Dynamic Characteristics of Great Bronze Buddha of
Kamakura using microtremor
Yutaka Nakamura1, Jun Saita1, Mitsuhiro Tachibana1 andTsutomu Sato1

Abstract
The second largest bronze Buddha in Japan built in around 1250AD
at Kamakura immediately above the focal region of the 1923 Kanto
earthquake. Great Buddha of Kamakura has still remained basically its
original shape, though it has been suffered several natural disasters as
losing its hall. Especially, although the 1703 and 1923 Kanto earthquakes caused settlement and sliding of the basement over 0.3 m, thebody has been not suffered serious damage. This statue was casted inorder from the bottom with many joints. The joint between the head
and the body was noticed because it is reinforced by FRP, Fiber Reinforced Plastic, at the time of the last major repair in 1961. And ingenuity was exercised to fence off the earthquake motion over 400 Gal
with sliding the body on the basement, to reduce the load for the neckduring earthquake. This is the first example of the earthquake isolation
system for cultural properties in Japan. Over 50 years passed after thelast major repair, deterioration of FRP is feared. Concerning safety
during earthquake motion, microtremor measurement was conducted.
As a result of the preliminary investigation in 2009, the surrounding
ground was estimated that liquefaction was occurred at the front andright sides of the basement and the basement suffered damage as settlement. However, it is considered that the propagation of the earthquake motion for the statue was interrupted because of the liquefaction. Thus, it seems that the damage for the statue itself was prevented
because of namely the natural isolation system. Additionally in 2013,
microtremor of the statue itself was measured for making clear theconnection status between the body and the head.
_______________________________
1 System and Data Research, Tokyo, Japan.
1

Yutaka Nakamura et al.

2

1. Introduction
Great Buddha of Kotokuin Temple in Kamakura (see Figure 1) isthe second largest bronze Buddha in Japan built in around 1250AD.
Kamakura locates at the high earthquake activity area in Japan as Figure 2.
Repair report of Showa era (1926-1989) says that although Great
Buddha of Kamakura has repeatedly been attacked by several disasters
as earthquake, rain storm or flood, the statue itself has still remained
its original shape without serious damage until today. Although thisstatue is outside at present, it had its hall at first and finally lost thehall at the time of disaster in 14 or 15 century. Great Buddha of Kamakura suffered many large earthquakes. At least at the time of the1703 Kanto earthquake (M7.9 to M8.2) and the 1923 Kanto earthquake (M7.9), these focal regions are shown in Figure 2, although thedamage as collapse of the basement and shift and settlement of thestatue was reported, the statue itself was not damaged severely. It isinteresting why this Great Buddha has not suffered severe damage andFigure 1. Great bronze Buddha of Kamakura

Dynamic Characteristics of Great Bronze Buddha of Kamakura

3

remained the original shape in spite of suffering large earthquake motion repeatedly and collapse of surrounding buildings.
The damage of the 1923 Kanto earthquake was soon repaired, andadditionally a major repair in Showa era was done in 1960 to complement the repair for the 1923 damage. At the time of Showa major
repair, the neck of the statue was reinforced by FRP, Fiber Reinforced
Plastic. With reinforcing the basement and the bottom of the statue by
concrete, a stainless steel plate was applied under the reinforced concrete of the bottom of the statue to slide on the granitic block withbush-hammering attached above the basement during large earthquake
motion (see Figure 3). This ingenuity is known as the first seismic isolation system for cultural properties in Japan.
Momentum to consider countermeasures for Great Buddha of
Kamakura against earthquake motion is increasing again covering theconfirmation of the degradation situation of FRP reinforcement for theneck more than 50 years after execution. This paper reports the result
Epicenters of Damaged Earthquakes after AD 5C

KamakuraTokyo
0

Yokohama
Kamakura

050

100 kmFigure 2. Location of Kamakura and its surrounding seismicity

200

400 kmYutaka Nakamura et al.

4of the microtremor measurement of the statue taken in the result of thepreliminary microtremor measurement of the statue and surrounding
ground.

Rigid frame on
RC Beam tosupportthe upper load

RC Beams to reinforcethe open-end bottom of the statue

Stainless steel sheet with stud tofix bottom side of RC Beam

Upper surface of Podiumfilled byGranite Planks with smoothed surface
rimed with Copestones

Figure 3. Base isolation system for the Great Buddha of Kamakura

2. Summary of results of the preliminary microtremor measurement of the statue and surrounding ground [2]Figure 4 shows a distribution of points for microtremor measurement on ground. Figure 5 is QTS (H/V) derived from measurement results. Figure 6 shows the predominant frequency F and amplification
factor A corresponding to the measured location with the value follow-

Dynamic Characteristics of Great Bronze Buddha of Kamakura

5

ing to the size of the bubble. This figure shows that the ground becomes softer from west to east or from north to south. This is also
confirmed from Figure 7 as the distribution of Kg value, derived fromF and A as Equation (1).
⁄(1)

Here, Kg value can roughly estimate the strain of the surface
ground multiplying the maximum acceleration value at base ground,so large Kg value corresponds to large shear strain of surface groundcaused by earthquake motion.
Next, the relationship between Kg value and the earthquake damage is concerned. The 2011 off the Pacific coast of Tohoku Earthquake occurred two years after the preliminary investigation. This
earthquake caused damage for this temple as turnover of some stonelanterns, but some of bronze lanterns were survived. Figure 8 shows
OG9
OG7 between
OG8 thethe relationshipdamage OG10
situation and Kg value measured
OG6Z4
at near point. Large Kg value is measured near the turnover and small
＃4
IG8

＃5

Z3 IG7
GNS1

IG6
OG5

IG10u IG11IG9OG6F7 IG10d ＃1 IG12

GNS2

F6

Z2
Z1
＃2

GNS3

IG5
IG4
OG4

F8

GNS4

F5

GEW1

F4
IG1

OG2

F13

GEW5

F9

GNS5

OG1

GNS6
GNS7

N
基壇
基壇周辺床

ZIG3

IG10u

F4

F8

Z0
F13
F12

IG1
F3

＃6

IG13

F9

GNS8

BT: N,NE,E,SE,S,SW,W,
NW
BF: N,NE,E,SE,S,SW,W,WB, NW

IG19

IG21
IG20

IG22

常時微動測点
ボーリング調査位置
近傍柱石位置Measurement points aroundthe Statue
Location of base stone near the measurement

N
常時微動測点Location
microtremor measurement
図 2 of大仏周辺の詳細測点配置
常時微動測点
ボーリング調査位置
Locationof Boring
Investigation
基壇
BT；N、NE、E、SE、S、、SW、W、
NW
ボーリング調査位置
基壇周床 BF；N。NE、E、SE、S、、SW、W、WB、NW
近傍柱石位置
柱石基礎

常時微動測点

BT；N、NE、E、SE、S、、SW、W、

NW

基壇周床

BF；N。NE、E、SE、S、、SW、W、WB、NW

IG22

F1

(1) around corridor(2) around the statue (Z0)
Air view of
Measurement
pointsaround
図 2 大仏周辺の詳細測点配置
Figure 4. Measurement
measurement
pointspoints
in of microtremor on ground of Kotokuin Temple
the Statue
the temple ground

基壇

Z

IG17
F10 ＃3
IG18

基壇
BT: N,NE,E,SE,S,SW,W,
NW
基壇周辺床 BF: N,NE,E,SE,S,SW,W,WB, NW

F1

X

IG14
IG16

F11
F2

Y

IG15

IG21
OG2
N
IG20

IG11

F7 IG10d ＃1 IG12

IG2

OG3

OG10

＃4
IG8

Z1

＃2
F5

OG1

IG19

F2

IG4

OG4
IG14
IG16

F11

X Z2

IG5

IG17
F10 ＃3
IG18
F12

F3

＃6

N

GEW4

IG2

OG3

F6

IG15

OG9

OG8

YIG6 Z3 IG7 IG9
OG5

Z0

IG3

OG7

＃5

IG13

GEW3

GEW2

Z4

ボーリング調査位置
柱石基礎

Yutaka Nakamura et al.

6

Kg value is closed to survived bronze lanterns.
Figure 9 shows Kg value as a size of bubble at a location corresponding to the damage pictures of Great Buddha at Kamakura shotfrom three direction at the time of the 1923 Kanto earthquake. It is
confirmed that Kg value shows good correlation with earthquake
damage level or situation. Although Kg value around the basement isabout 10 at maximum and not so large value, the acceleration was
possibly over 500 Gal and the shear strain might reach a few 1000 μ.
Therefore, the settlement of the basement over 30cm was estimated tobe caused by liquefaction.

Z4: outside10

1

Z3: inside1
10

10 0.10.1
100

1

Amplification Factor

Close tothe statue

1

0.1

増

Z4:回廊外側

10

0.1

10

0.1

1 Z3:回廊内側
10
100

1

0.1

10

1
10 pavement
100
0.1
1
10
100
Z2: stone
Z2:周辺石畳
10

1

1

0.1

幅
倍
率

0.1

10

0.1

0.1
Z1: aroundthe1
10
100 base
10

0.1

1

0.1
10

1 Z1:基壇周辺
10
100

1

0.1

1
100
Z0: onthe10 base
10 0.10.1

1

10
Z0:基壇上

100

1

10

100

1

1

0.1

0.1
0.1

1

10

100

0.1

Frequency
in Hz
Frequency
振動数(Hz)振動数(Hz)in Hz
Component
X (EW)
Component Y (NS)
(1)Ｘ方向(2)Ｙ方向The HVSR for around of cloister

図 5 回廊周辺 Z0～Z4 での H/V スペクトル比
Figure
5. QTS (H/V spectral ratio) for around of cloister

Dynamic Characteristics of Great Bronze Buddha of Kamakura

PredominantFrequency F

7Amplification
Factor A

050m

Figure 6. predominant frequency F and its amplification factor A

Kg of EW comp.

Kg of NS comp.

Figure 7. Kg-values distribution

Yutaka Nakamura et al.

8Bronze Lanterns and Flowers etc.:

Survived
Stone Lantern:
DamagedN
W

E

After the 2011.3.11 Quake
Before the 3.11 Quake
2009-01-25

S

K-net Kamakura Amax = 50Gal
Photo by Professor Sato ©2011Kotokuin

Figure 8. Damage example by the 2011.3.11 Tohoku earthquake
10
8
NW
6
4
EW 2
0
W

N

Kg_x
Kg_y

NE

NW

E

NS
SW

SE
S

W

10
8
6
4
2
0

NE

E

SW

SE

(a)基壇周辺地盤

S (b)基壇

Kg-values around the podium

40cm sliding
30cm sinking(a) West sideN(b) South side(c) East side

Figure 9. Comparison between Kg-values and Damage caused by
the 1923 earthquake of M7.9

Dynamic Characteristics of Great Bronze Buddha of Kamakura

9

3. Measurement situation and analysis method of the Great
BuddhaThe microtremor measurement was carried out on July 23-25, 2013.
Figure 10 shows the distribution of the microtremor measurement
points for the main body of the Great Buddha. Figure 11 and Figure
12 show the appearance around measurement points. Here, the three-

DBH2R

Z
X

DBHL

DBHR
DER

DBH2R
DBHR
DBHL
DER
DAC DEL

2m

DEL
DAC
DUWL

DWR

DWL
Z

DPL

DPR

DPKR

DUWL

Y

DKR

DSL
DSR
DKC

DSW

DFFC
DRC DFCC

DPKL

BFC

DFL

DFR

DWR

DKR
DKC
DKL
DPKR
DFFC
DPKL

DWR
DWL

DSR
DSL
DSW
DFR DFCC
DFL

DRC

BFC

DWL
DRC

DPR

DKL

2m

DPR
DPL

DPL

Y

DBH2R

X
DBHR
DSW

DER
DAC

DFR
DKR
DPKR

DSR

DBHL
DEL

DFCC
DSL
BFC
DKC

DFL
DKL

DFFC

DPKL

2m

Figure 10. Microtremor measurement points in the Great Buddha of Kamakura

図1

測点配置

Yutaka Nakamura et al.

10

digit number after the site code indicates the date of measurement, forexample, 723 means July 23. It was impossible to set the sensor
immediately because a small Buddha was placed inside the jaw of theGreat Buddha and a money offering was deposited during opening aplatform having honor of seeing. However they are removed in themorning at July 25 and it became possible to measure microtremor.
The total weight of a small Buddha and a money offering were 155 kg.
On July 25 after removing the small Buddha and a money,
microtremor was recorded again at the earlobe measured before July
23 to grasp the change of the dynamic characteristics caused by thevariation of the weight, and the vibration characteristics are compared
between before and after removing and the change are considered.
Also the small Buddha (the weight is 40.4 kg) was put back into placeat July 26.
Continuous measurement was carried out at the point DRC under
the platform, and the measurement at the other two points was carriedout simultaneously standardized by the point DRC. So microtremor ofeach three points shown in Figure 10 was measured simultaneously to

Inner View
Figure 11. Inner view of Great Buddha of Kamakura

Dynamic Characteristics of Great Bronze Buddha of Kamakura

11

DER723

DEL723Hygrothermograph723

Hygrothermograph725

DEL723

DER723

DAC725Hygrothermograph725

DER725
DEL725
DAC725
DBHL723

Center line of back of head

DBH2R723
Inner statue and etc.(155 kg)
existed at July 23 and 24 (723
and 724). The measurement at
July 25 (725) were conducted
after removing them.
After measurement at July
26, inner statue (40.4 kg) was
put back to the original place.

DBHR723

Center line of back of head

DBH2R723

DBHR723

Figure 12. Measurement points in Head

DBH2R723

Yutaka Nakamura et al.

12device to have same result of frequency analysis measuring all the
point at the same time.
Sampling frequency was set 100 Hz and generally microtremor wasrecorded for five minutes. More than five analysis sections with 40.96
seconds were chosen from each recorded microtremor and appliedfrequency analysis, and then an averaged spectrum was calculated
100
W

Humidity湿度（単位％RH）(unit: %RH)

90

B

80

A
S

B
C

70
F
60
A
50

W
S

40

A

F

C

B

W
30

F

B

C

S

温度（単位℃）
Temperature (unit: °C)
20
720
1440
2160
2880
3600
4320
7/23
00:00 7/23
12:00 7/24
00:00 7/24
12:00 7/25
00:00 7/25
12:00
7/22 2013
12:00 からの経過分
月日時分
Figure7/23
13. 12:00
Change 7/24
of temperatureand humidity
at the periodof
00:00
7/24 12:00
7/25 00:00
7/25 12:00
microtremor measurement

7/23 00:00

図3

常時微動を計測している期間の温度と湿度の変化

Dynamic Characteristics of Great Bronze Buddha of Kamakura

13from three to five sections.
On the other hand, because a vibrational trajectory is known to beeffective to understand the vibration characteristics [1], here thevelocity locus of 60 seconds was drawn and considered to grasp thewhole motion.
Microtremor was measured moving points in the daytime and thenmeasured at point DRC and the other point continuously till the nextmorning. Microtremor was measured at the points DRC, DUWL and
DBH2R from the evening of July 23 to the morning of July 24, and at
the points DRC, DSL and DSR from the evening of July 24 to themorning of July 25.
A fireworks festival in Kamakura was held 2 km south from theGreat Buddha in the evening of July 23 and the vibration of fireworks
were also measured. Continuous measurement aimed to observe not
only seismic events but also the other vibrations as frictional vibration
caused by the change of temperature between the morning and theevening but there was no seismic event.
Because the differences of temperature was not so large shown in
Figure 13, the existence of frictional vibration was also not clear. Here,Figure 13 shows the change of the temperature and humidity in every
minutes with 0.5 ℃ and 0.5 %RH resolution during microtremor
measurement specifying the location of the sensors. It is confirmed
from this figure that both temperature and humidity show different
behavior at each measurement point in the body.
Although the relationship between the vibration characteristics andthe change of temperature or humidity, or the vibration of thefireworks are impressive topics, they will discussed for another day,not in this article.

4. Result of analysis
4.1 Locus of microtremor
Figure 14 shows the locus of microtremor at all the measurement
points, projecting to an elevation, a profile and a plan. Backgroundfigures of an elevation and a profile are figures of casting joints (see[3]). For a plan background figure is contour map based on the three-Yutaka Nakamura et al.

14dimensional measurement [7]. Locus in warm color and cold color
indicates the points at right side and center or left side, respectively.
According to this figure, it is possible to grasp the vibration situationof each point mentioned below. Notice that these figures include anerror with drawing so the center of the locus may not correspond tothe measurement point.

ZX

2m
0.1cm/s

ZY

2m
0.1cm/sBack Part of the HeadY
X

Rocking
RockingVibration
Vibration
X-Direction Y-Direction(Head)(Body)

2m
0.1cm/s

Figure 14. Locus of microtremor in Great Buddha of Kamakura
図 4 各部常時微動の速度軌跡

Dynamic Characteristics of Great Bronze Buddha of Kamakura

15

4.1.1 The vibration of a platform having honor of seeing for the innersmall BuddhaThis platform is a stage inside the body to having honor of seeing
for the inner small Buddha and can access the window at the backside.
This platform has been not opened to public and removed its stairs
about ten years ago. At the time of measurement in 2009, the authors
found an evidence that this platform had contacted to the inner wall of
the body and it can be estimated that this platform may swing widely
during large earthquake motion and attack the inner wall. For thisreason, microtremor measurement was carried out for the platform.
The locus of the microtremor is shown in Figure 14, and it can
indicate the structural characteristics of this platform. Because theplatform consists of the other vibration system from that of the bodyof the Great Buddha and it is available to show that the structuralcharacteristics appears at the microtremor characteristics, it isexplained in rather detail.
The platform is supported by four columns as Figure 11, and thespan of the column width is forced to enlarge at left side of the inner
body because of the location of the stairs from the entrance putting thecolumn on the intercepting beam. On the other hand, the column spancorresponds to the width of the stage and is rather narrow at the rightside of the inner body. The horizontal motion predominates in thevibration of the stage, and reflecting the difference of the structure, thelocus projected to a profile is seemed falling forward slightly becauseof a vibration like the rocking vibration in the right side whereas thelocus shows almost horizontal shape with slight small horizontal
amplitude except for tiny vertical motion because the supporting span
is comparatively long in the left side. The tiny vertical motion in theleft side seems to be affection of the structure of the column supportedby the beam.
As mentioned above, the difference of the structure appears clearlyat the microtremor. And it can be understood that sway and torsional
vibrations appear clearly on the vibration of the platform projectedhorizontal plane.
4.1.2 The vibration of the body of the Great Buddha

16

Yutaka Nakamura et al.

The vibrations in left and right direction of the body are almost
same amplitude regardless of the measured points and it shows well
the characteristics of the body of the Buddha broad in left and right
direction as the rigid body.
On the other hand, a remarkable tendency can be seen that thevibration in back and forth direction becomes larger toward to higher
point of measurement, and it can be estimated appearing the bending
vibration including the rocking vibration with the rocking center at thelower part of the basement or the shear vibration.
Anyway, this vibration shows the characteristics of the structure at
the measured point and shows comprehensible behavior as rather
predominating the vibration corresponding to the motion of the rack
where locates in the back of the hand with mudra or crossing leg.
4.1.3 The vibration of the head of the Great Buddha
Six measurement points could be installed in the head as threepoints at back of the head, one point in jaw and two points at the baseof the earlobe. The microtremor locus in velocity is highly
distinguishing for each measurement point. One minute long locus ofhorizontal motion of each point shows mainly ellipse shape withvarious vibrations inside the ellipse. It shows that the head moves invarious amplitudes and the maximum amplitude is the outmost ellipse.
Although the size of the outmost ellipse was larger at the earlobe
before removal of the inner small Buddha, it became almost similar toeach point after removal. It can be understood that the fixing in thehorizontal plane of the head has a certain level of flexibility and thefixing is not so differ from the measured points.
On the other hand, the locus projected at the elevation or side planeis quite differ between the three points at back of the head and thethree points at the jaw and the earlobe. The vibration at back of thehead draws a locus as constricted vertical motion and a forward-andbackward and a left-and-right motions seem to draw a locus ofrocking vibration mainly consisted of the vibration of the body and thehead, respectively. Both a back-and-forth vibration and a left-andright vibration of the jaw and the earlobe draw a large ellipse locus
predominating vertical motion.

Dynamic Characteristics of Great Bronze Buddha of Kamakura

17

Amplification Factor Amplification Factor Amplification Factor Amplification Factor

A load is differ about 155 kg before and after removal of the innersmall Buddha and other deposits. Microtremor at the jaw and theearlobe was measured before and after removal, and the locus of
microtremor after removal is drawn in light color. This shows that thevibration after removal, decreasing the load about 155 kg from on thejaw, becomes not only significantly smaller amplitude but also smaller
scattering. Right side vibrates obviously larger before removal and it
100

DBH21
DBH22
DBHL
DBHL2
DBHR
DEL
DER
DAC1
DAC2
DEL1
DEL2
DER1
DER2

Head / DRC
10
1
0.1
100 1

10

Upper Body / DRC
10
1

0.1
100 1

10

Lower Body / DRC
10

100

DUW
DWL
DWR
DUW
DSL
DSR
DUW1
DUW2
DUW3
DSR1

100
DSW
DKL
DKC
DKR

1
0.1
100 1

10

100
DPL
DPR
DFL
DFR
BFC

10
1

Platform or Floor / DRC

0.1
1

10

100

Frequency in Hz
Figure 15. Spectral Ratios against DRC Spectrum for X-component

Yutaka Nakamura et al.

100

DBH21
DBH22
DBHL
DBHL2
DBHR
DEL
DER
DAC1
DAC2
DEL1
DEL2
DER1
DER2

10
1

Head / DRC
0.11000 1

Amplification Factor

Amplification Factor Amplification Factor

Amplification Factor

18

10

100
DUW
DWL
DWR
DUW
DSL
DSR
DUW1
DUW2
DUW3
DSR1

100
10
1
0.1
100 1

Upper Body / DRC
10

100
DSW
DKL
DKC
DKR

10
1

0.1
1000 1

Lower Body / DRC
10

100
DPL
DPR
DFL
DFR
BFC

100
10
1

Platform or Floor / DRC

0.1
1

10

100

Frequency in Hz
Figure 16. Spectral Ratios against DRC Spectrum for Y-component

Dynamic Characteristics of Great Bronze Buddha of Kamakura

19

Amplification Factor Amplification Factor Amplification Factor Amplification Factor

seems that there becomes a little difference between right side and left
side vibration after removal. It is not apparent how the vibration atback of the head changed after removal because the measurement was
carried out only at the jaw and the earlobe after removal.
This apparent change of the characteristics is estimated roughly
from overlapped one-minute long amplitude fluctuating in time, andthis is considered in detail resolving into each frequency in the next
section.
100

DBH21
DBH22
DBHL
DBHL2
DBHR
DEL
DER
DAC1
DAC2
DEL1
DEL2
DER1
DER2

Head / DRC
10
1
0.1
100 1

10

Upper Body / DRC
10
1

0.1
100 1

10

100

DUW
DWL
DWR
DUW
DSL
DSR
DUW1
DUW2
DUW3
DSR1

100

Lower Body / DRC
DSW
DKL
DKC
DKR

10
1
0.1
100 1

10

10

100
DPL
DPR
DFL
DFR
BFC

1

Platform or Floor / DRC

0.1
1

10

100

Frequency in Hz
Figure 17. Spectral Ratios against DRC Spectrum for Z-component

20

Yutaka Nakamura et al.

4.2 Result of the frequency analysis
Figure 15 to Figure 17 show the result of the transfer function
analysis of the microtremor measured at each point as standardized
spectral ratio with the point DRC, separated in the head, in the upper
body, in the lower body, on the floor and on the platform. Thesefigures show the measured spectra in dotted and solid line before andafter removal of the inner small Buddha and other deposits,
respectively. This shows that each points at the body of the Buddha
has slightly differ vibration peak for each other. The vibration
characteristics of the head and the body have big difference for eachother.
The vibration less than 10 Hz predominates only at the head andthat over 20 Hz shows many peaks predominating at both the bodyand the head. It represents the high rigidity with corresponding thatthe body and the head is collective entity consisted of many members,
and it indicates that the joint between the body and the head is relative
loose.
Figure 18 is a kind of vibration mode diagram indicating theamplification factor corresponding to various predominant frequencies
shown in Figures 15 to 17 with the height of the measurement point.
The difference of the amplification factor at each point can be grasped
by this figure.
Figure 19 shows the spectral ratio using the left side as base in caseof the measurement at both left and right side and it corresponds to thesituation before removal the inner little Buddha and other deposits.
Figure 20 shows the amplification spectra of earlobe based on the
point DRC and the spectral ratio at the point left and right side earlobe
based on the left side for before and after the removal.
Hereinafter, the frequency characteristics of the Great Buddha areconsidered for each vibration component referring these figures.
4.2.1 Left and right direction (X-component)
In case of left and right direction, each points at the head, the upper
body, the lower body, the floor and the platform show different
characteristics.

3

4

5

6

7

8

9

100

-1
0
2020 25

0

4
3

4

L3

D

12002

-1
30 4
5

-1
6 0
50

0

3

4

5

6

7

8

3

4

5

6

7

8

9

10

10100

20

1
0
-1
20
20 30
0

2
1
0
-1

2
1
0
-1
15
200 0 300

2

3

100

10

7.568Hz

3

3

DFR

DPKR

8

7
6
5
4
3
2

8

7
6
5
4
3
2

20

30

9

10

-1
0

10

9

10

14.16Hz20

Y Y-Comp.
方向Predominant
胴体下部共振Frequency

5.615Hz

卓越振動数

Z 方向

2

3

4

5

6

7

8

7.568Hz

卓越振動数

Z 方向

2

3

4

5

6

7

8

Figure 18. Vibration modes of the Great Buddha at Kamakura

9

10

10

8

0

9

-1

0

againstFactor
Amplification
Amplification
FactoragainstDRC
DRC

100

7.935Hz

顎部他共振

9

30 50

0

10

020

etc.

床部
Floor

1

2

3

4

5

6

7

measured

18.311Hz

卓越振動数

Z 方向

Z

Z

DPL

DWL

DSL
DSR
DKC

DPR

DUWL

DEL

DBHL
DAC

DBH2R

DWR

DBHR
DER

BFC

DKR

X

DPKR
DFFC
DPKL

DSW

DPR
DPL

DBH2R
DBHR
DBHL
DER
DAC DELBFC

DFFC
DRC DFCCDFR DFCC
DFL

DSR
DSL

2m

DPL

DSL
DSR
DKC

DPR

DWL

DUWL

DAC

DEL

DBHL

DSW

DBH2R

DWR

DBHR
DER

BFC

DSW

DKR
DKC
DKL

Y

DSR
DSL
DFR DFCC
DFL

DKR

X

-1
40 1050 0 20
10 2030 30 40 50

0

1

2

3

18.311Hz

6

Y 方向Z

DPKR
DFFC
DPKL

DKR
DKC
DKL

左右逆相

5
Z-Comp.
Z 方向
Predominant4
卓越振動数
Frequency

65
5
Z-Comp.
Z 方向
Predominant
4
4
卓越振動数
Frequency

6

6

7

7

7

7

8

8

8

9

10

左右同相

9

X 方向

10

旧拝観台 3 次 7.202Hz

1014.16Hz

8

左右逆相

9

9

0

Y 方向

10

-1

10

5.615Hz

-1
5 0
100

0

1

2

3

Y-Comp.
Predominant
Y 方向
Frequency

10

-1

0
5.737Hz0

Hand 1
印相部他

2

7Upper 6
上窓
Window
Lower 5
窓下
Window
4
Platform3
旧拝観台

6

1
Frequency
後頭部共振

測
点 7
の 6
高 5
さ
（ 4
ｍ 3
） 2

30

5
5
Z-Comp.
Z 方向
Predominant
4
4
卓越振動数
Frequency

左右同相

9

X 方向

10

20

0

1

2

3

10
Amplification
DRC
R C 10 に 対 すFactor
る 増 against
幅 倍
率

-1
100 0

0

1

10

旧拝観台 2 次 5.615Hz

4.224Hz

5

5

0

6

6

0

7.935Hz

顎部他共振

Y 方向

2
2
Z-Comp.
Z 方向
Predominant
1
1
卓越振動数
Frequency

7

7

2

8

9

10

8

R

左右同相

9

Y 方向

10

-1

0

7

9

Y-Comp.

10

床部

印相部他 12

旧拝観台 3緑 7/23 測定
99measured
後頭部
Head
灰 7/24 測定
さまざまな卓越振動数に対する振動モード（DRCに対する増幅倍率分布）
耳朶部 88measured
8
Ear
顎部Lobe橙 7/25 測定
Jaw

10

10 15
10

図6

5

6.665Hz

1

-1

30 50

X-Comp. 2
X 方向
Predominant1
卓越振動数
Frequency

左右同相

X 方向

10

2
Y 方向
Predominant

0

00

020

2

測
点 7
の 6
高
5
さ
（ 4
ｍ 3
）

8

9

10

-1
-1

00

11

測
点 77
測
の 66
点
高 5
の
5
さ
高
44
さ
（
（
ｍ 33
ｍ
） 22
）

88

99

10
10

-1

旧拝観台 1 次 4.224Hz

1005.737Hz

0

0

1
後頭部共振

1

-1

2
Y 方向

Height of Measurement Point in m

3

2

Height of Measurement Point in m

ｍ 3
）

DFL

DPKL

DKL

2m

DRC

DWR
DWL

DUWL

DKL

2m

DRC

Dynamic Characteristics of Great Bronze Buddha of Kamakura
21

There are six measurement points in the head and all the points
shows same characteristics at least less than 10 Hz. It means that thehead behaves monolithically. The predominant frequency is about 6.7

Yutaka Nakamura et al.

22

Hz with amplification factor more than 10. It is considered asresonance combined the head and the upper body motion shown in
Figure 18, and the predominant frequency was not so changed bydecreasing the weight of 155 kg from the jaw.
At that time the amplitude at the body is considerably smaller thanthat at the head. Therefore the body is assumed as rigid and setting
as the spring constant of horizontal spring connecting the body and thehead, the mass relating to the vibration and the decreased mass ,the estimation ofandis attempted. When the predominantfrequencies before and after decreasing the weight are and , they
can be expressed as follows.
(

)
(

( ⁄ )

⁄(
)

(

)
⁄

)⁄

⁄

( ⁄ )
(2)
If the frequency was changed as same level of the minimum
dissolution about 0.0244 Hz from 6.690 Hz although the change of thefrequency can not be recognized by decreasing the load, it is possible
to estimate the mass relating to this vibration as follows.
21.2 tons
This is almost same level of the estimated mass of the head, 20 tons.
It also suggests that this is the vibration of entire head part. Here thespring constant of connection springis estimated as follows.
()

37.7 MN/m = 38.5 ton/cm

Although this result coincides with estimation from the frequency
Hz using estimated mass of the head and suggests the hypothesis usedin this estimation is proper, the detail will be examined hereafter.

Dynamic Characteristics of Great Bronze Buddha of Kamakura

23

In addition, a number of peaks over 10 Hz can be recognized at the
body. These high frequencies seem to reflect the vibration
characteristics of the parts of the body, and there are basically only
high frequencies at the lower body.
All the points at the floor show almost same vibration
characteristics to the basing point and it suggests high rigidity of thefloor.
There are three predominant frequencies, 4.2 Hz, 5.6 Hz and 7.2 Hzat the platform. The amplification factors are roughly 15, 75 and 45,
and that corresponding to 5.6 Hz is the largest.
The predominant frequency of each part of the left and rightcomponent has not changed after decreasing the load at least less than
10 Hz.
4.2.2 Back and forth direction (Y-component)
In case of backand forth direction, there are two significant peaks
less than 10 Hz except at the floor and the platform. Although thevibration around 8.0 Hz has changed little by decreasing the load fromthe jaw, that around 5.7 Hz has shifted to around 6.4 Hz by decreasing
the load. The vibration modes of them at the head are distinguishing.
The amplification factor after shifting to 6.4 Hz from 5.7 Hz by
decreasing the load is relative small as 5.5 at the jaw, but it becomeslarger as around 20 at back of the head.
On the other hand, the amplification factor corresponding to thevibration around 8.0 Hz is increased more than 20 excited by the bodyat the jaw, but it becomes about 10 at back of the head smaller thanthat of the upper part of the body at the back side.
This means that although these two frequencies predominate at thehead, the one around 5.7 Hz shifted to around 6.4 Hz by removal theload and make the part back of the head vibrate largely, and the otherone around 8.0 Hz has changed little by decreasing the load and makethe jaw vibrate largely. Because the vibration around 6 Hz is
responsive to the variation in weight of the jaw, this vibration seems
to relate to only some portion of the head. Whereas, the vibration
around 8 Hz is resonance of the body and it is estimated that thevibration is little affected by the change of the weight of the jaw
because the head vibrates as dragged by this motion.

Yutaka Nakamura et al.

24

Also the vibration over 10 Hz observed at the upper body isestimated as the localized motion at each portion.
4.2.3 Up and down direction (Z-component)
In case of up and down direction, the vibration less than 10 Hz
predominates only at the head and that over 15 Hz predominates at the
body. The amplification factor distributes under 15 for the vibration
less than 10 Hz at the head, and the amplitude is smaller than that of
the horizontal motion.
Significant peaks for the head appear around 5.6 Hz, 7.6 Hz and18.3 Hz. The peak at 5.6 Hz can be seen only at the point DER or
DEL at the base of the earlobe before removal and its amplification isabout 8. The body moves little by the vibration at 7.6 Hz and theamplification factor becomes larger from back of the head to the jaw
and exceeds 10. Contrary to this, the amplification factor of thevibration around 18.3 Hz exceeds 20 toward to back of the head.
The vertical motion at 7.6 Hz has changed little after removal andis confirmed to have high correlation with the vibration of back andforth direction. The vibration at 5.6 Hz and 18.3 Hz has shifted tohigher frequency as around 6 Hz and 20 Hz after removal. The
vibration at 18.3 Hz is a motion that the head moves up and down
dominantly and the motion at the body is considerably small withoutthat behind the knee.
Therefore assuming the body as rigid and the weight of the head as
20 tons same as a back and forth motion, the spring constant ofconnecting spring for vertical motion to the headcan be estimatedas follows.
(

) (

)

264 MN/m = 269 ton/cm

This is 7 times more than the spring constantof horizontal
spring, and the properness of this result will be validated hereafter.
4.2.4 Measurement points corresponding between left and right side
Figure 19 shows the spectral ratio referenced by the left side pointin case of the measurement corresponding between left and right side.
This figure shows a situation before removal of the inner small

Dynamic Characteristics of Great Bronze Buddha of Kamakura

25

Buddha and other deposits. And Figure 20 shows the similar spectral
ratio of the measurement at the earlobe before and after the removal
and additionally shows the amplification spectra against the point
DRC. Here the consideration is advanced noticing the frequency range
displaying large amplification.
With Figure 19, L/R ratio of vertical motion shows similar shapefor the points DBHL and DBHR at back of the head and the points
DEL and DER at the earlobe and slightly different shape for the points
DKL and DKR at the knee. And the ratio becomes about 1 at
frequency range less than 20 Hz same as the points DSL and DSR at
the supporting frame work, which means that the motion is almost
same for both left and right side. It is estimated that the supporting
10

DWRL
DKRL
DSRL
DBHRL
DERL

X component

Spectral Ratio Right and Left sides

1

0.1
10 1

10

DWRL100
DKRL
DSRL
DBHRL
DERL

10

DWRL100
DKRL
DSRL
DBHRL
DERL

10

100

Y component
1

0.1
10 1

Z component
1

0.1
1

Frequency in Hz
Figure 19. Spectral ratio of right and left sides (before removal of weight)

Yutaka Nakamura et al.

26

Spectral Ratioof Right and Left sidesof Right and Left sides

against DRC

Spectral Ratio

against DRC

Spectral Ratioof Right and Left sides

against DRC

100
DELRC1DELRC2DERRC1DERRC2
DERRC
DELRC

10

1

0.1
10 1

X component
10

100

DERL1

DERL2
DERL

1

0.1
100 1

10

10

100

Y component
10

100
DERL1

DERRC1DELRC1DERRC2DELRC2
DERRC
DELRC

1

0.1
10 1

DERL2
DERL

1

0.1
100 1

10

10

100

Z component
10

100
DERL1

DELRC1DELRC2DERRC1DERRC2
DERRC
DELRC

1

0.1

10 1

DERL2
DERL

1

0.1
1

10

100

Frequency in Hz
Figure 20. Spectral ratios between earlobes and DRC,and spectral ratio
between right and left of earlobe (before and after removal of weight)

Dynamic Characteristics of Great Bronze Buddha of Kamakura

27

situation of the head on the vertical direction is mostly same for bothleft and right side.
The left and right motion is differing little from the points at left
and right side at the earlobe or the points DSL and DSR at the
supporting frame work. However, R/L ratio is about 0.6 at around 6.7
Hz, which estimated to be the resonance of the head, and it means thatthe left side motion at back of the head is 1.7 times larger than theright side motion. Also in case of back and forth motion, the left side
motion is rather large at around 8 Hz as the predominating frequency
range of it. These phenomena are noticed relating to the fact that theconnecting sitution to the body is differing between the left and rightsides.
Hereafter, the authors will consider this situation in detail because
the difference of the vibration characteristics for left and right side
relate to the connecting situation of casting.
4.2.5 For a further understanding
Finally, an animation is developed as an attempt to grasp visually
the total vibration characteristics of whole the Great Buddha withprojecting not only the vibration mode of each component but also thevibration locus for each frequency to XY, YZ and XY plane [6]. This
animation draws a vibration locus considering the degree ofcorrelation for the vibration direction component at each plane.
Therefore, note that the movement at each plane is independent foreach other and this animation does not draw one motion projecting toeach plane. Also because the locus on this animation is drawn back to
the measured point after one period, the drawing direction of the locus
can be confirmed.
As mentioned above, it is confirmed from this animation that thevibration less than 10 Hz mainly makes the head move largely andvarious frequencies are appeared as a large motion of various portion
continuously. Although this Great Buddha is bilaterally symmetricseating statue, the vibration characteristics are slightly differ between
right and left sides and it is estimated to reflect the characteristics ofthis Great Buddha with a lot of connection.
The change of the characteristics caused by removal of the load on
the jaw is unexpectedly large. However it is expected to be able to28

Yutaka Nakamura et al.

grasp precisely the local situation with grasping the vibration
characteristics by changing the load actively. Hereafter, the authors
would like to continue research in detail keeping in mind these points.

5. Concluding remarks
It is quite important for the Great Buddha of Kamakura tounderstand the vibration characteristics of the head because it relates
to integrity of the connection between the body and the head.
The report of a major repair in Showa era was done in 1960 saysthat the problem of the connection exists mainly at back of neck andthere is little problem from the chest to front of neck. And it also saysthat although the portion back of neck at right side (west side) was
almost succeeded to connect at the time of casting, that at left side
(east side) was almost failed to connect and it was repaired bytinkering or other technique after casting.
As a result of microtremor measurement at some points in the head,the vibration less than 10 Hz predominates at the head. Also it iscleared that the vibration over 20 Hz predominates at the body and the
predominant frequency of the vibration related to the connection
between the body and the head is lower frequency less than 10 Hz.
The weight of the head has been estimated about 20 tons and it isremarkable that the vibration characteristics is significantly affectedby change of the load about 155 kg with removal of the inner small
Buddha and other deposits. It suggests that the welding connection
moves with a certain level of degrees of freedom but the head vibrates
as a unit. Therefore, it pointed out the necessity to consider carefully
the connecting situation at each portion in the head. Hereafter it isexpected to carry out more detailed measurement with increasing thenumber of measurement points around the connection between thehead and the body to grasp the dynamic situation. It seems that it isnecessary to take a proper countermeasure based on the result of thisdetailed measurement.
The frequency of the horizontal motion at the platform is 4.2 Hz,
5.6 Hz and 7.2 Hz, and these vibrations are torsional vibration exceptthat at 4.2 H. So, sway vibration at 4.2 Hz of back and forth direction

Dynamic Characteristics of Great Bronze Buddha of Kamakura29

is estimated to predominate during earthquake motion. In this time theamplification factor becomes large value 175 at the right side.
The gap between the stage and the body of the Great Buddha isabout 2 cm and the amplitude of the motion at the stage might beestimated about 2 cm in maximum if the earthquake motion reaches 8
Gal or Japanese Seismic Intensity 3 at the floor of the Great Buddha,
assuming that the amplification factor is kept during the earthquake
motion. The earthquake motion larger than this has a possibility ofcollision against the body of the Great Buddha. It seems that it isnecessary to take a countermeasure for conservation of the Great
Buddha.

Acknowledgement
This investigation was conducted under the committee of repair forGreat Buddha of Kamakura. The authers would like to express our
deepest appreciation to the committee and relations.

References[1] Nakamura, Y., Saita, J., and Sato, T.: Application to World
Heritage Sites, Workshop Proceedings on Increasing Seismic Safety
by Combining Engineering Technologies and Seismological Data,
Edited by M. Mucciarelli, M. Herak and J. Cassidy, Springer, pp.293324, 2009.
[2] Nakamura, Y., Saita, J., Tachibana, M., Morii, M., Inoue, S. andOhmachi, T.: On the Dynamic Characteristics of Great Buddha of
Kamakura and its surroundings (in Japanese with English abstract),
Proceedings of the 13th Japan Earthquake Engineering Symposium,
2006.11.
[3] Sekino, M. (editor): Report on Conservation of the Great Image of
Buddha, National Treasure, Kotokuin-Temple at Kamakura (inJapanese with English summary), Kotokuin-Temple, 1961.7.
[4] Sekino, Masaru: Seismic Reinforcement using Fiber Reinforced
Plastic for the Great Buddha of Kamakura (in Japanese), “SeisanKenkyu” Monthly Journal of the Institute of Industrial Science,
University of Tokyo, Vol.13, No.2, 1961.2.

30

Yutaka Nakamura et al.

[5]Sato, Takao: Damage Pictures of Lanterns in Area of KotokuinTemple (in Japanese), private communication with the chief priest of
Kotokuin-Temple, 2011.3.24.
[6]SDR: Vibration Mode of the Great Bronze Buddha at Kamakura,www.sdr.co.jp/eng_page/paper.html, 2014.4.
[7]CAD CENTER（www.cadcenter.co.jp）