100

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Yutaka Nakamura

measurement. Figure 3 shows QTS of earthquake motion layered with
H/H spectrum ratio, horizontal component of the site to that of hardground, for some earthquakes. These spectrums are almost similar toeach other even with scattering. QTS of microtremor showed in thesame figure shifts beneath largely, although the amplification characteristics curve and its shape agree with the amplification characteristics of strong motion.
On the other hand, Figure 3 also shows the result of calculation ofspectrum ratio from estimated base ground waveform derived fromthe proposed technique in green line and the adjusted QTS of microtremor to fit the first peak in blue dot line. Because corrected QTS canalmost agree with targeted spectrum, it shows that the proposed technique is appropriate.
3.2. Result of measurement at Urayasu
Although Urayasu locates more than several hundred kilometersfrom the focal region of the 2011 Off the Pacific Coast of Tohoku
Earthquake (hereafter the 3.11 earthquake), there was one of the severe damaged areas of liquefaction. Here the result of microtremor
measurement after the 3.11 earthquake is described.

Figure 4. The Site for Application of Proposed MethodA modified estimation method for amplification factor of ground…

Figure 4 shows the distribution mapof measured sites G1-G13 from a
railway station to coast line. This
area is rather new reclaimed landfilled up till 1980’s with pumped
sediment from under the sea. Severe liquefaction attacked this areaat the time of the 3.11 earthquake
and the situation of liquefaction canbe seen on YouTube for example
recorded between G8 and G9.
There was significant liquefaction
between G8 and G10 along thismeasurement line, several photos
are shown on Google Earth. And
ground subsidence about 40cm wascaused by the blow off of sand at
G9 shown in Photo 1.
10

10

X-component

G1X
0.1
100.1

UG1M
UG1MR
UG1MM
0.1
10 100.1

1

G2X
0.1
100.1

1

10

0.1
100.1

0.1
10 100.1

1

G3X
1

G5X

1

1

UG3M
UG3MR
UG3MM
0.1
10 0.1Y

0.1
10 100.1

X

1

UG4M
UG4MR
UG4MM

G4Y
1

10

G6X
1

1

0.1
10 100.1

1

10

0.1
10 100.1

1

0.1
100.1

0.1
10 100.1

1

1

0.1
100.1

1

10

UG10M
UG10MRUG10MM
0.1
10 100.1

10

G10Y

1

UG11M
UG11MRUG11MM

G11X
1

10

0.1
10 100.1

G11Y
1

10

1
UG12M
UG12MRUG12MM

G7Y

1

1

1

UG7M
UG7MR
UG7MM

G7X

G10X

1

UG11M
UG11MRUG11MM
10

G9Y

1

0.1
100.1

G6Y

UG9M
UG9MR
UG9MM

0.1
10 10 0.1

1

1
UG6M
UG6MR
UG6MM

1
UG7M
UG7MR
UG7MM

0.1
10 0.1

UG10M
UG10MRUG10MM

G5Y

Y-component

G9X

1

UG5M
UG5MR
UG5MM

10

1
UG9M
UG9MR
UG9MM

1
UG6M
UG6MR
UG6MM

G3Y
1

X-component

1

0.1
10 100.1

1

10

Y-component

0.1
10 100.1

1

UG5M
UG5MR
UG5MM

1
UG3M
UG3MR
UG3MM

Photo 1. Situation of around G9:
9 month after the 3.11 Eartquake

G4X

1

G2Y

1

0.1
0.1

UG4M
UG4MR
UG4MM

1

1

Around G9:
Subsidence causedby sand eruption

1

UG1M
UG1MR
UG1MM

UG2M
UG2MR
UG2MM

UG2M
UG2MR
UG2MM

30-40cm

10

1

G1Y

G10
↑

X-component

1

1

Amplification Factor

10

Y-component

279

0.1
100.1

UG12M
UG12MRUG12MMG12X
1

0.1
10 100.1

G12Y
1

10

1
UG8M
UG8MR
UG8MM

0.1
0.1

1

Frequency in Hz

1

UG8M
UG8MR
UG8MM

G8X
0.1
10 0.11Frequency in Hz

1
UG13M
UG13MRUG13MM

G8Y
10

0.1
0.1

UG13M
UG13MRUG13MM

G13X
1Frequency in Hz0.1
10 0.1G13Y
1Frequency in Hz

Figure 5. Original and Modified QTS for G1 to G13 at Urayasu

10Yutaka Nakamura

280

Table 1.Results: Predominat Frequency, Amplification Facotrs, Kg-value,
Basement Ground Depth h and Shear Velocity Vs in Surface Layer for each Sites
direction
X-comp.
Y-comp.
Urayasu
Site

F
A
Hz
1.00 1.94
0.61 1.33
0.59 1.95
0.68 0.94
1.05 1.85
0.76 2.11
1.15 1.78
0.81 1.94
0.71 2.01
0.83 2.25
0.51 2.18
0.56 1.55
0.39 2.59

G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
G11
G12
G13

MA

Kg
m/Gal
13
14
9
11
9
11
13
16
11
25
11
12
15

3.63
2.90
2.33
2.77
3.02
2.91
3.82
3.58
2.84
4.59
2.33
2.55
2.40

h

Vs
F
A
m/s Hz83
1.05 1.95
104
1.00 1.53
129
0.61 1.47
108
0.66 0.86
99
0.71 1.76
103
0.88 1.47
79
1.05 1.41
84
1.07 1.55
106
0.29 1.91
65
0.85 1.32
129
0.68 1.72
118
0.49 1.49
125
0.39 2.48

m
21
42
55
40
24
34
17
26
37
20
63
52
80

MA
4.23
3.94
2.34
2.89
2.84
2.99
3.60
4.47
2.67
3.77
2.13
2.22
2.39

Kg
m/Gal
17
16
9
13
11
10
12
19
24
17
7
10
15

h
m
17
19
52
39
37
29
20
16
96
23
52
69
80

Vs
m/s
71
76
128
104
105
100
83
67
112
80
141
135
126

Predominant Frequency in Hz

1.4
1.2

G1 G2

G7

G5

Predominant Frequency● X-Direction

1
0.8

G9

G3

0.6

G12

G8

G6

G4

0.4

G10 ○ Y-Direction

G11

G13

0.2
0
-100

0

100

200

300

400

500

600

700

800

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

Distance from JR-Keiyo Line in m
5

Amplification Factor● X-Direction

Amplification Factor

4.5
4○ Y-Direction

3.5
3
2.5

G1

2

G7

Modified

G6
G4 G5

G2

G8

G9

1.5

G3

1

Original

G10

G12
G13
G11

0.5
0
-100

0

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

Distance from JR-Keiyo Line in m

Figure 6. Estimated Predominant Frequencies and its Amplification Factors

A modified estimation method for amplification factor of ground…

281

Figures 5 to 10 show the result of microtremor measurement. Figure 5
shows the result of comparison of amplification factor between before
and after applying the proposed technique. Figure 6 show the distribution of estimated predominant frequency and its amplification factor
with modified amplification factor. There seems to be pulsed waveform in many portions on the microtremor waveform in Figure 7. The
amplification factor does not differ from before and after the correction at G13, and there is almost no pulse noise on the microtremor
waveform shown in Figure 7.

G1

G6

G11

G2

G7

G12

G3

G8

G13
Predominant Frequency in Hz

1.4

G4

1.2

G1 G2
G3

0.6

G6

G4

0.4

G7 Predominant Frequency● X-Direction
G10 ○ Y-Direction
G9
G12
G8
G11

G13

0.2
0
-100

G9

G5

1
0.8

0

100

200 300

400 500

600 700

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

Distance from JR-Keiyo Line in m
5

Amplification Factor● X-Direction

Amplification Factor

4.5
4○ Y-Direction

3.5
3
2.5

G1

2

G7

Modified

G2

G4 G5

G6

G8

G9

1.5
1

Original

G3

G10

G12
G13
G11

0.5
0
-100 0100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

Distance from JR-Keiyo Line in m

G5

G10

Almost all amplification factors
A are changed by modification.
But A of G13 did not change bymodification. The waveforms
measured at G13 did not include
spike noise.

Figure 7. Waveforms of Microtremor at Urayasu

Yutaka Nakamura

282

Distance from JR-Keiyo Line in m

Depth h in m to Hard Ground

-100

0

100 200

300

400

500 600

700 800

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

0

G1
20

G4

40

G5 G6

G7 G8

G10
G9

G2

60

G3

80

● X-Direction

100○ Y-Direction

G11 G12

Rough Depth of Basement Groundbased on Other Investigation Results

Thickness h (m) of Surface Layer

G13

120

Figure 8. Distribution of Depth h of Basement Ground along themeasuring line of Urayasu

Vs of surface ground in m/s

Table 1 shows the calculated Kg-value, depth of base ground andshear
wave velocity of surface ground derived from the predominant160
Vs ofcorrected
Surface amplification
Layerfrequencyof QTS andfactor. Table G13
1 also140
G9the shear wave veloci120 the used equations (see detail [2]). Here,shows
G11 in comG3
ty of100base
G12
G1 ground is assumed 300m/sec, instead of 600m/sec
G5 investigations
G6
mon,80 from the result G4of boringin this area.● X-Direction○ Y-Direction
60
G7 indices corresponding
Figures
8 toG210 are distribution of theseto eachG8
G1040
measured site. Figure 8 for estimated depth of base ground also shows
20
outlineof the interpreted depth of base ground from a map in public,
0-100 0 depth
100 200 agrees
300 400 500
600 700
800 900
1000 1100
1200 1300 1400
1500 1600 1700
1800 1900 2000 2100ofand thesewitheachother.
Figure9 shows
distribution
Kg-value, location of large
Kg-valuecorresponds
toseveredamagedDistance from JR-Keiyo Line in m
Kg-value in micro-strain/Gal

30

20

G10

Kg-value

25

G8

G1 G2

15

G3

G9

G4 G5 G6 G7● X-Direction○ Y-Direction

G11

G13

10

G12
5
0
-100

0

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

Distance from JR-Keiyo Line in m

Figure 9. Ditribution of Kg-value along the measuring line of Urayasu

A modified estimation method for amplification factor of ground…

283

Vs of surface ground in m/s

160

Vs of Surface Layer

140

100

G13

G9

120

G4 G5 G6

80
60

G2

40

G11
G12

G3

G1

● X-Direction

G7

G8

G10

○ Y-Direction

20
0
-100

0

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100

Distance from JR-Keiyo Line in m
30

Figure 10. Distribution of Vs along the measuring line of Urayasu

Kg-value in micro-strain/Gal

G10
Kg-valuearea25and to damage situation
clearly. However, the result of analysis● X-Direction
G8 ofG9
on G9,
in the area with blowing up heavily
liquefaction
sand, shows
20
G1○ Y-Direction
G2
quite15 different result G4
depending on G7
the direction. It suggests that
G5 G6
G11 G13Kg
value is possiblyG3changed by the liquefaction during earthquake motion.10 There is no wonder if Kg value is changed by land deformation.
G12
5
For example,
repeated liquefaction was observed during 2010 to 2011
in New
Zealand and there is a possibility that it is able to grasp the0-100 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100
change of Kg value if microtremor was measured in each case of liqDistance from JR-Keiyo Line in m
uefaction occurrences. Figure 10 is distribution of Vs of surface
ground. According this figure, Vs are distributed between 70m/s and140m/s around 100m/s, and low velocity corresponds to large Kgvalue. The result of analysis of microtremor at Urayasu shows propriety of the amplification factor correction with the proposed technique.
4. Conclusions
This paper proposed a technique to solve phenomenon not to beable to estimate the amplification properly with pulse noise, one of the
problems on estimation of surface ground characteristics from QTS.
This technique is simple technique that estimating a waveform at baseground from observed waveform based on the wave theory, estimating
amplification factor of noticed frequency from each spectrum, andthen correcting the amplification factor estimated from QTS. This paper confirmed that this technique can correct the amplification factor

284

Yutaka Nakamura

properly and estimate the surface ground characteristics more effectively with applying to the actual measured records. The author believes that this technique improves the reliability of QTS method andextends its application range.
Acknowledgement
The author appreciates cooperation of CIRES, Centro de Instrumentación y Registro Sísmico, for arranging microtremor measurements and provision of strong motion records in Mexico City. The author had a lot of helping from Mr. Saita of the senior research engineerof SDR, System and Data Research. I would like to express my gratitude to him.
References[1] Nakamura, Y.: A Method for Dynamic Characteristics
Estimation of Subsurface using Microtremor on the Ground Surface,
Quarterly Report of RTRI, Vol.30, No.1, pp.25-33, 1989.1.
[2] Nakamura, Y.: Real-Time Information Systems for Hazards
Mitigation, Proceedings of 11th World Conference on Earthquake
Engineering, Acapulco, Mexico, 1996.6.
[3] Nakamura, Y,: Clear Identification of Fundamental Techniqueand its Applications, Proceedings of 12th World Conference on
Earthquake Engineering, paper #2656, Auckland, New Zealand,
2000.7.
[4] Gurler, D. G., Nakamura, Y., Saita, J. and Sato, T.: Local Site
Effect of Mexico City Based on Microtremor Measurement,
Proceedings of 6th International Conference on Seismic Zonation,
2000.11.