HEALTH MONITORING OF BUILDING USINGSEISMIC INTERFEROMETRY
ALVAREZ REYES Ronald Stephan
MEE17707

Supervisor:

Toshihide KASHIMAABSTRACTThe objective of the health monitoring of building using seismic interferometry is to clarify thereliability and effectiveness of the deconvolution interferometry to recognize and to identify damages
in buildings due to the loss of stiffness after earthquakes to mitigate disaster risk. Therefore, the analysis
procedure has been divided into three cases. Case A is the study of the technique validation by visualinspection of the annex BRI building suffered from the Great East Japan Earthquake. Case B illustrates
the applicability to Sakishima Office high-rise Building to detect damages and shear stiffness estimation.
Case C indicates the evaluation of the sloshing effect into the experimental wooden sixth-story building.
The methodology demonstrated here, provides the analysis of strong motion and ambient
vibration data to evaluate the dynamic properties of the building in the time periods before, during andafter the quake to estimate damages and loss of shear stiffness, using system identification as a tool forseismic interferometry. Moreover, to assess the changes in the dynamic parameters due to the sloshingwater effect.
By comparison of the results in the time periods before and after the quake, using ambient
vibration, the shear wave velocity degradation located in each floor is assessed. The overall tendency
on Case A indicates the dependency of the shear wave velocity degradation with the width of cracks.
Case B shows the well estimation of shear stiffness and dependence of its accurateness due to the numberof sensors. Case C shows that seismic interferometry is a suitable technique and has high sensitivity toevaluate the wave patterns to estimate the sloshing effect.
Keywords: Health Monitoring, System Identification, Seismic Interferometry, Sloshing Effect.

1. INTRODUCTION
Structural health monitoring (SHM) is defined as the tracking of the structural condition, and detects
damages in the buildings through observation of the changes in the wave patterns, which are expressed
regarding changes in the geometry and mechanicals material properties. While those damages are welldefined as unforeseen changes in the system, which tends to modify parameters such as wave travelingtime, shear wave velocity, stiffness, etc., caused by natural disaster or human events, leaving thosestructures to expose to the risk.
Early detection and identification of the damages in the structures are the critical tasks thatthe engineering must cope with. Therefore, due to the exhibited risk a quick methodological
implementation for health monitoring of buildings and infrastructures are needed.
The principal feature that SHM must have is to enable to deliver enough accuracy in theestimated parameters that reveal the structural integrity and safe level of the building, owing to data used
to incorporate risk management strategies (Early Warning System) and structural rehabilitation, as wellas the updating of seismic code.

University of Santiago of Chile, Chile.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

1

On the other hand, efficient, prompt detection of the damages gives the chance to reduce
the loss of life and to reestablish the characteristics of the building before the damages progress, and therepairing procedure becomes economically unviable.

2. FUNDAMENTALS OF DIGITAL SIGNAL ANALYSIS AND PROCESSING
2.1. Seismic Interferometry
The term interferometry is ordinarily related to the study of interference phenomena between pairs ofreceivers that capture a signal, to acquire information from the source, medium and the differences
between them (Andrew Curtis, 2008).
SHM of a building is necessary to separate building response to an earthquake from soilstructure coupling and wave propagation below the base of the building because building response has
been contaminated with them. Seismic interferometry based on deconvolution is a method to unravel
the building response and later estimate the wave velocity which travels through the building (NoriNakata, 2013).
In arithmetic, deconvolution is described as a set of rules funded in the procedure to reverse
the effects of convolution on a recorded signal. The goal of deconvolution is to recover the first signal
before it has been contaminated with noise. In other words, it is to extract the pure response of thebuilding regardless of ground coupling (Nori Nakata, 2013).
The following procedure to describe mathematically the deconvolution interferometry isbased on the paper of Nori Nakata et al. (2013) funded on Snieder and Safak (2006):∞

𝑢(𝑧) = ∑ 𝑆(𝑤)𝑅 𝑚 (𝑤){𝑒 𝑖𝑘(2𝑚𝐻+𝑧) 𝑒 −𝛾|𝑘|(2𝑚𝐻+𝑧) + 𝑒 𝑖𝑘(2(𝑚+1)𝐻−𝑧) 𝑒 −𝛾|𝑘|(2(𝑚+1)𝐻−𝑧) }𝑚=0

𝑆(𝑤){𝑒 𝑖𝑘𝑧 𝑒 −𝛾|𝑘|𝑧 + 𝑒 𝑖𝑘(2𝐻−𝑧) 𝑒 −𝛾|𝑘|(2𝐻−𝑧) }=1 − 𝑅(𝑤)𝑒 2𝑖𝑘𝐻 𝑒 −2𝛾|𝑘|𝐻(1)

when the height of the building is H, the recorded signal of an earthquake in the frequency domain at anarbitrary receiver at height z is given by Eq. (1), where S(w) is the incoming waveform to the base of
the building, R(w) is the reflection coefficient related to the SSI and foot of the building, k is thewavenumber, 𝛾 is the attenuation coefficient, and i the imaginary unit.
The input waveform S(w) includes the information of the earthquake and the effect ofpropagation such as attenuation and scattering along the path from the hypocenter to the foundation of1
the building while the attenuation coefficient 𝛾 is denoted by 𝛾 = 2𝑄 with Q as the quality factor.
Eq. (1) with m = 0, the first term 𝑆(𝑤)𝑒 𝑖𝑘𝑧 𝑒 −𝛾|𝑘|𝑧 indicates the incoming upgoing wave
and the second term 𝑆(𝑤)𝑒 𝑖𝑘(2𝐻−𝑧) 𝑒 −𝛾|𝑘|(2𝐻−𝑧) the downgoing wave, which is reflected off the top of
the building. Therefore, m represents the number of reverberations between the base and the top of thebuilding.
In order to attain the impulse response of the building at the level z by deconvolution at thelocation of reference (𝑧𝑎 ), it is introduced the Eq. (2). The summation term in the Eq. (2) is represented
the Taylor Expansion. In this case the receiver at the location 𝑧𝑎 works as a virtual source:𝐷(𝑧, 𝑧𝑎 , 𝑤) =𝑢(𝑧)𝑆(𝑤){𝑒 𝑖𝑘𝑧 𝑒 −𝛾|𝑘|𝑧 + 𝑒 𝑖𝑘(𝑠𝐻−𝑧) 𝑒 −𝛾|𝑘|(2𝐻−𝑧) }=𝑢(𝑧𝑎 ) 𝑆(𝑤){𝑒 𝑖𝑘𝑧𝑎 𝑒 −𝛾|𝑘|𝑧𝑎 + 𝑒 𝑖𝑘(2𝐻−𝑧𝑎) 𝑒 −𝛾|𝑘|(2𝐻−𝑍𝑎 }∞= ∑(−1)𝑛 {𝑒 𝑖𝑘(2𝑛(𝐻−𝑧𝑎)+𝑧−𝑧𝑎 ) 𝑒 −𝛾|𝑘|(2𝑛(𝐻−𝑧𝑎 )+𝑧−𝑧𝑎)
𝑛=0+ 𝑒 𝑖𝑘(2𝑛(𝐻−𝑧𝑎 )+2𝐻−𝑧−𝑧𝑎) 𝑒 −𝛾|𝑘|(2𝑛(𝐻−𝑧𝑎 )+2𝐻−𝑧−𝑧𝑎) }2(2)however, Eq. (2) is unstable due to the spectral division. Therefore,
parameter ε making (Nori Nakata, 2013):
𝐷(𝑧, 𝑧𝑎 , 𝑤) =Eq. (2) needs regularization by𝑢(𝑧)𝑢(𝑧) ∗ 𝑢(𝑧𝑎 )≈𝑢(𝑧𝑎 ) |𝑢(𝑧𝑎 )|2 + 𝜀〈|𝑢(𝑧𝑎 )|2 〉(3)

where * is a complex conjugate and 〈|𝑢(𝑧𝑎 )|2 〉 the average power spectrum of 𝑢(𝑧𝑎 ). In general, εtake the value of 1% (Nori Nakata, 2013). It is shown that the deconvolution presented in Eq. (2) isindependent of the incoming waveform S(w) and the ground coupling R(w).
When 𝑧 > 𝑧𝑎 , Eq. (2) depicts a wave that is excited at 𝑧𝑎 (base of the building) andreverberated between the bottom and the top of the building. Using the normal-mode analysis of
deconvolution interferometry, Eq. (2) is based on the summation of normal-mode waves and applying
the contour integration proposed by Snieder and Safak (2006) (Nori Nakata, 2013). Then, using theinverse Fourier transform to 𝐷(𝑧, 𝑧𝑎 , 𝑤) is possible to attain the expression to define the fundamental
mode using shear wave velocity (c):𝑇0 =4(𝐻 − 𝑧𝑎 )𝑐(4)

3. HEALTH MONITORING SYSTEM OF BUILDING
3.1. Case A: Annex BRI Building
Study Case A has the objective to show the reliability of deconvolution interferometry on how thesystem is identified to detect structural damages through tracking the shear wave velocity in the Annex
BRI building and to validate its results by visual inspection in the Great East Japan Earthquake on March
11th, 2011, where the structure was affected in each floor by several secondary structural damages, suchas flexural and shear cracking on columns and shear walls, respectively (see Figure 1). Moreover, several
cracking patterns affected the slab in each floor.

Figure 1. Cracking patterns on west entrance lobby. Numbers show length andwidth of cracks related to Figure 2.
As reported by SHM and visual inspection on the Annex BRI building and to validate thetechnique to detect damages, it is possible to relate the cracking to the shear wave velocity degradationaccording to Figure 2.
Regarding Figure 2 it is found that increment of the cracking in walls and columns increase
the shear wave velocity degradation on the north-south direction. From the 1st to the 4th floor, thecracking pattern declines (0.2 mm to 0.8 mm) as the shear wave velocity degradation in agreement.
While from the 4th to the 6th floor, the shear wave velocity degradation increased as well as the cracks
pattern (0.2 mm to 0.8 mm). On the other hand, on the 7th floor, the shear velocity degradation decreased
due to the reduction of the cracking. Besides, at the same time, the growth of the shear wave velocity

3degradation with the increment of the width cracks between 0.2 mm and 0.8 mm according to the chartin Figure 2 is recognized. Therefore, the width crack has a significant effect in the shear velocity
degradation. Due to these facts, the seismic interferometry is suitable to perceive and to identify damages
through the shear wave velocity to travel inside of the building.
085Shear Wave Velocity Degradation (%)
10
15

20

25

0
0.2mm ~ less than

2.65

7
6

0.2mm ~ 0.8mm

13.4
10.65

Story

5

0.8mm ~ 1.0mm

8.05

4

1.0mm ~ more
11.05

3
2

16.8

Shear Wave Velocity
Degradation

1

21.4

0

20000

40000

60000
Length Crack (mm)80000

100000120000Figure 2. Relationship between shear wave velocity degradation and length
cracks per stories on the north-south direction.

3.2. Case B: Sakishima Office High-Rise Building
Case B has the task to reveal the effectiveness and usefulness of the seismic interferometry to estimate
shear stiffness. The building is analyzed using the Great East Japan Earthquake on March 11th, 2011 andambient vibration data before and after the shake. Consequently, Figure 3 indicates the estimated shear
stiffness by ambient vibrations before and after the quake on the X direction in Sakishima Office andcompares with shear stiffness designed. While Figure 4 illustrates the average designed stiffness and its
variation per floor.
Figure 3 reveals a well estimation of the shear stiffness from the 52 nd to the 18th floor byambient vibrations, when the stiffness variation in each story is similar. However, when the shear
stiffness in the lower stories increments drastically due to the design (see Figure 4), in another word, theshear stiffness considerably changes among stories, the utilization of the more accelerometers to increase
the accurateness is necessary. Thus, the location of two sensors among the 1st and 18th determines a low
accuracy of the shear stiffness owing to high stiffness variation.
3.3. Case C: Experimental Wooden 6F Building
Case C discusses the sloshing effect due to the temporary water pools using seismic interferometry.
Normally, the evaluation of the fundamental period, increasing the load into the building increment it.
Consequently, Figure 5 in the East-West direction reveals the rise of the natural period observed fromthe ambient vibrations measured. It can be appreciated in the increment of the dispersion in the grey
wave, increasing the wave traveling time, reducing the shear wave velocity (Eq. (4)). However, NorthSouth direction illustrates decrement of the natural period. Because the grey wave shows the decrementin the wave traveling time, increasing the shear wave velocity (Eq. (4)). This drop and growth in thefundamental period are specially called sloshing water effect. It was reported by George W. Housner,
who studied the dynamic behavior of the water into the tanks during the Chilean earthquake of May
1960. On the other hand, it is appreciable the wave’s shape changed, which is expressed as reducing its
amplitude and increment of the dispersion. It phenomenon is associated to the attenuation factor growth.

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3
1

51
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1

2011-03-1100:00:00
2011-03-1212:00:00
Design - Average

0.00 0.25 0.50 0.75 1.00 1.25

Design - Average
Design per Floor

0

20

40

60

Figure 3. Shear stiffness on X Figure 4. Shear stiffness on X
direction (10^9N/m).
direction due to design (10^9N/m).

North-South

East-West

Figure 5. Variation of wave patterns. The black line shows the behavior without
additional load, while the grey line illustrates the wave conducts with extra load
(water pool).

5CONCLUSIONS
Case A reveals the reliability, high sensitivity, and effectiveness to detect damages using the shear wave
velocity propagation through the building. The validation of the method by visual inspection illustrated
the closeness that exists between cracking patterns and shear wave velocity degradation, furthermore,
the strong dependence of the shear wave velocity of width cracking. However, the estimated dynamic
properties during the earthquake could address to overestimate dynamic parameters due to themagnitude of the damages. It is because of the degradation of the shear wave velocity owing to bending,shear, torsional and open and close of cracking patterns during the quake.
Case B illustrated the well-balance in the applicability of the deconvolution interferometry
to estimate the shear stiffness through the shear wave velocity. However, it has shown a high dependence
on the number of sensors with regards to a drastic variation of the design stiffness. Thus, it is necessary
to have more sensors to capture improvement in the accurateness of the estimated results.
Case C indicated critical agreement of the estimated dynamic parameters by seismic
interferometry due to capturing of the sloshing water effect and was in coherence with G. Housner.
Therefore, it can explain the amplification and reduction of the natural period in the experimental
wooden Sixth-Storied Building. Hence, the seismic interferometry is an appropriate technique to study
the building responses, to detect damages and to assess sloshing effect due to the reconstruction of the
wave interference patterns.

ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to Dr. Toshihide Kashima for supervising me and giving
me very valuable and helpful advice, suggestions, data and knowledge to develop this research. I am
thankful for precious support and inspiration that my family is providing me every day for continue thislong task.

REFERENCES

Andrew Curtis, P. G. (2008). Seismic Interferometry - turning noise to signal. In S. o.
Geophysicist, Seismic Interferometry: History and Present Status (pp. 14 - 22). Tulsa,
Oklahoma: Geophysics reprint series.
Housner, G. W. (1963). The Dynamic Behavior Of Water Tanks. Bulletin of the SeismologicalSociety of America (pp. 381-387). Pasadena, California: California Institute of Technology.
Kashima, T. (2004). Dynamic behavior of an eight-story SRC building examined from strong
motion records. 13th World Conference on Earthquake Engineering. Vancouver, B.C.,
Canada.
Morita, K. (2018, March 28). System identification in vibration analysis. Tsukuba, Tokyo,
Japan: International Institute of Seismology and Earthquake Engineering.
Nakata, N., & Snieder, R. (2014). Monitoring a Building using deconvolution interferometry.
II: Ambient-vibration analysis. Bulletin of the Seismological Society of America, (pp. 204213).
Nori Nakata, R. S. (2013). Monitoring a building using deconvolution interferometry. I:
Earthquake-data analysis. Bulletin of the Seismological Society of America, 1662–1678.
Yokoi, T. (2008). Introduction to Digital Data Processing. Tsukuba, Japan: IISEE.

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