Western Australian School of Mines

IMPROVING THE ACCURACY OF VELOCITY WAVEFORM

USING TRANSFER FUNCTION OBTAINED BY GEOPHONE

AND ACCELEROMETER

TITTU BABU

16320587

Curtin University

Date: 27/10/2013

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I declare that this dissertation is my own original work, except where acknowledged or referenced, and it has not been submitted for academic credit elsewhere, and acknowledge that the assessor of this item may, for purposes of assessing this item and subject to any confidentiality limitations:

• Reproduce this assessment item and provide a copy to another member of the University; and/or

• Communicate a copy of this assessment item to a plagiarism checking service (which may then retain a copy of the assessment item on its database for the purpose of future plagiarism checking).

I certify that I have read and understood the University Rules in respect of Student Rights and Responsibilities (details of which can be found at:

http://students.curtin.edu.au/administration/responsibilities.cfm).

Name of Student: TITTU BABU

Student Number: 16320587

Signed: Tittu babu

Date: 27/10/2013

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ABSTRACT

In order to break rocks at mines blasting operations are done. Along with rock breakage

blasting also produces unwanted by products such as air blast, seismic waves, noise and fly

rocks. Seismic waves result in ground vibrations .Noise and ground vibrations have a wider

impact on the environment and the people .When the vibration occurs each ground particle

possess a velocity and the maximum velocity is termed as Peak Particle Velocity (PPV).The

intensity of vibration is measured by PPV. If the ground vibration exceeds the PPV limit

potential damage will occur to the structure.So it is necessary to measure the ground

vibrations precisely inorder to avoid any kind of damages. In order to measure ground

vibrations , measuring instruments called Blast Seismographs ( geophone or accelerometer )

are used.Usually at mines, blast vibrations are measured by geophones .But the

measurement by a geophone is not precise as that of an accelerometer and the usage of

accelerometers at mines for vibration measurement is limited due to its cost. So it is

necessary to measure the blast vibrations effectively and economically.

The project objective is to improve the accuracy of velocity waveform using transfer

function obtained by geophone and accelerometer. For carrying out this research project the

blast vibrations produced by KCGM (Kalgoorlie Consolidated Gold Mine) will be

measured at WASM laboratory. All the essential literature materials about geophone,

accelerometer ,theory about rock breakage, blasting operations, ground vibrations, peak

particle velocity ,Fast Fourier transform(FFT) etc. are collected. Accelerometer selected for

this research project is TEAC 708LF and geophone selected for this project is PC-801

LPC.In order to acquire the same vibration both geophone and accelerometer are attached

together. Almost twenty six blast vibration readings are taken. Only data with same units

can be compared. So the acceleration data is integrated to convert it into velocity data.

Comparison of data in time domain has no meaning, so it is to be converted to frequency

domain. Then these values in time domain is converted to frequency domain using FFT in

OriginPro7J software. Then transfer function is obtained by dividing the integrated

acceleration data with geophone data. Finally in order to improve the accuracy of velocity

waveform, it is multiplied with the geophone data. Then this newly obtained waveform is

compared with the corresponding accelerometer and geophone data to obtain the desired

result. Finally suitable conclusions in support of the result are derived and it shows the

degree of accuracy of the final result.

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ACKNOWLEDGEMENTS

I would like to thank and extend my sincere gratitude to all the academic staff of Mining

Engineering Department, Western Australian School of Mines (WASM) Kalgoorlie Curtin

University Western Australia.

I am deeply thankful to my supervisor Dr. Youhei Kawamura without whom this project would

never happen. His instructive advice and valuable suggestions helped me a lot for the completion of

this thesis. Support from the supervisor for the completion of this research project was outstanding.

I would also like to thank Prof .Erkan Topal , Head of Mining Engineering Department , for his full

support for me as an international student during the last one and half year. I am deeply grateful to

Mr .Mahroof for granting me permission to use the Geology department lab.

Finally I would like to thank the almighty god, my parents and my brother for their unconditional

love and support. Once again I would like to thank each and every one who has helped me in my

entire work.

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Table of Contents ABSTRACT 2

ACKNOWLEDGEMENTS 3

LIST OF FIGURES 6

LIST OF TABLES 8

LIST OF SYMBOLS AND ACRONYMS 9

1 INTRODUCTION TO PROJECT 10

1.2. Background to Project 11

1.3. Project Problem Statement 12

1.4. Project Objectives 12

1.5. Project Activities 13

1.6. Project Scope 13

2 LITERATURE REVIEW 14

2.1 Introduction to Literature Review 14

2.2 Literature Review 14

2.2.1 Ground Vibrations Induced By Blasting 14

2.2.2 Ground Vibration Measurement –PPV 18

2.2.3 Types of Waves 22

2.4 Ground Vibration Measuring Instruments 26

2.4.1 Geophone 26

2.4.2 Accelerometer 30

2.5 Transfer function 32

2.6 Fast Fourier Transform 35

2.7 Sampling Frequency 39

2.8 Summary of Literature Review 41

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3 RESEARCH METHOD & EXPERIMENTAL/ANALYTICAL DESIGN 42

3.1 Introduction 42

3.2 Instruments used 43

3.2.1 Geophone 43

3.2.2 Accelerometer 44

3.2.3 Amplifier 45

3.2.4 Data logger and computer 46

3.3 Experimental set up 47

3.4 Obtaining the amplification factor 48

3.5 Measuring the blast vibrations 49

3.6 Summary of Research Method & Experimental/Analytical Design 51

4. RESULT AND ANALYSIS 52

4.1 Blast vibrational waveform 52

4.2 Time domain spectra 52

4.3 Filtering off low frequency signals 56

4.4 Frequency domain spectra 57

4.5 Obtain transfer function 59

4.6 Improving the accuracy of velocity waveform 61

5 CONCLUSIONS AND RECOMMENDATIONS 66

5.1 Conclusions 66

5.2 Recommendations for Further Work 67

6 REFERENCES 68

7APPENDIX A 71

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LIST OF FIGURES

Figure 1 Ground wave propagation (reproduced from Adrian J. Moore and Alan B. Richards

1997) .................................................................................................................................................. 17

Figure 2 Peak article Velocity (PPV) (reproduced from Nicholls,1971 ) .................................... 18

Figure 3- Recommended safe levels for blast vibrations (reproduced from USBM RI 8507 and

AS 2187.2—2006). ............................................................................................................................ 20

Figure 4- Probability damage analysis for low frequency blasts and shaker test (reproduced

from USBM RI8507) ........................................................................................................................ 21

Figure 5– Different types of waves (reproduced from Adrian J. Moore and Alan B. Richards

1997). ................................................................................................................................................. 22

Figure 6- P wave (reproduced from Nicholls 1971) ...................................................................... 23

Figure 7- S wave (reproduced from Nicholls 1971). ..................................................................... 24

Figure 8– Rayleigh wave (reproduced from Nicholls 1971) ......................................................... 25

Figure 9-Arrival time of P, S and R wave for a single hole blasting (reproduced from

Dowding 1985). ................................................................................................................................. 25

Figure 10– isometric and cross sectional view of a geophone (reproduced from Aaron Barzilai

2000) .................................................................................................................................................. 26

Figure 11 -Frequency responses of geophone PC-801 LPC (obtained from the experiment) .. 29

Figure 12- Frequency responses of geophone PC-801 LPC (obtained from the experiment) .. 29

Figure 13–Structural components and internal circuits of a piezoelectric accelerometer

(Michael Hons 2006) ........................................................................................................................ 30

Figure 14-Typical acceleration data of a piezoelectric accelerometer,TEAC 708 LF(obtained

from the experiment) ....................................................................................................................... 32

Figure 15- Sample wave form (reproduced from Bradley 1989) ................................................ 36

Figure 16- Fast Fourier Transform of the sample waveform (reproduced from Bradley 1989)

........................................................................................................................................................... 36

Figure 17 General illustration of FFT (reproduced from Dennis H.Shreve 1995) .................... 38

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Figure 18- An example of voltage time data (reproduced from Dennis H.Shreve 1995) .......... 38

Figure 19- An example of frequency data obtained after FFT (reproduced from Dennis

H.Shreve 1995) ................................................................................................................................. 39

Figure 20- sampling frequency or frequency rate (reproduced from Dennis H Shreve 1995) . 39

Figure 21-An example of sampling frequency (reproduced from Dennis H Shreve 1995) ....... 40

Figure 22-Geophone PC-801 LPC .................................................................................................. 43

Figure 23-Accelerometer TEAC 708 LF ........................................................................................ 44

Figure 24- TEAC SA- 611 Charge Amplifier ................................................................................ 45

Figure 25-TEAC Data logger .......................................................................................................... 47

Figure 26-geophone and accelerometer attached together .......................................................... 48

Figure 27-Experimental set up ....................................................................................................... 48

Figure 28-Experimental set up to obtain amplification factor .................................................... 49

Figure 29-recorded blast vibration waveform .............................................................................. 50

Figure 30- recorded blasting wavelet ............................................................................................. 52

Figure 31-velocity waveform from geophone (case 1) .................................................................. 53

Figure 32- velocity waveform from geophone (case 2) ................................................................. 54

Figure 33-acceleration waveform from accelerometer (case 1) ................................................... 54

Figure 34- acceleration waveform from accelerometer (case 2) .................................................. 55

Figure 35-Integrated accelerometer data (case 1) ........................................................................ 55

Figure 36- Integrated accelerometer data (case 2) ....................................................................... 56

Figure 37-Low frequency filtered data (case 1) ............................................................................ 56

Figure 38- Low frequency filtered data (case 2) ........................................................................... 57

Figure 39 –Integrated Acceleration waveform after FFT (case 1) .............................................. 57

Figure 40- Integrated Acceleration waveform after FFT (case 2) .............................................. 58

Figure 41-Velocity waveform after FFT (case 1) .......................................................................... 58

Figure 42- Velocity waveform after FFT (case 2) ......................................................................... 59

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Figure 43-Graphical representation of transfer function ............................................................ 60

Figure 44-Velocity waveform obtained by multiplying transfer function with geophone data61

Figure 45-Integrtaed Acceleration waveform ( acceleration data) ............................................. 61

Figure 46-Velocity waveform (geophone data) ............................................................................. 62

Figure 47- Velocity waveform obtained by multiplying transfer function with geophone data

........................................................................................................................................................... 62

Figure 48-Integrated Acceleration waveform (acceleration data) .............................................. 63

Figure 49- Velocity waveform (geophone data) ............................................................................ 63

Figure 50- Velocity waveform obtained by multiplying transfer function with geophone data

........................................................................................................................................................... 64

Figure 51- Integrated Acceleration waveform (acceleration data) ............................................. 64

Figure 52 -Velocity waveform (geophone data) ............................................................................ 65

LIST OF TABLES

Table 1- SA-611 main specifications .............................................................................................. 46

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LIST OF SYMBOLS AND ACRONYMS

PPV…………………………………………………………………Peak Particle Velocity

WASM……………………………………………….Western Australian School of Mines

KCGM………………………………………………..Kalgoorlie Consolidated Gold Mine

FFT……………………………………………………………...…Fast Fourier Transform

USBM…………………………………………………….. United States Bureau of Mines

AS…………………………………………………………………… Australian Standards

MIC………………………………………………………Maximum Instantaneous Charge

SD………………………………………………………………………….Scaled Distance

DFT………………………………………………………..... ..Discrete Fourier Transform

CFT……………………………………………………..….Continuous Fourier Transform

SAA……………………………………………………Standards Association of Australia

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1 INTRODUCTION TO PROJECT

Blasting operations are done in mines for rock breakage. Along with rock breakage blasting

also produces unwanted by products such as air blast, seismic waves, noise and fly rocks.

Seismic waves result in ground vibrations. Ground vibrations can produce a huge impact on

the environment by creating discomfort to the people and potential damage to the nearby

structures. The factor responsible for damages induced by ground vibration is its Peak

Particle Velocity (PPV).Each structure has a particular level of peak particle

velocity(PPV).If the ground vibration exceeds the PPV limit, potential damages will occur

to the structure.So it is necessary to measure the ground vibrations precisely inorder to

avoid any kind of damages. In order to measure ground vibrations , measuring instruments

called Blast Seismographs are used.

Geophone and accelerometer are the commonly used blast seismographs.The out put of a

geophone is velocity waveform and that of an accelerometer is acceleration waveform. A

geophone is a kind of motion transducer with moving coil and a magnet and it is highly

sensitive in nature. It converts the movement or displacement produced in the ground into

voltage and that voltage may be recorded at a recording station. Accelerometer works on the

principle of simple harmonic motion of a damped mass.

Usually in mines geophones are used for vibration measurement.It is due to the fact that

geophones are cheap compared to accelerometers.Eventhough geophones are cheap,

vibration measured by geophones are not precise when compared to an accelerometer.

There lies the relevance of this research project.As already stated that the blast vibration

measurements should be precisely done inorder to avoid damages associated with it.In order

to carryout precise vibration measurement with a geophone , its accuracy is to be

improved.The aim of this research project is how to improve the accuracy of velocity

waveform of a geophone so that so that blast vibrations can be accurately measured.

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1.2. BACKGROUND TO PROJECT

During blasting operations explosives are charged into the rocks via drill holes. When these

explosives are detonated hot high pressure gases are produced which in turn melts the rock around

the blast holes to a certain limit. Beyond this limit the rocks no longer possess its inelastic

properties. So there will be some radial cracks. The excessive explosive energy not used in the

breakage of the rock will be transferred to the elastic rock zone and they will travel as elastic waves.

When they propagate through the ground, particle movement will occurs. These particle

movements are called ground vibration. Ground vibration takes place in three directions such as

transverse, radial and vertical. When vibration occurs each ground particle possess a velocity and

the maximum velocity is termed as Peak Particle Velocity (PPV).Peak Particle Velocity is used

for measuring the intensity of vibration. PPV is measured in inches per second or millimetres per

second.

Noise and ground vibrations are produced along with blasting operations has a wider impact on the

environment and the people. High level ground vibrations induced by blasting causes discomfort to

the people and potential damage to the nearby structures.It also harms the ecology and the ground

water of the nearby area.Each structure or a building has a PPV value,if the intensity of vibration

exceeds this limit damage will occurs.So it is necessary to control and measure ground vibrations

precisely.

The vibrations produced by blasting can be measured accurately by an accelerometer. But

accelerometers are expensive. So instead of that geophones are used. They are more frequently

used because of its low cost and simple construction. Even though geophones are widely employed

in measuring vibrations at mines, the data measured by geophones are not precise due to some

limitations in its structure. Usually geophone’s wide and dynamic range, linearity and performance

are unbeatable by the technically advanced accelerometers. The aim of this research project is

improving the accuracy of velocity wave form using transfer function obtained by geophone and

accelerometer. Thus the output of geophone is multiplied with the obtained transfer function. So a

precise velocity waveform will be obtained and finally it is compared with the accelerometer data

to check its precision.

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1.3. PROJECT PROBLEM STATEMENT

The project problem is how to improve the accuracy of velocity waveform using transfer function

obtained by geophone and accelerometer. Even though geophones are cheap compared to

accelerometers, the measured vibration data from a geophone is not precise compared to an

accelerometer. The output of a geophone is not precise because of its structural limitation and high

sensitivity. Geophone is highly sensitive because it uses natural frequency aggressively. On the

mean while accelerometer is more precise and accurate, but its usage is limited due to its financial

constraints compared to geophone .So in order to get the exact vibration data (velocity waveform)

from a geophone, its accuracy has to be improved. This is carefully done in this research project. At

the end, the transfer function obtained is multiplied with the geophone data and compared it with

the accelerometer data. All these calculations and comparisons are in done in frequency domain.

1.4. PROJECT OBJECTIVES

The primary objective of this research project is to improve the accuracy of velocity waveform

using transfer function. In order to attain this objective, transfer function has to be obtained. So

obtaining transfer function can be stated as the secondary objective of this research project. For

obtaining transfer function various steps are undertaken .As already stated that geophone and

accelerometer gives velocity and acceleration waveform respectively when they are subjected to

ground vibration. Then the velocity and acceleration waveforms from the geophone and

accelerometer for the same input vibration are compared to obtain the transfer function. For

obtaining transfer function almost twenty six blast vibration data from KCGM are collected and

analysed. It can be stated as the next objective. Since the accelerometer is aided with an amplifier,

its amplification factor is to be found out .Then the next objective is to convert the acceleration data

(acceleration waveform) into velocity waveform through integration. It is then followed by Fourier

transform with the help of FFT (Fast Fourier Transform) function in OriginPro 7J software. This is

usually done to change the time domain to frequency domain. Then the next step is to obtain the

transfer function .After obtaining the transfer function, it is to be multiplied with the measured

geophone data and finally it is subjected for comparison with the acceleration data to achieve the

final objective of the research project.

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1.5. PROJECT ACTIVITIES

In order to attain the research goal, various project activities are coordinated .First of all the

literature materials about geophone, accelerometer, theory about rock breakage, blasting operations,

ground vibrations, peak particle velocity, Fast Fourier transform(FFT) etc. are collected and

summarized in chapter 2.Thus the blast vibrations can be analysed from a wider perspective with

the help of the above mentioned literatures. Then it comes the research methodology. It deals with

the method of carrying out the research project. It includes setting up vibration measuring devices

such as geophone and accelerometer. Along with this devices various supporting devices such as

amplifier, data logger and a computer is used for appropriate data recording and collection. Chapter

3 gives the details about the research methodology and procedure of vibration measurement. This

chapter incorporates the all the essential details of vibration measurement procedure which also

includes the recorded data. Chapter 4 reveals the data analysis and results with all the essential

details such as blast vibrations recorded by geophone and accelerometer, data transformation from

time domain to frequency domain using Fast Fourier Transform (FFT), process of obtaining

transfer function , utilization of transfer function to improve the accuracy of velocity waveform

obtained by geophone and accelerometer. Chapter 5 summarizes and concludes all the details about

transfer function. Thus it acknowledges the relevance of transfer function for improving the

accuracy of velocity waveform. Chapter 6 ends with all essential references required for the

successful completion of the research project.

1.6. PROJECT SCOPE

The important aspect of this research project is to improve the accuracy of velocity waveform of a

geophone with the help of transfer function and it is the research goal. The aim or goal of this

research project reveals its scope .As already mentioned that geophones are not precise when

compared to an accelerometer .But on the other hand, the usage of accelerometers in mines for

vibration measurement is limited due to its cost. Through this research project it can be shown that

the obtained transfer function can improve the accuracy of geophone. Thus the final result will be a

much more precise velocity waveform from a geophone. Thus the application of transfer function is

not only limited to this research project but also can be employed in large scale blast vibration

measurements so that geophones can be used effectively and economically. Thus this research

project will result in precise vibration measurement at low cost in mines.

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2 LITERATURE REVIEW

This chapter incorporates all the essential material required for the successful completion of the

research project. Almost all the relevant literatures regarding this research project are collected and

summarized in this chapter. It reveals vital theoretical knowledge behind this research project.

2.1 INTRODUCTION TO LITERATURE REVIEW

The primary and secondary objective of this research project is improving the accuracy of velocity

waveform and obtaining a transfer function. In order to successfully carry out this research project,

all the necessary literatures are collected. This research project deals with ground vibration induced

by blasting, Peak Particle Velocity (PPV), vibration measuring techniques , types of vibration

waves , vibration measuring instruments ( geophone and accelerometer ), transfer function, Fast

Fourier Transform (FFT) .In order to analyse the blast vibration measurement with a wider

perspective the literatures related to above said materials are compiled together in chapter 2.These

literatures can assist in the detailed theoretical analysis of this research project. The structure of the

literature review begins with an introduction. The main content of literature review is categorized

into various titles such as ground vibration induced by blasting, Peak Particle Velocity (PPV), types

of vibration waves , vibration measuring instruments ( geophone and accelerometer ), transfer

function, Fast Fourier Transform (FFT). Each title and its related parts are justified clearly with

sufficient figures and graphs. Therefore this literature review will give clear cut information which

will be very much useful in this research project to attain the result.

2.2 LITERATURE REVIEW

2.2.1 GROUND VIBRATIONS INDUCED BY BLASTING

For blasting operations in mines, explosives are charged into the rock mass through drill holes.

When the explosive charge is fired the energy produced will get transmitted from the drill holes to

the surrounding rock mass in the form of shock waves. Shock waves create a dynamic stress field.

The hot gases produced by the firing of the explosives continue to expand and it leads to further

movement of the rock thereby creating an expanding stress field and in blasting operations , when

the free surface is near to the explosive charge, rock will breakdown in that direction. In all other

directions located away from the free surface, the energy of the shock waves will get gradually

decreased below the required energy level for rock breakage.

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In a blasting operation there are different types of rock fracture. The fracture and breakage of rocks

usually occurs in the region located close to charge .The fracture of rocks will occur only if the

compressive stress produced by the blasting exceeds the compressive strength of the rock. After

blasting, the area which was located close to charge will undergo plastic deformation and this zone

is called Plastic zone .The zone outside the plastic zone is called Transition Zone .In the transition

zone the rock behaves like a nonlinear elastic solid i.e. there occurs a transition in rock behaviour

from plastic nature to elastic nature. Next to the transition zone is the Elastic zone and further

deformation will be elastic. The zone of rock in that area is called as Elastic Zone. In this zone the

deformation produced by the strain energy will be within the Elastic limit. So the rock will returns

to its original shape and structure after deformation .The amount of Elastic strain produced in this

zone is given by the equation

εm = Vmc

(1)

Where 𝜀m = Elastic strain, Vm the peak particle velocity in mm/s and C is Wave propagation

velocity of the rock in m/s (Martahan Silitonga 1986). So the amount of explosive energy not utilized for rock breakage will get transferred in the elastic

rock zone and they will travel as elastic waves. When they propagate through the ground, particle

movement will occurs. These particle movements are called ground vibration. The main purpose of

using explosives in blasting operation is to break rocks. Along with rock breakage blasting also

produces unwanted by products such as air blast, seismic waves, noise and fly rocks. So a lot of

energy created by the blasting of explosives will get wasted by the production of this unwanted

waste products .There are mainly three types of elastic waves or seismic waves which causes

vibration. Out of the three, the first two are body waves .They are called body waves because they

can propagate inside the ground. The third type of elastic wave is known as Rayleigh waves. They

are also called surface waves. These waves can transfer energy along the surface. Rayleigh waves

are given much more importance during analysis because it is a surface wave and it undergoes less

spreading loss than body waves (Leet 1960).

Noise and ground vibrations are a part of blasting operations in mines .So for many years blast

vibrations are carefully measured and monitored in order to avoid the damages caused by ground

vibrations induced by blasting. Ground vibrations can produce a huge impact on the environment

by creating discomfort to the people and potential damage to the nearby structures.Since 1927 the

the damages produced in the buidings due to blasting has been under examination (Rockwell 1927).

A lot of efforts have been put by the researchers to determine which parameter of ground vibration

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will be nearly related to the damage of the building.There are different types of parametres such as

displacement , velocity or speed of movement , acceleration or force that affects structures. From a

published statistical data analysis about damage to structures induced by blasting ,it can concluded

that the factor or parameter that responsible for damages induced by ground vibration is its partice

velocity (Duvall and Fogelson ).This particle velocity will be in three directions such as transverse ,

vertical and radial.The maximum velocity is termed as Peak Particle Velocity (PPV).United States

Bureau of mines pointed out that if any of the three components of vibration near a structure or

building has a PPV in more than 50 mm/s, then there is more chance for damage .It can be also

stated that if the PPV near to a structure or buiding is less than 50 mm/s , the chance of getting

damaged is less ( Nicholls 1971).

Thus the chance of getting damaged will increase when the peak particle velocity is increased

above 50 mm/ s and similarly the chance of damage will decrease when the peak particle velocity

level decreases below 50 mm/s.So this criteria based in the PPV of 50 mm/s is accepted as safe

vibration level by the blast design engineers (Dick 1979).Blast vibrations not only affect the

structures located close to mine but also to the people living in the nearby areas .

When the blast vibration levels are high it can create human annoyance and discomfort.Due to

adverse human response to ground vibrations and noise effects more importance is given to reduce

the level of human discomfort caused by blast vibrations ( Martahan Silitonga 1998).As already

stated before that the parameter that responsible for damages induced by ground vibration is its

partice velocity.So different studies are conducted to compare human response with the

ParticleVelocity (Wiss 1968).From the results of the studies it can be conclude that for a particle

velocity of 0.5 mm/s human response will be noticable , for a particle velocity of 5.0 mm/s human

response will be annoying and for a particle velocity of 17.5 mm/s human response will be

uncompromising.From these results it can be pointed out that people are highly responsible to

ground vibrations(Wiss 1968). According to the Australian Standards (AS )2187 for ground

vibration , the suggested ppv limit for houses are 10 mm/s and 2 mm/ s for historical buildings and

monuments

Ground vibrations are measured with the help of measuring instruments such as geophone or

accelerometer placed between the blasting point and the structure(SAA 1983).Ground vibrations

propagates in the form of waves.It originates from the blast point and propagates with decreasing

intensity.When the distance from blast point increases the perception level of ground vibrations

decreases.If the rock conditions are uniform ground vibrations produced from the blast point

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spreads out and reduce equally in all directions.But rock is an imperfect medium , so the ground

vibrations propagates unevenly (Livingston 1956).

Ground vibrations depends on the structutral and physical properties of ground.The amplitude of

ground vibration induced by blasting at any point depends on the following factors such as distance

from the measruing point to the point of origin of blast vibration , wight of the explosives fired at a

time, propagation charcteristics of the medium and finally energy coupling between the explosive

and the propagating medium (Adrian J. Moore and Alan B. Richards 1997).

Figure 1 Ground wave propagation (reproduced from Adrian J. Moore and Alan B. Richards 1997)

Ground wave propagation is shown in figure 1.Ground vibrations propagates in the form of waves

.It originates from the blast point and propagates with decreasing intensity. As the distance

increases amplitude of the wave decreases .At particular point amplitude, acceleration, velocity and

frequency can be measured.

A lot of investigations were done by the researchers to predict the ground vibration level and

different formulas were proposed to predict the peak vibration level. They are Langefors Formula,

square root scaled distance formula and cube root scaled distance formula. Out of this the first one

is Langefors formula (Langefors and Kihlstrom, 1973) which is as follows

V = k� QD1.5 (2)

Where v = peak vibration in mm/s , K= rock transmission factor, Q = instantaneous charge mass in

Kg and D is the distance in m.

The second type of equation for the prediction of peak vibration level is square root scaled distance

formula (United States Bureau of Mines (USBM),1980; ICI ,1990 Australian Standard (AS)

2087.2, 1993) which is as follows

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V= k ( D�Q

) −e (3)

The third type of equation for the prediction of peak vibration level is Cube root scaled distance

formula which is as follows

V= k ( D�Q3 ) –e (4)

Where v = peak vibration in mm/s , k=site constant, Q = instantaneous charge mass in Kg ,D is the

distance in m and e is the site exponent.

2.2.2 GROUND VIBRATION MEASUREMENT –PPV

At a selected point ground vibration induced by blasting can be measured.Ground vibartion has

different parameters such as displacement, velocity , particle acceleration , fequency etc. Research

studies and experience shows that the main parameter that is responsible for damages associated

with ground vibrations is its particle velocity. Therefore the instruments which can measure

particle velocity is used for monitoring ground vibrations.These instrument are called as Blast

seismographs( Geophone , accelerometer etc) The propagation of ground vibrations causes the

ground particles to move in a complex three dimensional manner.So the ground particles possess

velocities in three mutually perpendicular directions such as longotudinal(VL) , transverse(VT) and

vertical(VV).Thus the particle velocity at a given point will be the vector sum of these three

components measured at the same instant of time. The equation for particle velocity is

V = �VL + VT + VV .

Figure 2 represents the three mutually perpendicular components of Peak Particle Velocity (PPV)

and they are longitudinal component, vertical component and transverse component .The peak

value or Peak Vector Sum or Peak Particle Velocity (PPV) is the highest value of vector sum of

Figure 2 Peak article Velocity (PPV) (reproduced from Nicholls,1971 )

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vector sum of three velocity components. PPV is the velocity of motion of the ground particles and

not the velicity of the wave. PPV is measured in inches per second or millimetres per second.

Proper design and alteration of blast design can result in reducing the intensity of blast vibraions to

a great extend.

There are different methods through which the blast design can be altered such as decreasing the

maximum instantaneous charge (MIC) by using delay, reducing hole diameter or deck

loading.Another way to decrease the intensity of blast vibration is changing the spacing and

burden, alternating the pattern of the drill and hole inclination.Optimum use of explosives and

proper orientation of the drill holes can also help in reducing the level of ground vibrations.And not

but the least is precise vibration measuring instruments such as geophone,accelerometer etc.

(Dowding C.H 1985)

Regulations for mine blasting limits are mainly designed to control the complaints from the people

and building occupiers living near to the mine sites. The Australian standards set to limit the blast

vibration levels so that there could no harm to the people and structures or buildings located close

to mines. According to the Australian Standards (AS 2187.2 -1993) the recommnded Peak Particle

Velocity (PPV) for houses and low rise residential buidings are 10 mm/ s and for commercial and

industrial buidings or structures of reinforced concrete or steel construction is 25 mm/s and for

historical buildings and monuments the recommended PPV is 2 mm/s.

From this information it can be understood that the chance of damage in residential areas will

increase if the (PPV) is above 10 mm/s and similarly in the case of industrial buidings damages will

occur if the PPV is above 25 mm/s. Also there are some heritage sites where the vibration

standards are set on the basis of some conservative values obtained from overseas standards.

Usually for heritage sites the maximum Peak Particle Velocity ranges from 2 mm/ s to 5 mm/ s.

P a g e | 20

Figure 3- Recommended safe levels for blast vibrations (reproduced from USBM RI 8507 and AS 2187.2—2006).

The recommended safe levels for blast vibrations are shown in figure 3.The USBM (United States

Bureau of Mines) and AS (Australian Standards) studies and tests are conducted on weakest

material exposed to vibration. The material selected by USBM was plaster which is one of the

weakest materials in construction. So from these two standards the maximum peak particle

velocities for plaster and drywall are 12.7 mm/s and 19 mm/ s respectively. Figure 3 also reveals

the frequency dependent vibration level criteria .The important feature of this criteria is that for

constructing blasting at close quarters the most important blast vibration frequency is above 40 Hz,

then a limit of 2 inches per second is suitable .When the vibration level exceeds the above limit that

doesn’t mean that sudden damage to the structures will occur, but there will be more chance of

damage with increasing vibration level above the limit.

USBM in RI 8507 pointed out that the best parameter to describe the single ground vibrations is the

particle velocity. A safe PPV of 2 in/s is recommended for all homes for frequencies above 40 Hz

and there is a low chance of damage from a blast having PPV below 0.5 in/s. Variation of peak

particle velocity at different frequencies shown in the above graph (USBM RI 8507) are supported

by various researches conducted after its publication.

P a g e | 21

Figure 4- Probability damage analysis for low frequency blasts and shaker test (reproduced from USBM RI8507)

For the entire frequency range the probability or chance of damage versus Peak Particle Velocity is

shown in figure 4 .Three types of damages shown in figure 4 are threshold damage, minor damage

and major damage. This figure reveals the fact that all the three types of damages follow the same

pattern. For a range of particle velocity from 10 -100 mm/s the damage probability varies from 5 to

60 percentages.

After many years of research it was found out that PPV values from blast induced vibrations for

cylindrical explosive geometry (ratio of length to diameter of charge greater than 6) are related to

scaled distance .One of the most widely used empirical relation to predict PPV established by

USBM is

PPV = K( SD)−β (5)

P a g e | 22

Or PPV = K ( 𝑅�𝑄

)−β

where K is the calibrated parameter called site factor , SD is the scaled distance for cylindrical

charge which is equal to 𝑅�𝑄

, R is the distance from the charge in metres , Q is the maximum

instantaneous charge ( effective charge per mass delay) weight in Kg , β is site factor.

2.2.3 TYPES OF WAVES

Ground vibrations are complex seismic events consisting of mainly three different kinds of waves

such as P waves (or compressional waves),S waves (or shear waves) and R waves (or Rayleigh

waves) .

Figure 5– Different types of waves (reproduced from Adrian J. Moore and Alan B. Richards 1997).

In figure 5 different types of seismic waves induced by blasting are shown. The particle motion

associated with different waves and their direction of propagation are also indicated in the above

figure. Ground waves or seismic waves propagate in all directions from the blasting point. The

three important types of seismic waves are P waves, S waves and Rayleigh waves. The

compressional waves (P waves) and shear waves (S waves) are called body waves since they

propagate inside the ground and the Rayleigh waves (R waves) are called surface waves and it is

associated with energy flow along the surface (Leet 1960) .

(a)P waves or Primary waves – The first type of seismic wave are P waves or Primary waves. They

are also called as compressional waves. They can travel through solid, liquid and air.They are

P a g e | 23

longitudinal waves and when they propagates the material particle vibrates in the same direction of

motion. P waves travel faster than other seismic waves through the earth’s surface and can be

detected first by the seismographic stations .That is why they are called as primary waves. P waves

have the ability to travel at twice the speed of S waves.When they propagates through a material its

volume will be changed (i.e. compression and dilation will takes place) without any change in its

shape .Hence they are called Compressional waves. P wave propagates in the radial direction from

the blast hole at different velocities and it depends upon the characteristic of material medium of

propagation.

The velocity of a P wave is given by the equation

Vp = �𝑘+43µ

ρ (6)

Where Vp = Velocity of P wave, K = Bulk (Compressibility) modulus, µ = Shear modulus and ρ is

the density of medium of propagation.

Figure 6- P wave (reproduced from Nicholls 1971)

The propagation of P wave is indicated in the figure 6. When they propagate compression and

dilation of the particles of medium of propagation takes place.

P a g e | 24

(b) S waves or Secondary waves - Second type of seismic wave are S waves or Secondary wave. S

waves are also called as secondary waves because they are detected secondly after the P wave when

they are measured at seismographic stations. S waves travel only through solid rock. When S waves

propagates through a medium the particle of the medium moves perpendicular to the direction of

propagation. Thus shear movement of particles takes place .So they are called shear waves. Shear

waves travel at 50 to 60 percentage speed of P waves. During propagation of S waves shape of the

medium will be altered but the volume remains the same.

Figure 7- S wave (reproduced from Nicholls 1971).

In figure 7 describes the propagation of S waves. When they propagates through a medium the

particles of the medium moves perpendicular to the direction of propagation.

The velocity of S wave is given by the equation

Vs = �µρ

(7)

where Vs = Velocity of S wave, µ = Shear modulus and ρ is the density of medium of propagation.

(c) R waves or Rayleigh waves - The third type of seismic wave is Rayleigh waves. It is a kind of

seismic wave which travels through solid surface. When Rayleigh waves propagate through a

medium, they become weaker rapidly with depth and it travels slower than other two waves. During

propagation its particle vibrates both longitudinally and transversely. Then the amplitude of this

waveform will decrease exponentially when the distance from the surface increases. The speed of

Rayleigh waves is lower than shear waves. The speed of Rayleigh waves depends on the constant

of elasticity of the material medium of propagation.

P a g e | 25

Figure 8– Rayleigh wave (reproduced from Nicholls 1971)

Figure 8 describes the propagation of Rayleigh waves.When they propagate through a medium the

particles of the medium moves both longitudinally and transversely.

Figure 9-Arrival time of P, S and R wave for a single hole blasting (reproduced from Dowding 1985).

Figure 9 demonstrates a case study of blast vibrations recorded at a point of almost 1800 metres

from a single hole blast of 1000 kg explosives fired in the overburden of a Hunter Valley coal mine.

During recording it was proved that P waves or Primary waves were first arrived. This vibration

P a g e | 26

gradually reduced till almost 800 ms later. Then S or Secondary waves arrived. Then almost 900

ms later waves arrived. Then the vibration level was gradually decreased and returned to zero.

(Dowding, Siskind,, Stagg, and Kopp1980).

2.4 GROUND VIBRATION MEASURING INSTRUMENTS

The peak particle velocity of the blast vibrations are measured by instruments called Blast

seismographs. Blast seismograph consists of a transducer (a geophone or an accelerometer)

connected to a processor (data logger), which collects, analyse and gives the output.

2.4.1 GEOPHONE

A geophone is a kind of motion transducer which is highly sensitive in nature .It converts the

movement or displacement produced in the ground into voltage and that voltage may be recorded at

a recording station. Geophones are cheap and it has a high sensitivity due to the fact that it uses the

natural frequency aggressively. Geophones are widely used by the seismologists and geophysicists

for ages. Geophones are widely used in oil exploration, mining engineering, scientific research etc.

The construction of a geophone is very simple. It consists of case (or housing), coil, magnet, a leaf

spring and a cylinder.

Figure 10– isometric and cross sectional view of a geophone (reproduced from Aaron Barzilai 2000)

Figure 10 illustrate the isometric and cross sectional view of a geophone. The construction of a

geophone is very simple. It consists of case (or housing), coil, magnet, a leaf spring and a cylinder.

Geophones works on the basis of inertial mass or proof mass suspended from a spring. Here either

the magnet or the coil will be fixed to the casing (or housing).but in modern geophones the magnet

P a g e | 27

is attached to the case and the proof mass will be the coil. As a result of ground vibrations the

displacement produced in the ground will be transmitted to the casing in which the magnet is

mounted .As a result of this the magnet moves while the coil remains stationary. Thus the magnetic

flux linked with the coil changes .The relative motion between the coil and magnet causes a voltage

to be generated across the coil windings.

According to Faradays law of electromagnetic induction, the voltage produced is given by the

equation.

Vα∂x∂t

or V = SG ∂x∂t

(8)

where SG = sensitivity constant of geophone, V is the voltage and x stands for the displacement of

the magnet relative to the coil.

Thus the voltage is directly proportional to the rate at which the magnetic flux cut by the coil. That

is why geophones are classified under velocity sensitive devices. The proof mass velocity with

respect to the housing of the geophone is transformed into voltage. So the recorded data given by

the geophone is the product of velocity of the magnet with respect to the coil and the sensitivity

constant in V/ m/s.

As already stated that the working of a geophone is based on the motion of a proof mass (coil)

suspended from the spring and is governed by forced simple harmonic oscillator equation

∂2x∂t2

+2λ ω0∂x∂t + ω0

2 x = ∂2u∂t2

(9)

Taking the Fourier transform of the forced simple harmonic oscillator equation which in turn

replace the time derivative with frequency derivative and after some rearrangements the equation

for a geophone’s output can be obtained as follows.

VG=SG∂x∂t

=SG−𝑖ω

−ω2+2𝑖ωω0+ω02 ∂

2u∂t2

(10)

where x is the displacement of the proof mass relative to the case, u is the displacement of the

ground, λ is the damping ratio and ω0 is the resonant frequency (Michael Hons 2008).

P a g e | 28

The frequency response of a geophone is limited because the coil is suspended by a spring system

and the properties of the system will change around the natural frequency of the suspension system.

The frequency at which the geophone oscillates with a specific resonance in its working direction is

called Natural Frequency. At this frequency the phase difference between the measured particle

velocity and the output voltage is zero and it goes on changing from – 90° to +90° either side of it.

Usually the natural frequency of geophone sensor ranges from 4 Hz to 14Hz. So above the natural

frequency, geophone gives a reasonable output, but its resolution decrease at lower frequency

ranges (10 mHz -1Hz). This is one major disadvantage of geophone .This problem arises because

the output is proportional to velocity of proof mass or inertia mass (cylinder and coil

assembly).Therefore geophones are usually used for seismological experiments having frequency

range from 4 Hz to 400 Hz .Since the geophones are highly sensitive rather than a precise velocity

waveform the output obtained will be a magnified one. This is also another major disadvantage of

geophone.

Sensitivity of a geophone depends on the number of loops in the coil and strength of the magnetic

field. The sensitivity of a geophone can be improved by providing the feedback and position

sensing of the proof mass. Geophone’s sensitivity is a function of frequency and it can be changed

by feeding back the conventional output. When the conventional output is again feedback to the

geophone, there will not be any change in its resolution but it will amplify low signals. By

measuring the position of the proof mass resolution of the geophone can be improved. As already

mentioned before geophone is less sensitive in the low frequency region .So in order to recover the

signals in the low frequency region an inverse filtering is done, which means inverting the

frequency response of the geophone. Inverse filtering is done by using a frequency response

function which is common for all geophones of a particular type. (Aaron Barzilay ,Tom Van Zandt

and Tom Kenny 1998).At frequency above resonance the amplitude of geophone’s output

waveform will be flat in response to the velocity. This is due to the fact that output voltage is

directly proportional to the ground velocity .So when recording frequency above resonant

frequency, the displacement of the proof mass will be proportional to the ground displacement and

the velocity of the proof mass will be transformed into voltage. While measuring high frequencies

voltage produced by a geophone will be directly proportional to its ground velocity and it can be

called as a ‘velocimeter’ (Barzilai 2000).

P a g e | 29

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-10

-5

0

5

10

15

Vol

tage

(m

V)

Time (s)

Figure 11 -Frequency responses of geophone PC-801 LPC (obtained from the experiment)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-25

-20

-15

-10

-5

0

5

10

15

20

Voltag

e (

mV

)

Time (s)

Figure 12- Frequency responses of geophone PC-801 LPC (obtained from the experiment)

Figure 11 and figure 12 demonstrate two frequency responses of geophone PC-801 LPC

(geophone used in this research project). It is important that the geophone measuring the vibrations

must have a frequency response that covers the entire range of frequencies to be measured.

P a g e | 30

2.4.2 ACCELEROMETER

Figure 13–Structural components and internal circuits of a piezoelectric accelerometer (Michael Hons 2006)

The different structural components and internal circuits of a piezoelectric accelerometer are

described in figure 13.The main components of a piezoelectric accelerometer are accelerometer

base, centre post, seismic mass and piezoelectric element. Accelerometers are sensors that can

detect acceleration. It works on the principle of simple harmonic motion. The vibration

measurement by an accelerometer is more precise than that of a geophone. Accelerometers are of

different types such as capacitive, piezoelectric, piezoresistive, strain gauge based, servo

accelerometers etc. In this project only piezoelectric accelerometer is used. So it is be dealt in

detail.

A piezoelectric accelerometer consists of base, seismic mass, centre post and piezoelectric element.

Out of this, the basic element is its seismic mass and its active element is piezoelectric material.

One side of the piezoelectric material is attached to the centre post at accelerometer base and the

other side to the seismic mass. The seismic mass is mounted to the case of the accelerometer. When

the body of the accelerometer is subjected to vibration, the seismic mass attached to the

piezoelectric crystals moves. But it actually wants to stay in its original place due to inertia force.

So the compression and stretching of the piezoelectric material will takes place .When a

piezoelectric material is subjected to a compression or shear force correspondingly an output charge

proportional to the applied force will be produced. Thus the force which causes the movement of

the seismic mass or piezoelectric material is the product of acceleration and seismic mass (As per

Newton’s second law of motion (F = ma).Since the seismic mass is constant the output produced

P a g e | 31

will be proportional to the acceleration of the mass. For a wide range of vibration frequencies both

seismic mass and accelerometer base have same acceleration magnitude. The output charge

obtained from a piezoelectric accelerometer is sometimes transformed into a low impedance

voltage with the help of integral circuits (Bernstein 2003).

In piezoelectric accelerometers the piezoelectric material acts as a sensing element as well as a

precision spring. Usually the piezoelectric material will be quartz, lead zirconate titanate etc.

Piezoelectric accelerometers are widely accepted for measuring vibration. Compared to other type

of vibration measuring instruments like geophone these type of accelerometers have many

advantages such as wide dynamic range , high precision , exceptional linearity on amplitude over

the entire dynamic range , high sensitivity etc. The range between the lowest and the highest

acceleration detectable by an accelerometer is called its dynamic range. A small force is enough to

deform the piezoelectric material As already stated before that the output produced by a

piezoelectric accelerometer is proportional to the force applied to the material and thereby

proportional to the acceleration. So a piezoelectric material can detect lowest to highest range of

acceleration. The linearity in amplitude of an accelerometer is the degree of accuracy of an output

voltage produced by an accelerometer while measuring lowest to the highest level of acceleration.

This accuracy in vibration measurement is termed as linearity.

The dynamic range shows lowest to highest level of detected acceleration. Dynamic range of an

accelerometer depends on the type of electronic material used in the accelerometer. Because of the

rugged and robust construction accelerometers are widely employed in hazardous environments

.Besides measuring blast vibrations accelerometers are used for testing machine parts such as

motors , gearboxes etc. The major disadvantage of an accelerometer is its low dynamic frequency

response below 10 Hz, so it can’t be used for measuring low frequency measurements (Michael

Hons 2006).

P a g e | 32

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.10

-0.05

0.00

0.05

0.10

0.15

Accele

ration (

m/s2

)

Time (s)

Figure 14-Typical acceleration data of a piezoelectric accelerometer,TEAC 708 LF(obtained from the experiment)

Figure 14 describes the acceleration data of a piezoelectric accelerometer, TEAC 708 LF. In this

research project the type of accelerometer used is manufactured by TEAC Corporation and the

model number is 708 LF.

2.5 TRANSFER FUNCTION

Transfer function is a relationship between the input and output of a system and it is expressed in

terms of transfer characteristics.

BA

= T (11)

where B is the output, A is the input and H is the transfer function.

When transfer function operates in the input of a system corresponding output will be obtained.

Both accelerometer and geophone are based on proof mass or inertial mass held by a spring. They

are both damped harmonic oscillators with single degree of freedom and they follow the simple

harmonic equation of motion which is as follows

∂2x∂t2

+ 2 λ ω0∂x∂t + ω0

2 x = ∂2u∂t2

(12)

P a g e | 33

where x is the displacement of the proof mass relative to the case, u is the displacement of the

ground, λ is the damping ratio and ω0 is the resonant frequency (Michael Hons 2008) .

When any spring mass system like geophone or an accelerometer is considered the response and the

output produced by such systems depends on the operating frequency. When the operating

frequencies are low compared to the resonant frequency the spring system, upon which the seismic

mass is attached, becomes tight and the displacement of the proof mass will be away from the

outdriven hanging position due to acceleration. If the operating frequency is near to the resonant

frequency the displacement of the proof mass or inertia mass will be related to the velocity but in a

complex manner and can be described by simple harmonic oscillator equation .Because of this

reason a geophone is sometimes referred as a velocimeter.

The ground motion is converted into an electrical signal by geophone or an accelerometer. The

input is given to a transducer (geophone or an accelerometer) in terms of ground vibrations or

displacements and the corresponding electrical output will be obtained from the transducer in terms

of proof mass or inertial mass displacement .So a transfer function can be derived directly from

damped simple harmonic oscillator equation.

In geophones principle of electromagnetic induction is used to convert the ground displacement or

vibration into voltage. Due to this fact the inertia mass or proof mass velocity will be considered as

unscaled electrical output .In the case of accelerometer the proof mass or inertia mass displacement

will also be the same.

Researchers found the following solutions for a geophone which are obtained from some

rearrangements in simple harmonic oscillator equation (11) and by the application of Fourier

transform.

jω 𝜕𝑥𝜕𝑡

+ 2λωo𝜕𝑥𝜕𝑡

+ ω02

jω𝜕𝑥𝜕𝑡

= - 𝜕2𝑈𝜕𝑡2

(13)

𝜕𝑥𝜕𝑡𝜕2𝑈𝜕𝑡2

= −jω−ω2+2jλωω0+ω0

2 (14)

P a g e | 34

Assuming ω << ω0

∂x∂t∂2U∂t2

= −jω−ω2+2jλωω0+ω0

2

∂x∂t∂U∂t

= −jω−ω2+2jλωω0+ω0

2 (15)

This equation can also be written as

HG =

∂x∂t∂U∂t

= ω2

ω02

−ω2

ω02+

2𝑗ωλω0

+1 (16)

This is the equation for the transfer function of a geophone where HG is the transfer function, x is

the displacement of the proof mass relative to the case, u is the displacement of the ground, λ is the

damping ratio and ω0 is the resonant frequency.

The transfer function for an accelerometer can obtained similarly with the help of simple harmonic

oscillator equation and Fourier transforms and it as follows

-ω2X +2j𝛌ωω0x + ω02x = -∂

2U∂t2

(17)

Or

X∂2U∂t2

= −1−ω2 +2jλωω0+ ω0

2 (18)

This equation can also be written as

HG = X

∂2U∂t2

= −1ω02

−ω2

ω02+

2𝑗ωλω0

+1 (19)

where HA is the transfer function of an accelerometer ,x is the displacement of the proof mass

relative to the case, u is the displacement of the ground, λ is the damping ratio and ω0 is the

P a g e | 35

resonant frequency. These equations will be valid over the range of frequencies for which they are

derived (Michael Hons 2006).The voltage output from an accelerometer is the time derivative of

the voltage output of a geophone .For an accelerometer the acceleration of the ground vibration

causes a displacement between the inertia mass or proof mass and the case .As a result of this

displacement an output voltage will be produced which is directly proportional to the acceleration.

For the case of a geophone, the displacement between the proof mass or inertia mass and the case is

due to velocity of the ground vibration. Due to this an output voltage directly proportional to

velocity is produced. In the case of a geophone or an accelerometer the output is similar over the

frequency range where the transfer functions have identical response. Thus the transfer functions

derived are true for all frequencies when the ground motion is related to the motion of the inertia

mass or proof mass and are only transfer functions when they symbolize the transducer output to

input (Maxwell 2001).

The actual transfer function that is to be dealt in the research project is a slight modification of the

above said transfer function of geophone and accelerometer. The transfer function explained in this

section is taken from the past literature papers .Here the transfer functions of geophone and

accelerometer are found out and explained separately. But in actual research project both

accelerometer and geophone are attached together in order to acquire the same vibration. Then the

acceleration waveform will be integrated in order to obtain the velocity waveform. Finally the

velocity waveform of an accelerometer and a geophone are divided to get the required transfer

function.

2.6 FAST FOURIER TRANSFORM

Fourier Transformation is done in order to obtain the transfer function in frequency domain. Thus it

serves as a bridge between time domain and frequency domain. Fourier transform has been used for

a long time for obtaining linear solutions and determining frequency components of a waveforms.

When the waveform is sampled finite and discrete version of Fourier transform called Discrete

Fourier Transform is used. DFT is most important in frequency analysis since it takes a discrete

signal from the time domain and converts it into discrete frequency transform (reproduced from

Bradley 1989).

Because of the speed and discrete nature of the FFT, analysis of the signal spectrum in OriginPro 7J

is possible. In this tis research project the software used for Fast Fourier Transform is OriginPro 7J.

In DFT most properties of Continuous Fourier Transform (CFT) are used, some differences are

there in the sampled waveforms defined over definite time intervals.

P a g e | 36

Fast Fourier Transform is an algorithm used for calculating DFT first published by J.W. Cooley

and J.W Tuckey in 1965.It has brought a great revolution to the modern experimental mechanics

and signal system. FFT algorithm applies mainly to signals consisting of a number of elements

equal to 2m (for example 212 = 4096) .The main advantage of FFT is reduction in computation time

by a factor of the order m/log2m. FFT is the most common form of signal processing. It is defined

as a method of accepting a real time varying signal and differentiating it into components with

amplitude, phase and frequency.

Today all modern instruments use FFT in order to provide frequency domain information (Dennis

H. Shreve 1995). Almost all portable instruments use FFT processing as the method for taking the

overall time varying input sample and then it is then differentiated into individual frequency

components. FFT is a faster version of DFT. FFT converts signals from time domain to frequency

domain. It is a computer algorithm which forms the basis for signal processing in sound analysis

and visualization of algorithms in decoding digital signals for audio, video and images. Fast Fourier

Transform converts the signals into magnitudes and phases of different sine and cosine frequencies

resulting in the formation of the signal (Bradley and Dan 1989)

Figure 15- Sample wave form (reproduced from Bradley 1989)

Figure 16- Fast Fourier Transform of the sample waveform (reproduced from Bradley 1989)

P a g e | 37

Figure 15 and 16 describes a simple case study about FFT conducted in the sample waveform. In

sample waveform there are 32 equally spaced points or real valued points. After doing the FFT in

the sample waveform 32 complex valued points will be formed. These 32 points have symmetry

.Only sixteen points are shown in figure and rest sixteen points are the mirror image.

FFT is not directly linked with the signal spectrum. FFT can vary frequently depending upon the

number of points and number of periods of signal. FFT contains information from zero to sampling

frequency. Sampling frequency (fs) must be at least twice the highest frequency. Real signals have

a transform magnitude and are symmetrical for the positive and negative frequencies .So it is

necessary to have a spectrum form −fs2

to fs2 .This is done by using FFT function in OrijinPro 7J

software. As already stated that FFT is a fast algorithm that can compute DFT.In order to compute

the DFT of an N point sequence the following equation is used

Ak = ∑ 𝑊𝑁𝑘𝑛𝑎𝑛𝑁=1

𝑛=0 (20)

where WN = 𝑒−𝑖2𝜋𝑁

The sequence Ak is called the discrete Fourier Transform of the sequence an .Each is a sequence of

N complex numbers. Using Nyquist Sampling theorem the obtained sampling frequency is utilized

for the calculation of FFT .Keeping the first element as such rest is truncated .In order to scale all

the elements will be divided with FFT size. Then under the section Fold first element is left (DC)

and the last (Nyquist) will remain unchanged and all the other elements will be multiplied by 2.It is

followed by the calculation of magnitude of each component i.e real and imaginary. Also other

spectral parameters like phase are to be calculated. Finally the calculation for values of frequency

from 0 to Nyquist frequency is to be done with a step of Δf and at the end the required spectrum is

to be plotted.

P a g e | 38

Figure 17 General illustration of FFT (reproduced from Dennis H.Shreve 1995)

Figure 17 describes the general illustration of FFT (Fast Fourier Transform).In this figure sine

waves with three frequencies are explained .The first sine wave is of frequency 5 KHz and for the

second sine wave both the frequencies ( 5KHz and 10Khz) are added together so that its amplitude

is increased. For the third sine wave frequencies 5KHz, 10KHz and 20 KHz are also added .It

resulted in further increment in amplitude. Using FFT time domain is changed into frequency

domain.

Figure 18- An example of voltage time data (reproduced from Dennis H.Shreve 1995)

P a g e | 39

Figure 19- An example of frequency data obtained after FFT (reproduced from Dennis H.Shreve 1995)

Figure 18 shows a sample voltage and time data .But for the research purpose , the data in time

domain are not worth enough .i.e it has no meaning in the real life applications .So Fast Fourier

Transform is applied to convert the data in time domain to frequency domain. It is shown in figure

19.

2.7 SAMPLING FREQUENCY

Sampling frequency (fs) is the frequency at which the measurements are captured from the

sensors (geophone and accelerometer).Sampling frequency defines the number of samples

per unit time (in seconds) taken from a continuous analog signal in order to make it discrete

signal . Sampling frequency is expressed in Hertz (Hz) for time domain signals. The

reciprocal of sampling frequency gives sampling period or sampling interval. Sampling time

can defined as the length of time used for taking measurements and the number of samples

means the quantity of individual measurement recorded during waveform analysis.

Figure 20- sampling frequency or frequency rate (reproduced from Dennis H Shreve 1995)

Sampling frequency or sampling rate is described in figure 21 .Here the analog signals

(marked in light blue) is sampled with signals (marked in red colour) with a fixed spacing or

sampling rate. In regarding to the context of sampling frequency, the phenomenon of

P a g e | 40

Aliasing is to be defined. If the detected frequency is f and the sampling frequency is too

low (fs ≤2f), a low spurious frequency will be obtained. This is called Aliasing.

Sampling frequency is calculated by the formula, fs = 𝐷𝑡 (21)

where D is the no of rows of data or number of samples acquired , t is the time interval (Dennis H

Shreve 1995).The sampling rate or sampling frequency affects the highest frequency .It is clearly

explained by Nyquist–Shannon sampling theorem. According to this theorem the perfect

reconstruction of signal is only possible when the sampling frequency is greater than twice the

maximum frequency of the signal to be sampled .The maximum frequency is termed as Nyquist

frequency (fnyquist or fmax).Or it can also be stated that the Nyquist frequency is half of the

sampling frequency or sampling rate. fnyquist = fmax = SR2

(22) where SR is the sampling rate or sampling frequency.

From figure 22 it is clear that if the sampling frequency or sampling rate is low, the original signal

information can’t be recovered from sampled signal .In this figure an example of 2Hz signal is

shown. When a 2Hz signal is to sampled with a sampling frequency of 2Hz, a straight line will be

obtained that does not indicate the original signal. (shown in figure with green dots).Consider

another example of sampling 100 Hz signal , then according to Nyquist–Shannon sampling theorem

the sampling frequency or sampling rate must greater than or equal to 200 Hz

Figure 21-An example of sampling frequency (reproduced from Dennis H Shreve 1995)

After all above mentioned signal processing in the data logger the analog data will be

converted to digital data. Then this digital vibration data will undergoes Fast Fourier

Transforms in the computer system with the OriginPro7J. FFT converts time domain to

frequency domain. Then the acceleration waveform [A(ω)] will be integrated to obtain the

velocity waveform V(ω). Then the velocity waveform from the accelerometer and geophone

P a g e | 41

will be compared to obtain the transfer function. Transfer function is obtained by dividing

the newly obtained velocity waveform from accelerometer with the velocity waveform

obtained by geophone.

V(ω)G(ω)

= T(ω) (23) where G(ω) is the velocity waveform obtained by geophone, V(ω) is the velocity waveform

obtained by accelerometer and T(ω ) is the transfer function.

2.8 SUMMARY OF LITERATURE REVIEW

In order to carry out the research project literature materials regarding ground vibrations induced

by blasting ,vibration measurement , Peak Particle Velocity (PPV) , vibration measuring

instruments ( geophone , accelerometer ) , Transfer function , Fast Fourier Transform (FFT) etc are

collected. These materials can be used as a supporting theory in the research project. The goal of

this research project is to improve the accuracy of velocity waveform using transfer function

obtained by geophone and accelerometer. Since the research topic is related to ground vibrations

induced by blasting, literature material about blasting induced ground vibrations and its impact on

environment is first collected .It helped to understand the cause and effect of ground vibrations.

Then the literature study about PPV is conducted .In this research project PPV is to be measured.

So it is necessary to understand all the essential information about PPV (such as PPV limits for

different structures).Vibration measuring instruments used in this research project are geophone

and an accelerometer. So literature study about geophone and accelerometer is conducted. It

revealed the advantages and limitations of geophone and accelerometer. FFT plays an important

role in deriving the Transfer function and moreover it is necessary to understand Transfer function

and its effect on velocity waveform. So for the better understanding of Transfer function and FFT,

all essential literature materials are collected. Almost all the materials necessary for the future

research project is collected which will help to understand the research project at a wider angle.

P a g e | 42

3 RESEARCH METHOD & EXPERIMENTAL/ANALYTICAL DESIGN

3.1 INTRODUCTION

This research project aims at improving the accuracy of velocity waveform of geophone using

transfer function obtained by geophone and accelerometer. For carrying out this research project

the blast vibrations produced by KCGM will be measured at WASM laboratory. The KCGM Super

pit is one of the largest open pit gold mines in Australia. It is located in the south east edge of

Kalgoorlie, Western Australia.

The main instruments used in this project are accelerometer, geophone, amplifier, data logger and a

computer system. When the geophone is subjected to blast vibrations an output voltage is produced

which is directly proportional to the velocity of blast vibration. Similarly when the accelerometer is

subjected to blast vibrations the output voltage produced is directly proportional to the acceleration

of blast vibration. After measurement of blast vibrations the output obtained from geophone is

velocity waveform and the output obtained from an accelerometer is acceleration waveform. The

output obtained from a geophone is not precise when compared it with an accelerometer. In order to

compare the output of geophone and accelerometer, both of them will be attached together and will

be subjected to the same vibration.

The type of accelerometer used in this research project is Touch 708LF.Geophone used in this

research project is PC-801 LPC, manufactured by Oyo Corporation and it has a natural frequency

of 4.5Hz.The analog signal from the geophone and accelerometer is collected by data logger or data

recorder. It acts an interface between a personal computer and the vibration measuring instrument.

They have the ability to collect data on a 24 hour basis. In the data logger the analog to digital

signal conversion takes place.

Once the blasting took place corresponding vibration is produced .Then these vibrational

waveforms are detected using a geophone and accelerometer .Finally they are recorded using the

OPS software .The measured vibrational waveforms are stored as CSV files in the computer.

The stored CSV files are then subjected to various calculations in order to get the desired result. In

this chapter all the steps related to research method and experimental design are explained in detail

under various sub titles.

P a g e | 43

3.2 INSTRUMENTS USED

3.2.1 GEOPHONE

A geophone is a kind of motion transducer which is highly sensitive in nature. It consists of case

(or housing), coil, magnet, a leaf spring and a cylinder. The main part of a geophone is its housing.

The coil and the magnet assembly are enclosed in the housing. The leaf spring supports the coil

mass and it helps in the axial movement of the coil relative to the magnet. As a result of ground

vibrations the displacement produced in the ground will be transmitted to the casing in which the

magnet is mounted .The magnet moves while the coil remains stationary. Thus the magnetic flux

linked with the coil changes .The relative motion between the coil and magnet causes a voltage to

be generated across the coil windings. Thus the geophone operates according to the Faradays law of

electromagnetic induction. Vα∂x∂t

.The output voltage produced is directly proportional to the

velocity .When the frequency of a recorded waveform is higher than the natural frequency of a

geophone, the proof mass displacement will be directly proportional to the ground displacement .At

higher frequencies the output voltage produced by a geophone is directly proportional to the

ground velocity. The geophone used in this research project is PC-801 LPC. It is manufactured by

Oyo Corporation .Its natural frequency is 4.5 Hz. The sensitivity of this geophone is 1 mV/m/s.

Figure 22-Geophone PC-801 LPC

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3.2.2 ACCELEROMETER

Accelerometers are sensors that can detect acceleration. It works on the principle of simple

harmonic motion. The vibration measurement by an accelerometer is more precise than that of a

geophone. Accelerometers are of different types such as capacitive, piezoelectric, piezoresistive,

strain gauge based, servo accelerometers etc. In this project only piezoelectric accelerometer is

used. The main components of a piezoelectric accelerometer are accelerometer base, center post,

seismic mass and piezoelectric element. A piezoelectric accelerometer consists of base, seismic

mass, center post and piezoelectric element. Out of this, the basic element is its seismic mass and

its active element is piezoelectric material. One side of the piezoelectric material is attached to the

center post at accelerometer base and the other side to the seismic mass. The seismic mass is

mounted to the case of the accelerometer. When the body of the accelerometer is subjected to

vibration, the seismic mass attached to the piezoelectric crystals moves. But it actually wants to

stay in its original place due to inertia force. So the compression and stretching of the piezoelectric

material will takes place .When a piezoelectric material is subjected to a compression or shear force

correspondingly an output charge proportional to the applied force will be produced. Thus the force

which causes the movement of the seismic mass or piezoelectric material is the product of

acceleration and seismic mass (As per Newton’s second law of motion F = ma).Since the seismic

mass is constant the output produced will be proportional to the acceleration of the mass. The

accelerometer used in this research project is TEAC 708 LF manufactured by Teach Instruments

Corporation Japan. It has range of ± 150 G. Sensitivity of this accelerometer is 9.97 mV/G and the

frequency response varies from 0.2 to 22000Hz.

Figure 23-Accelerometer TEAC 708 LF

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3.2.3AMPLIFIER

The output voltage produced by an accelerometer is not quite good enough for measurement .So it

has to be amplified or boosted up to the required level. So an amplifier is used to perform this job.

The amplifier used in this research project is TEAC SA- 611 Charge Amplifier. SA- 611 is mainly

used for piezoelectric accelerometers (for both charge and pre-amplifier type of accelerometers).Its

sensitivity can be set by a three digit digital switches and it is easy to set up for different

accelerometer sensors. This amplifier is compact and light weight .It can be operated with three

types of power supplies such as built in batteries (4 AA batteries), external dc and ac adaptor. It has

two types of inputs .The first one is ‘CHARGE’ for charge type sensors and second is ‘FET’ for

IEPE type sensors. The main specifications of SA-611 charge amplifier is listed in table 1.

Figure 24- TEAC SA- 611 Charge Amplifier

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Table 1- SA-611 main specifications

Input Switched Charge Type or IEPE Type

Sensitivity Setting Three Digits Digital Switch

Input Ranges 1, 10, 100

Output Filter Low Pass Filter(LPF) : 1kHz, 10kHz

High Pass Filter(HPF) :5Hz

Calibration Voltage (CAL) Rectangular Wave 200Hz±20Hz,

2Vpp±5%

Current Sources 0.5mA, 4mA,24V DC

3.2.4DATA LOGGER AND COMPUTER

Geophone and accelerometer transmit continuous analog signal A computer cannot detect analog

signal, so a data logger is used to convert the anlog signal to digital signal. It is impossible and

inefficient to record every bit of transmitted data. So the data collection instrument (data logger or

data recorder) is to be manipulated in order to get the readings at specific intervals. Three important

parameters are to be controlled in data logger in order to obtain accurate measurement. They are

sampling frequency, sampling time and number of samples. A data logger is an instrument which

can record the measured data over time .they can be used in interface with a personal computer.

Thus it can act as a local interface device with a computer. Data loggers are generally used for wide

range of applications. The main components of a data logger are input channel, analog to digital

convertor, microprocessor, memory, power supply, data output port, weatherproof enclosure and

software. The output from the geophone and accelerometer are connected to the input channel of

data logger. The channel composed of circuitry design which is specially designed to guide a sensor

signal (output voltage of geophone and accelerometer) to data logger processor .Usually a data

logger has four to eight channels. The next main component is analog to digital convertor. It

P a g e | 47

converts the analog signal obtained from the sensors (geophone and accelerometer) to digital signal.

Microprocessor is a basically a logical circuit which has the ability to process the necessary basic

instructions to run a computer or a data logger. Then the measured data are recorded in the memory

of data logger. Data logger uses two types of memory such as RAM (Random access Memory) and

EEPROM (Electronically Erasable and Programmable Read Only Memory).Another unique feature

of a data logger is its low power requirement. Most data logger requires a 12 V dc power. But the

one used in this research project utilizes ac power for its working. A data logger communicates

with a computer through a serial port. It allows the data to get transfer in a series to the computer.

Some kinds of data loggers are embedded with special software in order to get synchronized with

the computer. Finally using the OPS software the measured data are recorded and stored in the

computer as CSV files.

Figure 25-TEAC Data logger

3.3 EXPERIMENTAL SET UP

As already stated that in order to obtain the project objective transfer function is required. So the

transfer function between a geophone and accelerometer is to be obtained. Thus for the sake of this

purpose both the instruments are attached together so that they can acquire the same blast vibration.

The site selected to carry out this research project was a small area located close to the geology

building.

P a g e | 48

Figure 26-geophone and accelerometer attached together

After attaching the geophone and accelerometer together, output of the accelerometer is connected

to the amplifier .From the amplifier connection goes to the data logger. On the mean while the

output of the geophone is connected directly to the data logger. Finally the output of the data logger

is connected to the computer. Amplifier is very essential to boost the output signal of an

accelerometer. Figure 27 shows the schematic diagram of experimental set up.

Figure 27-Experimental set up

3.4 OBTAINING THE AMPLIFICATION FACTOR

The next step, after the experimental set up, is obtaining the amplification factor. The type of

amplifier used in this research project is TEAC SA-611 charge amplifier. An amplifier is used to

P a g e | 49

increase or amplify the power of a signal. It performs this job by acquiring energy from the power

supply and it controls the output to match with the shape of the input signal but with greater

amplitude. An accelerometer output is not quite strong enough to detect and measure .So it has to

be amplified up to a certain level to make it easy to detect and measure. In order to obtain the

amplification factor some connection rearrangements are done in the experimental set up. It is

shown clearly in figure 28.

Figure 28-Experimental set up to obtain amplification factor

Figure 28 shows the experimental set up to obtain the amplification factor. In order to obtain this

some rearrangements are done in the previous experimental set up connections. Accelerometer is

detached from the geophone. Geophone output has two connection leads. One connection wire goes

directly to the data logger and the other connection wire is connected to the data logger via an

amplifier. Then the geophone is subjected to vibrational input and corresponding output is obtained

and recorded. Thus two output waveforms are obtained. The first one is the native one and the

second one is the magnified or amplified one. The amplification factor is obtained by dividing the

amplified output waveform with the normal output waveform. So after careful calculations and

considerations the amplification factor is obtained as 10.Thus it can be concluded that the

accelerometer data (acceleration waveform) is amplified ten times by the amplifier.

3.5 MEASURING THE BLAST VIBRATIONS

The blast vibrations from KCGM are recorded using the OPS software. It is one of the best

professional and functional blast wave recording software. Before taking measurements all the

necessary settings in the software should be done. The first step is to set up the range. It is essential

to define the range of blast waves. At first the range was set as 500 mV for the first channel and

P a g e | 50

200 mV for the second channel .Later on it was identified as 500 mV was too large for the blast

vibration waves which would make the recorded wavelet too much steady .So it would be too

difficult to analyze. Finally the range for the first and second channel was set as 200 mV and 100

mV respectively. This newly selected range was absolutely perfect to offer the exact wavelet for the

analysis. The trigger level was set as 1% (1 % of 200 mV = 2 mV).The filter type selected was low

pass filter. Then the filter frequency was set up. It is the filter frequency which decides up to what

range of frequency an instrument can detect and record. Filter frequency was set as 500 Hz, so that

blast vibrations with frequency above 500 Hz will not be recorded. Next step was to determine the

sampling frequency. Sampling frequency is defined as the number of samples per unit time (in

seconds) taken from a continuous analog signal in order to make it discrete.

In this research project the sampling frequency was set as 10000 Hz. Finally the memory was set as

100µs/10 KHz and the block size was 32KW*32.So all the above said settings were done and

proceeded to the experiment. Before recording the blast vibrations, all the electrical connections

were rechecked in order to avoid any kind of loose contacts. Then the OPS software was selected in

the simulation mode. After obtaining a steady waveform from geophone and accelerometer, the

record button in OPS software was clicked. Then waited for the blasting from KCGM. Once the

blasting had occurred corresponding waveforms were recorded using the OPS software and they

were stored as CSV files in the computer. Almost 26 different blast vibration data were collected

and measured.

Figure 29-recorded blast vibration waveform

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Figure 29 shows an example of recorded blast vibration waveform. The waveform is in time

domain. The waveform shown in red colour is the accelerometer data and the waveform shown in

blue colour is the geophone data. Here the X axis is time in µs and Y axis is voltage in mV. From

this two waveforms it can observed that the output waveforms of both the instruments are in the

same trend. There is some difference is in amplitude due to the difference in sensitivity of both the

instruments.

3.6 SUMMARY OF RESEARCH METHOD & EXPERIMENTAL/ANALYTICAL DESIGN

The method and procedure of carrying out this research project is clearly summarised in this

chapter. This chapter is mainly categorised under five titles including the introduction. The main

titles are instruments used, experimental set up, obtaining amplification factor and measuring blast

vibrations. The title, instruments used is again categorised into geophone, accelerometer, amplifier,

data logger and computer. All the essential features and requirements of these instruments are

described in detail under each title (geophone, accelerometer, amplifier, data logger and

computer).It also includes the specifications of each instrument. Under the title experimental set up

the method of conducting the research project is explained. It also reveals the strategy adopted to

obtain the desired result. This section incorporates the entire vital schematic diagram necessary for

the better understanding of the research project from a wider perspective. It shows the connection

between various instruments used for the research project. It is then followed by the title obtaining

the amplification factor. This section explains how to obtain the amplification factor.

Accelerometer output waveform is not strong enough for recording and measurement. So it has to

be boosted up .Amplification factor is obtained by doing some rearrangements in the connections

made for experimental set up. Finally the amplification factor is obtained as 10.Therefore it can be

concluded that output waveform of an accelerometer is amplified by ten times. After that the

obtained blast vibrations from KCGM are recorded. They are measured and recorded using the OPS

software. It is one most functional and professional blast wave recording software. Before taking

measurements all the necessary settings in the software should be done. First among this was

setting up of the range. So the range for the first and second channel was set as 200 mv and 100 mV

respectively. Then the filter frequency was as 500 Hz. It is the filter frequency which decides up to

P a g e | 52

what range of frequency an instrument can detect and record. Next the sampling frequency was set

as 10000 Hz. The trigger level was set as 1%. At the end memory and block size was set as

100µs/10 KHz and 32KW*32 respectively. The vibrational waveforms detected and recorded by

the OPS software are stored in computer as CSV files. Almost 26 different blast vibration data were

collected and measured.

4. RESULT AND ANALYSIS

4.1 BLAST VIBRATIONAL WAVEFORM

Almost twenty six blast vibration data were obtained .Among them the best twenty data are

collected and compared. Using OPS software the velocity waveform and acceleration waveform for

the corresponding blast vibrations are recorded. A sample of the recorded blasting wavelet is shown

in figure 30.

Figure 30- recorded blasting wavelet

Figure 30 shows an example of recorded blasting wavelet. Here the wave form is in the time

domain. The blue waveform indicates the geophone data and the red waveform indicates the

accelerometer data. Both the output waveform will be in mV and the time interval is 0.0001 s. Both

the velocity and acceleration waveform shows the same trend and there are some differences in

amplitude for both these waveforms due to the difference in sensitivity of geophone and

accelerometer.

4.2 TIME DOMAIN SPECTRA

The recorded blasting wavelets are stored as CSV files. Then all the manipulations are done in

these files. Suitable time interval of 0.0001 second is provided. For each recorded blasting wavelet

P a g e | 53

there are 32000 data. So the time interval is defined up to 32000 data. The next step is to divide the

accelerometer data by 10. It is because the amplification factor has to be taken to consideration. In

this case the amplification factor is 10.It is obtained by dividing the amplified geophone data with

the original geophone data subjected to same input vibration. The output of geophone and

accelerometer is in mV. But for this research project the data from the geophone is to be obtained in

m/s and the data from the accelerometer is to be obtained in m/s2. The sensitivity of geophone is 1

mV/m/s. and that of accelerometer is 9.97mv/G or 9.97mV/9.98m/s2 which is equivalent to 1

mV/m/s2 .From this it can concluded that for an output of 1 mv from the geophone the

corresponding velocity will be 1 m/s. Similarly for an output of 1 mV from the accelerometer the

corresponding acceleration will be 1 m/s2.In order to obtain the transfer function, both the

geophone data and accelerometer data has to be compared. But only data with same units can be

compared. Here geophone and accelerometer detect the same wave but the output will be in

different unit, one is m/s and the other in m/s2.So the obtained acceleration data is integrated to

convert it into velocity data.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-10

-5

0

5

10

15

Volta

ge (m

V)

Time (s)

Figure 31-velocity waveform from geophone (case 1)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-25

-20

-15

-10

-5

0

5

10

15

20

Vol

tage

(mV

)

Time (s)

Figure 32- velocity waveform from geophone (case 2)

Case 1 and case 2 shown in figure 31 and 32 are two examples of velocity waveform obtained from

geophone during the experiment (blast vibration measurement). The graphs show the variation of

voltage with time (with a time interval of 0.0001s).As it is mentioned before that 1 mV is equal to 1

m/s .So the above shown graphs can be considered as velocity waveforms.

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.10

-0.05

0.00

0.05

0.10

0.15

Accele

ration (

m/s2

)

Time (s)

Figure 33-acceleration waveform from accelerometer (case 1)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.2

-0.1

0.0

0.1

0.2

0.3

Accele

ration (

m/s2

)

Time (s)

Figure 34- acceleration waveform from accelerometer (case 2)

Case 1 and case 2 shown in figure 33 and 34 are two examples of acceleration waveform obtained

from an accelerometer during the experiment (blast vibration measurement).The graphs show the

variation of acceleration with time in seconds (time interval is 0.0001s).As already stated that the

output data of both accelerometer and geophone must be compared to get the transfer function. But

in order to compare, both the data should be in the same unit. So the acceleration data is integrated

to obtain the velocity data. Thus it can be easily compared with geophone data. Integration of

acceleration data shown in figure 33 (case 1) and figure 34 (case 2) gives the velocity data shown in

figure 35(case 1) and figure 36 (case 2).

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Vel

ocity

(m/s

)

Time (s)

Figure 35-Integrated accelerometer data (case 1)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Velo

city

(m/s)

Time (s)

Figure 36- Integrated accelerometer data (case 2)

4.3 FILTERING OFF LOW FREQUENCY SIGNALS

The values obtained after the integration of accelerometer data has some drift components .These

drift components are unnecessary low frequency signals. It is shown in red coloured lines in figure

35 and 36. So it has to be eliminated before doing all the calculations. It is done in OriginPro 7J

software. Thus the low frequency signals are removed from the integrated accelerometer data. The

required filtered data from figure 35(case 1) and figure 36 (case 2) is shown below in figure 37

(case 1) and 38 (case 2).

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

Vel

ocity

(m/s

)

Time (s)

Figure 37-Low frequency filtered data (case 1)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.0008

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

Vel

ocity

(m/s

)

Time (s)

Figure 38- Low frequency filtered data (case 2)

4.4 FREQUENCY DOMAIN SPECTRA

Comparison of data in time domain has no meaning, it has no real life applications .It is not a better

method to describe the relationship between geophone and accelerometer in time domain. So the

measured velocity data from the geophone and integrated accelerometer data has to be converted

from time domain to frequency domain. This is done through the Fourier Transform. Using FFT

function (Fast Fourier Transform) in OriginPro 7J software accelerometer data and geophone data

from time domain is converted to frequency domain. It is shown in figures below.

Figure 39 –Integrated Acceleration waveform after FFT (case 1)

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Figure 40-Integrated Acceleration waveform after FFT (case 2)

Figure 39 and figure 40 shows the acceleration waveform after Fast Fourier Transformation for

both case 1 and case 2.

Figure 41-Velocity waveform after FFT (case 1)

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Figure 42- Velocity waveform after FFT (case 2)

Similarly FFT is done for geophone data in the OriginPro7J software and is shown in above

figures. Figure 41 and figure 42 shows the velocity waveform after Fast Fourier Transformation for

both case 1 and case 2.

4.5 OBTAIN TRANSFER FUNCTION

Next step was to obtain the transfer function between the geophone and accelerometer .Thus in

order to obtain the transfer function almost twenty vibration measurements are collected for both

geophone and accelerometer. The transfer function is obtained by dividing the integrated

accelerometer data in frequency domain with the geophone data in frequency domain.

Let G (ω) is the velocity waveform obtained by geophone after Fourier transformation. V(ω) is the

velocity waveform obtained by accelerometer after integration. Therefore transfer function will be

T (ω) = V(ω)G(ω)

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-6000 -4000 -2000 0 2000 4000 6000

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

Fourier

Am

plit

ude

Frequency (Hz)

Figure 43-Graphical representation of transfer function

The transfer function obtained in this research project is graphically represented in figure 43 with

transfer function in the Y axis and frequency in the X axis .It is obtained from OriginPro 7J

software. There are 32770 different frequency points. The frequency ranges from -5000 Hz to 5000

Hz .from the graph it is clear that the maximum Fourier amplitude is 0.00021 and the average

Fourier amplitude is 0.0001.Using this transfer function the accuracy of velocity waveform of a

geophone can be improved.

P a g e | 61

4.6 IMPROVING THE ACCURACY OF VELOCITY WAVEFORM

The project objective is improving the accuracy of velocity waveform using transfer function

obtained by geophone and accelerometer. So the next step is to utilize this transfer function to

improve the accuracy of velocity waveform. Besides twenty vibration measurements three

additional readings are taken. Then these three readings were subjected to Fourier transformation

using fft function in OriginPro7J software .After that the transfer function is multiplied with the

three geophone data ( case 1, 2 and 3).Then newly obtained improved velocity waveform is

compared with the corresponding geophone and accelerometer data.

Case 1

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Four

ier

Ampl

itude

Frequency Hz

Figure 44-Velocity waveform obtained by multiplying transfer function with geophone data

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

Four

ier A

mpl

itude

Frequency Hz

Figure 45-Integrtaed Acceleration waveform (acceleration data)

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0 20 40 60 80 100 120 140 160 180 200

0

2000

4000

6000

8000

Fourier

Am

plit

ude

Frequency Hz

Figure 46-Velocity waveform (geophone data)

Case 2

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Fourier

Am

plit

ude

Frequency (Hz)

Figure 47- Velocity waveform obtained by multiplying transfer function with geophone data

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0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Fourier

Am

plit

ude

Frequency (Hz)

Figure 48-Integrated Acceleration waveform (acceleration data)

0 50 100 150 200

0

2000

4000

6000

8000

10000

Fourier

Am

plit

ude

Frequency (Hz)

Figure 49- Velocity waveform (geophone data)

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Case 3

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Fourier

Am

plit

ude

Frequency (Hz)

Figure 50- Velocity waveform obtained by multiplying transfer function with geophone data

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

0.5

Fourier

Am

plit

ude

Frequency

Figure 51- Integrated Acceleration waveform (acceleration data)

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0 50 100 150 200

0

1000

2000

3000

4000

5000

Fourier

Am

plit

ude

Frequency (Hz)

Figure 52 -Velocity waveform (geophone data)

In order to obtain the result, three graphs [Velocity waveform obtained by multiplying transfer

function with geophone data, Integrated acceleration waveform (acceleration data) and Velocity

waveform (geophone data)] are compared. After comparison of first two graphs for all the three

cases (improved velocity waveform and integrated acceleration waveform), it can concluded that

the peaks and valleys of both the graphs almost look alike. Noticeable waveform occurs between

the frequency ranges 0 to 200 Hz for all the cases .Thus while generating graphs waveform

generated between 0 to 200 Hz is only considered for the final analysis. When the three waveforms

in all the three cases are closely studied, the main thing which can be noticed is that the occurrence

of peak amplitude .In all the cases the peak amplitude occurs between the range of 0 to 50 Hz. For

the first case the value of the highest peak in integrated acceleration waveform is 1.7 times the

value of highest peak in accuracy improved velocity waveform and for the second case the value of

the highest peak in integrated acceleration waveform is 1.5 times the value of highest peak in

accuracy improved velocity waveform. Finally for the third case the value of the highest peak in

integrated acceleration waveform is 1.25 times the value of highest peak in accuracy improved

velocity waveform. Thus from three cases it can be concluded that the average range will be 1.48

times. This value will change if more results are considered. Thus the project objective of

improving the accuracy of velocity waveform using transfer function, obtained by geophone and

accelerometer, is achieved.

P a g e | 66

5 CONCLUSIONS AND RECOMMENDATIONS

After obtaining the result suitable conclusions should be derived. The research project as a whole is

dependent on geophone and accelerometer .The primary aim of the research project was to improve

the accuracy of velocity waveform using transfer function. So the transfer function between

geophone and accelerometer is obtained .Obtaining the transfer function was the secondary aim of

the research project. Thus the main conclusions obtained in the research project are summarized

below.

5.1 CONCLUSIONS

(1) As already stated that the objective of this research project was to improve the accuracy of

velocity waveform using transfer function obtained by geophone and accelerometer. This is

considered as the primary objective.

(2) In order to achieve this primary objective transfer function has to be obtained. So obtaining

transfer function was set as the secondary objective. In order to obtain transfer function almost

twenty blast vibration measurements were taken and it was followed by subsequent necessary

calculations .Finally the transfer function was obtained. Transfer function for twenty results was

obtained. Then the final transfer function was obtained by taking the average of all the twenty

transfer functions.

(3) In order to apply these transfer function three additional blast vibrational measurements were

taken. Then the transfer function is multiplied with the corresponding geophone data for all the

three cases .This resulted in the improvement of accuracy of velocity waveform. After that all the

three waveforms are compared.

(4) After comparison of first two graphs for all the three cases (improved velocity waveform and

integrated acceleration waveform), it can be stated that the peaks and valleys of both the graphs

almost look alike.

(5) From the comparison of three waveforms, it can be concluded that noticeable waveform always

occurs between the frequency ranges 0 to 200 Hz for all the cases.

(6) By the careful study of all the three waveforms a conclusion can derived that the peak amplitude

occurs between the ranges of 0 to 50 Hz.

P a g e | 67

(7) From the observation and analysis of three graphs the variation of amplitude between the

accuracy improved velocity waveform and integrated acceleration waveform is noticeable .For the

first case the amplitude of the highest peak in integrated acceleration waveform is 1.7 times the

value of highest peak in accuracy improved velocity waveform. For the second and third case it is

1.5 and 1.25 times respectively. Thus from three cases it can be concluded that the average range

will be 1.48 times.

(8) For this research project almost twenty six blast vibration measurements were taken. The

accuracy of the final result depends on the transfer function. Transfer function was obtained from

average of twenty readings The degree of accuracy depends upon the number of readings. The

accuracy of the final result would have been improved if more readings were taken (such as 50 or

100 readings)

5.2 RECOMMENDATIONS FOR FURTHER WORK

This research project entirely depends on transfer function .But the transfer function between

geophone and accelerometer depends on the recorded blast vibration waves. Sometimes the results

will cause some ambiguity .It is due to the presence of some existing errors in the instruments .So it

is always recommended to collect as many blast vibration data to minimize the error. And it can

maximize the degree of accuracy of final result.

Through this research project it can be shown that the obtained transfer function can improve the

accuracy of geophone. Thus the final result will be a much more precise velocity waveform from a

geophone. Thus the application of transfer function is not only limited to this research project but

also can be employed in large scale blast vibration measurements so that geophones can be used

effectively and economically. Thus this research project will result in precise vibration

measurement at low cost in mines.

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6 REFERENCES

1.Silitonga, Martahan,1986.Prediction of Ground Vibration Due to Blasting,pp74-76 (The

AusIMM Illawarra Branch ,Ground Movement and Control related to Coal Mining Symposium :

Australia ).

2.Leet ,L.D ,1960.Vibrations from Blasting Rock ,pp 65-73(Harvard University Publishers (p) Ltd :

United States of America).

3.Rockwell ,E.H, 1927.Vibration Caused by Quarry Blastings And Their Effect On Structure,pp 58-

81 ( Rock products publishers (p) Ltd : United States of America ).

4.Dick ,R.A,1979.A Review Of The Federal Surface Coal Mine Blasting Vibrations, pp 55-63

(Proc.Fifth conference on Explosives and Blasting Technique ,St .Louis , MIT University

Publishers (p) Ltd: United States of America).

5.Duvall,W.T and Fogelson,D.E.1962.Review of criteria for estimating damage to residences from

blast vibrations, pp 85-98 (Bureau of Mines, report of investigations 5968 : Canada).

6.Nicholls,H.R , Johnson , C.F and Duvall,W.I ,1971.Blasting Vibrations And Their Effects On

Structures.pp 100-110 ((Bureau of Mines, Bulletin 656: Canada).

7.Sen ,G.C and Siltonga ,M,1984.Effect of confinement on ground vibrations due to blasting , pp

213-215(Institute of Mining and Metallurgy publishers(p) Ltd: Australia).

8.Wiss , J.F ,1968.Effect Of Blasting Vibrations On Building And People pp46-48(Institute of

Mining and Metallurgy publishers(p) Ltd: Australia).

9.Livingston ,C.W ,1956.Fundamental Concepts of Rock Failure pp 102-118 ( Coorado school of

mines journal : United States of America).

10.Standard Association of Australia (SAA),1983.Explosive Code ,AS 2187 Part 2.pp110-116

(Standards australia : Australia).

P a g e | 69

11. Standards Association of Australia, AS.2187.2-1993. Explosives - Storage Transport and Use-

Part2-Use of explosives. pp118-122 (Standards australia : Australia).

12. Richards, A. B., Moore, A. J., and Evans, R. (1994). 'Blast Vibration Wavefront Reinforcement

Model'. pp. 11-20( Proceedings of the Tenth Symposium on Explosives and Blasting Research,

International Society of Explosives Engineers, Austin, Texas, :United States of America).

13. Langefors, U. and Kihlstrom, B. (1976 ,1978). 'The Modern Technique of Rock Blasting'. pp50-

65(John Wiley& Sons.Inc: United States of America).

14. Siskind, D. E., Stagg, M.S., Kopp, J. W. and Dowding, C. H. (1980). Structural Response and

Damage Produced by Ground Vibration from Surface Mine Blasting. pp55-65.(USBM Report of

Investigations 8507: United States of America).

15. Dowding, C. H. (1985). Blast Vibration Monitoring and Control. pp119-126 (

Prentice Hall Publishers (p) Ltd : United States of America).

16. Shreve ,Dennis H (1995).Signal Processing For Effective Vibration Analysis.pp 4-6

( IRD Mechanalysis, Inc Columbus, Ohio :United States of America).

17. Bradley, Dan, (1989). Introduction to FFT Terms and Parameters.pp 45-68( IRD

Mechanalysis,Inc,Technical (p) Ltd :United kingdom).

18. Sek ,Michael (2000). Frequency Analysis Fast Fourier Transform, Frequency Spectrum.pp 4-11(Victory University Publishers Melbourne : Australia). 19.Cooley,J.W and Tuckey,J.W( 1965). An Algorithm For The Machine Calculation Of Complex Fourier Series pp 297-301.(Math computer volume 2 : United States of America) 20.Maxwell ,P(2001).Sensor improves image quality,pp41-44( Hart’s E&P (p) Ltd :United States

of America).

P a g e | 70

21. S.Hons , Michael and Stewart ,Robert R .(2006) .Transfer functions of geophones and

accelerometers and their effects on frequency content and wavelets. pp 1- 6 (CREWES Research

Report — Volume 18 : Canada).

22.Bernstein, J, (2003). An overview of MEMS sensing technology .pp 13- 45(Sensors Magazine.

CREWES Research Report :Canada).

23. Barzilai, A., (2000). Improving a geophone to produce an affordable broadband seismometer.

pp 15-35 (Stanford University Publishers : United States of America).

24. Aaron Barzilay, Tom VanZandt and Tom Kenny(1998): Improving the Performance of a

Geophone Through Capacitive Positioning Sensing and Feedback. pp1-4 (In Proc. Of the ASME

International Congress : United States of America ).

25. S.Hons , Michael (2008) . Seismic sensing: Comparison of geophones and accelerometers using laboratory and field data. pp 1-20 ( University of Calgary:Canada).

P a g e | 71

7APPENDIX A

RECORDED VIBRATION DATA (1 OUT OF 26)

time(s) Geo(mv) Acc(m/s2) Vel(m/s)0 0.48 0.036 0 0

0.0001 0.36 0.024 0.0000030 0.00000300.0002 0.48 0.024 0.0000024 0.00000540.0003 0.48 0.024 0.0000024 0.00000780.0004 0.36 0.036 0.0000030 0.00001080.0005 0.36 0.024 0.0000030 0.00001380.0006 0.36 0.036 0.0000030 0.00001680.0007 0.36 0.036 0.0000036 0.00002040.0008 0.48 0.036 0.0000036 0.00002400.0009 0.48 0.036 0.0000036 0.0000276

0.001 0.36 0.036 0.0000036 0.00003120.0011 0.36 0.036 0.0000036 0.00003480.0012 0.36 0.024 0.0000030 0.00003780.0013 0.48 0.024 0.0000024 0.00004020.0014 0.48 0.024 0.0000024 0.00004260.0015 0.36 0.024 0.0000024 0.00004500.0016 0.36 0.024 0.0000024 0.00004740.0017 0.36 0.036 0.0000030 0.00005040.0018 0.36 0.036 0.0000036 0.00005400.0019 0.36 0.036 0.0000036 0.0000576

0.002 0.36 0.024 0.0000030 0.00006060.0021 0.36 0.024 0.0000024 0.00006300.0022 0.36 0.036 0.0000030 0.00006600.0023 0.48 0.024 0.0000030 0.00006900.0024 0.36 0.024 0.0000024 0.00007140.0025 0.36 0.024 0.0000024 0.00007380.0026 0.36 0.024 0.0000024 0.00007620.0027 0.24 0.036 0.0000030 0.0000792

P a g e | 72

TRANSFER FUNCTION CALCULATIONS

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18 T19 T20 T avg50197.9 10616.85 12206.76 46684.05 38976.3610 55217.69 13242.78 45178.11 115958.7 61059.39 8804.728 9528.51 8804.01 59736.9 66756.7 38960.8 5967.524 122059.9 880.5591 11656.5 39124.73

35182.44 2976.472 18535.85 32719.67 12997.2827 38700.68 3180.19 31664.19 17609.06 14355.9 4713.608 3162.343 4713.657 45825.38 51149.73 12995.8 1285.339 18536.53 471.279 2976.675 17687.6257.8727 895.6961 1635.646 239.8216 1721.6484 283.6599 873.961 232.0854 1553.864 399.6054 5169.651 1046.396 5177.023 283.5071 299.4501 1719.12 351.3044 1634.786 519.2343 895.7565 1259.5041291.725 239.6261 858.7663 1201.304 736.8108 1420.898 377.9149 1162.553 815.828 261.3851 494.4237 291.084 495.0295 1876.375 2013.82 738.1108 1205.216 858.9983 49.49454 239.0973 831.4232506.965 152.7771 1731.075 2331.478 2450.7540 2757.662 289.4264 2256.269 1644.522 214.3632 784.6756 47.4502 787.8987 1982.625 1614.537 2450.739 691.5743 1730.274 78.76129 152.4459 1332.8141142.318 56.42133 299.5469 1062.355 3527.7086 1256.55 61.20453 1028.086 284.5695 557.0367 1077.056 161.1349 1076.053 805.1334 691.3274 3526.897 1736.687 300.6123 107.5417 56.02577 940.71321762.089 2579.704 2398.572 1638.743 6925.8300 1938.298 3998.209 1585.88 2279.58 1328.566 1217.824 1406.446 1215.817 2091.513 2290.635 6935.815 1964.486 2397.483 121.4869 2581.872 2432.9422013.078 2083.1 959.8498 1872.163 8320.5307 2214.386 3534.066 1811.77 912.099 639.5602 2777.802 3096.312 2780.779 6096.19 4159.373 8304.563 1854.936 960.6722 277.9553 2083.651 2837.6422476.883 440.4307 4624.408 2303.501 1408.3864 2724.571 612.1803 2229.194 4393.187 299.4498 12787.09 600.0613 12812.12 1700.093 1151.505 1407.34 3393.503 4623.439 1277.83 439.7227 3085.2452522.491 865.9501 706.3591 2345.917 5875.3161 2774.74 1099.343 2270.242 671.2405 3040.592 2158.62 1064.429 2157.493 1990.248 1547.001 5876.661 3852.62 707.2346 215.7406 866.4162 2130.4333542.197 1146.531 3421.126 3294.243 22188.1931 3896.417 1761.26 3187.977 3250.069 6862.194 2335.705 1064.952 2337.674 2335.288 1926.795 22183.22 5536.56 3419.797 233.6706 1146.565 4753.52121345.64 4196.226 28292.8 19851.45 33123.1616 23480.21 4871.66 19211.08 26897.39 1630.118 2182.971 3043.519 2182.555 16507.59 10476.18 33133.04 10786.06 28290.7 218.2454 4196.75 14695.8722301.22 4498.211 30853.25 20740.13 7622.6366 24531.34 5277.709 20071.09 29287.52 2343.374 1191.456 5414.382 1191.941 6590.972 4568.786 7621.739 2449.71 30842.34 119.1927 4497.795 11600.749496.555 25467.67 22985.09 8831.796 21909.5684 10446.21 30320.5 8546.899 21843.83 9096.042 4600.967 18776.91 4599.658 3807.079 2920.607 21925.58 3599.607 22975.58 459.8757 25468.75 13903.943456.138 8593.084 19036.32 3214.208 10593.2923 3801.751 8731.012 3110.524 18097.43 4706.15 28822.71 10435.62 28796.46 7479.451 6477.925 10586.32 1338.738 19038.25 2883.553 8592.587 10389.5826174.09 4777.332 84581.31 24341.91 89179.4804 28791.5 5319.132 23556.68 80422.42 11043.04 15538.81 6841.778 15549.55 9613.544 6244.813 89363.55 4973.71 84581.42 1552.548 4777.445 30861.220315.23 27662.83 90698.64 18893.16 27725.9670 22346.75 29397.25 18283.7 86118.5 9754.006 35726.01 12766.2 35651.9 11867.98 8125.994 27720.52 10403 90696.97 3576.08 27661.54 30769.617507.525 28044.47 53800.41 6981.998 39435.4391 8258.278 33389.64 6756.773 51110.39 32733.19 6062.929 33492.38 6062.302 4061.095 3197.153 39451.8 6857.047 53794.51 606.4714 28044.68 22482.429594.531 33841.55 60783.05 8922.914 15819.1253 10553.98 41206.28 8635.078 57752.88 28112.93 22519.03 28784.3 22525.66 4477.752 3577.183 15811.93 12265.22 60792.02 2251.332 33841.42 24103.4121839.9 15424.16 16195.1 20311.11 3540.6128 24023.89 18899.29 19655.91 15385.34 11522.1 154070.7 17232.71 154068.9 19684.79 10092.46 3540.517 9439.774 16195.78 15417.24 15424.31 29098.23

16448.43 27491.11 21515.24 15297.04 20336.4756 18093.27 32718.77 14803.59 20443.67 35042.75 23573.66 30670.61 23574.51 7548.598 5971.144 20335.89 34194.93 21513.09 2357.672 27491.05 20971.0758933.71 13859.94 21993.75 54808.35 54115.0120 64827.09 15938.93 53040.34 20895.48 4604.164 146165.7 12980.55 145994.9 26238.63 19226.68 54104.46 18695.44 21993.85 14631.8 13860.04 41845.4438164.58 25901.08 26583.24 35493.06 32566.5807 41981.03 27509.18 34348.12 25257.37 86632.36 59268.31 23265.17 59266.64 17215.2 13914.06 32577.43 28801.33 26582.9 5926.072 25900.76 33357.7223481.71 37645.64 24851.57 21837.99 16015.9482 25829.88 44325.21 21133.54 23609 17249.43 16382.3 45552.4 16379.5 27786.72 14533.51 16011.09 52968.81 24852.05 1638.807 37638.21 25486.1627232.11 37716.41 36113.34 25325.86 24524.5493 29955.32 45719.56 24508.9 34307.67 3454.264 6220.613 35692.04 6221.017 13199.5 10598.69 24523.8 21701.13 36119.13 621.7623 37716.42 24073.6

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18 T19 T20 T avg25914.65 31483.32 46445.83 24100.63 33280.7324 28506.12 36703.52 23323.19 35778.71 23712.84 57927.52 31235.22 57897.94 10768.68 3755.987 33295.13 26090.73 37657.73 5795.889 31398.94 30253.6726649.05 32929.2 48216.55 24783.62 34297.2913 29313.95 38380.24 23984.14 36497.69 24469.39 60646.1 32695.1 60614.94 10671.5 3264.829 34312.27 27339.82 38414.49 6067.898 32835.14 31319.1627383.45 34375.08 49987.28 25466.61 35313.8501 30121.79 40056.96 24645.1 37216.66 25225.94 63364.69 34154.99 63331.94 10574.31 2773.671 35329.41 28588.91 39171.24 6339.908 34271.35 32384.6628117.84 35820.95 51758 26149.59 36330.4090 30929.63 41733.68 25306.06 37935.63 25982.49 66083.27 35614.87 66048.95 10477.13 2282.513 36346.56 29838 39928 6611.917 35707.56 33450.1528852.24 37266.83 53528.72 26832.58 37346.9679 31737.46 43410.39 25967.02 38654.6 26739.04 68801.86 37074.76 68765.95 10379.94 1791.355 37363.7 31087.09 40684.75 6883.926 37143.76 34515.6529586.64 38712.7 55299.44 27515.57 38363.5268 32545.3 45087.11 26627.97 39373.58 27495.59 71520.45 38534.64 71482.95 10282.76 1300.197 38380.84 32336.18 41441.5 7155.936 38579.97 35581.1430321.03 40158.58 57070.17 28198.56 39380.0857 33353.14 46763.83 27288.93 40092.55 28252.14 74239.03 39994.53 74199.95 10185.58 809.0385 39397.99 33585.27 42198.26 7427.945 40016.18 36646.6431055.43 41604.46 58840.89 28881.55 40396.6446 34160.97 48440.55 27949.89 40811.52 29008.69 76957.62 41454.41 76916.95 10088.39 317.8804 40415.13 34834.36 42955.01 7699.954 41452.38 37712.1331789.83 43050.33 60611.61 29564.54 41413.2035 34968.81 50117.27 28610.85 41530.5 29765.25 79676.21 42914.3 79633.95 9991.206 -173.278 41432.27 36083.45 43711.77 7971.963 42888.59 38777.6332524.23 44496.21 62382.33 30247.53 42429.7623 35776.65 51793.99 29271.8 42249.47 30521.8 82394.79 44374.19 82350.96 9894.021 -664.436 42449.42 37332.54 44468.52 8243.973 44324.79 39843.1333258.62 45942.09 64153.05 30930.52 43446.3212 36584.48 53470.7 29932.76 42968.44 31278.35 85113.38 45834.07 85067.96 9796.836 -1155.59 43466.56 38581.62 45225.28 8515.982 45761 40908.6233993.02 47387.96 65923.78 31613.51 44462.8801 37392.32 55147.42 30593.72 43687.42 32034.9 87831.97 47293.96 87784.96 9699.652 -1646.75 44483.7 39830.71 45982.03 8787.991 47197.21 41974.1234727.42 48833.84 67694.5 32296.5 45479.4390 38200.16 56824.14 31254.67 44406.39 32791.45 90550.55 48753.84 90501.96 9602.467 -2137.91 45500.85 41079.8 46738.78 9060 48633.41 43039.6135461.81 50279.72 69465.22 32979.49 46495.9979 39007.99 58500.86 31915.63 45125.36 33548 93269.14 50213.73 93218.96 9505.282 -2629.07 46517.99 42328.89 47495.54 9332.01 50069.62 44105.1136196.21 51725.59 71235.94 33662.48 47512.5568 39815.83 60177.58 32576.59 45844.33 34304.55 95987.73 51673.61 95935.96 9408.097 -3120.23 47535.13 43577.98 48252.29 9604.019 51505.82 45170.636930.61 53171.47 73006.67 34345.46 48529.1157 40623.67 61854.29 33237.55 46563.31 35061.1 98706.31 53133.5 98652.97 9310.912 -3611.38 48552.27 44827.07 49009.05 9876.028 52942.03 46236.1

37665 54617.34 74777.39 35028.45 49545.6745 41431.5 63531.01 33898.5 47282.28 35817.65 101424.9 54593.38 101370 9213.728 -4102.54 49569.42 46076.16 49765.8 10148.04 54378.24 47301.638399.4 56063.22 76548.11 35711.44 50562.2334 42239.34 65207.73 34559.46 48001.25 36574.2 104143.5 56053.27 104087 9116.543 -4593.7 50586.56 47325.25 50522.55 10420.05 55814.44 48367.0939133.8 57509.1 78318.83 36394.43 51578.7923 43047.18 66884.45 35220.42 48720.23 37330.75 106862.1 57513.15 106804 9019.358 -5084.86 51603.7 48574.34 51279.31 10692.06 57250.65 49432.59

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OBTAINED TRANSFER FUNCTION ( Frequencies from -5000 Hz to 5000 Hz are taken into consideration)

-6000 -4000 -2000 0 2000 4000 6000

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

Fourier

Am

plit

ude

Frequency (Hz)

ω Tavg-5000 0.000006

-4999.69 0.000011-4999.39 0.000008-4999.08 0.000007-4998.78 0.000007-4998.47 0.000012-4998.17 0.000010-4997.86 0.000010-4997.56 0.000007-4997.25 0.000013-4996.95 0.000014-4996.64 0.000017-4996.34 0.000008-4996.03 0.000014-4995.73 0.000020-4995.42 0.000016-4995.12 0.000011-4994.81 0.000013-4994.51 0.000010-4994.2 0.000007-4993.9 0.000009

-4993.59 0.000010-4993.29 0.000008-4992.98 0.000013-4992.68 0.000012-4992.37 0.000006-4992.07 0.000007-4991.76 0.000024-4991.46 0.000011-4991.15 0.000039-4990.84 0.000015-4990.54 0.000011-4990.23 0.000010-4989.93 0.000010-4989.62 0.000008

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FFT CALCULATIONS AND RESUILT USING ORIGINPRO 7J SOFTWARE

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Velo

city

(m/s)

Time (s)

E Data1_E の1000点 隣接平均スムージング

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

Velo

city

(m/s)

Time (s)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.0008

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

Velo

city

(m/s)

Time (s)

0 20 40 60 80 100 120 140 160 180 200

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Four

ier

Am

plitu

de

-180

0

180

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

角度

(度

)

Geo

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0 20 40 60 80 100 120 140 160 180 200

0

2000

4000

6000

8000

10000

Frequency (Hz)

Fourier

Am

plitude

-180

0

180

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)角

度 (度

)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-20

-15

-10

-5

0

5

10

15

20

Y A

xis

Title

Time (s)

B

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.2

-0.1

0.0

0.1

0.2

Accele

ration(m

/s2

)

Time (s)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Velo

city

(m/s)

Time (s)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

Velo

city

(m/s)

Time (s)

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-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-10

-5

0

5

10

15

Voltag

e (

mV

)

Time (s)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.10

-0.05

0.00

0.05

0.10

0.15

Accele

ration (

m/s2

)

Time (s)

P a g e | 80

0 20 40 60 80 100 120 140 160 180 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Frequency (Hz)

Fourier

Am

plitude

-180

0

180

0 20 40 60 80 100 120 140 160 180 200

Frequncy (Hz)

角度

(度

)

0 20 40 60 80 100 120 140 160 180 200

0

2000

4000

6000

8000

10000

Frequency (Hz)

Fourir

ampl

itude

-180

0

180

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

角度

(度

)

3

P a g e | 81

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Velo

city

(m/s)

Time (s)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.0008

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

Velo

city

(m/s)

Time (s)

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-25

-20

-15

-10

-5

0

5

10

15

20

Voltag

e (

mV

)

Time (s)

P a g e | 82

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.2

-0.1

0.0

0.1

0.2

0.3

Accele

ration (

m/s2

)

Time (s)

0 20 40 60 80 100 120 140 160 180 200

0.0

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Fourier

Am

plitude

-180

0

180

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)

角度

(度

)

P a g e | 83

0 20 40 60 80 100 120 140 160 180 200

0

2000

4000

6000

8000

10000

12000

Frequency (Hz)

Fourier

Am

pliy

tude

-180

0

180

0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)角

度 (度

)

Geo

-6000 -4000 -2000 0 2000 4000 6000

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

Fourier

Am

plit

ude

Frequency (Hz)

P a g e | 84

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Fourier

Am

plit

ude

Frequency Hz

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

Fourier

Am

plit

ude

Frequency Hz

0 20 40 60 80 100 120 140 160 180 200

0

2000

4000

6000

8000

Fourier

Am

plit

ude

Frequency Hz

P a g e | 85

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Fourier

Am

plit

ude

Frequency (Hz)

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Fourier

Am

plit

ude

Frequency (Hz)

P a g e | 86

0 50 100 150 200

0

2000

4000

6000

8000

10000

Fourier

Am

plit

ude

Frequency (Hz)

0 50 100 150 200

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Fourier

Am

plit

ude

Frequency (Hz)

P a g e | 87

0 50 100 150 200

0.0

0.1

0.2

0.3

0.4

0.5

Fourier

Am

plit

ude

Frequency

0 50 100 150 200

0

1000

2000

3000

4000

5000

Fourier

Am

plit

ude

Frequency (Hz)