Dynamic Characteristics of the Colosseum at
the Pillar #40 Comparing the Results ofMicrotremor Measurement in 1998 and 2013
Yutaka Nakamura1, Jun Saita1 and Tsutomu Sato1

Abstract
Our first extensive microtremor measurement at Colosseum was in1998, and we had an opportunity to measure again near the pillar #40
in 2013 at almost the same point of the past measurement. Here, theresults of the measurement in 1998 and 2013 at the pillar #40 can becompared. As a result, both spectral shapes basically agree well inwide frequency range. But with confirming the detail of the predominant frequency and the amplification factor, they slightly differ foreach other. The result of measurement in 2013 shows that the peaks
shift to a little higher for the radial direction and lower for the tangential direction, and the amplification factor becomes larger for each direction. And the mode changing the phase for 180 degrees between 3Fand 4F can be commonly observed in 1998 but not in 2013. Thereseems to be something structural difference between 3F and 4F, forexample the affection of the 2009 L’Aquila earthquake or the work of
the floors and the fences of 4F and 3F in 2010.
If the degradation of the structure can be grasped quantitatively
with periodic microtremor measurement, it is possible to maintain rationally and is not impossible to take a countermeasure as reinforcement of maintenance prophylactically and properly. It is necessary forestablishing the application method to confirm the accuracy of the microtremor measurement, and to make clear the reason of changing the
dynamic characteristics at pillar #40 quantitatively.

_______________________________
1 System and Data Research Co, Ltd., Tokyo, Japan.
25

26

Y. Nakamura, J. Saita and T. Sato

1. Introduction
The Colosseum is a huge amphitheater which Roman Emperor
Vespasian built to amuse common people on a reclaimed artificial
lake at the garden of Nero’s Domus Aurea as if to wipe away thememory of nightmare caused by Nero a tyrant from common people[1, 2, 3]. Plane plan is ellipse with 188 m of long axis, 156 m of shortaxis and 49 m of height. Although there are different stories, it had
been started construction during the early part of AC 70’s and completed at AC 80 of next Emperor Titus era. Because huge structure
was built on a soft ground at a valley enclosed by hills on three sides,
extremely hard foundation had been constructed. A discotic foundation with more than 12 m of thickness had been constructed by twolayers made with ancient concrete, or Roman concrete, and the shapeis like a donut because of avoiding the area as a field.
Huge construction of Colosseum was built on this hard foundation,
but as a result of keeping exposition of the natural or artificial action
for a quite long time near 2000 years, it is suffered seriously damage
although the extensive repair works was done repeatedly. However thefoundation has remained, a half of outer upper structure had been lostby the 1354 and other earthquakes. Additionally some part had been
moved away as a stone material for other structures at the Middle age.
At the survived area, the outer wall has still remained almost to thetop, but the inner structure has remained almost to the second floor, 2F,
and partially fourth floor, 4F, the top floor. Upper structure is supported by pillars from ground floor, GF, to 2F in appearance, and there iswall over third floor, 3F. The each side of the survived structure wasreinforced in early 19th century, and the eastern and western part iscalled Stern and Valadier from the name of conducting engineers today, respectively.
In these recent days, the environment surrounding Colosseum has
been changed largely and the affection of the vibration caused by social activity, so called traffic vibration has been concerned. Additionally the subway Linea B constructed after the World War II, there areroad and tram line passing the northern to the western side, and the
new subway Linea C is recently under construction in the northernside [4]. Under this situation, a restoration project has been started by·Dynamic Characteristics of the Colosseum at the Pillar #40···27

a large sum of donation by a benefactor since 2013 [5]. The restoration is seems to be not for changing the actual condition but for consolidation with reinforcing or protecting the degraded or weakened
parts properly without changing the actual situation with the purpose
for mainly cleaning.
Aside from the impact investigation of the vibration caused by theexisting subway, a research group considers what kind of vibration
will be caused by the new subway line construction and affect Colosseum, and how to decrease the influence. And they discuss about thevehicle as not only the iron wheel type but also rubber tire type ormagnetic levitation type. A large scale FEM numerical model wasconstructed for this consideration [6]. Because the model requires accurate physical parameters, results of past investigations on Colosseum are gathered and additional investigations are planned.
The first microtremor measurement on Colosseum was conductedby Clemente et al. in 1985, and also other measurements has been reported [7, 8]. Among those measurements, our measurement in 1998
is recognized as the systematic distribution of the largest number ofmeasurement point. We have reanalyzed the data and kept conducting
additional measurement for the ground around Colosseum in a chanceof visiting Rome with the view of this situation.
And we could measure again partially not only at the surrounding
ground but also at the underground area of the arena and the main
body of Colosseum in 2013. These measurements give almost same
result and there is no other result of measurement at precisely thesame point with time distance. But in 2013 we could measure, likely
as a measurement in 1998, at almost same points with almost same instruments in the same procedure as simultaneously measurement at
two points, so we can consider the difference of microtremor characteristics measured in a time span of 15 years.
This must be the first attempt to substantiate that this kind of measurements can make clear the degree of degradation quantitatively byconducting the same kind of measurements in the future with clarifying the measuring error, the statistical scatter or other parameters.
Our first measurement of Colosseum was on November, 1997. After this preliminary measurement, we conducted the first extensive
measurement on July, 1998. The results of these measurements have

Y. Nakamura, J. Saita and T. Sato28

been opened in some conferences [9, 10]. Here describes the result ofcomparison of microtremor characteristics at each layer measured on
July 7, 1998 and on December 13, 2013 at the pillar #40 of the outer
ring, with the numbering system of totally 80 pillars of the outer ringas counterclockwise rotation from the south pillar as Figure 4 of [11].
2. Measured Points and the Procedure of Measurement andAnalysis
Figure 1 shows the measured points in 1998 and 2013. Figure 2
shows the location of the pillar #40 and the location of microtremor
measurements in 2013 on the floor plan picture. And Photo 1 shows
the situation of the measurement points in 1998 and 2013. Althoughboth measurement were conducted almost at the same points, the location of the point at GF differs for each other. The location was outside
R

V

T

4F
3F
2F

This point was measured in 2013,
but no mention in this report

This figure is modified from a figureof pillar #40 of Colosseum fromCROCI,G. and CERONE, M.(2002):
RESTAURO DELL’ ANFITEATROFLAVIO STUDI RICERCHE E
CONSULENZE-ANALISI DOCUMENTAZIONEDEI DISSESTI STRUTTURALI ED
INDIVIDUAZIONE DELLE SITUAZIONI DI RISCHIO AS TIPOLOGIE STRUTTURALI DEI DISSESTI SEZIONI-Points 1F to 4F were measured
in 2013 and 1998.

1F

GF
1998

GF
2013

0 1 3 6m
Figure 1 Location of measurement points at pillar #40 of the Colosseum·

Dynamic Characteristics of the Colosseum at the Pillar #40···

29

Pillar #40
Monument
North

0 10
50m

20 30 40

Figure 2 Measurement points in 2013 (small greens are measured in 1998)

the pillar in 1998 and inside the pillar in 2013 because of the difference of the public area configuration.
In 2013, microtremor of three directions, tangential direction T, radial direction R and vertical direction V, was recorded in 1/100 seconds of sampling time with a fixed instrument at the highest floor, 4F,
and with a moving instrument at 4F, 3F, 2F, 1F or GF. This meansthat this measurement recording the data simultaneously at two points
including the fixed point is devised to get a same result of simultaneous measurement at the entire point with same instruments. The
measurement in 1998 was also conducted simultaneously at two
points with three components, R, T and V, but the characteristics of
the instrument were not complemented.
The measurement in 1998 recorded microtremor as a 40.96 seconds
data, 4096 samples, repeating three times, and that in 2013 recorded
microtremor as a five minutes data at each point, chose five sectionsof 40.96 seconds data, 4096 samples, and then averaged the five data
sections with frequency analysis. Earthquake motion response characteristics of each floor based on GF are derived for each measurement.

Y. Nakamura, J. Saita and T. Sato30

4F

2013Dec.

3F

2013Dec.

1998July
4F

1998July
3F

1998July
2F

2F

2013Dec.

1F

2013Dec.

GF

2013Dec.

1998July
1F

1998July
GF

Photo 1 Measurement points at pillar #40 in 2013 and 1998
Red circles: sensor location, Blue triangle: sensor location in 2013·

Dynamic Characteristics of the Colosseum at the Pillar #40···

31

And 𝐾𝑏 value is derived from the earthquake motion response
characteristics. This 𝐾𝑏 value is an index to indicate the vulnerabilityof the structures focusing the drift angle and is formulated as follows[10] (see Figure 3).
Assuming that the predominantfrequency dominates and each floor
vibrates as the vibration mode of the
predominant frequency, then the response displacement 𝛿i of ith floor
against the earthquake acceleration α
from GF becomes as flows;
𝛿i ＝𝐴i 𝛼/(2𝜋𝐹)2(1)of structure
Figure 3Mode
Modeshapes
shape ofstructure

Here, 𝐴i is the amplification factor of ith floor. Then, the drift an3 建物のモード形状
gle 図
betweenith and jth floors 𝛾j at jth floor becomes as follows;
γj ＝|Ai – Aj |α/(2πF)2 /Hj ＝|Ai – Aj |/(4π2 F 2 Hj ) × α＝K bj × α(2)Here, 𝐻j is the height of the pillar at jth floor, |*| is an absolute value of *, and j = i + 1.
The 𝐾𝑏𝑗 value can be considered as an index relating to the vulnerability of this pillar. With setting the unit of the drift angle to 10-6, aheight of a pillar in m and acceleration in Gal (= cm/sec2) the 𝐾𝑏𝑗 value can be expressed as follows;
K bj ＝104 × |Ai – Aj |/(4π2 F 2 Hj )(3)This is the 𝐾𝑏𝑗 value for the vulnerability of a structure. The predominant frequency and the amplification factor for each floor can bederived from the result of the microtremor measurement. Although theestimation based on the microtremor is only a result of the response at

Y. Nakamura, J. Saita and T. Sato32

a minute level and does not suppose a large deformation, it is considered to be able to order the measured points by the vulnerability.
As mentioned above, the 𝐾𝑏𝑗 value estimated from the result of the
microtremor and the dimension of the structure is expected to orderthe structure with the vulnerability of each structure, the component or
the floor, and to clarify the weak points. This paper calculates the 𝐾𝑏𝑗
value for comparison of the measurement result at each time and location.
3. Results of Analysis
Figure 4 shows the result of the comparison between the measurement in 1998 and in 2013. The shape of the transfer function wellagrees for each measurement at a wide frequency range for the threecomponents. However noticing to the detail of the predominant frequency and the amplification factor, they differ slightly for each other.
Table 1 shows the predominant frequency and its amplification factor.
It can be seen that the predominant frequency of the measurement in2013 shifts higher for R component and lower for T component thanthat of the measurement in 1998. The amplification factor of themeasurement in 2013 becomes larger than that in 1998 for each direction. That of V component changes slightly large and the predominantfrequency seems to shift higher.
Table 1 Predominant frequency and its amplification factor

Table 1. Predominant Frequencies, its Amplification and Kb values for Column #40 of Colosseum

2013

Height(m) Tangential Radial Vertical

Predom. Fre. (Hz)Amplification
against GF

13.330Kbi (m/Gal)
between Height(m)Tangential Radial Vertical

37.5

16.7

23.9

7.3

4F and 3F

34.79

2.4

98.5

0.20

3F

32.08

16.3

17.5

6.5

3F and 2F

28.02

19.5

75.7

0.30

2F

23.96

11.9

10.3

4.8

2F and 1F

18.215

19.0

51.4

0.28

1F

12.47

5.8

3.2

2.5

1F and GF

6.235

13.8

15.2

0.18

GF

0.0

1.0

1.0

1.0

1998

·

1.733

4F

Height(m) Tangential Radial Vertical

Predom. Fre. (Hz)Amplification
against GF

2.661

2.905

1.685

10.547

Kbi (m/Gal)
between Height(m)Tangential Radial Vertical

4F

37.5

14.1

18.5

5.3

4F and 3F

34.79

8.1

71.3

0.16

3F

32.08

12.7

14.1

5.0

3F and 2F

28.02

12.5

61.9

0.26

2F

23.96

9.3

8.5

4.0

2F and 1F

18.215

12.2

42.8

0.35

1F

12.47

4.6

3.0

2.3

1F and GF

6.235

8.7

14.4

0.24

GF

0.0

1.0

1.0

1.0

#40T

10

1

10

Frequency in Hz

1

1F

10

10

1998

#40V

2013

Frequency in Hz

Figure 4 Comparison between the measurement in 1998 and in 2013

Frequency in Hz

0.1

10

0.1

1

10

2F

2F

1998
1F

3F

3F

0.1

10

4F

4F

1

1998

1

1F

#40R

1

1F

2F

3F

4F

1

10

100

Amplification Factor to GF#40V

for 1998 measurement
Spectra at Pillar #40 of Colosseum
Amplification
100
100

0.1
1

10

2F

1F

3F

2F

2013

0.1
10

10

4F

3F

100

4F

#40R

0.1

1F

100

1

1

2013

2F

3F

#40T

4F

Amplification Spectra at Pillar #40 of Colosseum for 2013 measurement

1

Amplification Factor to GF

1

10

100

Dynamic Characteristics of the Colosseum at the Pillar #40···
33

34

Y. Nakamura, J. Saita and T. Sato

According to the structure of Colosseum, because especially the Tcomponent and the V component of the higher layer are the direction
along the wall, it is estimated that the degradation of the structure iseasy to be seen. Meanwhile, because the R component is perpendicular to the wall and affected by the bending, this component is seems to
be sensitive for the local effect. On the other hand, because the sensor
is set at a point on a floor for measurement, leaving from the wall
makes sensitive against the vibration of the floor. Especially in case of
the vertical motion, it is impossible to ignore the effect when the rigidity of the floor is poor. However looking at the cross-section as shownin Figure 1, the rigidity of the floor close to a wall or a pillar is rather
high because the floor is supported by an arch structure. So the vibration of the floor seems to have only a small impact. Although the GF
point was set outer and inner side of the pillar #40 for each measurement as described previously, both the dynamic characteristics with adistance of 2 m are basically not much difference because the points
are on the hard ancient concrete foundation 12 m thick. We would liketo verify precisely the effect caused by the difference of the measurement point for the result of the analysis in the future. See Photo 1 tograsp the difference of the location in detail.
From the result of the measurement in 2013, the predominant frequency of R component becomes higher than that in 1998 and that of
T component becomes obviously lower than that in 1998. The obvious
decreasing the predominant frequency of T component is feared to bea phenomenon relating to a structural problem, because the horizontal
components seem to be little affected by the location of the measurement point.
Figure 5 shows a vibration mode of the frequency maximizing theamplification factor at 4F. There can be seen a lot of other peaks on
the transfer function. Especially for the vertical motion, the peak is athigh frequency range and corresponding roughly to each measurementin 1998 and 2013, however it has a possibility to be not corresponding
precisely.
The vibration mode at various frequencies is animated with sweeping the frequency to understand precisely the vibration mode at thepeak frequency. Please see this animation on our website [12].

·Dynamic Characteristics of the Colosseum at the Pillar #40···

35

From the animated mode diagram shown in Figure 6, there aremany modes changing the phase 180 degrees between 3F and 4F at R
component increasing the predominant frequency for the measurementin 1998, however these modes are little seen for that in 2013 measurement. It suggests that there must be some structural changes beTangential

Radial

40

40T

35

40

40R

35

40V

35

1998

1998

30

30

2.905 Hz

Height in m

Vertical

40

25

25

20

20

1998
30

1.685 Hz2013

10.547 Hz

25

1.733 Hz

20

2013
15

2013
15

15

10

10

10

5

5

5

2.661 Hz13.330 Hz

0

0
0

5

10

15

Amplification Factor

20

0
0

10

20

Amplification Factor

30

0

2

4

6

8

Amplification Factor

Figure 5 First modes for each component at pillar #40

Figure 6 An Example of animated mode diagram from the animation

Y. Nakamura, J. Saita and T. Sato36

tween 3F and 4F during 1998 to 2013. During this period the 2009
L'Aquila Earthquake M6.3 occurred at around 90 km in the northeastof Colosseum. It is estimated that Rome might experience the earthquake motion of Realtime Intensity RI 3, almost same as the JMA intensity [13], corresponding to MMI 5, but there is no report on the serious damage for Colosseum.
Table 1 also shows the Kb value of the structure derived from thepredominant frequencies and their amplification factors. Figure 7
shows the vertical distribution of derived Kb value. Comparing the Kb
value at each component, R component shows predominantly large
value and it suggests this component is weakened. The value for T
component is around a fifth of that for R component. In response of
the value for R component becoming lager for upper layer, that for T
component is small at GF and 3F and large at 1F and 2F. The value
for V component reaches maximum at 1F or 2F but the value is considerably small. The distribution of the Kb value for T and V components is thought to reflect the situation becoming less deformable by
the wall structure over 3F. Almost all the component shows lager value for the measurement in 2013 against that in 1998. Despite the decreasing the predominant frequency, it becomes the largest for R
component and the value corresponding to reaching 1 % of the story
drift againstTangential
the earthquake motionof 100 Gal at the Verticalwall of 3F. The
Radial
40

40

40T

35

35

25

30

30

2013

25

20

20

20

15

15

15

10

10

10

5

5

5

0

0
10

20

Kb value (m/Gal)

30

2013

1998

25

1998

0

40V

35

1998

2013

30

Height in m

40

40R

0
0

50

100

Kb value (m/Gal)

150

0

0.1

0.2

0.3

Kb value (m/Gal)

Figure 7 Kb value distribution for the first modes at pillar #40·

0.4

Dynamic Characteristics of the Colosseum at the Pillar #40···

37

value for T component of the measurement in 2013 becomes 1.4 times
larger than that in 1998. It is startling that such a large change is occurred at most 15 years. It is considered that the result of the analysis
may include not only the measurement error but also the statistical error for the measured data.
As mentioned above, the change of the mode, the predominant frequency, the amplification factor and the Kb value was unpredictably
large between the measurement in 1998 and 2013. So we tried confirming a change on appearance around the measurement points basedon the movies and pictures during the measurement. Photo 2 shows
the situation around the point 4F both in 1998 and 2013.
At first focusing the floor setting the sensor, it is confirmed that
there is an original travertine pavement at GF, a concrete pavement
between 1F and 3F, and a mortar pavement with brick pieces at 4F.
The pavement between 1F and 3F seems to be mainly casted before
1998 with unknown thick. The floor contacts the wall at 3F and 4F. A
concrete is casted with a distance 15 cm around the pillar at 1F and
2F. Although there are mainly radial joints, there were concentricjoints at 4F in 1998 as Photo 2. But in 2013, the concentric joints
changed to radial joints. And the fences were also changed clearly between 1998 and 2013 at 4F. It is possible to confirm the concentricjoints on the picture of Google Earth dated July 29, 2007, but the situation of the floor was clearly changed on November 10, 2011 from thebackground picture of Figure 2. And the shadow of the fence on thefloor at that time suggests that it was same as the one at the time of themeasurement in 2013. So it is possible to say that a work refurbishing
the floor and the fences of 4F between July 29, 2007 and November
10, 2011. Finally the subsequent investigation made clear that workfor 3F and 4F conducted between March and November 2010 shownin Photo 3.
The pavement of the 4F floor in 1998 was separated mainly in three
sections by two concentric joints to the fences. There are concentricjoints on the pavement contacting the wall and it seems to be unified
totally to the wall.

Y. Nakamura, J. Saita and T. Sato38

Difference between 1998 and 2013:
Fence, Joint and Floor

2013Dec. 1998July

2013Dec.
Difference between 1998 and 2013:
Fence, Joint and Floor

1998JulyComparison of measurement situation around Column #40 between in
Photo 2 Comparison of measurement situation around pillar #40
1998 and in 2013
between in 1998 and in 2013
写真 2 4F 測点周辺の状況：1998 年と 2013 年の比較
2010-03-20
Old Fence

2010-11-24
New Fence

This photo taken at 2010-11-24 from web

Photo 3 Old and new fences appeared in photos·

Dynamic Characteristics of the Colosseum at the Pillar #40···

39

On the other hand, the 4F floor in 2013 was separated with a distance 2 m to 3 m by radial joints from the wall to the fence. Although
the strength of the floor pavement is unclear, assuming the floor
pavement connected tightly by the joints, the 4F floor pavement in1998 and 2013 seems to have an effect to reinforce the tangential T
component and the radial R component from the direction of thejoints, respectively. It is agreeable that the predominant frequency of
T direction becomes lower in 2013, that of R component becomes
higher in 2013, and the phenomenon reversing the vibration mode of
R component at 3F and 4F is confirmed in 1998 and not in 2013. The
measurement points without GF locate at an area not opened to public
and then there seems to be no degradation for the floor pavement
caused by passing tourers, but the floor concrete at 1F and 2F showsdegradation clearly as expanding opening with increasing cracks on
the floor pavement or exfoliation and fracture of joints. However it isdifficult to confirm the situation of the degradation clearly because of
the dark image at 3F, a structural factor of the degradation may exist.
Meanwhile, the fence itself and its location at 1F and 2F differ for themeasurement in 1998 and 2013 as shown in Photo 1.
The changes above are impressive because of the relation to thechange of the dynamic characteristics derived from microtremor. We
would like to grasp quantitatively the relation to the change of the microtremor characteristics with confirming the description of work at
4F and grasping the detailed structural characteristics. We expect thatthe microtremor measurement will be applied as a powerful tool forreasonable maintenance of the structure.
4. Conclusion
This paper considered the change of the dynamic characteristics ofColosseum with comparing the result of the microtremor measurement
at the pillar #40 in 1998 and 2013. As a result, an unexpected largechange was grasped for the predominant frequency and its amplification. The factors for this change are considered as the effect of the2009 L'Aquila Earthquake, the effect of the work modifying the 4F
floor and the fence, and additionally the factors on the measurement
itself as the measuring or the statistical error. This comparison made

40

Y. Nakamura, J. Saita and T. Satoconfirm specifically the possibility that the measured microtremor
characteristics reflect the change of the structural characteristics, so it
seems to be necessary to consider precisely making clear the impact
rate of each factor as a future issue.
It is important for reinforcing the structure of Colosseum to grasp
the stiffening effect quantitatively. So it is necessary to investigate before and after the reinforcement. Additionally it is possible to maintainthe structure reasonably and not impossible to provide preventive andproper countermeasures for reinforcement or conservation, if the degradation of the structure can be grasped quantitatively with a periodical microtremor measurement. It is necessary for establishing this utilization method to confirm the accuracy of the microtremor investigation and also to explain quantitatively the reason changing the dynamic characteristics of the pillar #40.
Acknowledgement
The measurement in Colosseum is greatly attributed to the heavy
work done by Prof. Antonio Rovelli of INGV, Prof. Gianfranco
Valente of L’Aquila University and Dr. Paolo Clemente of ENEA.
And Ms. Cinzia Conti of Soprintendenza speciale per i Beni Archeologici di Roma and other concerned personnel gave admissions agreeably and full facilities to our measurement.
We greatly appreciate their help.
References[1] Anna Maria Liberati and Fabio Bourbon: Ancient Rome, White Star, Italy, 1996, pp.74-75.
[2] Leonardo B. Dal Maso: Rome of the Caesars, Italy.
[3] Roberto Luciani: The Colosseum, DeAGOSTINI, Italy, 1990.
[4] https://en.wikipedia.org/wiki/Rome_Metro.
[5] http://www.enit.it/ja/sediestere/asia/tokyo/comunicati/1346-restauri-deimonumenti-simbolici-di-roma2.html[6] Caserta, A., Cerone, M., Crisi, F., Delladio, A.,D’Ovidio, G.,Govoni, A.,
Marra, F., Nakamura, Y., Rovelli, A. and Valente, G.: Dynamic interaction of soil and structure by rail traffic, Proceedings of the Dynamic In-·Dynamic Characteristics of the Colosseum at the Pillar #40···

41

teraction of Soil and Structure, DISS_10, L’Aquila, 19 March 2010,
Aracne, 2011, pp.89-108.
[7] Clemente, P., Bongiovanni, G.: Ambient vibration effects on the Colosseum, IABSE Symposium on Structural Preservation of the Architectural Heritage, Rome, 1993, pp.107-114.
[8] Pau, A., Vestroni, F.: Vibration analysis and dynamic characterization of
the Colosseum, Structural Controll and Health Monitoring, Ed. J. Wiley& Sons, 2008.
[9] Nakamura, Y., Saita, J., Rovelli, A. and Donati, S.: Seismic Response of
Roman Colosseum and its Foundation by using Micro-tremor Measurements, The 10th Earthquake Engineering Symposium, 1998.11,
pp.2625-2630.
[10] Nakamura, Y., Gurler, E.D., Saita, J., Rovelli, A., Donati, S.: Vulnerability Inveastigation of Roman Collisseum using Ambient Vibration,
12WCEE, paper#2660, 2000.
[11] Nakamura, Y. , Saita, J., Sato, T. and Valente, G.: Attempts to Estimate
the Physical Property of Surrounding Ground and Foundation Concreteof Colosseum using Microtremor, Proceedings of the DISS_15 in Rome,
December 2015.
[12] SDR: Vibration Mode of the Colosseum of Rome, www.sdr.co.jp, September 2014.
[13] Nakamura, Y.: Earthquake Early Warning and Realtime Earthquake
Disaster Prevention, Proceedings of the DISS_10, L’Aquila, 19 March
2010, Aracne, 2011, pp.153-165.